Optical fourier transform device

Abstract

A Fourier transform waveguide comprising input ports (111) arranged in a first array, output ports (121) arranged in a second array, an interference region (130) having a perimeter defined by the first array and second array and by virtual planes extending between respective ends of the first array and second array; and a stray light region (140a,b) surrounding or adjacent the perimeter of the interference region (130). The stray light region (140a,b) comprises: a redirecting portion (143) arranged to receive stray light directly from the input ports (111) and redirect said stray light other than towards the interference region (130); and / or a light sink (144,146) arranged to absorb or attenuate stray light received directly or indirectly from the input ports (111).

Description

[0001] Optical Fourier Transform Device

[0002] Field

[0003] The present disclosure relates to optical Fourier transform devices, in particular Fourier transform waveguides.

[0004] Optical and photonic computing approaches promise to perform mathematical operations such as Fourier transforms at much higher speed whilst consuming much lower energy compared to performing similar operations using electronic circuits.

[0005] Optical Fourier transform (OFT) is traditionally performed using free-space optics and, more recently, integrated photonics. Free-space OFT systems are well known and comprise a Fourier transform lens that is illuminated with beams of coherent light, either arranged in one or two dimensions. In the focal plane of the lens is the OFT of the input beams. Integrated photonics include in-silicon (or in-wafer) designs in which waveguides and other optical components are etched or otherwise imprinted / carved / engraved into a block or slab of semiconductor, glass or other solid material.

[0006] Integrated photonics may be relief or embossed structures, or a combination of both. OFT devices of this category may be referred to as Fourier transform waveguides.

[0007] The use of integrated photonic devices for performing OFTs provides the benefit of baked-in, high- tolerance alignment of the optical components at manufacturing, thereby improving the accuracy, efficiency and / or reliability of the OFTs performed using the device. However, the accuracy and efficiency of such OFT devices can be improved.

[0008] There is provided a Fourier transform waveguide comprising: input ports arranged in a first array; output ports arranged in a second array; an interference region having a perimeter defined by the first array and second array and by virtual planes extending between respective ends of the first array and second array; and a stray light region surrounding or adjacent the perimeter of the interference region. The stray light region comprises: a redirecting portion arranged to receive stray light directly from the input ports and redirect said stray light other than towards the interference region; and / or a light sink arranged to absorb or attenuate stray light received directly or indirectly from the input ports.

[0009] Optionally, the stray light region is arranged to cause the surface integral of the flux of light through the perimeter other than through the input ports to at most 1 / e, at most 1 / e2, at most 5%, at most 1% or at most 0.1% of the surface integral of the flux of light exiting the interference region other than through the output ports. Optionally, the surface integral of the flux of light through the perimeter other than through the input ports includes only the surface integral of the flux of light entering the interference region and travelling directly towards the input ports or output ports.

[0010] Optionally, the Fourier transform waveguide is a slab waveguide or another waveguide based on guided modes.

[0011] Optionally, the redirecting portion is arranged to redirect the stray light other than towards the input or output ports.

[0012] Optionally, the redirecting portion is a boundary at which there is a step change in refractive index or a boundary region within which there is a gradual change in refractive index.

[0013] Optionally, the redirecting portion is arranged to redirect the stray light towards a portion of the Fourier plane other than that containing the output ports.

[0014] Optionally, the stray light region comprises a first stray light region adjacent a first side of the interference region and a second stray light region adjacent a second side of the interference region opposite the first side.

[0015] Optionally, the redirecting portion comprises a first redirecting portion in the first stray light region and a second redirecting portion in the second stray light region.

[0016] Optionally, a distance between the first redirecting portion and second redirecting portion increases in a direction from the first array to the second array.

[0017] Optionally, the distance between the first redirecting portion and second redirecting portion increases over at least one quarter, or one half of the distance between the centre of the first array and the centre of the second array.

[0018] Optionally, either the first stray light region or second stray light region comprises the light sink and the light sink is arranged to receive the light redirected by the first or second redirecting portions.

[0019] Optionally, the light sink is arranged to attenuate or absorb: light received directly from the input ports, and / or light redirected by the redirecting portion.

[0020] Optionally, the light sink is positioned at or parallel to the Fourier plane adjacent the second array. Optionally, the Fourier transform waveguide further comprises: additional output ports arranged in a third array, wherein a spacing between adjacent ends of the second array and third array is greater than the spacing between the output ports and greater than the spacing between the additional output ports; an additional interference region having a perimeter defined by the first array and third array and by virtual planes extending between respective ends of the first array and third array. The light sink may be disposed at or parallel to the Fourier plane between the interference region and the additional interference region.

[0021] Optionally, the light sink comprises at least one of: an absorber, an antireflective surface, an antireflective structure, a light extractor, or a beam dump.

[0022] Optionally, the light sink is a waveguide other than an output port such that the light extracted by the light extractor is other than for detection or calculating the result of an optical Fourier transform.

[0023] Optionally, the stray light region is arranged to cause the surface integral of the flux of light through any continuous section of the perimeter other than through the input ports to at most 1 / e, at most 1 / e2, at most 5%, at most 1% or at most 0.1% of the surface integral of the flux of light exiting the interference region through the same continuous section of the perimeter.

[0024] Optionally, the stray light region borders any part of the perimeter of the interference region other than where input ports or output ports are located.

