Mode multiplexer / demultiplexer using metamaterials for optical fiber communications

Abstract

Systems, apparatuses, and techniques are described for performing wavelength division multiplexing or demultiplexing using one or more metamaterials in optical communication systems. An optical device can be configured to shift one or more phase profiles of an optical signal using one or more stages of metamaterials to multiplex or demultiplex wavelengths of the optical signal. The optical device can be an example of a stacked design in which two or more stages of metamaterials are stacked on top of each other. The optical device can be an example of a folded design that reflects the optical signal between different stages of metamaterials.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. Provisional Application Serial No. 62 / 968,549, filed January 31, 2020, pursuant to 35 U.SC §119, and is based on the content of that provisional application, which is incorporated herein by reference in its entirety. Background Technology

[0003] The following text generally refers to one or more optical communication systems, and more specifically to mode multiplexers or demultiplexers using metamaterials for optical fiber communication.

[0004] Optical communication systems are widely deployed to provide various types of communication content, such as voice content, video content, packet data, message sending and receiving, broadcast content, and so on. Optical communication systems rely on various types of adjustments to the optical signals on the common transmission optical fiber to increase the amount of information that can be transmitted over the transmission fiber. Summary of the Invention

[0005] The systems, methods, and apparatuses disclosed herein each have several new and innovative aspects. This disclosure provides some examples of these new and innovative aspects, but may include new and innovative aspects not included in this disclosure.

[0006] An apparatus may include: a first substrate, the first substrate being transparent; a first metamaterial stage positioned close to or in contact with the first substrate; and a second metamaterial stage positioned close to or in contact with the first substrate, the first and second metamaterial stages being configured to: receive a second optical signal having a second mode via a second optical communication link; generate a third optical signal having a third mode by shifting a first phase profile of the first optical signal; generate a fourth optical signal having a fourth mode by shifting a second phase profile of the second optical signal; and transmit the third and fourth optical signals via a third optical communication link, the third optical communication link including a multimode optical communication link.

[0007] In some examples, the first metamaterial stage can be configured to shift a first phase profile of the first optical signal and a second phase profile of the second optical signal, and output the first shifted optical signal and the second shifted optical signal, and the second metamaterial stage can be configured to shift a third phase profile of the first shifted optical signal and a fourth phase profile of the second shifted optical signal, and output the third optical signal and the fourth optical signal.

[0008] Some examples of the device may include a second substrate, which may be light-transmitting, positioned close to or in contact with a second metamaterial level, wherein the first substrate, the first metamaterial level, the second substrate, and the second metamaterial level form a stacked structure.

[0009] Some examples of the device may include a spacer positioned close to or in contact with a first substrate and a second substrate, creating a space between a first surface of the first substrate and a second surface of the second substrate, wherein a second metamaterial level may be positioned within the space created by the spacer.

[0010] Some examples of the device may include a liquid optically transparent adhesive positioned in a space created by a spacer, wherein a second metamaterial level may be positioned close to or in contact with a second surface of a second substrate, and the liquid optically transparent adhesive may be positioned between the second metamaterial level and a first surface of a first substrate.

[0011] Some examples of the device may include a first reflector and a second reflector configured to reflect a first optical signal and a second optical signal, with a first substrate positioned between the first reflector and the second reflector.

[0012] Some examples of the device may include a cladding layer positioned between the first metamaterial level and the first reflector, the thickness of which is configured to mitigate the loss of optical signals interacting with the first metamaterial level, or to protect the first metamaterial level, or a combination thereof.

[0013] In some examples, the first metamaterial level and the second metamaterial level may be positioned close to or in contact with the first reflector; or the first metamaterial level may be positioned close to or in contact with the first reflector, and the second metamaterial level may be positioned close to or in contact with the second reflector.

[0014] In some examples, a first reflector forms a first aperture for receiving a first optical signal and a second optical signal, and a second reflector forms a second aperture for outputting a third optical signal; or a first reflector forms both a first aperture and a second aperture, with the first aperture for receiving the first optical signal and the second optical signal, and the second aperture for outputting the third optical signal.

[0015] In some examples, a first substrate, a first reflector, a second reflector, a first metamaterial level, and a second metamaterial level form a Fabry-Perot cavity, which is configured to generate one or more resonant reflections of a first optical signal and a second optical signal.

[0016] In some examples, the first metamaterial level may contain operations, features, components, or instructions for a set of metamaterial structures arranged in a pattern to shift the phase profile of an optical signal based on one or more parameters of each metamaterial structure in the set.

[0017] In some examples, one or more parameters of the metamaterial structure include the height of the metamaterial structure, the cross-sectional profile of the metamaterial structure, the diameter of the metamaterial structure, the dielectric properties of the metamaterial structure, or a combination of the above.

[0018] In some examples, the total phase shift caused by the first metamaterial level can be based on the phase shift profile of each metamaterial structure and the pattern of the set of metamaterial structures.

[0019] An apparatus may include: a substrate that is light-transmitting; and a metamaterial level positioned close to or in contact with the substrate and configured to: generate a third optical signal having a third mode from a first optical signal based on a first phase profile shifted by the metamaterial level; generate a fourth optical signal having a fourth mode from a second optical signal based on a second phase profile shifted by the metamaterial level; transmit the third optical signal having the third mode via a second optical communication link; and transmit the fourth optical signal having the fourth mode via a third optical communication link.

[0020] A method may include the following steps: growing a light-transmitting substrate; depositing a metamaterial layer on the substrate; depositing a photoresist layer on the metamaterial layer; etching a portion of the photoresist layer to form a hard mask set; and etching the hard mask set and exposed portions of the metamaterial layer based on the etched portion of the photoresist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0021] An apparatus may include: a processor, a memory in electronic communication with the processor, and instructions stored in the memory. The instructions are executable by the processor to cause the apparatus to: grow a light-transmitting substrate; deposit a metamaterial layer on the substrate; deposit a photoresist layer on the metamaterial layer; etch a portion of the photoresist layer to form a hard mask set; and etch the hard mask set and exposed portions of the metamaterial layer based on the etched portion of the photoresist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0022] Another apparatus may include: a component for growing a light-transmitting substrate; a component for depositing a metamaterial layer on the substrate; a component for depositing a resist layer on the metamaterial layer; a component for etching a portion of the resist layer to form a hard mask set; and a component for etching the hard mask set and the exposed portion of the metamaterial layer based on the etching of the portion of the resist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile having a first optical signal of a first mode and a second phase profile having a second optical signal of a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0023] A non-transitory computer-readable medium storing code is described. The code may contain instructions executable by a processor to: grow a light-transmitting substrate; deposit a metamaterial layer on the substrate; deposit a resist layer on the metamaterial layer; etch a portion of the resist layer to form a hard mask set; and etch the hard mask set and the exposed portion of the metamaterial layer based on the etched portion of the resist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0024] Examples of the methods, apparatus, and non-transitory computer-readable media described herein may further include operations, features, components, or instructions for depositing reflective material at one end of a metamaterial structure set based on the exposed portions of an etched hard mask set and a metamaterial layer.

[0025] Examples of the methods, apparatus, and non-transitory computer-readable media described herein may further include operations, features, components, or instructions for depositing a cladding layer on a metamaterial structure set and on exposed portions of a substrate based on an etched hard mask set and exposed portions of the metamaterial layer, wherein the deposition of reflective material may be based on the deposition of the cladding layer.

[0026] In some examples of the methods, apparatuses, and non-transient computer-readable media described herein, reflective materials can be deposited on a cladding that may be located between a metamaterial structure set and the reflective material.

[0027] In some examples of the methods, apparatuses and non-transient computer-readable media described herein, each metamaterial structure in the metamaterial structure set may have one or more parameters, including the height of the metamaterial structure, the cross-sectional profile of the metamaterial structure, the diameter of the metamaterial structure, the dielectric properties of the metamaterial structure, or a combination of the above.

[0028] In some examples of the methods, apparatuses and non-transient computer-readable media described herein, at least some of the parameters of one or more metamaterial structures may be based on the second cross-sectional profile of an associated hard mask.

[0029] A method may include the following steps: depositing a light-transmitting substrate; depositing a resist layer on the substrate; etching a portion of the resist layer to form a cavity set in the resist layer; depositing a metamaterial layer on the resist layer forming the cavity set, the metamaterial layer filling at least some cavities in the cavity set formed in the resist layer; and etching the metamaterial layer and the resist layer based on the deposition of the metamaterial layer on the resist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0030] An apparatus may include: a processor, a memory in electronic communication with the processor, and instructions stored in the memory. The instructions are executable by the processor to cause the apparatus to: deposit a light-transmitting substrate; deposit a resist layer on the substrate; etch a portion of the resist layer to form a cavity set within the resist layer; deposit a metamaterial layer on the resist layer forming the cavity set, the metamaterial layer filling at least some cavities in the cavity set formed within the resist layer; and etch the metamaterial layer and the resist layer based on the deposition of the metamaterial layer on the resist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0031] Another apparatus may include: a component for depositing a light-transmitting substrate; a component for depositing a resist layer on the substrate; a component for etching a portion of the resist layer to form a cavity set in the resist layer; a component for depositing a metamaterial layer on the resist layer forming the cavity set, the metamaterial layer filling at least some cavities in the cavity set formed in the resist layer; and a component for etching the metamaterial layer and the resist layer based on the deposition of the metamaterial layer on the resist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0032] A non-transitory computer-readable medium storing code is described. The code may contain instructions executable by a processor to: deposit a light-transmitting substrate; deposit a resist layer on the substrate; etch a portion of the resist layer to form a cavity set in the resist layer; deposit a metamaterial layer on the resist layer forming the cavity set, the metamaterial layer filling at least some cavities in the cavity set formed in the resist layer; and etch the metamaterial layer and the resist layer based on the deposition of the metamaterial layer on the resist layer to form a metamaterial structure set, wherein the metamaterial structure set is configured to shift a first phase profile of a first optical signal having a first mode and a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0033] Examples of the methods, apparatuses, and non-transitory computer-readable media described herein may further include operations, features, components, or instructions for depositing reflective material based on etched metamaterial layers and resist layers to form a reflector at one end of a metamaterial structure set.

[0034] The methods, apparatus, and non-transitory computer-readable media described herein may further include operations, features, components, or instructions for depositing a cladding layer on a metamaterial structure set and on exposed portions of a substrate based on an etched metamaterial layer and a resist layer, wherein the deposition of the reflective material may be based on the deposition of the cladding layer.

[0035] In some examples of the methods, apparatuses, and non-transient computer-readable media described herein, reflective materials can be deposited on a cladding that may be located between a metamaterial structure set and the reflective material.

[0036] In some examples of the methods, apparatuses and non-transient computer-readable media described herein, each metamaterial structure in the metamaterial structure set may have one or more parameters, including the height of the metamaterial structure, the cross-sectional profile of the metamaterial structure, the diameter of the metamaterial structure, the dielectric properties of the metamaterial structure, or a combination of the above.

[0037] In some examples of the methods, apparatuses and non-transient computer-readable media described herein, at least some of the parameters of one or more metamaterial structures may be based on the second cross-sectional profile of the associated cavity in the resist layer. Attached Figure Description

[0038] Figure 1A An example of a schematic diagram of an optical system according to the examples disclosed herein is shown, which supports mode multiplexers or demultiplexers for optical fiber communication using metamaterials.

[0039] Figure 1BAn example of a diagram is shown, which can form at least a portion of a mode multiplexer or demultiplexer using metamaterials for optical fiber communication.

[0040] Figure 1C An example diagram of a decoupled multi-core optical communication link supporting a mode multiplexer or demultiplexer, according to the examples disclosed herein, is shown, which uses metamaterials for optical fiber communication.

[0041] Figure 1D An example diagram of a multi-core optical communication link coupled with a mode multiplexer or demultiplexer, according to examples disclosed herein, is shown, which uses metamaterials for optical fiber communication.

[0042] Figure 2A An example of an optical device according to the examples disclosed herein is shown, which may form at least a portion of a mode multiplexer or demultiplexer using metamaterials for optical fiber communication.

[0043] Figure 2B An example of an optical device supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication.

[0044] Figure 2C An example of the phase profile of an optical device supporting a mode multiplexer or demultiplexer according to the examples disclosed herein, which uses metamaterials for optical fiber communication.

[0045] Figure 3 An example of an optical device supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication.

[0046] Figures 4A to 4E An example of an optical device supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication.

[0047] Figures 5A to 5F An example of a method for manufacturing an optical device according to the examples disclosed herein is shown, which supports mode multiplexers or demultiplexers for optical fiber communication using metamaterials.

[0048] Figures 6A to 6F An example of a method for manufacturing an optical device according to the examples disclosed herein is shown, which supports mode multiplexers or demultiplexers for optical fiber communication using metamaterials.

[0049] Figure 7 and Figure 8 A flowchart is shown illustrating one or more methods for supporting the use of metamaterials for mode multiplexers or demultiplexers in optical fiber communications, based on examples disclosed herein. Detailed Implementation

[0050] Optical communication systems are widely deployed to provide various types of communication content, such as voice content, video content, packet data, message sending and receiving, broadcast content, and so on. Optical communication systems rely on various types of multiplexing of optical signals on a common transmission fiber to increase the amount of information that can be transmitted over the fiber. Some types of multiplexing can include wavelength division multiplexing (WDM), polarization division multiplexing (PDM), frequency division multiplexing (FDM), time division multiplexing (TDM), space division multiplexing (SDM), and mode division multiplexing (MDM). Optical communication links can include one or more multimode fibers (MMF), one or more few-mode fibers (FMF), one or more single-mode fibers (SMF), one or more multi-core fibers (MCF), or any combination thereof.

