Spectroscopic apparatus

Abstract

A one-by-four optical splitting device is disclosed. The optical splitting device can include a main waveguide, a first coupling waveguide, and a second coupling waveguide. The main waveguide can couple light from the main waveguide into both the first coupling waveguide and the second coupling waveguide. Due to manipulation of the coupling modes, one fundamental mode of light can be input and four fundamental modes of light can be output. In some examples, the main waveguide can input a fundamental mode of light, which can be converted to a first hybrid mode, which can be a four-lobe mode. The first coupling waveguide and the second coupling waveguide can be tapered and separated by a gap, such that the first hybrid mode can be converted to two second hybrid modes, which can then be converted back to the four fundamental modes of output light.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This Patent Cooperation Treaty application claims priority to U.S. Provisional Patent Application No. 63 / 082,461, filed September 23, 2020, and U.S. Non-Provisional Patent Application No. 17 / 408,122, filed August 20, 2021, the contents of which are incorporated by reference in their entirety. TECHNICAL FIELD

[0003] The present disclosure relates generally to an optical system for splitting light. More specifically, embodiments herein relate to an optical system for splitting light by using waveguides to convert light modes. BACKGROUND

[0004] Generally, optical systems can employ multiple light sources for everyday devices, such as computer mice, laser printers, and the like. Although these systems can have multiple light outputs, there can be more light outputs than light sources because light can be demultiplexed or split. In some examples, the size of the optical system can increase to an unreasonable size because the optical system tends to scale with the number of cascaded light splitting stages. Additionally, these larger optical systems are not energy efficient and can introduce optical power loss into the optical system. SUMMARY

[0005] Embodiments of systems, devices, methods, and apparatuses described in the present disclosure relate to an optical device for splitting light. Systems, devices, methods, and apparatuses relating to splitting light using mode coupling between waveguides are also described. In some examples, the optical device can act as a one-by-four splitter as long as light can be input on an input waveguide and light can be output on four waveguides. The input waveguide can provide light having a fundamental mode, where the input waveguide is positioned between a first coupling waveguide and a second coupling waveguide. Light can be coupled from the input waveguide to both the first coupling waveguide and the second coupling waveguide, and light can be converted from the fundamental mode of light to a first hybrid mode. The first coupling waveguide and the second coupling waveguide can be spaced apart from each other, and light can be converted from the first hybrid mode to a second hybrid mode. Each of the first coupling waveguide and the second coupling waveguide can have a Y-junction, and the second hybrid mode can be converted to a fundamental mode propagating on each of the four outputs of the two Y-junctions.

[0006] In some examples, the disclosure describes a light splitting device. The light splitting device can include a first region configured to provide a fundamental mode of light, a second region configured to convert the fundamental mode of light into a first hybrid mode of light, the second region including: a main waveguide having a first side and a second side, a first coupling waveguide adjacent to the first side of the main waveguide, and a second coupling waveguide adjacent to the second side of the main waveguide. The light splitting device can further include a third region configured to convert the first hybrid mode of light into a plurality of second hybrid modes of light, the third region including a first Y-junction in the first coupling waveguide and configured to convert one of the plurality of second hybrid modes of light into the fundamental mode of light, and a second Y-junction in the second coupling waveguide and configured to convert another of the plurality of second hybrid modes of light into the fundamental mode of light. In some examples, the first hybrid mode of light is a four-lobe mode of light, the plurality of second hybrid modes of light are each a two-lobe mode of light, and the main waveguide terminates proximate to the region where the fundamental mode of light is converted into the first hybrid mode of light. In some examples, the fundamental mode of light is input on the main waveguide, and the Y-junctions are configured to output four converted fundamental modes of light.

[0007] In some examples, the first coupling waveguide and the second coupling waveguide are wider than the main waveguide. In some examples, the first coupling waveguide and the second coupling waveguide in the second region are tapered waveguides, and the optical coupling from the main waveguide to the first coupling waveguide and the second coupling waveguide depends at least on a taper ratio of the first coupling waveguide and the second coupling waveguide. In some examples, the first coupling waveguide and the second coupling waveguide in the second region decrease in width. In some examples, the first coupling waveguide and the second coupling waveguide in the third region are separated by a gap that increases in width. In some examples, in the second region, a width of a first gap between the main waveguide and the first coupling waveguide is the same as a width of a second gap between the main waveguide and the second coupling waveguide. In some examples, one of the plurality of second hybrid modes of light is a first two-lobe mode of light propagating to the first Y-junction in the first coupling waveguide of the third region, and another of the plurality of second hybrid modes of light is a second two-lobe mode of light propagating to the second Y-junction in the second coupling waveguide of the third region.

[0008] In some examples, this disclosure describes a beam splitting device. The beam splitting device may include: an input region configured to provide light having a fundamental mode; an interaction region configured to convert the fundamental mode into a first mixed mode; and a fan-shaped region configured to convert the first mixed mode into a plurality of second mixed modes and convert the plurality of second mixed modes into a plurality of converted fundamental modes. In some examples, the first mixed mode has four lobes, the plurality of second mixed modes each have two lobes, and the beam splitting device may further include a silicon substrate, a main waveguide disposed on the silicon substrate, a first coupling waveguide disposed on the silicon substrate, and a second coupling waveguide disposed on the silicon substrate, the first and second coupling waveguides being ribbed waveguides in the interaction region, and the first and second coupling waveguides converting into strip waveguides in the fan-shaped region. In some examples, the fan-shaped region includes a first coupling waveguide having a first Y-junction, a second coupling waveguide having a second Y-junction, and the first mixed mode having four lobes to reduce optical loss near at least one or both of the first or second Y-junction.

[0009] In some examples, the beam splitter may further include a silicon substrate, a first rib waveguide disposed on the silicon substrate in a sector region, and a second rib waveguide disposed on the silicon substrate in the sector region, wherein the first and second rib waveguides are separated from each other by a gap whose width increases along the sector region, and the gap includes a low-refractive-index cladding region. In some examples, the beam splitter further includes a first rib waveguide that transforms into a first strip waveguide in the sector region and a second rib waveguide that transforms into a second strip waveguide in the sector region, thereby decoupling the first and second strip waveguides from each other. In some examples, the sector region converts multiple second mixed modes into fundamental modes, thereby outputting four fundamental modes with equal optical power. In some examples, the beam splitter further includes a first rib waveguide that transforms into a first strip waveguide in the sector region and a second rib waveguide that transforms into a second strip waveguide in the sector region, and the first rib waveguide completes its transformation into the first strip waveguide and the second rib waveguide completes its transformation into the second strip waveguide before the first mixed mode is converted into the second mixed mode.

