Spot size converter including two-dimensional bianisotropic sub-wavelength grating structure

Abstract

The invention relates to a spot size converter including a two-dimensional bianisotropic sub-wavelength grating structure. In some embodiments, a photonic integrated circuit (PIC) may include a spot size converter (SSC). The SSC may include a tapered waveguide having a length along a first direction and a width along a second direction. The first direction may be parallel to the propagation direction and the second direction may be perpendicular to the propagation direction. The SSC may include a two-dimensional (2D) bianisotropic sub-wavelength grating (SWG) structure. A portion of the 2D bianisotropic SWG structure may surround a portion of the tapered waveguide along the first direction in the second direction.

Description

Cross-references to related applications

[0001] This patent application claims priority to U.S. Provisional Application No. 63 / 717,650, filed November 7, 2024, entitled "Mode Size Converter Including Subwavelongth Grating Metamaterials". The disclosure of the earlier application is considered part of this patent application and is incorporated herein by reference. Technical Field

[0002] This disclosure generally relates to a spot size converter (SSC) and an SSC comprising a two-dimensional (2D) bi-anisotropic subwavelength grating (SWG) structure. Background Technology

[0003] SSC is an optical device that can be used to achieve fiber-to-chip coupling by matching the mode field diameter (also known as the spot size) of an optical fiber to the mode size of a photonic waveguide on an integrated chip. The mode field diameter of a standard single-mode fiber (e.g., at a wavelength of 1550 nanometers (nm), in the range of about 8 micrometers (μm) to about 10 μm) is significantly larger than the mode size in the waveguide on the photonic chip (e.g., in the range of about 0.5 μm to about 2 μm).

[0004] Without SSC (Synchronous Coupling Controller), a significant mismatch exists between the field distributions of the fiber and waveguide modes, leading to low coupling efficiency and high insertion loss. SSC reduces this mismatch, thereby improving power delivery between the fiber and waveguide. The improved mode matching provided by SSC also reduces back reflections, which would otherwise degrade the performance of the optical system. Summary of the Invention

[0005] In some embodiments, a photonic integrated circuit (PIC) including an SSC includes: a tapered waveguide having a length along a first direction and a width along a second direction, wherein the first direction is parallel to the propagation direction and the second direction is perpendicular to the propagation direction; and a 2D bi-anisotropic SWG structure, wherein a portion of the 2D bi-anisotropic SWG structure surrounds a portion of the tapered waveguide along the first direction in the second direction.

[0006] In some embodiments, a PIC including an SSC includes: a first segment including a first portion of a tapered waveguide; a second segment including a second portion of the tapered waveguide and a first portion of a bi-anisotropic SWG structure (which includes a plurality of grating elements), wherein the second portion of the bi-anisotropic SWG structure surrounds the second portion of the tapered waveguide along the length of the second segment; and a third segment including the second portion of the bi-anisotropic SWG structure.

[0007] In some embodiments, a PIC including an SSC includes: a waveguide having a length along a first direction and a width along a second direction perpendicular to the first direction; and a 2D bi-anisotropic SWG structure surrounding a portion of the tapered waveguide along the first direction, wherein the dielectric constant of the bi-anisotropic SWG structure relative to the first direction is different from the dielectric constant of the bi-anisotropic SWG structure relative to the second direction, and wherein the dielectric constant of the bi-anisotropic SWG structure relative to a third direction is different from the dielectric constant of the bi-anisotropic SWG structure relative to the first direction and the dielectric constant of the bi-anisotropic SWG structure relative to the second direction. Attached Figure Description

[0008] Figures 1A to 1B This is a diagram illustrating an example implementation of an SSC including the 2D bi-anisotropic SWG structure described herein.

[0009] Figure 2 This is a diagram illustrating the grating elements of the 2D bi-anisotropic SWG structure described in this paper, based on a Gaussian distribution along the propagation direction.

[0010] Figure 3-6 This is a figure illustrating simulation results associated with various example implementations of the SSC, including the 2D bi-anisotropic SWG structure described herein.

[0011] Figure 7-12 The figure illustrates the simulation results, showing the effects of different parameter variations associated with the SSC, including the 2D bi-anisotropic SWG structure described in this paper.

[0012] Figure 13-14 The figure illustrates the simulation results, showing the insertion loss and PDL associated with the SSC, including the 2D bi-anisotropic SWG structure described in this paper. Detailed Implementation

[0013] The following detailed description of the exemplary embodiments is given with reference to the accompanying drawings. The same reference numerals in different drawings may identify the same or similar elements. Note that references to optical bands designated by letters (e.g., O-band, C-band, L-band, etc.) herein refer to the International Telecommunication Union (ITU) optical bands in the near-infrared region.

[0014] Fiber-to-chip coupling presents a challenge in the development of silicon photonics-based devices, which are essential for improving the efficiency of optical communication systems. Two common techniques for connecting standard single-mode fiber (e.g., SMF-28) to silicon photonics (SiPho) waveguide interfaces are edge coupling and grating coupling. Each of these fiber-to-chip coupling techniques presents advantages and trade-offs in terms of efficiency, bandwidth, and fabrication complexity.

[0015] Edge coupling offers a wide bandwidth and low polarization dependence, and is therefore commonly used in a variety of applications. However, edge coupling is not a suitable solution for high-power applications because two-photon absorption in silicon leads to increased insertion loss. To address these challenges, the use of silicon (Si) and silicon nitride (SiN) has been proposed. x Improve the design of edge-coupled SSCs. In some cases, SiN... x It may be a better material choice because, compared to Si, SiN... x This provides lower optical loss, reduced surface roughness, and reduced nonlinearity. These improvements can enhance the reliability and effectiveness of edge-coupled SSCs in some applications. Trident-shaped, partially etched Si SSCs can reduce coupling loss (e.g., to below 1.25 dB) while exhibiting low polarization-dependent loss (PDL). This design utilizes a trident-shaped configuration and enhances mode overlap while reducing sensitivity to variations in etch depth, providing a robust solution for coupling in the O-band (e.g., 1260 nm to 1360 nm). However, the high nonlinearity of Si leads to losses when exposed to higher power, making this design unsuitable for high-power applications.

[0016] In some cases, subwavelength grating (SWG) structures (also known as metamaterials) can be used to enhance the performance of SSCs. SWG structures can achieve lower losses, higher bandwidth, and reduced nonlinearity, which is crucial for some applications, such as high-power applications. One example uses anisotropic SiN. xMetamaterials can provide improvements in bandwidth. However, such SWG structures face challenges in terms of insertion loss, which can exceed 2 dB for both transverse electric (TE) and transverse magnetic (TM) polarization. In another example, a Si anisotropic metamaterial SSC was proposed with a worst-case loss of 1.2 dB. In this SSC, the SWG structure comprises a 1D array of grating elements. However, further improvements using SWG designs are desired. What is needed is an SSC design that meets the increasingly stringent requirements of photonic systems, which require efficient, low-loss coupling that can operate over a wide spectral range and at high power levels without significant performance degradation.

[0017] Some embodiments described herein provide a switch-channel unit (SSC) including a 2D bi-anisotropic waveguide (SWG) structure. In some embodiments, the SSC (e.g., on a photonic integrated circuit (PIC)) may include a tapered waveguide and a 2D bi-anisotropic SWG structure. The tapered waveguide may have a length along a first direction and a width along a second direction, wherein the first direction is parallel to the propagation direction and the second direction is perpendicular to the propagation direction. A portion of the 2D bi-anisotropic SWG structure may surround a portion of the tapered waveguide along the first direction in the second direction.