[0051] An MCF (Multi-Chip Fiber) may be an example of an optical fiber containing multiple cores within a common cladding. An MCF can include multiple SMFs, multiple FMFs, multiple MMFs, or any combination thereof. For example, an MCF can include fibers of a single type (e.g., all SMFs), or it can include fibers of different types (e.g., one SMF and three MMFs). Using an MCF, the core design, number of cores, core layout, cladding thickness (e.g., the minimum distance between the outer core center and the cladding-coating interface), cladding diameter, or any combination thereof can be designed to achieve the optical and mechanical properties of the MCF. The ideal fiber design may vary depending on the application. In some examples, an MCF may include a first core, a second core, a third core, and a fourth core. An MCF can contain any number of cores.

[0052] An MCF can be an example of a coupled or uncoupled MCF. Some MCFs may encounter problems related to inter-core crosstalk or other interference. An uncoupled MCF can be one in which each individual core is assumed to be an independent optical path. A coupled MCF can be one in which one core is assumed to be at least partially dependent on another core. In some examples, the distance between at least some cores in an uncoupled MCF may be greater than the distance between at least some cores in a coupled MCF.

[0053] MDM technology can be used in short-range optical communication systems (e.g., connections within data centers) and long-range optical communication systems (e.g., connections between data centers, metropolitan environments, and submarine environments such as transcontinental optical communication links). By using multiple optical signals traveling in different guided modes (FMF or MMF) (e.g., possible paths of light propagation in an optical fiber), the communication capacity of an optical communication link can be effectively increased. In such optical systems, mode multiplexers and mode demultiplexers can be used to perform MDM technology. For example, a multiplexer can combine optical signals traveling in SMF to form optical signals traveling in different modes of FMF or MMF, while a demultiplexer can separate optical signals traveling in different modes of FMF or MMF into optical signals traveling in SMF. In other examples, multiplexers or demultiplexers can be used with an MCF to convert between different modes of different optical signals in different cores of the MCF.

[0054] Systems, apparatuses, and techniques for performing mode division multiplexing or demultiplexing using one or more metamaterials in optical communication systems are described. Optical devices can be configured to use one or more stages of the metamaterial to shift one or more phase profiles of an optical signal to multiplex or demultiplex corresponding spatial modes of the optical signal. The optical device can be an example of a stacked design, where two or more stages of the metamaterial are stacked on top of each other. The optical device can also be an example of a folded design, which reflects the optical signal between different stages of the metamaterial.

[0055] First, refer to Figure 1A The features of this disclosure are described in the context of the optical system being described. (See reference...) Figures 2A to 8 The features of this disclosure are further described in the context of optical devices, phase profiles, and flowcharts.

[0056] Figure 1A An example illustrating a schematic diagram of an optical system 100 according to the examples disclosed herein, the optical system 100 supporting mode multiplexers or demultiplexers for fiber optic communications using metamaterials. The optical system 100 may include an optical communication link 105, a transmitter system 110, and a receiver system 115.

[0057] Optical system 100 can utilize MDM technology to increase the amount of information transmitted through a single optical communication link 105. MDM technology can include using different guiding modes (FMFs or MMFs) to multiplex a certain number of optical signals carried on a certain number of SMFs onto a smaller number of FMFs or MMFs (or vice versa). In some examples, such technology can enable bidirectional communication or capacity multiplication on a single optical fiber. In practice, MDM can convert an optical signal from a first mode in a first fiber to a second mode in a second fiber, where the first mode is different from the second mode. In some cases, MDM technology can convert an optical signal from a first mode in a first fiber to a first mode in a third fiber. In some cases, MDM technology can convert an optical signal from a first mode in a second fiber to a second mode in a third fiber, where the first mode is different from the second mode. Such conversions can be performed simultaneously by the same optical device. MDM technology can also include demultiplexing techniques that can demultiplex optical signals (such as a single optical signal) with different information in different spatial modes into more optical signals (such as two or more optical signals). MDM technology can increase the communication capacity of optical communication link 105.

[0058] Optical communication link 105 may be an example of an optical fiber used to transmit one or more optical signals. An optical fiber can transmit light from one end to the other using the principle of internal reflection. Information can be used to modulate one or more optical signals transmitted by optical communication link 105 to support communication between transmitter system 110 and receiver system 115. Optical communication link 105 may include one or more MMFs, one or more FMFs, one or more SMFs, or any combination thereof.

[0059] Transmitter system 110 can be configured to transmit optical signals via optical communication link 105. Transmitter system 110 may include a multiplexer 120 and one or more transmitters 125 that can be coupled using one or more optical communication links 130. Optical communication link 130 may include an SMF, FMF, MMF, MCF, or any combination thereof. Transmitter 125 can be configured to transmit optical signals comprising light energy operating at an optical wavelength (e.g., an optical band) and modulated with information. In some cases, each transmitter 125 may be configured to transmit optical signals traveling using one or more guide modes. For example, each transmitter 125-a, 125-b, etc., may transmit optical signals downwards along an SMF. Transmitter system 110 may be an example of a system implemented at a central office (CO), front end, switching center, etc. In other examples, transmitter system 110 may be implemented at a customer premises equipment (CPE) or other facility.

[0060] Multiplexer 120 can be configured to multiplex several optical signals together into one or more multimode optical signals, which include multiple optical modes traveling in different modes using optical fibers. Multiplexer 120 can receive one or more optical signals from transmitter 125 (e.g., via one or more optical communication links 130) and can output one or more optical signals on optical communication link 105. Multiplexer 120 can be configured to implement MDM technology to convert a first mode of different optical signals into a different second mode.

[0061] Receiver system 115 can be configured to receive optical signals transmitted via optical communication link 105. Receiver system 115 may include demultiplexer 135 and one or more receivers 140, wherein one or more receivers 140 may be coupled to demultiplexer 135 via one or more optical communication links 145. Optical communication link 145 may include SMF, FMF, MMF, MCF, or any combination thereof. Demultiplexer 135 can be configured to receive one or more optical signals traveling along optical communication link 105 in different modes and convert the optical signals(s) into several single-mode optical signals. In some examples, demultiplexer 135 may receive optical signals transmitted via optical communication link 105 and may (e.g., via one or more optical communication links 145) output one or more optical signals to receiver 140. Demultiplexer 135 may be configured to implement MDM technology to convert different modes of optical signals into different modes.

[0062] Receiver 140 can be configured to receive optical signals, including light energy operating at an optical wavelength (e.g., an optical band) and modulated with information. In some cases, each receiver 140 can be configured to receive optical signals traveling using one or more guided modes. For example, each of receivers 140-a, 140-b, etc., can receive optical signals from an SMF. In some cases, receiver system 115 can be an example of a system implemented at a CO, front end, switching center, etc. In other examples, receiver system 115 can be implemented at a CPE or similar device.

[0063] Optical communication links 105, 130, and 145 can be examples of a wide variety of optical components known as waveguides, which utilize internal reflection (e.g., total internal reflection) to confine and guide light within a solid or liquid structure. Some optical fibers can use a structure known as step-index fiber, which can have an inner core made of a material with a higher refractive index than the surrounding cladding. In an optical fiber, there exists a critical angle of incidence such that light is reflected from the core / cladding interface rather than refracted into the surrounding medium. For total internal reflection to occur within the fiber, the angle of incidence of light incident on the fiber must be smaller than a given angle.

[0064] Optical fibers can support more than one guiding mode. Each potential path through which light propagates in an optical fiber can be referred to as a guiding mode of the fiber. The number of modes supported by an optical fiber can depend on its physical parameters (e.g., core / cladding region, refractive index, and wavelength of light). Examples of fiber types can include SMFs that support a single guiding mode, FMFs that support a first number of modes, and MMFs that support any number of modes. In some examples of multimode fibers, lower-order modes may spatially guide light closer to the fiber core (e.g., closer to the fiber's central axis), while higher-order modes may spatially guide light further away from the fiber core and closer to the core / cladding interface. In some examples, one or more modes in the fiber may be examples of cladding modes, where the intensity distribution of light may substantially fill both the cladding and core regions. In some examples, one or more modes in the fiber may be examples of orbital angular momentum modes exhibiting a helical structure with respect to the fiber. In some examples, one or more modes in the fiber may be examples of resonator modes.

[0065] As described herein, MDM involves acquiring optical signals traveling in different spatial modes supported by one or more MMFs, one or more FMFs, one or more SMFs, or combinations thereof, and converting those optical signals into different spatial modes. For example, a mode multiplexer can receive multiple optical signals via an SMF and can convert the optical signals into different modes that can communicate along a single MMF or FMF fiber. In some examples, a mode demultiplexer can receive multiple optical signals traveling in different optical modes within a single MMF or FMF and can convert those optical signals into single-mode optical signals propagating down along an individual SMF. Other examples can include any type of FMF-FMF, FMF-MMF, MMF-FMF, or MMF-MMF mode conversion. Other examples of MDM can include multiplexing or demultiplexing between any number of SMFs, FMFs, or MMFs having any number of optical signals.

[0066] Figure 1B An example of graph 160 is shown, illustrating a mode multiplexer or demultiplexer according to the examples disclosed herein, which uses metamaterials for optical fiber communication. Graph 160 may include plot 165, which shows the effective refractive index (n) of the optical fiber. eff How do modes change within the same mode group and across different mode groups? The effective refractive index of an optical fiber can be based on the refractive index of the core and the refractive index of the cladding.

[0067] Figure 160 may also include depictions of different modes in the optical fiber. Figure 170 may show an optical fiber with a single mode. Figure 175 may show different mode configurations of an optical fiber with two modes. Figure 180 may show different mode configurations of an optical fiber with four modes. Figure 185 may show different mode configurations of an optical fiber with higher-order modes. Optical communication links or optical fibers may use illustrative modes, or any other modes or mode configurations, to transmit one or more optical signals, and such alternative modes or mode configurations are within the scope of this disclosure.

[0068] MDM technology can be used in short-range optical communication systems (e.g., for connections within data centers) and long-range optical communication systems (e.g., for connections between data centers, metropolitan environments, and submarine environments such as transcontinental optical communication links). By using multiple optical signals of different modes, the communication capacity of optical communication link 105 can be effectively increased. In such an MDM system, a mode multiplexer (e.g., a mux) or a mode demultiplexer (e.g., a demultiplexer) or both can be used to perform MDM technology. For example, multiplexer 120 can convert optical signals of different modes from different input fibers (e.g., an SMF with a single-mode optical signal) into a single output fiber (e.g., an FMF or MMF with optical signals traveling in different modes in a single fiber), and demultiplexer 135 can separate optical signals with multiple different modes from one input fiber (e.g., an FMF or MMF) to different output fibers (e.g., multiple SMFs).

[0069] To increase the capacity of optical communication systems, various multiplexing and multiplexing techniques have been considered, utilizing various properties of light, including amplitude, phase, wavelength, and polarization. Space is considered a dimension that can be used to increase the bandwidth of optical communication systems. In some cases, optical communication systems can use space division multiplexing (SDM) technology. A first approach to implementing SDM may involve using (coupled or uncoupled) multi-core fibers to carry optical signals in multiple cores embedded in the same cladding. In such a method, the communication capacity can be equal to the combination of the number of fibers and the number of cores in each fiber. In a second approach, FMF or MMF can transmit optical signals in different modes of the fiber, such that the communication capacity can be associated with (e.g., equal to) the combination of the number of fibers and the number of modes transmitted by each fiber.

[0070] When using SDM technology (including MDM technology), optical systems can implement multiplexing / demultiplexing techniques to convert optical signals between different types of optical fibers, different types of modes, different types of spatial configurations, or any combination thereof. For example, multiplexers and demultiplexers can be used to convert optical signals between SMFs and FMFs or MMFs, or to convert signals between FMFs or MMFs into different FMFs or MMFs. In some cases, mode multiplexers can use optical signals received from an SMF to excite specific fiber modes in an FMF, while mode demultiplexers can separate different fiber modes in an FMF into different SMFs.

[0071] Some optical systems can perform MDM using one or more of several techniques. Examples of devices that can implement MDM can include free-space optics-based systems, directional coupler-based devices, or photonic lanterns, etc.

[0072] Free-space optics-based systems can include multiple optical components, such as lenses, mirrors, beam splitters, or phase plates, within a free-space setup. Such systems can be bulky and may require aligning and combining a number of optical components, potentially exhibiting high optical loss scaling based on the number of components.

[0073] Directional coupler-based devices can be configured to switch modes by controlling the coupling between adjacent waveguides or adjacent optical fibers. Such devices are typically sensitive to process errors, and the number of accessible modes may be space-limited.

[0074] A photonic lantern may include multiple SMFs at one end, an FMF at the other end, and a transition section in between. The number of accessible modes may also be limited by space, and due to the difficulty in manufacturing such a device, it may be difficult to scale this method to a large number of modes.

[0075] Optical system 100 can support systems, devices, and techniques for performing mode division multiplexing or demultiplexing using one or more metamaterials. In some examples, the metamaterial can be or may include a metasurface. Devices with metamaterials can use one or more phase masks (e.g., high-resolution phase masks) implemented by optical metamaterials to multiplex or demultiplex modes of optical signals. The device can be an example of a stacked design, where two or more levels of the metamaterial are on top of each other. The device can be an example of a folded design, where the folded design reflects optical signals between different levels of the metamaterial. As further described herein, the phase profiles of the metamaterial levels in the device can be designed using adjoint analysis techniques (e.g., adjoint optimization techniques), wavefront matching techniques, or any combination thereof. Some fabrication methods used in MDM techniques may be difficult to scale (e.g., directional couplers or photonic lanterns) or may be lossy (e.g., free-space optical devices). In contrast, devices using metamaterials can be efficiently fabricated using a single photolithography step, regardless of the number of modes to be multiplexed.

[0076] Mode multiplexing and demultiplexing are useful functions in optical communication systems. An example of mode multiplexing and demultiplexing is the ability to convert light propagating in an optical fiber in one or more modes into optical signals with one or more different modes, each of which is then included in a different output fiber.

