Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction

Adjoint Algorithm Design of Selective Mode Reflecting Metastructure for BAL Applications

Broad-area lasers (BALs) have found applications in a variety of crucial fields on account of their high output power and high energy transfer efficiency. However, they suffer from poor spatial beam quality due to multi-mode behavior along the waveguide transverse direction. In this paper, we propose a novel metasurface waveguide structure acting as a transverse mode selective back-reflector for BALs. In order to effectively inverse design such a structure, a digital adjoint algorithm is introduced to adapt the considerably large design area and the high degree of freedom. As a proof of the concept, a device structure with a design area of 40 × 20 μm2 is investigated. The simulation results exhibit high fundamental mode reflection (above 90%), while higher-order transverse mode reflections are suppressed below 0.2%. This is, to our knowledge, the largest device structure designed based on the inverse method. We exploited such a device and the method and further investigated the device's robustness and feasibility of the inverse method. The results are elaborately discussed.

Multi-channel broadband nonvolatile programmable modal switch

Mode-division multiplexing (MDM) in chip-scale photonics is paramount to sustain data capacity growth and reduce power consumption. However, its scalability hinges on developing efficient and dynamic modal switches. Existing active modal switches suffer from substantial static power consumption, large footprints, and narrow bandwidth. Here, we present, for the first time, to the best of our knowledge, a novel multiport, broadband, non-volatile, and programmable modal switch designed for on-chip MDM systems. Our design leverages the unique properties of integrating nanoscale phase-change materials (PCM) within a silicon photonic architecture. This enables independent manipulation of spatial modes, allowing for dynamic, non-volatile, and selective routing to six distinct output ports. Crucially, our switch outperforms current dynamic modal switches by offering non-volatile, energy-efficient multiport functionality and excels in performance metrics. Our switch exhibits exceptional broadband operating bandwidth exceeding 70 nm, with low loss (< 1 dB), and a high extinction ratio (> 10 dB). Our framework provides a step forward in chip-scale MDM, paving the way for future green and scalable data centers and high-performance computers.

Inverse design of asymmetric Y-junctions for ultra-compact, broadband, and low crosstalk mode (de)multiplexers

Asymmetric Y-junctions, compared with mode coupling-based devices, possess considerably smaller wavelength dependence and thus are more promising for ultra-broadband mode (de)multiplexing in integrated optics. However, these devices also feature relatively high mode crosstalk and insertion loss. Here, we show that the mode crosstalk and loss of an asymmetric Y-junction can be significantly reduced by optimizing the waveguide shape of the Y-junction using an adjoint-based inverse design. Based on such inverse-designed asymmetric Y-junctions, we realize ultra-compact, broadband, and low crosstalk silicon photonic TE00 & TE1 and TE0 & TE2 mode (de)multiplexers with sizes of only 4.5 × 1.2 µm2 and 6 × 1.4 µm2, respectively. From simulations it is shown that the TE0 & TE1 and TE0 & TE2 mode (de)multiplexers contain wide bandwidths of 160 nm (1460-1620 nm) and 140 nm (1460-1600 nm), respectively, over which the mode crosstalks are below about -20 dB, and the losses are <0.41 dB and <0.88 dB, respectively. The experimental results show that in the corresponding TE0 & TE1 and TE0 & TE2 mode division multiplexing systems, the crosstalks are less than -15.5 dB and -15 dB over the spectral ranges of 1453-1580 nm and 1460-1566 nm, respectively, and the losses are <1.7 dB at 1520 nm and <8.24 dB over the entire measured wavelength range.

Inverse-designed counter-tapered coupler based broadband and compact silicon mode multiplexer/demultiplexer

A mode multiplexer/demultiplexer (MUX/DeMUX) is a crucial component for constructing mode-division multiplexing (MDM) systems. In this paper, we propose and experimentally demonstrate a wide-bandwidth and highly-integrated mode MUX/DeMUX based on an inverse-designed counter-tapered coupler. By introducing a functional region composed of subunits, efficient mode conversion and evolution can be achieved, greatly improving the mode conversion efficiency. The optimized mode MUX/DeMUX has a size of only 4 µm × 2.2 µm. An MDM-link consisting of a mode MUX and a mode DeMUX was fabricated on the silicon-on-insulator (SOI) platform. The experimental results show that the 3-dB bandwidth of the TE fundamental mode and first-order mode can reach 116 nm and 138 nm, respectively. The proposed mode MUX/DeMUX is scalable and could provide a feasible solution for constructing high-performance MDM systems.

