Polarizing beam splitter-rotator

Abstract

The invention relates to a polarizing beam splitter-rotator. A photonic integrated circuit (PIC) may include a polarization rotator. The polarization rotator may include a first waveguide layer including a first set of waveguides. At least one waveguide in the first set of waveguides may be a segmented waveguide. The polarization rotator may include a second waveguide layer including a second set of waveguides. The refractive index of the core material of the second set of waveguides may be less than the refractive index of the core material of the first set of waveguides.

Description

Cross-references to related applications

[0001] This patent application claims priority to U.S. Provisional Patent Application No. 63 / 717,659, filed November 7, 2024, entitled “MULTI-CORE METAMATERIAL-ENHANCED ON-CHIP POLARIZATION SPLITTER-ROTATOR”. The disclosure of that earlier application is considered part of this patent application and is incorporated herein by reference. Technical Field

[0002] This disclosure generally relates to polarization beam splitter-rotator (PSR) and PSRs comprising one or more segmented waveguides. Background Technology

[0003] A polarization beamsplitter-rotator (PSR) is a passive photonic component that splits polarized light into two separate paths based on the polarization state of the light. A PSR can operate with transversely electrically (TE) or transversely magnetically (TM) polarized light. In PSR operation, one polarized light input is converted to its orthogonal polarization state at the output of one path, while the other polarized light input retains its original state at the output of the other path. For example, a PSR can convert TM-polarized light to TE polarization and retain TE-polarized light in its original state. This capability improves the manipulation and management of light within photonic integrated circuits (PICs), contributing to advancements in devices requiring polarization insensitivity, the efficiency of coherent optical transceivers, and on-chip optical communication systems. Summary of the Invention

[0004] In some embodiments, a photonic integrated circuit (PIC) including a polarization rotator includes a first waveguide layer comprising a first set of waveguides, wherein at least one of the waveguides in the first set is a segmented waveguide; and a second waveguide layer comprising a second set of waveguides, wherein the refractive index of the core material of the second set of waveguides is less than the refractive index of the core material of the first set of waveguides.

[0005] In some embodiments, the PIC including a polarization beamsplitter-rotator includes a polarization rotator comprising: a first set of waveguides in a first waveguide layer, wherein at least one of the waveguides in the first set is a segmented waveguide; a second set of waveguides in a second waveguide layer, wherein the refractive index of the core material of the second set of waveguides is less than the refractive index of the core material of the first set of waveguides; and a polarization beamsplitter and a mode beamsplitter, wherein the polarization beamsplitter is optically connected to the mode beamsplitter.

[0006] In some embodiments, the PIC including the polarization rotator includes a silicon (Si) waveguide layer comprising a group of segmented Si waveguides, wherein the periodicity of the segmented Si waveguides is less than about 900 nanometers (nm), and wherein the fill factor of the segmented Si waveguides is in the range of about 0.1 to about 0.8; and silicon nitride (SiN). x Waveguide layer, the SiN x The waveguide layer includes a set of SiN x waveguide. Attached Figure Description

[0007] Figure 1 This is a schematic diagram illustrating an example implementation of a PSR that includes one or more segmented waveguides as described herein.

[0008] Figure 2 Examples of calculated dielectric constants relative to fill rates for various wavelengths are illustrated.

[0009] Figure 3 This is a diagram illustrating the effective refractive indices of the basic transverse electric (TE0) mode, the basic transverse magnetic (TM0) mode, and the first-order TE (TE1) mode of an example implementation of a PSR with different spacer region heights described herein.

[0010] Figure 4-7 It is a diagram showing the process of... Figure 3 The diagram shows the field distribution determined by the effective refractive index.

[0011] Figure 8 The illustration shows the intrinsic mode expansion for the excitation of TE0 and TM0 modes in an example implementation of the PSR described herein.

[0012] Figure 9 The effect of fill ratio on power constraint in the waveguide of the PSR described in this paper is shown as the spacer height varies.

[0013] Figure 10 This paper illustrates the effect of fill rate on power constraint in the waveguide of the PSR described herein, with respect to a given spacer height and a change in another fill rate.

[0014] Figure 11 The figure illustrates the effective refractive index of the rotating segment of the PSR described in this paper for different width values ​​of the segmented waveguide.

[0015] Figure 12 This is a graph illustrating the coupling factor associated with the PSR described in this paper as the spacing between the waveguides of the PSR varies.

[0016] Figure 13Examples of effective refractive indices for different modes supported by the waveguide of the PSR described in this paper along the mode beamsplitter of the PSR are illustrated.

[0017] Figure 14-17 This is a schematic diagram illustrating the field distribution determined by the effective refractive index, which shows how the modes are distributed along the beam length of the PSR described in this paper.

[0018] Figure 18 This is a diagram illustrating an example associated with the mode transition length of the PSR described in this article.

[0019] Figure 19 This is a diagram illustrating examples of coupling factors associated with different values ​​of the fill rate relative to the PSR mode beam splitter described herein.

[0020] Figure 20 The diagram illustrates the effective refractive indices of the fundamental and first-order modes over the entire length of the PSR described in this paper. Detailed Implementation

[0021] The following detailed description of exemplary embodiments is based on the accompanying drawings. The same reference numerals in different drawings may identify the same or similar elements.

[0022] Silicon photonics is a promising platform for PSR because of its high refractive index, which supports higher-order TE modes (e.g., TE1) and facilitates extensive hybridization and coupling between TE1 modes and the fundamental TM (TM0) modes. This hybridization and coupling can be used to rotate TM0 modes to TE1 modes within silicon (Si) waveguides. Notably, materials with relatively low refractive indices (such as silicon nitride (SiN)) are also suitable for this purpose. x Waveguides made of SiN require wider dimensions to achieve similar hybridity and coupling. This is because SiN... x The birefringence between the TE1 and TM0 modes in the waveguide is minimal. Weak birefringence means that significant perturbations are needed to increase mode clutter and coupling, resulting in longer mode transition lengths, which may be impractical for some PIC applications.

[0023] However, passive photonic components, such as PSRs, can benefit from using SiN coated with silicon dioxide (SiO2). x Waveguide. This is because, compared to conventional silicon waveguides, SiN... x It provides improved performance. For example, SiN x It exhibits significantly reduced optical nonlinearity and thermo-optical effects, which makes SiN... x Suitable for applications such as high power. Furthermore, SiN... xThe waveguide has a low refractive index, which reduces waveguide loss due to scattering (caused by sidewall roughness), meaning that SiN... x Waveguides allow for variations in waveguide dimensions. Therefore, SiN x PSR can play an important role in PIC.

[0024] Some technologies use hybrid SiN x -Si PSR. Pure SiN x PSR based on SiN is not commonly used, possibly due to the fact that pure SiN... x The low birefringence and minimal perturbation effect of pure SiN-based PSRs. Additionally, due to perturbations at lower wavelengths, pure SiN-based PSRs are conventionally designed for relatively short wavelength ranges (e.g., from about 800 nm to about 1000 nm). However, the perturbations are relatively small (e.g., 0.00286), which requires a longer taper length (typically in the millimeter range), making integration into a compact device a challenge.