[0018] In some implementations, the SSC including the 2D bi-anisotropic SWG structure can be on a Si material platform or SiN. x Fabrication on a material platform. It is worth noting that, although 1D anisotropic SWG / metamaterials have been used in some conventional SSCs as mentioned above, this design faces challenges in terms of insertion loss, high nonlinearity, and tolerance due to variations in waveguide parameters during fabrication. Furthermore, while conventional SSCs based on anisotropic Si 1D SWGs can provide lower nonlinearity, even at high power levels, SSCs including the 2D bi-anisotropic SWG structure described in this paper can further enhance tolerance and reduce nonlinearity. Similarly, while conventional SiN-based SSCs... x SWG's SSC inherently has low nonlinear coefficients, but this includes the 2D bi-anisotropic SiN described in this paper. x SSCs with SWG structures further reduce nonlinearity and improve fabrication tolerance.

[0019] In some implementations, the SSC, including the 2D bi-anisotropic SWG structure described herein, can (1) reduce high nonlinear losses at high optical power (e.g., within the Si platform) and (2) improve tolerance to parameter variations (e.g., in Si and SiN). x (3) Platform, supports combination of Si and SiN xThe hybrid design provides flexibility for a variety of applications and / or (4) is applicable across multiple bands (e.g., O-band, C+L-band, etc.), thereby enhancing its applicability in a wider range of photonic systems.

[0020] Furthermore, according to the aforementioned conventional techniques, an SSC can, in some cases, comprise an SWG structure composed of a 1D grating element array. In this design, refractive index engineering can occur only relative to one dimension—along the propagation direction (e.g., the z-direction). However, to control the mode field, it is necessary to control two directions (e.g., the x-direction and the z-direction) to match the mode field diameter to the single-mode fiber. With this mode field control, conventional 1D array designs may suffer from high loss, high nonlinearity, and low tolerance, which are unsuitable for high-power applications. In some implementations, an SSC including the 2D bi-anisotropic SWG structure described herein can be used to provide the SSC and address these issues while enhancing performance. That is, in some implementations, the 2D bi-anisotropic SWG structure enables control of the refractive index in two directions (e.g., the x-direction and the z-direction). In some implementations, the grating elements of a 2D bi-anisotropic SWG structure can be distributed according to a pattern (e.g., based on Gaussian, linear, apodization, or parabolic patterns) to achieve a smooth mode transition (e.g., from waveguide to fiber mode or from fiber mode to waveguide), while reducing insertion loss, absorption loss (e.g., at high power), and reflection. Furthermore, SSCs incorporating a 2D bi-anisotropic SWG structure can depend less on variations in tip width, thereby increasing fabrication tolerance. Additional details are provided below.

[0021] Figures 1A to 1B This is a diagram illustrating an example embodiment of the SSC 100, which includes the 2D bi-anisotropic SWG structure described herein. Figure 1A and 1B The image above shows a floor plan of SSC 100 (e.g., in...). x - z (on a plane), and Figure 1A and Figure 1B The following figure illustrates a cross-sectional view along the centerline of SSC 100 (e.g., in...). y - z (On a flat surface). In some implementations, the SSC 100 can be implemented in a PIC. For example... Figure 1A and 1B As shown, the SSC 100 may include a tapered waveguide 102, a 2D bi-anisotropic SWG structure 104 including multiple grating elements (indicated by black squares), and a cladding 106.

[0022] In some embodiments, one or more elements of the SSC 100 may be formed using a Si platform. Therefore, in some embodiments, one or more grating elements of the tapered waveguide 102 and / or the 2D bi-anisotropic SWG structure 104 may comprise Si. Additionally or alternatively, one or more elements of the SSC 100 may utilize SiN. x Platform formation. Therefore, in some embodiments, one or more grating elements of the tapered waveguide 102 and / or the 2D bi-anisotropic SWG structure 104 may include SiN... x In one example implementation, the 2D bi-anisotropic SWG structure 104 includes SiN surrounded by a cladding 106. x Grating elements. In another example embodiment, the 2D bi-anisotropic SWG structure 104 includes Si grating elements surrounded by cladding 106. In some embodiments, the SSC 100 may use a hybrid design, wherein one or more elements of the SSC 100 (e.g., the tapered waveguide 102) comprise Si, and one or more other elements of the SSC 100 (e.g., the grating elements of the 2D bi-anisotropic SWG structure 104) comprise SiN. x .

[0023] In some embodiments, cladding 106 may include one or more of silica, an index-matching fluid, or air. For example, the bottom portion of cladding 106 (e.g., the portion of cladding 106 below the grating elements of the tapered waveguide 102 and the 2D bi-anisotropic SWG structure 104) may include silica, and the top portion of cladding 106 (e.g., the portion of cladding 106 above the grating elements of the 2D bi-anisotropic SWG structure 104 and between the grating elements of the 2D bi-anisotropic SWG structure 104) may include an index-matching fluid and / or air. In some embodiments, the index-matching fluid may be an adhesive designed to have a refractive index at a selected wavelength close to that of the material of another portion of cladding 106 (e.g., to reduce reflection and scattering at the interface between silica and the index-matching fluid). In one example, the bottom portion of cladding 106 may include silica, and the top portion of cladding 106 may include an index-matching fluid in the form of an epoxy resin with a refractive index close to that of silica.

[0024] In some implementations, such as Figure 1A-1B As illustrated, the tapered waveguide 102 has a first direction (referred to herein as...) z The length of the first direction and along the second direction (referred to in this paper) x The width of the direction. Here, z The direction is parallel to the direction of light propagation through the SSC 100, and xThe direction is perpendicular to the propagation direction. In some embodiments, as shown, the width of the tapered waveguide 102 is within the tapered length. L t Up along z The change in direction makes the width of the tapered waveguide 102 the same as the width at the input / output facets of the SSC 100. w And it is the width at the tip of the tapered waveguide 102. w tip ( w > w tip In some embodiments, the tapered waveguide 102 has a high h tw In some embodiments, the tapered waveguide 102 may be a segmented waveguide. That is, in some embodiments, the tapered waveguide 102 may include multiple waveguide segments, with a portion of the cladding 106 between a given pair of adjacent waveguide segments of the tapered waveguide 102. In this embodiment, the tapered waveguide 102 may be relative to... x The direction is segmented, so that the tapered waveguide 102 is in x It is periodic in direction, and / or can be relative to z The direction is segmented, so that the tapered waveguide 102 is in z It exhibits periodicity in direction.

[0025] The 2D bi-anisotropic SWG structure 104 includes a plurality of grating elements. In some embodiments, one or more grating elements of the 2D bi-anisotropic SWG structure 104 may have a rectangular shape (e.g., a square shape), such as... Figure 1A and 1B As illustrated. Additionally or alternatively, one or more grating elements of the 2D bi-anisotropic SWG structure 104 may have another type of shape, such as an elliptical shape, trapezoidal shape, circular shape, annular shape, etc. As shown, in some embodiments, the grating elements of the 2D bi-anisotropic SWG structure 104 may be based on relative to... x - z The grating elements are distributed in a planar Gaussian distribution. Alternatively, the grating elements can be distributed or arranged in another manner, such as based on linear patterns, apodization patterns, or parabolic patterns. In some embodiments, the distribution of the grating elements can be selected to smooth mode transitions (e.g., from waveguide to fiber mode or from fiber mode to waveguide) while reducing insertion loss, absorption loss (e.g., at high power), and reflection. In some embodiments, the grating elements of the 2D bi-anisotropic SWG structure 104 can be symmetrically distributed along the tapered waveguide 102 and can be distributed along... x directional extension.