[0077] Such functionality can be useful in a wide range of communication applications, such as long-distance communication networks employing MDM, access networks using multiple modes in both downstream (e.g., from CO to CPE in Fiber to the Premises (FTTP) architectures or other network architectures) and upstream transmission (e.g., from CPE to CO in FTTP network architectures), and data center applications. Each application may have different performance requirements, resulting in different specifications for mode multiplexing and demultiplexing functions, such as the number of modes to be multiplexed or demultiplexed, optical performance specifications (e.g., insertion loss, crosstalk, channel bandwidth, channel spacing, other specifications, or any combination thereof), environmental conditions, cost requirements, or density requirements. Specifically, in some data centers and some access applications, density requirements related to containing more optical signals in a smaller volume are becoming increasingly important.

[0078] Spatial mode multiplexers or demultiplexers can be implemented using free-space optics, which employ multi-plane optical conversion methods. This approach modulates the wavefront of the optical field using a series of phase plates along with optical Fourier transforms. An advantage of the free-space optics approach is its scalability to a large number of modes. A disadvantage is its use of micro-optical components (including collimating lenses, mirrors, and phase plates), which may require precise mechanical alignment and integration of these components, increasing cost and limiting the device's form factor. Another drawback is that the phase plates used in current devices may have relatively low spatial resolution (on the order of 10 µm), potentially leading to a relatively large number of phase plates required for mode multiplexing, and again, bulky devices. Other approaches can include devices using directional couplers and photonic devices, which can convert modes by controlling the coupling between adjacent waveguides and photonic lanterns. Such devices can be bulky, sensitive to fabrication errors, difficult to scale to a large number of modes, or any combination thereof.

[0079] In some examples, applications such as fiber optic connections to server architectures may use mode multiplexers or mode demultiplexers over hundreds of fibers, and devices with small form factors can therefore be useful in such applications. Multiplexers and demultiplexers that perform MDM using metamaterials exhibit highly compact form factors. Such size differences allow metamaterial devices to be integrated into optical connectors.

[0080] In some examples, the fabrication process for metamaterial-based optical devices can be relatively simple compared to other MDM devices. For instance, commercial spatial light modulators (SLMs) or multilayer silicon dioxide substrates may require iterative photolithography and multilayer etching to form a phase plate. In some cases, metamaterials can be fabricated using a single photolithography step or nanoimprint technology. This fabrication simplicity can improve the yield of such devices and reduce their cost compared to other devices that use more complex manufacturing techniques.

[0081] In some examples, metamaterial-based optical devices can be monolithically integrated, and a single layer of metamaterial (e.g., can be decomposed into multiple levels) can be used to perform mode multiplexing and demultiplexing. Such features can produce devices with a smaller footprint than other devices and that do not require complex packaging processes, further reducing manufacturing and assembly costs. In some cases, the sole alignment application of metamaterial-based optical devices may be for aligning the input and output fibers.

[0082] Compared to SLM and multilayer silica devices, metamaterial-based optical devices may exhibit high spatial resolution (smaller than wavelength). Such spatial resolution allows metamaterial-based optical devices to better control the wavefront, meaning that similar device performance can be achieved with fewer phase plates, further reducing size and potentially reducing optical losses due to less reflection.

[0083] In some examples, metamaterial-based optical devices utilizing the principle of reflection can be used in folded designs, or resonant folded designs can exhibit high transmission efficiency. In some examples, the design of phase profiles using adjoint analysis methods (e.g., adjoint optimization techniques) can allow additional degrees of freedom to tune the device's performance (e.g., mode-dependent loss compensation). In some examples, metamaterials can be configured to be polarization-insensitive, allowing metamaterial-based multiplexers / demultiplexers to operate without interfering with polarization multiplexing. Note that the terms metamaterial and metasurface described herein can refer to materials whose properties are based on their intrinsic structure (e.g., geometry, arrangement, size, shape, orientation, etc.) and can be configured for a variety of purposes, applications, or technologies.

[0084] Figure 1C Figure 190 illustrates an example of a decoupled multi-fiber optical communication link 191 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein, which uses metamaterials for fiber optic communication. The uncoupled multi-fiber optical communication link 191 can be as shown in the reference... Figure 1A Examples of optical communication links 105, 130, and 145 are described.

[0085] An MCF may be an example of an optical fiber containing multiple cores within a common cladding. An MCF may include multiple SMFs, multiple FMFs, multiple MMFs, or any combination thereof. For example, an uncoupled multi-core optical communication link 191 may include a first core 192-a, a second core 192-b, a third core 192-c, and a fourth core 192-d, and a cladding 193 positioned close to (e.g., near, adjacent to, without one or more materials between them, or with one or more materials between them) or in contact with each of the cores 192. The cores 192 of the uncoupled multi-core optical communication link 191 may be examples of SMFs, FMFs, MMFs, or any combination thereof. In several cases, an MCF may include fibers of a single type (e.g., all SMFs), or may include fibers of different types (e.g., one SMF and three MMFs). Using MCFs, the core design, number of cores, core layout, cladding thickness (e.g., the minimum distance between the outer core center and the cladding-coating interface), cladding diameter, or any combination thereof, can be designed to achieve the optical and mechanical properties of the MCF. The ideal fiber design may vary depending on the application. MCFs can include any number of cores (e.g., two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, etc.).

[0086] An MCF can be an example of a coupled or uncoupled MCF. Some MCFs may encounter problems related to inter-core crosstalk or other interference. An uncoupled MCF can be one in which each individual core is assumed to be an independent optical path. A coupled MCF can be one in which one core is assumed to be at least partially dependent on another core. In some examples, the distance between at least some cores in an uncoupled MCF may be greater than the distance between at least some cores in a coupled MCF.

[0087] The uncoupled multi-core optical communication link 191 may be an example of an uncoupled MCF. In some cases, the parameters of the different cores 192 may be the same. In other examples, at least one of the multiple cores 192 may have parameters different from the other cores. Examples of the parameters of the cores 192 may include the core diameter, the core dielectric properties, the relative difference between the dielectric properties of the core 192 and the dielectric properties of the cladding 193, the distance from the center of the core to the center of the uncoupled multi-core optical communication link 191, the core modulus, the refractive index distribution (e.g., Δn), or combinations thereof. In some examples, the diameter of each core 192 may be approximately 8.2 micrometers, the refractive index distribution of the core 192 may be approximately 0.35% (e.g., Δn = 0.35%), and the center-to-center distance of the cores may be approximately 45 micrometers.

[0088] The first graph 190-a shows the intensity distribution of the optical signal in the first fiber core 192-a, where other fiber cores (e.g., fiber cores 192-b, 192-c, and 192-d) do not transmit optical signals. The second graph 190-b shows the intensity distribution of the optical signal in the second fiber core 192-b, where other fiber cores (e.g., fiber cores 192-a, 192-c, and 192-d) do not transmit optical signals. The third graph 190-c shows the intensity distribution of the optical signal in the third fiber core 192-c, where other fiber cores (e.g., fiber cores 192-a, 192-b, and 192-d) do not transmit optical signals. The fourth graph 190-d shows the intensity distribution of the optical signal in the fourth fiber core 192-d, where other fiber cores (e.g., fiber cores 192-a, 192-b, and 192-c) do not transmit optical signals.

[0089] Figure 1D Figure 195 illustrates an example of a coupled multi-fiber optical communication link 196 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein, which uses metamaterials for fiber optic communication. The coupled multi-fiber optical communication link 196 can be as shown in the reference... Figure 1A Examples of optical communication links 105, 130, and 145 are described.

[0090] The coupled multi-fiber optical communication link 196 may include a first fiber core 197-a, a second fiber core 197-b, a third fiber core 197-c, and a fourth fiber core 197-d, as well as a cladding 198 adjacent to or in contact with each fiber core 197. The fiber cores 197 of the coupled multi-fiber optical communication link 196 may be examples of SMF, FMF, MMF, or any combination thereof. In several cases, the MMF may include fibers of a single type (e.g., all SMF), or may include fibers of different types (e.g., one SMF and three MMFs).

[0091] The coupled multi-core optical communication link 196 can be an example of a coupled MCF. In some cases, the parameters of the different cores 197 can be the same. In other examples, at least one of the multiple cores 197 can have parameters different from the other cores. Examples of the parameters of the core 197 can include the core diameter, the core dielectric properties, the relative difference between the dielectric properties of the core 197 and the dielectric properties of the cladding 198, the distance from the center of the core to the center of the uncoupled multi-core optical communication link 196, the core modulus, the refractive index distribution (e.g., Δn), or combinations thereof. In some examples, the diameter of each core 197 can be approximately 8.2 micrometers, the refractive index distribution of the core 197 can be approximately 0.35% (e.g., Δn = 0.35%), and the center-to-center distance of the cores can be approximately 20 micrometers.

[0092] Figures 195 (e.g., first figure 195-a, second figure 195-b, third figure 195-c, ​​and fourth figure 195-d) can illustrate different intensity distributions of optical signals in different fiber cores 197. In the first figure 195-a, the distribution in each fiber core 197 can be approximately the same. In the second figure 195-b, the second fiber core 197-b can have a strong distribution in the center (e.g., around 0.9), the third fiber core 197-b can have a strong distribution in the center (e.g., around -0.9), the fourth fiber core 197-d can have a moderate distribution in the center (e.g., around -0.5), while the first fiber core 197-a can have a moderate distribution in the center (e.g., around 0.5). In the third diagram 195-c, ​​the fourth core 197-d may have a strong distribution at the center (e.g., around 0.9), the first core 197-a may have a strong distribution at the center (e.g., around -0.9), the third core 197-c may have a moderate distribution at the center (e.g., around -0.5), and the second core 197-b may have a moderate distribution at the center (e.g., around 0.5). In the fourth diagram 195-d, the first core 197-a may have a strong distribution at the center (e.g., around -0.9), the second core 197-b may have a strong distribution at the center (e.g., around 0.9), the third core 197-c may have a strong distribution at the center (e.g., around 0.9), and the fourth core 197-d may have a strong distribution at the center (e.g., around -0.9).

[0093] Figure 2A An example of an optical device 201 according to the examples disclosed herein is shown. This optical device 201 can form at least a portion of a mode multiplexer or demultiplexer using metamaterials for optical fiber communication. The optical device 201 can be as described in reference... Figure 1A Examples of the described multiplexer / demultiplexer devices using metamaterials. In some cases, the optical device 201 may be an example of a modal multiplexer / demultiplexer device.

[0094] Optical device 201 may include a substrate 205 and multiple metamaterial structures 210. In some cases, optical device 201 may also include a cladding (not shown). In some cases, the cladding may be air or other ambient gas surrounding the metamaterial. The metamaterial (sometimes called a metasurface) may be a nanophotonic structure that can control the properties of light passing through the metamaterial (e.g., the phase or direction of light propagation) with relatively high spatial resolution (e.g., subwavelength, depending on the operating wavelength window, on the order of hundreds of nanometers). In some examples, each or at least some metamaterial structures 210 may have one or more parameters that affect how the properties of light change as light passes through the metamaterial structure 210. Arrays of metamaterial structures 210 may be patterned (thus forming a metamaterial level) to produce a desired shift in the properties of the optical signal when the optical signal interacts with the metamaterial level. The phase profile and nanostructures of the metamaterial can be configured to manipulate the spatial profile of light, and thus can be used for fiber mode multiplexing and demultiplexing applications. High spatial resolution and the ability to perform multiple optical functions within a single level or single metamaterial structure, among other examples, enable small devices that can be monolithically integrated onto a single substrate. A simple manufacturing process reduces the overall loss and packaging complexity of such multiplexers or demultiplexers.

[0095] In some cases, metamaterials may refer to a class of materials that possess properties not found in naturally occurring materials. Optical metamaterials can be smaller than the wavelength of light, but may be able to interact with and influence light. Examples of interactions between metamaterials and light can include negative refraction, fast and slow light propagation at zero refractive index, notch structures, plane lenses, thin lenses, perfect lenses, or any combination thereof.

[0096] Individual metamaterial structure 210 can influence light passing through it based on one or more properties of the metamaterial structure 210. Examples of properties of the metamaterial structure 210 that can influence light may include the height of the metamaterial structure (e.g., the dimension of the metamaterial structure 210 extending away from the substrate 205), the cross-sectional profile of the metamaterial structure 210 (e.g., the cross-sectional shape of the metamaterial), the cross-sectional area of ​​the metamaterial structure 210, the volume of the metamaterial structure 210, the diameter of the metamaterial structure 210, the dielectric properties of the metamaterial structure 210, the relative difference between the dielectric properties of the metamaterial structure 210 and the dielectric properties of the substrate 205, the relative difference between the dielectric properties of the metamaterial structure 210 and the dielectric properties of the cladding, or any combination thereof. In some cases, the metamaterial structure 210 may be an example of a multilayer metamaterial structure, wherein a first metamaterial structure having a first set of parameters is stacked on top of a second metamaterial structure 210 having a second set of parameters. The multilayer metamaterial structure may include any number of metamaterial structures. In some cases, different metamaterial structures in the stack may have different dielectric properties or other properties.

