BRICKED SUB-WAVELENGTH PERIODIC WAVEGUIDE, MODAL ADAPTER, POWER DIVIDER AND POLARISATION SPLITTER THAT USE SAID WAVEGUIDE

Abstract

A bricked sub-wavelength periodic waveguide and a modal adapter, power divider and polarization splitter that use the waveguide. The waveguide includes blocks disposed periodically with a period “L.sub.z” on a substrate and which alternate with a covering material. The first blocks have a width “a.sub.x” and the second blocks have a width “b.sub.x”, alternating on the substrate according to a period “L.sub.x”, the second blocks being shifted a distance “d.sub.z” the first blocks in the direction of propagation. A modal adapter, a power divider and a polarization splitter all use the periodic waveguide and can operate with larger wave periods without leaving the sub-wavelength regime.

Claims

1. A bricked sub-wavelength periodic waveguide through which a wave propagates in a propagation direction, the periodic waveguide comprising: a substrate on which there is arranged a plurality of blocks of a core material arranged in a periodic manner with a period ‘Λ.sub.z’ in the propagation direction, and a covering material, arranged between and on the plurality of blocks, there being first blocks of width ‘a.sub.x’ and second blocks of width ‘b.sub.x’, alternating on the substrate perpendicularly to the propagation direction according to a period ‘Λ.sub.x’, and the second blocks being shifted a distance ‘d.sub.z’ in the propagation direction with respect to the first blocks.

2. The periodic waveguide of claim 1, wherein the period ‘Λ.sub.Z’ fulfills: ${\Lambda }_{\text{z}}<\lambda \text{/}\left(2\cdot {\text{n}}_{\text{eff}}\right)$ λ being the wavelength of the wave that propagates through the periodic waveguide and n.sub.eff being the effective index of the mode.

3. The periodic waveguide of claim 1, wherein the period ‘Λ.sub.Z’ fulfills: ${\Lambda }_{\text{z}}<\lambda \text{/}\left(2\cdot {\text{n}}_{\text{eff}}\right)$ λ being the wavelength of the wave that propagates through the periodic waveguide and n.sub.eff being the effective mode index.

4. The periodic waveguide according to claim 1, wherein the shift ‘d.sub.Z’ of the second blocks of width ‘b.sub.x’ is selected such that a first effective index (n.sub.TE) of a zero-order transverse electric mode (TE.sub.0) is different from a second effective index (n.sub.TM) of a zero-order transverse magnetic mode (TM.sub.0).

5. The periodic waveguide according to claim 1, wherein the shift ‘d.sub.Z’ of the second blocks of width ‘b.sub.x’ is selected such that a first effective index (n.sub.TE) of a zero-order transverse electric mode (TE.sub.0) is equal to a second effective index (n.sub.TM) of a zero-order transverse magnetic mode (TM.sub.0).

6. The periodic waveguide according to claim 1, wherein the periodic waveguide is of a variable width (W).

7. The periodic waveguide according to claim 1, wherein the periods (Λ.sub.z and Λ.sub.x) according to which the blocks are arranged are variable in the propagation direction and in the direction perpendicular to the propagation direction.

8. The periodic waveguide according to claim 1, of the wherein the distance (d.sub.z) is variable in the propagation direction.

9. The periodic waveguide according to claim 1, wherein the cover material and the plurality of blocks of core material feature constant geometrical properties along the length of the waveguide.

10. The periodic waveguide according to claim 1, wherein the cover material and the plurality of blocks of core material feature variable geometric properties along the length of the waveguide.

11. The periodic waveguide according to claim 1, wherein the blocks are of silicon and the substrate is an insulating material, preferably silicon dioxide, in a silicon-on-insulator (SOI) configuration.

12. The periodic waveguide according to claim 1, wherein the cover material is a material selected from silicon dioxide, polymer and air.

13. The periodic waveguide according to claim 1, wherein the blocks, are of silicon and the cover material is a polymer that features a variation of the refractive index changing with temperature of sign opposite to the variation of the refractive index of the silicon.

