Array waveguide diffraction grating

Abstract

An array waveguide diffraction grating (500) according to one aspect of the present disclosure comprises: a first slab waveguide (502); a second slab waveguide (504); and a waveguide array (506) having a plurality of waveguides that couple the first slab waveguide (502) and the second slab waveguide (504). In the waveguide array (506), at least one of the plurality of waveguides has a plurality of straight sections and a plurality of curved sections, and at least one of the plurality of curved sections has an S-shape.

Description

Arrayed Waveguide Grating

[0001] The present disclosure relates to arrayed waveguide gratings.

[0002] With the further increase in capacity of optical communications such as wavelength division multiplexing optical communications, research and development into broadening the bandwidth of optical waveguide devices such as optical wavelength multiplexing / demultiplexing circuits and / or optical switch circuits that support optical communications technologies is actively underway. For example, arrayed waveguide gratings (AWGs) are sometimes used in optical wavelength multiplexing / demultiplexing circuits used to multiplex and / or demultiplex signal light.

[0003] CR Doerr et al., “Planar Lightwave Circuit Eight-Channel CWDM Multiplexer With < 3.9-dB Insertion Loss,” J. Lightwave Technol. 33(15), 1326-1332 (2005).W.-C. Kim et al., Opt. Engineering 55(8), 087110 (2016).Y. Hibino, IEEE J. Sel. Top. Quantum Electron. 8(6), 1090-1101 (2002).Kenya Suzuki et al., J. Lightwave Technl. 35(4), 596-606 (2017).

[0004] For example, the smaller the path length difference (ΔL) between the waveguides constituting the waveguide array, the wider the wavelength range that can be operated by the AWG. Also, the more the number of waveguides constituting the waveguide array is increased and the narrower the spacing, the narrower the wavelength sampling intervals, in other words, the higher the resolution of the AWG.

[0005] However, increasing the bandwidth and / or resolution of the AWG may increase the size of the AWG, which may limit the size of the AWG depending on, for example, an allowable chip size, and as a result, the performance of the AWG, such as increasing the bandwidth and / or resolution, may be limited.

[0006] One of the objectives of the present disclosure is to reduce the size of arrayed waveguide gratings.

[0007] Therefore, an arrayed waveguide grating according to one aspect of the present disclosure comprises a first slab waveguide, a second slab waveguide, and a waveguide array having a plurality of waveguides coupling between the first slab waveguide and the second slab waveguide, wherein in the waveguide array, at least one of the plurality of waveguides has a plurality of straight sections and a plurality of curved sections, and at least one of the plurality of curved sections has an S-shape.

[0008] 1 is a schematic plan view showing a configuration example of an arrayed waveguide grating (AWG); FIG. 2 is a plan view showing a design example of an AWG in which the path length difference of arrayed waveguides is reduced; FIG. 3 is a schematic plan view showing a configuration example of an S-type AWG in which arrayed waveguides are laid out in an S-shape; FIG. 4 is a diagram showing a configuration example of an optical wavelength demultiplexer; FIG. 5 is a schematic view of an AWG according to a first embodiment; FIG. 6 is a diagram showing an example of a change in evaluation index A with respect to a change in structural parameters (d and Xc) in the AWG according to the first embodiment; FIG. 7A is a schematic view showing a configuration example of an AWG including a waveguide array whose layout is defined by structural parameters derived based on evaluation index A, and FIG. 7B is a schematic view showing a comparative example of FIG. 7A is a graph for explaining the area reduction effect of the waveguide array in the first embodiment; FIG. 8 is a schematic view showing a configuration example of an optical wavelength multiplexing / demultiplexing circuit according to a second embodiment; FIG. 9 is a schematic view showing a configuration example of a wavelength selective switch according to a third embodiment;

[0009] Hereinafter, embodiments will be described with reference to the drawings. Note that the present disclosure is not limited to these embodiments. In addition, in the description of the drawings, the same or corresponding elements are appropriately designated by the same reference numerals. The drawings are schematic, and the dimensional relationships and ratios of each element may differ from the actual. Even between drawings, there may be parts in which the dimensional relationships and ratios differ. When numerical values ​​are described in the following description, they are merely examples, and other numerical values ​​may be used in addition or instead.

