text:
1893 Introduction
Up, and being sent for by my Lady Batten, I to her, and there she found fault with my not seeing her since her being a widow, which I excused as well as I could, though it is a fault, but it is my nature not to be forward in visits. But here she told me her condition, which is good enough, being sole executrix, to the disappointment of all her husband's children, and prayed my friendship about the accounts of the prizes, which I promised her. And here do see what creatures widows are in weeping for their husbands, and then presently leaving off; but I cannot wonder at it, the cares of the world taking place of all other passions. Thence to the office, where all the morning busy, and at noon home to dinner, where Mr. John Andrews and his wife come and dined with me, and pretty merry we were, only I out of humour the greatest part of the dinner, by reason that my people had forgot to get wine ready, I having none in my house, which I cannot say now these almost three years, I think, without having two or three sorts, by which we were fain to stay a great while, while some could be fetched. When it come I begun to be merry, and merry we were, but it was an odd, strange thing to observe of Mr. Andrews what a fancy he hath to raw meat, that he eats it with no pleasure unless the blood run about his chops, which it did now by a leg of mutton that was not above half boiled; but, it seems, at home all his meat is dressed so, and beef and all, and [he] eats it so at nights also. Here most of our discourse is of the business of the Parliament, who run on mighty furiously, having yesterday been almost all the morning complaining against some high proceedings of my Lord Chief Justice Keeling, that the gentlemen of the country did complain against him in the House, and run very high. It is the man that did fall out with my cozen Roger Pepys, once, at the Assizes there, and would have laid him by the heels; but, it seems, a very able lawyer. After dinner I to the office, where we all met with intent to proceed to the publique sale of several prize ships, but upon discourse my Lord Anglesey did discover (which troubled me that he that is a stranger almost should do more than we ourselves could) that the appraisements made by our officers were not above half of what he had been offered for one of them, and did make it good by bringing a gentleman to give us 700l. for the Wildboare, which they valued but at 276l., which made us all startle and stop the sale, and I did propose to acquaint the Duke of York with it, and accordingly we did agree on it, and I wrote a severe letter about it, and we are to attend him with it to-morrow about it. This afternoon my Lord Anglesey tells us that the House of Commons have this morning run into the inquiry in many things; as, the sale of Dunkirke, the dividing of the fleete the last year, the business of the prizes with my Lord Sandwich, and many other things; so that now they begin to fall close upon it, and God knows what will be the end of it, but a Committee they have chosen to inquire into the miscarriages of the war. Having done, and being a little tired, Sir W. Pen and I in his coach out to Mile End Green, and there drank a cup of Byde's ale, and so talking about the proceedings of Parliament, and how little a thing the King is become to be forced to suffer it, though I declare my being satisfied that things should be enquired into, we back again home, and I to my office to my letters, and so home to supper and to bed.
28 Annotations
Terry Foreman on 17 Oct 2010 • Link
The Royal Society today at Arundel House — from the Hooke Folio Online
Oct: 17. 1667. Dr. [ Richard ] Lower [ http://munksroll.rcplondon.ac.uk/Biography/Detail… ] peircing the sides of a dog made and cutting 2 nerues passng to his liuer made him broken winded) The Bellows expt. being againe considerd) It was obserued by mr. Hooke that this expt seemd to shew that an animal might be kept aliue wthout any motion of the Lungs [(only by a continued supply of fresh air [In margin]Vz and that the motion of the lungs] did not contribute to the circulation of the blood, he was desired to bring in an exact Description of this expt. as it was now Improued. It was also moued that it might be considerd whether it was the emission and Discharge of fumes or the intromission of fresh air that preserued this animall aliue)
Sr. Th Devaux his paper about Soap making was deliuerd by order to mr Hooke, who hath vndertaken to giue an account of that trade.
(transfusion to be tryd on men)
For the next meeting was orderd by mr Hookes suggestion the experiment of making the blood of an animall passe from one side to another out of the vena arteriosa into the aorta without passing through the Lungs Dr. Lower & mr Hooke were desired to take care of this expt. -
http://webapps.qmul.ac.uk/cell/Hooke/hooke_folio.…
John Evelyn's Diary
17th October, 1667. Came Dr. Barlow, Provost of Queen's College and Protobibliothecus of the Bodleian library, to take order about the transportation of the Arundel Marbles [ http://en.wikipedia.org/wiki/Arundel_marbles ] .
http://is.gd/fY53a
Ossory to Ormond
Written from: [London]
Wonder has been expressed - as the writer is told - by many members of the House [of Commons] how it is that Lord Orrery has won so much credit in Ireland, whilst that of the Duke of Ormond is impaired.
The writer would be glad to have copies of the Addresses which have been made to the Duke by the House of Commons of Ireland.
Notices recent proceedings in the English Parliament, and, more particularly, an address of thanks to the King for the removal of the late Chancellor.
http://www.rsl.ox.ac.uk/dept/scwmss/projects/cart…
Arlington to Sandwich
Written from: Whitehall
Imparts the views of the Government as to an alliance offensive & defensive with Spain; as to the existing relations between Spain and France, and as to the probabilities of an accommodation between them.
Adds that the King will thank Lord Sandwich with his own hand for the Treaty sent to him by his Lordship. Other Correspondents will communicate the recent proceedings in Parliament.
Robert Gertz on 17 Oct 2010 • Link
"...only I out of humour the greatest part of the dinner, by reason that my people had forgot to get wine ready..."
I know that's the greatest calamity I can experience at dinner.
Ok, Andrews: Vampire or werewolf? Not zombie, pray God...They're so unfashionable this year.
Paul E on 17 Oct 2010 • Link
"And here do see what creatures widows are in weeping for their husbands, and then presently leaving off; but I cannot wonder at it, the cares of the world taking place of all other passions."
Sam goes from callous to kind in two seconds flat, and with unsurpassed prose.
"...there drank a cup of Byde's ale..."
Once again, friends...That's Byde's ale. Byde's ale, the one ale to have when you're trying to digest Parlimentary procedings with your true enemy.
"I tole you to mention the wineseller as well..." Bess hisses.
Australian Susan on 18 Oct 2010 • Link
Lady Batten needs Pepys' help, but does not put herself in the position of a petitioner to begin with, but charges him (and quite rightly so as she and Sam know) of bad manners. Once she can take the moral high ground, she then brings up her problems and gets Sam's support. Clever lady.
More dog torture at the Royal Society I see. I find these blunt descriptions (with no thought of the concomitant suffering) of experiments on live dogs distressing for my 21st century mind. I know, however, it was normal for the times and that these men were not being sadistic, but were trying to discover how anatomical processes worked.
Michael Robinson on 18 Oct 2010 • Link
" ... my people had forgot to get wine ready, I having none in my house, which I cannot say now these almost three years, ..."
Alas, an occasion for display lost:
" … my new bottles made, with my crest upon them, …"
http://www.pepysdiary.com/diary/1663/10/23/
" ... odd, strange thing to observe of Mr. Andrews what a fancy he hath to raw meat, that he eats it with no pleasure unless the blood run about his chops, ..."
Sounds as if 'rare,' or 'medium rare,' unusual in the mid C 17th.
Ruben on 18 Oct 2010 • Link
"Sounds as if 'rare,' or 'medium rare,' unusual in the mid C 17th."
There is not much historic literature about how to eat your meat. But there are good reasons to have your meat completely cooked. This way you kill all kind of germs and parasites, that were common in Pepys days. Just remember there was no veterinary control, and mutton is specially apt to have unwanted guests in its body. Brucella, Triquinosis, Cysticercosis, Helminths and Flat Worms dissapeared from view in our day but they are still with us and may come back without warning, should the veterinary control lose grip. That happened in some industrialized countries in the "crazy cow" case just because vegetarian animals where fed "balanced food" containing cheap parts of other animals, instead of their normal diet. Some lost their lifes, and others made money out of this kind of unwarranted "balance".
In my copy of Mrs Beeton, she has many cautions about buying your meat - saying that the best way to get mutton was to buy it from someone you knew and trusted who had a property in the country which farmed sheep.
When my grandmother was forced to move to Ireland in 1914 (her husband's job), she continued to order all her meat from Harrod's, so mistrustful was she of Irish produce and she never ate pork in the summer wherever she lived. We have forgotten (as Ruben points out) how risky eating meat could be when it was not thoroughly cooked and of good provenance. Sam is right to be uneasy about his guest's behaviour. Interesting too that he accepts the guest's commands about the meat (which renders it unpalatable to everyone else). i think nowadays, when we are guests at a dinner party, we would not lecture the host about his cooking practices. (unless there were medical reasons). I think RG's right: he's a vampire.....
I left it open: werewolf, vamp, even...so unfashionable, zombie. But...
As for dog experiments, Tom Wolfe in "The Right Stuff" and others note the chimp and other animal experiments of the early space age and nuclear era and the suffering inflicted in the name of "fighting the Cold War", "beating the [communist enemy] Russians] to the Moon", etc by men and women who were not of the aberrant sadist [ie, Nazi]persuasion but felt the knowledge had to be acquire for both "advancement" and "national security". And of course the grisly horror of human experimentation in the twentieth century (again by supposed non-aberrant societies as well as brutally perverted ones} still emerging certainly outstrips anything Sam's Royal Society did in their first efforts to learn about the world.
"...and how little a thing the King is become to be forced to suffer it, though I declare my being satisfied that things should be enquired into..."
Our politic Pepys...He could run for office today easily.
"So we are here with Mr. Samuel Pepys, of the Naval Office. So I understand Mr. Pepys that you support the PM's contention that in Naval affairs the government should have an absolute authority?"
"Yes, Betty...And may I say you are as lovely as always...I firmly support the PM on such matters. The government's authority over the Navy must remain absolute if the Navy is to continue to perform in an effective and efficient manner...If I may document..."
Desperate intervention by director...No, no...
"But you also favor a full and unimpeded access by the public and media into these affairs?"
"Uh..." Sam frowns at missing chance to pull up his extensive Powerpoint collection... "Well, of course...I am always for complete access. A full inquiry with complete access, subject of course to the necessary restrictions of retaining the government's full authority...And if I may show a few records of our performance during the incident in question..."
Oh, Lord...Director sighs...
"Perhaps we could discuss these matters in detail over lunch tomorrow...?" Sam whispers to reporter Betty, post-interview.
"I can't believe you always say yes..." female assistant hisses to Betty. "Hands off, Mr. Pepys." snarl to grinning Sam as he heads off stage to dressing rooms.
"Eh...He has this little-boy's charm..." Betty sighs back, watching Sam eagerly questioning the camera- and sound- persons about their equipment.
"And he's always chasing women named Betty...You know his wife's name's Elisabeth."
"PM loved it, Mr. P!" Hewer in wings enroute to dressing room gives thumbs up.
"I'm telling you boys, that Pepys is a potential Francis Urquhart." Admiral Sir Will Penn IV, Lord of the Admiralty to colleagues, fuming as Pepys' interview plays.
language hat on 18 Oct 2010 • Link
"there are good reasons to have your meat completely cooked."
Of course there are, but people like their food the way they like it, and doctors be damned. Some people focus on safety and eschew anything that might threaten it; others focus on enjoyment and ignore medical warnings. Of the latter, some die early, giving pleasure to the doctors (and another warning example they can use); others live to be a hundred, giving pleasure to themselves and to those of us who enjoy taking chances.
"dog torture"
Nota bene "(transfusion to be tryd on men)"....
Jesse on 18 Oct 2010 • Link
"being sole executrix"
Wonder how she pulled that off? In that day and age - second wife too.
"weeping for their husbands, and then presently leaving off"
Not just "cares of the world." Sir W. was hardly a young man and Lady Batten had already been there done that widow thing.
"above half boiled"
I wonder if that also might have been (is?) an English thing. Of course, in the US at least, many fast food and large chain establishments have policies against undercooking beef and supermarket warnings are common on raw poultry products.
cum salis grano on 18 Oct 2010 • Link
Well cooked meat, 'tis why British food was never liked by their cozens in the new lands, not bludy enough.
"there are good reasons to have your meat completely cooked."
It is easy to "take a risk" and ignore the problem when meat comes to market supervised by a veterinarian, etc. in a first world country.
The State is protecting you and you never have to worry. You may bite a living cow and nothing bad will happen to you, if the cow is yours. Maybe an association for compassion for the cows will protest, but that is it.
AND, if you somehow get infected there are antibiotics developed by those damned doctors.
For Pepys that was a serious gamble, in spite he could not know exactly what the problem was.
You do not read about Pepys drinking water, because a diarrhea happened in a few hours, so the reason was very evident and the solution easy (have a beer, drink wine).
But an infection or "consumption" by a parasite infection can take weeks, months or years to develop.
"some high proceedings of my Lord Chief Justice Keeling, that the gentlemen of the country did complain against him in the House"
L&M note that "the gentlemen of the country" were the rural party -- critics of the court and its high-handed ways in the conduct of what passed for "justice".
In fairness to Lady Elizabeth Batten...She'd have no great reason or desire to do her mourning before Samuel Pepys. And we never heard via Sam any complaints from Sir William... I'll choose to believe she does her mourning where it counts.
Indeed, if Sir Will made her sole executrix over his children, it goes a long way in saying his regard and care of her.
Batten's Will - Mingo
"Sir William Batten was granted Letters Patent by King James I (sic) to operate the Harwich Lighthouse, a profitable concern because of its strategic importance to shipping in 1664.
"and to the office, where we sat late, and then I to write my letters, and then to Sir W. Batten's, who is going out of towne to Harwich to-morrow to set up a light-house there, which he hath lately got a patent from the King to set up, that will turne much to his profit."
These extracts from his will reveal that Batten wanted his 'servante Mingoe a Negroe' ( http://www.pepysdiary.com/encyclopedia/2575/ ) to become lighthouse keeper upon his death. The servant was also left a legacy of £20 per year for life - a substantial sum of money at the time."
Photo reproduction of excerpts:
http://www.nationalarchives.gov.uk/pathways/black…
That's neat about Mingo. Not as good as letting him go home but if he's now free, perhaps he liked England enough to honestly wish to stay.
All around, given his care for wife and servant, it seems nothing became Sir William Batten in life like his leaving of it.
Terry Foreman on 8 Oct 2016 • Link
"This afternoon my Lord Anglesey tells us that the House of Commons have this morning run into the inquiry in many things; as, the sale of Dunkirke, the dividing of the fleete the last year, the business of the prizes with my Lord Sandwich, and many other things; so that now they begin to fall close upon it, and God knows what will be the end of it, but a Committee they have chosen to inquire into the miscarriages of the war. "
Journal of the proceedings of the House of Commons today
http://www.british-history.ac.uk/commons-jrnl/vol…
Miscarriage of the War.
¶Resolved, That a Committee be appointed to inquire into the Miscarriage of Affairs in the late War; viz. [members named]
Dunkirke.
¶Resolved, &c. That a Committee be appointed to inquire into the Reasons of the Sale of Dunkirke; and whether any Money were paid into the Hands of any private Person; viz. [members made]
Terry Foreman on 17 Aug 2019 • Link
L&M note that "the gentlemen of the country" were the rural party -- critics of the court. Kelyng's conduct of two capital trials (in which he had fines both juries) had led to the appointment of a committee of investigation by the Commons on the 16th. . When they reported on 11 December, it was voted that he had been guilty of innovations amounting to the exercise of 'an arbitrary and illegal Power', that he had vilified Magna Carta (which he had called 'Magna Farta'), and thhat he should be brought to trial. After he had appeared before the house on 13 December, it was resolved to take no further action against him but a motion was passed declaring illegal the fining or imprisoning of juries. See https://www.pepysdiary.com/diary/1667/12/12/ and
https://www.pepysdiary.com/diary/1667/12/12/
https://www.pepysdiary.com/diary/1667/10/17/?c=54…
"It is the man that did fall out with my cozen Roger Pepys, once, at the Assizes there, and would have laid him by the heels;"
L&M: In 1665 at the Cambridge assizes he had bound over Roger Pepys (Recorder of the borough) fir speaking slightingly of Chief Justice Hyde: Diary Sam. Newton (ed. Foster), p. 10.
About these events
All diary entries from October 1667
Read a summary of this month's events