Different-mode power splitters based on a multi-dimension direct-binary-search algorithm

In this work, we design, fabricate, and characterize a different-mode (waveguide-connected) power splitter ((W)PS) by what we believe to be a novel multi-dimension direct-binary-search algorithm that can significantly balance the device performance, time cost, and fabrication robustness by searching the state-dimension, rotation-dimension, shape-dimension, and size-dimension parameters. The (W)PS can simultaneously generate the fundamental transverse electric (TE0) and TE1 mode with the 1:1 output balance. Compared with the PS, the WPS can greatly shorten the adiabatic taper length between the single-mode waveguide and the grating coupler. The measured results of the different-mode (W)PS indicate that the insertion loss and crosstalk are less than 0.9 (1.3) dB and lower than -17.8 (-14.9) dB from 1540 nm to 1560 nm. In addition, based on the tunable tap couplers, the different-mode (W)PS can be extended to multiple output ports with different modes and different transmittances.

Bayesian design of mosaic-based mode multiplexers for various wavelength bands

Ultracompact mode multiplexers based on mosaic structure for various wavelength bands designed by Bayesian technique are investigated. C-, O-, and C + O band, TE0-TE1 2-mode multiplexers can be designed with the same footprint, by only changing the mosaic-pattern, showing the great flexibility of mosaic-based devices. Bayesian direct binary search method is used for the design, and it is demonstrated that the Bayesian technique is superior to conventional design method in terms of the best-structure search for the same number of iterations. The designed devices are fabricated for Si-waveguide platform, and the proof-of-concept results are obtained. These results indicate that the mosaic-based devices are promising candidates for future compact optical transceivers.

Mode-independent thermo-optic switch based on the total-internal-reflection effect

A broadband mode-independent thermo-optic (TO) switch using the total-internal-reflection (TIR) effect is proposed and experimentally demonstrated on a polymer waveguide platform. By optimizing geometric parameters of the TIR switch, a mode-independent TO switching function with a large bandwidth and extinction ratio can be realized for E₁₁, E₁₂, and E₂₁ modes. The measurement results show an extinction ratio larger than 18.1 dB with a driving power of 160 mW for each mode over the wavelength range of 1500-1620 nm. The designed structure can also be cascaded to form a 1 × N switch network for mode-division multiplexing (MDM) systems, which greatly improves the network flexibility.

Broadband, compact and reflection-less silicon polarizer and polarization beam splitter using chirped anti-symmetric multimode nanobeams

We present chirped anti-symmetric multimode nanobeams (CAMNs) based on silicon-on-insulator platforms, and describe their applications as broadband, compact, reflection-less, and fabrication-tolerant TM-pass polarizers and polarization beam splitters (PBSs). The anti-symmetric structural perturbations of a CAMN ensure that only contradirectional coupling between symmetric and anti-symmetric modes is possible, which can be exploited to block the unwanted back reflection of the device. The new possibility of introducing a large chirp on an ultra-short nanobeam-based device to overcome the operation bandwidth limitation due to the coupling coefficient saturation effect is also shown. The simulation results show that an ultra-compact CAMN with a length of ∼4.68 um can be used to develop a TM-pass polarizer or a PBS with an ultra-broad 20 dB extinction ratio (ER) bandwidth of >300 nm and an average insertion loss of <1.3 dB. The CAMN-based polarizer and PBS were fabricated and experimentally characterized in a wavelength range from 1507 to 1575 nm. The measured ERs were >20 dB over the entire tested wavelength range and the average insertion losses were <0.5 dB for both devices. The mean reflection suppression ratio of the polarizer was ∼26.4 dB. Large fabrication tolerances of ±60 nm in the waveguide widths of the devices were also demonstrated.

Three-dimensional mode-division multiplexing system

Blindly increasing the channels of the mode (de)multiplexer on the single-layer chip can cause the device structure to be too complex to optimize. The three-dimensional (3D) mode division multiplexing (MDM) technology is a potential solution to extend the data capacity of the photonic integrated circuit by assembling the simple devices in the 3D space. In our work, we propose a 16 × 16 3D MDM system with a compact footprint of about 100 µm × 5.0 µm × 3.7 µm. It can realize 256 mode routes by converting the fundamental transverse electric (TE₀) modes in arbitrary input waveguides into the expected modes in arbitrary output waveguides. To illustrate its mode-routing principle, the TE₀ mode is launched in one of the sixteen input waveguides, and converted into corresponding modes in four output waveguides. The simulated results indicate that the ILs and CTs of the 16 × 16 3D MDM system are less than 3.5 dB and lower than -14.2 dB at 1550 nm, respectively. In principle, the 3D design architecture can be scaled to realize arbitrary network complexity levels.

