1. Field of the Invention
The present invention relates generally to photonic band-gap crystal waveguides, and particularly to photonic band-gap crystal waveguides having a low refractive index core region. The invention is also directed to a method of making low refractive index core photonic band-gap crystal waveguides.
2. Technical Background
Knowledge of how to guide light in a material by means of total internal reflection is old in physical science. One of the drawbacks of light guides using total internal reflection lies in the very principle of total internal reflection. That is, total internal reflection occurs at the interface between a first and a second material having different refractive indexes. Light traveling in the material of higher refractive index is reflected (totally reflected for incident angles lower than the critical angle) at the interface with the material of lower refractive index. Thus, the total internal reflection mechanism acts to confine the light to the higher index material. The higher index material typically is higher in density and so is characterized by higher attenuation due to Rayleigh scattering and by a higher non-linear coefficient. The non-linear effects can be mitigated by designing total internal reflection waveguides that have relatively high effective area. However, the complexity of the core refractive index profile usually increases for designs that provide larger effective area. This complexity usually translates to higher cost.
More recently, diffraction has been studied as a means to guide light in a material. In a light guiding protocol in which the confinement mechanism is diffraction, the material in which the light is guided, i.e., the core of the optical waveguide, can have a relatively low refractive index and thus a lower density. In fact, the use of a gas or a vacuum as a waveguide core becomes practical.
A particular structure well suited for use as a diffraction type optical waveguide is a photonic band-gap crystal. The photonic crystal itself is a regular lattice of features in which the spacing of the features is of the order of the light wavelength to be guided. The photonic crystal can be constructed of a first material having a first refractive index. Embedded in this first material, in the form of a regular lattice or array, is a second material having a second refractive index. This is the basic photonic crystal structure. Variations on this basic design can include more than two materials in the make up of the photonic band-gap crystal. The number of useful variations in the details of the lattice structure is also large. In the basic photonic crystal structure, the second material can simply be pores or voids formed in the first material. Depending upon the refractive index difference of the materials and the spatial arrangement and pitch (center to center distance between features) of the embedded features, the photonic crystal will not propagate light having a wavelength within a certain wavelength band. This is the xe2x80x9cband-gapxe2x80x9d of the photonic crystal and is the property of the photonic crystal that provides for light confinement. It is due to this property that the structure is given the name, photonic band-gap crystal.
To form an optical waveguide (or more generally, a structure that guides electro-magnetic energy), a defect is formed in the photonic band-gap crystal. The defect is a discontinuity in the lattice structure and can be a change in pitch of the lattice, the replacement of a portion of the lattice by a material of different refractive index, or the removal of a portion of the photonic band-gap crystal material. The shape and size of the defect is selected to produce or support a mode of light propagation having a wavelength that is within the band-gap of the photonic crystal. The walls of the defect are thus made of a material, a photonic band-gap crystal, which will not propagate the mode produced by the defect. In analogy with the total internal reflection optical waveguide, the defect acts as the waveguide core and the photonic band-gap crystal acts as the clad. However, the mechanism of the waveguide allows the core to have a very low refractive index thus realizing the benefits of low attenuation and small non-linear coefficient.
Because of the potential benefits provided by a photonic band-gap crystal waveguide, there is a need to identify defect structures that produce modes that have useful wavelengths, the modes being efficiently propagated over practical distances. More particularly, there is a need to investigate whether photonic band-gap crystal defect structures exist that will allow photonic band-gap crystal waveguides to propagate light signals over distances compatible with telecommunication systems.
Other uses of the photonic band-gap crystal waveguide include those that involve the delivery of high electromagnetic power levels such as in devices for excising material or welding material.
One aspect of the present invention is a photonic band-gap crystal optical waveguide which includes a photonic crystal having a band-gap. Typically, the photonic band-gap crystal is characterized by a pitch, the center to center distance between repeating features that make up the photonic crystal lattice. The photonic band-gap crystal has a defect, that is, a break or discontinuity in the regularity of the lattice. The defect is characterized by a boundary enclosing a plane cross section of the defect. The enclosing boundary is the locus of points in a plane where the photonic band-gap crystal structure abuts the defect. Perpendicular to the plane cross section is a characteristic length dimension of the defect. In the case disclosed and described herein of a photonic band-gap crystal waveguide structure, the defect length dimension extends through the photonic band-gap crystal so that one has access to either end of the defect.
The boundary of the defect is characterized by a numerical value, which can have units of length. The numerical value can be, for example, a radius, if the defect cross section is circular, the distance of a boundary point from a feature in the cross section (such as the geometrical center), or the perimeter measure of the boundary. The numerical value characteristic of the defect boundary is such that localized modes produced by (supported in) the defect propagate in the wavelength range in the band-gap of the photonic band-gap crystal. Further, the ratio of the numerical value to the photonic band-gap crystal pitch is selected so that the excitation of surface modes within the photonic band-gap is avoided.