[0025] To design an efficient PSR operating in different optical bands (e.g., O-band, E-band, S-band, C-band, or L-band), hybridization of TE1 and TM0 modes (i.e., The engineering design is important. This engineering process may involve the use of SiN... x The region contains hybrid segments of Si and N. x Hybrid PSR in the Si transition section has been used in the transition back to SiN x The layers before the transition facilitate mode rotation and beam splitting within the Si waveguide. However, due to the transition section (e.g., SiN...) x to Si and Si to SiN x Such methods may introduce additional losses, especially in TM modes. Additionally, significant two-photon absorption (TPA) losses can occur in Si waveguides due to their high nonlinearity at higher power levels. Alternative methods include SiN... x A conventional Si waveguide is placed beneath the waveguide. This method enhances the perturbation between the TE1 and TM0 modes, making the mode more stable in SiN. x Rotation within the waveguide becomes easier. However, this straying tends to be weak, meaning a longer transition length is required. Additionally, this type of configuration causes significant optical leakage into conventional silicon waveguides, which induces nonlinear absorption and limits its usability in high-power applications.

[0026] Some embodiments described herein provide a PIC including a polarization rotator comprising one or more segmented waveguides. In some embodiments, the polarization rotator includes a first waveguide layer (e.g., a Si waveguide layer) comprising a first set of waveguides (e.g., a set of Si waveguides), wherein at least one of the waveguides in the first set is a segmented waveguide. The polarization rotator also includes a second waveguide layer (e.g., SiN...). x The second waveguide layer includes a second set of waveguides (e.g., a set of SiN waveguides). x (Waveguide). Here, the refractive index of the core material of the second waveguide can be less than the refractive index of the core material of the first waveguide.

[0027] In some implementations, one or more parameters of the segmented waveguide, such as fill factor... or periodic This can be selected to control the propagation of light along the segmented waveguide of the polarization rotator. In some implementations, the segmented waveguide introduces anisotropy and provides precise control over the effective refractive index of the modes, and reduces absorption loss when handling high power, while simultaneously enhancing mode hybridization and coupling (e.g., in SiN). x In segmented waveguides, due to the large straying introduced from the underlying Si segmented waveguide, the conversion length is reduced and the total optical loss is reduced.

[0028] Some implementations include segmented SiN x The use of Si metamaterials enables high-power PSRs to exhibit low optical and absorption losses as well as reduced mode transition lengths. In some embodiments, segmented SiN... x Segmented / metamaterial waveguides in Si can be used to enhance coupling and hybridization between the TE1 and TM0 modes, effectively reducing the mode transition length in both the rotating and beam-splitting sections. Notably, the segmented waveguides described in this paper provide low nonlinearity, which reduces absorption losses at high power. Furthermore, most of the optical power can be confined within SiN. x Within the waveguide, this further reduces nonlinearity and overall optical loss. It is worth noting that although the implementation described in this paper is based on SiN... x This technique is applicable to Si periodic segmented structures or subwavelength gratings (SWGs), but the techniques described in this paper are suitable for conventional SiN waveguides with both periodic and aperiodic structures. x (i.e., non-segmented) waveguide or SiN x Various material platforms for segmented waveguides are available, and they can accommodate different waveguide sizes. Additional details are provided below.

[0029] Figure 1This diagram illustrates an example embodiment of the PSR 100, which includes one or more segmented waveguides. In some embodiments, the one or more segmented waveguides of the PSR 100 form an SWG structure or metamaterial. Figure 1 The image above illustrates a plan view of the PSR100 (e.g., on the xz plane), while Figure 1 The figure below illustrates a cross-sectional view of the PSR 100 (e.g., on the yz plane). In some implementations, the PSR 100 can be implemented in a PIC. Figure 1 As shown, PSR 100 may include: a first waveguide layer 102, which includes a first set of waveguides 104 (e.g., waveguides 104a and 104b); a second waveguide layer 106, which includes a second set of waveguides 108 (e.g., waveguides 108a and 108b); and a covering 110. In some embodiments, such as Figure 1 As shown, at least one waveguide 104 is a segmented waveguide (e.g., both waveguides 104a and 104b are segmented waveguides). Figure 1 (segmented waveguide in the middle).

[0030] In some implementations, such as Figure 1 As shown, the PSR 100 includes a polarization rotator. The polarization rotator can be used with... Figure 1 The “rotation” segment of PSR 100, as indicated by the symbol, corresponds to and can be a segment of PSR 100, wherein polarization or mode rotation of light is provided (e.g., when light propagates from left to right along the z-direction through PSR 100). In some embodiments, the polarization rotator of PSR 100 may include one or more segmented waveguide segments (e.g., segmented waveguide 104a, segmented waveguide 104b, waveguide 108a along length...). L 1 arrive L 4 (segmented sections). Additionally or alternatively, the polarization rotator of the PSR 100 may include one or more tapered waveguide segments (e.g., waveguides 104a and 104b along the length of the segmented sections). L 2 arrive L 3 The tapering section, waveguide 108a along the length L 3 Additionally or alternatively, the polarization rotator of the PSR 100 may include curved waveguide segments that taper exponentially (e.g., waveguides 104a and 104b in length...). L 1 arrive L 5 (within the section).

[0031] As further shown, in some embodiments, the PSR 100 also includes a mode beam splitter. The mode beam splitter can be used with... Figure 1 The “beam splitter” segment of PSR 100, as indicated by the symbol, corresponds to and can be a segment of PSR 100, wherein mode beam splitting is performed (e.g., when light propagates from left to right through PSR 100 along the z-direction). In some embodiments, the mode beam splitter of PSR 100 may include one or more segmented waveguide segments (e.g., segmented segments of waveguide 108a and waveguide 108b). Additionally or alternatively, the mode beam splitter of PSR 100 may include one or more tapered waveguide segments (e.g., tapered segments of waveguide 108a and / or waveguide 108b). Additionally or alternatively, the mode beam splitter of PSR 100 may include curved waveguide segments that taper exponentially (e.g., waveguide 108b at length...). L 5 (within the section). Here, the polarization rotator of the PSR 100 can be optically connected to the mode beam splitter. In some embodiments, the mode beam splitter of the PSR 100 can be a directional coupler (e.g., two parallel SiN...). x Segmented waveguides (but narrow band due to phase matching length) or thermal couplers (e.g., for wide band operation).

[0032] As further shown, in some embodiments, the PSR 100 also includes a separator. The separator can be connected with... Figure 1 The term "splitter" corresponds to the "splitter" section of PSR 100 and can be a section of PSR 100 that provides separation of light (e.g., when light propagates from left to right through PSR 100 along the z-direction). Here, the mode beam splitter of PSR 100 can be optically connected to the splitter. In some embodiments, the splitter of PSR 100 may include one or more circular bends, Euler bends, or S-shaped bends.

[0033] Additional details regarding the operation of the polarization rotator, mode beam splitter, and separator of the PSR 100 are provided below.

[0034] In some implementations, the refractive index of the core material of the second waveguide 108 is less than that of the core material of the first waveguide 104 (e.g., at a given wavelength). In one example, the first waveguide layer 102 may be a Si waveguide layer, and the second waveguide layer 106 may be a SiN waveguide layer. x Waveguide layers, which means that the core material of the first waveguide 104 is Si, and the core material of the second waveguide 108 is SiN. x At a wavelength of 1550 nanometers (nm), the refractive index of Si is approximately 3.5, and SiN...x The refractive index of (e.g., Si3N4) is approximately 2.0. Therefore, the refractive index of the core material of the second waveguide 108 is less than the refractive index of the core material of the first waveguide 104 (e.g., 2.0 < 3.5).