[0025] Brief description of the drawings

[0026] The embodiments of the invention will now be described, by way of example, with reference to the drawings, of which:

[0027] Figure 1 shows a known OFT device;

[0028] Figure 2a shows the OFT device of Figure 1 including examples of stray light exiting and re-entering an interference region between arrays of input ports and output ports;

[0029] Figure 2b shows a plot of intensity vs position in the Fourier plane of the OFT device of Figure 2a; Figure 3 shows a schematic of an OFT device according to embodiments including examples of stray light being treated so as to prevent at least a portion of it from re-entering an interference region;

[0030] Figure 4 shows a schematic of an OFT device having angled boundaries and a light sink;

[0031] Figure 5 shows an embodiment exemplifying the concepts shown in Figure 4 and including tapered absorbers; and

[0032] Figures 6a and 6b show further embodiments including tapered absorbers. In the drawings, like reference numerals refer to like parts, features or components.

[0033] Overview and detailed description of embodiments

[0034] A 1 D OFT device (such as an integrated photonics OFT device) can be realised in a two-dimensional structure, where the light is confined in one dimension and diffracts freely in the other two. In an example of such an OFT device, the input and output of the OFT device are arrays of input and output ports serving as the exit or entrance of waveguides or light channels. The light from each input port is diffracted into a wavefront wide enough to cover all output ports. At each output port, the contribution from each input port has the same intensity when the optical power at all the input ports is the same t. The angle of the wavefront at the output array is determined by the angle of the input port, and sets the phase delay at each output port.

[0035] One way to do this is to have the input and output arrays arranged on the arc of a different circle, on which lies the centre of the other circle. The Fourier transform of the input array forms on the line of the second circle. For a given radius of circle and number of input ports the angular spacing of the input and output arrays can be calculated so that the output ports sample a single order of the Fourier transform of the input data.

[0036] The device will have some tolerance to how close the input and output ports need to be to the arc, with small changes in radial distance or lateral distance (but not angle) able to be compensated. If the radius is long enough, the arc can be approximated to a straight line. ‘Long enough’ means the distance between the arc and its tangent at the edge of the zero order FT is much less than a wavelength.

[0037] The inventors have recognised that OFT devices can be inefficient or in some cases inaccurate. These deficiencies can be amplified especially when using single mode waveguides forming the input and output ports in the array with only a small fraction of the input light being extracted at the output ports.

[0038] Figure 1 shows a known 1 D OFT device (or Fourier transform waveguide) 100 of this type. In brief summary, Figure 1 shows a Fourier Transform slab waveguide 100 where the light is constrained in one (cartesian) dimension (z) and diffracts freely in the other two dimensions (x and y). The OFT device includes a first array 110 of input ports 111 , a second array 120 of output ports 121. The second array 120 of output ports is arranged along the Fourier plane of the Fourier transform waveguide. As will be understood by the skilled person, the Fourier plane may be a plane or a curved surface at which the Fourier transformation of the light at the input ports is formed. An interference region 130 is defined in the space or volume between the first array and second array, and may include an input coupling region connecting the first input array and the diffraction region and an output coupling region connecting the diffraction region and the second output array. The interference region 130 is surrounded in the x and y plane by a boundary 141. The boundary 141 may be directly adjacent the interference region 130 or there may be a spatial margin between at least some edges (perimeters) of the interference region 130 and the boundary 141.

[0039] The interference region and any surrounding volume in which the light from the input ports propagates can be formed by etching or machining a block, slab or wafer of material to form the interference region and any surrounding volume within the boundary 141 (.e.g. as a relief therein or as a standalone block or an embossed structure). The boundary 141 surrounding or adjacent the interference region 130 therefore includes sides (as in the minor faces of a three dimensional slab). The interference region is constrained in the z-direction (as in the thickness direction of the slab) by faces (as in the major faces of the slab). The faces of the boundary surrounding or adjacent to the interference region 130 are exposed to the light emitted from the input ports.

[0040] The slab waveguide is any photonic waveguide and may be realised using any of the following technology or combination of:

[0041] • A slab waveguide in silicon-on-insulator (SOI)

[0042] • A photonic crystal (PhC) with or without periodic defects or sub-wavelength holes

[0043] • A slab waveguide in silicon nitride (SiN)

[0044] • A waveguide on a compound photonic technology (lll-V or ll-VI)

[0045] • Any plasmonic waveguide

[0046] • A metasurface

[0047] • Or another photonic technology

[0048] In the interference region, there may be a void or, alternatively, a (for example, homogenous) medium, and / or a medium with uniform refractive index or engineered to have a uniform refractive index.

[0049] The first array 110 is arranged on (or along) a first arc 110a of a first circle 110c and the second array 120 is arranged on (or along) a second arc 120a of a second circle 120c offset from the first circle. Preferably, the first circle 110c has a centre which lies on the second arc 120a and the second circle 120c has a centre which lies on the first arc 110a. Preferably, the centre of the first circle 110c lies at or near the centre of the second array 120 and the centre of the second circle 120c lies at or near the centre of the first array 110.