[0010] In some examples, this disclosure describes a method for beam splitting. The method may include: inputting light having a fundamental mode of light into a first region using a main waveguide; converting the fundamental mode of light into a first mixed mode of light in a second region by coupling the fundamental mode of light from the main waveguide to a first coupled waveguide and a second coupled waveguide; converting the first mixed mode of light into a plurality of second mixed modes of light in a third region, wherein the first coupled waveguide and the second coupled waveguide are separated by a gap; and converting the plurality of second mixed modes of light back into a plurality of fundamental modes of light for output on a plurality of waveguide channels in the third region. In some examples, the first coupled waveguide is a first rib waveguide in the second region, and the second coupled waveguide is a second rib waveguide in the second region. In some examples, the method may include converting the first mixed mode into a second mixed mode of a plurality of second mixed modes after the first rib waveguide in the third region is converted into a first strip waveguide and after the second rib waveguide in the third region is converted into a second strip waveguide. In some examples, the first mixing mode of light has four lobes, with a non-zero center equally separating the four lobes, and each of the plurality of second mixing modes of light has two lobes and a blank at the center between the two lobes. In some examples, the method may include decoupling one second mixing mode of light from another second mixing mode of light, wherein the decoupling depends at least in part on the increased refractive index contrast between the first and second coupled waveguides in the third region.

[0011] In addition to the exemplary aspects and embodiments described above, further aspects and embodiments will become apparent from the accompanying drawings and by studying the following description. Attached Figure Description

[0012] FIG. 1A A block diagram of a one-to-eight cascaded separator is shown.

[0013] FIG. 1B A block diagram of a 1x16 cascaded separator is shown.

[0014] FIG. 1C An exemplary Y-shaped separator is shown.

[0015] FIG. 2A An example of a 1x4 splitter is shown.

[0016] FIG. 2B An enlarged cross-section of a 1x4 splitter is shown.

[0017] FIG. 2C Another example of a 1x4 splitter is shown.

[0018] FIG. 3A Another example of a 1x4 splitter is shown.

[0019] FIG. 3B An enlarged cross-section of a 1x4 splitter is shown.

[0020] The use of crosshairs or shading in the accompanying drawings is generally provided to clarify the boundaries between adjacent elements and also to improve the readability of the drawings. Therefore, the presence or absence of crosshairs or shading does not indicate or suggest any preference or requirement for a particular material, material properties, element proportions, element dimensions, commonalities of similar illustrated elements, or any other feature, property, or characteristic of any element shown in the accompanying drawings.

[0021] It should be understood that the proportions and dimensions (relative or absolute) of the various features and elements (as well as their sets and groups), and the boundaries, spacing, and positional relationships therebetween, are provided in the accompanying drawings solely to facilitate understanding of the various embodiments described herein, and are therefore unnecessarily presented or shown to measure and not intended to indicate any preference or requirement for the illustrated embodiments, in order to exclude embodiments in conjunction with them. Detailed Implementation

[0022] Reference will now be made specifically to the representative embodiments shown in the accompanying drawings. It should be understood that the following description is not intended to limit the embodiments to a single preferred embodiment. Rather, it is intended to cover alternative forms, modifications, and equivalents that may be included within the substance and scope of the embodiments defined by the appended claims.

[0023] Directional terms such as “top,” “bottom,” “upper,” “lower,” “above,” “below,” “below,” “front,” “rear,” “above,” “below,” “left,” and “right” are used in reference to the orientation of some components in some of the figures described below. Because components in various embodiments may be positioned in multiple different orientations, directional terms are for illustrative purposes only and are not intended to be limiting in any way. Directional terms are intended to be interpreted broadly and should therefore not be construed as excluding components oriented in different ways.

[0024] As used herein, the term "adjacent" refers to two elements sharing a common boundary or otherwise contacting each other, while the term "adjacent" refers to two elements that are close to each other and may (or may not) contact each other. Therefore, adjacent elements are also adjacent, but the reverse is not necessarily true. Two elements "coupled" to each other may be permanently or removably physically coupled and / or operationally or functionally coupled. Additionally, two elements "optically coupled" to each other allow light to pass from one element to the other.

[0025] As used throughout this specification, a reference numeral without the character α following it may refer to a corresponding reference, a group of all references, or one or more of some references within a group of references. For example, “205” may refer to any segment of the main waveguide 205 (e.g., segment 205A, segment 205B, etc. of the main waveguide 205), may refer to all segments of the main waveguide 205, or may refer to some segments of the main waveguide 205 (e.g., both segments 205A and 205B of the main waveguide 205 in the first and second regions), depending on the context in which it is used.

[0026] The accompanying drawings will be referenced in the following description of the examples, which illustrate specific examples that can be implemented by way of example. It should be understood that other examples may be used and structural changes may be made without departing from the scope of the individual examples.

[0027] Typically, optical systems can employ multiple light sources, where light can be split, allowing the number of output ports to exceed the number of input ports. Various systems can be used to separate light emitted by a light source, but may include different components and can differ from one another in various ways, such as size, optical efficiency, energy efficiency, wavelength dependence or independence, or any combination thereof. In some examples, cascaded stages in an optical system can be used to separate light, and the size of the optical system can increase with the number of cascaded beam splitters. Because cascaded beam splitters are proportional to the number of output ports, these devices can become unreasonably large and may not be easily incorporated into an optical system. Furthermore, cascaded beam splitters may introduce unwanted optical beat frequencies into the optical system.

[0028] In other examples, star splitters can be used to separate light using an input waveguide, a free-propagating region, and an output waveguide. The size of a star splitter may not be proportional to the number of output ports, as another output waveguide can be added without significantly increasing the footprint. However, the free-propagating region through which light propagates can result in large optical losses, with up to 35% of the input optical power potentially being lost between the input and output waveguides. Even if the size of the star splitter is appropriate, the optical power loss may be too great to use in an optical system; therefore, compact, low-loss optical systems are desirable.

