Two-dimensional grating coupler and method for manufacturing the same

By using an asymmetric triangular tapered structure in a two-dimensional grating coupler to connect the grating region to the waveguide, the problem of large optical loss in the coupling between the waveguide and the optical fiber is solved, and efficient optical coupling and simplified design are achieved.

CN114815054BActive Publication Date: 2025-10-03TAIWAN SEMICONDUCTOR MANUFACTURING CO LTD
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Patent Information

Application Number
CN202110599643.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Priority Date
2021-04-01
Filing Date
2021-05-31
Publication Date
2025-10-03
Estimated Expiration
2041-05-31

AI Technical Summary

Technical Problem

In the existing technology, direct coupling between waveguide and optical fiber leads to huge light loss, and the design of conventional 2D grating couplers is complex, consuming a lot of hardware resources and simulation time.

Method used

A two-dimensional grating coupler designed with an asymmetric triangular tapered structure is proposed. By forming asymmetric first and second triangular tapered structures in a planar layer, the grating region is connected to the corresponding waveguide, and the tapered shape and size are optimized to minimize optical power loss.

Benefits of technology

It effectively reduces optical power loss, improves optical coupling efficiency, simplifies the design process, and saves hardware resources and simulation time.

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Abstract

Disclosed are an apparatus and method for optical coupling. In one example, the apparatus includes: a planar layer; a grating region comprising an array of scattering elements arranged in the planar layer to form a two-dimensional grating; a first tapered structure formed in the planar layer to connect a first side of the grating region to a first waveguide, wherein the first tapered structure has a shape of a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region in the planar layer; and a second tapered structure formed in the planar layer to connect a second side of the grating region to a second waveguide, wherein the second tapered structure has a shape of a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region in the planar layer, wherein the first side and the second side are substantially perpendicular to each other.
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Description

Technical Field

[0001] Embodiments of the present invention relate to a two-dimensional grating coupler and a method for manufacturing the same. Background Art

[0002] Optical gratings are commonly used to couple light between waveguides and optical fibers. Due to the significant difference in the dimensions of the waveguide and optical fiber, direct coupling results in significant optical losses. The incident light coupled into the waveguide is typically in an unknown and arbitrary polarization state. Therefore, a two-dimensional (2D) grating coupler is required to deliver polarized light in the transverse magnetic (TM) or transverse electric (TE) polarization mode from the optical fiber to the waveguide.

[0003] Conventional 2D grating couplers consist of two symmetrical tapered structures coupled to a 2D grating. To reduce power loss and improve the coupling efficiency of conventional 2D grating couplers, complex 2D grating designs have been proposed to find the appropriate output field to match the given tapered design of the 2D grating coupler, which consumes a lot of hardware resources and simulation time.

[0004] Therefore, it is necessary to develop a method and apparatus for efficient optical coupling using a novel tapered design. Summary of the Invention

[0005] An embodiment of the present invention provides a device for optical coupling, comprising: a planar layer; a grating region, comprising an array of scattering elements arranged in the planar layer to form a two-dimensional (2D) grating; a first conical structure formed in the planar layer to connect a first side of the grating region to a first waveguide, wherein the shape of the first conical structure is a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region in the planar layer; and a second conical structure formed in the planar layer to connect a second side of the grating region to a second waveguide, wherein the shape of the second conical structure is a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region in the planar layer, wherein the first side and the second side are substantially perpendicular to each other.

[0006] An embodiment of the present invention provides a two-dimensional (2D) grating coupler, comprising: a planar layer; a grating region comprising an array of scattering elements arranged in the planar layer to form a two-dimensional grating; a first tapered structure located in the planar layer to connect a first side of the grating region to a first waveguide; and a second tapered structure located in the planar layer to connect a second side of the grating region to a second waveguide, wherein each of the first tapered structure and the second tapered structure has a shape and size that minimizes optical power loss due to light transmission and light reflection relative to the two-dimensional grating.

[0007] An embodiment of the present invention provides a method for forming an optical coupler, comprising: forming an insulating layer on a semiconductor substrate; epitaxially growing a semiconductor material on the insulating layer to form a semiconductor layer; etching the semiconductor layer according to a predetermined pattern to form: an array of etched holes in the semiconductor layer to form a grating region, a first conical structure extending from a first side of the grating region, wherein the shape of the first conical structure in the semiconductor layer is a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region, and a second conical structure extending from a second side of the grating region, wherein the shape of the second conical structure in the semiconductor layer is a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region, wherein the first side and the second side are substantially perpendicular to each other; and depositing a dielectric material into the array of etched regions to form an array of scattering elements in the semiconductor layer, wherein the scattering elements are arranged to form a two-dimensional (2D) grating. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Aspects of the present disclosure are best understood from the following detailed description when read in conjunction with the accompanying drawings. It should be noted that the various features are not necessarily drawn to scale. In fact, the size and geometry of the various features may be arbitrarily increased or decreased for clarity of illustration.

[0009] Figure 1 An exemplary block diagram of a device according to some embodiments of the present disclosure is shown.

[0010] Figure 2A A top view of an exemplary two-dimensional (2D) grating coupler is shown according to some embodiments of the present disclosure.

[0011] Figure 2B An exemplary grating region comprising an array of scattering elements in a 2D grating coupler is shown according to some embodiments of the present disclosure.

[0012] Figure 2C An exemplary optical fiber is shown coupled to a 2D grating coupler at an incident angle according to some embodiments of the present disclosure.

[0013] Figure 3A An exemplary diagram showing a 2D grating coupler with designed tapered shape and dimensions according to some embodiments of the present disclosure.

[0014] Figure 3B An exemplary diagram showing another 2D grating coupler with designed tapered shape and dimensions according to some embodiments of the present disclosure.

[0015] Figure 4A A perspective view illustrating a 2D grating coupler according to some embodiments of the present disclosure is shown.

[0016] Figure 4BA cross-sectional view of a 2D grating coupler according to some embodiments of the present disclosure is shown.

[0017] Figures 5A to 5K Cross-sectional views of an exemplary grating coupler are shown at various stages of the fabrication process according to some embodiments of the present disclosure.

[0018] Figure 6 A flow chart illustrating an exemplary method for fabricating an exemplary 2D grating coupler according to some embodiments of the present disclosure is shown.