[0050] The first arc 110a and second arc 120a respectively define a first portion 131a and second portion 131 b of the perimeter 131 of the interference region 130. A third portion 131c and fourth portion 131 d of the perimeter 131 join respective ends (or edges) of the first portion 131a and second portion 131 b. That is, the third portion 131c is a virtual face which extends in a plane between a first end of the first portion 131a and first end of the second portion 131 b, and the fourth portion 131 d is a virtual face which extends in a straight line (or a plane) between a second end of the first portion 131a and second end of the second portion 131 b. The first to fourth portions 131a-d constitute the whole of the perimeter 131 in the x-y plane (the plane in which the input and output ports are arranged). The input ports 111 are the exits (e.g. exit pupils or exit apertures) of input waveguides 101 or coupling structures. That is, the input ports can be connected to any of the following, or combination of:

[0051] • Waveguides manufactured using the same technology, methods and / or materials as the free space Fourier Transform slab waveguide region

[0052] • Coupling structures such as grating couplers or edge couplers, that couple in light from an external source

[0053] • Coupling structures such as tapered couplers, that couple in light between vertically displaced waveguides (i.e. waveguides in a silicon layer coupling light into a SiN Fourier Transform slab waveguide region).

[0054] • Impedance matching structures that reduce the reflection between the free space Fourier Transform slab waveguide and any of the above.

[0055] Embodiments can be used with existing photonic technology. For example, both the phase and amplitude of light in input waveguides 101 connected to the input ports 111 can be controlled or modulated using any of the following or a combination of:

[0056] • Mach Zehnder Modulators

[0057] • PN modulators

[0058] • Ring modulators

[0059] • Thermal modulators

[0060] • A different PIC with different photonic functionality

[0061] • Waveguides manufactured using the same technology, methods and / or materials as the free space Fourier Transform slab waveguide region

[0062] • Coupling structures such as grating couplers or edge couplers, that couple light out to an external waveguide or detector

[0063] • Coupling structures such as tapered couplers, that couple light out to vertically displaced waveguides (i.e. waveguides in a silicon layer coupling light into a SiN Fourier Transform slab waveguide region)

[0064] • Impedance matching structures that reduce the reflection between the free space Fourier Transform slab waveguide and any of the above

[0065] • A photodetector

[0066] • Another photonic integrated circuit for further processing or analysis.

[0067] The output ports 121 can be placed to sample one or more orders of the Fourier transform of the input data either as a fast Fourier transform or otherwise. Generally, the output ports are positioned to capture or sample the zero-order Fourier transform; however, in some embodiments, output ports may alternatively or in addition be positioned to capture or sample higher order Fourier transform modes, such as the first or second order. Embodiments may be directed to sampling a Fast Fourier transform. If sampling a fast Fourier transform, the number of output ports used to extract data must be the same as the number of input ports.

[0068] In operation, the Fourier Transform slab waveguide is illuminated with modulated or unmodulated light at one or more of the input ports 111. The inserted modulated or unmodulated light undergoes diffraction within the interference region 130. The output ports 121 are placed on the Fourier plane, i.e. where the diffracted light forms the optical Fourier transform of the light pattern from the input ports 111.

[0069] The input ports 111 bring light into the interference region 130. The light at an input port 111 has information encoded into the phase and amplitude of the field. The size and shape of the optical field contained within each input port 111 to the free space Fourier transform slab waveguide will define the envelope function of the Fourier transform according to the convolution theorem.

[0070] The output ports 121 are placed in the Fourier plane (which lies along the second arc 120a). Light arrives at the output ports 121 as a set of waves at a range of angles which match the relative positions of the input ports 111. The waves from all input ports 111 sum (e.g., coherently) to form an analog Fourier transform. The Fourier transform in the Fourier (or output) plane (which lies along the second arc 120a) contains the full Fourier transform of the light pattern at the input plane (which lies along the first arc 110a), including the input mode shape and input envelope function.

[0071] The FT is sampled for detection by the output ports 121 , and then the detection method will determine if the solution to the Fourier transform is analog or digital. Light collected by the output ports 121 is detected using photodiodes. Said light is either detected on a single photodiode per channel or the signal is mixed with a reference beam for homodyne detection. The output ports that are used to extract data for detection must preserve the amplitude of the Fourier transform, and the phase if the phase is being detected.

[0072] In addition to the first arc 110a and the second arc 120a, the waveguide also comprises boundaries adjacent to, and outside of, the third portion 131c and fourth portion 131 d of the perimeter 131 interference region 130. In particular, the waveguide of Figure 1 comprises a first waveguide boundary 141a and a second waveguide boundary 141 b. The first waveguide boundary 141a is a planar surface extending between a first end of the first arc 110a and a first end of the second arc 120a. The second waveguide boundary 141a is a planar surface extending between a second end of the first arc 110a and a second end of the second arc 120a.

[0073] The inventors have recognised that in Fourier transform waveguides exemplified by that shown in Figure 1 , reflections from waveguide boundaries (e.g. edges or sides) of the Fourier transform waveguide can interfere with the operation of the device, for example by creating an unwanted optical interference pattern in the Fourier plane (e.g. at the output ports) or by otherwise interfering with the light emitted through the input ports (e.g. by back reflections into the input ports), both of which can reduce the accuracy of the output data and thus adversely affect the operation of the OFT device. In this case, an unwanted optical interference pattern is that which is not accurately representative of the intended optical interference pattern created by pure interference involving light received only directly from the input ports. In other words, ideally, other than the light which travels directly from the input ports to the output ports, no other light should be present at the output ports, or otherwise the accuracy of the optical Fourier transform operation can be adversely affected.