text:
IFS, Ltd. — The Book Trust Prospectus
Filed to
Investment Futures Strategies, Limited (IFS, Ltd)
The Book Trust Prospectus
Investment Futures Strategy, Ltd. is pleased to announce The Book Trust, a site specific collaboration and publication to be presented at the New York Art Book Fair, 5–7 November, 2010. The semi-fictional IFS, Ltd., comprised of five graduate students from the Department of Graphic Design at the Yale School of Art – Benjamin Critton, Harry Gassel, Brendan Griffiths, Zak Klauck, and Mylinh Nguyen – will offer an original publication for trade in a series of barters executed by its authors during the three days of the NY Art Book Fair.
The Trust and the accompanying Book Trust Prospectus speak to matters of micro-economies and distribution, as well as prescribed and perceived value. The project suggests a new currency specific to the setting of the Book Fair, a context in which a distinct set of commodities is exchanged by like-minded vendors in a finite space and time. It is only in this setting that a book could be posited as capital—a literal stand-in for the money that commonly exchanges hands at the Fair. Perceived worth is no longer dictated by edition or price, but instead by a potential traders' subjective notion of the values they assign to each book.
The book, produced in a fixed quantity of 500, will vary in value as each negotiation determines and redetermines its worth in the marketplace. With each transaction, the Prospectus will assume the value of the book for which it was exchanged. The traded commodities will ultimately comprise The Book Trust, a value-appreciating book bank. By trading with IFS, Ltd. participants acquire a single theoretical share of the bank, the Prospectus a document of the transaction.
In framing the project in a format similar to that of a stock exchange, the performance emphasizes the tenuous and abstract value of the book as a designed object, as a medium for content, as a traded commodity, and as a symbol of participation in the project itself.
Previews, November 4th; opening bell, November 5th. Online at http://IFS-L.BIZ.
BUY YOUR SHARES IN THE BOOK TRUST PUBLICATION TODAY!
NY Art Book Fair, MoMA PS1, New York

redpajama_set_name: RedPajamaCommonCrawl


Happy New Year dear readers! Ms. Jeannie has missed you, missed you, missed you! It has been several months since the last post in October, and in that interim between then and now, a flurry of behind-the-scenes activity has been occurring in the land of Ms. Jeannie Ology.
Indie was quite the little helper!
Most notably, there was a move to a new house and a new town.
As Ms. Jeannie said goodbye to the garden and the greenhouse, and the friends she made of the birds and the butterflies and the bald-faced hornets of the last few years, she said hello to a history-soaked house and a bustling university town.
Not too much has changed in appearance from that picture to today, except maybe the yard is a little more tame:) All the character and all the history are still exactly where they are supposed to be and that is pretty fantastic.
Replace the wheat fields above with acres and acres of cotton and knock down most of the trees and that would be the agricultural landscape here of the 1800 and 1900's. While the church still remains open and active next door, the original schoolhouse caught fire and burned down completely. In 1936 it was rebuilt and continued to be operated as a public school for black children up until the 1960's when desegregation put it out of commission entirely.
While it is unclear why Mary had to leave school after second grade, we do know that the process of educating black children in the rural South both before and after the Civil War was not an easy task on many fronts. Back in the 20th century the original schoolhouse was considered primitive by many standards. By 1915, the children still had no desks or even a cloak room to hang their coats and they would have just sat on benches lining the wall. Black teachers made 1/3 of the salary of white teachers, which meant their monthly take home pay was about $25.00 and if white teachers were teaching black children, they would have had to tolerate a lot of ridicule from the white community for their professional choices.
All this seems pretty unfair from both sides, but this schoolhouse, in particular, was actually considered pretty great back in its day because it was in a good location, had ample grounds for playing and the exterior was painted and therefore not subject to rot and mildew.
Next In the Kitchen with Indie: Organic Homemade Dog Treats!
Thanks for the update Ms. Jeannie Ology! Congrats on your new home! What will Ms. Jeannie find in her new location to delight us all? Looking forward to your new adventures!
Nice blog…love the puppy/kitty pictures!
Amazing new home! What history! Ive always wanted to live in a warehouse loft or an old church. keep us posted. Im looking forward to how you finish your nest.
Oh thank you so much Mary! Yes, more adventures indeed!
What an utterly charming new home! Thanks for bringing us up to date on your latest news…as always, I'll look forward to hearing about the adventures Spring brings you in your new town. P.S. This has just now reminded me that years ago we talked of finding an old firehouse to make our nest. Hmmm.


The library is located upstairs in block 20. We are open throughout the school day and beyond for all students and staff.
Our aim is to provide students with a purposeful learning environment in which, with our encouragement and support, they can achieve high standards of academic and personal achievement.
The library is very well used with approximately a thousand students visiting us each week. It is mainly open plan with areas for group and individual study, soft seating and beanbags are also available for relaxing and reading for pleasure. Our IT suite consists of 16 individual computer bays all of which have access to the internet and a printer.
We have a wealth of resources available including a well stocked selection of fiction and non-fiction books; journals and magazines; daily newspapers; DVD's; Maps; CD's; Internet Access; a subscribed database, study skills leaflets and lots more... If we don't have what you are looking for then we will do our best to get it for you by either borrowing from another school or public library. All our resources are clearly labelled to allow students the option of locating them independently.
As well as supporting and assisting students with their academic studies, the library is devoted to encouraging students to read for pleasure and we have several lunch time clubs to inspire and create. Book vs Movie Club - Mondays; The Page Eaters - Wednesdays and Samwhit knit wits - Fridays. We are looking forward to taking part in the Carnegie National Shadowing Award Scheme and working towards creating a recommended reading list. The library works closely with our learning support department hosting their reading booster class three mornings a week and making sure that we have a good selection of resources for our less able readers.
We regularly check these websites below as they are great for reading reviews and finding out what's hot or what's not, they also have great competitions.
Students are encouraged to take part in our new Student Librarian Training Programme. We always have an exceptional number of student library helpers and in order to provide them with a more structured experience I have created a new training programme. The students work towards compiling a portfolio which contains evidence of completed duties including cataloguing, issuing and creating eye-catching displays. Upon completion the students receive a certificate, a badge and their portfolio which can be used to provide evidence of work experience once they have left school.
Our library management system is called Eclipse and can be accessed by using the button below.
The system is internet based and can be accessed from home as well as school and even downloaded onto a mobile phone or tablet. The catalogue can be searched without logging on however once logged on students can write reviews, make reservations and see which books they have on loan and when they need to be returned. When using the system from home, students can also make use of the hundreds of websites the library also has catalogued, these website are specially chosen for their academic value.
SWA library is continually evolving to suit the needs of its primary users - the students. Students are encouraged to help develop the library and we are always happy to receive requests or suggestions via our suggestions box, face to face or email lfreeman@bestacademies.org.uk.
'Don't just google it' when searching the internet, google is the first search engine most of us go to. We would like to encourage students to go beyond google. If you can't find what you're looking for don't give up, set yourself a time limit and then try a different search engine there are hundreds out there!


Approx. 1450 – or + SF commercial Retail unit. It is ideal for large variety of general office or retail uses. This Unit has its own entrances and front glass window. Tenant pays for inside insurance, water, electric utilities and trash.
Tenant or tenant agent please verify the true measure of the SF if they desire to do so.


text:
\section{Introduction}
\label{sec:introduction}

Presented as two-dimensional equivalents of volumetric
metamaterials~\cite{holloway_ieeemap2012}, metasurfaces have
attracted a significant interest in recent years. Metasurfaces
are typically realized as a doubly periodic array of small
polarizable particles over a subwavelength thickness. With
a distinct advantage of low loss over volumetric metamaterials,
a wide range of novel reflection, transmission, and absorption
applications ranging from microwave to optical frequencies
have been
reported~\cite{kildishev_science2013,yu_natmater2014,meinzer_natphoton2014,
glybovski_physrep2016,chen_repprogphys2016}.