[0097] Figure 2A The illustrated metamaterial structure 210 shows examples of metamaterial structures with circular, rectangular, and hexagonal cross-sectional shapes, different cross-sectional areas, and different heights. These illustrative metamaterial structures 210 are merely examples of some properties of metamaterial structures. For example, in some cases, the metamaterial structure 210 can have any cross-sectional profile, such as circular, triangular, square, rectangular, pentagonal, hexagonal, other geometric cross-sectional profiles, other shaped cross-sectional profiles, or any combination of the above. Figure 2A As shown, each metamaterial structure 210 may correspond to a unit cell 212 in a set of unit cells for a metamaterial structure level. Additionally or alternatively, the unit cells 212 in a set of unit cells for a metamaterial structure level may include two or more metamaterial structures 210. In some examples, metamaterial structures 210 may have the same one or more parameters, and may have different one or more parameters. For example, in some cases, all metamaterial structures 210 may have the same cross-sectional shape (e.g., circular), but may have different cross-sectional shapes (e.g., different dimensions, different diameters). For example, in some cases, all metamaterial structures 210 may have the same height (e.g., relative to the substrate), but may have different cross-sectional areas (e.g., different dimensions, different diameters). In some examples, one or more parameters relating to a set or subset of metamaterial structures 210 may be the same or may be different.

[0098] The substrate 205 may be an example of a material that forms a support substrate for optical elements (such as metamaterials), other components, or any combination thereof. In some cases, the metamaterial structure 210 is coupled to the substrate 205. In some cases, the substrate 205 may be light-transmitting, allowing optical signals to pass through it.

[0099] Each individual metamaterial structure 210 can be relatively small. To shift the phase profile of an optical signal, multiple metamaterial structures 210 can be arranged in a pattern and configured to shift the phase profile of the optical signal. An array or pattern of metamaterial structures 210 may be referred to as a metamaterial structure level. Each individual metamaterial structure 210 can have its own set of parameters affecting light. The overall phase-shift profile of the metamaterial level can be based on the parameters of each individual metamaterial structure 210 in that level. In some cases, a cladding can be positioned close to or in contact with the metamaterial structure 210, the substrate 205, or any combination thereof. The cladding can be configured to mitigate the loss of optical signals interacting with the metamaterial structure 210, or to protect the metamaterial structure 210 from damage, or any combination thereof. In some cases, the metamaterial structure 210 may be an example of a reflective metamaterial structure and can be configured to be achromatic or highly dispersive.

[0100] Each metamaterial structure 210 is shown as a separate, independent structure. In some examples, at least some or all of the metamaterial structures 210 may be formed from a single, larger region. In such examples, the unit cell may refer to an individual configurable portion of the larger region of the metamaterial, which can be modified to achieve a desired phase profile.

[0101] Figure 2B An example of an optical device 202 according to the examples disclosed herein is shown. This optical device 202 can form at least a portion of a mode multiplexer or demultiplexer using metamaterials for optical fiber communication. The optical device 202 can be as shown in Figure 1 and... Figure 2A Examples of the described multiplexer / demultiplexer devices using metamaterials. In some cases, the optical device 202 may be an example of a modal multiplexer / demultiplexer device.

[0102] Optical device 202 may include a substrate 205, a plurality of metamaterial structures 210, a cladding 215 surrounding the metamaterial structures 210, and a reflector 220. Optical device 202 may be an example of a metamaterial level using a reflective design. In such a design, light can pass through the metamaterial structure 210, be reflected by the reflector 220, and then pass through the metamaterial structure 210 again after being reflected. In such a design, the phase profile of the metamaterial level may be based on both the phase shift caused by the light that first (e.g., initially) passes through the metamaterial structure 210 and the phase shift caused by the reflected light that passes through the metamaterial structure 210. (See reference...) Figure 2A The features of substrate 205 and metamaterial structure 210 are described and are incorporated herein by reference.

[0103] Cladding 215 may be a material layer. In some cases, cladding 215 may have a lower refractive index than metamaterial structure 210. In some cases, cladding 215 may be configured to mitigate the loss of optical signals interacting with metamaterial structure 210. In some cases, cladding 215 may be configured to protect metamaterial structure 210 from damage.

[0104] In some examples, the cladding 215 may be located between the surface 225 of the metamaterial structure 210 and the reflector 220. In such examples, a distance 230 may be formed between the surface 225 of the metamaterial structure 210 and the surface 235 of the reflector 220. The distance 230 may be configured to mitigate the loss of optical signals passing through the metamaterial structure 210 and reflected by the reflector 220. In some cases, the distance 230 may be approximately 500 nanometers. In some cases, the distance 230 may be between zero nanometers and several micrometers (e.g., one micrometer, two micrometers, or three micrometers). The surface 225 of the metamaterial structure 210 may be positioned opposite a different surface of the metamaterial structure 210 that is in contact with the substrate 205.

[0105] Reflector 220 may be formed of one or more reflective materials. Examples of reflective materials may include gold or another metal. In some cases, the reflective material may be coated with another material to help reflect light. Figure 2B The light field is shown as perpendicular to the metamaterial structure 210, substrate 205, cladding 215, and / or reflector 220. In some examples, the light field may arrive and / or depart at an angle not perpendicular to the metamaterial structure 210, substrate 205, cladding 215, and / or reflector 220.

[0106] Each metamaterial structure 210 is shown as a separate, independent structure. In some examples, at least some or all of the metamaterial structures 210 may be formed from a single, larger region. In such examples, the unit cell may refer to an individual configurable portion of the larger region of the metamaterial, which can be modified to achieve a desired phase profile.

[0107] Figure 2C An example of a phase profile 203 of an optical device supporting a mode multiplexer or demultiplexer, according to the examples disclosed herein, is shown. This mode multiplexer or demultiplexer uses metamaterials for fiber optic communication. The shading of the phase profile 203 can indicate different phase shifts caused by different parts of the optical device (e.g., optical device 201 or 202). As described herein, the phase profile 203 can be an example of a phase profile designed using wavefront matching techniques or adjoint analysis (e.g., adjoint optimization).

[0108] Multiple metamaterial structures can be patterned and configured to shift the phase profile of an optical signal. An array or pattern of metamaterial structures can be called a metamaterial structure level. Each metamaterial structure in a level of metamaterial elements can be configured to shift a portion of the phase of an optical signal. In some cases, an individual metamaterial structure can be considered as an individual pixel (or unit cell) of a larger metamaterial level. In some cases, depending on the operating wavelength window, the size of the metamaterial structure can be on the order of hundreds of nanometers (e.g., a unit cell size of 500 nm × 500 nm when the operating wavelength is 1550 nm). The overall phase shift performed by the metamaterial level can be a combination based on each individual phase shift performed by each individual metamaterial structure in the metamaterial structure level. By varying the parameters of the individual metamaterial structures within the metamaterial level, the metamaterial level can be designed to have different phase profiles. In some examples, light is transmitted through a substrate and the metamaterial structure (e.g., a metamaterial pillar), and the phase transition in each unit cell is determined by the geometry of the structure (e.g., cross-sectional profile, cross-sectional area, height, etc.). In some cases, metamaterial structures can have anisotropic geometries that can produce a birefringent response to control the polarization of light in space. In other cases, cladding (using transparent materials) can be added to encapsulate the pillars and protect the structure.

[0109] Phase profile 203 is an example of a phase profile caused by one or more levels of a metamaterial. Based on the parameters of various metamaterial structures forming the metamaterial levels, the metamaterial levels can have different phase profiles. In some cases, the wavelength-dependent behavior of the phase (or dispersion) can be tuned, allowing the metamaterial device to be achromatic or relatively highly dispersive. Furthermore, the metamaterial structure can be designed to operate in a reflective mode when light passes through the pillar and is reflected back by one or more reflective materials, such as metals.

[0110] Depending on the operating wavelength window, different materials can be selected for the substrate and metamaterial structure. For example, for the O-band (1260-1360 nm), C-band (1530-1565 nm), or L-band (1565-1625 nm) windows, crystalline silicon, amorphous silicon, silicon nitride (Si3N4), and chalcogenide glasses can be used for the metamaterial structure. For shorter wavelength windows (e.g., 850-940 nm), other materials (such as titanium oxide (TiO2) and silicon nitride (Si3N4)) can be used for the metamaterial structure. Transparent materials such as glass or polymers (e.g., SU8) can be used for the substrate and cladding.

[0111] In some cases, different design techniques can be used to design metamaterial-level phase profiles. Examples of design techniques may include wavefront matching, adjoint analysis, or any combination thereof.

[0112] Mode multiplexing and demultiplexing in optical fibers can be achieved by modifying the wavefront of the optical field using a series of phase plates (e.g., metamaterial-level) and free-space propagation. To achieve low-loss and low-crosstalk mode multiplexing or demultiplexing, multi-level metamaterials (whether stacked or folded) can be used. The phase profile of the metamaterial-level metamaterials for mode multiplexing or demultiplexing can be designed using various methods, including wavefront matching, adjoint analysis, or any combination thereof.

[0113] In wavefront matching methods, the forward-propagating input field is compared with the backward-propagating target field to obtain the field difference for each stage of the metamaterial. This difference can be compensated for by designing the stages of the material's phase plates, resulting in precise field matching. Such steps can be performed iteratively to achieve the design. Based on the analysis using wavefront matching methods, the metamaterial stages can be designed with phase profiles that produce devices with low loss and low crosstalk performance.

[0114] In adjoint analysis methods (e.g., adjoint optimization methods), the design quality factor (FOM) can be defined as the power throughput of each individual input-output pair. Given the FOM, its derivative with respect to each design parameter can be calculated. In some cases, the derivative of the FOM can be calculated based on the propagation field at each metamaterial structure. Given the derivative, efficient gradient-based nonlinear enhancement routines (e.g., conjugate gradient (CG), Newton-CG, sequential least squares programming (SLSQP), Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, etc.) can be used to search for enhanced phase profiles. Depending on the application, additional FOMs can be efficiently added (e.g., when they can be written as analytical expressions for design variables or field variables). For example, to reduce the complexity of the phase mask, an FOM term corresponding to the average difference in phase values ​​between each pair of adjacent pixels (or cells) can be added to the analysis. In other examples, instead of enhancing the average loss across all channels, the worst-case (maximum) loss across all channels can be minimized, or the loss based on a specific distribution (e.g., channel bandwidth) can be enhanced.

[0115] Figure 3 An example of an optical device 300 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication. The optical device 300 can perform mode multiplexing or demultiplexing techniques using a light-transmitting metamaterial structure and a light-transmitting substrate stacked on top of each other. The optical device 300 can be a reference. Figure 2A An example of the optical device 201 described. Figure 3The diagram shown may be a cross-sectional view of the optical device 300.

[0116] Optical device 300 may include multiple substrates 305 positioned close to or in contact with multiple stages 310 of a metamaterial. Each stage 310 of the metamaterial may include multiple metamaterial structures. The multiple substrates 305 and multiple stages 310 may be stacked on top of each other. Optical device 300 may also include one or more spacers 315 and one or more optically transparent adhesives (OCAs) 320 located between each layer of substrate 305 and the metamaterial stage 310. Optical device 300 may include any number of metamaterial layers to perform modal multiplexing or modal demultiplexing techniques. For example, optical device may include a first stage 310-a, a second stage 310-b, a third stage 310-c, or any number of stages 310-N. In such an example, optical device 300 may include any number of substrates 305, spacers 315, and OCAs 320 to support platform 310. In some examples, the number of substrates 305 may be the same as the number of metamaterial stages 310. The number of layers may be determined based on the desired phase profile of optical device 300.

[0117] Substrate 305 may be a light-transmitting substrate configured to support metamaterial grade 310. Substrate 305 may have one or more parameters defining the structure, such as height (h). Substrate 305 may be a reference. Figure 2A and Figure 2B Examples of substrate 205 described. In some examples, each substrate 305 in the optical device 300 may have the same parameters. Additionally or alternatively, based on the desired phase profile of the optical device 300, one or more substrates 305 may have different parameters than other substrates in the optical device 300 (e.g., the height (h) of one or more substrates 305 may be different).

[0118] Metamaterial stage 310 may include one or more light-transmitting metamaterial structures configured to shift the phase profile of an optical signal (e.g., light) passing through the metamaterial structure. Each stage 310 of the metamaterial may be positioned in proximity to or in contact with at least one substrate 305. The metamaterial structure of stage 310 may be a reference. Figure 2A and Figure 2BExamples of described metamaterial structures 210 are given. In other examples, the metamaterial structure of metamaterial level 310 may have one or more parameters defining the metamaterial structure, such as cross-sectional profile, cross-sectional area, or height, etc. In some examples, each level 310 of the metamaterial may be designed to have a different phase profile, and the combined phase profile of each level 310 may produce the overall phase profile of the optical device 300. In some examples, based on the desired phase profile of the optical device 300, one or more levels 310 of the metamaterial may have parameters different from those of other levels 310 of the metamaterial in the optical device 300. In some examples, each level 310 of the metamaterial in the optical device 300 may have the same parameters.

[0119] Spacers 315 can be located between two different substrates 305 and can be configured to create a space 325 between the different substrates 305. Spacers 315 can be positioned close to or in contact with the first substrate 305 and the second substrate 305 to create the space 325. Metamaterial grade 310 can be positioned within the space 325 created by the spacers 315. Spacers 315 can have one or more defining structural parameters, such as height. In some examples, each spacer 315 in the optical device 300 can have the same parameters. In some examples, one or more spacers 315 can have different parameters than other spacers 315 in the optical device 300 (e.g., the heights of one or more spacers 315 can be different). Any number of spacers 315 can be located between different substrates.

[0120] OCA 320 can be positioned within a space 325 created by spacer 315. OCA 320 can be an example of liquid OCA or gel OCA or any combination thereof. OCA 320 can be a light-transmitting material. OCA 320 can be configured to protect metamaterial level 310. OCA 320 can be positioned such that metamaterial level 310 is positioned close to or in contact with the surface of substrate 305, and also positioned close to or in contact with OCA 320. In such an example, OCA 320 can be positioned between one or more surfaces of metamaterial level 310 and the bottom surface of substrate 305. For example, OCA 320 can be located between one or more surfaces of the metamaterial structure of second level 310b of metamaterial and the bottom surface of substrate 305. In some cases, OCA 320 can be an example of a refractive index-matching material, wherein the refractive index of OCA 320 can be similar to the refractive index of one or more surrounding materials.