[0035] In some embodiments, the covering 110 may include one or more of silica, an index-matching fluid, or air. For example, the bottom portion of the covering 110 (e.g., the portion covering 110 up to the surface of the second waveguide layer 106) may include silica, and the top portion of the covering 110 (e.g., the portion covering 110 above the second waveguide layer 106) 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 close to that of another portion of the material covering 110 at a selected wavelength (e.g., to reduce reflection and scattering at the interface between silica and the index-matching fluid). In one example, the bottom portion of the covering 110 may include silica, and the top portion of the covering 110 may include an index-matching fluid in the form of an epoxy resin with a refractive index close to that of silica. Therefore, in some embodiments, the first set of waveguides 104 or the second set of waveguides 108 may be surrounded by one or more of silica, an index-matching fluid, or air.

[0036] In some embodiments, as described above, the first group of waveguides 104 may include one or more segmented waveguides. That is, in some embodiments, the first group of waveguides 104 may include one or more waveguides comprising core material segments (e.g., Si), wherein a portion of the cladding 110 is between a given pair of adjacent waveguide segments of waveguide 104. In such embodiments, waveguide 104 may be segmented relative to the x-direction, such that waveguide 104 is periodic in the x-direction, and / or may be segmented relative to the z-direction, such that waveguide 104 is periodic in the z-direction. For example, as... Figure 1 As shown, the first group of waveguides 104 may include waveguide 104a and waveguide 104b, wherein waveguide 104a and waveguide 104b are periodic in the z-direction. Λ Si Segmented waveguides. In some implementations, such as Figure 1 As shown, the length of a given waveguide 104 (e.g., waveguide 104a or waveguide 104b) is relative to the z-direction, and the width of a given waveguide 104 is relative to the x-direction. Here, the z-direction is parallel to the propagation direction of light through the PSR 100, and the x-direction is perpendicular to the propagation direction. In some embodiments, as shown, the width of waveguide 104 varies along the z-direction. For example, waveguide 104 varies along its entire length. L 1 The top has width w1,Si Then, the width of waveguide 104 is in length L 2 Above from w 1,Si Increase (e.g., linearly increase) to w 2,Si And in length L 3 Above from w 2,Si Reduce (e.g., linearly reduce) to w 1,Si The width of waveguide 104 is along its entire length. L 4 and length L 5 Part of it is w 1,Si In some implementations, the width of waveguide 104 is... w 2,Si It can be smaller than approximately 450 nm. In some embodiments, waveguide 104 has a high... h Si .

[0037] In some implementations, such as Figure 1 As shown, one or more waveguide segments of the waveguides in the first set of waveguides 104 (e.g., each waveguide segment of waveguide 104a and each waveguide segment of waveguide 104b) may have a shape elongated in length at a 90-degree (°) orientation relative to the propagation direction (e.g., the z-direction). Alternatively, in some embodiments, one or more waveguide segments of the waveguides in the first set of waveguides 104 may have a shape elongated in length at an arbitrary angle (e.g., less than 90°) relative to the propagation direction. For example, one or more waveguide segments of waveguide 104a or waveguide 104b may have a shape elongated in length at an angle tilted to 90° (such as an angle between about 70° and 90°, or an angle between about 50° and 90° (e.g., about 85°)). Alternatively, in some embodiments, one or more waveguide segments of the waveguides in the first set of waveguides 104 may have a shape elongated in length at an orientation that is nearly parallel to the propagation direction (e.g., parallel within manufacturing tolerances).

[0038] In some implementations, a given waveguide 104 of the first set of waveguides 104 may include one or more curved waveguide segments that taper exponentially. For example, in Figure 1 In the middle, waveguide 104a and waveguide 104b each include lengths of L 1 or length L 5The waveguide 104 comprises two exponentially tapering curved waveguide segments (e.g., such that the first group of waveguides 104 includes four exponentially tapering curved waveguide segments). In some embodiments, the curved segments of waveguide 104 (e.g., waveguide 104a or waveguide 104b) can facilitate a smooth field transition with minimal loss. Furthermore, in some embodiments, waveguide 104 can be arranged symmetrically with respect to the centerline of waveguide 108a, such as... Figure 1 As shown. In some embodiments, along the taper length associated with waveguides 104a and 104b (e.g., along the length...) L 2 The spacing between waveguide 104a and waveguide 104b ranges from about 0.3 micrometers (μm) to about 2.5 μm.

[0039] In some embodiments, the second set of waveguides 108 may include one or more waveguides that are at least partially segmented. That is, in some embodiments, the second set of waveguides 108 may include one or more waveguides that include core material segments (e.g., SiN). x ), wherein a portion of the covering 110 lies between a given pair of adjacent waveguide segments of waveguide 108. In such embodiments, waveguide 108 may be segmented relative to the z-direction such that waveguide 108 is periodic in the x-direction, and / or may be segmented relative to the z-direction such that waveguide 108 is periodic in the z-direction. For example, as Figure 1 As shown, the second group of waveguides 108 may include waveguide 108a and waveguide 108b. Here, waveguide 108a is periodically oriented in the z-direction. Λ SiN From the entire length L 1 to length L 6 It is segmented. Similarly, waveguide 108b is periodically segmented in the z-direction. Λ SiN In length L 5 Above a part and throughout the entire length L 6 The upper part is segmented. In some implementations, such as Figure 1 As shown, the length of a given waveguide 108 (e.g., waveguide 108a or waveguide 108b) is relative to the z-direction, and the width of a given waveguide 108 is relative to the x-direction. In some embodiments, as shown, the width of waveguide 108 varies along the z-direction. For example, waveguide 108a varies in length... L 0 Above from w 0,SiN Increase to w 1,SiNM And throughout the entire length L1 and length L 2 The top has width w 1,SiN Then, the width of waveguide 108a is in length L 3 Above from w 1,SiN Increase to w 2,SiN And throughout the entire length L 4 and length L 5 The top has width w 2,SiN The width of waveguide 108a and then its length L 6 Above from w 2,SiN Decrease back w 3,Si And in length L 7 Above has width w 3,Si Similarly, the width of waveguide 108b varies with its length. L 5 Above a part is w 4,SiN In length L 6 Above from w 4,SiN Increase to w5 ,SiN And in length L 7 Above has width w 5,SiN In some implementations, a given waveguide 108 has a high h SiN In some implementations, the height of waveguide 108 h SiN The height can be different from (e.g., greater than) that of waveguide 104. h Si Additional or alternative ground, waveguide 108 height h Si It can be matched with the height of waveguide 104 h Si Matching (e.g., approximately equal).