14. The periodic waveguide according to claim 13, wherein the ratio of cover material to block materialwithin a period ‘Λ.sub.z’ is selected such that a variation with temperature of the first effective index (n.sub.TE) and the second effective index (n.sub.TM) is minimized.

15. The periodic waveguide according to claim 1, wherein its diagonal tensor (n) is given by an expression of the form: $n=\left[\begin{array}{ccc}{n}_{xx}\left(d_z\right)& 0& 0\\ 0& n_{yy}& 0\\ 0& 0& n_{zz}\left(d_z\right)\end{array}\right]$ where: $\begin{array}{c}{n}_{xx}\left(d_z\right)=\frac{1}{2}\left(n_{xx}+\sqrt{n_{xx}\cdot n_{zz}}\right)+\frac{1}{2}\left(n_{xx}-\sqrt{n_{xx}\cdot n_{zz}}\right)\cdot \cos \left(2\pi \frac{d_z}{{\Lambda }_z}\right)\\ n_{yy}=n_{yy}\\ n_{zz}\left(d_z\right)=\frac{n_{xx}\cdot n_{zz}}{n_{xx}\left(d_z\right)}\end{array}$ [n.sub.xx, n.sub.yy, n.sub.zz] being the components of a diagonal tensor (n) of the equivalent homogeneous anisotropic medium of a sub-wavelength structure.

16. A modal adapter for wave transverse electric mode (TE) and transverse electric mode (TM), the modal adapter using a periodic waveguide, the periodic waveguide comprising: a substrate on which there is arranged a plurality of blocks of a core material arranged in a periodic manner with a period ‘Λ.sub.z’ in the propagation direction, and a covering material, arranged between and on the plurality of blocks, there being first blocks of width ‘a.sub.x’ and second blocks of width ‘b.sub.x’, alternating on the substrate perpendicularly to the propagation direction according to a period ‘Λ.sub.x’, and the second blocks being shifted a distance ‘d.sub.z’ in the propagation direction with respect to the first blocks, the modal adapter comprising a first zone of conversion from a conventional waveguide to a sub-wavelength, SWG, waveguide of the same width as the conventional waveguide and with a period in longitudinal direction ‘Λ.sub.z’, wherein the waveguide (SWG) comprises bars of core material alternating with a central bridge of core material, the bars and the central bridge being arranged on a substrate-and wherein the central bridge progressively decreases in width until it disappears, a second zone of conversion of the SWG waveguide resulting from the first zone into the periodic waveguide, wherein the shift ‘d.sub.z’ of the second blocks varies from an initial value equal to zero to a final value.

17. The modal adapter of claim 16, wherein the width of the periodic waveguide gradually increases to a final width value.

18-19. (canceled)

20. A device comprising: at least one input waveguide, at least a first output waveguide, at least a second output waveguide, a multi-mode interference device comprising a periodic waveguide in its central part, at least a first modal adapter, arranged between the at least one input waveguide and the multimode interference device, and at least a second modal adapter, arranged between the multimode interference device and at least one of the first and second output waveguides; wherein the periodic waveguide comprises a substrate on which there is arranged a plurality of blocks of a core material arranged in a periodic manner with a period ‘Λ.sub.z’ in the propagation direction, and a covering material, arranged between and on the plurality of blocks, there being first blocks of width ‘a.sub.x’ and second blocks of width ‘b.sub.x’, alternating on the substrate perpendicularly to the propagation direction according to a period ‘Λ.sub.x’, and the second blocks being shifted a distance ‘d.sub.z’ in the propagation direction with respect to the first blocks, and wherein the at least the first modal adapter and the at least the second modal adapter each comprise a modal adapter type, the modal adapter type comprising: a first zone of conversion from a conventional waveguide to a sub-wavelength, SWG, waveguide of the same width as the conventional waveguide and with a period in longitudinal direction ‘Λ.sub.z’, wherein the waveguide (SWG) comprises bars of core material alternating with a central bridge of core material, the bars and the central bridge being arranged on a substrate, and wherein the central bridge progressively decreases in width until it disappears, and a second zone of conversion of the SWG waveguide resulting from the first zone into the periodic waveguide, wherein the shift ‘d.sub.z’ of the second blocks varies from an initial value equal to zero to a final value.