[0026] In some implementations, such as Figure 1Aand 1B As illustrated, one or more grating elements of the 2D bi-anisotropic SWG structure 104 can be oriented at 90 degrees (°) relative to the propagation direction. Additionally or alternatively, one or more grating elements of the 2D bi-anisotropic SWG structure 104 can be oriented at any angle (e.g., less than 90°) relative to the propagation direction. For example, one or more grating elements of the 2D bi-anisotropic SWG structure 104 can be oriented at an angle between 50° and 90° or between 70° and 90°. In some embodiments, one or more grating elements can be oriented at any angle to control one or more performance characteristics of the 2D bi-anisotropic SWG structure 104, such as the back reflection of the 2D bi-anisotropic SWG structure 104. In some embodiments, the total width of the 2D bi-anisotropic SWG structure 104 can be a tapered length. L t Up along z The directional change (e.g., based on the distribution of grating elements) makes the total width of the 2D bi-anisotropic SWG structure 104 equal to the radius of the 2D bi-anisotropic SWG structure 104 at the output / input facets of the SSC 100. R swg twice (i.e., 2×) R swg ).

[0027] In some implementations, such as Figure 1A The illustrated height of one or more grating elements in the 2D bi-anisotropic SWG structure 104. h swg The height may be different from (e.g., smaller than) that of the tapered waveguide 102. h tw Additional or alternative land, such as Figure 1B The illustrated height of one or more grating elements of the 2D bi-anisotropic SWG structure 104. h swg The height of the tapered waveguide 102 can be compared with h tw Matching (e.g., approximately equal to the height of the tapered waveguide 102) h tw ).

[0028] As shown, a portion of the 2D bi-anisotropic SWG structure 104 (e.g., some grating elements of the 2D bi-anisotropic SWG structure 104) can be along... x Length in direction L t and zThe direction surrounds a portion of the tapered waveguide 102. As further shown, in some embodiments, along the length of SSC 100 L swg Only a portion of the grating elements and cladding 106 of the 2D bi-anisotropic SWG structure 104 exist (i.e., the tapered waveguide 102 is not along the length of the SSC 100). L swg exist).

[0029] like Figure 1A and 1B As shown, the grating element of the 2D bi-anisotropic SWG structure 104 has periodicity. Λ x and relative to x directional fill rate ρ x Given a grating element in x The width in the direction is equal to Λ x ρ x The value, and the gap between a pair of adjacent grating elements is x The width in the direction (e.g., a portion of the cladding 106 between a pair of adjacent grating elements in) x The width in the direction is equal to (1- ρ x ) Λ x The value. Similarly, the grating elements of the 2D bi-anisotropic SWG structure 104 have periodicity. Λ z and relative to z directional fill rate ρ z Given a grating element in z The length in the direction is equal to Λ z ρ z The value, and the gap between a pair of adjacent grating elements is z The length in the direction (e.g., a portion of the cladding 106 between a pair of adjacent grating elements) is in z The length in the direction is equal to (1- ρ z ) Λ z The value of .

[0030] In some implementations, periodic Λ x and periodicity Λ z Possibly less than the operable wavelength of SSC 100 (For example, for the C-band, (Possibly around 1550 nm). In some implementations, by periodicity... Λ x and Λ z Set to less than This can reduce or minimize diffraction effects. In one example, periodicity... Λ x and / or periodic Λ z It can be smaller than approximately ,in It is the operable wavelength associated with SSC 100, and n This refers to the refractive index of the 2D bi-anisotropic SWG structure 104. Therefore, in some embodiments, the dimensions (e.g., width and / or length) of a given grating element of the 2D bi-anisotropic SWG structure 104 can be based on the wavelength range associated with the SSC 100 (e.g., to provide a refractive index that is appropriately small relative to the operable wavelengths of the SSC 100). n 2D bi-anisotropic SWG structure 104).

[0031] In some embodiments, the periodicity of the grating elements of the 2D bi-anisotropic SWG structure 104 Λ x The periodicity of the grating element with the 2D bi-anisotropic SWG structure 104 Λ z Different. In this implementation, this periodic difference may result in the 2D bi-anisotropic SWG structure 104 being different from... x Dielectric constant of direction ( ) and 2D bi-anisotropic SWG structure 104 relative to z Dielectric constant of direction ( The difference is that, in addition, the dielectric constant is made different. and dielectric constant Unlike the 2D bi-anisotropic SWG structure 104 relative to y Dielectric constant of direction ( )(For example These three different dielectric constants define the 2D bi-anisotropic SWG structure 104 as comprising a bi-anisotropic metamaterial. Alternatively, in some embodiments, periodicity... Λ x Can be associated with periodicity Λ z Matching (e.g., approximately equal to). Furthermore, in some implementations, the fill rate... ρ x Can be compared with fill rate ρz Different. Alternatively, in some implementations, the fill rate... ρ x Can be compared with fill rate ρ z Matching (e.g., approximately equal to fill rate) ρ z The bi-anisotropic properties of the 2D bi-anisotropic SWG structure 104 metamaterial can be achieved by selecting periodicity. Λ x Periodicity Λ z Fill rate ρ x and / or fill rate ρ z One or more of them are provided.

[0032] In some implementations, periodic Λ x (and fill rate) ρ x ) may follow x Directional change (e.g., periodicity) Λ x and fill rate ρ x You can follow x (The direction gradually increases or decreases). Additionally or alternatively, periodically. Λ z (and fill rate) ρ z ) may follow z Directional change (e.g., periodicity) Λ z and fill rate ρ z You can follow z (The direction gradually increases or decreases). In some implementations, periodicity... Λ x and Λ z (and fill rate) ρ x and ρ z It can be designed to control along z Light propagates along the axis.

[0033] In some implementations... Figures 1A to 1B The illustrated 2D bi-anisotropic SWG structure 104 can be modeled using Effective Medium Theory (EMT) as follows: in:

[0034] here, Indicates the fill rate of the core material and, depending on the orientation, is specified as or Any one of them. Furthermore, It can represent periodicity along a certain direction, and can be... or Either of them. Additionally, This represents the core dielectric constant (e.g., for silicon-based SSC 100). Or for SiN x Base SSC 100 is Furthermore, This represents the dielectric constant of cladding 106 (e.g., for silicon dioxide). In some implementations, this modeling approach homogenizes the 2D bi-anisotropic SWG structure 104, thereby simplifying the geometry and analysis.

[0035] As indicated above, provide Figures 1A to 1B As an example. Other examples can be related to... Figures 1A to 1B The descriptions differ. Provided Figures 1A to 1B The number and arrangement of the components shown are for illustrative purposes only. In practice, with... Figures 1A to 1B Compared to the components shown, there may be additional components, fewer components, different components, or components arranged differently. Furthermore, Figures 1A to 1B The two or more elements shown can be implemented within a single element, or Figures 1A to 1B The single element shown can be implemented as multiple distributed elements. Additionally or alternatively, Figures 1A to 1B The set of components shown (e.g., one or more components) can perform actions described as being composed of Figures 1A to 1B The other set of elements shown performs one or more functions.

[0036] In some implementations, as mentioned above, the grating elements of the 2D bi-anisotropic SWG structure 104 can be based on a Gaussian distribution along the propagation direction (e.g., z (Direction) distribution. The Gaussian distribution can be defined by the following function:

[0037] According to the Gaussian distribution in Equation 2, as follows Figure 2 As shown. In some implementations, such as Figure 2 As illustrated, the grating element of the 2D bi-anisotropic SWG structure 104 can be based on Equation 2 along... x The directions are arranged in a Gaussian distribution to approximately one end of the tapered waveguide 102, and can then be 2× Rswg The fixed total width continues to be arranged. Alternatively, the arrangement of the grating elements of the 2D bi-anisotropic SWG structure 104 can be linear, apodized, parabolic, etc. In some embodiments, the distribution of the grating elements of the 2D bi-anisotropic SWG structure 104 can be designed to meet the performance requirements of a given application. In some embodiments, the effective radius of the grating elements of the 2D bi-anisotropic SWG structure 104 (e.g., ...) Figures 1A to 1B The depicted R swg The mode distribution can be designed to match a specific mode field diameter (MFD) (e.g., 10 μm MFD or any other specified MFD). In the example provided below, the MFD of SSC 100 will be matched with the MFD of 10 μm MFD in SMF-28 fiber.