[0074] The interference region is positioned between the input ports (i.e. at the input plane of the OFT device) and the output ports (i.e. at the output or Fourier plane of the OFT device). In the interference region, the light from the individual input ports interferes to produce a diffraction pattern. The output ports are positioned to capture the diffraction pattern at the Fourier plane (though a diffraction pattern will be present throughout the interference region).

[0075] Light emerging from the input ports and travelling in a straight line directly from the input ports to the output ports is considered to be useful light in the sense that it is this light that forms the intended interference (or diffraction) pattern which is formed at the Fourier plane. Light emerging from the input ports travelling in directions other than directly toward the output ports may be considered to be stray light.

[0076] Reflections of stray light (e.g. from boundaries or other regions or portions surrounding or adjacent the interference region can cause some of the stray light to be reflected (back) into the interference region. The reflected stray light can cause interference at the output ports or upstream in the input waveguides (if back reflected through the input ports).

[0077] Figure 2a illustrates three examples of this phenomenon occurring in the Fourier transform waveguide of Figure 1. Like reference numerals refer to like parts.

[0078] In Figure 2a, a first example shows a first incident ray (or wavefront propagation vector) 191 i in a direction from the input ports 111 , through and out of the interference region 130, and toward the first waveguide boundary 141 a. Upon reflection from the first waveguide boundary 141a, a first reflected ray 191 r is shown in a direction back into the interference region 130.

[0079] In a second example, a second incident ray 192i is shown in a direction from the input ports 111 , through and out of the interference region 130, and toward the first waveguide boundary 141a. Upon reflection from the first waveguide boundary 141a, a second reflected ray 192r is shown in a direction back into the interference region 130 and towards the output ports 121 . In a third example, a third incident ray 193i is shown in a direction from the input ports 111 , through and out of the interference region 130, and toward the second arc 120a at a position spaced apart from the output ports 121 . Upon reflection from the second arc 120a, a third reflected ray 193r is shown in a direction toward the interference region 130 and towards the input ports 111.

[0080] In each of the three example light paths of Figure 2a, the light originates from the input ports, travels through and exits the interference region 130, is reflected from a waveguide boundary and re-enters the interference region 130. In the second and third examples, light is reflected directly towards the output ports 121 and input ports 111 respectively. Thus, in the second example, the reflected light may adversely effect the interference pattern at the output ports, leading to an erroneous measurement of the Fourier transform; and in the third example, the reflected light may interfere with the light emerging from the input ports by interfering with components (for example encoders or modulators) further upstream, for example. In the first example, the light is reflected towards the interference region but does not travel directly to the input or output ports. However, this can still cause adverse effects in the interference pattern at the Fourier plane. For example, if the first reflected ray 191 r is re-reflected from the second waveguide boundary 141 b (and subsequently from the first waveguide boundary 141a again), the reflected light may still travel towards the output ports 121.

[0081] Thus, in all three examples, the reflected rays can alter the diffraction pattern which would otherwise be formed at the Fourier plane without the interference from the reflections. In these ways, reflections of stray light back into the interference region and either directly or indirectly towards the input or output ports can adversely affect the operation of the OFT device.

[0082] The present disclosure is directed to OFT devices arranged to reduce or minimise the extent to which (reflections of) stray light interfere with the Fourier transform operation. This is achieved by reducing or avoiding reflections of stray light (back) into the interference region and / or towards the input ports or output ports.

[0083] As exemplified in Figure 2a and the description thereof, the reflections of stray light can be caused by changes in refractive index between mediums at the boundaries surrounding or adjacent the interference region. However, the changes in refractive index causing the reflections can be gradual (for example in GRIN materials) as well as abrupt as in the changes from air to glass or silicon (or vice versa) or from one type or configuration of crystal to another. Alternatively, boundaries or regions surrounding or adjacent the interference region may cause reflection in other ways, for example if there is an abrupt change in medium from a transmissive one to a non-transmissive one or a film, coating or other layer which causes reflections.

[0084] Figure 2b is a plot of shows a plot of intensity vs position in the Fourier plane of the OFT device of Figure 2a. The horizontal axis 202 shows arbitrary units of position in the Fourier plane with 0 representing the centre of the Fourier plane and -1 representing the position of the first waveguide boundary 141 a, which is represented by a dotted line 141 a. The vertical axis 201 shows arbitrary units of intensity with 0 representing 0 intensity and 1 .0 representing the maximum intensity at the Fourier plane. A solid line 210 represents the plot of intensity vs position at the Fourier plane ignoring reflections. A dashed line represents the intensity of light at the Fourier plane taking into account only the reflections from the first waveguide boundary 141 a. As will be understood by the skilled person, Figure 2 illustrates that the reflected light will have a significant influence on the interference pattern at the Fourier plane, especially toward the outer edges of the interference region.

[0085] A schematic of some of the ways in which at least a portion of the stray light can be prevented from reentering the interference region is shown in Figure 3. Like reference numerals refer to like parts. Figure 3 shows a schematic of a Fourier transform waveguide 200 similar to that shown in Figure 1 , but for the following differences. The Fourier transform waveguide 200 of Figure 3 does not include the first and second waveguide boundaries 141 a and 141 b adjacent the interference region 130 shown in Figure 1 .