There are a host of metasurface applications in the transmission
mode. Based on the phased array antenna principle~\cite{hansen2009} and
the generalized law of refraction~\cite{yu_science2011},
a linear gradient of transmission phase imparted on the
transmitted wave can bend an incident beam or plane wave in an
anomalous
direction~\cite{pfeiffer_prl2013,aieta_nanolett2012b,pfeiffer_nanolett2014,
yu_lasphotonrev2015}. A flat focusing lens is obtained by
spatially nonlinear transmission phase
distributions~\cite{monticone_prl2013,lin_science2014,
wang_advopticalmat2015,khorasaninejad_science2016}.
Local modulation of transmission amplitude and/or phase leads
to holograms~\cite{ni_natcommun2013,huang_natcommun2013,
arbabi_natnanotech2015}. As polarization transformers,
thin metasurfaces can replace electrically
thick wave plates by assigning distinct transmission phases to
two orthogonal polarization
components~\cite{zhao_natcommun2012,pfeiffer_ieeejmtt2013,
grady_science2013}.

A high transmission magnitude toward unity and a
wide transmission phase range toward $2\pi$ are highly
desirable for high-efficiency operation of transmitted
wave shaping. At optical frequencies, a single layer of
plasmonic or dielectric resonant particles are commonly adopted
for transmissive metasurfaces, owing to relative ease of
fabrication. It was recognized that an infinitesimally
thin layer of electrically polarizable particles support
a complete $2\pi$ range for the cross-polarized transmission
phase, but not for the co-polarized transmission.
Accordingly, formalization of the generalized laws of
reflection and refraction as well as their experimental
demonstrations were performed for the cross-polarized
components scattered by $V$-shaped optical antennas under linearly
polarized illuminations~\cite{yu_science2011,aieta_nanolett2012},
albeit at a low cross-polarized transmission efficiency.
It was later revealed that the maximum cross-coupled power
efficiency is 25\%~\cite{monticone_prl2013}.
Another approach to achieve a $2\pi$ transmission phase
coverage is to exploit the Pancharatnam-Berry phase together with
circularly polarized illuminations. For the transmitted
circularly polarized wave of the opposite handedness,
the phase can be adjusted simply by rotating the principal
axes of a wave-plate
element~\cite{lin_science2014,zheng_natnanotech2015,
huang_natcommun2013}. Still, this approach involves cross-polarized
transmitted waves and a completely reflectionless operation
is not possible.

For polarization-preserving applications to date,
reflectionless metasurfaces with a complete $2\pi$
transmission phase coverage are based on Huygens'
meta-atoms~\cite{pfeiffer_prl2013,yu_lasphotonrev2015,
shalaev_nanolett2015,decker_advoptmat2015,chong_acsphoton2016}.
A Huygens' meta-atom is designed such that an orthogonal set
of tangential electric and magnetic dipole moments are induced
upon external plane-wave excitation. When the two induced
dipoles satisfy a balanced condition, full transmission
and zero reflection can be obtained for lossless cases
with the transmission phase that can be designed to have any
value within a complete $2\pi$ range. In the microwave regime,
short conductor traces are typically used for electric dipoles.
For equivalent magnetic dipoles, either metallic
ring resonators~\cite{pfeiffer_prl2013}
or conductor traces in a multi-layer dielectric
substrate~\cite{pfeiffer_ieeejmtt2013,wong_ieeejmtt2015,epstein_josab2016}
are utilized.
{\color{red}Utilizing a combination of continuous and discrete
printed multi-layer conductor traces for realizing Huygens' meta-atoms,
microwave transmissive metamaterials for lenses, beam deflectors,
and vortex beam generators with efficiencies as high as 91\% have
been demonstrated~\cite{cai_advoptmat2017,luo_prappl2017,cai_prappl2017}.}
In the optics regime, a dielectric resonator meta-atom can
be designed to support both electric and equivalent magnetic
polarization currents at the same
wavelength~\cite{decker_advoptmat2015,yu_lasphotonrev2015,
shalaev_nanolett2015}. It is challenging to design induced
electric and magnetic polarizations to satisfy
a balanced amplitude and phase relation at the same frequency
due to strong mutual coupling between them.
Furthermore, the bandwidth of the magnetic resonance tends to be
narrower than that of the electric one.
At microwave frequencies, the length and shape of a thin conductor
wire may be designed to strike a balance between the induced
electric and equivalent magnetic dipole moments. This approach
has been demonstrated with a circularly polarized Huygens spiral
particle in \cite{niemi_ieeejap2013}.

In this paper, a fundamental principle behind full power
transmission with a complete phase coverage is investigated
for polarization-preserving metasurfaces.
It is shown that generation of an
anti-symmetric scattering component by the
induced polarizations and its destructive interference with the
symmetric scattering component in nullifying the total reflected wave
is the key design principle. In Huygens' metasurfaces, a tangential
magnetic dipole moment provides the necessary anti-symmetric scattering.
However,
it is not the only possible source of anti-symmetric scattering.
It has been recently shown that the effect of a tangential
magnetic polarization can be equivalently generated by a spatially
varying normal electric polarization~\cite{albooyeh_prb2017}.
Taking advantage of this equivalence,
a meta-atom configuration comprising entirely of electric
dipole moments that is capable of full transmission with a $2\pi$
phase coverage is presented. The new reflectionless metasurface
configuration is available for oblique illuminations in the
TM polarization. Here, the anti-symmetric scattering is provided
by an electric dipole that is polarized normal to the metasurface.

{\color{red}When a combination of tangential and normal
induced electric dipoles are realized with a tilted electric dipole
meta-atom, the identical frequency dispersion of the
two orthogonal dipole moments permits
\emph{dispersionless} full transmission
at a \emph{fixed} oblique incidence angle. Furthermore,
the resonance of a dipole meta-atom can be tuned in order to
achieve a full transmission phase coverage.
It is known that metallic gratings having an array
of narrow slits or apertures allow dispersionless broadband
extraordinary transmission
under a TM-polarized illumination at some
fixed oblique angle~\cite{huang_prl2010,alu_prl2011,fan_advmat2012}.
The underlying physics of this broadband full transmission
is an impedance match between an oblique TM-polarized illumination
and a propagating mode inside a slit~\cite{alu_prl2011}.
In contrast, the dispersionless transmission property
of a tilted dipole array in this study is of geometrical nature
of the dipole pattern null directions. This allows the frequency
dispersion of a dipole meta-atom to be exploited for transmission
phase synthesis.}

Furthermore, the inevitable effect of absorption in
practical metasurface realizations on the transmission phase
coverage is discussed.
It is revealed that a complete $2\pi$ range of transmission
coverage is still available regardless of the amount of loss
for reflectionless designs.
Finally, illustrative uniform metasurface design
examples are provided and analyzed.
As a microwave example, a tilted thin conducting strip dipole
array is shown for providing full transmission and a complete phase
coverage. As its lossy variant, an impedance-loaded
strip dipole array is
analyzed for full phase coverage as well as for perfect absorption.
For an example in the optical
regime, high transmission and full phase coverage by an
all-dielectric metasurface composed of dielectric bars
of rectangular cross section are demonstrated.

In the following time-harmonic analysis at an angular frequency
$\omega$, an $e^{j\omega t}$ time dependence is assumed
and suppressed.

\section{TM-mode reflection and transmission}
\label{sec:model}

\begin{figure}[t]
 \centering
 \includegraphics{tm_refl_trans.pdf}
 \caption{Reflection and transmission of a TM-polarized plane
wave by a metasurface in the $xy$-plane situated in free space.}
 \label{fig:tm_refl_trans}
\end{figure}

We treat a uniform (non-gradient), single-layer metasurface
in free space. As will be shown, lossless metasurfaces supporting
electric polarizations only are capable of full-power transmission
in the TM polarization. Figure~\ref{fig:tm_refl_trans} illustrates
a planar metasurface in the $xy$-plane illuminated by a TM-polarized
plane wave propagating in the $xz$-plane with an angle of incidence
$\theta^\t{i}$. The unit-cell
dimensions are $a$ and $b$ in the $x$- and $y$-axis directions,
respectively.
The dimensions are set such that only the fundamental Floquet
mode fields propagates away from the metasurface. Away from the
metasurface where all evanescent higher-order Floquet mode
waves vanish, the incident, reflected, and transmitted electric
fields can be written as
\begin{equation}
\mathbf{E}^\t{p}=\mathbf{E}^\t{p}_0e^{-j(k^\t{p}_xx+k^\t{p}_zz)};\ \
\t{p}=\t{i},\t{r},\t{t},
\label{def:E-fields}
\end{equation}
where the superscripts `i,' `r,' and `t' denote the incident,
reflected, and transmitted fields, respectively, and
$\mathbf{E}^\t{p}_0$ denotes the corresponding E-field vector amplitude.
The associated wave vectors in the $xz$-plane are given by
$(k^\t{i}_x,k^\t{i}_z)=(k\sin\theta^\t{i},-k\cos\theta^\t{i})$,
$(k^\t{r}_x,k^\t{r}_z)=(k\sin\theta^\t{r},k\cos\theta^\t{r})$,
and $(k^\t{t}_x,k^\t{t}_z)=(k\sin\theta^\t{t},-k\cos\theta^\t{t})$,
with $k$ denoting the free-space wavenumber. All magnetic
fields are $y$-polarized. For a uniform metasurface, all three
angles are the same $(\theta^\t{i}=\theta^\t{r}=\theta^\t{t})$.

For metasurfaces that do not scatter cross-polarized fields,
the transmission and reflection in Fig.~\ref{fig:tm_refl_trans}
can be described using a two-port network in terms of $S$-parameters,
with plane-wave ports
1 and 2 defined in positive- and negative-$z$ half spaces.
With the phase reference planes for both ports set to $z=0$,
the reflection coefficient $r=S_{11}$ and the transmission
coefficient $t=S_{21}$ are defined as the ratios of
tangential E-field amplitudes as
\begin{equation}
r=\frac{\hat{x}\cdot\mathbf{E}^\t{r}_0}{\hat{x}\cdot\mathbf{E}^\t{i}_0}
=\frac{E^\t{r}_{0x}}{E^\t{i}_{0x}},\ \
t=\frac{\hat{x}\cdot\mathbf{E}^\t{t}_0}{\hat{x}\cdot\mathbf{E}^\t{i}_0}
=\frac{E^\t{t}_{0x}}{E^\t{i}_{0x}}.
\label{def:r_and_t}
\end{equation}

\begin{figure}[t]
 \centering
 \includegraphics*{elemental_dipoles.pdf}
 \caption{Three elemental dipole meta-atoms for TM-polarization
reflection and scattering. (a) An $x$-directed electric dipole.
(b) A $z$-directed electric dipole. (c) A $y$-directed magnetic
dipole.}
 \label{fig:elemental_dipoles}
\end{figure}

There are three elemental dipole meta-atoms that scatter
TM-polarized fields, which are assumed to be excited by
the incident wave.
They are two orthogonal electric dipoles in the
plane of incidence (the $xz$-plane)
and one magnetic dipole that is directed
normal to the plane of incidence, as shown in
Fig.~\ref{fig:elemental_dipoles}. Each point dipole is positioned
at the coordinate origin. A general meta-atom can
be represented as a superposition of these three dipoles.
The scattering characteristics of the elemental dipoles
are discussed next.