[0029] This document discloses a beam splitter comprising a main waveguide, a first coupling waveguide, and a second coupling waveguide. The beam splitter can be a 1x4 splitter and can be wavelength-independent. The main waveguide supplies light to the beam splitter, and light can be coupled from the main waveguide to both the first and second coupling waveguides. Due to manipulation of the coupling modes (which depends on one or more of the waveguide width, waveguide taper, waveguide taper ratio, waveguide spacing, waveguide material, and any combination thereof), fundamental modes of light can be supplied to the beam splitter, and four converted fundamental modes of light can be provided as outputs on four output ports or waveguide channels. The terms "output port" and "waveguide channel" are used interchangeably herein.

[0030] In some examples, the main waveguide can receive the fundamental mode of light as input. As light propagates through the main waveguide, it can be coupled equally from the main waveguide to the first and second coupled waveguides. Once the fundamental mode of light in the main waveguide has no optical power and has been optically coupled to the first and second coupled waveguides, the light can be converted into a first mixed mode, which can be a four-lobed mode. The first and second coupled waveguides can be tapered and separated by a gap, such that the first mixed mode can be converted into two second mixed modes, which are two-lobed modes. Each of the first and second coupled waveguides can have a second mixed mode of light propagating through them. The first and second coupled waveguides can then be separated by increasingly larger gaps to prevent further optical coupling. The first and second coupled waveguides can each have a Y-junction that converts the second mixed mode of light back to the fundamental mode of light, providing four converted fundamental modes of light output on the four waveguide channels.

[0031] The following text is for reference only. FIGS. 1A-3B These and other embodiments are discussed. However, those skilled in the art will readily understand that the detailed descriptions given herein with respect to the accompanying drawings are for illustrative purposes only and should not be construed as limiting.

[0032] FIG. 1A A block diagram of a 1x8 cascaded splitter is shown. The 1x8 cascaded splitter 100 may include an input optical path 102, a 1x4 splitter 104, intermediate optical paths 106A-106D, a 1x2 splitter 108A-108D, and optical outputs 112A-112D. FIG. 1A In this configuration, the 1x8 splitter 100 receives a single optical input via input 102 and has eight distinct output ports via outputs 112A-112D. Typically, the size of this type of splitting system can increase with the number of output ports, and in many applications, it may be desirable to minimize the footprint of the splitting device.

[0033] Input 102 may be an input waveguide that provides input light to a one-to-four splitter 104. The input light may be provided by a light source, which may be connected to or otherwise integrated into the photonic device. In some examples, the photonic device may include more than one light source, such as a laser, a light-emitting diode, a semiconductor laser, a coherent light source, a semi-coherent light source, any combination thereof, etc. In some examples, the photonic device is a device with photonic and / or optical functions and components. As used herein, the photonic device may include a beam splitter.

[0034] In the first separation stage, a 1x4 splitter 104 can equally separate and output light in four intermediate optical paths 106A-106D. In some examples, there may be optical losses associated with each separation stage. In some examples, the intermediate optical paths 106A-106D can be waveguides that can be optically coupled to the 1x4 splitter 104 to receive the output light from it. The intermediate optical paths 106A-106D can also be optically coupled to the 1x2 splitters 108A-108D and can supply light to them. Each of the two splitters 108A-108D can provide optical outputs 112A-112D. The 1x2 splitter 108A can provide two optical outputs 112A, the 1x2 splitter 108B can provide two optical outputs 112B, and so on. FIG. 1A As shown, a 1x2 splitter 108A can separate and provide optical output 112A, a 1x2 splitter 108B can separate and provide optical output 112B, and so on. Similar to a 1x4 splitter 104, each of the 1x2 splitters 108A-108D can equally separate and output light at optical outputs 112A-112D. A second separation stage with 1x2 splitters 108A-108D can also be associated with optical loss.

[0035] Furthermore, the size of the 1x8 splitter 100 can be increased with each additional splitting stage. For example, instead of using a 1x4 splitter 104, input 102 can be provided to a 1x2 splitter, and then for each of those two outputs, another set of 1x2 splitters can be used to achieve four intermediate outputs. Because additional splitting stages are added in the example described, this exemplary system can be more efficient than... FIG. 1A The system shown is large. Because optical systems are being incorporated into increasingly smaller form factor devices, the size of a cascaded separator may be too large to be reasonably incorporated into smaller form factor devices (such as mobile devices).

[0036] FIG. 1B A block diagram of a 1x16 cascaded separator is shown. Similar to... FIG. 1AThe size of the cascaded splitter, a 1x16 cascaded splitter 101, can increase with the number of output ports, even if it may be desirable to minimize the footprint of the splitting device. The 1x16 cascaded splitter 101 includes an optical input 102, a 1x4 splitter 104, intermediate optical paths 106A-106D, 1x4 splitters 109A-109D, and optical outputs 113A-113D. The 1x16 cascaded splitter 101 provides another example of a cascaded splitter where optical loss can occur and its size increases with each cascade stage. The 1x16 cascaded splitter 101 can be implemented using all 1x4 splitters to achieve a 16-port output device. As the number of cascade stages increases, optical beat frequency can become an issue, thus requiring the device to have the ability to split light while maintaining a reasonable size and desirably reducing optical beat frequency.

[0037] FIG. 1C An exemplary Y-shaped waveguide is shown. The Y-shaped waveguide 116 includes an input waveguide 103, a first coupling waveguide 107, and a second coupling waveguide 111. FIG. 1C The Y-shaped splitter 116 is thermally adiabatic and wavelength-independent. Furthermore, the Y-shaped splitter 116 is an example of a one-to-two splitter, and optical power can be gradually transferred from the input waveguide 103 to the first coupled waveguide 107 and the second coupled waveguide 111, provided that light can be coupled between the input waveguide 103 and the first coupled waveguide 107 and the second coupled waveguide 111. The Y-shaped splitter 116 has three regions, including a first region for input light, a second region for coupling light from the input waveguide 103 to the first coupled waveguide 107 and the second coupled waveguide 111, and a third region for output light from the first coupled waveguide 107 and the second coupled waveguide 111.

[0038] The first region of the Y-shaped waveguide 116 includes segment 103A of the input waveguide 103, the second region includes segment 103B of the input waveguide 103, segment 107A of the first coupling waveguide 107, and segment 111A of the second coupling waveguide 111, and the third region includes segments 107B and 107C of the first coupling waveguide 107 and segments 111B and 111C of the second coupling waveguide 111. In the first region of the Y-shaped waveguide 116, segment 103A of the input waveguide 103 can provide light to the Y-shaped waveguide 116.