[0121] Optical device 300 can be configured as a mode multiplexer. In some cases, optical device 300 can be configured as a mode demultiplexer. In this case, the input and output of optical device 300 can be reversed. Input fiber 330 can be positioned at a first distance (d1) from the first stage 310-a of the metamaterial and can be configured to transmit one or more optical signals through optical device 300. Input fiber 330 can be a reference. Figure 1A Examples of optical communication links 105, 130, or 145 are described. The output fiber optic cable 335 may be positioned at a second distance (d2) from the last layer (e.g., the last substrate 305) of the optical device 300 and may be configured to receive one or more optical signals output from the optical device 300. The output fiber optic cable 335 may be a reference. Figure 1A Examples of optical communication links 105, 130, or 145 are described. In some cases, the input fiber 330, the output fiber 335, or any combination thereof may be examples of an optical fiber array having multiple fibers. In some cases, the size of the first distance (d1) may be the same as the size of the second distance (d2). In some cases, the size of the first distance (d1) may be different from the size of the second distance (d2). In some cases, the input fiber 330 may include one or more SMFs, and one or more input signals may be single-mode input signals. In other examples, the input fiber 330 may include one or more FMFs or MMFs, and at least one input signal may be a multimode signal. Additionally or alternatively, the output fiber 335 may include one or more SMFs, and one or more output signals may be single-mode output signals. In other examples, the output fiber 335 may include one or more FMFs or MMFs, and at least one input signal may be a multimode signal. In some cases, additional spacers, additional OCAs, or combinations thereof may be located between the input fiber 330 and the first stage 310-a of the metamaterial. In some cases, additional spacers, additional OCAs, or combinations thereof may be located between the output fiber 335 and the last layer of the optical device 300 (e.g., the last substrate 305). Such additional spacers or additional OCAs may be configured to reduce back reflection, protect metamaterials, or provide spacing between the fiber and the optical device, or any combination thereof.

[0122] In an example where the optical device 300 is configured as a mode multiplexer, the input fiber 330 may be an example of a fiber array, and two or more optical signals having different modes or multiple versions of the same mode can be transmitted into the optical device 300. The two or more optical signals can pass through different stages 310 of the metamaterial of the optical device 300 (and other components). At each stage 310, the phase profiles of the two or more optical signals can be shifted or altered. Through the different stages 310, the optical device 300 can convert the two or more optical signals into different optical signals traveling along different modes of the FMF or MMF. The output fiber 335 may be an example of a single output fiber and can be configured to receive optical signals traveling along different guided modes.

[0123] In an example where the optical device 300 is configured as a mode demultiplexer, the input fiber 330 may be a single fiber, and optical signals traveling in different modes can be transmitted into the optical device 300 along this single fiber. The optical signals can pass through different stages 310 (and other components) of the metamaterial of the optical device 300. At each stage 310, the phase profile of the optical signal can be shifted or altered. Through the different stages 310, the optical device 300 can convert the optical signal into two or more distinct optical signals with different modes (e.g., multiple optical signals propagating along the SMF). The output fiber 335 may be an example of a fiber array and can be configured to receive two or more optical signals that have been demultiplexed from the original optical signal.

[0124] In some cases, optical device 300 can be used for SDM / MDM applications. Optical device 300 can coherently shape the modes of light from one mode to another. Light in the first stage of the metamaterial can propagate in many directions and may interfere with each other as it travels into or through the second stage of the metamaterial. Light in the second stage of the metamaterial can propagate in multiple directions and may interfere with each other as it travels into or through the third stage of the metamaterial. Spacer 315 can be configured to allow light propagating between metamaterial stages 310 to interfere with each other.

[0125] Figures 4A to 4E An example of an optical device supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication. Figures 4A to 4E The optical device shown can be an example of a folded design for an optical device that uses reflective surfaces to transmit light between different levels of a metamaterial. Figures 4A to 4E The optical device shown may be a reference Figure 2B An example of the optical device 202 described. Figures 4A to 4EVarious configurations of folded designs for optical devices used as modal multiplexers or modal demultiplexers are shown. This disclosure is not limited to the illustrated fast optical device configurations. Figures 4A to 4E Any feature of any optical device configuration shown can be associated with Figures 4A to 4E Any other combination of features in any optical device configuration shown. First refer to... Figure 4A Describe various aspects of the optical device, but Figures 4B to 4E The description of the optical device is omitted in the text. Figures 4A to 4E In optical devices, features with similar numbers or similar implementations can be handled similarly. Figures 4A to 4E An optical device with four metamaterial levels is shown. However, Figures 4A to 4E The optical devices can be configured with any number of metamaterial levels (e.g., one level, two levels, three levels, four levels, five levels, six levels, seven levels, eight levels, nine levels, etc.). Figures 4A to 4E The diagram shown may be a cross-sectional view of an optical device.

[0126] Figure 4A An example of an optical device 401 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication. The optical device 401 can utilize a transparent metamaterial structure, a transparent substrate, and a reflector in a folded design to perform mode multiplexing or demultiplexing techniques. The optical device 401 can be a reference... Figure 2B An example of the optical device 202 described.

[0127] Optical device 401 may include a substrate 405 positioned close to or in contact with a plurality of metamaterial stages 410, a first reflector 415, and a second reflector 420. Each metamaterial stage 410 may include a plurality of metamaterial structures. The substrate 405, the plurality of stages 410, the first reflector 415, and the second reflector 420 may exhibit a folded design, wherein light bounces between the two reflectors 415 and 420 and interacts with the metamaterial stage 410 based on the light following the reflection path. Optical device 401 may include any number of metamaterial stages 410 to perform modal multiplexing or modal demultiplexing techniques. For example, the optical device may include a first stage 410-a, a second stage 410-b, a third stage 410-c, or any number of stages 410-N.

[0128] Substrate 405 may be a light-transmitting substrate configured to support metamaterial grade 410. Substrate 405 may have one or more parameters defining the structure, such as height or cross-sectional area. Substrate 405 may be a reference. Figure 2A and Figure 2B An example of the substrate 205 described.

[0129] Metamaterial stage 410 may include one or more light-transmitting metamaterial structures configured to shift the phase profile of an optical signal (e.g., light) passing through the metamaterial structure. Each stage 410 of the metamaterial may be positioned close to or in contact with the substrate 405. The metamaterial structure of stage 410 may be a reference. Figure 2A and Figure 2B Examples of described metamaterial structures 210. The metamaterial structure of metamaterial level 410 may have one or more parameters defining the metamaterial structure, such as cross-sectional profile, cross-sectional area, or height. In some examples, each level 410 of the metamaterial may be designed to have a different phase profile, and the combined phase profile of each level 410 may produce the overall phase profile of the optical device 401. In some examples, based on the desired phase profile of the optical device 401, one or more levels 410 of the metamaterial may have parameters different from those of other levels 410 of the metamaterial in the optical device 401. In some examples, each level 410 of the metamaterial in the optical device 401 may have the same parameters.

[0130] The first reflector 415 may be connected to the substrate 405. The first reflector 415 may be configured to reflect optical signals in the optical device 401 along the optical path and to subsequent stages 410 of the metamaterial, the second reflector 420, or any combination thereof. In some cases, the first reflector 415 may be formed of a reflective material (such as gold) with relatively high reflectivity. In some cases, the first reflector 415 may be coated with a reflective material (such as gold) with relatively high reflectivity.

[0131] The second reflector 420 may be positioned close to or adjacent to the metamaterial stage 410. The second reflector 420 may be configured to reflect optical signals in the optical device 401 along the optical path and to the subsequent metamaterial stage 410, the first reflector 415, or any combination thereof. In some cases, the second reflector 420 may be formed of a reflective material (such as gold) with relatively high reflectivity. In some cases, the second reflector 420 may be coated with a reflective material (such as gold) with relatively high reflectivity.

[0132] In some examples, the optical device 401 may include a cladding 425, which may be configured to protect the metamaterial structure of the metamaterial level 410 from damage, mitigate the loss of optical signals interacting with the metamaterial structure, or any combination thereof. In some cases, the cladding 425 may be positioned between the surface of the metamaterial structure and the second reflector 420 adjacent to the metamaterial level 410. In such cases, a distance may be formed between the surface of the metamaterial structure and the surface of the second reflector 420 (e.g., see reference 425). Figure 2BThe distance described is 230. The surface of the metamaterial structure near the second reflector 420 can be relative to a different surface of the metamaterial structure in contact with the substrate 405.

[0133] The first reflector 415, the second reflector 420, and the metamaterial stage 410 can be configured to guide an optical signal along a desired optical path in the optical device 401. In some cases, one or more positions of the first reflector 415 and the second reflector 420 can be configured to redirect light in different directions. For example, the optical signal may strike the reflector at an angle approximately orthogonal to the plane of the reflector, and the reflector may be configured to guide the optical signal in different directions. In some examples, the metamaterial stage 410 can be configured to change the direction of the optical signal. In some cases, at least one stage 410 of the first reflector 415, the second reflector 420, or the metamaterial, or any combination thereof, can be configured to change the direction of travel of the optical signal.

[0134] Optical device 401 may include an input aperture 430 for receiving an input optical signal into optical device 401, or an output aperture 435 for outputting an output optical signal from optical device 401, or both. In an illustrative example, optical device 401, input aperture 430, and output aperture 435 are formed by a first reflector 415. One or more sidewalls 440 of the first reflector 415 may form the input aperture 430. Similarly, one or more sidewalls 445 of the first reflector 415 may form the output aperture 435. In some examples, the first reflector 415 may form one aperture (e.g., either input aperture 430 or output aperture 435), and a second reflector 420 may form another aperture (e.g., either input aperture 430 or output aperture 435).

[0135] Optical device 401 can be configured as a mode multiplexer. In some cases, optical device 401 can be configured as a mode demultiplexer. In this case, the input and output of optical device 401 can be reversed. Input fiber 450 can be positioned at a first distance from input aperture 430 and can be configured to transmit one or more optical signals to optical device 401. Input fiber 450 can be a reference... Figure 1A Examples of optical communication links 105 or one or more optical communication links 130 described herein. Output fiber 455 may be positioned at a second distance from the output aperture 435 of optical device 401 and may be configured to receive one or more optical signals output from optical device 401. Output fiber 455 may be a reference... Figure 1AAn example of the described optical communication link 105. In some cases, the input fiber 450, the output fiber 455, or any combination thereof may be an example of a fiber optic array having multiple fibers. In some cases, the magnitude of the first distance may be the same as the magnitude of the second distance. In some cases, the magnitude of the first distance may be different from the magnitude of the second distance. In some cases, an additional spacer, an additional OCA, or a combination thereof may be located between the input fiber 450 and the optical device 401. In some cases, an additional spacer, an additional OCA, or a combination thereof may be located between the output fiber 455 and the optical device 401. Such an additional spacer or additional OCA may be configured to reduce back reflection, protect metamaterials, or provide spacing between the fiber and the optical device, or any combination thereof.

[0136] In an example where optical device 401 is configured as a mode multiplexer, input fiber 450 may be an example of an fiber array, and two or more optical signals having different modes or multiple versions of the same mode may be transmitted to optical device 401. The two or more optical signals may be reflected through optical device 401 by first reflector 415 and second reflector 420, and may pass through different stages 410 (and other components) of the metamaterial of optical device 401. At each stage 410, the phase profiles of the two or more optical signals may be shifted or altered. Through different stages 410, optical device 401 can convert two or more optical signals into different optical signals traveling along different modes of an FMF or MMF. Output fiber 455 may be an example of a single output fiber, and may be configured to receive optical signals traveling along different guide modes. In some cases, input fiber 450 may include one or more SMFs, and one or more input signals may be single-mode input signals. In other examples, input fiber 450 may include one or more FMFs or MMFs, and at least one input signal may be a multimode signal. Additionally or alternatively, the output fiber 455 may include one or more SMFs, and one or more output signals may be single-mode output signals. In other examples, the output fiber 455 may include one or more FMFs or MMFs, and at least one input signal may be a multimode signal.

[0137] In an example where optical device 401 is configured as a mode demultiplexer, input fiber 450 may be a single fiber, and optical signals traveling in different modes can be transmitted into optical device 401 along this single fiber. The optical signals can be reflected through optical device 401 by first reflector 415 and second reflector 420, and can pass through different stages 410 (and other components) of the metamaterial of optical device 401. At each stage 410, the phase profile of the optical signal can be moved or altered. Through different stages 410, optical device 401 can convert the optical signal into two or more different optical signals with different modes (e.g., multiple optical signals traveling along the SMF). Output fiber 455 may be an example of a fiber array, and can be configured to receive two or more optical signals that have been demultiplexed from the original optical signal.

[0138] In some cases, optical device 401 can be used in SDM / MDM applications. Optical device 401 can coherently shape the modes of light from one mode to another. Light in the first stage of the metamaterial can propagate in many directions and may interfere with each other as it travels into or through the second stage of the metamaterial. Light in the second stage of the metamaterial can propagate in multiple directions, and these lights may interfere with each other as they travel into or through the third stage of the metamaterial.

[0139] Figure 4B An example of an optical device 402 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for fiber optic communication. The optical device 402 can utilize a transparent metamaterial structure, a transparent substrate, and a reflector in a folded design to perform mode multiplexing or demultiplexing techniques. The optical device 402 can be a reference... Figure 2B and Figure 4A Examples of optical devices 202 and 401 are described. Optical device 402 can be similarly represented as optical device 401, and similarly numbered and named elements can be similarly represented.