[0040] In some implementations, such as Figure 1 As shown, the segmented waveguide 104 can be periodic. Λ Si and fill rate ρSi (For example, in the case of segmentation along the z-direction, relative to the z-direction). The width of a given segment of waveguide 104 is equal to... Λ Si ρ Si The value, and the width of the gap between a pair of adjacent segments of waveguide 104 (e.g., the width of a portion of the covering 110 between the pair of adjacent segments of waveguide 104) is equal to (1- ρ Si ) Λ Si The value of . It is worth noting that in some embodiments, waveguide 104 may be segmented in a similar manner (e.g., having the same periodicity / fill rate or having different periodicity / fill rates) relative to the x-direction (e.g., perpendicular to the propagation direction). In some embodiments, the periodicity of the segmented waveguide 104 Λ Si It can be smaller than approximately ,in It is the operating wavelength of PSR 110, and n This is the refractive index of the segmented waveguide 104. In some implementations, this is achieved by using periodicity... Λ Si Set to less than The diffraction effect is reduced or minimized. Therefore, in some embodiments, the dimensions (e.g., width and / or length) of a given segment of waveguide 104 can be based on the wavelength range associated with PSR 100. As a specific example, in some embodiments, the periodicity of segmented waveguide 104... Λ Si It can be smaller than approximately 400 nm (e.g., enabling the use of PSR 100 in the O-band). As another example, the periodicity of the segmented waveguide 104... Λ Si It can be less than about 500 nm (e.g., enabling the use of PSR 100 in the C+L band). In some embodiments, the fill rate associated with the segmented waveguides 104 in the first set of waveguides 104. ρ Si It can be in the range of about 0.1 to about 0.8.

[0041] Similarly, such as Figure 1 As shown, the segmented waveguide 108 can be periodic. Λ SiN and fill rate ρ SiN (For example, in the case of segmentation along the z-direction, relative to the z-direction). The width of a given segment of waveguide 108 is equal to... Λ SiN ρSiN The value, and the width of the gap between a pair of adjacent segments of waveguide 108 (e.g., the width of a portion of the covering 110 between the pair of adjacent segments of waveguide 108) is equal to (1- ρ SiN ) Λ SiN The value of . It is worth noting that in some embodiments, waveguide 108 may be segmented in a similar manner (e.g., having the same periodicity / fill rate or having different periodicity / fill rates) relative to the x-direction (e.g., perpendicular to the propagation direction). In some embodiments, the periodicity of the segmented waveguide 108 Λ SiN It can be smaller than approximately ,in It is the operable wavelength of PSR 110, and n It is the refractive index of the segmented waveguide 108, as described above. In some embodiments, by periodicity... Λ SiN Set to less than The diffraction effect is reduced or minimized. Therefore, in some embodiments, the dimensions (e.g., width and / or length) of a given segment of waveguide 108 can be based on the wavelength range associated with PSR 100. As a specific example, in some embodiments, the periodicity of segmented waveguide 108... Λ SiN It can be smaller than approximately 700 nm (e.g., enabling the use of PSR 100 in the O-band). As another example, the periodicity of the segmented waveguide 108... Λ SiN It can be smaller than about 900 nm (for example, enabling the use of PSR 100 in the C+L band).

[0042] In some embodiments, the PSR 100 includes a spacer region between the first waveguide layer 102 and the second waveguide layer 106. Figure 1 In the example shown, the spacer area is a region with height h space The area, and includes a portion of covering 110. Alternatively, in some embodiments, the second waveguide layer 106 may be on the first waveguide layer 102 (e.g., h space = 0nm), or the first waveguide layer 102 can be on the second waveguide layer 106 (e.g., h space = 0 nm).

[0043] As indicated above, provide Figure 1 This is just one example. Other examples can be found related to... Figure 1 The examples described are different. Provided Figure 1 The number and arrangement of layers and components shown are for illustrative purposes. In practice, with... Figure 1 Compared to what is shown, there may be additional components and / or layers, fewer components and / or layers, different components and / or layers, or components and / or layers with different arrangements. Furthermore, Figure 1 The two or more elements and / or layers shown can be implemented within a single element, or Figure 1 The single element shown can be implemented as multiple distributed elements and / or layers. Additionally or alternatively, Figure 1 The set of elements and / or layers shown (e.g., one or more elements and / or layers) can perform what is described as being composed of Figure 1 The other set of elements and / or layers shown perform one or more functions. As a specific example, in some embodiments, PSR 100 may include a third waveguide layer (e.g., a waveguide layer different from the first waveguide layer 102 and the second waveguide layer 106). In some embodiments, the third waveguide layer may serve as a core layer. In this embodiment, the third waveguide layer may guide light, and the first waveguide layer 102 and the second waveguide layer 106 may be used to modify the polarization state of the light guided in the third waveguide layer, rather than primarily operating to provide light guidance. Alternatively, the third waveguide layer may serve as a cladding layer. In this embodiment, the third waveguide layer may surround the other layers of PSR 100 to, for example, help to confine light more effectively and reduce interaction with the external environment of PSR 100.

[0044] In some implementations, the segmented waveguide structures described herein (e.g., segmented waveguide 104 or segmented waveguide 108) can be modeled using Effective Medium Theory (EMT) as follows: (1a) (1b) in ,as well as here, Indicates the material's fill rate (e.g., or i ), Indicates periodicity along the direction of propagation (e.g., or ), This refers to the dielectric constant of the core material (e.g., in SiN-based materials). x In the case of segmented waveguide 108, Or, in the case of a segmented waveguide 104 based on Si, for ),and This refers to the dielectric constant of the 110 coating (e.g., in the case of 110 coated with silicon dioxide). It is worth noting that the above equation simplifies the segmented / metamaterial structure by homogenizing the segmented / metamaterial structure.

[0045] Equations 1a and 1b can be used to calculate the dielectric permittivity or dielectric constant of a homogenized medium, which is an artificial medium representing a segmented waveguide (e.g., segmented waveguide 104 and / or segmented waveguide 108) having a dielectric constant that varies with direction. Therefore, using Equations 1a and 1b, the characteristics of segmented waveguide 104 and / or segmented waveguide 108 required to maintain effective dielectric properties at different wavelengths can be determined. Figure 2 The figure shows the relative fill rate for various wavelengths λ. Calculated dielectric constant Examples. In particular, Figure 2 (a)-(c) and Figure 2 (d)-(f) show the results for Si-based segmented waveguide 104 and SiN, respectively. x Calculation of the base segmented waveguide 108 and Examples of dielectric constants. Figure 2 As shown, in order to maintain effective dielectric properties, the operating wavelength... It should be significantly greater than the periodicity. Therefore, in Figure 2 In (a)-(c), It can be smaller than about 400 nm (e.g., capable of operating in the O band) and smaller than about 500 nm (e.g., capable of operating in the C+L band). Similarly, in Figure 2 In (d)-(f), It can be smaller than about 700 nm (e.g., capable of operating in the O band) and smaller than about 900 nm (e.g., capable of operating in the C+L band). Figure 2 The arrow in the middle shows when and With operating wavelength The EMT violation at that time. Relative to Figure 2 An EMT violation refers to a situation where the EMT is no longer applicable, i.e., when the EMT (the homogenized medium is designed based on it) is no longer effective. For example, if the periodicity or characteristic size of the segmented waveguide (e.g., segmented waveguide 104 or segmented waveguide 108) is no longer valid, , If the wavelength of the light source (e.g., the wavelength of the incident light) is equal to or greater than the wavelength of the incident light, making the diffraction effect significant, an EMT violation may occur. For example, when the ratio... Λ / λ Approaching or exceeding 1 / n At that time, an EMT violation occurred, among which Λ It is the periodicity of the segmented waveguide. λ It is the wavelength of the incident light, and n This is the refractive index of the segmented waveguide. As mentioned above, it provides... Figure 2 This is just one example. Other examples can be found related to... Figure 2 The descriptions are different.