[0010] 1 is a schematic plan view showing an example of the configuration of an arrayed waveguide grating (AWG) 100. As shown in Fig. 1, the AWG 100 includes a first slab waveguide 102, a second slab waveguide 104, and a waveguide array 106 that couples between these slab waveguides 102 and 104 via a plurality of waveguides arranged in an array.

[0011] Here, when the path length difference ΔL between the waveguides constituting the waveguide array 106 is reduced, adjacent waveguides may overlap. FIG. 2 shows a design example of an AWG 200 in which the path length difference ΔL of the waveguide array 206 is reduced. In FIG. 2, each of the waveguides constituting the waveguide array 206 consists of two straight waveguides and one curved waveguide located between these straight waveguides, as described in, for example, Non-Patent Document 3. Note that reference numerals 202 and 204 each indicate a slab waveguide. In the configuration of the AWG 200 illustrated in FIG. 2, the diffraction grating order is illustratively 6.

[0012] 2, on the inner periphery side of the curved portion of the waveguide array 106, gaps exist between the waveguides that make up the waveguide array 206, and a waveguide pattern is formed, as shown in the enlarged partial view indicated by the reference numeral 212. In contrast, on the outer periphery side of the curved portion of the waveguide array 206, as shown in the enlarged partial view indicated by the reference numeral 214 in FIG. 2, the multiple waveguides that make up the waveguide array 206 overlap, so the gaps between the waveguides are crushed and no waveguide pattern is formed.

[0013] As an example of a configuration that avoids overlap between adjacent waveguides when the path length difference ΔL between the waveguides that make up the waveguide array 106 is reduced, an S-shaped layout of the waveguide array 106 is considered. Note that a waveguide array laid out in an S-shape is sometimes referred to as an "S-type waveguide array" for convenience, and an AWG having an "S-type waveguide array" is sometimes referred to as an "S-type AWG."

[0014] 3 shows an example of the configuration of an S-shaped AWG 300 in which a waveguide array 306 is laid out in an S-shape to avoid overlapping between the waveguides. The AWG 300 includes a first slab waveguide 302, a second slab waveguide 304, and a waveguide array 306 that couples these slab waveguides 302 and 304 with a plurality of waveguides arranged in an array. In the configuration shown in FIG. 3, the order of the diffraction grating is illustratively 6, as in FIG. 2.

[0015] 3, the waveguide array 306 can be divided into a first block #1, a second block #2, and a third block #3. Note that "block" may be read as "section."

[0016] If the path length difference in the first block #1 is ΔL, then by setting the path length difference in the third block #3 to −ΔL, the path length difference in the first block #1 can be canceled by the path length difference in the third block #3. Thus, the path lengths of the first block #1 and the third block #3 are equalized.

[0017] A desired path length difference (e.g., target path length difference) ΔL′ may be set for the second block, although the path length difference in the second block may be adjusted by slightly varying the path length difference between the first block and the third block.

[0018] In this case, the first block #1 having a path length difference of ΔL and the third block #3 having a path length difference of −ΔL exist to prevent overlapping of the waveguides and do not contribute to the function of the AWG 300. Therefore, the first block #1 and the third block #3 are redundant sections or paths, and as a result, the size of the AWG 300 may increase.

[0019] Furthermore, in an optical wavelength multiplexing / demultiplexing circuit in which an AWG can be used, narrowing the guard band width, which determines the multiplexing / demultiplexing performance, can have a significant impact on the performance of optical communications. Fig. 4 shows an example of the configuration of an optical wavelength demultiplexer 400 that can achieve narrowing of the guard band width.