[0019] Figure 7A Exemplary optical power performance of a 2D grating coupler with different input light wavelengths according to some embodiments of the present disclosure is shown.

[0020] Figure 7B A magnified view showing an exemplary selected wavelength range of input light to a 2D grating coupler according to some embodiments of the present disclosure.

[0021] Figure 8 A flow chart illustrating an exemplary method for designing an exemplary 2D grating coupler according to some embodiments of the present disclosure is shown. DETAILED DESCRIPTION

[0022] The following disclosure describes various exemplary embodiments for implementing different features of the subject matter. Specific examples of components and arrangements are described below to simplify the disclosure. Of course, these components and arrangements are merely examples and are not intended to be limiting. For example, it should be understood that when an element is referred to as being "connected to" or "coupled to" another element, it can be directly connected to or coupled to the other element, or one or more intervening elements can be present.

[0023] A waveguide surrounded by a cladding can confine light based on the refractive index contrast between the waveguide and the materials in the cladding. For example, a silicon waveguide with submicron dimensions can confine infrared light (having wavelengths greater than approximately 700 nm or 700 nm) due to its strong refractive index contrast with the silicon oxide cladding, where the refractive indices of silicon and silicon oxide are approximately 3.47 and 1.45, respectively. To receive or transmit an optical signal, the light needs to be coupled between the waveguide and the optical fiber. While the outgoing light from the silicon waveguide is typically in the transverse electric (TE) mode and can be vertically coupled to the optical fiber using a single polarization grating coupler, the incident light to the silicon waveguide is typically in an unknown and arbitrary polarization state, so a polarization splitting grating coupler (PSGC) is required to provide polarized light in the transverse magnetic (TM) or transverse electric (TE) polarization mode from the optical fiber to the waveguide. In one embodiment, the PSGC can be a two-dimensional (2D) grating coupler formed by two single polarization grating couplers that are nearly perpendicular to each other. Each single-polarization grating coupler has a tapered structure coupled to a common 2D grating region, which contains grating lines with scattering elements at the intersections of the grating lines. Different designs of the tapered structure can reduce power loss and improve the efficiency of light coupling from the optical fiber to the 2D grating coupler.

[0024] In one embodiment, beam propagation is simulated as input light to a 2D grating coupler based on a plane wave expansion method. Based on the simulated beam propagation, a wavelength range of the input light is determined to minimize optical power loss due to light transmission and reflection relative to the 2D grating. Within this wavelength range, the shape and size of the tapered structures of the 2D grating coupler are adjusted to fit the output light from the 2D grating. For example, increasing values ​​of the length and displacement of each tapered structure are simulated to determine the optimal tapered design that minimizes optical power loss.

[0025] In one embodiment, the two cones of a 2D grating coupler are shaped like two congruent triangles that are symmetrical about a diagonal line spanning the grating region. However, the triangles are not isosceles and have a shift in the perpendicular bisector from the vertex to the base side opposite the vertex. The length and shift of each triangle can be determined based on the position of the optical fiber coupled to the 2D grating and / or the angle of incidence of the incident light from the optical fiber.

[0026] Figure 1 FIG1 shows an exemplary block diagram of a device 100 according to some embodiments of the present disclosure. It should be noted that the device 100 is merely an example and is not intended to limit the present disclosure. Therefore, it should be understood that additional functional blocks may be provided in the Figure 1 The device 100 is coupled to Figure 1 The device 100 is shown in FIG. 1 , and some other functional blocks may only be briefly described herein.

[0027] refer to Figure 1 Device 100 includes an electronic die 102, a light source die 104, a photonic die 106, an interposer 110, and a printed circuit board (PCB) substrate 114. The electronic die 102, the light source die 104, and the photonic die 106 are coupled together via input / output interfaces (not shown) on the interposer 110. In some embodiments, the interposer 110 is fabricated using silicon. In some embodiments, the interposer 110 includes at least one of interconnect wiring, through silicon vias (TSVs), and contact pads. In some embodiments, the interposer 110 integrates all components including the electronic die 102, the light source die 104, and the photonic die 106. In certain embodiments, each of the dies 102 / 104 / 106 is coupled to the interposer 110 using a flip-chip (C4) interconnection method. In some embodiments, the dies 102 / 104 / 106 are coupled to the interposer 110 using high-density solder microbumps. Furthermore, the interposer 110 is coupled to a PCB substrate 114 using solder balls through wire bonds 112 or through silicon vias (TSVs) 116. The TSVs 116 may comprise conductive paths that extend vertically through the interposer 110 and provide electrical connectivity between the electronic die 102 and the PCB 114. In some embodiments, the PCB substrate 114 may comprise a support structure for the device 100 and may include insulating and conductive materials for isolating the devices, as well as providing electrical contact to the active devices on the photonic die 106 and the circuits / devices on the electronic die 102 via the interposer 110. Furthermore, the PCB substrate 114 may provide a thermally conductive path to carry away heat generated by the devices and circuits in the electronic die 102 and the light source die 104.

[0028] In some embodiments, the electronic die 102 includes circuitry (not shown) including amplifiers, control circuitry, digital processing circuitry, and driver circuitry for controlling components in the light source die 104 or photonic die 106. In some embodiments, the light source die 104 includes multiple components (not shown), such as at least one light-emitting element (e.g., a laser or light-emitting diode), a transmission element, a modulation element, a signal processing element, a switching circuit, an amplifier, an input / output coupler, and light sensing / detection circuitry. In some embodiments, the light source die 104 is on the photonic die 106. In some embodiments, the photonic die 106 includes an optical fiber array 108 attached thereto, an optical interface, and a plurality of fiber-to-chip grating couplers 118. In some embodiments, the plurality of fiber-to-chip grating couplers 118 are configured to couple the photonic die 106 to the optical fiber array 108. In some embodiments, the optical fiber array 108 includes a plurality of optical fibers, each of which can be single-mode or multimode. In some embodiments, the optical fiber array 108 may be epoxied on the photonic die 106 .

[0029] In some embodiments, each of the plurality of fiber-to-chip grating couplers 118 is capable of coupling an optical signal between the optical fiber array 108 and a corresponding photodetector on the light source die 102 or the photonic die 106. Each of the plurality of fiber-to-chip grating couplers 118 includes a plurality of gratings and a waveguide designed to improve coupling efficiency between optical fibers on the corresponding waveguide, as will be discussed in detail in various embodiments disclosed below.