21. The device according to claim 20, further comprising a third modal adapter arranged between the multimode interference device and the second output waveguide; wherein the device is a polarization splitter of wave transverse electric mode and transverse magnetic mode; wherein the at least one input waveguide receives wave transverse electric mode and transverse magnetic mode, the first output waveguide is for the polarization of the transverse electric mode, the second output waveguide is for the polarization of the transverse magnetic mode, and the second modal adapter being arranged between the multimode interference device and the first output waveguide; wherein the third modal adapter comprises the modal adapter type.

22. The device according to claim 20, wherein the device is a power divided; wherein: the at least one input waveguide receives a wave transverse electric mode, the first output waveguide is for the output transverse electric mode and with a power portion of the output transverse electric mode, and the second output waveguide is for the input transverse electric mode and with the remaining portion of power of the output transverse electric mode out of phase by a certain amount with respect to the output transverse electric mode of the at least a first output waveguide.

Description

DESCRIPTION OF THE FIGURES

[0076] With the aim of helping for a better understanding of the features of the invention in accordance with a preferred example of a practical embodiment thereof, and to complement this description, the following figures, which are illustrative and not limiting, are included as an integral part of this description:

[0077] FIG. 1.- Shows a perspective view of a conventional waveguide of the prior art.

[0078] FIG. 2.- Shows a perspective view of a conventional SWG waveguide of the prior art.

[0079] FIG. 3.- Shows a graph representing the variation of the effective index of a Floquet mode in a conventional SWG waveguide as a function of the quotient between the wavelength and the repetition period, as well as the three possible zones of operation.

[0080] FIG. 4.- Shows how the curve of the effective index of a Floquet mode in a conventional SWG waveguide is modified as a function of the wavelength when the duty cycle is decreased.

[0081] FIG. 5.- Shows how the curve of effective index of a Floquet mode in a conventional SWG waveguide is modified as a function of the wavelength when the repetition period is decreased.

[0082] FIG. 6.- Schematically shows, a bricked sub-wavelength periodic waveguide, in accordance with a preferred embodiment of the invention.

[0083] FIG. 7.- Schematically shows, in a top view, a bricked sub-wavelength periodic waveguide, in accordance with a preferred embodiment of the invention.

[0084] FIG. 8.- Shows a graph showing the effective index of the zero-order transverse electric (TE.sub.0) Floquet mode as a function of the wavelength of a bricked sub-wavelength periodic waveguide, for different values of the period (Λ.sub.z) and with a longitudinal shift (d.sub.Z) equal to zero, in accordance with a preferred embodiment of the invention.

[0085] FIG. 9.- Shows a graph showing the effective index of the zero-order transverse electric (TE.sub.0) Floquet mode as a function of the wavelength of a bricked sub-wavelength periodic waveguide, for different values of the longitudinal shift (d.sub.Z), in accordance with a preferred embodiment of the invention.

[0086] FIG. 10.- Shows a graph showing the effective index of the zero-order transverse magnetic (TM.sub.0) Floquet mode as a function of the wavelength of a bricked sub-wavelength periodic waveguide, for different values of the longitudinal shift (d.sub.Z), in accordance with a preferred embodiment of the invention.

[0087] FIG. 11.- Shows a modal adapter between a conventional waveguide and a bricked sub-wavelength periodic waveguide, and vice versa, in accordance with a preferred embodiment of the invention.

[0088] FIG. 12.- Shows a multi-mode interference coupler based on bricked sub-wavelength periodic waveguides operating as 3 dB/90° power divider, in accordance with a preferred embodiment of the invention.

[0089] FIG. 13.- Shows a graph showing the beat length as a function of the wavelength of the first two transverse electric (TE.sub.0 and TE.sub.1) Floquet modes of a bricked sub-wavelength periodic waveguide, for different values of the longitudinal shift (d.sub.Z), in accordance with a preferred embodiment of the invention.

