Patent Description:
It is desirable to improve known light polarisation converters.

Examples described herein relate to a light polarisation converter for a PIC.

A PIC may be constructed from basic building blocks intended for the construction of the PIC. The basic building blocks include various components, each having a particular function. An example of a basic building block is a waveguide structure. Basic building blocks typically have a particular effect on light incident thereon. The examples described herein relate to a light polarisation converter that can be used as a basic building block for a PIC.

In examples described herein and in accordance with the accompanying claims, a waveguide has: a first waveguide portion offset from a second waveguide portion along two orthogonal axes, with a first thickness of the first waveguide portion different to a second thickness of the first waveguide portion. The combination of these features, in examples, gives a more efficient light polarisation converter than known converters. This could be considered an increased polarisation conversion power per unit length. With such improved efficiency, a footprint (surface area occupied) of the converter on a PIC, a thickness and/or a length may be less than known light polarisation converters. For example, the length of the light polarisation converter is less than <NUM> micrometres and, for example, with a > <NUM>% polarisation conversion efficiency.

This combination of features also gives a designer of a PIC more design options and freedom to obtain a desired polarisation conversion from a given input light to a desired output light. By differently setting i) an extent of offset between the first and second surfaces, relative to ii) a change of thickness of the first waveguide portion, a designer can set and customise the polarisation conversion characteristics of the converter for a given purpose. Indeed, as will be appreciated in due course, further parameters of the converter can also be tuned, such as the shape and size of a region (not part of the waveguide) between the first and second layers.

Compared with known converters, more control of the angle of light propagation through the polarisation converter (e.g. to increase the rate of conversion between desired polarisation modes) and the birefringence between two hybrid modes in the converter (e.g. to increase birefringence and in turn shorten the length of the converter that is required) can be obtained by setting i) and/ or ii) appropriately.

The light polarisation converter can have greater tolerance to imperfections during fabrication, compared with known converters. This greater tolerance can facilitate a light polarisation converter with an increased operating bandwidth for polarisation conversion compared with known polarisation converters. This is useful in applications where multiple wavelengths of light are used, such as Wavelength division multiplexed (WDM) optical communication systems and light detection and ranging (LiDAR) systems. Further, the extra design freedom described herein can mean that a given performance can be obtained by a so-called single-section polarisation converter with a smaller footprint than known so-called double-section or multi-section light polarisation converters (with two or more polarisation converters respectively).

Examples will now be described in detail, for which it is useful first to elaborate on the function of a polarisation converter. A polarisation converter is a component for an optical system (such as a PIC) which converts light between different polarisations. A suitably configured light polarisation converter can convert between a first linear polarisation of light and a second linear polarisation of light of a different orientation from the first linear polarisation (e.g. to convert horizontally polarised light into vertically polarised light and vice versa). Or in another example, a suitably configured light polarisation converter can convert between linearly polarised light and circular or elliptical polarised light. A light polarisation converter may also be referred to as a light polarisation rotator or a birefringent rotator.

<FIG> illustrates schematically a side cross-section of a light polarisation converter <NUM> of first examples. The light polarisation converter <NUM> is for a PIC. The light polarisation converter <NUM> comprises a first layer <NUM> comprising a first surface S102 and a second surface S104. The second surface S104 is offset from the first surface S102 along a first axis <NUM> and a second axis <NUM>. The first axis <NUM> is perpendicular to the first surface S102, and the second axis <NUM> parallel to the first surface S102. The first axis <NUM> and the second axis <NUM> are each perpendicular each other and in some examples perpendicular to a light propagation axis LPA of the waveguide <NUM>. The left- and right-most sides of the first layer <NUM> are illustrated with dashed lines, indicating that the layer may extend laterally beyond the illustration (e.g. as part of a PIC). The first layer <NUM> can be considered to be a substrate, but in other examples is envisaged as a separate layer on which the so-called first layer is provided or formed, possibly with one or more intermediate layers between the substrate and the first layer.

The light polarisation converter <NUM> comprises a second layer <NUM> and a waveguide <NUM>. The waveguide <NUM> is between and in contact with each of the first layer <NUM> and the second layer <NUM>. The waveguide <NUM> comprises: a first waveguide portion 104A in contact with the first surface S102; and a second waveguide portion 104B in contact with the second surface S104. Thus the waveguide <NUM> is configured with the second waveguide portion 104B offset from the first waveguide portion 104A. A first thickness W102 of the first waveguide portion 104A is different to a second thickness W104 of the first waveguide portion <NUM>. For example the first thickness is greater than the second thickness. The first thickness W102 and the second thickness W104 are parallel each other, and are perpendicular to the first surface S102 and perpendicular the light propagation axis (LPA). Each such thickness can be considered a height.

The first waveguide portion can be considered to be tapered, with the different thicknesses, as viewed in <FIG>. The taper is such that there is a decrease in thickness of the waveguide from one point on the second axis <NUM> to a second point on the second axis <NUM>. The taper is for example a linear taper, such that the thickness decreases linearly from a larger thickness, such as the first thickness, to a smaller thickness such as the second thickness. The first thickness is e.g. a maximum thickness and the second thickness is e.g. a minimum thickness. The first waveguide portion may therefore decrease in thickness outwards.

With the first waveguide portion having different thicknesses, an orientation of the first surface can be set in accordance with desired polarisation conversion properties. And as a result of the taper, a third surface S106 of the waveguide <NUM> can be considered to tilt or slope, for example by an internal (relative to the waveguide) angle α (illustrated in <FIG>) taken relative to the first surface S102 of the waveguide <NUM>. Hence with the third surface S106 being angled in this way, differently from the first surface S102, the third surface is for example non-parallel to the first S102 and second S104 surface.

Related to this, and with the third surface angled as described above, the first portion 104A of the waveguide <NUM> contacts a first surface S102 of the first layer <NUM> and the first waveguide portion 104A of the waveguide <NUM> contacts a first surface S110 of the second layer <NUM>. Thus, the first waveguide portion of the waveguide contacts a larger surface area of the first surface S102 of the first layer than a surface area of the first surface S110 of the second layer <NUM>; in alternative examples the opposite is true.

With the third surface angled in this way, the third surface S106 is for example at least partly recessed from a first plane A100 substantially coplanar (e.g. in the same plane within acceptable tolerances) with a surface S111 of the first layer <NUM> and a second surface S112 of the second layer <NUM>. The first plane A100 is for example perpendicular the second axis <NUM> and corresponds with a side of the polarisation converter.