[0020] The optical wavelength demultiplexer 400 shown in Fig. 4 has an AWG tandem configuration in which a first AWG 402 and a second AWG 404 are cascaded together by an optical coupling circuit 406 in which the path lengths are equalized for each wavelength (channel). M (M is an integer of 2 or more) is branched to any of ports A, B, and C.

[0021] In the optical wavelength demultiplexer 400 with an AWG tandem configuration, the first AWG 402 samples wavelengths at narrow intervals with high resolution, and by adjusting the input position of the light to the second AWG 404, it is possible to transmit a desired wavelength to any output port.

[0022] Therefore, the optical wavelength demultiplexer 400 using the AWG tandem configuration can realize transmission spectrum characteristics with a narrower guard band width by increasing the rectangularity (which may also be referred to as the sharp cut level) in the wavelength range. Note that, based on the principle of reverse light propagation, the optical wavelength demultiplexer 400 with the AWG tandem configuration can also function as an optical wavelength multiplexer.

[0023] Because the bandwidth and / or resolution of an AWG may be limited by the expected size (e.g., chip size) of the optical device incorporating the AWG, the performance of an AWG tandem configuration may similarly be limited by the expected chip size.

[0024] Therefore, in the embodiments described below, an AWG configuration that can reduce (e.g., minimize) the waveguide array area that can increase with increasing bandwidth and / or resolution of the AWG is illustrated, and an optical device (e.g., an optical wavelength multiplexing / demultiplexing circuit) that can achieve a wider bandwidth and a narrower guard band width by using such an AWG tandem configuration is also illustrated.

[0025] 5 is a schematic diagram of an arrayed waveguide grating (AWG) 500 according to a first embodiment. The AWG 500 shown in FIG. 5 exemplarily includes a first slab waveguide 502, a second slab waveguide 504, and a waveguide array 506 that couples between the slab waveguides 502 and 504 by a plurality of waveguides arranged in an array.

[0026] 5, the subscript i indicates a waveguide number when the number of waveguides constituting the waveguide array 506 is expressed as an integer N. The waveguide array 506 can be divided into, for example, three sections in the X-axis direction: a left (L) section, a center (C) section, and a right (R) section. The path length differences between the sections may be non-uniform.

[0027] In FIG. 5, d represents the waveguide spacing that satisfies the condition that light waves propagating through individual waveguides in the waveguide array 506 are not coupled with adjacent waveguides, and is derived, for example, based on the refractive index of the waveguide material and process conditions.

[0028] In the AWG 500 of this embodiment, the area of ​​the waveguide array 506 in a plane defined by the X-axis and Y-axis is defined as an evaluation index A by the following formula 1. The X-axis and Y-axis may correspond to axes in directions that define the size, in a planar view, of a substrate (not shown) on which the AWG 500 is configured.

[0029] The parameters (or variables) in Equation 1 can be expressed by the following Equations 2 to 6 using various structural parameters related to the length, curvature radius, and bending angle of the waveguide array 506, as shown in FIG. 5.

[0030] Y1 represents the distance (height) on the Y axis of the shortest path, and D i is the radius of curvature (R Ci ) represents the spacing (distance) between adjacent waveguides at the center. Table 1 below shows the definitions of the other structural parameters.

[0031]

[0032] Here, as shown in Table 1, the individual waveguides constituting the waveguide array 506 include straight waveguides (straight sections) and curved waveguides (curved sections), and when the layout of the waveguide array 506 is divided into nine sections, they can be classified into four straight sections and five curved sections.

[0033] For example, the four straight sections are Li , l Ri and two l Ci The curved portions of the five sections are defined by r Li , r Ci (Boundary side between the left section and the center section), R Ci , r Ci (the boundary between the central section and the right section), and r Ri The intervals are defined by

[0034] Of the five curved sections, the radius of curvature r of the curved waveguide in the left section Li and the radius of curvature r of the curved waveguide on the boundary side between the left section and the central section. Ci The curved portions defined by and have opposite directions of change in the bending angle.