[0039] In the second region of the Y-shaped splitter 116, light continues to propagate in segment 103B of the input waveguide 103 and can be optically coupled from the input waveguide 103B to both segment 107A of the first coupling waveguide 107 and segment 111A of the second coupling waveguide 111. In some examples, light can be coupled gradually over the length of segment 103B of the input waveguide 103. At the end of segment 103B of the input waveguide 103, most to all light can be coupled into the first coupling waveguide 107 and the second coupling waveguide 111.

[0040] In the third region of the Y-shaped splitter 116, light can continue to propagate separately through each of the coupling waveguides 107 and 111. For example... FIG. 1C As shown, segment 107B of the first coupled waveguide 107 and segment 111B of the second coupled waveguide 111 can be separated by increasingly larger distances, so that light can not couple between the two coupled waveguides in the third segment. FIG. 1C As shown, light can be output at segment 107C of the first coupling waveguide 107, and light can be output at segment 111C of the second coupling waveguide 111.

[0041] FIG. 2A This is an illustration of an exemplary 1x4 splitter. A 1x4 splitter can be configured with a single input of light having a fundamental mode and can output light as four converted fundamental modes across four waveguide channels. The fundamental mode of light can have a single lobe, such as... FIG. 2A As shown in Figure 2, the quad splitter 200 includes a main waveguide 205, a first coupling waveguide 210, a second coupling waveguide 215, and a substrate 223. The quad splitter 200 can be increased to have four output ports of the waveguide channels while maintaining a similar size to a quad splitter. Additionally, the quad splitter 200 can be wavelength independent. In some examples, portions of the first coupling waveguide 210 and / or the second coupling waveguide 215 can be extended to mitigate wavelength dependence. It is understood that all waveguides can be surrounded by a low-refractive-index cladding region to confine light within the waveguide. Typically, the waveguides described herein may include a core or propagation region with cladding layers on both sides of the propagation region.

[0042] In some examples, the 1x4 splitter 200 can be a low-optical-loss device, and the optical loss experienced can be primarily due to insertion loss and / or power imbalance between the arms or branches of the 1x4 splitter 200. The 1x4 splitter 200 can also be smaller than, as referenced... FIG. 1A and FIG. 1BThe cascaded splitter described herein suffers less optical loss than a 1x4 star splitter device, which loses approximately 35% of its optical power, primarily due to coupling between the free propagation region and the output waveguide. While both the 1x4 star splitter device and the 1x4 splitter 200 can be smaller in size... FIG. 1A and FIG. 1B The cascaded splitter, however, the quad splitter 200 experiences significantly less optical loss than the quad star splitter device because the insertion loss is reduced in the quad splitter 200.

[0043] The quad-splitter 200 has a first region 220 as an input region, a second region 225 as an interaction region (e.g., a coupling region), and a third region 230 as an output region (e.g., a fan-shaped region). The first region 220 may include a segment 205A of the main waveguide 205. The first region 220 can be the input region as long as the main waveguide 205 can input light into the quad-splitter 200. The light supplied by the main waveguide 205 can be a single wavelength or a range of wavelengths. Although a single wavelength of light can be supplied to the quad-splitter 200, different wavelengths of light can pass through the quad-splitter 200 at different times.

[0044] like FIG. 2A As shown, the light supplied to the 1x4 splitter 200 is the fundamental mode 235 of the light (e.g., single-mode). The fundamental mode 235 of the light can propagate through a segment 205A of the main waveguide 205 into a second region 225 of the 1x4 splitter 200. In some examples, the fundamental mode 235 of the light can be multimode light before reaching the segment 205A of the main waveguide 205. The main waveguide 205 can be designed with a specific width and / or taper to generate the fundamental mode of the light by confining the multimode light within the main waveguide 205.

[0045] In the second region 225, the first coupling waveguide 210 and the second coupling waveguide 215 may begin in the second region 225, and the main waveguide 205 may terminate near or up to the end of the second region 225. The phrase "terminates near the end of the second region 225" means that the main waveguide 205 may terminate closer to the end of the second region 225 than at the center of the second region 225. FIG. 2AAs shown, the main waveguide has a first side adjacent to segment 210B of the first coupling waveguide 210 and a second side adjacent to segment 215B of the second coupling waveguide 215. Additionally, near or up to the end of the second region 225, light in the main waveguide 205 can be coupled nearly or completely from the main waveguide 205 to the first coupling waveguide 210 and the second coupling waveguide 215. It can be understood that up to the end of the second region 225 of the quad splitter 200, there may be less than five percent of the light in the main waveguide 205.

[0046] In the second region 225 of the 1x4 splitter 200, segment 205B of the main waveguide 205 can be optically coupled to both segment 210B of the first coupling waveguide 210 and segment 215B of the second coupling waveguide 215. For example... FIG. 2A As shown, the width of the main waveguide 205 can taper and decrease as light propagates through it. Section 210B of the first coupling waveguide 210 can also be tapered and its width decreases in the second region 225. Similarly, section 215B of the second coupling waveguide 215 can be tapered and its width decreases. In some examples, the first coupling waveguide 210 and the second coupling waveguide 215 can be wider than the main waveguide 205 at any given point along the length of the main waveguide. Furthermore, the optical coupling from the main waveguide to the first and second coupling waveguides can depend on one or more of the taper ratios of the main waveguide, the first coupling waveguide, and / or the second coupling waveguide.

[0047] Additionally, in the second region 225 of the quad splitter 200, the main waveguide 205 may be adjacent to the first coupled waveguide 210 and the second coupled waveguide 215. In some examples, the gap between the main waveguide 205 and the first coupled waveguide 210 and the second coupled waveguide 215 may be as small as manufacturing allows and may be consistent throughout the second region 225. In some examples, the width of the gap may vary. Furthermore, although the main waveguide 205, the first coupled waveguide 210, and the second coupled waveguide 215 are depicted as having straight edges, in some examples the waveguides may be curved, provided that appropriate widths of the waveguides are maintained and the gaps between the waveguides are appropriately maintained to allow optical coupling between the waveguides. It is understood that in the second region 225, the gap may be filled with a material that allows coupling between the main waveguide 205 and the first coupled waveguide 210, and between the main waveguide 205 and the second coupled waveguide 215. In some examples, the gap may be air.