[0038] As indicated above, provide Figure 2 As an example. Other examples can be related to... Figure 2 The descriptions are different.

[0039] Figures 3 to 6 This is a graph illustrating simulation results associated with various example implementations of the SSC 100 described herein. Figure 3 In the example shown, the grating elements of the tapered waveguide 102 and the 2D bi-anisotropic SWG structure 104 comprise Si, and the cladding 106 comprises silicon dioxide. In this example, the height of the tapered waveguide 102 is... h tw The wavelength is 220 nm, and the height of the grating element is... h swg 90 nm (i.e., h tw > h swg Furthermore, periodicity It is 2000 nm, fill rate It is periodic Λ x The function, periodic It is 200 nm, and the fill rate is... It is 0.10.

[0040] Figure 3 (a) is a plan view of SSC 100 and SMF-28 optical fiber. Figure 3 (b) Illustration along the propagation length L Effective refractive index ( n eff The gray dots and black squares indicate the simulation in TE mode and TM mode, respectively. n eff The solid line shows the corresponding fit.n eff It is worth noting that the last two data points, indicated by the star-shaped plot (in... Figure 3 (b) Overlapping indicates the inherent mode of SMF-28 fiber. n eff In this example, TE mode n eff and TM mode n eff Smooth transition to the SMF-28 mode refractive index. Along the propagation length. L The corresponding field distribution is as follows Figure 3 As shown in (c). Figure 3 The upper part of (c) shows the TE mode distribution and how the mode smoothly transitions to the SMF-28 mode, while Figure 3 The lower part of (c) shows the transition of the TM mode distribution. Here, the mode diameter increases along the propagation length. L Increased. Notably, the TE mode distribution is tightly matched to the SMF-28 fiber (compared to the TM mode). This is due to the asymmetry relative to the waveguide height and width.

[0041] To further analyze along x Direction (e.g., horizontal) and y An MFD in a direction (e.g., vertical) can perform three-dimensional (3D) finite-difference time-domain (FDTD) analysis and examine the field distribution. Figure 3 The results shown in (d) to 3(f) are correlated with the TE mode, and Figure 3 The results in (i) through 3(k) are associated with the TM pattern. Figure 3 In (d) and 3(i), the top figure shows the field distribution along SSC 100 (e.g., relative to...). x - z (Planar), and the bottom portion shows the mode field distribution of SSC 100 and SMF-28 fibers— Figure 3 (d) is for TE mode, and Figure 3 (i) refers to the TM mode. Figure 3 (e) and 3(f) show the MFD of the field strength for TE mode. TE MFD for SSC (dashed line) and SMF-28 fiber (solid line). x like Figure 3 As shown in (e), and MFD x like Figure 3 As shown in (f). Similarly, Figure 3 (j) and 3(k) show the MFD for the field strength of the TM mode, where the MFD x exist Figure 3 (j) and MFD y exist Figure 3 In (k). As shown, in this example, TE mode MFD x and MFD y The MFD is tightly matched to the inherent TE mode of SMF-28 fiber—at 10 μm. However, the TM mode MFD... x and MFD y There is a certain amount of mismatch between the TE mode and the inherent TM mode of the SMF-28. This mismatch is attributed to the waveguide geometry, which complicates increasing the MFD along the vertical direction. This indicates that the TE mode has lower insertion loss compared to the TM mode.

[0042] exist Figure 4 In the example shown, the grating elements of the tapered waveguide 102 and the 2D bi-anisotropic SWG structure 104 comprise Si, and the cladding 106 comprises silicon dioxide. In this example, the height of the tapered waveguide 102 is... h tw It is 220 nm, and the height of the grating element is... h swg It is 220 nm (i.e., h tw = h swg Furthermore, periodicity It is 2000 nm, fill rate It is periodic The function, periodic It is 200 nm, and the fill rate is... It is 0.10. Figure 4 (a) is a plan view of the SSC 100 and SMF-28 optical fibers. Figure 4 As shown in (b), the effective refractive index n eff Along the propagation length L It exhibits a smooth transition. Here, although... n eff Only slight changes (e.g. with) Figure 3 (b) compared to the one shown), but in the inspection Figure 3 There are obvious slight differences in the field distribution in (c)—wherein Figure 3 The MFD shown in the field distribution of (c) is slightly greater than Figure 4 (c) shows the MFD. This is especially true relative to the TM mode field distribution. However, it is worth noting that, compared to Figure 4 The TM mode loss increases in the associated example implementations (e.g., due to scattering from the grating element), as described below. Figure 13 As shown in the diagram, Figure 13 The diagram illustrates the relationship with Figure 3 and 4The loss variation between related example implementations. Conversely, the loss reduction in TE mode (e.g., due to high...) h swg (caused by changes), which can also be described below. Figure 13 I saw it in the middle.

[0043] exist Figure 5 In the example shown, the grating elements of the tapered waveguide 102 and the 2D bi-anisotropic SWG structure 104 include SiN x The cladding 106 comprises silicon dioxide. In this example, the height of the tapered waveguide 102 is... h tw It is 160 nm, and the height of the grating element h swg It is 160 nm (i.e., h tw = h swg Furthermore, periodicity It is 2000 nm, fill rate It is periodic The function, periodic It is 200 nm, and the fill rate is... It is 0.10. Figure 5 (a) is a plan view of SSC 100 and SMF-28 optical fiber. Figure 5 (b) shows the TE pattern (dot) and TM pattern (square) along the propagation length. L effective refractive index n eff Star-shaped data points ( Figure 5 (b) (overlapping) illustrates the inherent TE and TM modes of SMF-28 fiber. These lines represent the fit between the TE and TM modes. n eff . n eff The graph illustrates the gradual transition from TE and TM modes to the inherent mode of SMF-28 fiber. n eff . Figure 5 (c) shows the corresponding mode distributions – the top of the TE mode and the bottom of the TM mode – and illustrates how the initial mode diameter is adjusted to approximate the mode diameter of the SMF-28 fiber. It is noteworthy that there is a match between the TE and TM mode distributions and SMF-28.

[0044] Here, a 3D FDTD analysis can be performed again, and the field distribution can be checked to evaluate the matching of the mode with these SMF-28 fiber modes. Figure 5 (d) and 5(i) illustrate the surface field distribution (e.g., relative to...)x - z Cross-sections of mode distribution in plane-shaped and SSC 100 and SMF-28 fiber modes. x - y view-- Figure 5 (d) is for TE mode and Figure 5 (i) refers to TM mode. For TE mode... Figure 5 In (e) and 5(f) and for TM mode in Figure 5 (j) and 5(k) show the relative to x shaft and y One-dimensional intensity distribution of the axis. It is worth noting the TE mode and TM mode MFD. x (that is, along) x (Direction) and MFD y (that is, along) y The orientation matches the inherent TE and TM modes of SMF-28 fiber. However, a certain amount of mismatch exists in the MFD, indicating that SiN... x The potential loss in the silicon-based 2D bi-anisotropic SWG structure 104 is slightly higher (e.g., compared to the silicon-based 2D bi-anisotropic SWG architecture 104).