\subsection{Symmetric scattering}
\label{sec:symmetric}

A planar array of the tangential electric dipole $\hat{x} p_x$ in
Fig.~\ref{fig:elemental_dipoles}(a) radiates plane waves
symmetrically into $z\to\pm\infty$. The scattered E-field
amplitudes, $\mathbf{E}^{\t{s},\t{r}}_0$ and $\mathbf{E}^{\t{s},\t{t}}_0$,
in the reflection and transmission directions, respectively,
are given by
\begin{eqnarray}
\mathbf{E}^{\t{s},\t{r}}_0 &=& \frac{j\omega\eta}{2S\cos\theta^\t{i}}
\hat{k}^\t{r}\times\hat{k}^\t{r}\times\hat{x} p_x,
\label{def:Esr0_px}\\
\mathbf{E}^{\t{s},\t{t}}_0 &=& \frac{j\omega\eta}{2S\cos\theta^\t{i}}
\hat{k}^\t{t}\times\hat{k}^\t{t}\times\hat{x} p_x,\label{def:Est0_px}
\end{eqnarray}
where $\eta\approx 377~\Omega$ is the free-space intrinsic
impedance and $S=ab$ represents the unit-cell area in the
$xy$-plane. Also, $\hat{k}^\t{r}=\mathbf{k}^\t{r}/k$ and
$\hat{k}^\t{t}=\mathbf{k}^\t{t}/k$ are the unit vectors in their respective
propagation directions.
The tangential components of $\mathbf{E}^{\t{s},\t{r}}_0$ and
$\mathbf{E}^{\t{s},\t{t}}_0$ are the same (symmetric). Denoting
this value by $E^{\t{s},\t{s}}_{0x}$, we find
\begin{equation}
E^{\t{s},\t{s}}_{0x}=\hat{x}\cdot\mathbf{E}^{\t{s},\t{r}}_0
=\hat{x}\cdot\mathbf{E}^{\t{s},\t{t}}_0=-\frac{j\omega\eta p_x}{2S}
\cos\theta^\t{i}.
\label{def:Ess0x}
\end{equation}
These scattered field amplitudes could be cast in terms of
the surface-averaged electric polarization current density
$J_x=j\omega p_x/S$.

\subsection{Anti-symmetric scattering}
\label{sec:anti-symmetric}

Both a normal electric dipole [Fig.~\ref{fig:elemental_dipoles}(b)]
and a tangential magnetic dipole
[Fig.~\ref{fig:elemental_dipoles}(c)] radiate anti-symmetrically
into $z\to\pm\infty$. First, the $z$-directed electric
dipole meta-atom generates scattered plane waves in the
$\hat{k}^\t{r}$, $\hat{k}^\t{t}$ directions with
the E-field amplitudes given by
\begin{eqnarray}
\mathbf{E}^{\t{s},\t{r}}_0 &=& \frac{j\omega\eta}{2S\cos\theta^\t{i}}
\hat{k}^\t{r}\times\hat{k}^\t{r}\times\hat{z} p_z,
\label{def:Esr0_pz}\\
\mathbf{E}^{\t{s},\t{t}}_0 &=& \frac{j\omega\eta}{2S\cos\theta^\t{i}}
\hat{k}^\t{t}\times\hat{k}^\t{t}\times\hat{z} p_z.
\label{def:Est0_pz}
\end{eqnarray}
The $x$-components of these two vectors
are different by sign (anti-symmetric).
Denoting the anti-symmetric component by $E^{\t{s},\t{a}}_{0x}$,
we find
\begin{equation}
E^{\t{s},\t{a}}_{0x}=\hat{x}\cdot\mathbf{E}^{\t{s},\t{r}}_0=
-\hat{x}\cdot\mathbf{E}^{\t{s},\t{t}}_0=\frac{j\omega\eta p_z}{2S}\sin\theta^\t{i}.
\label{def:Esa0x_pz}
\end{equation}

Next, a planar array of the $y$-directed magnetic dipole meta-atom
in Fig.~\ref{fig:elemental_dipoles}(c) creates
the E-field amplitudes for the scattered plane waves given by
\begin{eqnarray}
\mathbf{E}^{\t{s},\t{r}}_0 &=& \frac{j\omega}{2S\cos\theta^\t{i}}
\hat{k}^\t{r}\times\hat{y} m_y,
\label{def:Esr0_my}\\
\mathbf{E}^{\t{s},\t{t}}_0 &=& \frac{j\omega\eta}{2S\cos\theta^\t{i}}
\hat{k}^\t{t}\times\hat{y} m_y.
\label{def:Est0_my}
\end{eqnarray}
The anti-symmetric $x$-components can be written as
\begin{equation}
E^{\t{s},\t{a}}_{0x}=\hat{x}\cdot\mathbf{E}^{\t{s},\t{r}}_0=
-\hat{x}\cdot\mathbf{E}^{\t{s},\t{t}}_0=-\frac{j\omega m_y}{2S}.
\label{def:Esa0x_my}
\end{equation}
The field amplitudes can also be written in terms of the
surface-averaged polarization current densities,
$J_z=j\omega p_z/S$ and $M_y=j\omega m_y/S$.

\subsection{Transmission and reflection coefficients for total fields}
\label{sec:total_scattering}

Infinitely thin metasurfaces can support tangential
electric polarizations only and the resulting symmetric scattering
is the reason for low transmission power efficiencies for
polarization-preserving designs~\cite{monticone_prl2013}.
For Huygens' metasurfaces, the asymmetric scattering enabled
by a combination of orthogonally directed tangential electric
and magnetic dipoles allows full
transmission~\cite{yu_lasphotonrev2015,decker_advoptmat2015}.
In order to support an equivalent magnetic dipole realized
using a circulating electric polarization, a Huygens' metasurface
cannot have a vanishingly small thickness.

We note that the anti-symmetric scattering may be provided
by a normal electric dipole rather than a tangential magnetic
dipole. Regardless of the origin of anti-symmetric radiation,
the total tangential E-field components for the reflected
and transmitted waves can be written as a superposition as
\begin{equation}
E^\t{r}_{0x}=E^{\t{s},\t{s}}_{0x}+E^{\t{s},\t{a}}_{0x},\ \
E^\t{t}_{0x}=E^\t{i}_{0x}+E^{\t{s},\t{s}}_{0x}-E^{\t{s},\t{a}}_{0x},
\end{equation}
where the symmetric component $E^{\t{s},\t{s}}_{0x}$
is given by (\ref{def:Ess0x}). The anti-symmetric component
$E^{\t{s},\t{a}}_{0x}$ is given by (\ref{def:Esa0x_pz}) if
$\hat{z} p_z$ is used and by (\ref{def:Esa0x_my}) if
$\hat{y} m_y$ is used. Then, we can write the reflection and
transmission coefficients as
\begin{eqnarray}
r &=& \frac{E^\t{r}_{0x}}{E^\t{i}_{0x}}=r_\t{s}+r_\t{a};\ \
r_\t{s}=\frac{E^{\t{s},\t{s}}_{0x}}{E^\t{i}_{0x}},\
r_\t{a}=\frac{E^{\t{s},\t{a}}_{0x}}{E^\t{i}_{0x}},
\label{r:decomp}\\
t &=& \frac{E^\t{t}_{0x}}{E^\t{i}_{0x}}=t_\t{s}-r_\t{a},\ \
t_\t{s}=1+r_\t{s},
\label{t:decomp}
\end{eqnarray}
where $r_\t{s}$ and $r_\t{a}$ represent reflection coefficients
for the symmetric and anti-symmetric components, respectively.
In (\ref{t:decomp}), $t_s$ denotes the transmission coefficient
in the absence of anti-symmetric scattering.

\section{Transmission phase for lossless, reflectionless metasurfaces}
\label{sec:lossless}

For lossless metasurfaces, power conservation requires
$|r|^2+|t|^2=1$. In terms of $t_\t{s}$ and $r_\t{a}$, this
condition translates into
\begin{equation}
|t_\t{s}|^2+|r_\t{a}|^2-\Re\{t_\t{s}+r_\t{a}\}=0.
\label{cond_lossless:tsra}
\end{equation}
Now, we require a reflectionless operation for maximum power
transmission $(r=0)$, or set $r_\t{a}=1-t_\t{s}$. Using this
condition in (\ref{cond_lossless:tsra}), we obtain
$|t_\t{s}|^2=\Re\{t_\t{s}\}$, which can be rewritten as
\begin{equation}
|t_\t{s}|=\cos\phi_{t_\t{s}},
\label{cond_lossless:tts}
\end{equation}
if we write $t_\t{s}=|t_\t{s}|e^{j\phi_{t_\t{s}}}$
(i.e, $\angle t_\t{s}=\phi_{t_\t{s}}$). Using (\ref{cond_lossless:tts}),
the total transmission coefficient is found to be
\begin{equation}
\begin{split}
t &= t_\t{s}-r_\t{a}=2t_\t{s}-1=2\Re\{t_\t{s}\}-1+j2\Im\{t_\t{s}\}\\
&= 2|t_\t{s}|\cos\phi_{t_\t{s}}-1+j2|t_\t{s}|\sin\phi_{t_\t{s}}\\
&= \cos2\phi_{t_\t{s}}+j\sin2\phi_{t_\t{s}}=e^{j2\phi_{t_\t{s}}}.
\end{split}
\label{t:lossless}
\end{equation}
Hence, we find
\begin{equation}
\angle t=2\phi_{t_\t{s}}.
\label{anglet_lossless_ts}
\end{equation}
Starting from $t=1+2r_\t{s}$ instead, a similar analysis finds
\begin{equation}
\angle t=2\phi_{r_\t{s}}+\pi,
\label{anglet_lossless_rs}
\end{equation}
where $\phi_{r_\t{s}}=\angle r_\t{s}$.
From (\ref{anglet_lossless_ts})--(\ref{anglet_lossless_rs}),
we find that
the transmission phase range is twice those of the transmission
and reflection coefficients of the symmetric component.
The magnitude of the transmission coefficient is unity due to
full transmission, as it should be for lossless,
reflectionless metasurfaces.

Let us assume no bianisotropy and a standard Lorentz frequency
dispersion for the lossless electric polarizability $\alpha_\text{ee}$
for the horizontal electric dipole $p_x$.
The polarizability can be modeled as
\cite{bohren2004,asadchy_prx2015}
\begin{equation}
\alpha_\text{ee}=\frac{A_\t{e}}{\omega_\t{e}^2-\omega^2},
\label{alphaee_model}
\end{equation}
where $A_\t{e}$ is the resonance strength coefficient related
to the plasma frequency and $\omega_\t{e}$ is the electric resonance
frequency. The polarizability $\alpha_\text{ee}$ relates the induced
dipole moment to the local excitation field at the dipole location.
By defining an effective polarizability $\hat{\alpha}_\text{ee}$
for the dipole in an array environment, the induced dipole moment
can be written relative to the incident field as
$p_x=\hat{\alpha}^\text{ee} E^\t{i}_{0x}$. It is known that the two
polarizabilities are related by \cite{asadchy_prx2015}
\begin{equation}
\frac{1}{\eta\hat{\alpha}_\text{ee}}=\frac{1}{\eta\alpha_\text{ee}}
+\frac{j\omega}{2S}\cos\theta^\t{i}
\label{alphaee_eff}
\end{equation}
in the TM polarization.
Using (\ref{def:Ess0x}), (\ref{alphaee_model}), and
(\ref{alphaee_eff}), the expression for $r_\t{s}$ is found to be
\begin{equation}
r_\t{s}=-j\frac{\omega\cos\theta^\t{i}}{2S}
\left(\frac{\omega_\t{e}^2-\omega^2}{\eta A_\t{e}}
+\frac{j\omega}{2S}\cos\theta^\t{i}
\right)^{-1}.
\end{equation}
At a design frequency $\omega$,
the phase of $r_\t{s}$ can be adjusted to any value in the range
$[-\pi,-\pi/2]$ or $[\pi/2,\pi]$
by adjusting $A_\t{e}$, $\omega_\t{e}$, and $S$ of a resonant meta-atom.
From (\ref{anglet_lossless_rs}), it can be seen
$\angle t$ has a full $2\pi$ range.

\begin{figure}[t]
 \centering
 \includegraphics{patterns_comparison.pdf}
 \caption{Meta-atom scattering magnitude
patterns for zero reflection at $\theta^\t{i}=60\degree$.
(a) A combination of $\hat{x} p_x$ and $\hat{y} m_y$.
(b) A combination of $\hat{x} p_x$ and $\hat{z} p_z$.
The total pattern as well as the patterns of elemental
dipoles are shown. The patterns are in linear scale with
an arbitrary unit. All dipoles are treated as point dipoles.}
 \label{fig:patterns_comparison}
\end{figure}