When the defect boundary, together with the photonic band-gap crystal pitch are such that surface modes are excited or supported (exist), a large fraction of light power propagated along the defect is essentially not located in the defect. The surface mode propagates at least partially in the photonic band-gap crystal itself. Thus, the distribution of light power is not effective to realize the benefits associated with the low refractive index core of a photonic band-gap crystal optical waveguide.
In an embodiment of this first aspect of the invention, the defect has a circular cross section and the numerical value is the radius of the circle. The ratio of radius to pitch has a range from 0.75 to 1.15.
In a further embodiment of the first aspect of the invention, the ratio of radius to pitch is 1.3 to 1.5. In yet another embodiment in accord with a circular defect cross section, the ratio of radius to pitch is 1.7 to 2.1. At ratios between the ranges given in these circular cross section embodiments, surface modes appear, drawing light power out of the defect.
This first aspect of the invention and the embodiments thereof can advantageously be characterized by a defect which is either partially or entirely a void in the photonic band-gap crystal. As an alternative, this first aspect if the invention and the embodiments thereof can be characterized by a defect which is either partially or entirely a material which has a refractive index lower than at least one of the materials that form the photonic band-gap crystal lattice. As is known in the art, the photonic band-gap crystal lattice is generally formed from at least two materials which differ from one another in refractive index.
In a single mode waveguide embodiment in accord with the first aspect of the invention, the photonic band-gap crystal includes air. For example, the crystal lattice can be symmetrically spaced voids or pores formed in a material such as SiO2. The materials used to form photonic band-gap crystals are known in the art and are described for example in Photonic Crystals: Molding the Flow of Light, J. D. Joannopoulos, et al., Princeton University Press, Princeton, 1995. The fractional volume of air making up the photonic band-gap crystal can be specified as having a particular value or range of values. The term fractional volume of air is the ratio of the volume of the crystal that is air to the total volume of the crystal. The fractional volume of the pores that may make up the photonic crystal is also a useful measure. In this case, the pores may be filled with air, be evacuated, or filled with a material having a pre-selected refractive index.
In an embodiment in accord with the invention, the fractional volume of air is not less than 0.67, the defect has a circular cross section and the numerical value characteristic of the defect boundary is the cross section radius. To achieve a light mode propagating with not less than 0.5 of the mode power in the defect (the mode power fraction), the ratio of radius to pitch is in the range from about 0.61 to 1.22. To achieve a mode power fraction in the defect of not less than 0.7, the ratio of radius to pitch has a range from about 0.63 to 1.19. To achieve a mode power fraction not less than 0.8, the ratio of radius to pitch has a range from about 0.8 to 1.16.
A mode power fraction not less than 0.9 can be achieved in a photonic band-gap crystal having a defect of circular cross section and a fractional volume of air not less than 0.83, with a ratio of radius to pitch having a range from 1.07 to 1.08. This particular embodiment of the waveguide in accord with the invention is single mode.
In a further embodiment in accord with this aspect of the invention, the defect cross section is a void of hexagonal cross section, the photonic band-gap crystal includes pores having volume fraction not less than 0.67. The numerical value associated with the defect is the length of a line drawn from the center of the hexagon perpendicular to a side of the hexagon. For a mode power fraction within the defect not less than 0.6, the ratio of the numerical value to pitch has a range from 0.9 to 1.35. For mode power within the defect (mode power confinement fraction) not less than 0.8, the ratio of numerical value to pitch has a range from 1.45 to 1.65.
A second aspect of the invention is a method of making a photonic band-gap crystal optical waveguide. The method in accord with the invention includes the steps of a) fabricating a photonic band-gap crystal having a pitch; and, b) forming a defect in the photonic band-gap crystal. The defect has a boundary enclosing the defect cross section and a length perpendicular to the defect cross section. The defect can be located within, or partially within, the photonic band-gap crystal. The boundary is characterized by a numerical value, which is selected such that the wavelength of the localized mode produced by (supported in) the defect propagates in the wavelength range of the photonic crystal band-gap. The ratio of the numerical value characteristic of the defect boundary to the photonic band-gap crystal pitch is selected to avoid the excitation of surface modes within the photonic band-gap.
In an embodiment in accord with the method, the defect is formed by removing material from the photonic band-gap crystal. That is, the defect is a void in the photonic band-gap crystal.
In another embodiment of the method the photonic band-gap crystal is made by forming pores or voids in a material. In a further limitation of this embodiment, the voids or pores make up not less than 0.67, and preferably not less than 0.83, of the volume of the photonic band-gap crystal.
Additional features and advantages of the invention will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the invention as described herein, including the detailed description which follows, the claims, as well as the appended drawings.
It is to be understood that both the foregoing general description and the following detailed description are merely exemplary of the invention, and are intended to provide an overview or framework for understanding the nature and character of the invention as it is claimed. The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate various embodiments of the invention, and together with the description serve to explain the principles and operation of the invention.