Ultracompact programmable inverse-designed nanophotonic devices based on digital subwavelength structures

Inverse design is a powerful approach to achieve ultracompact nanophotonic devices. Here, we propose an ultracompact programmable near-infrared nanophotonic device platform to dynamically implement inverse-designed near-infrared devices with different functions by programming the state of the phase-change material filled in each pixel. By tuning PCM block by block, the subwavelength condition for inverse-designed ultracompact devices is satisfied with large tuning pixel size. Based on the inverse-design device platform with a footprint of 6.4µm×8µm, we design and theoretically demonstrate four power splitters with different split ratios and one mode multiplexer working in the near-infrared band. The average excess losses for the power splitters with ratios of 0:1,1:1, 2:1, and 3:1 are less than 0.82, 0.65, 0.82, and 1.03 dB over a wavelength span of 100 nm, respectively. Meanwhile, the insertion losses of the mode multiplexer are 1.4 and 2.5 dB for T E 0 and T E 1 mode, respectively, and the average crosstalk is less than -20 and -19d B, respectively. The five different devices could be configured online in a nonvolatile way by heating phase change materials with an off-chip laser, which may significantly enhance the flexibility of on-chip optical interconnections.

Compact hybrid five-mode multiplexer based on asymmetric directional couplers with constant bus waveguide width

We experimentally demonstrate a hybrid mode division multiplexer (MDM) based on asymmetric directional couplers (ADCs) without transition tapers in between. The proposed MDM can couple five fundamental modes from access waveguides into the bus waveguide as the hybrid modes (TE₀, TE₁, TE₂, TM₀, and TM₁). To eliminate the transition tapers between cascaded ADCs as well as to enable arbitrary add-drop to the bus waveguide, we maintain the bus waveguide width to be the same, while a partially etched subwavelength grating is introduced to reduce the effective refractive index of the bus waveguide. The experimental results demonstrate a working bandwidth of up to 140 nm.

93-THz ultra-broadband and ultra-low loss Y-junction photonic power splitter with phased inverse design

Optical power splitters with ultra-broadband and ultra-low insertion loss are desired in the field of photonic integration. Combining two inverse design algorithms for staged optimization, we present the design of a Y-junction photonic power splitter with 700 nm wavelength bandwidth (from 1200 nm to 1900 nm) within a 0.2 dB insertion loss, corresponding to a 93 THz frequency bandwidth. The average insertion loss is approximately -0.057 dB in the valuable C-band. Moreover, we comprehensively compared the insertion loss performance of different types and sizes of curved waveguides, and also give the cases of 1:4 and 1:6 cascaded power splitters. These scalable Y-junction splitters provide new alternatives for high-performance photonic integration.

Non-Volatile Reconfigurable Compact Photonic Logic Gates Based on Phase-Change Materials

Photonic logic gates have important applications in fast data processing and optical communication. This study aims to design a series of ultra-compact non-volatile and reprogrammable photonic logic gates based on the Sb₂Se₃ phase-change material. A direct binary search algorithm was adopted for the design, and four types of photonic logic gates (OR, NOT, AND, and XOR) are created using silicon-on-insulator technology. The proposed structures had very small sizes of 2.4 μm × 2.4 μm. Three-dimensional finite-difference time-domain simulation results show that, in the C-band near 1550 nm, the OR, NOT, AND, and XOR gates exhibit good logical contrast of 7.64, 6.1, 3.3, and 18.92 dB, respectively. This series of photonic logic gates can be applied in optoelectronic fusion chip solutions and 6G communication systems.