A distance by which the first surface of the waveguide is recessed from the first plane is perpendicular the thickness and may depend on a duration of removing waveguide material, e.g. by a so-called under-etching process.

A fourth surface S108 of the waveguide is in contact with the first layer and is at an angle equal to or greater than <NUM> degrees, and less than <NUM> degrees, relative to the first surface S102, the angle being taken internal to the waveguide. The fourth surface S108 can therefore be considered sloped relative to the first surface S102 and/or to the second surface S104. One surface sloped relative to another surface means that there is a non-zero angle between the two surfaces in question. As such, reference can be made to one such surface being at a particular angle relative to the other in the context of one surface being sloped relative to another. In such contexts, reference can also be made to a surface being tilted relative to the other. The terms "tilt", "angle" and "slope" are used interchangeably herein to refer to the angle of an entity relative to another entity or relative to a given axis.

The fourth surface S108 is between the first surface S102 and the second surface S104, meaning, for example, that the fourth surface S108 is interposed between the first surface S102 and the second surface S104, with a side of one surface adjoining a side of another surface. The fourth surface is for example immediately adjacent to each of the first surface S102 and the second surface S104 and can be considered to connect the first surface and the second surface. Thus, the first S102, second S104 and fourth S108 surfaces together can in examples be considered together to constitute the bottom or underside surface of the waveguide <NUM>. In some examples, the second surface S104 is offset from the first surface S102 along at least one of the first axis <NUM> or the second axis <NUM> by an amount greater than an extent of the first surface taken along at least one of the first axis <NUM> or the second axis <NUM>. The offset along at least one of the first axis <NUM> or the second axis is non-zero but less than a maximum thickness (along the first axis <NUM> or the second axis respectively) of the first waveguide portion; but in other examples the first axis offset is equal to or greater than the maximum thickness of the first waveguide portion and/or the second axis offset is equal to or greater than the maximum thickness of the first waveguide portion.

An offset in a direction parallel to an axis is relative to a position on that axis where the related entity in question lies. For example, in <FIG>, a side of the first surface S102 corresponds with a position on the first axis <NUM> and it will be appreciated that a zero offset of the second surface from the first surface S102 along the first axis <NUM> would mean that each of the first S102 and second S104 surfaces are co-planar with each other and correspond with the same position on the first axis <NUM>. And further, in examples such as those of <FIG>, an offset along the second axis <NUM> is large enough such that the second surface S104 does not overlap the first surface S102.

With the first surface S102 and the second surface S104 offset as explained above, with appropriate amounts of each offset, and with the different thicknesses of the first waveguide portion, the waveguide <NUM> can be designed to convert polarisation of light as desired.

The first surface S102 and an opposing surface S103 of the first layer are separated by a first distance W105 and the second surface S104 and the opposing surface S103 of the first layer are separated by a second distance W107, and the second distance is greater than the first distance. In other examples, the first distance is either the same or greater than the second distance. The first distance and the second distance can be considered a height of the bottom of the first portion of the waveguide and the bottom of the second portion of the waveguide respectively, and/or the first distance and the second distance can be considered as thicknesses of the first layer parallel to the first axis at the first surface and the second surface respectively.

As the skilled person will appreciate, particular optical modes of light propagate through the waveguide <NUM> depending on the desired function and design of the light polarisation converter <NUM>. The direction in which the optical modes propagate within the waveguide <NUM> is the light propagation axis LPA as referred to herein. The light propagation axis LPA is parallel to the Poynting vector of light propagating in the waveguide and the negative vector of the Poynting vector. In other words, the light propagation axis LPA is parallel to the general direction in which the energy of the optical mode travels through the waveguide <NUM> and is not necessarily, for example, the direction defined by the angle of incidence at a boundary of the waveguide <NUM>.

Again, as the skilled person will appreciate, the waveguide <NUM> is for guiding light. In use, light propagates within the waveguide <NUM> and is confined within the waveguide, for example in two directions, due to reflection at the boundaries of the waveguide <NUM>. The waveguide layer <NUM> has a refractive index higher than the refractive index of material in contact with the waveguide <NUM> at the boundaries at which confinement of light is desired. For example, due to this refractive index difference at the boundaries at which confinement of light is desired, total internal reflection takes place when the angle of incidence at these boundaries of the waveguide <NUM> is greater than the critical angle. For a particular optical mode to propagate in the waveguide <NUM>, it is required that the light reflected at the boundaries of the waveguide <NUM> is to fulfil the conditions for constructive interference of that particular optical mode, as will be appreciated by the skilled person.

In some examples, the waveguide <NUM> comprises a material which has a higher refractive index than the material of the first layer and the second layer. For example, the waveguide <NUM> comprises indium gallium arsenide phosphide (InGaAsP). In some examples, the waveguide <NUM> comprises (Al)InGaAs(P). The elements indicated in the parentheses are interchangeable and the composition of the different elements is selected depending on the desired function. For example, the composition of Ga and As in InGaAs can be selected according to the desired bandgap. In some examples, the waveguide <NUM> is a layer of (Al)InGaAs(P). In other examples, the waveguide <NUM> comprises a plurality of sub-layers. In some such examples, the waveguide <NUM> comprises a (Al)InGaAs(P)/(Al)InGaAs(P) multiple quantum well structure in contact with the first layer <NUM>. In some examples, the sub-layers are between <NUM> and <NUM> nanometres thick. The sub-layer stack of the waveguide <NUM> has a band gap selected in accordance with the desired application of the light polarisation converter <NUM>. The bandgap and therefore the refractive index of the InGaAsP, for example, can be tuned.

In some examples, the polarisation conversion efficiency of the polarisation converter is set by fabricating the light polarisation converter with a desired ratio of the volume of the first portion 104A of the waveguide to the volume of the second portion 104B of the waveguide. This ratio is, e.g., set by the ratio of the extent of the first surface S102 parallel to the second axis <NUM> to the extent of the second surface S104 parallel to the second axis <NUM>. Setting the ratio of the volume of the first portion 104A of the waveguide to the volume of the second portion 104B of the waveguide, for example, changes the ratio of the energy that propagates through the first portion 104A of the waveguide to the energy that propagates through the second portion 104B of the waveguide.