[0086] In Figure 3 a first stray light region 140a is located outside of the interference region 130 and adjacent to the third portion 131 c of the perimeter 131 of the interference region 130. A second stray light region 140b is located outside of the interference region 130 and adjacent to the fourth portion 131d of the perimeter 131 of the interference region 130.

[0087] In some embodiments, the boundaries or regions surrounding or adjacent the interference region of the OFT device are arranged to direct reflections of stray light in a direction other than into the interference region, and in addition preferably other than towards the input ports or output ports. This is demonstrated in a first example in the schematic of Figure 3, a redirecting surface 143 in the first stray light region 140a is positioned and angled to receive light travelling in the direction of a fourth incident ray 196i (or wavefront propagation vector). The fourth incident ray 196i is in a direction from the input ports 111 , through and out of the interference region 130, into the first stray light region 140a and toward the redirecting surface 143. Upon reflection from the redirecting surface 143, a fourth reflected ray 196r is shown in a direction away from the interference region 130 and away from the input ports 111 and output ports 121 .

[0088] Alternatively, or in addition, the relative dimensions of the OFT device in the areas surrounding the interference region are such that reflections from the sides are reduced or minimised. For example, the relative dimensions are such that the zero order mode or first or second order modes of the diffraction pattern does not reach the boundaries (lateral edges or faces of the device extending between the input plane (or surface) and the output plane (or surface)). In this case, at least one or an array of light sinks may be positioned at or parallel to the Fourier plane, e.g. either side of the output ports to prevent light from being reflected back into the interference region. Alternatively, or in addition, a region outside of and adjacent to the interference region may be configured to have an extinction co-efficient which causes the amplitude or intensity of the stray light to be attenuated. The extinction coefficient may be of a volume and be defined per unit depth of light penetration. This is demonstrated in a second example in the schematic of Figure 3, which shows a light sink in the form of an attenuator 145 in the second stray light region 140b positioned to receive a light travelling in the direction of a fifth incident ray 197i (or wavefront propagation vector). The fifth incident ray 197i is in a direction from the input ports 111 , through and out of the interference region 130, into the second stray light region 140b and through the attenuator 145. In this case the light may then be reflected back into the interference region 130 but, having been attenuated by the attenuator

[0089] 145, the amplitude of the light is reduced compared with its amplitude on originally exiting the interference region 130. The attenuator 145 is arranged such that the light re-entering the interference region 130 has an intensity of 1 / e or less, 1 / e2or less, 5% or less, 1% or less or even 0.1% or less of its value on initially exiting the interference region 130.

[0090] Alternatively, or in addition, a light sink in the form of an absorber is used to reduce or minimise reflections by reducing the reflection coefficient (or increasing the absorption co-efficient) at one or more of the boundaries of the OFT device. The reflection coefficient may be a reflection coefficient of a surface or, in the case of e.g., a textured, structured or composite surface, an average or effective reflection coefficient per unit area of the boundary. This is demonstrated in a third example in the schematic of Figure 3, which shows a light sink in the form of an absorber 146 in the second stray light region 140b. The absorber 146 is positioned and angled to receive a sixth incident ray 198i (or wavefront propagation vector). The sixth incident ray 198i passes from the input ports 111 , through and out of the interference region 130, into the first stray light region 140a and toward the absorber

[0091] 146. In this case, the light may then be reflected back into the interference region 130 but, having been absorbed by the absorber 146, the amplitude of the light is reduced compared with its amplitude on originally exiting the interference region 130.

[0092] The light sink is, for example, an antireflection layer (or stack) or photonic structure (e.g. a grating structure or photonic crystal), or other technology device, surface or structure arranged to suppress reflections. Other examples of a suitable light sink include tapered absorbers, beam dump arrays or photonic absorbers such as electro-absorption materials that are positioned or deposited at specific sites. In a detailed example, the light sink may include a tapered or v-shaped boundary portion arranged to receive light at or near its wider end and guide reflections from its sides toward its narrower end. At the narrower end, the width of the tapered absorbers is so narrow that there are no guided modes and this gives rise to absorption into the surrounding material. Such tapered or v- shaped boundary portions may be provided in plurality in an array along the boundary or region surrounding or adjacent the interference region. In this way, more of the stray light exiting the interference region at multiple positions along its boundary can be prevented from re-entering the interference region. The skilled person will appreciate that the reflection co-efficient at a boundary surrounding the interference region is determined by the medium of the interference region (i.e. the medium inside the boundary) and the medium surrounding the interference region (i.e. that outside the boundary) as well as the angle of incidence of the light at that boundary. For a reflectance co-efficient of less than 1 , it is natural that, even in known Fourier transform waveguides such as those illustrated in Figures 1 and 2, some of the light exiting the interference region will be absorbed by the boundaries surrounding the interference region. For example, if the Fourier transform waveguide of Figures 1 and 2 is fabricated by etching the waveguide including the interference region as a relief in a silicon wafer, the reflection co-efficient at the first and second waveguide boundaries 141 a, 141 b for a wavelength of, for example, 1000nm is approximately 0.32 (air to silicon boundary if the interference region is a void) for light of normal incidence. However, since much of the light from the input ports in the OFT device of Figures 1 and 2 meets the first and second waveguide boundaries 141 a and 141 b at an angle greater than the critical angle, total internal reflection occurs along most of the boundary, and therefore most of the light exiting the interference region is reflected back into the interference region, with a significant portion of that light being directed towards the output ports.