[0090] FIG. 14.- Shows a graph showing the performance (insertion losses and unbalance) of the 3 dB/90° power divider made with bricked sub-wavelength periodic waveguides, in accordance with a preferred embodiment of the invention.

[0091] FIG. 15.- Shows a multi-mode interference coupler based on bricked sub-wavelength periodic waveguides operating as polarization splitter, in accordance with a preferred embodiment of the invention.

PREFERABLE EMBODIMENT OF THE INVENTION

[0092] Next is described, with the aid of FIGS. 1 to 15, a preferred embodiment of the present invention.

[0093] FIG. 6 shows in schematic form a perspective view of a preferred realization of a bricked sub-wavelength periodic waveguide (600), preferably single-mode, that allows keeping all the control properties that conventional SWG waveguides (200) have (control of the effective index, of their dispersion, and of their birefringence), as that shown in FIG. 2, but operating with periods (Λ.sub.z) in the propagation direction that may be larger, and therefore, more feasible to manufacture. FIG. 6 shows the main geometrical parameters of the periodic waveguide (600) object of the invention.

[0094] The bricked sub-wavelength periodic waveguide (600) comprises a substrate (603), on which are arranged a series of blocks (601, 602) periodically distributed in a direction perpendicular to that of the propagation of the wave entering through the periodic waveguide (600). This transverse direction is represented as x direction in FIG. 6.

[0095] The bricked sub-wavelength periodic waveguide (600) is formed by a structure that features two types of periodicities, one in the transverse direction (x) and another one in the longitudinal (z) or propagation direction.

[0096] The periodicity in the transverse direction, indicated as ‘Λ.sub.x’ in FIG. 6, is obtained by combining blocks (601, 602) of core material having the same length ‘az’, but different width, ‘a.sub.x’ and ‘b.sub.x’ , first blocks (601) of width ‘a.sub.x’ and second blocks (602) of width ‘bx’.

[0097] The blocks (601 and 602) can have a relative shift between them in longitudinal direction ‘d.sub.Z’, which is what gives them different properties from those of conventional SWG waveguides (200) with relative shift between them equal to zero (d.sub.z=0).

[0098] The periodicity in the propagation direction ‘Λ.sub.z’ is achieved by alternating blocks (601, 602) of length ‘a.sub.z’ with gaps (604) of cover material of length ‘b.sub.z’. The sections of the blocks (601, 602) of core material of the periodic waveguide (600) have a width ‘W’ and a height ‘H’ and are supported on the support material or substrate (603) acting as an insulator.

[0099] The period in longitudinal direction ‘Λ.sub.z’ must fulfill the condition of not being in Bragg, that is to say, Λ.sub.z< λ/(2•n.sub.eff). Since there are two periods (Λ.sub.z and Λ.sub.x) two duty cycles are usually defined.

[0100] The first DC.sub.Z for defining the ratio of each block (601, 602) of silicon ‘a.sub.z’ in relation to the longitudinal period Λ.sub.z. The second DC.sub.x for defining the ratio of each block (601, 602) of silicon that is not shifted ‘a.sub.x’ in relation to the transverse period Λ.sub.x.

[0101] The particular values of all geometrical parameters are defined prior to the manufacturing of the periodic waveguide (600) by numerical simulations as described above.

[0102] In particular, the periodic waveguide (600) is preferably modeled as an equivalent guide with a core whose refractive index is a diagonal tensor (ñ) in accordance with the following expression:

[00001]$\tilde{n}=\left[\begin{array}{ccc}{\tilde{n}}_{xx}\left(d_z\right)& 0& 0\\ 0& {\tilde{n}}_{yy}& 0\\ 0& 0& {\tilde{n}}_{zz}\left(d_z\right)\end{array}\right]$

where:

[00002]${\tilde{n}}_{xx}\left(d_z\right)=\frac{1}{2}\left(n_{xx}+\sqrt{n_{xx}\cdot n_{zz}}\right)+\frac{1}{2}\left(n{}_{xx}-\sqrt{n_{xx}\cdot n_{zz}}\right)\cdot \cos \left(2\pi \frac{d_z}{{\Lambda }_z}\right)$