[0030] During operation, optical signals received from a remote server attached to one end of the optical fiber array 108 can be coupled to corresponding photodetectors on the photonic die 106 via a fiber-to-chip grating coupler 118 attached to the other end of the optical fiber array 108. Alternatively, optical signals received from the light source die 104 can be coupled to the optical fiber array 108 via the fiber-to-chip grating coupler 118 for further transmission to the remote server. In one embodiment, the fiber-to-chip grating coupler 118 can be a two-dimensional (2D) grating coupler.

[0031] Figure 2A 1 shows a top view of an exemplary 2D grating coupler 200 according to some embodiments of the present disclosure. Figure 2AAs shown in FIG, a 2D grating coupler 200 is formed by two single-polarization grating couplers that are nearly perpendicular to each other. Each single-polarization grating coupler has a corresponding tapered structure and a shared grating region 230. The first single-polarization grating coupler includes a first tapered structure 210 and a shared grating region 230; and the second single-polarization grating coupler includes a second tapered structure 220 and a shared grating region 230. The grating region 230 includes an array of scattering elements 232 (also referred to as a scattering element array) arranged in a planar layer to form a 2D grating.

[0032] In one embodiment, the first tapered structure 210, the second tapered structure 220, and the shared grating region 230 are all formed in a planar layer, which may be a semiconductor layer, such as a silicon layer on a silicon-on-insulator (SOI) substrate. In one embodiment, the first tapered structure 210 is formed in the planar layer to connect the first side 212 of the 2D grating 230 to the first waveguide 218 in the planar layer, and the second tapered structure 220 is formed in the planar layer to connect the second side 222 of the 2D grating 230 to the second waveguide 228 in the planar layer. The first side 212 and the second side 222 are substantially perpendicular to each other.

[0033] Figure 2B FIG. 2 shows an enlarged view of an exemplary grating region 230 including an array of scattering elements 232 in a 2D grating coupler according to some embodiments of the present disclosure. Figure 2B As shown in FIG, the shape of the grating region 230 can be square in the planar layer. In one embodiment, the array of scattering elements is arranged in the planar layer at a plurality of intersections where the first set of straight lines 216 and the second set of straight lines 226 intersect. Each of the first set of straight lines 216 is parallel to the first side 212 of the grating region 230; and each of the second set of straight lines 226 is parallel to the second side 222 of the grating region 230. Any number of straight lines 216, straight lines 226, and any number of scattering elements 232 on each straight line can be used and is within the scope of the present disclosure. Figure 2A and Figure 2B As shown in FIG, each scattering element 232 in the scattering element array has the same circular shape with the same size in the plane layer. In another embodiment, each scattering element in the scattering element array has the same square shape with the same size in the plane layer. Figure 2A and Figure 2B As shown in the figure, the array of scattering elements 232 is uniformly distributed in the planar layer so that the centers of each two adjacent scattering elements 232 have the same distance along the first direction (X direction) perpendicular to the first side 212 of the grating region 230 or the second direction (Y direction) perpendicular to the second side 222 of the grating region 230.

[0034] Return Reference Figure 2AThe 2D grating coupler 200 may scatter incident light received from the first waveguide 218 in a direction perpendicular to the first side 212 along the -X direction; and may also scatter incident light received from the second waveguide 228 in a direction perpendicular to the second side 222 along the -Y direction.

[0035] In one embodiment, the 2D grating coupler 200 scatters incident light received from an optical fiber having a fiber pattern 250 attached to the 2D grating. In one embodiment, the 2D grating 230 of the coupler 200 is configured to receive incident light from an optical fiber 290 at an incident angle 292, such as Figure 2C . The incident angle 292 is measured in the incident plane between the axis of the optical fiber 290 and the Z direction (the direction perpendicular to the planar layer). The incident plane is the plane containing the surface normal of the planar layer and the propagation vector of the incident light. That is, the incident plane is the plane formed by the Z direction and the X direction. In one embodiment, the incident angle 292 is non-zero. Both the optical fiber 290 and the 2D grating coupler 200 can be attached to the photonic tube core on the substrate or included in the photonic tube core on the substrate. The 2D grating coupler 200 includes an array of scattering elements 232 on the photonic tube core for transmitting light between the photonic tube core and the optical fiber 290.

[0036] The 2D grating coupler 200 can be configured to separate incident light received from an optical fiber on top of a planar layer into a parallel polarization component and an orthogonal polarization component. In one embodiment, the 2D grating coupler 200 couples the parallel polarization component to a first waveguide 218 via a first tapered structure 210, and couples the orthogonal polarization component to a second waveguide 228 via a second tapered structure 220. Alternatively, the 2D grating coupler 200 can couple the orthogonal polarization component to the first waveguide 218 via the first tapered structure 210, and couple the parallel polarization component to the second waveguide 228 via the second tapered structure 220.

[0037] like Figure 2A As shown, the first tapered structure 210 has a first width that decreases from the first side 212 to the first waveguide 218, and the second tapered structure 220 has a second width that decreases from the second side 222 to the second waveguide 228. In one embodiment, the first tapered structure 210 is configured to transmit a first portion of incident light from the optical fiber to the first waveguide 218 to achieve minimal insertion loss, and the second tapered structure 220 is configured to transmit a second portion of the incident light to the second waveguide 228 to achieve minimal insertion loss. The first portion of the incident light is substantially a parallel polarization component of the incident light, and the second portion of the incident light is substantially an orthogonal polarization component of the incident light. Each of the parallel polarization component and the orthogonal polarization component includes polarized light separated from the incident light. The polarized light has a transverse magnetic (TM) polarization mode or a transverse electric (TE) polarization mode.

[0038] Figure 3A Some embodiments of the present disclosure may be implemented as Figure 2A FIG. 3 is an exemplary block diagram of a 2D grating coupler 300 - 1 of the 2D grating coupler 200 with a designed tapered shape and size. Figure 3A As shown in FIG, a 2D grating coupler 300-1 includes a grating region 230 in a planar layer, a first tapered structure 310-1 in a planar layer connecting a first side 212 of the grating region 230 to a first waveguide, and a second tapered structure 320-1 in a planar layer connecting a second side 222 of the grating region 230 to a second waveguide. In one embodiment, the grating region 230 has a square shape, and the first side 212 and the second side 222 are substantially perpendicular to each other.