[0048] The fundamental mode 235A of light can continue to propagate from the first region 220 to the second region 225 through segments 205A and 205B of the main waveguide 205. While the term "segment" can be used to describe the main waveguide 205, it is understood that the main waveguide 205 is a continuous waveguide, provided that light can propagate uninterruptedly between segments of the waveguide, and the term "segment" is used for illustrative purposes only. Similarly, the first coupling waveguide 210 is a continuous waveguide and the second coupling waveguide 215 is a continuous waveguide, even though both waveguides will be described as having segments.

[0049] The second region 225 of the 1x4 splitter 200 can be an interactive region because the fundamental modes of light can be coupled from the main waveguide 205 to the first coupling waveguide 210 and the second coupling waveguide 215 along the length of the second region 225. For example... FIG. 2A As shown, segment 205B of the main waveguide 205 can supply light having a fundamental mode 235A. However, as segment 205B narrows and due to the proximity of the first coupling waveguide 210 and the second coupling waveguide 215 to the main waveguide 205, the light can be coupled approximately equally to each of the first coupling waveguide 210 and the second coupling waveguide 215. The fundamental mode 235A of the light having one lobe can be converted into a first mixed mode 245 of the light near or up to the end of the second region 225. That is, the fundamental mode 235A of the light can be converted into a first mixed mode near the end of the second region 225, wherein the termination point is closer to the end of the second region 225 than the middle of the second region 225. The first mixed mode 245 of the light can be as follows: FIG. 2A The four-lobed mode is depicted in the diagram. Optical loss can be reduced by effectively coupling the four-lobed mode to the second hybrid mode 240 in the third region 230. The terms "first hybrid mode" and "four-lobed mode" are used interchangeably herein.

[0050] In some examples, the conversion from the fundamental mode 235A of light to the first mixed mode 245 of light can depend at least in part on the width and taper of the waveguide and the material of the waveguide. Due to the width and taper, the first mixed mode 245 can be efficiently excited from the fundamental mode of light. FIG. 2AAs shown, the four-lobed mode can be symmetrical and can include a non-zero portion between the top two lobes and the bottom two lobes. The non-zero portion of the four-lobed mode can indicate the light between the top two lobes and the bottom two lobes. Even if the first mixing mode 245 can be a higher-order mode, the light can still experience low optical loss when coupled from the main waveguide 205 to the first coupling waveguide 210 and the second coupling waveguide 215. By employing the first mixing mode 245, loss can be avoided once the light encounters the Y-junction in the third region 230. Furthermore, it is understood that the first mixing mode 245 of the light can span segment 210B of the first coupling waveguide 210 and segment 215B of the second coupling waveguide 215, near or at the end of the interaction region or the second region 225. (Refer to...) FIG. 2C The first hybrid mode 245 is described in further detail.

[0051] The third region 230 of the 1x4 splitter 200 may include a first coupling waveguide 210 and a second coupling waveguide 215, and a Y-junction 255 in each. The third region can be a fan-shaped region as long as the first and second coupling waveguides can "fan out" or split into four optical outputs. FIG. 2A As shown, the first coupling waveguide 210 can form a Y-junction 255 having a first branch 210C1 and a second branch 210C2. Similarly, the second coupling waveguide 215 also has a Y-junction 255, which has a third branch 215C1 and a fourth branch 215C2. Furthermore, the first hybrid mode 245 can be converted into second hybrid modes 240 and 242, where the second hybrid modes 240 and 242 can be two-lobed modes. Additionally, the second hybrid modes 240 and 242 can be independent. The terms "second hybrid mode" and "two-lobed mode" are used interchangeably herein.

[0052] exist FIG. 2A In the third region 230, the first coupling waveguide 210 may have a second mixing mode 240 of light, and the second coupling waveguide 215 may have a second mixing mode 242 of light at the beginning of the third region 230. The second mixing mode 240 can be a stable mode as light transitions from the first mixing mode 245 to the second mixing mode 240. In some examples, in the third region 230, the first coupling waveguide 210 and the second coupling waveguide 215 may "fan out" or be separated from each other by an increasing distance. Because the first and second coupling waveguides become farther apart, light may not couple between the two waveguides in the third region 230.

[0053] like FIG. 2AAs shown, in a portion of the path traversing the third region 230, the first coupling waveguide 210 and the second coupling waveguide 215 can each form a Y-junction 255. In some examples of the Y-junction, the first branch 210C1 and the second branch 210C2 of the first coupling waveguide 210 can begin to “fan out” to create a larger gap, or can be separated from each other by an increasingly larger distance. The third branch 215C1 and the fourth branch 215C2 of the second coupling waveguide 215 can be configured similarly. As the gaps between the corresponding branches 250C1 and 250C2, and 250C3 and 250C4, begin to increase, the second hybrid modes 240, 242 can separate and transition back to the four transitioned basic modes 235C1-235C4. The “transitioned basic modes” have been transformed from the second hybrid modes to the basic modes in the third region 230. In some examples, the gap between the first coupling waveguide 210 and the second coupling waveguide 215 can be a low-refractive-index cladding region. It is understood that in the third region 230, the gap between the first coupled waveguide 210 and the second coupled waveguide 215 can be the region between the first and second coupled waveguides, which can be increased to separate the first and second coupled waveguides. The gap in the third region can differ from the gap in the second region, since the gap in the second region is a uniform distance and the gap in the third region is increased. Furthermore, the gap in the second region can be filled with a material that allows optical coupling, while the gap in the third region can be filled with a material that inhibits optical coupling.

[0054] Additionally, the gap in the third region may include any material that prevents further coupling of light between the first and second coupled waveguides. In some examples, the gap in the third region may be air. Although the terms "fundamental mode" and "converted fundamental mode" are used herein, both terms refer to the fundamental mode, the difference being that the converted fundamental mode is converted from the second mixed mode to the fundamental mode.

[0055] FIG. 2B An enlarged cross-section of a 1x4 splitter is shown. As shown in the diagram of the 1x4 splitter 200... FIG. 2A As shown in cross-sectional view 250 along line A-A', the substrate 223, segment 205B of the main waveguide 205, segment 210B of the first coupled waveguide 210, and segment 215B of the second coupled waveguide 215 may have approximately the same height but different widths. Cross-sectional view 250 also includes a gap 273B between segment 205B of the main waveguide 205, segment 210B of the first coupled waveguide 210, and segment 215B of the second coupled waveguide 215. In some examples, the waveguide may include layers, such as a top cladding layer, a propagation region, and a bottom cladding layer, which will be referenced... FIG. 3A Further detailed description. For example... FIG. 2BAs shown, segment 205B of the main waveguide has a first side adjacent to segment 210B of the first waveguide.