[00003]${\tilde{n}}_{yy}=n_{yy}$

[00004]${\tilde{n}}_{zz}\left(d_z\right)=\frac{n_{xx}\cdot n_{zz}}{{\tilde{n}}_{xx}\left(d_z\right)}$

[n.sub.xx, n.sub.yy, n.sub.zz] being the components of a diagonal tensor (n) of the equivalent homogeneous anisotropic medium of a conventional SWG structure (200), that is to say. without relative shift of blocks in longitudinal direction (d.sub.Z=0). This modeling can either provide a final shift value (d.sub.z), or serve as a first approximation, further refined in a second computational step by means of a full simulation of the structure (that is to say, without approximations of SWG structures as homogeneous media).

[0103] Alternatively, an alternative realization of the invention, the period ‘Λ.sub.z’ fulfills that Λ.sub.z ≥ λ/(2•n.sub.eff), where λ is the wavelength of the wave that propagates through the periodic waveguide (600) and neff is the effective index of the mode. Therefore, the periodic waveguide (600) would operate in a regime other than sub-wavelength, that is to say, operating in radiation mode or distributed reflector mode.

[0104] FIG. 7 schematically shows, but with a top view now, a preferred embodiment of a bricked sub-wavelength periodic waveguide (600), preferably single-mode.

[0105] To illustrate the potentiality of the invention, in FIG. 8 there is first shown how the effective index of the fundamental Floquet mode with TE polarization of a conventional SWG waveguide (200) is modified when the period Λ.sub.z is increased. In said preferred embodiment, the following materials have been used: the blocks (601, 602) of silicon core material, the substrate (603) of silicon dioxide, and the cover material (604), positioned between the blocks (601, 602), of silicon dioxide. The refractive indices at the free-space wavelength of 1.55 .Math.m are: n.sub.Si=3.476 and n.sub.Si02=1.444. The width W and thickness H were 3.3 .Math.m and 0.22 .Math.m, respectively.

[0106] As it can be seen in FIG. 8, upon increasing the size of the period, the curves of effective index shift towards larger effective indices and at the same time increase their negative slope.

[0107] In FIG. 9, there is demonstrated how the introduction of some shift ‘d.sub.z’ to the case of large Λ.sub.z periods allows to recompose the initial situation that was present with small Λ.sub.z periods, that is to say, the effective index of the Floquet mode TE.sub.0 decreases again in value and its dependence on the wavelength becomes flatter again.

[0108] In FIG. 10, on the other hand, there is shown how the effective index of the Floquet mode TM.sub.0 varies for various values of the shift ‘d.sub.z’. It can be seen that now the effective index of the TM.sub.0 mode is hardly affected.

[0109] In FIG. 11 there is shown a preferred embodiment of a modal adapter (1100) corresponding to the second aspect of the invention. The objective of the modal adapter (1100) or transition is to minimize the insertion losses between conventional waveguides (100) and periodic waveguides (600) of bricked aspect, that form part of a device making use of the same. The modal adapters (1100) must function correctly for the two TE and TM polarizations. In FIG. 6 there is represented the blocks (601, 602) in two different colors, for better understanding of the figure, but it should be noted that they are blocks (601, 602) of the same material. The same is true for the blocks (601, 602) depicted in FIGS. 12 and 15.

[0110] The modal adapter (1100) comprises two zones. A first zone (1101), for converting a conventional waveguide (100) of a certain width into another SWG waveguide (200) of the same width and with a period in longitudinal direction equal to the desired end period ‘Λ.sub.z’. For this purpose, the central bridge (1103) between the bars (201) of core material progressively decreases in width until it disappears. A second zone (1102), serves to convert the SWG waveguide (200) resulting from the first zone into the periodic waveguide (600) of desired bricked appearance.