[0035] Therefore, the curved portion has a radius of curvature r Li Bent waveguide and curvature radius r Ci Similarly, a bent waveguide with a radius of curvature r Ri The right section has a curved waveguide with a radius of curvature r Ci and the bent waveguide, where , forms another S-shaped waveguide.

[0036] Therefore, the evaluation index A expressed by the above-mentioned Equation 1 may be understood as an example of a function including structural parameters that define each of the multiple straight sections in the waveguide array 506, and structural parameters that define each of the multiple curved sections, including the S-shaped curved section.

[0037] The use of S-shaped waveguides in the waveguide array 506 reduces the path length difference ΔL, thereby enabling a smaller area for the waveguide array 506. This is because the left and right sections on either side of the central section are arranged so as to cancel each other's path length difference (however, they do not need to be of equal length), and therefore the first slab waveguide 502 and the second slab waveguide 504 are arranged to face each other linearly with an axial and angular offset.

[0038] The effect remains the same even if a straight waveguide is inserted between the two curved waveguides that make up the S-shaped waveguide. Furthermore, some or all of the straight waveguides that make up the straight section (for example, four sections) may be replaced with one or more curved waveguides that are bent at a small angle with a large radius of curvature.

[0039] When the waveguide array 506 is divided into a total of nine sections, including four straight sections and five curved sections, it is possible to reduce (smaller) the area of ​​the waveguide array 506. Note that the waveguide array 506 may be divided into more than nine sections, but the area reduction effect remains the same.

[0040] Here, the reason for dividing the waveguide array 506 into four straight sections and five curved sections will be explained. The AWG 500 of this embodiment has the following four exemplary requirements (a) to (d):

[0041] (a) The path length difference ΔL between adjacent waveguides in the waveguide array 506 is constant. (b) In order to reduce phase errors due to interactions between adjacent waveguides in the waveguide array 506, the waveguide spacing at both ends of the central section is d or more (since "wider spacing = wider area," a constant d is a condition for reducing the area). (c) The path of the waveguide array 506 is connected between the first slab waveguide 502 and the second slab waveguide 504 in a continuous and sharply bent state on the XY plane of Euclidean space (the radius of curvature Rx is equal to or greater than the allowable minimum value Rmin). (d) The XY coordinates {(Xi = X Li +X Ci +X Ri ), Yi}

[0042] Therefore, the predefined conditions are a total of nine conditions: ΔL, d, Rmin, the connection point (Xji, Yji) between the jth (j=1 or 2) slab waveguides 502, 504 and the waveguide array 506, and the connection angle θji.

[0043] The degrees of freedom required to derive a path that satisfies these nine conditions are also nine, but if there is collinearity between multiple variables, the degrees of freedom can be reduced accordingly (obviously).

[0044] The structural parameters shown in Table 1 are Li , r Li , θ Li , l Ci , r Ci , θ Ci , l Ri , r Ri , θ Ri There are a total of nine variables. Although a small area design is possible if the same number of variables are prepared, in order to simplify the path design method, a combination of a "four section" straight waveguide and a "five section" curved waveguide as a combination of length l, radius of curvature r, and bending angle θ is used as an example of structural parameters for deriving a small area configuration for the waveguide array 506. X Li , X Ci , X Ri The procedure for each of these is simple: analytically define the initial values ​​and derive nine variables suitable for each of the defined initial values.

[0045] The radius of curvature is R Ci The bent waveguide at the center of the central section, R, is inserted to adjust the relative position between the first slab waveguide 502 and the second slab waveguide 504, and is not treated as a variable in this embodiment. Ci is the radius of curvature r Ci In many cases, the central section is collinear with the curved waveguides at both ends, and in this embodiment, R Ci and Ci In this case, R Ci may be defined as a fixed constant in advance, or may be analytically derived using Equation 3.