[0056] The enlarged cross-sectional view 250 also shows a shoulder 213, which may be a region located between waveguides. Because the enlarged cross-sectional view 250 is located in the second region of a one-to-four splitter, the main waveguide 205 and the first coupled waveguide 210 and the second coupled waveguide 215 are ribbed waveguides. Therefore, the shoulder 213 may be made of the same material as the main waveguide 205 and the first and second waveguides 210 and 215. Although the gap 273B is in FIG. 2B The space shown is empty, but gap 273B can be filled with a material that allows coupling, such as a dielectric. In other examples, gap 273B can be air. Shoulder 213 and gap 273B separate the waveguide from each other. Enlarged cross-sectional view 250 shows a ribbed waveguide, which can be formed from a single material such as silicon.

[0057] In some examples, a 1x4 splitter 200 (in) FIG. 2A (As shown in the image) can be as follows: (refer to) FIG. 3A The rib-to-strip waveguides are described, wherein the stack of strip waveguides can be etched deeper than the stack of rib waveguides. In some examples of rib waveguides, the stack can be partially etched through to form gap 273B, such that shoulder 213 can still separate the waveguides, as shown in cross-sectional view 250. FIG. 2A The enlarged sections are for illustrative and explanatory purposes, not drawn to scale.

[0058] FIG. 2C Another example of a 1x4 splitter is shown. The 1x4 splitter 201 includes a main waveguide 206, a first coupling waveguide 211, and a second coupling waveguide 216. Similar to... FIG. 2A A 1x4 splitter 200, in FIG. 2C In this process, the input light may have a fundamental mode 235 provided by the main waveguide 211 in the first region 220. Typically, FIG. 2C The function of the 1x4 splitter 201 can be combined with FIG. 2A The 1x4 splitter 200 has the same function.

[0059] exist FIG. 2CIn the second region 226, the first coupled waveguide 211B can taper downwards uniformly to a small width until it terminates after the main waveguide 206B. After the main waveguide 206B terminates in the second region 226, the width of the first coupled waveguide 211B can increase to the beginning of the third region 231. The second coupled waveguide 216B can be mirrored from the first coupled waveguide 211B because it terminates after the main waveguide 206B; the width of the second coupled waveguide 216B can also increase. Immediately following the termination of the main waveguide 206B, the increased width of the uniform gap between the first coupled waveguide 211B and the second coupled waveguide 216B can be designed to convert the first mixing mode 245 into two separate second mixing modes 240 and 242 near the beginning of the third region 231. The waveguides and the gaps between them are not drawn to scale and are depicted in the figures for illustrative purposes only. In some examples, the first and second coupled waveguides may be wider than the main waveguide.

[0060] Near or at the end of the second region 226, the fundamental mode of light may no longer have any optical power because the optical power has been transferred to the first hybrid mode 245. As shown in the magnified four-lobed mode, the lobes may be symmetrical and may include a non-zero portion between the first two lobes and the second two lobes. The non-zero portion of the four-lobed mode may indicate the light between the first two lobes and the second two lobes. The four-lobed mode may be a suitable higher-order mode that can propagate across the gap between the first coupling waveguide 211 and the second coupling waveguide 216, and then transform into the second hybrid mode 240 in the third region 231.

[0061] In some examples, due to unintended reflections and / or couplings, excitation of modes other than or in lieu of the first mixing mode 245 or the four-lobed mode may occur. In some examples, a second mixing mode 240 of the light may appear due to these unintended reflections and / or couplings. Over a wide wavelength range, the first mixing mode 245 of the light may lose relatively more light around certain wavelengths, and the second mixing mode 240 of the light may increase around the same wavelengths. In this example, the loss can be mitigated even in the case of undesirable and accidental mode coupling. In some exemplary embodiments, "wide wavelength range" can typically be a set of emitted wavelengths within an approximate range of 1 μm.

[0062] Additionally, the second hybrid mode 240 can continue to propagate through the first coupling waveguide 211 and the second coupling waveguide 216 into the corresponding Y-junction, where the coupling may not be ideal, but will still result in two fundamental modes 235. Furthermore, accidental excitation of the second hybrid mode 240 may produce a power imbalance between the branches, but may not affect the insertion loss.

[0063] Near or at the beginning of the third region 231, the gap between the first coupled waveguide 211 and the second coupled waveguide 216 may be increased to prevent coupling between the two waveguides. For example... FIG. 2C As shown, the second mixing mode 240 of the light can have two lobes and a blank center. The second mixing mode 240 of the light can propagate in the third region 231 within the first coupling waveguide 206 and the second coupling waveguide 211, with very little to zero optical power loss and very little to zero reflection, until the second mixing mode 240 of the light encounters the corresponding Y-junctions of the first coupling waveguide 206 and the second coupling waveguide 211. Similar to... FIG. 2A A 1x4 splitter 200, in FIG. 2C In this process, light can be converted from the second mixing mode 240 to four basic conversion modes 235C1-235C4 in branches 211C1, 211C2, 216C1, and 216C2, and light can be output at ports 251C1, 251C2, 251C3, and 251C4. The "basic conversion mode" is the basic mode that has already been converted from the second mixing mode 240 to the basic mode in the third region 231.

[0064] FIG. 3A Another example of a 1x4 splitter is shown. The 1x4 splitter 300 can be a ribbed to a strip splitter. The 1x4 splitter 300 can be configured with a single input of light having a fundamental mode and can output light having a fundamental mode on four waveguide channels or ports. FIG. 3A The one-to-four splitter 300 includes a main waveguide 305, a first coupling waveguide 310, and a second coupling waveguide 315. FIG. 3A In this context, the 1x4 splitter 300 may also include a silicon substrate 323 beneath the waveguide, as the 1x4 splitter 300 is a rib-to-strip splitter, which will be discussed in further detail herein. It is understood that all waveguides can be surrounded by a low-refractive-index cladding region to confine light within the waveguide.

[0065] The quad-splitter 300 has a first region 320 as an input region, a second region 325 as an interaction region (e.g., a coupling region), and a third region 330 as an output region (e.g., a sector region). The first region 320 may include a segment 305A of the main waveguide 205. The first region 320 can be the input region as long as the main waveguide 205 can input light into the quad-splitter 200.