<FIG> illustrates schematically a side cross-section taken on a plane perpendicular the LPA, of a light polarisation converter <NUM> of further examples. Except where otherwise described below, the features of these examples are in common with those described for <FIG>, and so are not re-described here for conciseness. Where a feature in relation to <FIG> corresponds with a feature described using <FIG>, a reference numeral is used which is <NUM> greater than the corresponding reference numeral used for <FIG> (e.g. <NUM> in <FIG> is <NUM> in <FIG>); corresponding descriptions for such features apply here also.

The first surface S202 is angled relative to the third surface S206 by the internal angle α of <NUM> to <NUM> degrees, for example, and depending on a plane of a crystalline material, <NUM> to <NUM> degrees, such as approximately (within acceptable manufacturing tolerances) <NUM> degrees, or <NUM> to <NUM> degrees, such as approximately (within acceptable manufacturing tolerances) <NUM> degrees or <NUM> degrees, <NUM> to <NUM>, <NUM> to <NUM> or <NUM> to <NUM> degrees. In other examples (not shown), the internal angle α is greater than <NUM> degrees.

Similarly, as described for <FIG>, the fourth surface S208 is also sloped relative to the first surface S202 and/or to the second surface S204. The third surface S206 is, substantially parallel to the fourth surface S208 (e.g. parallel within acceptable manufacturing tolerances) with e.g. the third and fourth surfaces each at <NUM> degrees to the first surface. In other examples the third surface and the fourth surface are not parallel to each other , e.g. the third surface is at <NUM> degrees to the first surface and the fourth surface is at <NUM> degrees to the first surface (and thus <NUM> degrees to the third surface).

The material of which the waveguide is formed is for example a crystalline material, with the angle α between the first surface S202 and the third surface S206 corresponding with at least one of a {<NUM>-<NUM>}, {<NUM>} or {<NUM>} plane of the crystalline material. The {XYZ} notation is in accordance with the Miller index system for indicating a plane or family of planes in a crystal, as will be known to the skilled person. Such a plane may also be referred to as a crystal plane. As will be explained later, by using an appropriate manufacturing method, e.g. with a particular etchant selective for a particular crystal plane of the waveguide material, the angle α between the third surface S206 and the first surface S202 can be simply obtained.

Such an etching approach is selective so as to etch the material of the waveguide without etching (or notably more slowly etching) the material of the first layer <NUM> and second layer <NUM>. Hence, to form the angle α between the first surface S202 and the third surface S206, waveguide material is removed during the etching from between the first layer <NUM> and the second layer <NUM>, e.g. from under the second layer <NUM>. In examples there is therefore a region <NUM> between the first layer <NUM> and second layer <NUM> where the waveguide <NUM> is not present. In other words the waveguide <NUM> is absent from the region <NUM>, or the refractive index of the region <NUM> is sufficiently different from the refractive index of the waveguide <NUM> such that light is confined within the waveguide.

In examples, such as those of <FIG>, the waveguide <NUM> has a third waveguide portion 204C (otherwise referred to herein as an intermediate portion) in contact with the fourth surface S208 and between the first waveguide portion 204A and the second waveguide portion 204B. The first layer <NUM> with surfaces offset as described, and the fourth surface S208 sloped with a non-<NUM> degrees angle relative to the first surface, is at least partly formed before the waveguide <NUM> is formed on top of the first layer <NUM>. The sloped fourth surface S208 results in a corresponding slope of the third waveguide portion. Thus, the first waveguide portion 204A, the second waveguide portion 204B and the third waveguide portion 204C can be considered together to constitute the waveguide <NUM>.

<FIG> illustrates schematically a side cross-section taken on a plane perpendicular the LPA, of a light polarisation converter <NUM> according to further examples. Except where otherwise described below, the features of these examples are in common with those described for <FIG>, and so are not re-described here for conciseness. Where a feature in relation to <FIG> corresponds with a feature described using <FIG>, a reference numeral is used which is <NUM> greater than the corresponding reference numeral used for <FIG> (e.g. <NUM> in <FIG> is <NUM> in <FIG>); corresponding descriptions for such features apply here also.

In examples, such as those of <FIG>, a first portion 302A of the first layer <NUM> comprises the first surface S302, and a second portion 302B of the first layer <NUM> comprises the second surface S304. The first portion of the first layer <NUM> comprises (e.g. is formed of) a different material from a material of the second portion 302B of the first layer <NUM>. The first and second portions are illustrated in <FIG> using horizontal dashed lines, as also is a third portion 302C of the first layer between and in contact with the first and second portions 302A, 302B of the first layer. Each of the first, second and third portions can be considered sub-layers of the first layer with the third portion 302C formed of a different material from at least one of the first portion 302A or the second portion 302B.

A different material, relative to another material, is, for example, at least one of a different crystalline structure, a different alloy, a different isomer, a different isotope, a mixture of different proportions, or having different material properties, such as refractive index, different susceptibility to etching by a particular etchant, different crystalline structures, different crystalline plane orientations, and/or electrical conductivity, though other examples of a different material are envisaged. A different material relative to another material is therefore not the same material, even though each material may comprise the same chemical elements as each other without either material having more elements than the other. Two different materials may however have different proportions of the same elements relative to each other (e.g. with one material having more dopant than another). At least one of the second portion of the first layer or the third portion of the first layer is, for example, an etch stop to aid the formation of the first layer.

In some examples, such as those of <FIG>, at least one surface of the second layer in contact with the waveguide is not parallel to an opposing surface of the first layer also in contact with the waveguide. For example, a surface S309 of the second layer <NUM> is not parallel to the fourth surface S308 of the first layer <NUM>.

In some examples, the light polarisation converter <NUM> comprises a third layer <NUM>. The third layer is on and in contact with the second layer <NUM>. The third layer is, for example, an electrode, an insulator or a dielectric.

Referring now to <FIG>, a function of the waveguide <NUM>, <NUM>, or <NUM> for conversion of the polarisation of light will now be described. <FIG> relates to input light and <FIG> relates to output light. Note that this is in the context of linearly polarised light incident on the light polarisation converter <NUM><NUM> or <NUM>. <FIG> illustrate a transverse electric (TE) polarisation axis <NUM> and a transverse magnetic (TM) polarisation axis <NUM>. The light propagation axis LPA is, in <FIG>, into the page (perpendicular to both the TE polarisation axis <NUM> and the TM polarisation axis <NUM>). With respect to <FIG>, <FIG> or <FIG>, the TM polarisation axis <NUM> is parallel to the first axis <NUM>, <NUM> or <NUM>, and the TE polarisation axis <NUM> is parallel to the second axis <NUM>, <NUM>, or <NUM>.