[0045] exist Figure 6 In the example shown, the grating elements of the tapered waveguide 102 and the 2D bi-anisotropic SWG structure 104 include SiN x The cladding 106 comprises silicon dioxide. In this example, the height of the tapered waveguide 102 is... h tw It is 250 nm, and the height of the grating element h swg It is 250 nm (i.e., h tw = h swg (Here, altitude) h tw and h swg Greater than and Figure 5 Height in related examples. Furthermore, periodicity. Λ x It is 2000 nm, fill rate It is periodic Λ x The function, periodic It is 200 nm, and the fill rate is... It is 0.10. Figure 6 (a) is a plan view of SSC 100 and SMF-28 optical fibers. (Comparison) Figure 5 and Figure 6The performance shown in the figure, when the height h tw and height h swg At wavelengths greater than approximately 150 nm, there is no significant difference. This indicates that SiN... x The SSC 100 base is designed to accommodate various heights to fit different SiN substrates (e.g., various foundries or processes). x High standards.

[0046] Therefore, as indicated in the examples above, Si-based SSC 100 and SiN x The design of the SSC 100 is highly robust and can be implemented across different material platforms and foundries without significantly impacting performance.

[0047] As indicated above, provide Figures 3 to 6 As an example. Other examples can be related to... Figures 3 to 6 The descriptions are different.

[0048] Figures 7 to 12 The figure illustrates the simulation results, showing the impact of different parameter variations associated with the SSC 100 described in this paper. Figure 7 The diagram shows the fill rate. The values ​​of each are along the propagation direction of the Si-based SSC 100 (e.g., where the tapered waveguide 102 and the grating elements of the 2D bi-anisotropic SWG structure 104 are Si SSC 100). z Effective refractive index (direction) n eff TE mode occurs on the left and TM mode on the right. Figure 7 In the examples shown in (a) to 7(d), periodicity The change from 100 nm to 3000 nm affects the fill rate. (For example ).exist Figure 7 Different fill rates were used in (a) to 7(d): In (a) =0.10, in (b) =0.25, in (c) =0.50 and in (d) =0.75, while maintaining =200 nm. Furthermore, the 2D bi-anisotropic SWG structure 104 has a radius of... R swg =7μm, height h tw =220 nm and height h swg=90 nm. As shown, in larger periodicity... In this case, Changes in this do not lead to significant differences in the effective refractive index. However, at lower periodicity... (e.g., from about 100 nm to about 200 nm) with larger Compared to values ​​(e.g., 0.75), use smaller values. (e.g., 0.10) results in a propagation length of L The effective refractive index transitions rapidly. Therefore, smaller... This may contribute to increased losses. However, the 2D bi-anisotropic SWG structure 104 can exhibit larger periodicity. (For example Designed to be >1000 nm), this means that these are related to The inconsistency becomes negligible, indicating that the impact on performance is minimal.

[0049] right Figure 7 Perform 3D FDTD for each of cases (a) through 7(d), and the effective mode field diameter (MFD) eff The calculation is as follows: in E ( x, y )express x - y The mode electric field distribution on the plane, and A eff This refers to the effective pattern area. MFD eff Equations 3 and 4 can be used to calculate, and the corresponding mapping is as follows: Figure 7 As shown in (e) to 7(h). It is worth noting that when periodic... For wavelengths greater than 1000 nm, TE mode MFD eff With SMF-28 optical fiber MFD eff Closely matched, across various fill rates Achieving 10 μm MFD eff ,like Figure 7 As shown in (e) to 7(h). In contrast, for TM modes under similar conditions (i.e., periodic) >100 nm), MFD eff The range is from approximately 7 μm to approximately 8 μm. Figure 7 (e) to 7(h)), which means that the TM mode has more coupling / insertion loss compared to the TE mode. Moreover, in smaller periodicity... At (e.g., from about 100 nm to about 200 nm), the mode field diameter of the TE mode ranges from about 6 μm to about 8 μm, and the mode field diameter of the TM mode ranges from about 6 μm to about 7 μm. This indicates that in these smaller periodicities... Under these conditions, the losses in both TE and TM modes increase due to scattering from the grating elements. However, for larger periodicity... (For example >1000 nm), when coupled to SMF-28, both polarization modes can operate efficiently with minimal insertion loss. Therefore, SSC 100 relative to fill rate The changes are steady.

[0050] Figure 8 Figures (a) to (c) illustrate the radius of the Si-based SSC 100 being evaluated. R swg Effective refractive index of various values n eff The associated simulation results show that the TE mode occurs on the left and the TM mode on the right. In this example, periodicity... Λ x From 100 nm to 3000 nm, the fill rate It is periodic functions (e.g.) The radius used in this example R swg As follows Figure 8 As shown in (a) to 8(c): (a) R swg =5 μm, (b) R swg =7 μm, and (c) R swg =9 μm. Fill rate It is 0.10, periodic. It is 200 nm, and highly h swg It is 90 nm. The mapping curve shows that at a radius R swg Within the range, effective refractive index n eff The variation is minimal. However, in the periodicity from 100 nm to 200 nm... Λ x Below, there exists an effective refractive index n eff Rapid transitions along the direction of propagation (e.g., with periodicity) Λ x (Compared to larger values). This implies periodicity. Λ x SSC 100 with smaller values ​​will experience higher losses. Conversely, for larger periodicity values... Λ x (For example Λ x The smooth mode transition from the refractive index of the TE and TM modes to the refractive index of the SMF-28 mode (>1000 nm) indicates minimal loss.

[0051] Figure 8 (d) through 8(f) show the targets Figure 8 3D FDTD simulations performed for each scenario given in (a) through 8(c) and MFD eff The calculation results (using equations 3 and 4) are shown on the left in TE mode and on the right in TM mode. For various waveguide radii ( R swg =5 μm, 7 μm and 9 μm) and periodicity For wavelengths greater than 250 nm, TE mode MFD eff It is tightly aligned with the 10 μm MFD of the SMF-28 fiber. In contrast, the TM mode shows... MFD eff The insertion loss is approximately 8 μm, indicating a higher insertion loss compared to the TE mode. Both the TE and TM modes experienced significant mode mismatch, which increased periodicity. The insertion loss is smaller when the value is smaller, such as Figure 8 As shown in (d) to 8(f). However, in periodic... When the value is large, the radius R swg The variation is within a given range and will not affect the performance of the SSC. Therefore, the Si-based SSC 100 has a radius... R swg The changes are robust. It's worth noting that, relative to these examples, a design radius may be required. R swg This is to extend the mode field diameter to approximately 10 μm.

[0052] Figure 9 (a) to 9(b) showed a high degree of h swg and periodicity Effective refractive index of various values n eff Mapping: (a) for a height of 90 nm h swg and (b) for a height of 220 nm h swg Here, altitudeh tw It is 220 nm, periodic. It is 200 nm, fill rate It is 0.10, and the radius is... R swg It is 7 μm. Furthermore, periodicity... In nm, and fill rate As mentioned above, relative to Figure 7 and 8 Adjust as described. As shown, for larger heights... h swg At effective refractive index n eff Rapid changes exist in (e.g.) Figure 9 (b) shown), this may contribute to radiation loss. Conversely, in larger periodicity... (For example At >1000 nm, the effective refractive index n eff The mode transition is smoother, similar to that of... Figure 7 and 8 What was observed. At a height of 90 nm. h swg and a height of 220 nm h swg ,exist Figure 9 (c) and 9(d) respectively target Figure 9 The cases shown in (a) and 9(b) provide valid examples. MFD eff (Calculated using equations 3 and 4 based on 3D FDTD simulation). These figures show a larger periodicity. Copy relative to Figure 7 and 8 The findings are illustrated in the diagram. It is noteworthy that the height... h swg Changes MFD eff The impact is minimal, indicating a significant tolerance for height variations of the grating elements in the 2D bi-anisotropic SWG structure 104 during fabrication.