It is instructive to inspect the physical conditions for
zero reflection in terms of dipole moments.
For a combination of $\hat{x} p_x$ and $\hat{y} m_y$,
setting $r=r_\t{s}+r_\t{a}=0$ using (\ref{def:Ess0x}) and
(\ref{def:Esa0x_my}) gives
\begin{equation}
m_y+\eta p_x\cos\theta^\t{i}=0.
\label{cond:norefl_pxmy}
\end{equation}
{\color{red}In \cite{paniagua-dominguez_natcommun2016},
extended relations of (\ref{cond:norefl_pxmy})
between the electric and magnetic dipole amplitudes for
a generalized Brewster effect in dielectric metasurfaces
were derived for any given incidence angle, frequency,
and polarization.}
For normal incidence $(\theta^\t{i}=0)$,
{\color{red}(\ref{cond:norefl_pxmy})} corresponds to
a zero backscattering condition (in the $+z$-axis direction).
This condition for an orthogonal set of electric and magnetic
dipoles has also been utilized in antenna
designs~\cite{green_ieeejap1966,jin_ieeejawpl2010}.
In the case of planar array or metasurface designs, zero
specular reflection is of interest and (\ref{cond:norefl_pxmy})
is the necessary condition at any incidence angle.
In \cite{radi_prappl2015}, the same balance condition
was the principle behind thin Huygens sheet absorbers under
a normal incidence. As an example, the element (meta-atom)
scattering pattern of a balanced electric-magnetic dipole
pair for a 60\textdegree{} incidence case is shown
in Fig.~\ref{fig:patterns_comparison}(a). Together with
the total pattern, the individual scattering patterns of
$\hat{x} p_x$ and $\hat{y} m_y$ are also shown. In the specular
reflection $(\hat{k}^\t{r})$
direction, the two individual patterns destructively
interfere to create a null, while they interfere constructively
in the transmission $(\hat{k}^\t{t})$ direction.
The phases of the two moments $p_x$ and $m_y$ may
be varied under the condition
(\ref{cond:norefl_pxmy}) to tune the transmission phase.

For a combination of $\hat{x} p_x$ and $\hat{z} p_z$, the zero
reflection condition translates to
\begin{equation}
p_x\cos\theta^\t{i}=p_z\sin\theta^\t{i}.
\label{cond:norefl_pxpz}
\end{equation}
Hence, the two orthogonal induced dipole components should be
in phase and their magnitudes should scale properly as a function
of $\theta^\t{i}$.
The individual and total scattering patterns for a combination
of two electric dipoles satisfying (\ref{cond:norefl_pxpz})
are shown in Fig.~\ref{fig:patterns_comparison}(b) for the
same 60\textdegree{} oblique illumination. A destructive
interference creates a scattering null in the $\hat{k}^\t{r}$
direction. As indicated in Fig.~\ref{fig:patterns_comparison}(b),
this combination of two orthogonal dipoles corresponds to a single
tilted electric dipole. Hence, there exists an interesting
realization strategy in microwaves, where the direction of
a low-loss conduction current can be accurately controlled
by shaping thin conductors in meta-atoms.
{\color{red}Using a tilted straight dipole meta-atom
to realize $\hat{l}p_l$ in Fig.~\ref{fig:patterns_comparison}(b),
(\ref{cond:norefl_pxpz}) will be satisfied for any value of
$p_l$. The tangential and normal dipole moments will follow exactly
the same frequency dispersion. The result is dispersionless
zero reflection at the specific oblique incidence angle that
matches the dipole tilt angle in the opposite direction. For
lossless meta-atoms, this translates into dispersionless full
transmission.}
When volumetric
electric polarization currents are utilized, $\hat{x} p_x$ and
$\hat{z} p_z$ should be jointly designed to satisfy
the proper magnitude and phase relations, i.e.,
(\ref{cond:norefl_pxpz}).
A microwave metasurface design based on the former strategy
and an optical design based on the latter approach are
presented in Sec.~\ref{sec:examples}.

It is stressed that using tangential and normal electric dipoles
for creating reflectionless metasurfaces is limited to oblique
illuminations in the TM polarization.
At a normal incidence, the reflection
direction is also normal to the surface. Even if
the normal electric dipole, $\hat{z} p_z$, is induced by the
incident wave, it cannot scatter in the reflection and transmission
directions, which are the axial directions of $\hat{z} p_z$.
In comparison, the combination of tangential electric
and magnetic dipoles is available for any angle of incidence.

Since either a tangential magnetic dipole or a normal electric
dipole can contribute to creating zero reflection
together with a given
tangential electric dipole, we can find
a relation between $m_y$ and $p_z$ for contributing the same
effect. By equating the values of $r_\t{a}$ due to the two
dipoles from (\ref{def:Esa0x_pz}) and (\ref{def:Esa0x_my}),
we find $m_y=-\eta p_z\sin\theta^\t{i}$, which can be written
in the form
\begin{equation}
\hat{y} M_y=-\hat{n}\times\frac{\mathbf{k}_t}{\omega\epsilon_0}J_z;\ \
\hat{n}=\hat{z},\ \mathbf{k}_t=\hat{x} k\sin\theta^\t{i}
\label{equiv:my_pz}
\end{equation}
in terms of surface-averaged polarizations.
Here, $\epsilon_0$ is the free-space permittivity and
$\hat{n}$, $\mathbf{k}_t$ represent the unit surface normal and the
tangential wave vector, respectively.
Identified in \cite{albooyeh_prb2017}, (\ref{equiv:my_pz}) represents
an equivalence between a tangential magnetic
polarization and a spatially-varying normal electric polarization.

\section{Transmission magnitude and phase for lossy, reflectionless
metasurfaces}
\label{sec:lossy}

Absorption in lossy constituent materials
is inevitable in practical realizations, resulting in reduction
of the transmission power efficiency from 100\%.
On the other hand, zero reflection and zero transmission
are desired for absorber applications. In this Section,
we investigate if there is a limitation in designing the
transmission phase when absorption is present and how the phase
may be controlled.

Let the absorptance in the scattering described in
Fig.~\ref{fig:tm_refl_trans} be denoted by $A$ in the range
$0<A<1$. It is defined as the absorbed power within a unit cell normalized
by the incident power on the unit-cell area.
Then, the power relation dictates $|r|^2+|t|^2=1-A$.
Using the decompositions of $r$ and $t$ into the
symmetric and anti-symmetric
scattering components (\ref{r:decomp})--(\ref{t:decomp}), this
power conservation relation can be written in terms of $t_\t{s}$ and
$r_\t{a}$ as
\begin{equation}
\Re\{t_\t{s}+r_\t{a}\}-\left(|t_\t{s}|^2+|r_\t{a}|^2\right)=\frac{A}{2}.
\label{power_conserv_lossy}
\end{equation}
For both high-transmission and absorber applications, zero
reflection is desirable. Using $r_\t{a}=1-t_\t{s}$ in
(\ref{power_conserv_lossy}) gives
\begin{equation}
|t_\t{s}|^2-\Re\{t_\t{s}\}+\frac{A}{4}=0.
\label{eq:ts_lossy}
\end{equation}
The solution for $|t_\t{s}|$ is readily found to be
\begin{equation}
|t_\t{s}|=\frac{\cos\phi_{t_\t{s}}\pm\sqrt{\cos^2\phi_{t_\t{s}}-A}}{2}.
\label{sol:tsmag_lossy}
\end{equation}
We find that the passivity and power conservation principles
do not require a particular one of the two
branches to be taken for  the square root function in
(\ref{sol:tsmag_lossy}). Both values of
$|t_\t{s}|$ are valid solutions. For real-valued
solutions to exist for $|t_\t{s}|$, it is required that
$\cos^2\phi_{t_\t{s}}-A\geq 0$. Hence, we find that $t_\t{s}$ has
its phase limited to the range
\begin{equation}
-\cos^{-1}\sqrt{A}\leq\phi_{t_\t{s}}\leq\cos^{-1}\sqrt{A}.
\label{range_phits_lossy}
\end{equation}
Using (\ref{sol:tsmag_lossy}), the transmission coefficient
is expressed as
\begin{equation}
t=e^{j\phi_{t_\t{s}}}\left(\pm\sqrt{\cos^2\phi_{t_\t{s}}-A}+j\sin\phi_{t_\t{s}}\right).
\label{t:lossy}
\end{equation}
If we carry out a similar analysis in terms of $r_\t{s}$ instead
of $t_\t{s}$, it is found that the range of $\phi_{r_\t{s}}$ is limited
to
\begin{equation}
\cos^{-1}\left(-\sqrt{A}\right)\leq|\phi_{r_\t{s}}|\leq\pi.
\label{range_phirs_lossy}
\end{equation}
The transmission coefficient has an alternative expression
given by
\begin{equation}
t=e^{j\phi_{r_\t{s}}}\left(\pm\sqrt{\cos^2\phi_{r_\t{s}}-A}-j\sin\phi_{r_\t{s}}\right).
\label{t_alt:lossy}
\end{equation}
By allowing both branches in (\ref{t:lossy}) and
(\ref{t_alt:lossy}), it is easy to verify that the range of
transmission phase is $2\pi$ regardless of the value of $A$.
Hence, we conclude that
the presence of absorption does not fundamentally
require the transmission phase range to be reduced from
$2\pi$ associated with the lossless case.

Using a lossy meta-atom model, we inspect the range of a realizable
transmission phase and develop a design approach for achieving
a particular combination of $|t|$ and $\angle t$. A
lossy meta-atom having a Lorentz-type resonant response
can be modeled using a polarizability function given by
\begin{equation}
\alpha_\text{ee}=\frac{A_\t{e}}
{\omega_\t{e}^2-\omega^2+j\gamma_\t{e}\omega},
\label{alphaee_model_lossy}
\end{equation}
where $\gamma_\t{e}$ is the electric loss factor or collision
frequency. Using (\ref{def:Ess0x}), (\ref{alphaee_eff}), and
(\ref{alphaee_model_lossy}), the transmission coefficient,
written as $t=1+2r_\t{s}$ under a zero reflection condition,
is expressed as
\begin{equation}
t=\frac{\frac{\omega_\t{e}^2-\omega^2}{\eta A_\t{e}}+
j\omega\left(\frac{\gamma_\t{e}}
{\eta A_\t{e}}-\frac{\cos\theta^\t{i}}{2S}\right)}
{\frac{\omega_\t{e}^2-\omega^2}{\eta A_\t{e}}+
j\omega\left(\frac{\gamma_\t{e}}
{\eta A_\t{e}}+\frac{\cos\theta^\t{i}}{2S}\right)}.
\label{t:lossy_lorentz}
\end{equation}
For notational simplicity, let us introduce symbols
$u=\gamma_\t{e}\omega/\eta A_\t{e}$,
$v=\omega\cos\theta^\t{i}/2S$,
and $w=(\omega_\t{e}^2-\omega^2)/\eta A_\t{e}$.
It is noted that $u$ and $v$ are positive quantities, but
$w$ can take any real value. Enforcing an absorptance value of
$A=1-|t|^2$ relates $u$, $v$, $w$, and $A$. The resulting value of $w$
can be written in terms of the remaining quantities as
\begin{equation}
w=\pm\sqrt{2\left(\frac{2}{A}-1\right)uv-u^2-v^2}.
\label{w:lossy}
\end{equation}
For $w$ to be real-valued, the quantity under the square root
should be non-negative. This defines the region of a valid point
$(u,v)$ in the $uv$-plane. It is found that the ratio $u/v$ is
bound between two constants defined by $A$, i.e.,
\begin{multline}
2\left[\frac{1}{A}-\sqrt{\frac{1}{A}\left(\frac{1}{A}
-1\right)}\right]-1<\frac{u}{v}\\
<2\left[\frac{1}{A}+\sqrt{\frac{1}{A}\left(\frac{1}{A}
-1\right)}\right]-1.
\label{uoverv_range}
\end{multline}
Let us denote the lower and upper limits in
(\ref{uoverv_range}) by $s_{0}$ and $s_{1}$, respectively.
It is noted that
\begin{equation}
0<s_0<1,\ s_1>1,\ \text{and}\ s_0s_1=1,
\label{properties:s0s1}
\end{equation}
for all possible values of $A$.
In addition, let us introduce a slope function $s$ as a function
of a parameter $q$ via
\begin{equation}
s(q)=s_{0}+(s_{1}-s_{0})q,\ \ 0<q<1,
\label{def:sr}
\end{equation}
so that $u=s(q)v$.