For linearly polarised light, the direction of the electric field of light propagating as indicated by the symbol LPA can be indicated with respect to the TE polarisation axis <NUM> and the TM polarisation axis <NUM>. The arrow <NUM> indicates linearly polarised light that is TE polarised.

The waveguide <NUM>, <NUM>, <NUM> having a first waveguide portion 104A, 204A, 304A offset from a second waveguide portion 104B, 204B, 304B, and a first thickness W102, W202, W302 of the first waveguide portion different to a second thickness W104, W204, W304 of the first waveguide portion, causes there to be hybrid modes within the waveguide. This arrangement of the waveguide is a "tilted" or sloped boundary condition for the light propagating within the waveguide for the hybrid modes.

The tilted boundary condition causes there to be a first hybrid mode which has an electric field tilted with respect to the TE axis because of the geometry of the waveguide. The first hybrid mode occupies the first waveguide portion, the second waveguide portion, and, in some examples, the third waveguide portion. The terms "tilt", "angle" and "slope" are used interchangeably herein to refer to the angle of the first hybrid mode relative to the TE axis. There is also a second hybrid mode orthogonal to the first hybrid mode. A hybrid mode, as referred to herein, is a mode of light which has an electric field with a non-zero component along the TE polarisation axis and a non-zero component along the TM polarisation axis.

<FIG> show a first hybrid mode <NUM> and a second hybrid mode <NUM>. The first and second hybrid modes <NUM>, <NUM> illustrate an example of hybrid modes that may exist within the waveguide when light is propagating therethrough. In this example, the first and second hybrid modes <NUM>, <NUM> arise from light with TE polarisation (with the electric field along the TE polarisation axis <NUM>), as shown by arrow <NUM>, incident on the light polarisation converter for propagation through the waveguide.

The tilt angle (relative to the TE axis <NUM>) for the first hybrid mode <NUM> is assumed to be <NUM> degrees. Such a tilt angle for the first hybrid mode <NUM> arises as a result of the arrangement of the waveguide, for example. In these examples, the angle with respect to the TE axis <NUM> of the second hybrid mode <NUM> is also <NUM> degrees and the first and second modes <NUM>, <NUM> have electric fields with equal magnitude. Those skilled in the art will appreciate that the first and second modes <NUM>, <NUM>, with the tilt angle of <NUM> degrees and the phase relationship shown in <FIG>, have equal and opposite components along the TM polarisation axis <NUM> and in combination correspond to TE polarised light.

Furthermore, the described arrangement of the waveguide has a different propagation constant for the first and second hybrid modes <NUM>, <NUM>. The arrangement results in birefringence such that the first and second hybrid modes <NUM>, <NUM> experience different effective refractive indices to one another when propagating within the waveguide. This means that the phase difference between the first and second hybrid modes <NUM>, <NUM> changes as the first and second hybrid modes <NUM>, <NUM> propagate. In other words, the phases of the first and second modes <NUM>, <NUM> evolve differently as the first and second modes <NUM>, <NUM> propagate within the waveguide. The presence of the hybrid modes and their different propagation constants means that the arrangement of the waveguide can be used to convert the polarisation of light input into the light polarisation converter. The way in which polarisation is converted is described in further detail below.

<FIG> illustrates schematically a second side cross-section taken on a plane parallel the LPA, of a light polarisation converter <NUM> according to examples similar to those examples described above with <FIG>. Except where otherwise described below, the features of the examples described using <FIG> are in common with those described for <FIG>, and so are not re-described here for conciseness. Such features are referred to using reference numerals <NUM> greater than those used for <FIG>. Corresponding descriptions for such features apply here also.

The waveguide <NUM> has a length L502 as shown in <FIG>. The light propagation axis is indicated by arrow LPA. The light polarisation converter is for converting between a first polarisation of a given wavelength of light and a second polarisation of the given wavelength of light. The first polarisation and the second polarisation are each, e.g., a linear polarisation, elliptical polarisation or a circular polarisation. In some such examples, a length of the waveguide L502 in the light propagation axis LPA is substantially equal (e.g. equal within acceptable tolerances) to an odd integer multiplied by half of a beat length for the given wavelength of light.

A length L502 of the waveguide <NUM> for the phase of the modes of light propagating therein to be restored is referred to as the beat length. For example, if the first and second modes start their propagation within the waveguide <NUM> in phase, the modes will be back in phase after propagating an integer multiple of the beat length within the waveguide <NUM>. By selecting the waveguide length L502 in the light polarisation converter <NUM> based on the beat length, the relative phase of the modes of light propagating therein can be controlled for light output from the light polarisation converter <NUM>.

As discussed above, the described arrangement of the waveguide <NUM> causes a different propagation constant for the first and second hybrid modes. The described arrangement of the waveguide <NUM> (with portions offset in a direction parallel to the first axis <NUM>), causes there to be birefringence in that the first and second hybrid modes experience a different effective refractive index to one another. The propagation constant of the first hybrid mode in the waveguide <NUM> can be represented by β<NUM> and the propagation constant of the second hybrid mode can be represented by β<NUM>. The difference in these propagation constants can be represented as Δβ = β<NUM> - β<NUM>. Equation <NUM> below shows the beat length Lλ for the waveguide <NUM> for the first and second hybrid modes. Those skilled in the art will appreciate that β represents phase propagation. In Equation (<NUM>) below, λ is the given wavelength and Δn represents the difference in the effective refractive indices of the first and second hybrid modes: Δn = n<NUM> - n<NUM>.

In some examples, the beat length is affected by the thickness of the waveguide and/or the cladding of the waveguide. In some examples, the waveguide is curved, and consequently the light propagation axis is curved, and the beat length is taken along a curve.

An effective refractive index of a waveguide is a dimensionless number that describes how fast light travels through a waveguide and how light attenuates through the waveguide. A refractive index of a material is a dimensionless number that describes a phase velocity of a light wave in the material and how light attenuates through the material. Effective refractive index and refractive index are commonly expressed as a complex number; however, herein only the real component of refractive index is considered. The real component of a refractive index is the speed of light in vacuum divided by the phase velocity of the light wave in the material. In some examples, effective refractive index and/or refractive index is dependent on the wavelength of the light being considered. Herein when a comparison is made between two effective refractive indices or between to two refractive indices, the comparison is between the real components for the same wavelength of light.