Low Power Consuming Mode Switch Based on Hybrid-Core Vertical Directional Couplers with Graphene Electrode-Embedded Polymer Waveguides

We propose a mode switch based on hybrid-core vertical directional couplers with an embedded graphene electrode to realize the switching function with low power consumption. We designed the device with Norland Optical Adhesive (NOA) material as the guide wave cores and epoxy polymer material as cladding to achieve a thermo-optic switching for the E₁₁, E₂₁ and E₁₂ modes, where monolayer graphene served as electrode heaters. The device, with a length of 21 mm, had extinction ratios (ERs) of 20.5 dB, 10.4 dB and 15.7 dB for the E₂₁, E₁₂ and E₁₁ modes, respectively, over the C-band. The power consumptions of three electric heaters were reduced to only 3.19 mW, 3.09 mW and 2.97 mW, respectively, and the response times were less than 495 µs, 486 µs and 498 µs. Additionally, we applied such a device into a mode division multiplexing (MDM) transmission system to achieve an application of gain equalization of few-mode amplification among guided modes. The differential modal gain (DMG) could be optimized from 5.39 dB to 0.92 dB over the C-band, together with the characteristic of polarization insensitivity. The proposed mode switch can be further developed to switch or manipulate the attenuation of the arbitrary guided mode arising in the few-mode waveguide.

Multi-dimensional data transmission using inverse-designed silicon photonics and microcombs

The use of optical interconnects has burgeoned as a promising technology that can address the limits of data transfer for future high-performance silicon chips. Recent pushes to enhance optical communication have focused on developing wavelength-division multiplexing technology, and new dimensions of data transfer will be paramount to fulfill the ever-growing need for speed. Here we demonstrate an integrated multi-dimensional communication scheme that combines wavelength- and mode- multiplexing on a silicon photonic circuit. Using foundry-compatible photonic inverse design and spectrally flattened microcombs, we demonstrate a 1.12-Tb/s natively error-free data transmission throughout a silicon nanophotonic waveguide. Furthermore, we implement inverse-designed surface-normal couplers to enable multimode optical transmission between separate silicon chips throughout a multimode-matched fibre. All the inverse-designed devices comply with the process design rules for standard silicon photonic foundries. Our approach is inherently scalable to a multiplicative enhancement over the state of the art silicon photonic transmitters.

Broadband and efficient multi-mode fiber-chip edge coupler on a silicon platform assisted with a nano-slot waveguide

Mode-division multiplexing (MDM) has been extensively utilized to expand the capacity of chip-scale or fiber-based optical communication, whereas it is still challenging to implement the MDM for fiber-chip optical interconnects due to the huge mode mismatch between few-mode fiber (FMF) and multi-mode waveguide. In this work, we propose and design a silicon integrated six-mode edge coupler assisted with a slot waveguide, which achieves the efficient direct conversion of multiple modes between the waveguide and fiber in a broad bandwidth. Based on the principle of mode conversion, this edge coupler enables the mode conversion between six linear polarization (LP) modes (i.e. LPx/y01, LPx/y11a, LPx/y11b) in FMF and six on-chip waveguide modes (i.e. TE₀, TE₁, TE₂, TM₀, TM₁, TM₂) with low insertion loss, low mode crosstalk and broad bandwidth. The obtained results show that over the whole C-band the efficiency of mode conversion is higher than 98% and the mode crosstalk is low than -19 dB, while the total coupling loss is higher than 85%. The favorable results offer an important reference for designing related broadband photonic devices, and the presented scheme could be potentially exploited to further increase the transmission capability for prospective fiber-chip optical interconnections and communications.

Inverse design of compact power divider with arbitrary outputs for 5G applications

Since the recent on-demand applications need more sophisticated circuits and subsystems, components with configurable capabilities attract attention more than before in commercial systems, specifically the fifth generation (5G). Power dividers play a crucial role in 5G phased array systems, and their role becomes more significant if the output powers ratio is adjustable. Here, we suggest a design methodology by which planar power splitters with arbitrary output power levels can be designed in light of very simple perturbations, i.e., vias. Through our design procedure, we find an optimized pattern for hybrid vias-some of them are made of PEC, and others are dielectric, e.g., air, high-permittivity materials. Thanks to deep neural networks, we demonstrate that this technique can be employed to design power splitters whose output ports have different amplitudes. In light of the proposed method, we fabricated and measured a 4-way power divider realizing Chebyshev coefficients for sidelobe reduction of a 4-element array at 28 GHz as a proof-of-concept. We believe that this methodology in which hybrid perturbation is the key spot paves a way to implement complex functions in various platforms and other structures, e.g., SIWs, ridge waveguides, rather than the one we investigated (planar/microstrip).