[0039] exist Figure 3A In the illustrated example, the shape of the first tapered structure 310-1 is a first triangle that is asymmetric with respect to any line perpendicular to the first side 212 of the grating region 230 in the planar layer; and the shape of the second tapered structure 320-1 is a second triangle that is asymmetric with respect to any line perpendicular to the second side 222 of the grating region 230 in the planar layer. In one embodiment, the first triangle and the second triangle are congruent. While each of the first tapered structure 310-1 and the second tapered structure 320-1 can actually have a trapezoidal shape, the design of the triangular shape automatically determines the corresponding design of a trapezoid with a given width for the first and second waveguides. For example, once the shape and size of the first triangle 310-1 are determined, a corresponding trapezoid having a top side 318-1 with a given width w1 and three other sides located on the three sides of the first triangle 310-1 can be determined. Once the shape and size of the second triangle 320-1 are determined, a corresponding trapezoid having a top side 328-1 with a given width w2 and three other sides located on the three sides of the second triangle 320-1 can be determined. The width w1 can be determined based on the width of the first waveguide, and the width w2 can be determined based on the width of the second waveguide. Therefore, the remainder of this application will focus on the design of triangles rather than trapezoids.

[0040] like Figure 3A As shown in FIG, the first triangle has a first base side located on the first side 212 of the grating region 230, has a first vertex 313-1 opposite to the first base side 212, and has a first length L1 316-1 along the X direction; and the second triangle has a second base side located on the second side 222 of the grating region 230, has a second vertex 323-1 opposite to the second base side 222, and has a second length L2 326-1 along the Y direction. Figure 3AAs shown, the first vertex 313-1 has a first distance or first shift S1 315-1 to the perpendicular bisector 312-1 of the first substrate side 212 in the planar layer; and the second vertex 323-1 has a second distance or second shift S2 325-1 to the perpendicular bisector 322-1 of the second substrate side 222 in the planar layer.

[0041] In one embodiment, the first triangle and the second triangle are symmetrical to each other about the diagonal line 235 across the grating region 230. In this case, the first length L1 316-1 and the second length L2 326-1 are equal to each other; the first distance S1 315-1 and the second distance S2 325-1 are equal to each other.

[0042] According to various embodiments, the values ​​of the first length L1 316-1, the second length L2 326-1, the first distance S1 315-1, and the second distance S2 325-1 may be determined based on the angle of incidence and the position of the optical fiber relative to the 2D grating 230. According to various embodiments, each of the first length L1 316-1 and the second length L2 326-1 is between 20 microns and 500 microns; and each of the first distance S1 315-1 and the second distance S2 325-1 is between 0 microns and 20 microns. In some embodiments, each of the first length L1 316-1 and the second length L2 326-1 is between 100 microns and 150 microns; and each of the first distance S1 315-1 and the second distance S2 325-1 is between 0 microns and 10 microns. It is understood that once the first length L1 316-1, the second length L2 326-1, the first distance S1 315-1, and the second distance S2 325-1 are determined, the vertex angle a of the top vertex 313-1 and the vertex angle b of the top vertex 323-1 will also be automatically determined.

[0043] Figure 3B Some embodiments of the present disclosure may be implemented as Figure 2A FIG. 3 is an exemplary diagram of another 2D grating coupler 300-2 having a designed tapered shape and size of the 2D grating coupler 200. Figure 3B As shown in FIG. , a 2D grating coupler 300-2 includes a grating region 230 in a planar layer, a first tapered structure 310-2 in a planar layer connecting a first side 212 of the grating region 230 to a first waveguide, and a second tapered structure 320-2 in a planar layer connecting a second side 222 of the grating region 230 to a second waveguide. In one embodiment, the grating region 230 has a square shape, and the first side 212 and the second side 222 are substantially perpendicular to each other.

[0044] exist Figure 3BIn the illustrated example, the shape of the first tapered structure 310-2 is a first triangle that is asymmetric with respect to any line perpendicular to the first side 212 of the grating region 230 in the planar layer; and the shape of the second tapered structure 320-2 is a second triangle that is asymmetric with respect to any line perpendicular to the second side 222 of the grating region 230 in the planar layer. In one embodiment, the first triangle and the second triangle are congruent. While each of the first tapered structure 310-2 and the second tapered structure 320-2 can actually have a trapezoidal shape, the design of the triangular shape automatically determines the corresponding design of a trapezoid with a given width of the first and second waveguides. For example, once the shape and size of the first triangle 310-2 are determined, a corresponding trapezoid having a top side 318-2 with a given width w3 and three other sides located on the three sides of the first triangle 310-2 can be determined. Once the shape and size of the second triangle 320-2 are determined, a corresponding trapezoid having a top side 328-2 with a given width w4 and three other sides located on the three sides of the second triangle 320-2 can be determined. The width w3 can be determined based on the width of the first waveguide, and the width w4 can be determined based on the width of the second waveguide. Therefore, the remainder of this application will focus on the design of triangles rather than trapezoids.

[0045] like Figure 3B As shown in FIG, the first triangle has a first base side located on the first side 212 of the grating region 230, has a first vertex 313-2 opposite to the first base side 212, and has a first length L3 316-2 along the X direction; and the second triangle has a second base side located on the second side 222 of the grating region 230, has a second vertex 323-2 opposite to the second base side 222, and has a second length L4 326-2 along the Y direction. Figure 3B As shown, the first vertex 313-2 has a first distance or first shift S3 315-2 to the perpendicular bisector 312-2 of the first substrate side 212 in the planar layer; and the second vertex 323-2 has a second distance or second shift S4 325-2 to the perpendicular bisector 322-2 of the second substrate side 222 in the planar layer.

[0046] In one embodiment, the first triangle and the second triangle are symmetrical to each other about the diagonal line 235 across the grating region 230. In this case, the first length L3 316-2 and the second length L4 326-2 are equal to each other; the first distance S3 315-2 and the second distance S4 325-2 are equal to each other.

[0047] According to various embodiments, the values ​​of the first length L3 316-2, the second length L4 326-2, the first distance S3 315-2, and the second distance S4 325-2 may be determined based on the angle of incidence and the position of the optical fiber relative to the 2D grating 230. According to various embodiments, each of the first length L3 316-2 and the second length L4 326-2 is between 20 micrometers and 500 micrometers; and each of the first distance S3 315-2 and the second distance S4 325-2 is between 0 micrometers and 20 micrometers.