[0093] The light sinks described herein may be arranged to have an effective reflectance coefficient per unit area for light at normal incidence which is lower than the reflectance coefficient per unit area at the boundary between the medium of the interference region and the surrounding medium (e.g. the medium which causes the constraint of the light in the direction out of the plane including the input and output ports).

[0094] Alternatively, or in addition, the light sinks described herein (including but not limited to the attenuator 145 and absorber 146 described with reference to Figure 3) are arranged such that any light reentering the interference region after interacting with the light sink has an intensity or amplitude of 1 / e or less, 1 / e2or less, 5% or less, 1 % or less or even 0.1 % or less of its value on initially exiting the interference region.

[0095] Any of the light sinks described herein may be positioned along a boundary between the input plane and the Fourier plane or at the Fourier plane either side of the output ports. Alternatively, or in addition, the present disclosure encompasses a variation of the Fourier transform device illustrated in the Figures by virtue of having groups of output ports separated by a gap at the Fourier plane. The gap between groups is wider than a gap between output ports of the same group. In this case, the interference region referred to in this disclosure may be defined as the space between the input ports and one of the groups of output ports or the combination of multiple such spaces (one space for each group of output ports). In the case of two groups of output ports, a third stray light region is defined in a v-shape between the two intersecting such spaces. The light sinks between the groups of output ports therefore lie in the stray light region at or parallel to the Fourier plane and can reduce the light reentering the stray light region in the same way and to the same degree as described with respect to any of the other light sinks described herein. More generally, taking into account e.g. all three examples of Figure 3, it may be understood that the stray light region according to the present disclosure can prevent a significant proportion of the stray light from re-entering the interference region, especially in a direction towards the input or output ports. A significant proportion may be understood to mean that the light originating from the input ports and exiting the interference region other than through the output ports is greater than the light (re)entering the interference region other than through the input ports. The surface integral of the light flux (re)entering may be at most 1 / e, at most 1 / e2, at most 5%, at most 1% or even at most 0.1% of the surface integral of the light flux exiting. Another measure indicating significant proportions is that the light originating from the input ports and exiting the interference region through any continuous section of the perimeter of the interference region (other than the section at the input ports or output ports) is greater than the light (re)entering the interference region through the same continuous section of perimeter. The surface integral of the light flux (re)entering may be at most 1 / e, at most 1 / e2, at most 5%, at most 1% or even at most 0.1% of the surface integral of the light flux exiting.

[0096] It may be understood that the stray light region described herein is not a region containing input ports or output ports. Put another way, the stray light region borders a section of the perimeter of the interference region other than the sections at which any input or output ports are located. That is, the stray light region can be in any or every region surrounding the perimeter of the interference region other than at the output ports or input ports.

[0097] Alternatively, or in addition, the light originating from the input ports and exiting the interference region other than through the output ports is greater than the light (re)entering the interference region (other than through the input ports) in a direction towards the input ports or output ports. The surface integral of the light flux (re)entering in a direction towards the input ports or output ports may be at most 1 / e, at most 1 / e2, at most 5%, at most 1% or even at most 0.1% of the surface integral of the light flux exiting. The skilled person can determine if this is achieved using simple optical models or computer calculations to simulate the path of light through the Fourier transform waveguide and the various changes in the intensity of the light as it interacts with various surfaces and volumes. Such a model could be easily constructed by the skilled person taking into account reflection, attenuation and absorption at any boundary or region of the waveguide according to the materials and surfaces used in the construction of the waveguide and especially the stray light region. The surface integral of the light flux is through the boundary planes of the interference region extending between the respective ends of the array of input ports and the array of output ports and excludes any flux in the constrained direction (e.g. the z-direction) through the major faces of the slab waveguide. That is, the surface integral of the light flux described herein is taken e.g. through the perimeter 131 of the interference region 130. As described, the surface integral of the light flux exiting the interference region through the output ports and the surface integral of the light flux (re)entering the interference region through the input ports is ignored in these calculations. When the term ‘boundary or region surrounding or adjacent the interference region’ (or similar) is used herein, it may be understood to mean partially surrounding or adjacent on either side of the interference region between the input ports and output ports or at regions surrounding or adjacent the interference region other than where there are (arrays of) input or output ports. Furthermore, this term may be understood to mean immediately surrounding or adjacent the interference region; or surrounding or adjacent at a certain distance from the interference region (so as to create a spatial margin between the interference region and the boundary or region surrounding or adjacent the interference region).

[0098] Using a combination of a boundary or region for controlling the propagation direction of reflected stray light with a boundary or region configured as a light sink can produce a synergistic effect. That is, a first portion of the boundary or region surrounding or adjacent the interference region can be arranged to direct reflections of stray light in a direction other than into the interference region and / or other than toward the input and output ports. Meanwhile, a second portion other than the first portion includes a light sink for absorbing or attenuating light received directly from the input ports and / or light reflected from the first portion. This is exemplified in an extension of the first example shown in Figure 3. In this extended example, the fourth reflected ray 196r continues in the first stray light region until it is met by a first light sink 144. The first light sink 144 may be an attenuator or absorber such as the attenuator 145 or absorber 146 shown in (and described in relation to) the second stray light region 140b of Figure 3.