In some examples, the light polarisation converter is for rotating the linear polarisation of the given wavelength of light. As described above, in some such examples, the waveguide length is substantially (within acceptable tolerances) equal to an odd integer multiplied by half of the beat length. This is the case in examples in which the tilt angle of the first mode is <NUM> degrees relative to the TE axis. Factors determining the tilt are described further below. In other words, the waveguide length can be <NUM>/<NUM> of the beat length, <NUM>/<NUM> of the beat length, <NUM>/<NUM> of the length and so on, as indicated by Equation <NUM> below. In Equation <NUM>, m represents an odd integer such as <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, etc. <MAT>.

This means that the relative phase of the first and second modes after propagating through the waveguide is shifted by π radians. Those skilled in the art will appreciate that when TE polarised light as indicated by the arrow <NUM> is incident on the waveguide <NUM>, and the first and second modes <NUM>, <NUM> arise at the beginning of the waveguide <NUM>, the first and second modes <NUM>. <NUM> will be in phase with one another. In other words, after propagating through the waveguide <NUM> with a waveguide length of <NUM>/<NUM> the beat length (or <NUM>/<NUM> the beat length, or <NUM>/<NUM> of the beat length, etc.) the first and second modes <NUM>, <NUM> are out of phase with each other by <NUM> degrees.

<FIG> illustrates the TE and TM polarisation axes <NUM>, <NUM> shown in <FIG> relates to examples where linear TE polarised light is incident on the waveguide <NUM> as indicated by <FIG>, and the tilt angle of the first hybrid mode <NUM> relative to the TE axis <NUM> is <NUM> degrees. <FIG> illustrates the first and second modes <NUM>, <NUM> after having propagated through the waveguide <NUM> in the direction indicated by the symbol LPA for an integer multiple of half the beat length. Those skilled in the art will appreciate that the electric field for light oscillates between opposing quadrants of the space indicated by the TE and TM polarisation axes <NUM>, <NUM>. Accordingly, in comparison to the state shown in <FIG>, in <FIG>, the first mode <NUM> has completed an integer multiple of its electric field oscillations, whereas the second mode <NUM> has completed an odd integer multiple of half of its electric field oscillation (to end up in the top left quadrant).

Those skilled in the art will appreciate that the first and second modes <NUM>, <NUM> with the phase relationship shown in <FIG> have equal and opposite components along the TE polarisation axis <NUM>. The first and second modes <NUM>, <NUM> with the phase relationship shown in <FIG> would have TM polarised light as indicated by the arrow <NUM>, if the first and second modes <NUM>, <NUM> exit the waveguide <NUM>, <NUM>, <NUM> with the phase relationship shown in <FIG>. In other words, if the phases of the first and second modes <NUM>, <NUM> no longer evolve differently from the point shown in <FIG>, the result is TM polarised light. It should be noted in the examples of <FIG>, the first and second modes <NUM>, <NUM> have a <NUM> degree angle relative to the TM axis <NUM>.

In these examples, where the first hybrid mode <NUM> has a <NUM> degree angle relative to the TE axis <NUM>, by selecting the waveguide length to be an odd integer multiplied by half of the beat length, linear polarisation of the given wavelength of light can be rotated as described above. For example, a first linear polarisation (TE polarisation in the above examples) can be converted to a second linear polarisation (TM polarisation in the above examples).

The above examples are in the context of the first hybrid mode <NUM> having a <NUM> degree tilt relative to the TE axis <NUM>. In some examples, the arrangement of the first layer <NUM>, <NUM>, <NUM> and the waveguide <NUM>, <NUM>, <NUM> is such that when hybrid modes arise within the waveguide, the first hybrid mode <NUM> (e.g. the hybrid mode substantially aligned with the intermediate waveguide portion <NUM>) does not have a <NUM> degree angle relative to the TE axis <NUM>. Factors influencing the tilt of the first hybrid mode are discussed further below. In such examples, a <NUM> degree rotation of polarisation (e.g. from TE polarisation to TM polarisation) does not take place upon propagating through a length (corresponding with L502) equal to an odd integer multiplied by half of the beat length.

A series of two or more light polarisation converters as described herein (for example, each with a different tilt angle and/or length along their respective LPA) can be used to obtain a desired polarisation conversion. In some examples, for a light polarisation converter (e.g. the light polarisation converter <NUM>, <NUM>, <NUM>), a length (along the LPA and corresponding with L502) of the waveguide is equal to an odd integer multiplied by a quarter of the beat length. A pair of such light polarisation converters in series can be used where the tilt of one or both converters is not <NUM> degrees, or in other examples is <NUM> degrees, in order to obtain a <NUM> degree linear polarisation rotation, as described in the following. A first light polarisation converter (e.g. of <FIG>, <FIG> or <FIG>) of the pair has a length of the waveguide along the LPA axis which achieves <NUM> degree (π/<NUM> radians) phase difference between the first and second hybrid modes. This means that the length (corresponding to L502) can be <NUM>/<NUM> of the beat length, <NUM>/<NUM> of the beat length, <NUM>/<NUM> of the beat length and so on. A second light polarisation converter (e.g. of <FIG>, <FIG>, or <FIG>) of the pair has a length (along the LPA and corresponding with L502) of the waveguide which achieves a <NUM> degree (<NUM>/<NUM>π radians) phase difference between the first and the second hybrid modes. This means that the length of the waveguide in the second light polarisation converter can be <NUM>/<NUM> of the beat length, <NUM>/<NUM> of the beat length, <NUM>/<NUM> of the beat length and so on.

<FIG> is a sketch of the equator plane of the Poincaré sphere. Those skilled in the art will appreciate that all polarisation states can be mapped onto the surface of the so-called Poincaré sphere. Points lying on the equator of the Poincaré sphere represent all angles of linear polarisation. The poles of the Poincaré sphere represent clockwise and anticlockwise circular polarisations. The points corresponding to TE polarisation and TM polarisation can be seen in <FIG>.

Points corresponding to the first and second hybrid modes lie on the equator of the Poincaré sphere. The position of the hybrid modes on the equator depends on the tilt, in other words the angle, of the first hybrid mode relative to the TE axis.