[0140] Optical device 402 may include reference Figure 4AThe described optical device 401 has several different features. For example, an input aperture 430 may be formed in a second reflector 420 via one or more sidewalls 440, and an output aperture 435 may continue to be formed in a first reflector 415 via one or more sidewalls 445. The input optical signal may pass through the first stage 410-a of the metamaterial before passing through the substrate 405. In this case, the input aperture 430 may be located in the second reflector 420, which is located near the metamaterial stage 410. Additionally, the input signal may be transmitted at approximately orthogonal angles relative to the plane of the input aperture 430 or the plane of the first stage 410-a of the metamaterial. The first stage 410-a of the metamaterial may be configured to change the direction of travel of the optical signal. The last stage 410-N of the metamaterial may also be configured to change the direction of travel of the optical signal. In some cases, the second reflector 420, the last stage 410-N of the metamaterial, or any combination thereof, may be configured to change the direction of travel of the optical signal. In some cases, the first stage 410-a of the metamaterial can be an example of a transmissive metamaterial stage, while the subsequent stage 410 of the metamaterial can be an example of a reflective metamaterial stage.

[0141] Figure 4C An example of an optical device 403 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for fiber optic communication. The optical device 403 can utilize a transparent metamaterial structure, a transparent substrate, and a reflector in a folded design to perform mode multiplexing or demultiplexing techniques. The optical device 403 can be a reference... Figure 2B and Figures 4A to 4B Examples of optical devices 202, 401 and 402 are described. Optical device 403 can be similarly represented as optical device 401, and similarly numbered and named elements can be similarly represented.

[0142] Optical device 403 may include reference Figure 4AThe optical device 401 described has several distinct features. An input aperture 430 may be formed in a second reflector 420 via one or more sidewalls 440, and an output aperture 435 may continue to be formed in a first reflector 415 via one or more sidewalls 445. The input optical signal may pass through the cladding 425 (without any metamaterial level) before passing through the substrate 405. In this case, the input aperture 430 may be located in the second reflector 420, which is located near the metamaterial level 410. The input signal may be configured to enter the optical device 403 at an angle that is not orthogonal to the plane defined by the input aperture 430, the plane defined by the reflectors 415 and 420, the plane defined by the cladding 425, the plane defined by the metamaterial level 410, or the plane defined by the substrate 405, or any combination thereof. The non-orthogonal angle may be configured to cause the optical signal to be reflected between the reflectors 415 and 420 along the optical path to the metamaterial successive level 410. The final stage 410-N of the metamaterial can also be configured to change the direction of travel of the optical signal. In some cases, the second reflector 420, the final stage 410-N of the metamaterial, or any combination thereof can be configured to change the direction of travel of the optical signal.

[0143] Figure 4D An example of an optical device 406 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for fiber optic communication. Optical device 406 may utilize a transparent metamaterial structure, a transparent substrate, and a reflector in a folded design to perform mode multiplexing or demultiplexing techniques. Optical device 406 may be a reference. Figure 2B and Figures 4A to 4C Examples of optical devices 202, 401, 402 and 403 are described. Optical device 406 can be similarly represented as optical device 401, and similarly numbered and named elements can be similarly represented.

[0144] Optical device 406 may include reference Figure 4AThe optical device 401 is described with some different features. For example, the metamaterial stage 410 may be positioned near the first reflector 415, rather than near the second reflector 420 (compared to the optical device 401). An input aperture 430 may be formed in the second reflector 420 by one or more sidewalls 440, and an output aperture 435 may continue to be formed in the first reflector 415 by one or more sidewalls 445. The input aperture 430 is located in the second reflector 420, which is located on one side of the substrate 405 opposite to the metamaterial stage 410. An input signal may be transmitted into the optical device 403 at an angle that is not orthogonal to the plane defined by the input aperture 430, the plane defined by the reflectors 415 and 420, the plane defined by the cladding 425, the plane defined by the metamaterial stage 410, or the plane defined by the substrate 405, or any combination thereof. The non-orthogonal angle may be configured to cause the optical signal to be reflected between the reflectors 415 and 420 along the optical path to the metamaterial stage 410. The output signal can be transmitted out of the output aperture 435 at an angle that is not orthogonal to the plane defined by the input aperture 430, the plane defined by the reflectors 415 and 420, the plane defined by the cladding 425, the plane defined by the metamaterial grade 410, or the plane defined by the substrate 405, or any combination thereof.

[0145] Figure 4E An example of an optical device 407 supporting a mode multiplexer or demultiplexer according to the examples disclosed herein is shown, which uses metamaterials for optical fiber communication. The optical device 407 can utilize a transparent metamaterial structure, a transparent substrate, and a reflector in a folded design to perform mode multiplexing or demultiplexing techniques. The optical device 407 can be a reference... Figure 2B and Figures 4A to 4D Examples of optical devices 202, 401, 402, 403 and 406 are described. Optical device 407 can be similarly represented as optical device 401, and similarly numbered and named elements can be similarly represented.

[0146] Optical device 407 may include reference Figure 4AThe optical device 401 is described with some different features. The optical device 407 may include a metamaterial stage 410 located near both the first reflector 415 and the second reflector 420. For example, a first metamaterial stage 410-a may be positioned adjacent to the first reflector 415, and a second metamaterial stage 410-b may be positioned adjacent to the second reflector 420. The optical device 407 also includes a second cladding layer 425-a to protect the metamaterial stage 410 located near the first reflector 415. In the optical device 407, the metamaterial stage 410 may be located at each reflection point in the optical path. In some examples, at least one reflection point in the optical device 407 may not be associated with a metamaterial stage. In such examples, an optical signal may be reflected at least once by one of the reflectors 415 or 420 without passing through the metamaterial stage 410.

[0147] An input aperture 430 can be formed in a second reflector 420 via one or more sidewalls 440, and an output aperture 435 can be formed in a first reflector 415 via one or more sidewalls 445. The input optical signal can pass through the cladding 425 (without any metamaterial stage) before passing through the substrate 405. In this case, the input aperture 430 can be located in the second reflector 420, which is located near the metamaterial stage 410. In some examples, the metamaterial stage 410 can be positioned in the cladding 425 directly below the input aperture 430. Additionally or alternatively, in some examples, the metamaterial stage can be positioned in the cladding 425-a directly above the output aperture 435. The first stage 410-a and the last stage 410-N of the metamaterial can also be configured to change the direction of travel of the optical signal. In some cases, the first reflector 415, the first stage 410-a of the metamaterial, or any combination thereof can be configured to change the direction of travel of the optical signal. In some cases, the second reflector 420, the final stage 410-N of the metamaterial, or any combination thereof can be configured to change the direction of travel of the optical signal.

[0148] In some examples, optical devices 401, 402, 403, 406, or 407 can be configured as examples of resonant folding designs. In such designs, the overall structure of the optical devices is similar to that of a folding design. The difference between a folding design and a resonant folding design can include the design of the phase profile of the metamaterial level. For example, in both stacked and folded designs, there may be a fixed number of times light interacts with the metamaterial level. However, in a resonant folding design, light may interact with the metamaterial level a relatively large number of times (e.g., on the order of hundreds or thousands), or substantially indefinitely or infinitely many times. In a resonant folding design, the top and bottom surfaces of substrate 405 can form a Fabry-Perot cavity, in which one or more metamaterial levels 410 with specific phase profiles are located near these surfaces. In such examples, a single metamaterial level 410 can interact with light more strongly than in a design where a single metamaterial level interacts with light only once.

[0149] To find a suitable phase profile for the resonant structure, iterative solvers (such as conjugate gradient (CG), conjugate gradient squared (CGS), generalized minimum residual iteration (GMRES), relaxed GMRES (LGMRES), etc.) can be used to solve for the electric field within the metamaterial under fixed conditions. A similar adjoint analysis can be performed to calculate the derivative of the quality factor with respect to the phase profile, and nonlinear enhancements can be used to converge the design.

[0150] Figures 5A to 5F An example of a method for manufacturing an optical device according to the examples disclosed herein is shown, which supports mode multiplexers or demultiplexers for optical fiber communication using metamaterials. Figures 5A-5F Each of these figures shows a perspective view of a cross-section of a larger optical device. The cross-sections in each figure have been limited to show how various aspects of the optical device are formed, but additional structures and functions supporting mode multiplexers or demultiplexers using metamaterials for fiber optic communication are considered. The operations described herein can be used to form references. Figures 2A to 4E Any of the optical devices described. The method can be a top-down approach to forming the optical device.

[0151] Figure 5A An example of a first operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communications using metamaterials. This first operation may not be the first step in the manufacturing process of the optical device, but rather... Figures 5A to 5F The first operation described in the text. Figure 5AAn optical device 501 is shown, which includes a substrate 510 and a metamaterial layer 515. The optical device 501 is a device that appears after the completion of the first operation in the manufacturing process.

[0152] The first operation may include (e.g., forming substrate 510 via one or more deposition steps and / or one or more etching steps). Substrate 510 may be a reference. Figures 2A to 4E Examples of substrates 205, 305, and 405 are described. In some cases, substrate 510 may be formed of glass or fused silica. In some examples, substrate 510 may be grown rather than deposited. The terms deposition and growth may be used interchangeably herein.

[0153] Additionally, as part of the first operation, a metamaterial layer 515 may be deposited on the substrate 510. In some cases, the metamaterial layer 515 may be an example of a metamaterial used to form a metamaterial structure in a completed optical device. The metamaterial layer 515 may be a reference. Figures 2A to 4E Describe metamaterial structures or examples at the metamaterial level.

[0154] Figure 5B An example of a second operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials. The second operation is described in reference... Figure 5A The first operation described occurs after the first operation. In some cases, other steps or operations may occur between the first and second operations. Figure 5B An optical device 502 is shown, which includes a substrate 510, a metamaterial layer 515, and a photoresist layer 520. The optical device 502 is a device that appears after the completion of a second operation in the manufacturing process.

[0155] In the second operation, a resist layer 520 is deposited or coated onto the metamaterial layer 515. In some cases, the resist layer 520 may be an example of a hard mask material or a sacrificial layer or any combination thereof.

[0156] Figure 5C An example of a third operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for optical fiber communication using metamaterials, is shown. The third operation is described in reference... Figure 5B The second operation described occurs after the third operation. In some cases, other steps or operations may occur between the second and third operations. Figure 5C An optical device 503 is shown, comprising a substrate 510, a metamaterial layer 515, and a plurality of hard masks 525 formed of a resist layer 520. The optical device 503 is a device that appears after the completion of the third operation in the manufacturing process.

[0157] In the third operation, a portion of the resist layer 520 is removed to form a plurality of hard masks 525. Each of the plurality of hard masks 525 includes one or more parameters (e.g., cross-sectional profile, cross-sectional area, or height) configured to control the metamaterial structure produced by the plurality of hard masks 525. The plurality of hard masks 525 can be formed using one or more etching processes, electron beam lithography, photolithography, nanoimprint lithography, or any combination thereof.

[0158] Figure 5D An example of a fourth operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials, is shown. The fourth operation is described in reference... Figure 5C The third operation described occurs after the fourth operation. In some cases, other steps or operations may occur between the third and fourth operations. Figure 5D An optical device 504 is shown, comprising a substrate 510 and a plurality of metamaterial structures 530 formed by a metamaterial layer 515 and based on parameters of a plurality of hard masks 525. The optical device 504 is a device that appears after the completion of the fourth operation in the manufacturing process.

[0159] In the fourth operation, portions of the metamaterial layer 515 and the plurality of hard masks 525 are removed to form a plurality of metamaterial structures 530. In some cases, a pattern of the resist layer may be etched. Each of the plurality of metamaterial structures 530 includes one or more parameters (e.g., cross-sectional profile, cross-sectional area, or height) configured based on the parameters of the hard mask initially positioned above the metamaterial structure. The plurality of metamaterial structures 530 may be formed using one or more etching processes, electron beam lithography, photolithography, nanoimprint lithography, or any combination thereof. In some cases, a single process listed above may be used as part of the fourth operation. In some cases, two or more processes listed above may be used as part of the fourth operation.

[0160] Figure 5E An example of a fifth operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials. The fifth operation is described in reference... Figure 5D The fourth operation described occurs after the fifth operation. In some cases, other steps or operations may occur between the fourth and fifth operations. Figure 5E An optical device 505 is shown, which includes a substrate 510, multiple metamaterial structures 530, and a cladding 535. The optical device 505 is a device that appears after the completion of the fifth operation in the manufacturing process.

[0161] In the fifth operation, a cladding layer 535 is deposited on the substrate 510 and multiple metamaterial structures 530. The cladding layer 535 can be a reference. Figure 2A and Figures 4A to 4E Examples of cladding 215 or cladding 425 are described. Cladding 535 may be configured to protect metamaterial structure 530 from damage, mitigate loss of optical signals interacting with the metamaterial structure, or any combination thereof.

[0162] Figure 5F An example of a sixth operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials, is shown. The sixth operation is described in reference... Figure 5D The fifth operation described occurs after the sixth operation. In some cases, other steps or operations may occur between the fifth and sixth operations. Figure 5F An optical device 506 is shown, which includes a substrate 510, multiple metamaterial structures 530, a cladding 535, and a reflector 540. The optical device 506 is a device that appears after the completion of the sixth operation in the manufacturing process.

[0163] In the sixth operation, material is deposited to form reflector 540. In some cases, the material is a reflective material (e.g., a metal such as gold). In some cases, the material is coated with a reflective material (e.g., a metal such as gold) to form reflector 540. Reflector 540 may be formed to be positioned close to or in contact with cladding 535. In some cases, cladding 535 is located between metamaterial structure 530 and reflector 540. Reflector 540 may be a reference. Figure 2B and Figures 4A to 4E Examples of reflectors 220, 415, and 420 are described. In some cases, optical device 506 may represent a reference. Figures 2A to 4E A portion of the complete memory device described.