[0046] The structural parameters of the waveguide array 506 can be analytically derived by deriving the change in the evaluation index A with respect to the change in the structural parameters of the waveguide array 506 in FIG. 5 , including the waveguide spacing d, to find the gradient, and then optimizing the structural parameters so as to decrease the gradient.

[0047] In other words, the gradient method can be used to derive a solution for the structural parameters of the waveguide array 506 that approaches a direction that minimizes the area of ​​the waveguide array 506 (index A related to the area). Fig. 6 shows an example of how the evaluation index A changes with respect to changes in the structural parameters (d and Xc) (other structural parameters are fixed). Note that, as the "gradient method," for example, the "steepest descent method" or the "stochastic gradient descent method" may be applied.

[0048] Furthermore, the lengths of the first slab waveguide 502 and the second slab waveguide 504 in the light propagation direction (hereinafter also referred to as "slab lengths") can be made different from each other, in other words, the ratio of the slab lengths can be changed from 1, thereby adjusting the spot size of the light waves.

[0049] For example, since the spot size of the light wave received in the optical coupling circuit 406 connecting the first AWG 402 and the second AWG 404 as shown in FIG. 4 can be enlarged, a flat transmission spectrum with reduced ripples can be realized.

[0050] Furthermore, by changing the slab length ratio from 1, the waveguide array 506 can be laid out in an XY plane in which light propagates through the waveguide, without line symmetry with respect to a line dividing the AWG 500 at any position, and without point symmetry with respect to any coordinate within the AWG 500.

[0051] For example, when the ratio of the slab lengths is changed from 1, the connection angle θ between the jth (j=1 or 2) slab waveguide 502 or 504 and each of the waveguides constituting the waveguide array 506 ji However, the waveguides other than the central waveguide have different left and right symmetry in the X-axis direction. As a result, the waveguide array 506 has a layout that does not have the above-mentioned line symmetry and point symmetry.

[0052] On the other hand, in a waveguide array configuration with a small ΔL such that the diffraction order is less than 8, unless the left section and the right section are arranged so as to cancel the path length difference (for example, asymmetric arrangement), the expansion of the waveguide spacing d is restricted, and as described with reference to FIG. 2 , there is a risk that the gap between the waveguides will be crushed and a waveguide pattern will not be formed.

[0053] <Comparative Example> Fig. 7(A) is a schematic diagram showing a configuration example of an AWG 500 including a waveguide array 506 whose layout is defined by structural parameters derived based on evaluation index A. Fig. 7(B) is a schematic diagram showing a configuration example of an AWG 300 in which the waveguide array 306 is laid out in an S-shape, similar to Fig. 3, as a comparative example to Fig. 7(A).

[0054] In Figures 7(A) and 7(B), it is assumed that the order of the diffraction grating is 6, the number of waveguides in the waveguide array is 500, and the length ratio between the first slab waveguide 502 / 302 and the second slab waveguide 504 / 304 is 2.

[0055] As shown in FIG. 8, it was confirmed that the area of ​​the waveguide array 506 in the configuration of the AWG 500 illustrated in FIG. 7(A) can be reduced by about 58% compared to the configuration of the AWG 300 illustrated in FIG. 7(B).

[0056] Therefore, it is possible to reduce (e.g., minimize) the waveguide array area, which may increase as the bandwidth and / or resolution of the AWG 500 increases, which may in turn contribute to reducing the size of optical devices such as AWGs that include the waveguide array 506.

[0057] <Design Example> The following Table 2 shows a design example of structural parameters for waveguide numbers i=1 and 2, assuming that the length ratio between the first slab waveguide 502 and the second slab waveguide 504 of the AWG 500 is 2, the number of waveguides in the waveguide array 506 is 500, the waveguide spacing is 10 μm, and the path length difference ΔL of the waveguide array 506 is 10 μm.

[0058]

[0059] From Table 2, it can be seen that the desired path length difference ΔL can be achieved by slightly changing the structural parameters.