\begin{figure}[t]
 \centering
 \includegraphics*{tphase_range.pdf}
 \caption{Transmission phase design for a lossy,
reflectionless metasurface with an
absorptance of $A=0.9$. The values of a reflectance $R=0$
and a transmittance $T=0.1$ are also indicated in the inset.
The range of $u/v$ for this example is equal to
$0.520<u/v<1.925$.}
 \label{fig:tphase_range}
\end{figure}

For the time being, let us assume that $w>0$ in (\ref{w:lossy}).
From (\ref{t:lossy_lorentz}), the transmission phase is expressed as
\begin{equation}
\angle t=\tan^{-1}\frac{u/v-1}{|w|/v}
-\tan^{-1}\frac{u/v+1}{|w|/v}.
\label{anglet:lossy_lorentz}
\end{equation}
In (\ref{anglet:lossy_lorentz}), the quantity $|w|/v$ is positive
and $|w|/v\to 0^+$ as $s\to s_0$, $s_1$. Now, we inspect the
numerators in the argument of the arctangent functions in
(\ref{anglet:lossy_lorentz}).
For the second arctangent, it is
seen that $u/v+1$ remains positive in $0<q<1$
(i.e., its entire range) for all possible values of
$A$. The numerator in the first arctangent
function has a range
\begin{equation}
s_0-1<\frac{u}{v}-1<s_1-1.
\label{atan1_num}
\end{equation}
From (\ref{properties:s0s1}),
we note that the lower limit in (\ref{atan1_num})
is a negative quantity,
while the upper limit is a positive one, for all possible
$A$. Hence, the first term in
(\ref{anglet:lossy_lorentz}) changes from $-\pi/2$ to $\pi/2$
as $q$ is increased from 0 to 1. The second term in
(\ref{anglet:lossy_lorentz}) stays in the range between
0 and $\pi/2$, but it reaches $\pi/2$ at $q=0$, $1$. Hence,
we expect a range of $\pi$ for the transmission phase, in
$-\pi<\angle t<0$. For an example case of $A=0.9$,
Fig.~\ref{fig:tphase_range} shows
the transmission phase with respect to $q$. It can be
seen that there exists a unique value of $q$ for achieving
a desired value of $\angle t$.

For synthesizing a transmission phase in $-\pi<\angle t<0$,
a meta-atom design strategy can be described as follows.
For a given absorptance $A$, the transmission magnitude is
fixed at $|t|=\sqrt{1-A}$ for a reflectionless response.
The phase angle $\angle t$ spans $[-\pi,0]$ as a function
of $u/v$ in $s_0<s<s_1$ $(0<q<1)$.
Equation~(\ref{anglet:lossy_lorentz}) can be solved for
the value of $q$ that achieves a desired transmission phase
and the corresponding value of $u/v$ follows.
The associated value of $w/v$ is obtained from (\ref{w:lossy}).
At the design frequency $\omega$ and the incidence angle
$\theta^\t{i}$, a meta-atom is designed by determining
a combination
of values for $A_\t{e}$, $\omega_\t{e}$, $S$, and $\gamma_\t{e}$ for
giving the determined ratios $u/v$ and $w/v$.

A transmission phase in the range $0<\angle t<\pi$ can be
designed using the negative branch for $w$ in (\ref{w:lossy}).
For $w<0$, we note from (\ref{t:lossy_lorentz}) that
\begin{equation}
\angle t=-\left(\tan^{-1}\frac{u/v-1}{|w|/v}
-\tan^{-1}\frac{u/v+1}{|w|/v}\right),
\label{angletpos:lossy_lorentz}
\end{equation}
which is an opposite number for (\ref{anglet:lossy_lorentz}).
Therefore, to design a value of $\angle t$ in $[0,\pi]$,
meta-atom parameters can be first determined for achieving a phase of
$-\angle t$, following the approach described above for
realizing a transmission phase in $[-\pi,0]$. Then,
the sign of $w$ needs to be changed, which can be achieved
by setting $\omega_\t{e}<\omega$, i.e., by choosing the resonance
frequency of the lossy meta-atom lower than the design frequency.

Combining the two separate cases of the desired transmission phase
being in $[-\pi,0]$ or $[0,\pi]$, we conclude that
a reflectionless metasurface can be designed using
lossy meta-atoms
following the Lorentz dispersion model to achieve
a transmission phase in a full $2\pi$ range at any level of
absorption at any oblique angle of incidence.

\section{Numerical examples}
\label{sec:examples}

In this section, we will  present different alternatives for
Huygens' metasurfaces where the tangential and normal
electric dipole moments are carefully engineered for
satisfying the reflectionless condition
while providing a complete transmission phase coverage.
We will explore the possibilities for the design of
metasurfaces at microwave and optical frequencies for
lossless and lossy scenarios.

\subsection{Reactively-loaded tilted thin
conductor strip dipole array}
\label{sec:tilted_pec_array}

\begin{figure}[t]
 \centering
 \includegraphics*{tilted_dipole_tmagphase.pdf}
 \caption{Plane wave scattering by a planar array of tilted
conductor strip dipoles. The meta-atom comprises a conducting
strip dipole of dimensions $l\times w$.
The plane of the strip is the $xz$-plane
and the strip surface is assumed to be perfectly conducting.
A point load with a reactive impedance $Z_l=jX_l$ is connected
at the dipole middle point.
(a) The transmission magnitude and phase with respect to the
load reactance $X_l$ at 5~GHz.
The inset shows a side view of the
unit cell together with the illuminating plane wave.
(b) The transmission coefficient as a function of frequency
when the load port is shorted $(X_l=0)$.
The unit-cell dimension is $a=20~\text{mm}$ in both $x$-
and $y$-axis directions.
The length and width of the strip dipole are
$l=29.9~\text{mm}$ and $w=0.6~\text{mm}$.
{\color{red}The unit-cell scattering pattern at 5~GHz
is shown in the inset.}}
 \label{fig:tilted_dipole_tmagphase}
\end{figure}

At microwave frequencies, the direction of induced electric dipole
moments can be easily controlled using thin conductor wires and
traces. For supporting both tangential and normal electric
dipoles, a straight thin conductor dipole can be tilted to
{\color{red}produce zero reflection. Here, it is noted that
(\ref{cond:norefl_pxpz}) is the zero reflection condition for
point dipoles. For meta-atoms of practical dimensions,
zero reflection corresponds to a scattering pattern null in the
specular reflection direction. For a straight conductor dipole
of any length, aligning the dipole axis in the specular reflection
direction guarantees $r=0$.}
The transmission characteristics of a tilted straight dipole
array are analyzed in Fig.~\ref{fig:tilted_dipole_tmagphase}.
For a TM-polarized plane-wave illumination at an incidence angle
of 60\textdegree{}, a perfect electric conductor (PEC) strip
dipole tilted at the same 60\textdegree{} angle in the opposite
direction constitutes the meta-atom, as shown in the inset of
Fig.~\ref{fig:tilted_dipole_tmagphase}(a). At the middle point of the
dipole, a lumped load with an impedance $Z_l$ is connected.
{\color{red}While providing tunability for $t$,
such a load does not affect the reflectionless property.}
At a design
frequency of 5~GHz, the unit-cell dimensions are chosen to be
$a=b=20~\text{mm}$, so that there are no higher-order propagating
Floquet modes. For an
electrically thin width of $w=0.6~\text{mm}$, the length
of the strip was adjusted to $l=29.9~\text{mm}$
such that the transmission
phase for the unloaded case ($Z_l=0$) is equal to $\pi$.
The dipole meta-atom extends slightly into neighboring cells.
Using a phase-shift periodic boundary condition (PBC) on the
four vertical walls of the unit cell, the scattering
characteristics of an infinitely large planar array were
simulated using FEKO 2017 by Altair.

At the design frequency,
the magnitude and phase of $t$ are plotted in
Fig.~\ref{fig:tilted_dipole_tmagphase}(a) with respect to the
reactance $X_l$ of the reactive load impedance $Z_l=jX_l$.
Since the meta-atom is lossless and the dipole does not
reflect, the transmission magnitude is constant at unity.
By loading the dipole with different reactance $X_l$,
the transmission phase can be adjusted to any value in
the range $-\pi<\angle t\leq\pi$. Not the entire $2\pi$
phase range is visible in
Fig.~\ref{fig:tilted_dipole_tmagphase}(a).
Simulations with large loading reactances
show that the transmission
phase approaches a single value of
$\angle t=-19.6\degree$ from different directions as
$X_l\to\pm\infty$. Considering that the dipole meta-atom
is not electrically short, large loading reactances will not
make it effectively non-existent. Instead, the meta atom will
appear as two narrowly separated collinear dipoles of a length
$l/2$ each.

For an unloaded dipole $(X_l=0)$,
Fig.~\ref{fig:tilted_dipole_tmagphase}(b) plots the transmission
coefficient with respect to frequency. A standard Lorentz-type
resonant frequency response is observed for the phase.
{\color{red}In the inset, the normalized unit-cell scattering
pattern at 5~GHz in the $xz$-plane is shown as a polar plot.
The length of the dipole meta-atom of nearly a half wavelength
makes the pattern deviate noticeably from that of a point
dipole shown in Fig.~\ref{fig:patterns_comparison}(b).
Still, a scattering null is synthesized in the reflection direction
due to the tilt.}
In this design,
the bandwidth of full power transmission is in principle
infinite. This is due to satisfaction of the no reflection
condition of a geometrical origin. For a tilted straight dipole,
the normal and tangential surface-averaged
electric polarizations,
$J_x=j\omega p_x/S$, $J_z=j\omega p_z/S$, have the exact same
frequency dispersion. If zero reflection is achieved via
a balance of electric and equivalent magnetic polarizations
as is done in Huygens' metasurfaces, the high-transmission
frequency bandwidth is not expected to be wide.