[0099] The inventors have recognised that it is possible to reduce back reflections from the Fourier (output) plane where the plane is illuminated by the input port but light is not extracted for the result by output ports. This can be achieved by using light sinks at or along a portion of the Fourier plane. For example, the OFT device can be formed such that the portion of the Fourier plane that can be illuminated directly by the input ports is made wider than the array of output ports. This allows the boundaries or regions surrounding or adjacent the interference region that extend between (i.e. join) ends of the array of input ports and the Fourier output plane to be further apart at the Fourier plane than at the input plane. This effectively angles these boundaries or regions away from the input ports, thus redirecting (e.g. reflecting) stray light from the input ports in a direction other than towards the output ports, mostly in a direction towards the Fourier plane either side of the output ports. The light sinks at the Fourier plane either side of the output ports then prevent or reduce reflections of stray light from the input ports (or stray light reflected / redirected by the side boundaries or regions) back toward the input ports.

[0100] In one such arrangement, the shape and / or relative dimensions of a first portion of a boundary surrounding the interference region are arranged to direct reflections of stray light in a direction other than towards the output ports. However, while this can ensure that light from the input ports travels to the output ports without (or with reduced) interference from stray light reflections, in some cases it results in second portions of the boundary other than the first portions being angled so that light received directly from the input ports and / or stray light reflected by the second portions would be back- reflected towards the input ports. In this case, including a light sink as described herein at or along the second portions can reduce or minimise such back reflections.

[0101] This is exemplified in the schematic of Figure 4, which illustrates another embodiment of the Fourier transform waveguides described herein. In Figure 4, the Fourier transform waveguide includes a first angled boundary portion 441 a which extends from a first end of an arc on which the input ports 411 lie to the Fourier plane on which the output ports 421 lie. The Fourier transform waveguide also includes a second angled boundary portion 441 b which extends from a second end of an arc on which the input ports 41 1 lie to the Fourier plane. Each of the first and second angled boundary portions 441 a, 441 b shown in Figure 4 operates in the same manner as the redirecting surface 143 described with reference to Figure 3. The Fourier transform waveguide of Figure 4 also includes a first light sink 445a positioned at the Fourier plane to one side of the output ports 421 and a second light sink 445b positioned at the Fourier plane to the other side of the output ports 421 .

[0102] In operation, light from the input ports 411 travels through and out of the interference region 430 into the first stray light region 440a and second stray light region 440b; and is reflected from the first angled boundary portion 441 a and second angled boundary portion 441 b toward the first light sink 445a and second light sink 445b, respectively. The stray light is thereby prevented from re-entering the interference region 430 and adversely influencing the interference pattern at the output ports.

[0103] In other embodiments, the angled boundary portions are angled such that most of the stray light from the input ports does not reach them and instead travels directly to the light sinks in the Fourier plane. This is exemplified in the Fourier transform waveguide shown in Figure 5. In this embodiment, there is a first light sink array 545a and a second light sink array 545b at the Fourier plane positioned either side of the output ports 521 . Each of the first and second light sink arrays 545a, 545b comprises a series of tapered absorbers 5045 each having a wider end positioned on the Fourier plane and a narrower end positioned still further from the input ports 511 . The tapered absorbers 5045 are angled so that light from the input ports 511 enters the wider end and is guided by multiple reflections toward the narrower end undergoing absorption at each reflection such that no light is reflected back towards the input ports 511. In other embodiments, the tapered absorbers may be replaced by waveguides leading to an absorber (other than a detector) or other equivalent light extractor.

[0104] Figure 5 further shows the light intensity throughout the input waveguides 501 , output waveguides 502 and tapered absorbers 5045 as well as in the interference region 530 and stray light regions 540a, 540b. The interference pattern at the Fourier plane is such that some of the output ports 521 are positioned at a maxima of the interference pattern and some of the output ports are positioned at a minima. Some of the higher order maxima are incident on the tapered absorbers 5045. In Figure 5. the black outline shows the edges of the silicon structure in a Silicon on Insulator device. The simulation was carried out in Lumerical FDTD, with two of the four input ports supplied with light with the same amplitude and phase. The data displayed in grayscale is the intensity of light at a single frequency for a steady state input. The equivalent result calculated numerically is [1 .0, 0.0, 1 .0, 0.0], The diffraction pattern formed shows just over 3 repeats of the Fourier transform, with the centre pattern extracted by the output ports 521 and the other maxima absorbed into the silicon by the tapered absorbers 5045.

[0105] Another embodiment is shown in Figure 6a, in which tapered absorbers 6045a are positioned in a semi-elliptical pattern around the interference region rather than along the Fourier plane. Positioning absorbers to surround the interference region in this way reduces the re-entry of any stray light into the interference region 630a yet further due to the light sinks occupying a greater proportion of the boundary or region surrounding or adjacent to the interference region. Yet another embodiment is shown in Figure 6b in which the tapered absorbers 6045b are positioned closer to the interference region 630b. This increases the proportion of the boundary occupied by light sinks while allowing a smaller footprint per Fourier transform waveguide, for example to provide an increased density of such waveguides in an optical chip.