[0046] As mentioned above Figure 1 In some embodiments, the width of the waveguide 108a of the PSR can vary along the propagation direction (e.g., w 0,SiN w 1,SiN w 2,SiN Similarly, the width of a given waveguide 104 can transition along the propagation direction (e.g., w 1,Si w 2,Si w 1,Si In some implementations, variations in the width of waveguide 108a and / or waveguide 104 can facilitate polarization mode rotation. Relative to the operation of PSR 100, the mode rotation trajectory can be divided into six segments—length... L 0 to length L 5 , where the length L 1 arrive L 4 This includes polarization rotation sections (e.g., the polarization rotator of PSR 100). Within these lengths, the length... L 0 , L 1 and L 5 This can be considered a "relaxed" length, where interaction with other modes is minimal. Conversely, it may be necessary to choose a length that is less sensitive to interference. L 2 , L 3 and L 4 This is to ensure effective mode conversion.

[0047] In some implementations, the PSR 100 may include a dual waveguide segment comprising two thermally adiabatic segmented waveguide sections—in lengthL 6 A portion of waveguide 108a and in length L 6 It is part of waveguide 108b. In some implementations, such as Figure 1 As shown, these waveguide segments can extend along the length L 6 gap g Separation. In some implementations, the gap... g Mode switching from waveguide 108a to waveguide 108b can be achieved through adiabatic coupling. In some embodiments, as described above, along the length L 6 The PSR 100 segment can be referred to as a mode beam splitter. In some implementations, in length L 7 The bends in waveguides 108a and 108b (e.g., Figure 1 The S-shaped bend shown in the diagram can separate the two fundamental transverse electric (TEO) modes propagating through waveguides 108a and 108b. In some embodiments, waveguide 108b in the mode beam splitter of PSR 100 may include a bend (e.g., in length...). L 5 (in the middle), so as to facilitate a smooth field transition with minimal loss.

[0048] In some implementations, within the polarization rotator of the PSR 100, waveguides 104a and 104b can be positioned such that waveguides 104a and 104b are substantially located at the center of the boundary edge of waveguide 108a (e.g., as shown in the image). Figure 1 As shown, along the length L 2 and L 3 In addition, in some embodiments, waveguides 104a and 104b can be positioned such that the ends of waveguide 104a and 104b are away from waveguide 108a, such that waveguides 104a and 104b are substantially not below waveguide 108a (e.g., in areas such as...). Figure 1 The length shown L 1 In the region and along the length L 5 (within the region).

[0049] In some implementations, PSR 100 in L 1 arrive L 4 The segment provides polarization or mode rotation, followed by... L 6Pattern splitting is performed in the segment, and... L 7 Separate within the segment. Figure 3 The diagram illustrates the height of areas with different spacers. h space A graph showing the effective refractive indices of the PSR 100 in TE0, TM0, and TE1 modes. In some embodiments, the rotation section of the PSR 100 facilitates rotation from the TM0 mode to the TE1 mode while maintaining the integrity of the TE0 mode. Figure 3 The figures for 0 nm, 50 nm, 100 nm, and 150 nm are shown. h space The values ​​of the effective refractive indices for TE0, TM0, and TE1 modes. From Figure 3 As can be seen, strong spurious mixing exists between the TM0 and TE1 modes (indicated by dashed circles). This is because the segmented waveguide 104 (e.g., a Si-based segmented waveguide 104) (which excites the TE1 mode) enhances the perturbation coupled to the TM0 mode, thus causing spurious mixing. Figure 3 In the middle, at a high altitude h space With different values, the TM0 mode follows the path along any length. L Switch to TE1 mode. At altitude h space When the wavelength is 0 nm (i.e., when the second waveguide layer 106 is on the first waveguide layer 102), for TE0 mode and TM0... TE1 mode, at effective refractive index n eff Sharp peaks exist due to power leakage into segmented waveguide 104, introducing high photon absorption at high input power. For larger offsets (e.g., at least 50 nm in height)... h space There is no leakage to waveguide 104, but enhanced perturbation (meaning spurious activity) occurs. This applies to the high-power PSR 100 because the power is retained within the segmented waveguide 108, and the PSR 100 has very low nonlinearity, which reduces nonlinear power loss. It should be noted that for a height of 0 nm... h space You may need to select the fill rate. This is to ensure that there is no leakage to segmented waveguide 104, while maintaining condition 0.1. 0.5. Therefore, the thickness of the cladding 110 between the first waveguide layer 102 and the second waveguide layer 106 (e.g., the height of the cladding 110 between waveguide 104 and waveguide 108) is 0.5. h space It may be necessary to target specific The design aims to reduce or minimize nonlinear absorption losses while ensuring large perturbations facilitate hybridization. As described above, it provides... Figure 3 As an example. Other examples can be related to... Figure 3 The descriptions are different.

[0050] Figure 4-7 The diagram is drawn by Figure 3 The diagram showing the field distribution determined by the effective refractive index is used to illustrate the behavior of different modes within the polarization rotator of the PSR 100. Figure 4-7 The diagram illustrates how the power distribution pattern changes with altitude. h space It varies from 0 nm to 150 nm in increments of 50 nm. Figure 4 In the middle, corresponding to PSR 100, among which h space At 0 nm, the power of the TE0 and TM0 modes is significantly coupled into segmented waveguide 104, particularly at the location marked D. This coupling indicates higher leakage and potential nonlinear losses within segmented waveguide 104. Figure 5 The diagram shows the height. h space The field distribution of PSR 100 at 50 nm. Figure 6 and Figure 7 The diagram shows heights of 100 nm and 150 nm, respectively. h space The field distribution of PSR 100. In these cases, the power of the TE0 and TM0 modes is mainly retained within the segmented waveguide 108, especially at the same location D, which indicates a reduction in nonlinear power loss (e.g., SiN). x The reduction of nonlinearity in the PSR (Power Loss Reduction) is desirable for maintaining PSR efficiency, especially under high power conditions. Figure 4-7 The entire height shown h space During the change, the TM0 mode experienced spurious mixing with the TE1 mode. This spurious mixing was caused by a perturbation introduced by the segmented waveguide 104 and can be seen in the field distribution. Therefore, to the end of the rotation length (e.g., to the length) L 4 (At the end), TM0 mode changes to TE1 mode. As described above, it provides Figure 4-7 As an example. Other examples can be related to... Figure 4-7 The descriptions are different.

[0051] In some implementations, in order to achieve efficient mode switching along the rotational length of PSR 100, it is necessary to appropriately select the values ​​of a set of parameters (e.g., length). L0 ,length L 1 ,length L 2 ,length L 3 ,length L 4 ,length L 5 ,width w 0,SiN ,width w 1,SiN ,width w 2,SiN ,width w 1,Si or width w 2,Si Various heights are used in the following description. h space Values ​​(e.g., h space = 0 nm to 150 nm), and perform length adjustment. L 2 ,length L 3 and length L 4 Fine-tuning of the parameters. Note that before optimizing these lengths, it may be necessary to optimize one or more parameters of waveguide 104 (e.g., width). w 1,Si ,width w 2,Si Fill rate Si Periodicity Si (etc.) and / or one or more parameters of waveguide 108a (e.g., width, etc.) w 0,SiN ,width w 1,SiN ,width w 2,SiN Fill rate Si Periodicity SiN (etc.) so as to facilitate sufficient mixing as described above.