[0164] In top-down methods for manufacturing optical devices, processes such as chip bonding and / or thin-film deposition (e.g., plasma-enhanced chemical vapor deposition (PECVD), low-pressure chemical vapor deposition (LPCVD), atomic layer deposition (ALD), thermal evaporation, electron beam evaporation, sputtering, etc.) are employed. Figure 5A As described herein, material for the metamaterial structure is placed on substrate 510. Techniques for patterning structures (e.g., Figure 5B and Figure 5CPatterning can be achieved through lithographic methods such as electron beam lithography, photolithography, nanoimprint lithography, or any combination thereof. Other techniques, such as self-assembly, can also be used for patterning devices. Depending on the technology and materials chosen for the device, different resists and etching techniques can be employed to transfer the pattern to the metamaterial layer, such as... Figure 5D As shown (e.g., the technique could be a dry etching technique, such as reactive ion etching, inductively coupled plasma etching, or ion milling, or any combination thereof). In some cases, another layer of material can be added on top of the thin film layer (e.g., metamaterial layer 515) to serve as a hard mask in the etching process, instead of using a resist as an etching mask. Depending on the design, a cladding layer can be added to protect or support the structure, using coating techniques (such as spin coating) or deposition techniques (e.g., as described herein) Figure 5E (as shown) to add a cladding layer. The deposition techniques described herein (e.g., [example]) can be used. Figure 5F As shown, a reflector (e.g., metal) layer is added on top of the cladding.

[0165] Figures 6A to 6F An example of a method for manufacturing an optical device according to the examples disclosed herein is shown, which supports mode multiplexers or demultiplexers for optical fiber communication using metamaterials. Figures 6A to 6F Each of these figures shows a perspective view of a cross-section of a larger optical device. The cross-sections in each figure have been limited to show how various aspects of the optical device are formed, but additional structures and functions supporting mode multiplexers or demultiplexers using metamaterials for fiber optic communication are considered. The operations described herein can be used to form references. Figures 2A to 4E Any of the optical devices described. The method can be a bottom-up approach to forming the optical device.

[0166] Figure 6A An example of a first operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communications using metamaterials. This first operation may not be the first step in the manufacturing process of the optical device, but rather... Figures 6A to 6F The first operation described in the text. Figure 6A An optical device 601 is shown, which includes a substrate 610 and a resist layer 615. The optical device 601 is a device that appears after the completion of the first operation in the manufacturing process.

[0167] The first operation may include (e.g., forming substrate 610 via one or more deposition steps and / or one or more etching steps). Substrate 610 may be a reference. Figures 2A to 4EExamples of substrates 205, 305, and 405 are described. In some examples, substrate 610 may be grown instead of deposited (e.g., using the Czeklaussky process). The terms deposition and growth may be used interchangeably herein.

[0168] Additionally, as part of the first operation, a resist layer 615 may be deposited or coated on the substrate 610. In some cases, the resist layer 615 may be an example of a hard mask material or a sacrificial layer or any combination thereof.

[0169] Figure 6B An example of a second operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for optical fiber communication using metamaterials. The second operation is described in reference... Figure 6A The first operation described occurs after the first operation. In some cases, other steps or operations may occur between the first and second operations. Figure 6B An optical device 602 is shown, which includes a substrate 610, a resist layer 615, and a plurality of cavities 620 formed in the resist layer 615. The optical device 602 is a device that appears after a second operation in the manufacturing process is completed.

[0170] In the second operation, a portion of the resist layer 615 is removed to form a plurality of cavities 620. In some cases, the pattern of the resist layer 615 may be etched. Each of the plurality of cavities 620 may include one or more parameters (e.g., cross-sectional profile, cross-sectional area, or height) configured to control the metamaterial structure produced by the plurality of cavities 620. The plurality of cavities 620 may be formed using one or more etching processes, electron beam lithography, photolithography, nanoimprint lithography, or any combination thereof.

[0171] Figure 6C An example of a third operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials, is shown. The third operation is described in reference... Figure 6B The second operation described occurs after the third operation. In some cases, other steps or operations may occur between the second and third operations. Figure 6C An optical device 603 is shown, which includes a substrate 610, a resist layer 615, and a metamaterial layer 625. The optical device 603 is a device that appears after the completion of the third operation in the manufacturing process.

[0172] In the third operation, a metamaterial layer 625 can be deposited on the resist layer 615 and in the plurality of cavities 620 formed in the resist layer 615. In some cases, the metamaterial layer 625 may be an example of a metamaterial used to form a metamaterial structure in a completed optical device. The metamaterial layer 625 may be a reference. Figures 2A to 4E Examples of metamaterial structures or metamaterial-level structures are described. In some cases, the metamaterial layer 625 may also include multiple cavities after deposition. In such cases, the thickness of the deposited film can be uniform across the entire device. In such cases, the material filling the multiple cavities 620 of the metamaterial layer 625 may leave similar cavities in the metamaterial layer 625 above it.

[0173] Figure 6D An example of a fourth operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials, is shown. The fourth operation is described in reference... Figure 6C The third operation described occurs after the fourth operation. In some cases, other steps or operations may occur between the third and fourth operations. Figure 6D An optical device 604 is shown, comprising a substrate 610 and a plurality of metamaterial structures 630 formed from a metamaterial layer 625 and based on parameters of a plurality of cavities 620. The optical device 604 is a device that appears after the completion of the fourth operation in the manufacturing process.

[0174] In the fourth operation, a portion of the metamaterial layer 625 and the remainder of the resist layer 615 are removed to form (or expose) a plurality of metamaterial structures 630. Each of the plurality of metamaterial structures 630 includes one or more parameters (e.g., cross-sectional profile, cross-sectional area, or height) configured based on parameters into which the metamaterial layer 625 is deposited. In some cases, one or more chemicals may be applied to the optical device 604 to remove the remaining resist layer and the metamaterial on top of the remaining resist layer. In some cases, this process may be referred to as lift-off. The plurality of metamaterial structures 630 may be formed using one or more etching processes, electron beam lithography, photolithography, nanoimprinting, or lift-off processes, or any combination thereof. In some cases, one of the processes listed above may be used as part of the fourth operation. In some cases, two or more of the processes listed above may be used as part of the fourth operation.

[0175] Figure 6E An example of a fifth operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials. The fifth operation is described in reference... Figure 6DThe fourth operation described occurs after this operation. In some cases, other steps or operations may occur between the fourth and fifth operations. Figure 6E An optical device 605 is shown, which includes a substrate 610, multiple metamaterial structures 630, and a cladding 635. The optical device 605 is a device that appears after the completion of the fifth operation in the manufacturing process.

[0176] In the fifth operation, a cladding layer 635 is deposited on the substrate 610 and multiple metamaterial structures 630. The cladding layer 635 can be a reference. Figure 2A and Figures 4A to 4E Examples of cladding 215 or cladding 425 are described. Cladding 635 may be configured to protect metamaterial structure 630 from damage, mitigate loss of optical signals interacting with the metamaterial structure, or any combination thereof.

[0177] Figure 6F An example of a sixth operation of a method for manufacturing an optical device according to the examples disclosed herein, the optical device supporting mode multiplexers or demultiplexers for fiber optic communication using metamaterials, is shown. The sixth operation is described in reference... Figure 6E The fifth operation described occurs after the sixth operation. In some cases, other steps or operations may occur between the fifth and sixth operations. Figure 6F An optical device 606 is shown, which includes a substrate 610, multiple metamaterial structures 630, a cladding 635, and a reflector 640. The optical device 606 is a device that appears after the completion of the sixth operation in the manufacturing process.

[0178] In the sixth operation, material is deposited to form reflector 640. In some cases, this material is a reflective material (e.g., a metal such as gold). In some cases, the material is coated with a reflective material (e.g., a metal such as gold) to form reflector 640. Reflector 640 may be formed to be positioned close to or in contact with cladding 635. In some cases, cladding 635 is located between metamaterial structure 630 and reflector 640. Reflector 640 may be a reference. Figure 2B and Figures 4A to 4E Examples of reflectors 220, 415, and 420 are described. In some cases, optical device 606 may represent a reference. Figures 2A to 4E A portion of the complete memory device described.

[0179] In a bottom-up approach, lithography techniques similar to those used in a top-down approach can be used to first create a reverse pattern of the desired structure (e.g., see...). Figure 6A and 6B A thin film layer can then be grown on top of the patterned resist layer 615 to fill the holes (e.g., see...). Figure 6CAfter the stripping process (e.g., see...) Figure 6D This allows the removal of the resist layer 615 and the thin film on top of the resist, and the transfer of the pattern onto the thin film layer to form a metamaterial structure. Depending on the design, coating techniques described herein (such as spin coating) or deposition techniques (e.g., as described herein) can be used. Figure 6E (As shown) to add a cladding layer to protect or support the structure. The deposition techniques described herein (e.g., as shown) can be used. Figure 6F As shown, a reflector (e.g., metal) layer is added on top of the cladding.

[0180] Figure 7 A flowchart is shown illustrating method 700 for supporting the use of metamaterials for optical fiber communication in accordance with the examples disclosed herein. Operation of method 700 may be implemented by a manufacturing system or one or more controllers associated with the manufacturing system. In some examples, the one or more controllers may execute a set of instructions to control one or more functional elements of the manufacturing system to perform the described functions. Additionally or alternatively, the one or more controllers may use dedicated hardware to perform aspects of the described functions.

[0181] At 705, method 700 may include growing a light-transmitting substrate. The operation at 705 may be performed according to the method described herein.

[0182] At 710, method 700 may include depositing a metamaterial layer on a substrate. The operation at 710 may be performed according to the method described herein.

[0183] At 715, method 700 may include depositing a resist layer on the metamaterial layer. The operation at 715 may be performed according to the method described herein.

[0184] At 720, method 700 may include etching a pattern of the resist layer to form a hard mask set. In some cases, a portion of the resist layer may be etched. The operation at 720 may be performed according to the methods described herein.

[0185] At 725, method 700 may include etching an exposed portion of a hard mask set and a metamaterial layer based on an etched resist layer to form a metamaterial structure set, wherein multiple metamaterial structures are configured to shift a first phase profile of a first optical signal having a first mode with a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode. In some cases, the metamaterial structure set can be formed by simultaneously etching the metamaterial layer while using the resist as one or more hard masks during the etching process. The operation at 725 may be performed according to the method described herein.

[0186] In some examples, the apparatus described herein can perform one or more methods, such as method 700. The apparatus may include features, components, or instructions (e.g., a non-transitory computer-readable medium storing instructions executable by a processor) for growing a light-transmitting substrate, depositing a metamaterial layer on the substrate, depositing a resist layer on the metamaterial layer, etching a portion of the resist layer to form a hard mask set, and etching the hard mask set and exposed portions of the metamaterial layer based on the etching of the resist layer to form a metamaterial structure set. The metamaterial structure set may be configured to shift a first phase profile of a first optical signal having a first mode with a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0187] Some examples of the methods 700 and apparatus described herein may further include operations, features, components, or instructions for depositing reflective material based on etched hard mask sets and exposed portions of metamaterial layers to form a reflector at one end of the metamaterial structure set. Some examples of the methods 700 and apparatus described herein may further include operations, features, components, or instructions for depositing a cladding layer on the metamaterial structure set and on exposed portions of the substrate, based on etched hard mask sets and exposed portions of the metamaterial layer, wherein the deposition of the reflective material may be based on the deposition of the cladding layer. In some examples of the methods 700 and apparatus described herein, the reflective material may be deposited on a cladding layer that may be located between the metamaterial structure set and the reflective material.

[0188] In some examples of the method 700 and apparatus described herein, each metamaterial structure in the set of metamaterial structures may have one or more parameters, including the height of the metamaterial structure, the cross-sectional profile of the metamaterial structure, the diameter of the metamaterial structure, the dielectric properties of the metamaterial structure, or a combination of the above. In some examples of the method 700 and apparatus described herein, at least some of the one or more parameters of each metamaterial structure may be based on a second cross-sectional profile of an associated hard mask.

[0189] Figure 8 A flowchart is shown illustrating method 800 for supporting the use of metamaterials for optical fiber communication in accordance with the examples disclosed herein. Operation of method 800 may be implemented by a manufacturing system or one or more controllers associated with the manufacturing system. In some examples, the one or more controllers may execute a set of instructions to control one or more functional elements of the manufacturing system to perform the described functions. Additionally or alternatively, the one or more controllers may use dedicated hardware to perform aspects of the described functions.

[0190] At 805, method 800 may include depositing a light-transmitting substrate. The operation at 805 may be performed according to the method described herein.

[0191] At 810, method 800 may include depositing a resist layer on the substrate. Operation at 810 may be performed according to the method described herein.

[0192] At 815, method 800 may include etching a pattern of the resist layer to form a cavity assembly in the resist layer. In some cases, a portion of the resist layer may be etched. The operation at 815 may be performed according to the method described herein.

[0193] At 820, method 800 may include depositing a metamaterial layer on the resist layer forming the cavity set, the metamaterial layer filling at least some of the cavities in the cavity set formed in the resist layer. Operation at 820 may be performed according to the method described herein.

[0194] At 825, method 800 may include removing the metamaterial layer and the resist layer based on depositing a metamaterial layer on the resist layer to form a set of metamaterial structures, wherein multiple metamaterial structures are configured to shift a first phase profile having a first optical signal of a first mode and a second phase profile having a second optical signal of a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode. In some cases, one or more chemicals may be applied to the structure to remove the remaining resist layer and the metamaterial on top of the remaining resist layer. In some cases, this process may be referred to as stripping. The operation at 825 may be performed according to the methods described herein.