[0048] Although Figure 3A Vertex 313-1 in has a displacement S1 above perpendicular bisector 312-1 in the -Y direction, but Figure 3B The vertex 313-2 in has a displacement S3 below the perpendicular bisector 312-2 in the Y direction. Figure 3A Vertex 323-1 in has a shift S2 along the -X direction to the left of the perpendicular bisector 322-1, but Figure 3B The vertex 323-2 in FIG has a shift S4 to the right of the perpendicular bisector 322-2 along the X direction. The shift of the top vertex of each pyramidal triangle can be designed based on the position of the optical fiber coupled to the 2D grating and / or the incident angle of the incident light from the optical fiber.

[0049] Figure 4A 1 shows a perspective view of a 2D grating coupler 400 according to some embodiments of the present disclosure. Figure 4A As shown in FIG, 2D grating coupler 400 includes an array of scattering elements and two cones formed in a semiconductor layer 430. In one embodiment, each of scattering elements 431, 432, and 433 comprises a dielectric material such as silicon oxide, while semiconductor layer 430 comprises a semiconductor material such as silicon. In the illustrated embodiment, semiconductor layer 430 is fabricated on an insulating layer 420 formed on a semiconductor substrate 410.

[0050] Figure 4B Showing some embodiments of the present disclosure along Figure 4A4 is a cross-sectional view of a 2D grating coupler 400 taken along the direction A-A' in FIG. In the embodiment shown, the 2D grating coupler 400 fabricated on a semiconductor substrate 410 includes a multilayer structure including an insulating layer 420 and a semiconductor layer 430. In the embodiment shown, the semiconductor substrate 410 includes silicon. The insulating layer 420 includes a dielectric material such as silicon oxide and is fabricated on the semiconductor substrate 410 using chemical vapor deposition, physical vapor deposition, or the like. In some embodiments, according to various embodiments of the present disclosure, the insulating layer 420 may be replaced by other types of dielectric materials such as Si3N4, SiO2 (e.g., quartz and glass), Al2O3, and H2O. In some embodiments, the semiconductor layer 430 includes silicon and is deposited on the insulating layer 420 using chemical vapor deposition. In some embodiments, the semiconductor substrate 410, the insulating layer 420, and the semiconductor layer 430 are formed as a silicon-on-insulator (SOI) substrate.

[0051] In some embodiments, according to Figure 4A and Figure 4B The predetermined pattern shown in FIG. 4 forms scattering elements 431, 432, and 433. In some embodiments, scattering elements 431, 432, and 433 are formed as part of a cladding layer comprising silicon oxide. In some embodiments, the cladding layer may comprise other types of dielectric materials, including polysilicon and silicon nitride, depending on the application.

[0052] In some embodiments, the 2D grating coupler 400 may further include: a bottom reflective layer, located between the semiconductor substrate 410 and the insulating layer 420, comprising at least one of the following: Al, Cu, Ni, and combinations thereof; and / or a top reflective layer, located on the cladding layer, comprising at least one of the following: Al, Cu, Ni, and combinations thereof. In some embodiments, the top reflective layer covers only the tapered structure 402 of the 2D grating coupler 400. In some embodiments, the tapered structure 402 of the 2D grating coupler 400 comprises the same material as that used in the grating region 401 of the semiconductor layer 430. In other embodiments, the tapered structure 402 comprises a second material different from the first material used in the grating region 401 of the semiconductor layer 430.

[0053] Figures 5A to 5K Cross-sectional views of an exemplary grating coupler 500 are shown at various stages of the manufacturing process, according to some embodiments of the present disclosure. Figure 5A FIG2 is a cross-sectional view of a grating coupler 500-1 including a first layer 510 and a second layer 520 disposed on the first layer 510 at one of various stages of fabrication according to some embodiments of the present disclosure. The first layer 510 may be formed of silicon or another semiconductor material as a substrate. The second layer 520 may be formed of silicon oxide or another oxide material as an insulating layer.

[0054] Figure 5B FIG2 is a cross-sectional view of a grating coupler 500-2 including a semiconductor layer 530 formed on an insulating layer 520 at one of various stages of fabrication according to some embodiments of the present disclosure. The semiconductor layer 530 may be formed by epitaxially growing a semiconductor material, such as silicon, on the insulating layer 520.

[0055] Figure 5C is a cross-sectional view of a grating coupler 500-3 including a hard mask layer 540 deposited on a semiconductor layer 530 at one of various stages of fabrication according to some embodiments of the present disclosure. The hard mask layer 540 on the semiconductor layer 530 may include an organic or inorganic material.

[0056] Figure 5D is a cross-sectional view of a grating coupler 500-4 including a photoresist layer 550 deposited on a hard mask layer 540 at one of various stages of fabrication according to some embodiments of the present disclosure. The photoresist layer 550 on the hard mask layer 540 may include a photoresist material.

[0057] Figure 5E is a cross-sectional view of a grating coupler 500-5 including a patterned portion of a photoresist layer 550 formed on a hard mask layer 540 at one of the various stages of fabrication according to some embodiments of the present disclosure. Based on waveguide lithography and development, for example, by removing the patterned portion corresponding to the hard mask layer 540, Figures 1 to 4B The portion of the scattering element shown in FIG. 5 is patterned according to a predetermined pattern. Based on the pattern, the grating coupler can be divided into portions including a grating region 501 and a tapered structure 502 .

[0058] Figure 5F FIG2 is a cross-sectional view of a grating coupler 500-6 including a patterned portion of a hard mask layer 540 formed at one of the various stages of fabrication, according to some embodiments of the present disclosure. Because the photoresist layer 550 is patterned to have openings above the hard mask layer 540, portions of the hard mask layer 540 exposed by the photoresist layer 550 are removed, for example, via a wet or dry etching process. For simplicity of illustration, three openings are depicted in the grating region 501. It will be appreciated that any number of openings in the grating region 501 may be fabricated according to a predetermined pattern and remain within the scope of the present disclosure.