[0052] Figure 8 The illustration shows the eigenmode expansion of the fundamental modes excited by TE0 and TM0. In some embodiments, due to minimal interference with other modes, the length... L 0 , L 1 and L 5It can have relaxed constraints. In some implementations, to ensure a smooth transition in the modulus field distribution, the length can be... L 1 and L 5 Introducing a curved section of waveguide, such as Figure 1 As shown. During operation, TM0 and TE0 modes move from the input cone along the length... L 0 Excited, then the eigenmode travels along the length L 2 , L 3 and L 4 With height h space The value of the variation (e.g., different SiO2 thicknesses) expands and maintains the length. L 1 and L 5 Relaxation. For example... Figure 8 As shown in the figure above, when the TM0 mode is excited, along the length L 2 The mode extension will not significantly affect transmission or cause mode interference, thus making the length... L 2 Relaxation. However, length L 3 and L 4 Compared to TM0 Hybrid TE1 and Hybrid TE1 The conversion between TE1 modes is important. Therefore, length L 3 + L 4 It can be selected for implementing the overall TM0 The optimal conversion length for TE1 mode conversion. Conversely, in the case of TE0 input, such as Figure 8 As shown in the figure below, due to the high refractive index contrast, there is no interference from other modes, and the TE0 mode is present throughout the entire length. L 2 , L 3 and L 4 Transmission occurs without significant loss. Note that... Figure 8 The different lines in the diagram represent different heights. h space Different values ​​(e.g., 0 nm, 50 nm, 100 nm, and 150 nm). As described above, [the following is provided] Figure 8 As an example. Other examples can be related to... Figure 8 The descriptions are different.

[0053] Simulation can be used to determine different parameters (such as fill rate). Fill rate and gap g How does it affect the hybridization of modes within PSR 100? Figure 9 The fill rate is shown. With altitude h space The effect of changes on the power constraint in waveguide 104 and waveguide 108a. For example, in Figure 9 In (a), the power constraints for TE0 mode, hybrid TM0 mode, and hybrid TE1 mode are at a height of 0 nm. h space As shown. The dashed lines with markings indicate the power constraints in waveguide 104, while the solid lines indicate the power constraints in waveguide 108a. Note the difference in fill rate. At higher refractive indices, power leakage occurs into waveguide 104. This can be addressed by controlling the fill factor. It can control the maximum power within the segmented waveguide 108a. Figure 9 (f)-(j) illustrates the relationship with Figure 9 (a)-(e) Coupling coefficient factors under the same conditions The dots and solid lines represent the simulation and fitted data, respectively. As shown in the figure, with height... h space Increasing from 0 nm to 200 nm, such as Figure 9 As shown in (a)-(e), the increased power within waveguide 108a reduces leakage to waveguide 104. However, this also results in reduced straying in both the TM0 and TE1 modes, as... Figure 9 As shown in (f)-(j). Due to this trade-off, the optimal height should be chosen. h space This is to ensure maximum power and significant straying within waveguide 108a. It is worth noting that even with large offsets (e.g., 200 nm), a large fill ratio cannot be used. In some implementations, the fill rate It can be limited to a range of approximately 0.1 to approximately 0.8, such as Figure 9 The shaded areas in (a)-(j) are shown to achieve enhanced straying and maximum power coupling within waveguide 108a. As described above, this provides... Figure 9 As an example. Other examples can be related to... Figure 9 The descriptions are different.

[0054] Figure 10 This shows the effect of varying fill rates. 100 nm height h space Fill rate The impact on power constraints in waveguide 104 and waveguide 108a. Figure 10 (a)-(d) show the power constraints in waveguide 104 and waveguide 108, while Figure 10 (e)-(h) show when Figure 10 (a) and (e) – 0.2 Figure 10 (b) and (f) 0.4, Figure 10 (c) and (g) 0.6, and Figure 10 (d) and (h) Coupling factor when varying by 0.8 . Figure 10 The dashed and solid lines depicted in (a)-(d) illustrate the power constraints in waveguide 104 and waveguide 108a, respectively. As shown, for a smaller fill ratio... (For example, 0.2), most of the power remains within waveguide 108. However, as Figure 10 As shown in (e), when the fill rate Low impurities exist between approximately 0.5 and 1.0, while at higher filling ratios... When the value is less than 0.5, impurities are present. As the fill rate increases... As the number of particles increases, the amount of impurities increases, such as... Figure 10 As shown in (e)-(h), however, the power in waveguide 104 also increases, as... Figure 10 As shown in (a)-(d). Due to this trade-off, in some implementations, the fill rate... It can be targeted at a specific fill rate and height h space And thus designed. Figure 10 The shaded areas in (a)-(h) show the fill rate required to achieve the desired straying and maintain most of the power within waveguide 108a. As mentioned above, it provides Figure 10 As an example. Other examples can be related to... Figure 10 The descriptions are different.

[0055] Figure 11 The diagram illustrates the width. w 2,Si Different values ​​of the effective refractive index along the rotational section of PSR 100 n eff Note that in relation to Figure 11In related examples, width w 1,Si It is 150 nm, height h space It is 100 nm, fill rate It is 0.5, and the fill rate is... It's version 1.0. For example... Figure 11 As shown in (a)-(h), with the width w 2,Si The increasing frequency and strong pattern mixing result in a coupling factor that... It gets bigger. However, when the width w 2,Si At or above approximately 450 nm, mode power leaks into waveguide 104. The arrow indicates... Figure 11 This power leakage in (g)-(h) can limit the power leakage to such a large width. w 2,Si Therefore, in some implementations, the fill rate is used in the range of about 0.1 to about 0.8. ,width It can be smaller than approximately 450nm. As mentioned above, it provides... Figure 11 As an example. Other examples can be related to... Figure 11 The descriptions are different.

[0056] It also performed the spacing in the x-direction between waveguides 104 (e.g., in such a way as...) Figure 1 The length shown L 2 Analysis of the impact of internal (filling ratio) on impurities. In this analysis, the filling ratio... The fill rate is 0.5. It is 1.0 and the height is... h space It is 100nm. Figure 12 The diagram illustrates the coupling factor as the spacing between waveguides 104 changes. The image. Note, as... Figure 12 As shown, maximum straying and a shorter transition length are achieved with a spacing of approximately 1.3 μm. The shaded areas (e.g., spacing greater than or equal to approximately 0.3 μm and less than or equal to approximately 2.5 μm) indicate the spacing required between waveguides 104 to achieve a certain level of straying. As described above, [the following is provided] Figure 12 As an example. Other examples can be related to... Figure 12 The descriptions are different.