[0060] <Regarding the Termination Shape of Slab Waveguide> In the first embodiment described above, the shape in the XY plane of one or both of the two terminations of each of the slab waveguides 502 and 504 may be linear as illustrated in FIG. 5 rather than arc-shaped.

[0061] According to Huygens' principle, light waves incident on a slab waveguide spread concentrically within the slab waveguide. Therefore, the connection loss between the slab waveguide and the waveguide array can usually be reduced by making the end of the slab waveguide (for example, the connection part with the waveguide array) arc-shaped.

[0062] Forming the termination shape of the slab waveguide into an arc shape also aligns the phase when light transitions from the slab waveguide to the waveguide array, which has the effect of reducing loss or crosstalk caused by phase errors in the AWG.

[0063] On the other hand, if the end of the slab waveguide is linear, the above-mentioned characteristics may be degraded, but a plane wave can be generated at the end of the slab waveguide, which eliminates the need for a collimating lens or the like when extracting light waves propagated through the slab waveguide into free space.

[0064] In the above-described AWG 500, the creation of plane waves at the ends of the slab waveguides 502 and 504 can be achieved, for example, by making the path length difference ΔL between the waveguides constituting the waveguide array 506 non-uniform and finely adjusting the phase.

[0065] For example, the number of the waveguide in the waveguide array 506 is represented by i, and the difference in Euclidean distance between the case where the end shape is linear and the case where the end shape is arc is represented by df i , the effective refractive index of the slab waveguides 502 and 504 is n s , the wave number in vacuum is k o When the initial phase error of the adjacent waveguides is expressed as s k o df iThe phase advance is expressed as:

[0066] Therefore, the effective refractive index of the waveguide array 506 is n arr When expressed as i = ΔL + (n s / n arr ) df i By changing the conditions, the end shapes of the slab waveguides 502 and 504 can be formed linearly to generate a plane wave. Therefore, the AWG 500 can be effectively applied to a configuration using a spatial light modulator (SLM), which will be described later with reference to FIG. 10.

[0067] Second Embodiment Fig. 9 is a schematic diagram showing an example of the configuration of an optical wavelength multiplexing / demultiplexing circuit 900 according to a second embodiment. The optical wavelength multiplexing / demultiplexing circuit 900 shown in Fig. 9 illustratively includes a first AWG 902, a second AWG 904, and an optical coupling circuit 906 that tandemly couples these AWGs 902 and 904. Each of the AWGs 902 and 904 corresponds to the AWG 500 exemplified in the first embodiment, and the layout of the waveguide array 506 is designed using structural parameters derived based on the evaluation index A.

[0068] Since each of the AWGs 902 and 904 has the layout of the waveguide array 506 with a reduced area as described in the first embodiment, the area occupied by the AWGs 902 and 904 is reduced. Therefore, the optical wavelength multiplexing / demultiplexing circuit 900 according to the second embodiment can realize an optical wavelength filter with higher performance (for example, capable of widening the bandwidth and narrowing the guard band width) within a limited chip size. It is also possible to reduce the chip size of an optical wavelength filter with the same level of performance as existing technology.

[0069] Third Embodiment Fig. 10 is a schematic diagram showing an example of the configuration of a wavelength selective switch 1000 according to a third embodiment. The wavelength selective switch 1000 shown in Fig. 10 is illustratively a 1xn wavelength selective switch and may include n+1 (n is an integer equal to or greater than 2) AWGs 1002-1 to 1002-(n+1), a focusing unit 1004, and a spatial light modulator (SLM) 1006. The upper limit of n may be, for example, n = 32, but may also be n < 32 or n > 32. An example of the configuration of a wavelength selective switch is also described in Non-Patent Document 4. When the AWGs 1002-1 to 1002-(n+1) are not to be distinguished, they will be referred to as AWG 1002.