In the case of the first hybrid mode having a <NUM> degree angle relative to the TE axis, the first hybrid mode corresponds to point M1 and the second hybrid mode corresponds to the point M2. An axis crossing M1 and M2 is perpendicular to an axis crossing the TE and TM polarisation points on the equator of the Poincaré sphere. Propagation of the hybrid modes through the waveguide, where their phases evolve differently from one another, corresponds to rotation of a point that represents the polarisation when the hybrid modes recombine, about the axis crossing M1 and M2. A <NUM> degree rotation about an axis crossing M1 and M2 leads to e.g. polarisation conversion from TE polarisation to TM polarisation.

In the case of the first hybrid mode having an acute angle different to <NUM> degrees relative to the TE axis, points corresponding to the first and second hybrid modes are not points M1 and M2. In some examples, the first hybrid mode corresponds to point <NUM> and the second hybrid mode corresponds to point <NUM>. In these examples, a <NUM> degree rotation about an axis crossing points <NUM> and <NUM> does not arrive at the TM polarisation point. As described above, when the tilt angle is different to <NUM> degrees, a <NUM> degree phase difference between the first and second hybrid modes does not provide a <NUM> degree rotation of linear polarisation.

However, a <NUM> degree rotation about the axis crossing points <NUM> and <NUM> arrives at point <NUM>. Point <NUM> is a point on the surface of the Poincaré sphere above the page of <FIG>. In some examples, the first light polarisation converter is used to obtain a polarisation corresponding to point <NUM> on the Poincaré sphere. In these examples, a first light polarisation converter in accordance with examples described herein provides hybrid modes that have polarisations corresponding to points <NUM> and <NUM>. In other words, the first polarisation converter provides a tilt such that the hybrid modes have polarisations corresponding to points <NUM> and <NUM>.

A second polarisation converter in accordance with examples described herein, and in series with the first polarisation converter, provides a tilt in the opposite direction such that the hybrid modes in the second polarisation converter correspond to points <NUM> and <NUM>. This can be achieved by the second polarisation converter having a side cross-section (corresponding to the side cross-section shown in <FIG>) which is the mirror image of the side cross-section (corresponding to the side cross-section shown in <FIG>) of the first polarisation converter.

An axis crossing points <NUM> and <NUM> is a mirror image of the axis crossing points <NUM> and <NUM>, relative to the axis crossing points M1 and M2. Line <NUM> represent a trajectory from the TE point to point <NUM> after a <NUM> degree rotation about the axis crossing points <NUM> and <NUM>. It should be noted that line <NUM> is a straight line projection of the trajectory on the Poincaré sphere which would follow the surface of the Poincaré sphere.

A rotation about the axis crossing points <NUM> and <NUM> including the point <NUM> traces a circle on the surface of the Poincaré sphere which crosses the TM point. A rotation in the opposite direction from point <NUM> and about the axis crossing points <NUM> and <NUM> can be used to arrive at the TM point. The second polarisation converter having a mirrored side-cross section for rotation relative to the Poincaré sphere in the opposite direction to the first polarisation converter. Line <NUM> represents a straight line projection of a trajectory starting from point <NUM>, corresponding to rotation about the axis crossing points <NUM> and <NUM> in the opposite direction to the described <NUM> degree rotation to arrive at point <NUM>. The trajectory <NUM> crosses the TM point after a <NUM> degree rotation about the axis crossing points <NUM> and <NUM>.

In this manner, even in examples where the tilt of the first hybrid mode is not <NUM> degrees, a <NUM> degree rotation of the linear polarisation can be achieved by propagation light through the first light polarisation converter and then the second light polarisation converter.

In some examples, the light polarisation converter is for converting between linear and circular polarisation of the given wavelength of light. In such examples, the waveguide length is substantially (within acceptable tolerances) equal to an odd integer multiplied by a quarter of the beat length. In such examples, the tilt of the first hybrid mode is <NUM> degrees relative to the TE axis <NUM>. The waveguide length according to such examples is represented by Equation <NUM> below. <MAT> The first and second hybrid modes propagating in the waveguide for an odd integer multiple of a quarter of the beat length would result in a phase different of <NUM>/<NUM>π radians (or <NUM> degrees). Those skilled in the art will appreciate that introducing a phase difference of <NUM> degrees about the axis crossing points M1 and M2 is for conversion between linear and circular polarisations. Taking the example of linearly polarised light in the horizontal direction as indicated in <FIG> incident on the waveguide, the light polarisation converter with a waveguide length (e.g. corresponding to L502) according to Equation <NUM> would convert the TE polarised light into circularly polarised light. In examples where circularly polarised light is incident on the light polarisation converter for converting between linear and circular polarisations, the circularly polarised light would be converted into linearly polarised light.

How a light polarisation converter described in examples herein is manufactured will now be described. Broadly, such a method comprises at least partly forming the first layer described earlier, at least partly forming the waveguide described earlier on and in contact with the first layer, and at least partly forming the second layer described earlier on and in contact with the waveguide.

In some examples at least one of the first layer, the waveguide or the second layer feature are formed using a respective precursor structure, such as a precursor layer which is first formed or deposited, then further processed (e.g. by etching) to shape or otherwise produce the desired structure for the polarisation converter being manufactured. Examples are now described using such a precursor.

<FIG> is now referred to describe such a method. A method <NUM> of manufacturing a light polarisation converter comprises at least partly forming <NUM> a first layer using a precursor to the first layer. As explained for earlier examples, the first layer comprises a first surface and a second surface, the second surface is offset from the first surface along a first axis and a second axis, the first axis is perpendicular to the first surface, and the second axis is parallel to the first surface. The method <NUM> further comprises at least partly forming <NUM> a waveguide using a precursor to the waveguide. The waveguide is on the first layer and comprises, as explained previously, a first waveguide portion in contact with the first surface, and a second waveguide portion in contact with the second surface. A first thickness of the first waveguide portion is different to a second thickness of the first waveguide portion. The first thickness and the second thickness are perpendicular to the first surface. The method <NUM> further comprises at least partly forming <NUM> a second layer, using a precursor to the second layer. As for examples described previously, the second layer is on and in contact with the waveguide, the waveguide between the first layer and the second layer.

Such a manufacturing method will now be described in further detail using <FIG> which each illustrate schematically the first side cross-section of a light polarisation converter <NUM> at subsequent stages during a method of manufacture. Except where otherwise described below, features of <FIG> are in common with those described for <FIG>, and so are not re-described here for conciseness. Where a feature in relation to any of <FIG> corresponds with a feature described using <FIG>, a reference numeral is used which is <NUM> greater than the corresponding reference numeral used for <FIG> (e.g. <NUM> in <FIG> is <NUM> in any of <FIG>); corresponding descriptions for such features apply here also.