[0057] In some implementations, as described above, the mode beam splitter of the PSR 100 can be set at a length of L 6 (and length) L 7Within. In some embodiments, the mode beam splitter can operate to beam the TE1 mode, which rotates from the TM0 input in the rotating section of the PSR 100. In some embodiments, waveguide 108b is provided to beam the TE1 mode. In some embodiments, waveguide 108b is an adiabatic waveguide. In some embodiments, the width of waveguide 108b can be varied such that waveguide 108 includes a tapered section. For example, in one embodiment, as waveguide 108a extends along its length... L 6 From width w 2,SiN (For example, 3500nm) Gradually shrinks to the width w 3,SiN (e.g., 1000 nm), waveguide 108b can be along the length L 6 From width w 4,SiN (For example, a width that tapers from approximately 300 nm to 700 nm) w5 ,SiN In some implementations, waveguide 108b may include a curved section to reduce scattering loss and facilitate a smooth mode transition of the TE1 mode from the waveguide 108a to the TE0 mode at waveguide 108b, while maintaining the TE0 mode of waveguide 108a at waveguide 108a. Figure 13 The diagram illustrates the effective refractive index of different modes supported by waveguides 108a and 108b along the mode beamsplitter of PSR 100. n eff Examples. Figure 13 Each diagram in the figure represents a gap. g The value (e.g., in the range from 200 nm to 350 nm). TE 0A TE 1A TE 0B and TE 0B TE 1A This indicates the fundamental and first-order modes supported along the length of the mode beamsplitter. The modes of waveguides 108a and 108b are denoted by subscripts A and B, respectively. The dashed circle indicates the TE. 1A Pattern and TE 0B Strong hybrid regions between modes result in shorter TEs as described below. 1A TE 0B Transition length. Note that the TE1 mode of waveguide 108a follows the following... Figure 13 The path shown transitions to TE0 mode at waveguide 108b. Here, the gap... g Size does not significantly affect hybridization ( n=|n TE1A n TE0B |), which provides a relative gap g Robust tolerances in size. In some implementations, the PSR 100's mode beam splitter, after the adiabatic coupler (e.g., in the splitter section), has two S-shaped bends to ensure a length of robust tolerances. L 7 Internal separation TE 0A Mode (in waveguide 108a) and TE 0B Mode (in waveguide 108b). As described above, it provides... Figure 13 As an example. Other examples can be related to... Figure 13 The descriptions are different.

[0058] Figure 13 The effective refractive index shown n eff It indicates the field distribution, which shows how the mode is distributed along the beam length. Figure 14-17 The field distribution is shown. For example... Figure 14-17 As indicated, each figure has a different gap. g Correspondingly: Figure 14 middle g = 200 nm, Figure 15 middle g = 250 nm, Figure 16 middle g = 300 nm, and Figure 17 middle g = 350 nm. From Figure 14-17 As can be seen from the field distribution shown, due to the large refractive index contrast, TE 0A The mode remains within waveguide 108a without significant coupling or interference with other modes. However, the TE of waveguide 108a... 1A Pattern along length L 6 Gradually developed, and due to strong hybridization and coupling, it became the TE in waveguide 108b. 0B Patterns, such as Figures 14 to 17 As shown. Therefore, two TE0 modes are provided at the ends of the S-shaped bends in waveguides 108a and 108b. It is worth noting that, in addition to TE... 0A Pattern and TE 1A The TM0 mode (i.e., rotating from the TM0 mode) has no energy in other modes (ideally) because these other modes are not excited from the input terminals of the PSR 100. As described above, it provides Figure 14-17 As an example. Other examples can be related to... Figure 14-17 The descriptions are different.

[0059] As mentioned above Figure 13 As shown, in PSR 100, TE 1A Pattern and TE 0B Strong hybridization and coupling can exist between modes, resulting in short beam lengths. To calculate and verify TE... 1A TE 0B The beam splitting / conversion length, from the input end of the PSR 100 mode, excites the hybrid TE. 1A The pattern is defined, and intrinsic pattern extensions are performed. Figure 18 This is a diagram illustrating the correspondence between mode transition lengths. For example... Figure 18 As shown in the image above, in L = L TE1A TE0B Inside, TE 1A The power in the mode is completely converted to TE 0B Power in the mode (e.g., also as Figure 14-17 (As shown). Furthermore, as... Figure 18 As shown in the figure below, in TE 0A Excitation and length L for L TE0A TE0A In the case of TE 0A Most of the mode power is retained within waveguide 108a without any significant conversion or coupling (e.g., as well as...). Figure 14-17 (As shown). Figure 18 The different lines in the diagram represent gaps. g Different values ​​(e.g., 200 nm, 250 nm, 300 nm, and 350 nm). This further confirms the PSR 100 relative to the gap. g Large tolerances for variations. As mentioned above, providing... Figure 18 As an example. Other examples can be related to... Figure 18 The descriptions are different.

[0060] Figure 19 The diagram illustrates the fill rate of the mode beam splitter relative to PSR 100. Coupling factors with different values A diagram of related examples. (e.g.) Figure 19 As shown, the marked areas represent coupled and uncoupled regions, respectively. As illustrated, for fill ratios less than approximately 0.6... No coupling was observed (e.g., due to the low refractive index in the narrower waveguide). It is noteworthy that in some embodiments, waveguides 108a and 108b may have the same fill factor. Therefore, in order to achieve a larger coupling factor (On the contrary, shorter lengths) L 6 ), may require optimal fill rate (For example, approximately 0.9). As described above, it provides... Figure 19 As an example. Other examples can be related to... Figure 19 The descriptions are different.

[0061] Figure 20 The diagram illustrates the effective refractive indices of the fundamental mode and first-order mode along the entire length of the PSR 100. n eff . Figure 20 The diagram above identifies the rotating sections (e.g., polarization rotators), beam-splitting sections (e.g., mode beam splitters), and splitting sections (e.g., PSR 100 splitters) of the PSR 100. It also shows the effective refractive indices of the fundamental and first-order modes along the entire length of the PSR 100. n eff exist Figure 20 The figure below shows the results. As shown, the refractive index of the TE0 mode increases with the width of waveguide 108a, and becomes even larger when waveguides 104a and 104b have larger widths. The output is the TE0 mode in waveguide 108a, without any coupling or conversion due to its larger refractive index compared to other modes. On the other hand, in the rotating segment, the TM0 input is first coupled and strayed with the TE1 mode (in waveguide 108a), and then coupled and strayed with the TE0 mode (in waveguide 108b), and output as the TE0 mode at waveguide 108b. Most of the mode power is retained within waveguides 108a and 108b, which provides reduced optical and nonlinear losses for high-power applications. As described above, this provides... Figure 20 As an example. Other examples may differ from those regarding... Figure 20 As described.

[0062] In this way, one or more parameters of PSR 100 (e.g., fill rate) Si Fill rate SiN Periodicity Si Periodicity SiN (e.g., waveguides) can achieve precise control over mode propagation, ensuring that a given mode remains confined within a desired waveguide (e.g., waveguide 108a or waveguide 108b). This confinement can significantly reduce nonlinear losses caused by two-photon absorption. In some embodiments, the PSR 100 described herein exhibits lower nonlinearity (e.g., compared to conventional SiN...). xCompared to Si waveguides, this further reduces nonlinear losses. It is worth noting that the PSR 100 described herein can be used in a variety of applications, such as high-power applications, because the power is effectively contained within waveguides 108a and / or 108b, which may include inherently low-loss materials (e.g., SiN). x ).

[0063] It is worth noting that the PSR 100 described in this article is applicable across various bands, including O, E, S, C, and L bands, requiring only appropriate parameter adjustments. Furthermore, the PSR 100 described in this article can be used with Si platforms or SiN... x Platform compatibility, as described above, and compatibility with other material platforms (with appropriate tuning to waveguide dimensions).

[0064] 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 can be derived from practice with the embodiments. For example, the devices and behaviors described herein are based on the principle of reciprocal linear optics. However, the devices and behaviors described and claimed herein can be similarly applied to use in the opposite manner (e.g., light propagating in opposite directions through a PSR to achieve a polarization multiplexing combiner). Furthermore, any of the embodiments described herein can be combined unless the foregoing disclosure expressly provides reasons why one or more embodiments cannot be combined.