[0111] In the second zone (1102), the shift ‘d.sub.z’ is varied from an initial value equal to zero to the desired final value. In the second zone (1102), as the shift ‘d.sub.z’ is increased, the width of the guide is also gradually increased until achieving the desired width value. The reason for making in the first zone (1102) only the change from conventional homogeneous waveguide (100) to an SWG waveguide (200) of the same width, and not including in the first zone the change also between desired widths, is because the conventional waveguide (100) could enter into the Bragg zone in the first zone.

[0112] If the increase in width is done at the same time as the shift ‘d.sub.Z’, we avoid this danger because as we move the Bragg away the width can be increased. It is to be noted that the specific geometry of the modal adapter (1100) can be varied as long as a progressive, smooth modal transition is guaranteed and entering in Bragg is avoided, as this would greatly increase the reflection losses.

[0113] In FIG. 12 there is shown a preferred embodiment of a 3 dB/90° power divider (1200) corresponding to the third aspect of the invention. It comprises two input guides (1201 and 1202) and two output guides (1203 and 1204), all of them conventional waveguides (100), that are connected to a multimode interference device (1206) through respective modal adapters (1100), such as those in FIG. 11. The modal adapters (1100) comprise a wide guide of the bricked sub-wavelength periodic waveguide (600) type.

[0114] Arranged between both modal adapters (1100), output and input ones, the modal interference device (1206) comprising a central periodic waveguide (600) with width W.sub.MMI and length L.sub.MMI is arranged. The modal adapters (1100), which are arranged between the input waveguides (1201 and 1202) and the periodic waveguide (600), and between this one and the output waveguides (1203 and 1024), are as described in the second aspect of invention, and transform the field profiles of the input/output waveguides (1201, 1202, 1203, 1204) to the field profiles of the periodic waveguide (600) of the MMI.

[0115] Compared to a 2x2 MMI realized exclusively with conventional waveguides (100), the described power divider (1200) achieves a smaller and more compact size and to considerably increase the bandwidth. Compared to an MMI realized with conventional SWG waveguides (200), the power divider (1200) achieves the same performance characteristics (insertion losses, unbalance and phase error over a large bandwidth) but with a considerably larger minimum feature size (MFS), on the order of 50% larger

[0116] By first fixing the thickness of the blocks (601, 602) of silicon core material at H= 220 nm, the width (W.sub.a) and spacing (W.sub.s) of the periodic waveguides (600) of access to the central part of the power divider (1200), that is to say, to the MMI (1206), are determined by photonic simulation. It was decided to choose W.sub.a= 1200 nm and W.sub.s = 800 nm. Next, a first width of the central periodic waveguide (600) (W.sub.MMI) of the MMI is chosen, approximately equal to two times the sum of the widths of the access periodic waveguides (1205) to the central access part (W.sub.a) and the separation distance between them (W.sub.s), that is to say W.sub.MMI = 2(W.sub.a + W.sub.s).

[0117] The next step is to determine, making use of photonic simulations, the period (Λ.sub.z) and shift (d.sub.Z) that maximize the MFS and at the same time achieve a beat length of the first two modes of the MMI (1206) as flat as possible in the range of wavelengths of interest. For a 50 % duty cycle (a.sub.z=b.sub.z), in FIG. 13 there is shown an example of how the beat length of the first two modes (the TE.sub.0 and TE.sub.1) varies with wavelength for several values of shift ‘d.sub.z’ and with a longitudinal period ‘Λ.sub.z = 250 nm’.

[0118] The transverse period ‘Λ.sub.x’ was chosen for simplicity equal to the longitudinal ‘Λz’. It is to be noted that the case of zero shift (d.sub.Z = 0) corresponds to the conventional SWG waveguide case (200). As it can be seen from the curves, the zero-shift case (d.sub.Z = 0) features a poor behavior in the range of smaller wavelengths, as a consequence of being very close to the Bragg.

[0119] In order to achieve a flat behavior in wavelength for the zero-shift case, it is necessary to use significantly smaller longitudinal periods (Λ.sub.Z = 190 nm′), as also shown in FIG. 13. In order to use larger periods such as the indicated one of 250 nm, it is necessary to progressively increase the shift ‘d.sub.z’. That will achieve the flattening of the curves and select that combination of values that gives the desired result in the range of wavelengths of interest.