[0059] Figure 5G FIG. 5 is a cross-sectional view of a grating coupler 500 - 7 in which the photoresist layer 550 is removed at one of the various stages of fabrication according to some embodiments of the present disclosure. For example, the photoresist layer 550 may be removed by resist stripping.

[0060] Figure 5HFIG5 is a cross-sectional view of a grating coupler 500-8 including an array of etched regions 532, 534, and 536 formed at one of various stages of fabrication according to some embodiments of the present disclosure. Because the hard mask layer 540 is patterned to have openings above the semiconductor layer 530, portions of the semiconductor layer 530 exposed by the hard mask layer 540 are removed, for example, via a wet or dry etching process, to form the array of etched regions 532, 534, and 536.

[0061] In some embodiments, the surfaces of the etching areas 532, 534, and 536 can be smoothed by: oxidizing the silicon surfaces of the etching areas 532, 534, and 536; etching the silicon oxide surfaces; and repeating oxidation and etching several times to smooth the surfaces of the etching areas 532, 534, and 536.

[0062] Figure 5I is a cross-sectional view of a grating coupler 500-9 in which the hard mask layer 540 is removed at one of the various stages of fabrication according to some embodiments of the present disclosure. For example, the hard mask layer 540 can be removed by resist stripping.

[0063] Figure 5J FIG2 is a cross-sectional view of a grating coupler 500-10 including a cladding layer 560 formed at one of various stages of fabrication according to some embodiments of the present disclosure. The cladding layer 560 may be formed by depositing a dielectric material, such as silicon oxide, over the semiconductor layer 530 and into an array of etched regions 532, 534, and 536.

[0064] Figure 5K FIG1 is a cross-sectional view of a grating coupler 500-11 in which a top portion of a cladding layer 560 is polished at one of various stages of fabrication according to some embodiments of the present disclosure. The top portion of the cladding layer 560 can be polished, for example, based on a chemical mechanical polishing process to form an array of scattering elements 562, 564, 566 in the array of etched regions 532, 534, 536.

[0065] Figure 6 The method for manufacturing, for example, Figures 1 to 4BFlowchart of an exemplary method 600 for an exemplary 2D grating coupler according to any of the 2D grating couplers disclosed in

[0015] . At operation 602, an insulating layer is formed on a semiconductor substrate. At operation 604, a semiconductor material is epitaxially grown on the insulating layer to form a semiconductor layer. At operation 606, a hard mask is deposited on the semiconductor layer. At operation 608, a photoresist is deposited on the hard mask. At operation 610, a pattern is determined based on the shape and size of the grating and the taper. In various embodiments, the taper may be as follows: Figures 1 to 4A The tapers are shown in Figure 1 and have different shapes and sizes. The tapers can be designed based on simulations according to the desired fiber position and incident angle.

[0066] At operation 612, a photoresist is patterned according to the pattern. At operation 614, a hard mask is etched according to the pattern. At operation 616, the semiconductor layer is etched to form an array of etched regions. At operation 618, the surface of the etched regions is smoothed, for example, by repeatedly oxidizing the surface and etching the oxidized surface. At operation 620, the etched hard mask on the semiconductor layer is removed. At operation 622, a dielectric material is deposited in the array of etched regions and above the semiconductor layer. At operation 624, the top dielectric material is polished to form an array of scattering elements. The various embodiments of the present teachings may vary. Figure 6 The order of operations in .

[0067] Figure 7A For example, different input light wavelengths according to some embodiments of the present disclosure are shown. Figures 1 to 4B The exemplary optical power performance of a 2D grating coupler of any of the 2D grating couplers disclosed in

[15] is shown. This can be achieved by simulating the beam propagation as input light to the 2D grating coupler based on the plane wave expansion method. As discussed above, the tapered design aims to minimize the optical power loss when transmitting light from the optical fiber to the 2D grating coupler. The power loss can be attributed to the light transmission through the 2D grating (e.g., along the Figures 2A to 4A and due to light reflections returning from the 2D grating (e.g., along Figures 2A to 4A (Z direction in FIG). While curves 710 and 720 represent the optical power loss due to light transmission through the 2D grating and light reflection back from the 2D grating, respectively, curve 730 represents the sum of the two power losses. Based on simulated beam propagation, an optimal wavelength range 701 can be selected for the input light to minimize the optical power loss due to light transmission and light reflection relative to the 2D grating.

[0068] Figure 7B 7. A magnified view showing a selected wavelength range 701 of input light to a 2D grating coupler according to some embodiments of the present disclosure. Figure 7B As shown in FIG. 7 , the minimum point 702 of the total power loss 730 corresponds to a wavelength of approximately 1310 nanometers.

[0069] In one embodiment, the shape and size of each tapered structure of a 2D grating coupler can be adjusted to fit the output light from the 2D grating based on incident light having a selected wavelength of approximately 1310 nanometers. For example, various values ​​can be simulated for the length and displacement of each tapered structure to maximize the optical power received from the tapered structure at the corresponding waveguide. In one example, gradually increasing or decreasing values ​​can be simulated for the length and displacement of each tapered structure. According to various embodiments, the gradually increasing or decreasing values ​​for the length of the tapered structure can be between 20 microns and 500 microns, and the gradually increasing or decreasing values ​​for the displacement of the tapered structure can be between 0 microns and 20 microns.

[0070] In some embodiments, each of the first length L1 316-1 and the second length L2 326-1 is between 20 microns and 500 microns; and each of the first distance S1 315-1 and the second distance S2 325-1 is between 0 microns and 20 microns.

[0071] Figure 8 Some embodiments of the present disclosure are shown for designing, for example, Figures 1 to 4B Flowchart of an exemplary method 800 for an exemplary 2D grating coupler of any one of the 2D grating couplers disclosed in

[0065] . At operation 802, beam propagation is simulated as input light to the 2D grating coupler based on a plane wave expansion method. At operation 804, a wavelength range of the input light is determined based on the simulated beam propagation to minimize optical power loss due to light transmission and light reflection relative to the 2D grating. At operation 806, based on the wavelength range, a shape and size of each tapered structure of the 2D grating coupler is adjusted to fit the output light from the 2D grating based on gradually increasing values ​​of the simulation. The various embodiments of the present teachings may vary. Figure 8 The order of operations in .