[0066] like FIG. 3AAs shown, the light supplied to the quad-splitter 300 is the fundamental mode 335 of the light (e.g., single-mode). The fundamental mode 335 of the light can propagate through a segment 305A of the main waveguide 305 into a second region 325 of the quad-splitter 300. In some examples, the fundamental mode 335 of the light can be multimode light before reaching the segment 305A of the main waveguide 305. As previously mentioned, the main waveguide 305 can be designed with a specific width and / or taper to generate the fundamental mode of the light by confining the multimode light within the main waveguide 305. Additionally, the optical coupling from the main waveguide to the first and second coupling waveguides can depend on one or more taper ratios of the main waveguide, the first coupling waveguide, and / or the second coupling waveguide. For example, if all the main waveguides have a low taper ratio (e.g., starting wider and reaching a lower ratio over a longer length), the optical coupling may be more efficient. FIG. 3A If the same width is used (as shown), then optical coupling may be slower.

[0067] The second area 325 can be similar to FIG. 2A A one-to-four splitter 200, and a segment 305B of the main waveguide 305 can be optically coupled to both a segment 310B of the first coupling waveguide 310 and a segment 315B of the second coupling waveguide 315. In the second region 325, the main waveguide 305, the first coupling waveguide 310, and the second coupling waveguide 315 can similarly be adjacent and separated from each other by a consistent gap, as in FIG. 2A Furthermore, it can be similarly tapered to allow the coupling of the basic mode 335 to be converted into the first hybrid mode 345.

[0068] The third region 330 of the 1x4 splitter 300 may include a first coupling waveguide 310 and a second coupling waveguide 315, and a Y-junction 355 in each. The third region 330 and... FIG. 2A and FIG. 2C The difference in the third region 230 is that the first coupling waveguide 310C and the second coupling waveguide 315C can be separated by an increased gap and a silicon substrate 323, which in FIG. 3A For visibility purposes, the area is highlighted in black. Additionally, in the third region 330, the ribbed waveguide can be converted or transformed into a strip waveguide, which allows the conversion of the first hybrid mode 345 into the second hybrid modes 340, 342. It is understood that the rib-to-strip waveguide conversion or transformation can be completed near or at the hybrid mode conversion point. Furthermore, the rib-to-strip waveguide conversion or transformation can be completed before the first coupled waveguide 310 and the second coupled waveguide 315 form the Y-junction 355.

[0069] When the first coupled waveguide 310C and the second coupled waveguide 315C are isolated without a silicon substrate 323 connecting the two waveguides, the optical coupling between the waveguides decreases significantly, allowing the mode to be split from a four-lobed mode into a two-lobed mode. It is understood that the area between the first coupled waveguide 310C and the second coupled waveguide 315C where the silicon substrate 323 is not depicted can be filled with a low-refractive-index cladding. Furthermore, the third region 330 where the first coupled waveguide 310C and the second coupled waveguide 315C transition from a ribbed waveguide to a strip waveguide differs from that without the rib-to-strip transition. FIG. 2A Compared to the third region 230, the length can be shortened.

[0070] Similar to FIG. 2A In the third region 330, the first coupling waveguide 310C and the second coupling waveguide 315C can "fan out" or be separated by an increasingly larger gap. Because the first and second coupling waveguides become farther apart, light can avoid coupling between the two waveguides in the third region 330. FIG. 3A In the amplified section of the third region 330, the Y-junction 355 of the first coupling waveguide 310 can be "fanned out" to create a larger gap, or the branches can be separated from each other by increasingly larger distances. As shown, the first branch 350C1 can be a curved section, while the second branch 350C2 can be straight. It can be understood that all, some, or none of the branches 350C1, 350C2, 350C3, and 350C4 can be curved. The third branch 350C3 and the fourth branch 350C4 of the second coupling waveguide 315 can be configured similarly. As the gaps between the corresponding branches 350C1 and 350C2, and 350C3 and 350C4, begin to increase, the second hybrid modes 340, 342 can be converted back to the four basic modes 335C1-335C4. The "basic mode of conversion" has already been converted from the second hybrid mode to the basic mode in the third region 330.

[0071] FIG. 3B An enlarged cross-section of a 1x4 splitter is shown. In an enlarged cross-sectional view 350 along line B-B' of the 1x4 splitter 300, segment 305B of the main waveguide 305, segment 310B of the first coupling waveguide 310, and segment 315B of the second coupling waveguide 315 may have approximately the same height but different widths. As shown in cross-sectional view 350, the waveguides may include layers such as a top cladding layer 317, a propagation region 319, and a bottom cladding layer 321. The enlarged cross-sectional view 350 also shows the silicon substrate 323 and the gap 373b between the main waveguide 305 and the first and second coupling waveguides 310 and 315. Similar to FIG. 2BThe gap 373B in the second region may be filled with a material that allows optical coupling between the main waveguide 305 and the first coupled waveguide 310 and the second coupled waveguide 315. In some examples, the gap 373B may be air.

[0072] The magnified cross-sectional view 350 also includes shoulders 313, which may be regions located between waveguides. Shoulders 313 can separate waveguides from each other. The magnified cross-sectional view 350 shows a ribbed waveguide. In some examples of strip waveguides, the stack may be partially etched so that shoulders 313 (e.g., shoulders 313 are made of a different material than waveguides 315b, 305b, and 315b) of the silicon substrate 323 can separate the waveguides, as shown in cross-sectional view 350. FIG. 3B The enlarged sections are for illustrative and explanatory purposes and not drawn to scale. Strip waveguides can be etched further down than rib waveguides, allowing thinner layers to separate the waveguides from each other, and eliminating the need for... FIG. 3B The prominent shoulders depicted in the image 313.

[0073] Furthermore, although process steps or method steps may be described in a sequential order, such processes and methods can be configured to operate in any suitable order. In other words, any sequence or order of steps described in this disclosure does not itself indicate that the steps need to be performed in that order. Moreover, although described or implied to occur non-simultaneously (e.g., because a step is described after other steps), some steps may be performed concurrently. Furthermore, the illustration of the process in the accompanying drawings, by means of its description, does not imply that the process shown excludes other variations and modifications thereof, does not imply that any step of the process shown must be one or more of the examples, and does not imply that the process shown is preferred.