\subsection{Impedance-loaded tilted strip dipole array}
\label{sec:tilted_array_lossy}

\begin{figure}[t]
 \centering
 \includegraphics*{tilted_strip_rxload.pdf}
 \caption{The transmission coefficient with respect to the
lumped load resistance $R_l$ and reactance $X_l$ values.
(a) The magnitude. (b) The phase angle in degrees.
The white contour lines correspond to different absorptance
values of $A=\{0.2, 0.4, 0.6, 0.8, 0.9, 0.99\}$.
The $A=0$ contour is the $R_l=0$ axis.}
 \label{fig:tilted_strip_rxload}
\end{figure}

To the tilted conductor dipole array of
Sec.~\ref{sec:tilted_pec_array}, loss can be introduced to
make the metasurface absorptive. For this purpose, a resistive
component can be incorporated into the load impedance
$Z_l$ in Fig.~\ref{fig:tilted_dipole_tmagphase}(a).
At the same time, adjusting the reactance part is expected to
give a capability to tune the transmission phase. To the
tilted PEC strip dipole array considered in
Sec.~\ref{sec:tilted_pec_array}, a complex load with an impedance
$Z_l=R_l+jX_l$ is attached to the center point of the
meta-atom. In the range $0\leq R_l\leq 800~\Omega$,
$-400~\Omega\leq X_l\leq 400~\Omega$, the reflection and transmission
coefficients were simulated using FEKO at 5~GHz.
The simulated
reflection coefficient is zero. The transmission
coefficient is shown in Fig.~\ref{fig:tilted_strip_rxload}.
The magnitude plot in
Fig.~\ref{fig:tilted_strip_rxload}(a) demonstrates that
the entire range of $|t|$ between zero and unity
is available for synthesis.
For visualization, a few contours for constant-$|t|$
(in terms of the absorptance $A$) values are also plotted. The same
contours are reproduced in Fig.~\ref{fig:tilted_strip_rxload}(b),
where the transmission phase is plotted. It is clear that
for any given value of $A$, an arbitrary phase in a complete
$2\pi$ range can be achieved in principle by selecting
an appropriate value for $Z_l$. In practice, extreme values
of $R_l$, $X_l$ required for some combinations of
$|t|$ and $\angle t$ may be difficult to realize and
consequently limit the synthesis range.

\begin{figure}[t]
 \centering
 \includegraphics*{tilted_strip_absorber.pdf}
 \caption{Characteristics of the center-loaded strip dipole
array with the load impedance chosen for perfect absorption at 5~GHz.
(a) The magnitude of the reflection and transmission
coefficients with respect to frequency.
(b) A snapshot of the total $y$-directed magnetic field,
$H_y$.}
 \label{fig:tilted_strip_absorber}
\end{figure}

In Fig.~\ref{fig:tilted_strip_rxload}(a), an extreme case
of full absorption is observed with a selection of load impedance
$Z_l=115.9+j20.6~\Omega$. If the received power is guided
to a receiving circuitry rather than dissipated as heat,
the design corresponds to a planar receiving array with a 100\% receiving
efficiency. The frequency responses of $|r|$ and $|t|$ are
shown in Fig.~\ref{fig:tilted_strip_absorber}(a).
The metasurface does not transmit nor reflect at the design
frequency of 5~GHz. The bandwidth is reflection zero is extremely
wide. At 5~GHz, a snapshot at time $t=0$
of the $y$-component of the total magnetic field
in the $xz$-plane is plotted over the unit-cell dimension of
$-a/2<x<a/2$ in Fig.~\ref{fig:tilted_strip_absorber}(b).
Only the fields
associated with the incident wave is visible above the
metasurface and zero field penetrates behind the dipole array.

In this design, absorption occurs at the load connected
to the otherwise lossless meta-atom. Instead, it is possible to design
an absorber based on a distributed loss mechanism. One approach
will be realizing the dipole meta-atom using lossy conductive
material such as conductive ink films,
modeled as a resistive impedance sheet~\cite{wang_ieeejmtt2017}.
Such a lossy strip array variant was designed for perfect
absorption at 5~GHz and numerically analyzed.
Its simulated scattering characteristics exhibit
the same qualitative behavior presented in
Fig.~\ref{fig:tilted_strip_absorber} (not shown).

\subsection{Array of dielectric bars of rectangular cross section}
\label{sec:dielectric_cylinders}

\begin{figure}[t]
	\centering
 \includegraphics{dielectric_unoptimized.pdf}
 \caption{Scattering by an array of dielectric bars illuminated
obliquely at an incidence angle of
$\theta^{\rm{i}}=45\degree$. The refractive index
of the dielectric material is $n_{\rm d}=6$, the periodicity
is $a=730$~nm, the width is $w=300$~nm and the height is $h=360$~nm.
(a) Reflection spectrum.
(b-d) Field distributions at the three resonant frequencies:
(b) A tangential magnetic dipole;
(c) A tangential electric dipole;
(d) A vertical electric dipole.}
 \label{fig:dielectric_bars_reflection_non_optimized}
\end{figure}

Here we give an example of a high-transmission array offering full control of the transmission phase in the optical domain. In order to ensure small dissipation losses, we use an all-dielectric metasurface formed by an array of parallel bars made of a lossless high refractive index dielectric ($n_{\rm d}=6$)
with the axis of the bars oriented along
the $y$-direction. Due to the 2-D nature of the problem,
the $y$-periodicity is infinite so we ensure the absence
of higher order modes propagating in this direction.
In conventional realizations of high-transmission all-dielectric metasurfaces, the Huygens regime is realized by exciting both electric and magnetic moments at the operational frequency. Here, we illuminate the array by an obliquely propagating plane wave to ensure excitation of both tangential and normal electric polarizations and utilize the theory in this paper to realize
a full transmission with a complete phase control.
Following the previous example, we consider a TM-polarized incident plane wave [see Fig.~\ref{fig:dielectric_bars_transmission_optimized}(a)] and we define the incidence angle
to be 45\textdegree.

The reflection spectrum is presented in Fig.~\ref{fig:dielectric_bars_reflection_non_optimized}(a) when the periodicity is $a=730$~nm, the width is $w=300$~nm and the height is $h=360$~nm. It exhibits three reflection maxima which correspond to three dipole-mode resonances.
The first reflection peak, at 111~THz, corresponds to a
tangentially oriented magnetic dipole. Figure~\ref{fig:dielectric_bars_reflection_non_optimized}(b) shows the electric field vector in the $xz$-plane, where we can see that the electric field circulates inside the bars generating
an out-of-plane magnetic dipole moment.
At 157~THz, the reflection peak is caused by the resonance of
a
tangential electric dipole, as we can see in Fig.~\ref{fig:dielectric_bars_reflection_non_optimized}(c). The third resonance peak, at 177~THz, corresponds to the resonance of a
normal electric dipole [see Fig.~\ref{fig:dielectric_bars_reflection_non_optimized}(d)]. Adjusting  the shape parameters of the bars, the magnitude and phase of the induced dipoles can be tuned to fulfill the conditions in (\ref{cond:norefl_pxpz}).

\begin{figure}[t]
	\centering
 \includegraphics{dielectric_optimized.pdf}
	\caption{A high-transmission all-dielectric array
utilizing induced electric dipoles.
(a) Schematic of the studied structure:
an array of dielectric bars with a refractive index
$n_{\rm d}=6$ illuminated at an angle of $\theta^{\rm i}=45\degree$.
(b) Transmission amplitude and phase of arrays of bars at
a frequency of 194~THz with different shape parameters.
The periodicity of the bars is kept constant, $a=730$~nm,
and the width of the bars is $w=h+10~\text{nm}$.
(c) An electric field distribution at 194~THz for $h=275$~nm.
(d) A conceptual illustration of the induced dipole moment.}
	\label{fig:dielectric_bars_transmission_optimized}
\end{figure}

Finally, a combination of~$\hat{x}p_{x}$ and~$\hat{z}p_{z}$ can be tuned to transmit the
incident light with required phase variations within the $2\pi$ range. We consider a periodic array as shown in Fig.~\ref{fig:dielectric_bars_transmission_optimized}(a) with a period $a=730$~nm. The bars have a rectangular cross section with a height $h$ and a width $w=h+10$~nm. Figure~\ref{fig:dielectric_bars_transmission_optimized}(b) shows the transmission magnitude and phase for arrays of bars of different sizes, as a function of $h$. We see that the transmission phase indeed varies within the full $2\pi$ range while the transmission magnitude remains close to unity.  Figures~\ref{fig:dielectric_bars_transmission_optimized}(c,d) show the calculated field distribution and a conceptual illustration of an excited tilted electric dipole moment for $h=275$~nm. The simulations were performed using ANSYS~HFSS, setting PBCs on the vertical walls of the unit cell.

{\color{red}For absorptive applications, an array of dielectric
bars made from a suitable lossy material is a straightforward
extension of the high-transmission array in
Fig.~\ref{fig:dielectric_bars_transmission_optimized}.
An optical analogue of the array of
tilted dipoles in Sec.~\ref{sec:tilted_array_lossy}
is another possibility.
Using the approach of lossy surface impedance realization in
\cite{monti_oplett2016} exploiting the surface dispersion of
nanoparticles,
it can be envisaged that metal nanoparticles are deposited
on some dielectric support having periodic slanted walls.
The tilt angle of the dielectric support can enforce
(\ref{cond:norefl_pxpz}). The surface resistance may be
designed to achieve various levels of absorption, including
complete absorption. This approach needs further investigation.}

\section{Conclusion}
\label{sec:conclusion}

For polarization-preserving transmissive metasurface,
it has been shown that the origin of a full transmission
capability together with a complete $2\pi$ phase coverage is
synthesis of an asymmetric scattering pattern with respect to
the metasurface plane. In Huygens' meta atoms, a tangential
magnetic dipole is responsible for creating anti-symmetric
scattering. An alternative meta-atom arrangement is available
for full transmission in oblique TM-polarization scattering,
as a combination of tangential and normal electric dipoles.
A particular realization is an array of tilted straight
conductor dipole meta-atoms with the dipole axis aligned
with the reflection direction. The geometrical nature of
the synthesized scattering null allows an extremely wide bandwidth of
zero reflection. In the presence of loss in constituent
materials or intended power absorption, it has been
analytically proven and demonstrated using a numerical example
that a complete transmission phase coverage is
possible for reflectionless metasurfaces. The operation
principle and the new design strategy presented in this study will
facilitate development of a new class of transmissive metasurfaces for
wave manipulation with high power efficiencies.

\section*{Acknowledgment}
This work was supported in part by the Academy
of Finland (project 287894).

redpajama_set_name: RedPajamaArXiv


text:
Speeches of Rev. Sun Myung Moon from 1976
The Liberation of Heaven and Earth
March 3, 1976, Choongang Training Center (Sootaek-li), Kyungki-do, Korea.
The Central Figure and the Transitional Period
March 7, 1976, Chung-pa Dong Headquarters Church, Seoul, Korea.
God's Hope for America
June 1, 1976, Yankee Stadium, New York.
Past and Future Generations
August 1, 1976, Tarrytown, New York
America And God's Will
September 18, 1976, United States Bicentennial Speech given by Reverend Sun Myung Moon before an audience of 300,000 people at the rally in Washington DC at the Washington Monument.
Untitled Address to Conference of US and International Leaders
September 20, 1976, Tarrytown, New York
Perfection and Gratitude
October 3, 1976, Belvedere, New York
The Day of the Victory of Heaven
The Responsibility of Cain and Abel
November 1, 1976, Belvedere, New York
The Age of Judgment and Ourselves
November 21, 1976, Belvedere, New York
December 1, 1976, Belvedere, New York
Boundary Line
The Benefit and Grace of this Time in History
December 19, 1976, Belvedere, New York
God's Will and Christmas
December 25, 1976, Manhattan Center, New York
The Final Warning Concerning Good and Evil
Online archives of sermons by Rev. Sun Myung Moon.