[0053] The effect of geometric changes on SiN can be evaluated similarly. x The base SSC 100 (e.g., where the tapered waveguide 102 and the 2D bi-anisotropic SWG structure 104 are grating elements comprising SiN) x The effective refractive index of SSC 100 n eff The impact. Figure 10 (a) to 10(d) show the various fill rates. effective refractive index n eff Mapping, where configuration (a) is used. =0.10, (b) =0.25, (c) =0.50, and (d) =0.75. Here, the radius is... R swg It is 7 μm, height h swg It is 250 nm, and highly h tw It is 250nm. As shown, there is a smaller periodicity. This will lead to an effective refractive index n eff The rapid transition increases radiation loss. Furthermore, when... It is 0.75 and periodic. When the effective refractive index is less than 250 nm, n eff The refractive index is not close to that of silicon dioxide / SMF-28 mode, which affects the tightness of the field confinement within the grating element of the 2D bi-anisotropic SWG structure 104. However, when periodic... When the effective refractive index is greater than 1000 nm, n eff Periodicity across change The transition is relatively smooth, which indicates minimal impact on performance and a large preparation tolerance.

[0054] To verify the mode diameter, Figure 10 Perform 3D FDTD simulations for each configuration given in (a) through 10(d), and use equations 3 and 4 to calculate the corresponding... MFD eff The result is as follows Figure 10 As shown in (e) to 10(h). Here, for larger periodicity... TE mode MFD eff Greater than approximately 9 µm, while for TM mode, MFD eff The range is from approximately 7 µm to approximately 8 µm, indicating a higher insertion loss for the TM mode. Conversely, at lower periodicity... Below, both polarizations show a range of approximately 6 µm. MFD eff This can lead to significant mode mismatch and increased insertion loss. Therefore, in some implementations, periodicity can be used. Choose a sufficiently high value to ensure that both modes... MFD effWith SMF-28 MFD eff Matching, thus matching SiN x The width of the grating element varies along the propagation direction (i.e., This demonstrates a high tolerance.

[0055] Figure 11 (a) to 11(c) illustrate SiN x Base SSC 100 in radius R swg Effective refractive index when the value changes n eff The simulation results are shown, with the TE mode shown on the left and the TM mode shown on the right. Periodicity and fill rate With radius R swg The radius used in the simulation has changed. R swg As follows Figure 11 As shown in (a) to 11(c): (a) R swg =5 μm, (b) R swg =7μm, and (c) R swg =9 μm. Furthermore, periodicity It is 0.10, periodic. It is 200 nm, height h tw It is 250, and the height is... h swg It is 250 nm. For example... Figure 11 As shown in (a) to 11(c), when the radius R swg With a large periodicity When changing (e.g.) >1000 nm), effective refractive index n eff No significant difference was observed. However, for smaller periodicities... (with fill rate) (Irrelevant), effective refractive index n eff Rapid changes increase radiation loss.

[0056] Figure 11 (d) to 11(f) show Figure 11 3D FDTD simulations for each case given in (a) through 11(c) and MFD eff The results of the calculations (using equations 3 and 4). Regarding the radius...R swg The various values ​​and large periodicity (For example >1000 nm), TE mode MFD eff It is approximately 9 µm. In contrast, the TM model shows approximately 7 µm to approximately 8 µm. MFD eff This indicates a higher insertion loss compared to the TE mode. Both the TE and TM modes experienced greater mode mismatch, resulting in higher insertion loss during periodic changes. At smaller values, a larger insertion loss occurs, such as Figure 11 As shown in (d) to 11(f). However, in periodic... In the case of a larger radius R swg Variations within a given range are acceptable. It is worth noting that the radius... R swg It may need to be designed to correspond to the MFD of SMF-28. In this example, the MFD is 10 µm, and therefore a different radius was chosen. R swg To optimize the effective radius. For example... Figure 11 The data provided does not indicate any significant performance challenges for SiN. x Base SSC 100 for radius R swg The changes are steady.

[0057] Figure 12 (a) to 12(c) illustrate the height h swg The value of SiN changes x Effective refractive index obtained from simulation based on SSC 100 n eff The mapping curve: (a) h swg =160 nm, (b) h swg =250 nm, and (c) h swg =400nm. In this example, the height h tw With height h swg Matching. Furthermore, fill rate. It is 0.10, periodic. It is 200nm, and the radius R swg It is 7 μm. For example... Figure 12 As shown in (a), for smaller heightsh swg and larger periodicity There exists from SiN x A smooth mode transition from waveguide mode to SMF-28 fiber mode. For example... Figure 12 As shown in (a) to 12(c), in periodic In smaller cases, the fast effective refractive index from waveguide mode to SWG mode n eff Transitions can lead to radiation loss. During periods... In larger cases (e.g.) >1000 nm), there exists from SiN x Smooth effective refractive index to SMF-28 n eff Changes. It is worth noting that at high altitudes... h swg Within the variation, if periodic A relatively large effective refractive index n eff There are no significant changes, which means that the design can tolerate height in this case. h swg The changes.

[0058] Figure 12 (d) to 12(f) illustrate the height h swg The different values ​​are based on 3D FDTD simulation calculations. MFD eff .and Figure 10 and 11 The example shown is similar, TE MFD eff Approximately 9 µm, and TM MFD eff The insertion loss is approximately 7 to 8 µm. Therefore, the TM mode may have a higher insertion loss than the TE mode. In periodic... In larger cases, this example shows the same... Figure 10 and 11 The same observations were shown. Therefore, height h swg Changes MFD eff The impact is minimal, indicating minimal influence during preparation. h swg The variation has a large tolerance.

[0059] As indicated above, for illustrative purposes, the following is provided: Figures 7 to 12 As an example. More specifically, with Figures 7 to 12The associated parameter values ​​for SSC 100 are provided for illustrative purposes, and SSC 100 (e.g., Si-based SSC 100, SiN...) x Based on SSC 100 or Si / SiN x Base SSC 100) can be used with Figures 7 to 12 The related examples use different parameter values ​​in their design.

[0060] Figures 13 to 14 The figure illustrates the simulation results, showing the insertion loss and PDL associated with the SSC 100 described in this paper. Figure 13 The simulation results for the Si-based SSC 100 are illustrated. 3D FDTD simulations were performed on the Si-based SSC 100 with SMF-28 fiber for both TE and TM modes to analyze the performance. Figure 1A and 1B The wavelength-dependent loss, insertion loss, and polarization-dependent loss of the Si-based SSC 100 structure are shown. TE and TM modes are emitted as inputs to the SSC 100, and the field coupled to the SMF-28 fiber is monitored. Simulation results are as follows: Figure 13 As shown, (a) illustrates the TE mode, and (b) illustrates the TM mode. This is presented in two scenarios: height... h swg =90 nm and high h tw =220 nm (i.e., h swg < h tw ,like Figure 1A (as shown), and height h swg =220 nm and height h tw =220 nm (i.e., height) h swg =Height h tw ,like Figure 1B (As shown). Here, periodicity It is 200 nm, fill rate Fact 0.10, periodic It is 2000 nm, fill rate It is periodic functions (e.g.) ), and radius R swg It's 7 μm. (Targeting...) h swg < h twScene (top graph) and h swg = h tw Scene (bottom curve chart). Figure 13 (a) to 13(b) show the TE mode and TM mode at different wavelengths, respectively. The mode field distribution when propagating down into an SMF-28 fiber. For example... Figure 13 As shown in (a) to 13(b), the dashed arrows indicate minimal field distribution variation from approximately 1500 nm to approximately 1600 nm, indicating low wavelength-dependent loss and a low, flat insertion loss spectrum. (The above is relative to...) Figure 3 and 4 The described analysis shows that the MFD (Mean Difference) is tightly matched between the SSC 100 and SMF-28 fiber modes. Furthermore, the TE mode exhibits a tighter match compared to the TM mode. (The above is relative to...) Figures 7 to 9 The described parametric analysis confirms these observations.