[0074] This section describes representative applications of the methods and apparatus according to this disclosure. These examples are provided only to add context and aid in understanding. Therefore, it will be apparent to those skilled in the art that the examples can be practiced without some or all of the specific details. Other applications are possible, such that the following examples should not be considered limiting.

[0075] While the disclosed examples have been fully described with reference to the accompanying drawings, it should be noted that various changes and modifications will become apparent to those skilled in the art. It should be understood that such changes and modifications are considered to be included within the scope of the disclosed examples as defined by the appended claims.

Claims

1. A spectrophotometer, comprising: A first region, configured to provide a basic mode of light; A second region, configured to convert the fundamental mode of light into a first mixed mode of light, the second region comprising: Main waveguides with a first side and a second side; The first coupling waveguide adjacent to the first side of the main waveguide; and The second coupled waveguide adjacent to the second side of the main waveguide; and A third region, configured to convert the first mixing mode of light into a plurality of second mixing modes of light, the third region comprising: A first Y-junction, located in the first coupled waveguide and configured to convert one of the plurality of second mixing modes of light into the fundamental mode of light; and The second Y-junction is located in the second coupled waveguide and is configured to convert another of the plurality of second mixing modes of light into the fundamental mode of light.

2. The spectrophotometer according to claim 1, wherein: The first mixing mode of light is the four-lobed mode of light; Each of the multiple second mixing modes of light is a two-lobe mode of light; The main waveguide terminates near the region where the fundamental mode of light is converted into the first mixed mode of light.

3. The spectrophotometer according to claim 1, wherein: The fundamental mode of light is input into the main waveguide; and The Y-junction is configured to output four basic transformation modes.

4. The beam splitting device according to claim 1, wherein the first coupling waveguide and the second coupling waveguide are wider than the main waveguide.

5. The spectrophotometer according to claim 1, wherein: The first and second coupled waveguides in the second region are tapered waveguides; and The optical coupling from the main waveguide to the first and second coupled waveguides depends at least on the taper ratio of the first and second coupled waveguides.

6. The beam splitting device according to claim 1, wherein the widths of the first coupling waveguide and the second coupling waveguide in the second region are reduced.

7. The beam splitter according to claim 1, wherein the first coupling waveguide and the second coupling waveguide in the third region are separated by a gap with increasing width.

8. The spectrophotometer according to claim 1, wherein, In the second region, the width of the first gap between the main waveguide and the first coupled waveguide is the same as the width of the second gap between the main waveguide and the second coupled waveguide.

9. The spectrophotometer according to claim 1, wherein: One of the plurality of second mixing modes of light is a first two-lobe mode that propagates in the first coupled waveguide in the third region to the first Y-junction; and Another of the plurality of second mixing modes of light is a second two-lobe mode that propagates in the second coupled waveguide in the third region to the second Y-junction.

10. A spectrophotometer, comprising: An input region configured to provide light with a basic pattern; An interactive area, configured to convert the basic mode into a first hybrid mode; and The sector-shaped region is configured as follows: Convert the first mixing mode into multiple second mixing modes; as well as The multiple second hybrid modes are converted into multiple basic modes of conversion.

11. The spectrophotometer according to claim 10, wherein: The first hybrid mode has four lobes; Each of the multiple second hybrid modes has two lobes; The optical splitter also includes: Silicon plate; The main waveguide disposed on the silicon substrate; A first coupling waveguide is disposed on the silicon substrate; A second coupled waveguide is disposed on the silicon substrate; The first and second coupled waveguides are ribbed waveguides in the interaction region; and The first coupled waveguide and the second coupled waveguide are converted into strip waveguides in the sector region.

12. The spectrophotometer according to claim 10, wherein: The sector-shaped region includes: A first coupled waveguide having a first Y-shaped junction; A second coupled waveguide having a second Y-junction; and The first hybrid mode has four lobes to reduce optical loss near at least one or both of the first Y-junction or the second Y-junction.

13. The spectrophotometer according to claim 10, further comprising: Silicon plate; A first rib-shaped waveguide is disposed on the silicon substrate in the fan-shaped region; A second rib-shaped waveguide is disposed on the silicon substrate in the sector region, wherein: The first rib waveguide and the second rib waveguide are separated from each other by a gap whose width increases along the fan-shaped region; and The gap includes a low-refractive-index coated region.

14. The spectrophotometer according to claim 10, wherein: The optical splitter also includes: The first rib waveguide is transformed into the first strip waveguide in the fan-shaped region; The second rib waveguide transforms into the second strip waveguide in the sector region, thereby decoupling the first strip waveguide and the second strip waveguide from each other.

15. The beam splitter according to claim 10, wherein the sector region converts the plurality of second mixing modes into the basic modes, thereby outputting four basic modes with equal optical power.

16. The optical splitting device according to claim 10, wherein: The optical splitter also includes: The first rib waveguide is transformed into the first strip waveguide in the fan-shaped region; The second rib waveguide transforms into the second strip waveguide in the fan-shaped region; and Before the first hybrid mode is converted into the second hybrid mode, the first rib waveguide is converted into the first strip waveguide and the second rib waveguide is converted into the second strip waveguide.

17. A method for spectral dispersion, comprising: In the first region, light with the basic mode of light is input using the main waveguide; The fundamental mode of light is converted into a first mixed mode of light in the second region by coupling the fundamental mode of light from the main waveguide to the first coupled waveguide and the second coupled waveguide; In the third region, the first mixing mode of light is converted into multiple second mixing modes of light, wherein the first coupling waveguide and the second coupling waveguide are separated by a gap; as well as The multiple second mixed modes of light are converted back to multiple fundamental modes of light for output on multiple waveguide channels in the third region.

18. The method of claim 17, wherein: The first coupling waveguide is the first rib waveguide in the second region; The second coupling waveguide is the second rib-shaped waveguide in the second region; and The method further includes: After the first rib waveguide is transformed into the first strip waveguide in the third region, and after the second rib waveguide is transformed into the second strip waveguide in the third region, the first hybrid mode is transformed into the second hybrid mode among the plurality of second hybrid modes.

19. The method of claim 17, wherein: The first mixing mode of light has four lobes, wherein a non-zero center equally separates the four lobes; and Each of the plurality of second mixing modes of light has two lobes and a blank space at the center between the two lobes.

20. The method of claim 17, further comprising: Decouple one second mixing mode of light from another second mixing mode of light, wherein the decoupling depends at least in part on the increased refractive index contrast between the first and second coupled waveguides in the third region.

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