[0072] In one embodiment, a device for optical coupling is disclosed. The device includes: a planar layer; a grating region comprising an array of scattering elements arranged in the planar layer to form a two-dimensional (2D) grating; a first tapered structure formed in the planar layer to connect a first side of the grating region to a first waveguide, wherein the first tapered structure has a first triangle shape that is asymmetric with respect to any line perpendicular to the first side of the grating region in the planar layer; and a second tapered structure formed in the planar layer to connect a second side of the grating region to a second waveguide, wherein the second tapered structure has a second triangle shape that is asymmetric with respect to any line perpendicular to the second side of the grating region in the planar layer, wherein the first side and the second side are substantially perpendicular to each other.

[0073] In some embodiments, the shape of the grating region is square in the planar layer. In some embodiments, the scattering element array is arranged at a plurality of intersections where a first set of straight lines intersects a second set of straight lines in the planar layer; each of the first set of straight lines is parallel to the first side of the grating region; and each of the second set of straight lines is parallel to the second side of the grating region. In some embodiments, each scattering element in the scattering element array has the same square shape of the same size in the planar layer. In some embodiments, each scattering element in the scattering element array has the same circular shape of the same size in the planar layer. In some embodiments, the first triangle is congruent with the second triangle. In some embodiments, the first triangle and the second triangle are symmetrical to each other about a diagonal line crossing the grating region. In some embodiments, the scattering element array is uniformly distributed in the planar layer such that the centers of every two adjacent scattering elements have the same distance along a first direction perpendicular to the first side of the grating region or a second direction perpendicular to the second side of the grating region. In some embodiments, the first triangle has a first base side located on the first side of the grating region, has a first vertex opposite the first base side, and has a first length along the first direction; the first vertex is at a first distance from a perpendicular bisector of the first base side in the planar layer; the second triangle has a second base side located on the second side of the grating region, has a second vertex opposite the second base side, and has a second length along the second direction; the second vertex is at a second distance from a perpendicular bisector of the second base side in the planar layer; and the first distance and the second distance are equal to each other. In some embodiments, the two-dimensional grating is configured to receive incident light from an optical fiber at a non-zero incident angle; the incident angle is measured in an incident plane between the axis of the optical fiber and a direction perpendicular to the planar layer; and the first length, the second length, the first distance, and the second distance are determined based on the incident angle and the position of the optical fiber relative to the two-dimensional grating. In some embodiments, the first tapered structure is configured to transmit a first portion of the incident light to the first waveguide to achieve minimum insertion loss; and the second tapered structure is configured to transmit a second portion of the incident light to the second waveguide to achieve minimum insertion loss, wherein the first portion of the incident light is substantially a parallel polarization component of the incident light, and the second portion of the incident light is substantially an orthogonal polarization component of the incident light, each of the parallel polarization component and the orthogonal polarization component includes polarized light, and the polarized light has a transverse magnetic (TM) polarization mode or a transverse electric (TE) polarization mode separated from the incident light.In some embodiments, each of the first length and the second length is between 20 microns and 500 microns, and each of the first distance and the second distance is between 0 microns and 20 microns.

[0074] In another embodiment, a method for designing a two-dimensional (2D) grating coupler is disclosed. The method includes: simulating beam propagation as input light to the 2D grating coupler based on a plane wave expansion method, wherein the 2D grating coupler includes: a planar layer; a grating region including an array of scattering elements arranged in the planar layer to form a 2D grating; a first tapered structure located in the planar layer, connecting a first side of the grating region to a first waveguide; and a second tapered structure located in the planar layer, connecting a second side of the grating region to a second waveguide; determining a wavelength range of the input light based on the simulated beam propagation to minimize optical power loss due to light transmission and light reflection relative to the 2D grating; and adjusting the shape and size of each of the first tapered structure and the second tapered structure based on the wavelength range to fit the output light from the 2D grating.

[0075] In some embodiments, the shape of the first pyramidal structure is a first triangle that is asymmetric about any line perpendicular to the first side of the grating region in the planar layer; the shape of the second pyramidal structure is a second triangle that is asymmetric about any line perpendicular to the second side of the grating region in the planar layer; and the first side and the second side are substantially perpendicular to each other. In some embodiments, the first triangle has a first length from a first substrate side located on the first side to a first vertex opposite the first substrate side, and has a first displacement of a perpendicular bisector from the first vertex to the first substrate side; and the second triangle has a second length from a second substrate side located on the second side to a second vertex opposite the second substrate side, and has a second displacement of a perpendicular bisector from the second vertex to the second substrate side. In some embodiments, the first length, the second length, the first displacement, and the second displacement have values ​​that maximize the optical power in the first waveguide and the second waveguide. In some embodiments, the values ​​of the first length and the second length are between 20 microns and 500 microns; and the values ​​of the first displacement and the second displacement are between 0 microns and 20 microns.

[0076] In yet another embodiment, a method of forming an optical coupler is disclosed. The method includes: forming an insulating layer on a semiconductor substrate; epitaxially growing a semiconductor material on the insulating layer to form a semiconductor layer; etching the semiconductor layer according to a predetermined pattern to form: an array of etched holes in the semiconductor layer to form a grating region; a first pyramidal structure extending from a first side of the grating region, wherein the shape of the first pyramidal structure in the semiconductor layer is a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region; and a second pyramidal structure extending from a second side of the grating region, wherein the shape of the second pyramidal structure in the semiconductor layer is a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region, wherein the first side and the second side are substantially perpendicular to each other; and depositing a dielectric material into the array of etched regions to form an array of scattering elements in the semiconductor layer, wherein the scattering elements are arranged to form a two-dimensional (2D) grating.

[0077] In some embodiments, the shape of the grating region in the semiconductor layer is square; and the first triangle and the second triangle are symmetrical to each other about a diagonal line crossing the grating region in the semiconductor layer. In some embodiments, the semiconductor material comprises silicon; and the dielectric material comprises silicon oxide.

[0078] The foregoing summarizes the features of several embodiments so that those skilled in the art may better understand the various aspects of the present disclosure. Those skilled in the art will appreciate that they may readily use this disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and / or achieving the same advantages of the embodiments introduced herein. Those skilled in the art will also recognize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that various changes, substitutions, and modifications may be made herein without departing from the spirit and scope of the present disclosure.