The method of manufacturing a light polarisation converter comprises at least partly forming a precursor P802 to a first layer <NUM> comprising a precursor PS802 to a first surface S802 (see <FIG>) and a precursor PS804 to the second surface S804 (see <FIG>). The precursor to the second surface is offset from the precursor to the first surface along a first axis <NUM> and a second axis <NUM>, the first axis perpendicular to the precursor to the first surface, and the second axis parallel to the precursor to the first surface. At least partly forming the precursor to the first surface PS802 and the precursor to the second surface PS804, for example, comprises at least partly forming an etch mask <NUM> on the precursor to the first layer (e.g. on the precursor to the second surface PS804, <FIG>); at least partly etching the precursor P802 to the first layer to achieve the described offsets (<FIG>); and removing the etch mask (<FIG>). Instead of etching, lithography or grinding may be used.

Referring to <FIG>, the method comprises at least partly forming the waveguide <NUM> using a precursor P804 to the waveguide. The precursor P804 to the waveguide is formed on and in contact with the precursor P802 to the first layer. The precursor P804 to the waveguide has a precursor P804A to the first waveguide portion in contact with the precursor PS802 to the first surface, and a precursor P804B to the second waveguide portion in contact with the precursor PS804 to the second surface. As shown in <FIG> a precursor P806 to the second layer is at least partly formed on and in contact with the precursor P804 to the waveguide, with the precursor P804 to the waveguide between the precursor P802 to the first layer and the precursor P806 to the second layer. See now <FIG> which shows, compared with <FIG>, removing some of at least one of: the precursor P802 to the first layer, the precursor P804 to the waveguide, or the precursor P806 to the second layer to form the first layer <NUM> and the second layer <NUM>. In these examples some of each of these precursors is removed from one side (for example the right hand side as shown in the figures), e.g. using a downward etch process.

<FIG> shows at least partly forming a protective layer <NUM> on at least part of at least one of the first layer <NUM>, the precursor P804 to the waveguide or the second layer <NUM>. Some of the protective layer is removed to partly expose the layers covered by the protective layer, for example to expose a side of the precursor P804 to the waveguide (see <FIG> - the protective layer is removed from the left hand side of the covered layers, as illustrated).

To at least partly form the waveguide <NUM> from the precursor P804 to the waveguide, a portion of the precursor P804 to the waveguide is then removed from the exposed side, to form the waveguide <NUM> with a sloped third surface. The remaining protective layer therefore protects the non-exposed layers (e.g. the other side of the precursor of the waveguide) from any process which would otherwise remove or damage the covered layer(s) such as the waveguide material. As explained before, the formed waveguide <NUM> has a first thickness W802 of the first waveguide portion 804A different to a second thickness W804 of the first waveguide portion, the first thickness W802 and the second thickness W804 perpendicular to the first surface S802.

The remainder of the protective layer <NUM> is then removed to yield the polarisation converter, though in other examples any remaining protective layer <NUM> may be left in place for the completed polarisation converter.

Removing at least part of one or more of the precursors described above, and removing the protective layer, may be by known techniques such as etching or lithography. In removing a portion of the precursor of the waveguide, a technique selective for a particular crystal plane may be used to obtain the desired angle α between the third surface and the first surface. Such a technique is for example etching using an etchant comprising at least one of HCl, H<NUM>PO<NUM>, H<NUM>SO<NUM>, H<NUM>O<NUM>, or H<NUM>O, or a mixture of such. Other etchants are envisaged. Where an etch mask or the protective layer comprises a masking material, this is for example a dielectric or a silicon mask such as a silicon nitride. In some examples, the angle α is chosen by setting the orientation of the crystalline structure of the waveguide with respect to at least one of the first axis, the second axis or the LPA. In some examples, the angle α is chosen by utilising gravitational effects, e.g. by setting the orientation of the waveguide with respect to the LPA for the etching step of fabrication of the polarisation converter (see the step of <FIG>).

The method of <FIG> may be modified to manufacture the light polarisation converter of, for example, <FIG>. <FIG> are used to illustrate alternative methodology to that illustrated by <FIG>, then a similar methodology to that illustrated with <FIG> can be used. Where a feature of a light polarisation converter in relation to any of <FIG> corresponds with a feature described using <FIG>, a reference numeral is used which is <NUM> greater than the corresponding reference numeral used for <FIG> (e.g. <NUM> in <FIG> is <NUM> in any of <FIG>); corresponding descriptions for such features apply here also.

In <FIG> a precursor P902 to the first layer is formed. The precursor P902 to the first layer <NUM> comprises a first portion 902A, a second portion 902B, and a third portion 902C. Each such portion is a sub-layer. The first portion 902A of the first layer comprises, e.g. is of, a material different to the second portion 902B of the first layer <NUM>. The third portion 902C of the first layer is between and in contact with the first portion 902A and the second portion of the first layer <NUM>. The third portion 902C of the first layer comprises, e.g. is of, a different material to at least one of the first portion 902A or the second portion 902B of the first layer. Then an etch mask <NUM> is at least partly formed on the precursor P902 to the first layer (e.g. on the precursor PS904 to the second surface which is an upper surface of the second portion 902B), as shown in <FIG>. Then, as shown by <FIG>, some of the second portion 902B of the first layer <NUM> which is not covered by the mask is removed to modify the precursor P902 to the first layer, e.g. by etching. In this way the extent of offsets between the first and second surfaces of the waveguide can be determined.

<FIG> relate to further examples of a method of manufacturing a light polarisation converter of examples described herein. <FIG> each illustrate schematically a side cross-section of a light polarisation converter at subsequent stages during manufacture. Features in common with those described for <FIG> are not re-described here for conciseness; such features are referred to with a reference numeral which is <NUM> greater than the corresponding reference numeral used for <FIG> (e.g. <NUM> in <FIG> is <NUM> in any of <FIG>); corresponding descriptions for such features apply here also.

<FIG> corresponds with part of the method described earlier by <FIG>. Therefore, to arrive at the structure shown by <FIG>, a similar method to that described earlier using <FIG> may be used. Subsequent processing of the structure of <FIG> will now be described. In these examples, the sloped third surface of the waveguide is formed before the second layer, compared with the examples of <FIG> where the second layer is formed before the sloped third surface. This approach aids inspection of the third surface during manufacture, as shown by <FIG> (once the protective layer <NUM> is removed), to check that the angle of the slope of the third surface is as required.