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Rice is a major food in Sri Lankans diet. Different types of rice are available for human consumption and rice types are related with rice consumption in Sri Lanka. Rice type can be described based on mainly quality characteristics, physical characteristics and chemical characteristics of rice. Therefore, this study was conducted to determine consumer preference for rice type in Hambantota district, Sri Lanka. Main three physical attributes and two rice types were used for this study. Physical attributes of rice such as rice color, rice grain size, and degree of milling were considered for the study. Main rice types considered were raw rice and parboiled rice. A questionnaire survey of consumer preference for rice was carried out by using a purposively sample of 100 consumers in Hambantota administrative complex considering the easy access to respondents with different occupation categories. Data analysis was done by using preference ranking methods. Moreover, Chi- squire test was used for identify the significant of characters. The study revealed that consumers' most preferred rice color was red color rice. Based on rice grain size long slender (Basmati) was the most preferred. The majority (75%) of consumers preferred partially-milled rice. Raw rice had higher preference. Therefore, according to the present study, the most preferred rice types were long slender (Basmati) rice and partially-milled red color raw rice in Hambantota District, Sri Lanka.
.	Anang, B.T, Adjetey, S.N. & Abiriwe, S.A., 2016. Consumer Preferences for Rice Quality Characteristics and the Effects on Price in the Tamale Metropolis, Northern Region, Ghana. International Journal of AgriScience, Vol. 1(2)(January 2011), pp.67– 74.
.	Asante, M.D. et al., 2013. Farmer and consumer preferences for rice in the Ashanti region of Ghana : Implications for rice breeding in West Africa. Journal of Plant Breeding and Crop Science, 5(12), pp.229–238.
.	Azabagaoglu, M.O. & Gaytancioglu, O., 2009. Analyzing consumer preference to different rice varieties in turkey. Agricultura Tropica ET Subtopica, 42(3), pp.118– 125.
.	Breckenridge, C., 1979. Rice grain evaluation in sri lanka. Proceeding of the workshop on chemical aspects of rice grain quality, International Rice research institute, Manilla, pp.175–181.
.	Metropolis, T. & Region, N., 2016. Consumer Preferences for Rice Quality Characteristics and the Effects on Price in the. International Journal of AgriScience, Vol. 1(2)(January 2011), pp.67–74.
.	Tengpongsathon, K, Nanthaicahi, K, Mason, R, Rimkeeree, H., 2006. Consumer preference of rice-based products : cross cultural study between Thailand and Australia. Journal of Agricultural Technology, 2(2), pp. 137–153.
.	Walisinghe, B R & Gunaratne, L.H.., 2012. Consumer Preferences for Quality Attributes of Rice : A Conjoint Analysis. Sri Lankan Journal of Agricultural Economics, 10, p.pg 19-30.
The widespread use of computers in schools renders accessibility and preparedness in these technologies necessary. It is critical to understand whether mathematics teachers are accessible to computers and have the necessary attitudes regarding computer integration into their classrooms. The purpose of the study was to establish the influence of teacher accessibility and attitude towards integration of computers in mathematics instruction in secondary schools in Kenya. A descriptive survey design was adopted for this study. 147 mathematics teachers in 25 public secondary schools of Kakamega South were selected through urposive, stratified and simple random procedures. The instruments for data collection were the questionnaire and interview schedule. Reliability of the data collection instruments was determined by split –half method. The data collected was analyzed using descriptive statistics. The findings had implications on integration of computers in secondary school mathematics.
.	Angeli, C. and Valanides, N. (2005). A socio-technical analysis of the factors affecting the integration of ICT in primary and secondary education. In L.T.W. Hin and Subramaniam (Eds)_Literacy in technology at the K-12 level: Issues and challenges (pp.123-131). Heshey, PA: Idea Group, Inc. Education Media International, Routledge.
.	Demetriadis, S. Barbas, A., Molohides, A., Palageorgiou, G., Vlahavas, I, (2003). 'Cultures.in.negotiation'. Teachers'acceptance resistance.attitudes. considering.the. infusion .of.technology.into.schools.Computers and Education, 41, 19-37.
.	Dexter, S.L., Anderson, R.E., and Becker, H.J. (1999). Teachers' views of computers as catalysts for changes in their teaching practice. Journal of Research on Computing in Education, 31,221-238.
.	Ertmer, P. (2005). Teacher pedagogical beliefs: The final frontier in our quest for technology integration? Educational Technology Research and Development 53, 25-39.
.	Hawkins, B.L., and Oblinger, D.C (2006). The myth about digital divide.
.	Koohang, A.A. (1987). A study of the attitude of pre-service teachers toward the use of computer. Educational Communication and Technology Journal, 35 (3), 145 – 149.
.	Loyd, B. H. and Loyd, E. L. (1985). The Reliability and Validity of an Instrument for the Assessment of Computer Attitudes. Educational and Psychological Measurement,45, 903 ,909.
.	MOEST (2005). Kenya Education Sector Support programme 2005-2010:Delivering.Quality.Equitable.Education.and.Training to.all.Kenyans..Government.Printers.Nairobi, Kenya.
.	Muir-Herzig, R. G. (2004) Technology and its impact in the classroom. Computers and Education, 42,111-131.
.	Office of Technology Assessment (OTA). (1995). Teachers and technology:making the connection. Washington, DC: US Government Printing Office.
.	Pelgrum, W.J. (2001). Obstacles to the integration of ICT in education: Results from a worldwide educational assessment. Computers & Education, 37,163-178.
.	Polonoli, E. K. (2001). Integrating technology into classroom: Three questions concerned principals must ask. Principal Leadership, 2(4), 34-38.
.	SMASE, (2008). Records of discussions between Japan International Cooperation Agency and The Government of Kenya on Japanese Technical Cooperation for The Strengthening of Mathematics and Science Education (SMASE) Project. Government of Kenya Printers. Nairobi, Kenya.
.	Sutherland, R., Armstrong, V., Barnes, S., Brawn, R., Breeze, N., Gall, M.,(2004). Transforming teaching and learning: Embedding ICT into everyday classroom practices. Journal of Computer.Assisted.Learning,20,413-425.
.	UNESCO SchoolNet, Bangkok (2003). Final Report, Building Capacity of Teachers/Facilitators in Technology-Pedagogy Integration for Improved Teaching and Learning. Bangkok, Thailand June 18-20.
.	Wood, E., Mueller, Willoughby, Specht, J., and DeYoung, T. (2005). Teachers' perceptions: Barriers and supports to using technology in the classroom. Education, Communication, and information, 5,183-206.
.	Yuen, A. H. K. and Ma, W. C (2001). Teachers' Computer Attitudes: Factors influencing the instructional use of computers. Proceedings of the International Conference on Computer in Education, November, Korea, Tp.
This research was designed to explore the impact of favourable Quality of worklife (QWL) on Socio-psychological aspects of workers and make suggestions to the policy makers to improve the QWL and the factors of socio-psychological aspects of weaving mill workers. This present study concentrated on QWL of the workers of weaving mills (shuttle-less power looms) in specific and found the relationship between the prevailing factors of Quality of Worklife (QWL) and its impact on socio-psychological factors of workers' attitude and then how the weaving mill workers are behave in groups with present work environment. There are five principal socio-psychological factors are identified here, such as Job involvement, workers' behaviour pattern, sense of competence, response to family and physical activity in work. The researcher has used both primary and secondary data and they were analysed with appropriate statistical tools. It is found that the existing QWL factors influence 75% on the attributes of socio-psychological of the workers. This survey clearly indicates that the existing quality of worklife in weaving mills is positively influencing the socio-psychological aspects of the workers. The present study has a few limitations. Based on the study, analysis of data and the findings, some suggestions have been given. It is solemnly believed if the various measures suggested are fully implemented; the weaving mills in Tamilnadu will get an exemplary position on achieving better QWL of the workers and improve the socio-psychological aspects of workmen.
.	Allen Port G. (1992), "The Ego in contemporary psychology", Psychological review, Volume 5, 1992, PP.453.
.	Bolweg J.F. (1976), Job Design and Industrial Democracy: International Series of Quality of Work Life, Martinus Social Sciences Division.
.	Collier, Ann M (1970), A Handbook of Textiles, Pergamon Press, 2009, ISBN 0 08 0180574. PP 258.
.	Ellinger, Charles and Bruce Nissen (1987), "A Case Study of A Failed QWL Program implication for Labor Education", Labour Studies Journal, Volume 11, No. 3, 1987, PP 195-219.
.	Havlovic S. J. (1991), Quality of Work Life and Human Outcomes, Industrial Relations, Volume30/3, PP 469-79.
.	Indian Cotton Textile Sector Network Report, 2010 Network Overview, Within the initiative, Sustainable Industrial Networks and Its applications on Micro Regional Environmental Planning (SINET), SINET Secretariat, Nagpur, PP 4-8.
.	Nadler, D., and Lawler, E. (1983), "Quality of work life: Perspectives and directions. Organization Dynamics" International Review of Applied Psychology, Volume 11, PP 20-30.
.	Seashore S.E. (1975), Defining and measuring the quality of working life, In L.E. Davis and A.B. Cherns (Edition), The quality of working life, New York: The Free Press, PP 105-118.
.	Shareef, R. (1990), "QWL Programs Facilitate Change", Personnel Journal, (PEJ), Volume 69, Issue 9, PP. 58-61 & 427.
.	Stephen J. Havlovic (1991), "Quality of work life and human resource outcomes", Industrial relations, Volume 30, Regents of the University of California, PP 23-25.
.	Subba Rao. P, "Nature and Scope of Human resource management", Personnel and Human Resource Management Text & Cases, Himalaya Publishing House, Mumbai, Edition 2010, PP.5- 9.
.	Walton, R. E. (1974), Improving the Quality of Work Life, Harvard Business Review, May-June, 12 (a).
Investment scenario is changing very fast and financial literacy impacts financial decisions of individual investors. The present study is exploratory in nature and determines the factor that affects financial literacy and how they affect decision making. The sample consist of 649 individual investors to obtain information through structured questionnaire from various parts of India The result indicated that there are seven most influencing factors of financial literacy that affects investor decision making are: Attitude, Knowledge, Budgeting Habits, liquidity, self analytical skills, Emotional Inclination and Goal Planning. This study will help to determine strategies which will help to improve financial literacy of an individual investors.
.	Athreya, K. and Stilwell, A. (2009) "Rationalizing Financial Literacy Policy" published at The Federal reserve Bank of Richmond.
.	Bhushan.Punit, Medury.Yejulla et.al,( 2013). " Financial Literacy and its determinants ", International Journal of engineering, Business and enterprise application, Vol 4 (2), pp 155-160.
.	J.Tullio, (2009), Financial Litreacy: Discussion Paper.
.	K. Sobhesh, Agarwalla Samir, K. Barua, Joshy Jacob Jayanth R. Varma(2013) Financial Literacy Among Working Young In Urban W.P. No. 2013-10-02.
.	Kempson E., Collard S. and Moore N. (2005) Measuring financial capability: an exploratory study, Financial Services Authority, Consumer Research Report No. 37.
.	Lusardi, Mitchell (2007)," Financial literacy and Retirement Planning: New Evidence from American Life Pane" MRRC Working Paper 2007-15.
.	Organisation for Economic Co-operative and Development (2012), National Strategy for Financial Education.
.	Varma, J. R. (2003) "Indian Financial Sector After a Decade of Reforms" published at Indian Institute of Management, Ahmedabad 380 015, India.
.	Varma, J.R. (2002) "Governance, Supervision and Market Discipline: Lessons from Enron" the Indian School of Political Economy in which the paper was first published (October-December 2002), Volume 14 Number 4, 559-632).
.	W.Jason,(2012), "Financial Literacy Education And Behaviour Unhinged" International Journal Of Consumer Studies.
This study deals with the superior subordinate relationship and hence the factors which induce affect the relationship and factors which induce the superior and sub ordinate to perform well are discussed in detail and mathematically analyzed. It is obvious that, the superior and subordinate cordial relationship plays a vital role in successful functioning of the firm. Therefore it is necessary that the superior must keep a very good relation with the sub-ordinate to get their co operation in order to run the firm profitably.


text:
Proximity, no. 1
M. A. George
"M.A. George blended just the right amount of sci-fi and romance together to create a compelling debut novel that leaves readers needing the second installment in the series immediately. She developed a complex world that's unique to Proximity and a different planet from Earth altogether impeccably."
-- Mallory, Cover Bound
"Definitely a five star book, and one of my favourite reads this year.
Romance fans will love this, science fiction fans will love this and those who have to read anything even mentioning Jane Austen."
-- Unorthodox Mama
"I thoroughly enjoyed each and every page! It is a fast paced, unique love story that mixes in equal parts of romance, paranormal and suspense."
-- BookWorm Brandy
She's an alien whose home world doesn't even know she exists.
He just inherited a planet, and now he's running from it.
She has spent a lifetime hiding in plain sight.
He wants to escape the spotlight.
Her touch can heal.
His wounds are deep.
Two hearts, two planets collide. It's the perfect union.
Except the part where the world's about to end.
PROXIMITY is the first book in the Proximity series.
Draft2Digital, LLC
macystarr , 11/10/2012
Captivating and Intriguing...
I couldn't put it down....I stayed up until after 2am on my iPad to finish...thank goodness I had the next day off :)
I can hardly wait for book 2...!!!
More Books by M. A. George
Spectral Tales
Relativity (Proximity #2)
Vitality (Proximity #3)
Tales From the SFR Brigade
The Keeper
Into the Spiral (The Spiral Defenders Series: Book One)
A Lick of Immortality
Circumstellar
Echo Among Stars


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