[0061] To estimate insertion loss, the modes propagating in SMF-28 fiber overlap with the inherent modes of SMF-28 fiber. 3DFDTD further confirms the low insertion loss of the TE mode, such as... Figure 13 As illustrated in the intermediate curve of (a), the loss of the TM mode is slightly higher, such as Figure 13 (b) is illustrated by the intermediate curve. The dots and squares respectively indicate... h swg < h tw Scene and h swg = h twSimulation data for the scenarios, with polynomial fitting, are shown as solid lines. Notably, there is no significant difference in the insertion loss spectrum between the TE and TM modes. In the wavelength λ range from 1500 nm to 1600 nm, the insertion loss in the TE mode is less than approximately 0.6 dB, and the wavelength-dependent loss is less than approximately 0.03 dB. For the TM mode, the insertion loss is less than approximately 1.3 dB, and the wavelength-dependent loss is less than approximately 0.11 dB. At 1550 nm, the polarization-dependent loss is less than approximately 0.75 dB. Based on these results, the Si-based SSC 100 is suitable for 100 nm wide C-band applications (e.g., 1530 nm to 1565 nm), and the geometric properties of the tapered waveguide 102 and / or the 2D bi-anisotropic SWG structure 104 can be tuned for other bands, such as the O-band or L-band (e.g., 1565 nm to 1625 nm). Furthermore, the SSC 100 is tolerant of process variations and has low nonlinearity (e.g., compared to conventional Si SSC designs), which means that the SSC 100, including the 2D bi-anisotropic SWG structure 104, is suitable for high-power applications.

[0062] Figure 14 The diagram illustrates SiN x Simulation results based on SSC 100. For TE and TM modes, simulations of SiN with SMF-28 fiber are presented. x The SSC 100 was used to perform 3D FDTD simulations to analyze the data with... Figure 1B Wavelength-dependent loss, insertion loss, and polarization-dependent loss of the Si-based SSC 100 structure are shown. 3D FDTD analysis was performed on the geometry using SMF-28 fiber. TE and TM modes were excited as inputs to SiN. x The input of the SSC 100 and the field coupled to the optical fiber are monitored. Figure 14 The simulation results are presented, with (a) showing the TE mode and (b) showing the TM mode. Three scenarios were analyzed: height... h swg =Height h tw =160 nm, h swg =Height h tw =250 nm, and h swg =Height h tw =400 nm. Here, periodicity. It is 200 nm, fill rate It is 0.10, periodic. It is 2000 nm, fill rate It is periodic functions (e.g.) ), and radius R swg It is 7 μm. In Figure 14 In (a) through 14(b), the top (first and second) curves and the bottom curves show the mode shapes of the TE and TM modes transmitted into the SMF-28 fiber.

[0063] Here, the first scene (i.e., altitude) h swg =Height h tw =160 nm) is shown at the first top, and the second scene (i.e., height) is shown at the top. h swg =Height h tw =250 nm) is shown at the second top, and the third scene (i.e., height) is shown at the top. h swg =Height h tw =400 nm) is shown at the bottom. Wavelengths from 1500 nm to 1600 nm... λ The field distribution within the range shows minimal variation, as indicated by the dashed arrow, indicating low wavelength-dependent loss, low insertion loss, and a relatively flat spectral response. To estimate the insertion loss, data from SiN... x The propagation mode of the SSC 100 fiber overlaps with the inherent mode of the SMF-28 fiber. As described above... Figure 5 As illustrated, there is a match between the TE mode and TM mode MFDs of SiNx-based SSC 100 and SMF-28 fibers. (As shown above relative to...) Figure 12 The described parameter analysis shows that as altitude increases... h swg The minimal changes. 3D FDTD simulations support these observations, indicating lower insertion loss in the TE mode, such as... Figure 14 (a) shows the intermediate curve, and the insertion loss is slightly higher for TM mode, as shown in the figure. Figure 14 (b) is shown as the middle curve. Figure 14 The dots, squares, and triangles in the diagram represent the simulation data for the first, second, and third scenes, respectively, and their polynomial fitting is shown as a solid line. It is worth noting that the first scene (i.e., h swg =Height h tw =160 nm) has a lower insertion loss for TE mode and a higher IL for TM mode, while the third scenario (i.e., hswg =Height h tw =400) then illustrates the opposite result. This is due to the asymmetry of the waveguide height and width. Therefore, in some cases, dimensions similar to those in the second scenario can be chosen (i.e., h swg =Height h tw =250), to improve the insertion loss of TE and TM modes. For the second scenario, at wavelengths from 1500 nm to 1600 nm. λ Within the range, the insertion loss of TE mode (e.g.) Figure 14 (a) shows approximately 1.0 dB, and the wavelength-dependent loss is less than approximately 0.08 dB. Compared to the TM mode in the second scene, as shown... Figure 14 As shown in (b), the insertion loss is approximately 1.4 dB, and the wavelength-dependent loss is less than approximately 0.05 dB. Furthermore, at 1550 nm, the polarization-dependent loss is less than approximately 0.4 dB. Therefore, SiN… x SSC 100 based materials may be suitable for 100 nm wide C-band applications. Of course, SiN... x The geometric properties of the tapered waveguide 102 and / or the 2D bi-anisotropic SWG structure 104 based on the SSC 100 can be selected for operation in another band (such as the O-band or L-band). It is further worth noting that SiN... x The SSC 100 base can tolerate process variations and has reduced nonlinearity, which makes SiN... x The SSC 100 base can be used in high-power applications.

[0064] As indicated above, for illustrative purposes, the following is provided: Figures 13 to 14 As an example. More specifically, with Figures 13 to 14 The associated parameter values ​​for SSC 100 are provided for illustrative purposes, and SSC 100 (e.g., Si-based SSC100, SiN) x Based on SSC 100 or Si / SiN x Base SSC 100) can be used with Figures 13 to 14 The related examples use different parameter values ​​in their design.

[0065] In this way, the SSC 100, including the 2D bi-anisotropic SWG structure 104, can provide one or more of the following features and advantages: (1) an SSC capable of manipulating the beam mode field diameter or distribution; (2) using specific geometric parameters (e.g., periodicity). Periodicity Fill rate Fill rate ,radius (3) Smaller mode transition length or taper length compared to conventional SSCs; (4) Coupled with SMFs of arbitrary mode diameters (e.g., fibers with 6 μm MFD, 8 μm MFD, 10 μm MFD, etc.); (5) Lower nonlinearity compared to conventional waveguides, which reduces nonlinear loss and is particularly beneficial for high-power applications; (6) Improved tolerance to parameter (e.g., tip width), fabrication process and other process variations compared to conventional waveguides; (7) Applicability across different wavelength ranges (e.g., very close infrared, such as about 780 nm to about 1300 nm, and O-band, E-band, S-band, C-band or L-band) with only adjustment of waveguide parameters; or (8) Compatibility with other material platforms (by appropriate adjustment of waveguide dimensions).

[0066] The foregoing disclosure provides illustrations and descriptions, but is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. Modifications and variations can be made based on the foregoing disclosure, or modifications and variations can be derived from practice of the embodiments. Furthermore, any of the embodiments described herein can be combined, unless the foregoing disclosure explicitly provides for reasons why one or more embodiments may not be combined.

[0067] As used in this article, depending on the context, satisfying the threshold can mean a value greater than the threshold, greater than or equal to the threshold, less than the threshold, less than or equal to the threshold, equal to the threshold, not equal to the threshold, etc.