Starting with the structure shown by <FIG>, and as shown by <FIG>, a protective layer <NUM> is formed on the precursor P1004 to the waveguide, thus covering an upper surface of the precursor P1004 to the waveguide. The protective layer is for example at least one of a dielectric or an etch mask. As shown by <FIG>, and similar to the method described above with <FIG>, a portion of the precursor to the waveguide is removed thus forming the first waveguide portion with the first thickness W1002 and the second thickness W1004, and hence the sloped third surface S1006. The protective layer is then at least partly removed as shown in <FIG>, to expose at least part of the precursor P1004 to the waveguide. As <FIG> shows, a precursor P1006 to the second layer is formed on, in contact with, and covering the precursor P1004 to the waveguide. Portions of the precursors to each of the first layer, the waveguide and the second layer are then removed (e.g. using a masking and downward etching process) to form the first layer <NUM>, the second layer <NUM> and the waveguide <NUM> of the desired light polarisation converter (see <FIG> which shows portions removed on the right hand side of the precursors).

As the skilled person will appreciate, various techniques may be used to form, deposit, provide or remove portions or layers described here, e.g. using techniques such as: metalorganic vapour-phase epitaxy (MOVPE), surface passivation, photolithography, ion implantation, etching, dry etching, ion etching, wet etching, buffered oxide etching, plasma ashing, thermal treatment, annealing, thermal oxidation, chemical vapor deposition, atomic layer deposition, physical vapor deposition, molecular beam epitaxy (MBE), laser lift-off, electrochemical deposition, electroplating, or chemical-mechanical polishing. In some examples etching techniques are used to remove some not all of a layer, as the skilled person will appreciate.

Note too that the order of individual processing stages of methods described herein is not limiting, and further methods are envisaged within the skilled person's understanding with processing done in a different order than described.

The above examples are to be understood as illustrative examples. Further examples are envisaged, such as a polarisation converter as described previously, also with a first thickness of the second waveguide portion different to a second thickness of the second waveguide portion. Thus, the first thickness of the second waveguide portion is greater than the second thickness of the second waveguide portion. The first thickness of the second waveguide portion and the second thickness of the second waveguide portion are parallel to each other, and are perpendicular to the second surface and perpendicular the LPA. Each such thickness can be considered a height. Similarly to as described for the first waveguide portion earlier, the second waveguide portion can be considered to be tapered, with the different thicknesses. As a result of the taper, a further surface of the waveguide can be considered to tilt or slope, for example by an internal (relative to the waveguide) angle β (not shown) taken relative to the second surface of the waveguide S <NUM>. Hence with the further surface being angled in this way, differently from the second surface, the further surface is for example non-parallel to the first and second surface. With the further surface angled in this way, the further surface is for example at least partly recessed from a second plane substantially coplanar (e.g. in the same plane within acceptable tolerances) with a surface of the first layer and a surface of the second layer. The second plane is for example perpendicular to the second axis and corresponds with a side of the polarisation converter. A distance by which the further surface of the waveguide is recessed from the second plane is perpendicular to the thickness, and may depend on a duration of removing waveguide material, e.g. by a so-called under-etching process. Such a polarisation converter with two regions of waveguide material absent from between the first and second layers can give further design freedom, and potentially increase the efficiency of polarisation conversion. Indeed, the angles α and β may be the same or different from each other (e.g. in correspondence with different crystalline planes).

Further, <FIG> illustrates schematically a plan view of a PIC <NUM> comprising a light polarisation converter <NUM> in accordance with examples described herein. A commercially utilised material platform for PICs is indium phosphide (InP), which allows for integration of optically active and passive functions on the same chip; however, other material platforms such as silicon (Si), Gallium Arsenide (GaAs) or lithium niobite (LiNBO3), may be utilised as a platform for PICs. A PIC may comprise hundreds of components integrated in a single chip.

Note that a layer referred to herein is for example a single layer of the same homogenous material, though it is envisaged for other examples that a layer instead comprises one or more sub-layers or portions each deposited or formed independently of each other (e.g. one after another during a manufacture process to form a stack of sub-layers which together could be considered a layer). A layer may have sub-portions of different materials, for example, for fabrication. Sub-portions of a layer may have different dopant concentrations. At least one of the first layer, the waveguide or the second layer, or a sub-layer thereof, each comprise InP. In some such examples, the first layer and the second layer each comprise InP, and the waveguide comprises InGaAsP. In other examples, at least one of the layers or the waveguide, described herein, comprise at least one of indium phosphide (InP), gallium arsenide (GaAs), gallium antimonide (GaSb), gallium nitride (GaN), indium gallium arsenide (InGaAs), indium aluminium arsenide (InAlAs), indium aluminium gallium arsenide (InAlGaAs), indium gallium arsenide phosphide (InGaAsP), silicon (Si), silicon nitride (Si3N4), silicon oxide (SiO2), or lithium niobate (LiNbO3); however, other semiconductor, and/or photonic materials are envisaged in further examples.

Claim 1:
A light polarisation converter (<NUM>, <NUM>, <NUM>) for a photonic integrated circuit, comprising:
a first layer (<NUM>, <NUM>, <NUM>) comprising a first surface (S102, S202, S302) and a second surface (S104, S204, S304), the second surface offset from the first surface along a first axis (<NUM>, <NUM>, <NUM>) and a second axis (<NUM>, <NUM>, <NUM>), the first axis perpendicular to the first surface, and the second axis parallel to the first surface;
a second layer (<NUM>, <NUM>, <NUM>); and
a waveguide (<NUM>, <NUM>, <NUM>) between, and in contact with each of, the first layer and the second layer, the waveguide comprising:
a first waveguide portion (104A, 204A, 304A) in contact with the first surface, the first waveguide portion having a first thickness different to a second thickness of the first waveguide portion, the first thickness and the second thickness perpendicular the first surface, and
a second waveguide portion (104B, 204B, 304B) in contact with the second surface, such that the second waveguide portion is offset from the first waveguide portion,
characterised in that the light polarisation converter comprises a region (<NUM>) between the first layer and the second layer, the refractive index of the region different from the refractive index of the waveguide, the waveguide absent from the region, and the waveguide comprises a third surface (S106, S206), the third surface not in contact with the first layer or the second layer.