Claims

1. A device for optical coupling, comprising: Plane layer; a grating region comprising an array of scattering elements arranged in the planar layer to form a two-dimensional grating; a first tapered structure formed in the planar layer to connect a first side of the grating region to a first waveguide, wherein the shape of the first tapered structure is a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region in the planar layer; as well as a second tapered structure formed in the planar layer to connect a second side of the grating region to a second waveguide, wherein the shape of the second tapered structure is a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region in the planar layer, wherein the first side and the second side are perpendicular to each other, wherein: The scattering element array is uniformly distributed in the planar layer so that the centers of every two adjacent scattering elements have the same distance along a first direction perpendicular to the first side of the grating region or a second direction perpendicular to the second side of the grating region, The first triangle has a first base side located on the first side of the grating region, has a first vertex opposite the first base side, and has a first length along the first direction; The first vertex is at a first distance from a perpendicular bisector of the first base side in the planar layer; The second triangle has a second base side located on the second side of the grating region, has a second vertex opposite to the second base side, and has a second length along the second direction; The second vertex is a second distance from a perpendicular bisector of the second base side in the planar layer; and The first distance and the second distance are equal to each other. 2 . The device for optical coupling according to claim 1 , wherein the shape of the grating region is square in the planar layer.

3. The device for optical coupling according to claim 2, wherein: The scattering element array is arranged at a plurality of intersections where the first set of straight lines intersect the second set of straight lines in the planar layer; Each of the first set of straight lines is parallel to the first side of the grating region; and Each of the second set of straight lines is parallel to the second side of the grating region.

4. The device for optical coupling according to claim 1, wherein each scattering element in the scattering element array has the same square shape with the same size in the planar layer.

5. The device for optical coupling according to claim 1, wherein each scattering element in the scattering element array has the same circular shape with the same size in the planar layer. The device for optical coupling according to claim 1 , wherein the first triangle is congruent with the second triangle. 7 . The device for optical coupling according to claim 1 , wherein the first triangle and the second triangle are symmetrical to each other about a diagonal line spanning the grating region.

8. The device for optical coupling according to claim 1, wherein: The two-dimensional grating is configured to receive incident light from an optical fiber at a non-zero angle of incidence; The angle of incidence is measured in an incidence plane between the axis of the optical fiber and a direction perpendicular to the planar layer; and The first length, the second length, the first distance, and the second distance are determined based on the incident angle and a position of the optical fiber relative to the two-dimensional grating.

9. The device for optical coupling according to claim 8, wherein: The first tapered structure is configured to transmit a first portion of the incident light to the first waveguide to achieve minimum insertion loss; and The second tapered structure is configured to transmit a second portion of the incident light to the second waveguide to achieve minimum insertion loss, wherein The first part of the incident light is a parallel polarization component of the incident light, The second portion of the incident light is an orthogonal polarization component of the incident light, Each of the parallel polarization component and the orthogonal polarization component comprises polarized light, and The polarized light has a transverse magnetic polarization mode or a transverse electric polarization mode separated from the incident light.

10. The device for optical coupling according to claim 1, wherein: Each of the first length and the second length is between 20 micrometers and 500 micrometers, and Each of the first distance and the second distance is between 0 micrometers and 20 micrometers.

11. A two-dimensional grating coupler, comprising: Plane layer; a grating region comprising an array of scattering elements arranged in the planar layer to form a two-dimensional grating; a first tapered structure located in the planar layer to connect a first side of the grating region to a first waveguide, wherein the shape of the first tapered structure is a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region in the planar layer; as well as a second tapered structure located in the planar layer to connect a second side of the grating region to a second waveguide, wherein the shape of the second tapered structure is a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region in the planar layer, wherein each of the first tapered structure and the second tapered structure has a shape and size that minimizes optical power loss due to light transmission and light reflection relative to the two-dimensional grating, wherein: the first triangle having a first length from a first base side located on the first side to a first vertex opposite the first base side and having a first displacement of a perpendicular bisector from the first vertex to the first base side; the second triangle having a second length from a second base side located on the second side to a second vertex opposite the second base side and having a second shift of a perpendicular bisector from the second vertex to the second base side; The first shift and the second shift are equal to each other; and The first length, the second length, the first shift, and the second shift have values ​​that maximize optical power in the first waveguide and the second waveguide.

12. The two-dimensional grating coupler according to claim 11, wherein: The first side and the second side are perpendicular to each other.

13. The two-dimensional grating coupler according to claim 11, wherein: The values ​​of the first length and the second length are between 20 micrometers and 500 micrometers; and The values ​​of the first and second shifts are between 0 microns and 20 microns.

14. A method of forming an optical coupler, comprising: forming an insulating layer on a semiconductor substrate; epitaxially growing a semiconductor material on the insulating layer to form a semiconductor layer; The semiconductor layer is etched according to a predetermined pattern to form: An etching array in the semiconductor layer to form a grating region, a first pyramidal structure extending from a first side of the grating region, wherein a shape of the first pyramidal structure in the semiconductor layer is a first triangle that is asymmetric with respect to any line perpendicular to the first side of the grating region, and a second tapered structure extending from a second side of the grating region, wherein the shape of the second tapered structure in the semiconductor layer is a second triangle that is asymmetric with respect to any line perpendicular to the second side of the grating region, wherein the first side and the second side are perpendicular to each other; as well as depositing a dielectric material into the etched array to form an array of scattering elements in the semiconductor layer, wherein the scattering elements are arranged to form a two-dimensional grating, wherein: The scattering element array is uniformly distributed so that the centers of every two adjacent scattering elements have the same distance along a first direction perpendicular to the first side of the grating region or a second direction perpendicular to the second side of the grating region, The first triangle has a first base side located on the first side of the grating region, has a first vertex opposite the first base side, and has a first length along the first direction; The first vertex is a first distance from a perpendicular bisector of the first base side; The second triangle has a second base side located on the second side of the grating region, has a second vertex opposite to the second base side, and has a second length along the second direction; The second vertex is a second distance from a perpendicular bisector of the second base side; and The first distance and the second distance are equal to each other.

15. The method of forming an optical coupler according to claim 14, wherein: The shape of the grating region is square in the semiconductor layer; and The first triangle and the second triangle are symmetrical to each other about a diagonal line crossing the grating region in the semiconductor layer.

16. The method of forming an optical coupler according to claim 14, wherein: The semiconductor material comprises silicon; and The dielectric material includes silicon oxide.

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