[0106] The advantages of the embodiments described herein can be:

[0107] • accurate Fourier transform without interference from reflected light from the edges of the device; and / or

[0108] • reduced back reflections interfering with upstream components, for example those associated with the input waveguides.

[0109] The skilled person will understand that the Fourier transform waveguide may be designed and manufactured for a specific wavelength or wavelength range so that the input ports and output ports are positioned such that the optical Fourier transform is formed at the output ports. The skilled person knows how to design the relative and / or absolute dimensions of the Fourier transform waveguides described herein to accommodate different wavelengths of input light. For example, for a given wavelength, the distance between the array of input ports and the array of output ports and the spacings between the individual ports themselves can be determined by calculation. In addition, the skilled person knows how to design or optimise various forms of light sinks or light redirecting surfaces or regions (i.e. those which perform any of the functions described herein) if the wavelength of the input light (and hence stray light) is known.

[0110] The described embodiments are provided for illustration purposes and are not intended to be limiting. As the skilled person will understand, various modifications can be made to the embodiments. The invention is defined by the scope of the appended claims.

Claims

CLAIMS:1 . A Fourier transform waveguide comprising: input ports arranged in a first array; output ports arranged in a second array along a Fourier plane of the Fourier transform waveguide; an interference region having a perimeter defined by the first array and second array and by virtual planes extending between respective ends of the first array and second array; and a stray light region surrounding or adjacent the perimeter of the interference region and comprising: a redirecting portion arranged to receive stray light directly from the input ports and redirect said stray light other than towards the interference region, and / or a light sink arranged to absorb or attenuate stray light received directly or indirectly from the input ports.

2. The Fourier transform waveguide according to claim 1 , wherein the stray light region is arranged to cause the surface integral of the flux of light through the perimeter other than through the input ports to at most 1 / e, at most 1 Ze2, at most 5%, at most 1 % or at most 0.1 % of the surface integral of the flux of light exiting the interference region other than through the output ports.

3. The Fourier transform waveguide according to claim 1 or 2, wherein the surface integral of the flux of light through the perimeter other than through the input ports includes only the surface integral of the flux of light entering the interference region and travelling directly towards the input ports or output ports.

4. The Fourier transform waveguide according to any preceding claim, wherein the Fourier transform waveguide is a slab waveguide or another waveguide based on guided modes.

5. The Fourier transform waveguide according to any preceding claim, wherein the redirecting portion is arranged to redirect the stray light other than towards the input or output ports.

6. The Fourier transform waveguide according to any preceding claim, wherein the redirecting portion is a boundary at which there is a step change in refractive index or a boundary region within which there is a gradual change in refractive index.

7. The Fourier transform waveguide according to any preceding claim, wherein the redirecting portion is arranged to redirect the stray light towards a portion of the Fourier plane other than that containing the output ports.

8. The Fourier transform waveguide according to any preceding claim, wherein the stray light region comprises a first stray light region adjacent a first side of the interference region and a second stray light region adjacent a second side of the interference region opposite the first side.

9. The Fourier transform waveguide according to claim 8, wherein the redirecting portion comprises a first redirecting portion in the first stray light region and a second redirecting portion in the second stray light region.

10. The Fourier transform waveguide according to claim 9, wherein a distance between the first redirecting portion and second redirecting portion increases in a direction from the first array to the second array.

11. The Fourier transform waveguide according to claim 9 or 10, wherein the distance between the first redirecting portion and second redirecting portion increases over at least one quarter, or one half of the distance between the centre of the first array and the centre of the second array.

12. The Fourier transform waveguide according to any of claims 8-11 , wherein either the first stray light region or second stray light region comprises the light sink and the light sink is arranged to receive the light redirected by the first or second redirecting portions.

13. The Fourier transform waveguide according to any preceding claim, wherein the light sink is arranged to attenuate or absorb: light received directly from the input ports, and / or light redirected by the redirecting portion.

14. The Fourier transform waveguide according to any preceding claim, wherein the light sink is positioned at or parallel to the Fourier plane adjacent the second array.

15. The Fourier transform waveguide according to any preceding claim, further comprising: additional output ports arranged in a third array, wherein a spacing between adjacent ends of the second array and third array is greater than the spacing between the output ports and greater than the spacing between the additional output ports; an additional interference region having a perimeter defined by the first array and third array and by virtual planes extending between respective ends of the first array and third array, wherein the light sink is disposed at or parallel to the Fourier plane between the interference region and the additional interference region.

16. The Fourier transform waveguide according to any preceding claim, wherein the light sink comprises at least one of: an absorber,an antireflective surface, an antireflective structure, a light extractor, or a beam dump.

17. The Fourier transform waveguide according to any preceding claim, wherein the light sink is a waveguide other than an output port such that the light extracted by the light sink is other than for detection or calculating the result of an optical Fourier transform.

18. The Fourier transform waveguide according to any preceding claim, wherein the stray light region is arranged to cause the surface integral of the flux of light through any continuous section of the perimeter other than through the input ports to at most 1 / e, at most 1 / e2, at most 5%, at most 1% or at most 0.1% of the surface integral of the flux of light exiting the interference region through the same continuous section of the perimeter.

19. The Fourier transform waveguide according to any preceding claim, wherein the stray light region borders any part of the perimeter of the interference region other than where input ports or output ports are located.

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