[0065] As used in this article, depending on the context, "meeting the threshold" can mean greater than the threshold, greater than or equal to the threshold, less than or equal to the threshold, equal to the threshold, not equal to the threshold, etc.

[0066] Even if 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 the various embodiments. In fact, many of these features can be combined in ways not specifically listed in the claims and / or not specifically disclosed in the specification. Although each dependent claim listed below may directly depend on only one claim, the disclosure of the various embodiments includes a combination of each dependent claim with each other claim in the claim set. As used herein, the phrase “at least one of” referring to a series of items means any combination of those items, including a single member. 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 of multiple identical items.

[0067] When a component or one or more components (e.g., one or more 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 otherwise expressly stated (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 operations. For example, when a claim has “one or more components configured to: perform X; perform Y; and perform Z,” the claim should be interpreted as meaning “one or more components configured to perform X; one or more (possibly different) components configured to perform Y; and one or more (possibly different) components configured to perform Z.”

[0068] Unless explicitly stated otherwise, no element, action, or instruction used herein should be considered critical or necessary. Furthermore, as used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more.” Furthermore, as used herein, the article “the” is intended to include one or more items referenced in connection with the article “the” and may be used interchangeably with “the one or more.” Furthermore, 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 may be used interchangeably with “one or more.” Where only one item is intended, the phrase “only one” or similar language is used. Furthermore, as used herein, the terms “has,” “have,” “having,” etc., are intended to be open-ended terms. Furthermore, unless otherwise explicitly stated, the phrase “based on” is intended to mean “based, at least in part, on”. Additionally, as used herein, the term “or” is inclusive when used in a series and can be used interchangeably with “and / or” unless otherwise explicitly stated (e.g., if used in conjunction with “either of” or “only one of”). Furthermore, for ease of description, spatially relative terms such as “below,” “lower,” “above,” “upper,” etc., may be used herein to describe the relationship of an element or feature to another element(s) or feature(s) shown in the figures. In addition to the orientations depicted in the figures, spatially 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 otherwise), and the spatially relative descriptors used herein may be interpreted accordingly.

Claims

1. A photonic integrated circuit (PIC) including a polarization rotator, the polarization rotator comprising: A first waveguide layer, the first waveguide layer including a first group of waveguides, wherein at least one waveguide in the first group of waveguides is a segmented waveguide; as well as The second waveguide layer includes a second set of waveguides. The refractive index of the core material of the second group of waveguides is less than that of the core material of the first group of waveguides.

2. The PIC according to claim 1, wherein the first waveguide layer is a silicon (Si) waveguide layer, and the second waveguide layer is silicon nitride (SiN). x Waveguide layer.

3. The PIC according to claim 1, wherein the segmented waveguide has a periodicity of less than about 500 nanometers.

4. The PIC according to claim 1, wherein the segmented waveguide has a smaller than approximately The periodicity, in which It is the operable wavelength of the polarization rotator, and n It is the refractive index of the segmented waveguide.

5. The PIC of claim 1, wherein the fill factor associated with the first set of waveguides is in the range of about 0.1 to about 0.

8.

6. The PIC according to claim 1, wherein the first waveguide layer is on the second waveguide layer.

7. The PIC according to claim 1, wherein the second waveguide layer is on the first waveguide layer.

8. The PIC of claim 1, wherein one or more waveguide segments of the segmented waveguide have a shape that is elongated in a length oriented at 90 degrees relative to the propagation direction.

9. The PIC of claim 1, wherein one or more waveguide segments of the segmented waveguide have a shape that is elongated in a lengthwise direction oriented at an arbitrary angle relative to the propagation direction.

10. The PIC of claim 1, wherein the polarization rotator includes a spacer region between the first waveguide layer and the second waveguide layer.

11. The PIC of claim 1, wherein the first group of waveguides comprises four curved waveguide segments that taper exponentially.

12. The PIC of claim 1, wherein at least one of the waveguides in the second group of waveguides comprises a segmented waveguide.

13. The PIC of claim 12, wherein the segmented waveguide has a periodicity of less than about 900 nanometers.

14. The PIC of claim 12, wherein the segmented waveguide has a size less than approximately The periodicity, in which It is the operable wavelength of the polarization rotator, and n It is the effective refractive index of the polarization rotator.

15. The PIC of claim 1, wherein the first group of waveguides includes a first waveguide and a second waveguide, the first waveguide and the second waveguide being arranged symmetrically with respect to the centerline of one of the waveguides in the second group of waveguides.

16. The PIC of claim 1, wherein the first set of waveguides comprises a first waveguide and a second waveguide, wherein the spacing between the first waveguide and the second waveguide is in the range of about 0.3 micrometers (μm) to about 2.5 μm along a taper length associated with the first waveguide and the second waveguide.

17. The PIC of claim 1, wherein the width of the waveguide in the first group of waveguides is less than about 450 nanometers.

18. The PIC of claim 1, wherein the PIC further comprises a mode beamsplitter, wherein the polarization rotator is optically connected to the mode beamsplitter.

19. The PIC of claim 18, wherein the mode beam splitter comprises one or more segmented waveguides.

20. The PIC of claim 18, wherein the mode beam splitter comprises a first tapered waveguide and a second tapered waveguide.

21. The PIC of claim 18, wherein the mode beam splitter comprises an exponentially tapered flexural waveguide.

22. The PIC of claim 1, wherein one or more waveguide segments of the segmented waveguide are arranged along a direction substantially parallel to the propagation direction.

23. The PIC of claim 1, wherein one or more waveguide segments of the segmented waveguide are arranged along a direction substantially perpendicular to the propagation direction.

24. The PIC of claim 1, wherein the first set of waveguides and the second set of waveguides are surrounded by one or more of silicon dioxide, a refractive index matching fluid, or air.

25. The PIC of claim 1, wherein the polarization rotator further comprises a third waveguide layer, wherein the third waveguide layer serves as a core layer or a cladding layer.

26. The PIC of claim 1, wherein the segmented waveguide is positioned such that the segmented waveguide is substantially located at the center of the boundary edge of the waveguide in the second set of waveguides.

27. The PIC of claim 1, wherein the segmented waveguide is positioned such that the end of the segmented waveguide is away from the waveguide in the second group of waveguides and is not below the waveguide in the second group of waveguides.

28. A photonic integrated circuit (PIC) including a polarization beamsplitter-rotator, the polarization beamsplitter-rotator comprising: A polarization rotator, the polarization rotator comprising: The first group of waveguides in the first waveguide layer, wherein at least one waveguide in the first group of waveguides is a segmented waveguide, and The second group of waveguides in the second waveguide layer The refractive index of the core material of the second group of waveguides is less than that of the core material of the first group of waveguides; and A polarization beamsplitter and a mode beamsplitter, wherein the polarization beamsplitter is optically connected to the mode beamsplitter.

29. A photonic integrated circuit (PIC) including a polarization rotator, the polarization rotator comprising: A silicon (Si) waveguide layer, wherein the Si waveguide layer comprises a group of segmented Si waveguides. The periodicity of the segmented Si waveguides in one of the segmented Si waveguides is less than approximately 900 nanometers (nm), and The fill factor of the segmented Si waveguide is in the range of about 0.1 to about 0.8; and Silicon nitride (SiN) x Waveguide layer, the SiN x The waveguide layer includes a set of SiN x waveguide.

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