text: fig4 shows an embodiment of a coupler / splitter such as provided herein . such a coupler / splitter comprises two waveguides : a first waveguide 11 having a constant cross - section such as previously - described waveguides 1 and 2 and a second waveguide 13 which , in coupling portion l c , has a variable cross - section , that is , a variable width in the conventional case where the core of this waveguide has a constant thickness . beyond coupling area l c , second waveguide 13 has a constant width . assuming that the light comes from the left ( upstream side ), the width variation of waveguide 13 along coupling length l c is selected so that this waveguide initially has a width w 1 smaller than the width of the first waveguide and that it has in the output area a width w 2 greater than the width of the first waveguide . as a result , the effective index in the upstream portion of the second guide is lower than the effective index in its downstream portion . further , the widening profile in coupling area l c is selected so that the mode transfer occurs in adiabatic conditions , for example , such as defined in xiankai sun , hsi - chun liu , and amnon yariv &# 39 ; s article published in optics letters , volume 34 , n o 3 of feb . 1 , 2009 . it should be noted that this article considers the coupling between two superposed waveguides while the present description aims at the case of two coplanar waveguides . further , it relates to a specific design mode which provides an adiabaticity criterion for the shortest possible coupling length . due to the compliance with the adiabaticity conditions , an optimal transfer of the tm polarization mode from the first guide to the second guide is obtained with coplanar waveguides and this transfer remains satisfactory even if the dimensions are not strict . thus , the main conditions to be respected to provide a transfer of the tm wave with no transfer of the te wave are to provide a coupling area where there is an effective coupling index variation between upstream and downstream of the coupling area , the coupling length being selected so that the transfer is quasi - complete and the transfer of the tm mode is optimized . further , the effective index of the first guide , in the coupling area , should be within the variation interval of the effective index of the second guide . as known , and as results from the above - mentioned article , these optimal dimensions cannot be set by analytic formulas , except for forms specifically described in yariv &# 39 ; s article . however , generally , and for convention forms ( linear , exponential , polynomial ), the coupling length is determined ex post facto by simulation . in practice , length l c is set by simulation : the quantity of tm mode transferred to the second guide as it is moved in the downstream direction of the second guide is calculated , and the length corresponding to a maximum coupling of the tm mode is selected . the coupling portion of the second guide comprising a first surface 15 close to the first waveguide and parallel to the opposite surface of this first waveguide has been shown , second surface 16 remote from the first waveguide being rectilinear and non parallel to that of the first waveguide . it should be noted that this embodiment is likely to have various alterations . according to a first variation , the first surface is not necessarily parallel to the opposite surface of the first waveguide , although this is a preferred embodiment since it gives a greater robustness ( invariance with respect to variations of the manufacturing process ) to the coupler / splitter . according to a second variation , second surface 16 is not rectilinear , but may have any selected contour and for example corresponds to a quadratic , exponential , or polynomial function of distance z to the origin of the coupler / splitter . it should finally be noted that the second guide continues in a portion 18 . this portion can remain parallel to the first waveguide . this has little influence on the operation of the coupler / splitter since , given that portion 18 is much wider than first waveguide 11 , there is practically no coupling between waveguides in this area . fig5 illustrates the transmission rate in db of the tm and te modes from the first guide to the second guide for a coupler / splitter of the type in fig4 . curve tm indicates that from a given coupling length ( greater than approximately 30 μm the shown example ), the practically unattenuated tm mode is present in the second guide . curve te indicates that the portion of the te mode present in the second guide is very low , provided for the coupling length not to be excessive ( smaller than 75 in the shown example ). indeed , as underlined by the above - mentioned sun , liu , and yariv article in the last portion of its first paragraph “ an adiabatic coupler , . . . , does not require a precise definition of power - transfer length but it has to be sufficiently long to satisfy the adiabatic condition to reduce the coupling of power into other unwanted modes ”. fig6 shows an alternative embodiment of an adiabatic coupler / splitter with coplanar guides . in this variation , two guides 21 and 22 of regular cross - section extend parallel to each other . between these two guides is provided an interposed guide segment 24 having its left - hand portion comprising a coupling portion 25 similar to the coupling portion of length l c described in relation with fig4 , and having its right - hand portion comprising a coupling portion 26 symmetrical to the previous one , an intermediate parallel guide portion 27 being preferably interposed between coupling portions 25 and 26 . thus , when light l penetrates into waveguide 21 and comprises te - polarized light and tm - polarized light , the tm - polarized light is transferred to coupling portion 25 and then passes through intermediate portion 27 into coupling portion 26 from which it is coupled towards guide 22 . guides 21 and 22 may have different cross - sections , guide 21 having a width optimized to promote the propagation of the te mode and guide 22 having a width optimized to promote the propagation of the tm mode . according to a variation , portion 27 may be absent . in this case , the two portions 25 and 26 are directly connected to each other . according to an alternative embodiment illustrated in fig7 , the two guides 21 and 22 may be separated by a plurality of interposed coupling elements 24 - 1 , 24 - 2 . . . , these interposed coupling elements promoting the passing from one to the other and then into guide 22 of the tm - polarized light penetrating into guide 21 . this structure with several interposed guide segments especially has the advantage of decreasing the possible residual te - polarized light transferred to guide 22 . indeed , if the first interposed element lets through a small proportion ∈ of te - polarized light towards the next element , this next element will only let through a proportion ∈ 2 . if there are n − 1 interposed elements , there will only be in final guide 22 a proportion ∈ n of te - polarized light . fig8 shows a specific configuration of a first guide 31 having received te - polarized light and tm - polarized light , where the tm - polarized light has been transferred to another guide via a coupling system , not shown . there however remains a small portion ∈ of tm light in guide 31 . to further decrease this proportion , guide 31 comprises a series of turns 33 - 1 , 33 - 2 . . . , 33 - n . indeed , it is known that for turns having a small radius of curvature , the te - polarized wave is practically not attenuated while the tm - polarized light is strongly attenuated , for example , from 8 to 10 db . specific embodiments of the present invention have been described . various alterations , modifications , and improvements will occur to those skilled in the art . in particular , the present description has been made in the context of a polarization coupler / splitter . it should be noted that this coupler / splitter may also be used as a wavelength splitter in the case where the incident optical wave comprises two frequency components . in this case , the signal of the large wavelength will be transferred to another guide , while the signal of the small wavelength will remain in the input guide . various embodiments with different variations have been described hereabove . it should be noted that those skilled in the art may combine various elements of these various embodiments and variations without showing any inventive step . such alterations , modifications , and improvements are intended to be part of this disclosure , and are intended to be within the spirit and the scope of the present invention . accordingly , the foregoing description is by way of example only and is not intended to be limiting . the present invention is limited only as defined in the following claims and the equivalents thereto .