[0195] In some examples, the apparatus described herein can perform one or more methods, such as method 800. The apparatus may include features, components, or instructions (e.g., a non-transitory computer-readable medium storing instructions executable by a processor) for depositing a light-transmitting substrate, depositing a resist layer on the substrate, etching a portion of the resist layer to form a cavity set in the resist layer, depositing a metamaterial layer on the resist layer forming the cavity set (the metamaterial layer filling at least some of the cavities formed in the resist layer), and etching the metamaterial layer and the resist layer to form a metamaterial structure set based on the deposition of the metamaterial layer on the resist layer. The metamaterial structure set may be configured to shift a first phase profile of a first optical signal having a first mode with a second phase profile of a second optical signal having a second mode to generate a third optical signal having a third mode and a fourth optical signal having a fourth mode.

[0196] Some examples of the methods 800 and apparatus described herein may further include operations, features, components, or instructions for depositing reflective material based on etching a metamaterial layer and a resist layer to form a reflector at one end of a metamaterial structure assembly. Some examples of the methods 800 and apparatus described herein may further include operations, features, components, or instructions for depositing a cladding layer on the metamaterial structure assembly and on exposed portions of a substrate based on etching a metamaterial layer and a resist layer, wherein the deposition of the reflective material may be based on the deposition of the cladding layer. In some examples of the methods 800 and apparatus described herein, the reflective material may be deposited on a cladding layer that may be located between the metamaterial structure assembly and the reflective material.

[0197] In some examples of the methods 800 and devices described herein, each metamaterial structure in the set of metamaterial structures may have one or more parameters of the metamaterial structure, including the height of the metamaterial structure, the cross-sectional profile of the metamaterial structure, the diameter of the metamaterial structure, the dielectric properties of the metamaterial structure, or a combination of the above. In some examples of the methods 800 and devices described herein, at least some of the one or more parameters of each metamaterial structure may be based on a second cross-sectional profile of an associated cavity in the resist layer.

[0198] It should be noted that the above methods describe possible implementations, and the operations and steps can be rearranged or otherwise modified, and other implementations are possible. Furthermore, parts from two or more methods can be combined.

[0199] The information and signals described herein can be represented using any of a variety of different techniques and methods. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referred to throughout the above description can be represented by voltage, current, electromagnetic waves, magnetic fields or magnetic particles, optical fields or optical particles, or any combination of the above. Some figures may show signals as single signals; however, those skilled in the art will understand that signals can represent signal buses, where buses can have various bit widths.

[0200] The terms "electronic communication," "conductive contact," "connection," and "coupling" can refer to the relationship between components that support signal flow between them. Components are considered to be in electronic communication (or electrically connected, connected, or coupled) with each other if there is any conductive path between them that can readily support signal flow between them. At any given time, the conductive path between components that are in electronic communication (or electrically connected, connected, or coupled) can be open or closed, depending on the operation of the device including the connecting components. The conductive path between connected components can be a direct conductive path between the components, or it can be an indirect conductive path that may include intermediate components (such as switches, transistors, or other components). In some examples, for instance, using one or more intermediate components such as switches or transistors, the signal flow between connected components can be interrupted for a period of time.

[0201] The devices discussed herein (including optical devices) can be formed on semiconductor substrates such as silicon, germanium, silicon-germanium alloys, gallium arsenide, gallium nitride, etc. In some examples, the substrate is a semiconductor wafer. In other examples, the substrate can be a silicon-on-insulator (SOI) substrate (such as silicon-on-glass (SOG) or silicon-on-sapphire (SOP)), or an epitaxial layer of semiconductor material on another substrate. The conductivity of the substrate or a subregion of the substrate can be controlled by doping using various chemicals (including but not limited to phosphorus, boron, or arsenic). Doping can be performed during the initial formation or growth of the substrate by ion implantation or by any other doping method.

[0202] This document describes exemplary configurations in conjunction with the accompanying drawings and does not represent all examples that can be implemented or that are within the scope of the claims. The term "exemplary" as used herein means "serving as an example, instance, or illustration," and not "preferred" or "superior to other examples." This detailed description includes specific details to provide an understanding of the described techniques. However, these techniques can be practiced without these specific details. In some instances, well-known structures and apparatuses are shown in block diagram form to avoid obscuring the concepts of the described examples.

[0203] In the accompanying drawings, similar parts or features may have the same reference numerals. Furthermore, various parts of the same type may be distinguished by a dashed line following the reference numeral and a second reference numeral used to differentiate between similar parts. If only the first reference numeral is used in the description, the description may apply to any of the similar parts having the same first reference numeral, regardless of the second reference numeral.

[0204] The various illustrative blocks and modules described in connection with the disclosure herein may be implemented or executed using a general-purpose processor, digital signal processor (DSP), application-specific integrated circuit (ASIC), field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof, designed to perform the functions described herein. The general-purpose processor may be a microprocessor, but alternatively, it may be any processor, controller, microcontroller, or state machine. The processor may also be implemented as a combination of computing devices (e.g., a digital signal processor (DSP) and a microprocessor, multiple microprocessors, one or more microprocessors combined with a DSP core, or any other combination of such configurations).

[0205] The functions described herein can be implemented in hardware, software executed by a processor, firmware, or any combination thereof. If implemented in software executed by a processor, the functions can be stored on or transmitted via a computer-readable medium as one or more instructions or code. Other examples and implementations are within the scope of this disclosure and the appended claims. For example, due to the nature of software, the functions described above can be implemented using software executed by a processor, hardware, firmware, hardwiring, or any combination thereof. Features implementing the functions can also be physically located in various locations, including distributed such that different parts of the functions are implemented at different physical locations. Additionally, as used herein (including in the claims), the word “or” used in an item enumeration (e.g., an item enumeration beginning with phrases such as “at least one of…” or “one or more of…”) indicates an inclusive enumeration, such that an enumeration of at least one of, for example, A, B, or C means A or B or C or AB or AC or BC or ABC (i.e., A and B and C). Moreover, as used herein, the phrase “based on” should not be construed as a reference to a closed set of conditions. For example, an exemplary step described as “based on condition A” can be based on both condition A and condition B without departing from the scope of this disclosure. In other words, as used in this article, the phrase “based on” should be interpreted in the same way as the phrase “at least partially based on”.

[0206] Computer-readable media includes both non-transitory computer storage media and communication media, with communication media encompassing any medium that facilitates the transfer of a computer program from one place to another. Non-transitory storage media can be any available medium accessible by a general-purpose or special-purpose computer. By way of example, and not limitation, non-transitory computer-readable media may include random access memory (RAM), read-only memory (ROM), electronically erasable programmable read-only memory (EEPROM), compact disc (CD) ROM or other optical disc storage, magnetic disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to carry or store desired program code components in the form of instructions or data structures accessible by a general-purpose or special-purpose computer or a general-purpose or special-purpose processor. Furthermore, any connection is appropriately referred to as computer-readable media. For example, if software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technology (such as infrared, radio, and microwave), then coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technology (such as infrared, radio, and microwave) is included in the definition of media. The disks and optical discs used in this article include CDs, laser discs, optical discs, digital multifunction discs (DVDs), floppy disks, and Blu-ray discs, where disks typically reproduce data magnetically, while optical discs reproduce data optically using lasers. Combinations of the foregoing are also included within the scope of computer-readable media.

[0207] The description herein is provided to enable those skilled in the art to make or use the present disclosure. Various modifications to the present disclosure will be apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the scope of the present disclosure. Therefore, the present disclosure is not limited to the examples and designs described herein, but should be given the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. An apparatus comprising: a first substrate that is optically transparent; a first metamaterial stage in contact with the first substrate; a second metamaterial stage in contact with the first substrate, the first metamaterial stage and the second metamaterial stage configured to: receive a first optical signal having a first modal through a first optical communication link; receive a second optical signal having a second modal through a second optical communication link; generate a third optical signal having a third modal by shifting a first phase profile of the first optical signal; generate a fourth optical signal having a fourth modal by shifting a second phase profile of the second optical signal; and transmit the third optical signal and the fourth optical signal through a third optical communication link, the third optical communication link comprising a multimodal optical communication link.

2. The apparatus of claim 1, wherein: the first metamaterial stage is configured to shift the first phase profile of the first optical signal and the second phase profile of the second optical signal, and output a first shifted optical signal and a second shifted optical signal; and the second metamaterial stage is configured to shift a third phase profile of the first shifted optical signal and a fourth phase profile of the second shifted optical signal, and output the third optical signal and the fourth optical signal.

3. The apparatus of claim 1, further comprising: a second substrate that is optically transparent, the second substrate in contact with the second metamaterial stage, wherein the first substrate, the first metamaterial stage, the second substrate, and the second metamaterial stage form a stacked structure.

4. The apparatus of claim 3, further comprising: a spacer in contact with the first substrate and the second substrate, and creating a space between a first surface of the first substrate and a second surface of the second substrate, wherein the second metamaterial stage is positioned in the space created by the spacer.

5. The apparatus of claim 4, further comprising: a liquid optically transparent adhesive positioned in the space created by the spacer, wherein the second metamaterial stage is in contact with the second surface of the second substrate, and the liquid optically transparent adhesive is positioned between the second metamaterial stage and the first surface of the first substrate.

6. The apparatus of claim 1, 2, or 3, further comprising: a first reflector and a second reflector configured to reflect the first optical signal and the second optical signal, the first substrate positioned between the first reflector and the second reflector.

7. The apparatus of claim 6, further comprising: a cladding positioned between the first metamaterial stage and the first reflector, a thickness of the cladding configured to mitigate loss of optical signals interacting with the first metamaterial stage, or to protect the first metamaterial stage, or a combination thereof.

8. The apparatus of claim 6, wherein: ​ The first metamaterial stage is positioned proximate to the first reflector; or The first metamaterial stage is positioned proximate to the first reflector and the second metamaterial stage is positioned proximate to the second reflector.

9. The apparatus of claim 6, wherein: The first reflector forms a first aperture for receiving the first optical signal and the second optical signal and the second reflector forms a second aperture for outputting the third optical signal; or The first reflector forms the first aperture for receiving the first optical signal and the second optical signal and the second aperture for outputting the third optical signal.

10. The apparatus of claim 6, wherein the first substrate, the first reflector, the second reflector, the first metamaterial stage, and the second metamaterial stage form a Fabry-Perot cavity configured to generate one or more resonant reflections of the first optical signal and the second optical signal.

11. The apparatus of any one of claims 1-5, wherein the first metamaterial stage comprises: a plurality of metamaterial structures arranged in a pattern to shift a phase profile of an optical signal based at least in part on one or more parameters of each metamaterial structure of the plurality of metamaterial structures.

12. The apparatus of claim 11, wherein the one or more parameters of the metamaterial structure comprise a height of the metamaterial structure, a cross-sectional profile of the metamaterial structure, a diameter of the metamaterial structure, a dielectric property of the metamaterial structure, or a combination thereof.

13. The apparatus of claim 11, wherein a total phase shift induced by the first metamaterial stage is based at least in part on a phase shift profile of each metamaterial structure and the pattern of the plurality of metamaterial structures.

14. The apparatus of any one of claims 1-5, comprising a plurality of metamaterial stages, wherein there is no air space spacing between the plurality of metamaterial stages.

15. The apparatus of claim 14, further comprising an optically clear adhesive (OCA) positioned between at least one layer of a substrate and at least one metamaterial stage.

16. The apparatus of any one of claims 1-5, comprising a plurality of substrates and at least one set of first metamaterial stages is in contact with each of the substrates.

17. A method comprising the steps of: depositing a light-transmissive substrate; depositing a resist layer on the substrate; etching a portion of the resist layer to form a plurality of cavities in the resist layer; and depositing a metamaterial layer on the resist layer forming the plurality of cavities, the metamaterial layer filling at least some of the plurality of cavities formed in the resist layer; ​ etching the metamaterial layer and the resist layer to form a plurality of metamaterial structures based at least in part on depositing the metamaterial layer on the resist layer, wherein the plurality of metamaterial structures are configured to shift a first phase profile of a first optical signal having a first modal with a second phase profile of a second optical signal having a second modal to generate a third optical signal having a third modal and a fourth optical signal having a fourth modal.

18. The method of claim 17, further comprising the steps of: depositing a reflective material based at least in part on etching the metamaterial layer and the resist layer to form a reflector at one end of the plurality of metamaterial structures.

19. The method of claim 18, further comprising the steps of: depositing a cladding on the plurality of metamaterial structures and on an exposed portion of the substrate based at least in part on etching the metamaterial layer and the resist layer, wherein depositing the reflective material is based at least in part on depositing the cladding.

20. The method of claim 19, wherein the reflective material is deposited on the cladding between the plurality of metamaterial structures and the reflective material.

21. The method of any one of claims 17 to 20, wherein each metamaterial structure of the plurality of metamaterial structures has one or more parameters including a height of the metamaterial structure, a cross-sectional profile of the metamaterial structure, a diameter of the metamaterial structure, a dielectric property of the metamaterial structure, or a combination thereof.

22. The method of claim 21, wherein at least some of the one or more parameters of each metamaterial structure are based at least in part on a second cross-sectional profile of an associated cavity in the resist layer.

23. An apparatus comprising: a substrate that is optically transmissive; and a metamaterial stage in contact with the substrate and configured to: receive a first optical signal having a first modal and a second optical signal having a second modal through a first optical communication link, the first optical communication link comprising a multimode optical communication link; generate a third optical signal having a third modal from the first optical signal based at least in part on shifting a first phase profile of the first optical signal through the metamaterial stage; and generate a fourth optical signal having a fourth modal from the second optical signal based at least in part on shifting a second phase profile of the second optical signal through the metamaterial stage; transmit the third optical signal having the third modal through a second optical communication link; and transmit the fourth optical signal having the fourth modal through a third optical communication link.

24. The apparatus of claim 23, further comprising: a first reflector and a second reflector configured to reflect the first optical signal and the second optical signal, the substrate positioned between the first reflector and the second reflector, wherein there is no air space spacing between the first reflector and the metamaterial stage and between the second reflector and the metamaterial stage.

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