[0068] Even though specific combinations of features are listed in the claims and / or disclosed in the specification, these combinations are not intended to limit the disclosure of various embodiments. In fact, many of these features can be combined in ways not specifically listed in the claims and / or specifically disclosed in the specification. Although each dependent claim listed below may be directly dependent on only one claim, the disclosure of various embodiments includes every dependent claim combined with every other claim in the claim set. As used herein, the phrase “at least one of” in the list of references refers to any combination of these items, including single members. For example, “at least one of: a, b, or c” is intended to cover a, b, c, ab, ac, bc, and abc, as well as any combination having multiple identical items.

[0069] When a component or one or more components (e.g., a waveguide or one or more laser waveguides) is described or claimed (within a single claim or across multiple claims) to perform or be configured to perform multiple operations, this language is intended to broadly cover a wide range of architectures and environments. For example, unless explicitly claimed otherwise (e.g., by using “first component” and “second component” or other language distinguishing components in the claims), this language is intended to cover a single component performing or configured to perform all operations, a group of components jointly performing or jointly configured to perform all operations, a first component performing or configured to perform a first operation and a second component performing or configured to perform a second operation, or any combination of components performing or configured to perform these operations. For example, when a claim takes the form “one or more components are configured to: perform X; perform Y; and perform Z,” the claim should be interpreted as meaning “one or more components are configured to perform X; one or more (possibly different) components are configured to perform Y; and one or more (possibly different) components are configured to perform Z.”

[0070] Unless explicitly stated otherwise, the elements, actions, or instructions used herein should not be construed as critical or necessary. Furthermore, as used herein, the articles “a” and “an” are intended to include one or more items and are interchangeable with “one or more.” Further, as used herein, the article “the” is intended to include one or more items referenced in conjunction with the article “the” and is interchangeable with “one or more.” Additionally, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, or a combination of related and unrelated items) and is interchangeable with “one or more.” In cases referring to only one item, the phrase “only one” or similar language is used. Furthermore, as used herein, the terms “has,” “have,” “having,” etc., are intended as open-ended terms. Further, unless explicitly stated otherwise, the phrase “based on” is intended to mean “at least partially based on.” Furthermore, as used herein, unless otherwise explicitly stated (e.g., when used in combination with "either" or "only one of"), the term "or" is intended to be inclusive when used in series and may be used interchangeably with "and / or". Further, spatial relative terms (such as "below," "lower," "above," "upper," etc.) may be used herein for ease of description to describe the relationship of one element or feature to another element or feature illustrated in the accompanying drawings. In addition to the orientations depicted in the accompanying drawings, spatial relative terms are intended to cover different orientations of devices, apparatuses, and / or elements in use or operation. The device may be oriented in other ways (rotated 90 degrees or in other orientations), and the spatial relative descriptors used herein may be interpreted accordingly.

Claims

1. A photonic integrated circuit (PIC) including a spot size converter SSC, said SSC comprising: A tapered waveguide having a length along a first direction and a width along a second direction. Wherein the first direction is parallel to the propagation direction, and the second direction is perpendicular to the propagation direction; and A two-dimensional (2D) bi-anisotropic subwavelength grating (SWG) structure, wherein a portion of the 2D bi-anisotropic SWG structure is in the second direction and surrounds a portion of the tapered waveguide along the first direction.

2. The PIC according to claim 1, wherein the periodicity of the grating element of the 2D bi-anisotropic SWG structure along the first direction is different from the periodicity of the grating element of the 2D bi-anisotropic SWG structure along the second direction.

3. The PIC according to claim 1, wherein the periodicity of the grating element of the 2D bi-anisotropic SWG structure along the first direction matches the periodicity of the grating element of the 2D bi-anisotropic SWG structure along the second direction.

4. The PIC according to claim 1, wherein the fill rate of the grating element of the 2D bi-anisotropic SWG structure along the first direction is different from the fill rate of the grating element of the 2D bi-anisotropic SWG structure along the second direction.

5. The PIC according to claim 1, wherein the fill rate of the grating element of the 2D bi-anisotropic SWG structure along the first direction matches the fill rate of the grating element of the 2D bi-anisotropic SWG structure along the second direction.

6. The PIC according to claim 1, wherein one or more grating elements of the 2D bi-anisotropic SWG structure have a rectangular shape, an elliptical shape or a trapezoidal shape.

7. The PIC of claim 1, wherein the size of the grating element is based on the wavelength range associated with the SSC.

8. The PIC according to claim 1, wherein the grating elements of the 2D bi-anisotropic SWG structure are symmetrically distributed along the tapered waveguide and extend along the first direction.

9. The PIC according to claim 1, wherein the dielectric constant of the bi-anisotropic SWG structure along the first direction is different from the dielectric constant of the bi-anisotropic SWG structure along the second direction.

10. The PIC according to claim 1, wherein the dielectric constant of the bi-anisotropic SWG structure along the third direction is different from the dielectric constant of the bi-anisotropic SWG structure along the first direction and the dielectric constant of the bi-anisotropic SWG structure along the second direction.

11. The PIC according to claim 1, wherein the height of the grating element of the 2D bi-anisotropic SWG structure is different from the height of the tapered waveguide.

12. The PIC according to claim 1, wherein the height of the grating element of the 2D bi-anisotropic SWG structure is matched with the height of the tapered waveguide.

13. The PIC of claim 1, wherein the tapered waveguide comprises at least one of silicon or silicon nitride.

14. The PIC according to claim 1, wherein the tapered waveguide is a segmented waveguide.

15. The PIC of claim 1, wherein the 2D bi-anisotropic SWG structure comprises a silicon grating element surrounded by one or more of silicon dioxide, a refractive index matching fluid, or air.

16. The PIC of claim 1, wherein the 2D bi-anisotropic SWG structure comprises a silicon nitride grating element surrounded by one or more of silicon dioxide, a refractive index matching fluid, or air.

17. The PIC of claim 1, wherein the periodicity of the grating element of the 2D bi-anisotropic SWG structure along the first direction and the periodicity of the grating element of the 2D bi-anisotropic SWG structure along the second direction are less than approximately ,in It is the operable wavelength associated with the SSC, and n It is the refractive index of the 2D bi-anisotropic SWG structure.

18. The PIC of claim 1, wherein the grating element of the 2D bi-anisotropic SWG structure is oriented at 90° relative to the propagation direction.

19. The PIC of claim 1, wherein the grating element of the 2D bi-anisotropic SWG structure is oriented at an arbitrary angle relative to the propagation direction.

20. The PIC of claim 1, wherein the grating elements of the 2D bi-anisotropic SWG structure are arranged in a Gaussian pattern, a linear pattern, an apodization pattern or a parabolic pattern relative to the plane defined by the first direction and the second direction.

21. A photonic integrated circuit (PIC) including a spot size converter (SSC), wherein the SSC comprises: The first section includes the first part of the tapered waveguide; The second section includes: a second part of the tapered waveguide, and a first part of a bi-anisotropic subwavelength grating (SWG) structure comprising multiple grating elements. The second portion of the bi-anisotropic SWG structure surrounds the second portion of the tapered waveguide along the length of the second segment; and The third section includes the second part of the bi-anisotropic SWG structure.

22. A photonic integrated circuit (PIC) including a spot size converter (SSC), said SSC comprising: A waveguide having a length along a first direction and a width along a second direction perpendicular to the first direction; as well as A two-dimensional (2D) bi-anisotropic subwavelength grating (SWG) structure surrounds a portion of the tapered waveguide along the first direction. The dielectric constant of the bi-anisotropic SWG structure relative to the first direction is different from the dielectric constant of the bi-anisotropic SWG structure relative to the second direction, and The dielectric constant of the bi-anisotropic SWG structure relative to the third direction is different from the dielectric constant of the bi-anisotropic SWG structure relative to the first direction and the dielectric constant of the bi-anisotropic SWG structure relative to the second direction.

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