[0070] For example, a lens or a metamaterial may be used for the light-collecting unit 1004. For example, a liquid crystal or semiconductor refractive index modulation device may be used for the SLM 1006. Each of the AWGs 1002 corresponds to the AWG 500 exemplified in the first embodiment, and the layout of the waveguide array 506 is designed based on structural parameters derived on the basis of the evaluation index A.

[0071] The n+1 AWGs 1002 may be, for example, n+1 AWG chips having a single waveguide array pattern, or may be configured such that AWGs with n+1 patterns are arranged side by side on a single chip.

[0072] Each of the AWGs 1002 has K ports (K is an integer of 2 or more) and has the function of dispersing light into K wavelengths, and the light is collected for each wavelength onto the SLM 1006 via the collecting unit 1004. Note that the number of ports K may be, for example, a value obtained by dividing the transmission bandwidth (F) by the channel frequency interval (f: minimum 6.25 GHz), but is not limited to this value and may be a value optimized for a specific application.

[0073] The diameter of the focused spot in the SLM 1006 can be adjusted by the ratio of the slab lengths of the first slab waveguide 502 and the second slab waveguide 504 in the AWG 1002. Light output from the AWG 1002 on the optical input side to the focusing unit 1004 is subjected to phase modulation by the SLM 1006 for each focused spot of each wavelength, and is thereby focused onto ports of each wavelength in M ​​AWGs 1002 different from the AWG 1002 on the optical input side. This operation realizes the function of a wavelength selective switch.

[0074] The wavelength resolution of the wavelength selective switch 1000 can be determined by the diameter of the focused spot in the SLM 1006 (in other words, the ratio of the slab lengths of the first slab waveguide 502 and the second slab waveguide 504 in the AWG 1002).

[0075] <Terminology> In the above-described embodiments, any reference to elements followed by designations such as "first..." or "second..." does not limit the quantity or order of those elements. These designations are merely used as a convenient way to distinguish between two or more elements. For example, references to first and second elements do not mean that only two elements can be employed, nor do they mean that the first element must take precedence over the second element in any physical quantity.

[0076] Although the present disclosure has been described in detail above, it is clear to those skilled in the art that the spirit and scope of the present disclosure are not limited to the contents described throughout the present disclosure. The present disclosure can be implemented in modified and altered forms without departing from the spirit and scope of the present disclosure as defined by the claims. Therefore, the description of the present disclosure is intended for illustrative purposes only and does not have any limiting meaning on the spirit and scope of the present disclosure.

[0077] According to the present disclosure, for example, it is possible to provide an AWG having a waveguide array with a reduced size compared to existing configurations, which is useful for optical devices using an AWG.

[0078] 500, 902, 904, 1002-1 to 1002-(n+1) AWG 502, 504 Slab waveguide 506 Waveguide array 900 Optical wavelength multiplexing / demultiplexing circuit 1000 Wavelength selection switch 1004 Light collecting section 1006 Spatial light modulator (SLM)

Claims

1. An arrayed waveguide grating comprising: a first slab waveguide; a second slab waveguide; and a waveguide array having a plurality of waveguides coupling between the first slab waveguide and the second slab waveguide, wherein in the waveguide array, at least one of the plurality of waveguides has a plurality of straight sections and a plurality of curved sections, and at least one of the plurality of curved sections has an S-shape.

2. The arrayed waveguide diffraction grating according to claim 1, wherein the waveguide array has a layout determined based on an index correlated with the area of ​​the waveguide array, the index being expressed by a function including structural parameters defining each of the plurality of straight line sections and structural parameters defining each of the plurality of curved sections including the S-shaped curved section, and the layout is determined by a combination of structural parameters corresponding to a solution of the function that approaches the direction that minimizes the area.

3. An arrayed waveguide grating according to claim 1 or 2, wherein the length of said first slab waveguide is different from the length of said second slab waveguide.

4. The arrayed waveguide grating according to claim 1 or 2, wherein the termination shapes of the first slab waveguide and the second slab waveguide are linear.

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