[0120] Once the longitudinal period ‘Λ.sub.z’ and shift ‘d.sub.z’ with which the power divider (1200) will operate have been set, the rest of the parameters can be determined by successive photonic simulations, as well as making small readjustments to those already preset.

[0121] FIG. 14 shows the response in wavelength that is obtained in simulation of the preferred realization of the power divider (1200) 3 dB/90°, corresponding to the third aspect of the invention. Specifically, two figures of merit are represented, the insertion losses, defined as the quotient between the power that appears in the output guides (1203 and 1204) in the fundamental mode TE.sub.0, with respect to the power that enters the input guide (1201); and the unbalance, defined as the quotient between the powers that appear in the output guides (1203 and 1204). As it can be seen in said figure, the power divider (1200) designed achieves insertion losses and an unbalance lower than 1 dB in a bandwidth close to the 400 nm.

[0122] In FIG. 15 there is shows a preferred embodiment of a polarization splitter (1500) corresponding to the fourth aspect of the invention. For this application it is entered by an input guide (1501) with the fundamental modes of the two polarizations TE.sub.0 and TM.sub.0. The polarization splitter (1500) is designed to split both polarizations and cause the appearance of the TE.sub.0 polarization in a first output waveguide (1502) and the TM.sub.0 polarization in a second output waveguide (1503), with the minimum possible losses and maximizing the operating bandwidth.

[0123] For this application the periodic waveguide (600) is designed by means of optimization by photonic simulation so that the beat length of the TM mode (L.sub.πTM) is an integer number of times larger than the beat length of the TE mode (L.sub.πTE), preferably twice as large. With the aim of optimizing the focusing of the self-images of the TE and TM modes in the first output waveguide (1502) and the second output waveguide (1503) respectively, the total length of the multimode interference coupler is three times greater than L.sub.πTM and six times greater than L.sub.πTE. Between the input waveguide (1501) and the periodic waveguide (600), modal adapters (1100) should be used to facilitate the transition.

[0124] Preferred embodiments of the third and fourth aspects of the invention described above make use of an MMI (1206, 1504) in a 2x2 configuration. However, other configurations are possible, such as 1x2, 1x4, 2x3, 3x3 or 2x4, all of them featuring in the central area a sub-wavelength periodic waveguide (600) of bricked aspect. The dimensions in each case will depend on the application for which they are intended

[0125] It is to be noted that the preferred embodiments of the device, both the periodic waveguide (600) of bricked aspect, first object of invention and of the associated systems making use thereof (power divider (1200) 3 dB/90° and polarization splitter (1500) based on said periodic waveguide (600)) are preferably implemented in silicon on insulator, SOI, to thus benefit from the high contrast of index of SOI.

[0126] However, particular embodiments could be implemented on other different photonic platforms. That is to say, all the waveguides used in the various embodiments, be it conventional waveguides (100) or periodic waveguides (600) are preferably realized by means of core of silicon, deposited on an insulating layer such as, for example, silicon dioxide. The cover material (604) may vary for different embodiments of the invention, some of the possibilities being silicon dioxide, polymers or air, without this list limiting the use of other possible options.

[0127] Regarding the manufacturing of the proposed devices, it is to be noted that the sub-wavelength periodic waveguides (600) of bricked aspect, regardless of the shift ‘d.sub.Z’, do not increase the difficulty or the number of steps with respect to the manufacturing of conventional waveguides (100). That is to say, all the structures used by the power divider (1200) 3 dB/90° and the polarization splitter (1500) objects of the invention can be manufactured by means of a single full-depth exposure step of any conventional microelectronics etching technique, such as, for example, by means of electron beam exposure (e-beam) or deep-UV exposure.

[0128] In view of this description and figures, the person skilled in the art will understand that the invention has been described according to some preferred embodiments thereof, but that multiple variations may be introduced in said preferred embodiments, without departing from the object of the invention as it has been claimed.