Series of ultra-low loss and ultra-compact multichannel silicon waveguide crossing

Ultra-compact waveguide crossing (UC-WC) is a basic component in optoelectronic fusion chip solutions, as its footprint is smaller in the orders of magnitude than that of traditional photonic integrated circuits (PICs). However, a large loss of UC-WC (decibel level) becomes a barrier to scaling and practicality. Here, we propose a series of ultra-low loss UC-WC silicon devices using an advanced hybrid design that combines the adjoint method with the direct binary search (DBS) algorithm. Simulation results show that our 2 × 2 UC-WC has an insertion loss as low as 0.04 dB at 1550 nm, which is about ten times lower than the previous UC-WC results. In the valuable C-band (1530-1565 nm), the insertion loss of UC-WC is lower than -0.05 dB, and the channel crosstalk is lower than -34 dB. Furthermore, for the 3 × 3 UC-WC device, the highest insertion loss in the entire C-band is approximately -0.07 dB, and the highest channel crosstalk is lower than -33 dB. Additionally, the 4 × 4 and more complex 8 × 8 UC-WC devices were also analyzed. The highest insertion loss for 4 × 4 and 8 × 8 UC-WC in the C-band is only -0.19 dB and -0.20 dB, respectively, and the highest channel crosstalk is approximately -22dB and -28 dB, respectively. These results confirm that the designed devices possess two attractive features simultaneously: ultra-compactness and ultra-low insertion loss, which may be of great value in future large-scale optoelectronic fusion chips.

Fabrication error tolerant broadband mode converters and their working principles

Computational inverse design techniques have shown potential to become reliable means for designing compact nanophotonic devices without compromising the performance. Much effort has been made to reduce the computation cost involved in the optimization process and obtain final designs that are robust to fabrication imperfections. In this work, we experimentally demonstrate TE0-TE1 and TE1-TE3 mode converters (MCs) on the silicon-on-insulator platform designed using the computationally efficient shape optimization method. These MCs have mode conversion efficiencies above 95%, and the insertion loss ranges from 0.3 dB to 1 dB over a wavelength span of 80 nm ranging from 1.5 µm to 1.58 µm. Maximum modal crosstalk found experimentally in the C-band is -19 dB. The conversion efficiency drops at most by 2.2% at 1.55 µm for 10 nm over/under etch, implying good robustness to dimensional variations. We present the mode conversion mechanism of these MCs by studying the simulated electromagnetic field patterns and validate with supportive data. We also demonstrate their performance in the time domain with a 28 Gbps OOK and a 20 GBaud PAM-4 payload transmissions, which supports their utility for high throughput data communications. The open eye diagrams exhibit Q-factors of 8 dB.

On-chip mode division (de)multiplexer for multi-band operation

We propose an on-chip mode division (de)multiplexer based on asymmetric directional couplers (ADCs) for multi-band operation. In mode-coupling process, the minimum coupling length is wavelength-dependent. The longer the wavelength is, the shorter the minimum coupling length is. A light of longer wavelength can be coupled back and forth multiple times with a total coupling length which equals to the minimum coupling length of a shorter wavelength light, thus realizing multi-band transmission at different wavelengths. As a proof-of-concept experiment, a four-mode (de)multiplexer for joint operation in the C- and O-Bands is designed and experimentally demonstrated. For the four modes (TE₀, TE₁, TE₂ and TE₃), the measured insertion losses (ILs) and crosstalk (CT) of the (de)multiplexer are < 4.7 dB and < -10.1 dB respectively from 1290 nm to 1360 nm, and they are < 3.5 dB and < -11.8 dB respectively from 1510 nm to 1580 nm.

Fundamental analyses of fabrication-tolerant high-performance silicon mode (de)multiplexer

Mode-division multiplexing (MDM) has been extensively exploited to expand the capacity of chip-scale optical interconnects, whereas high-volume manufacturing of on-chip mode (de)multiplexers is still full of challenges. In this paper, we analyze the fabrication errors (sidewall, width, height) of silicon mode (de)multiplexer and present two cases of fabrication-tolerant high-performance silicon mode (de)multiplexer. The presented mode (de)multiplexer could eliminate the mode mismatch and mode hybridization caused by the fabrication errors. When sidewall errors are 0°, 5°, width errors are 0, ± 20, ± 30 nm, and height errors are 0, ± 10 nm, the designed fabrication-tolerant high-performance silicon mode (de)multiplexer can achieve low excess loss less than 2.5 dB and low inter-mode crosstalk less than -15 dB over a broad bandwidth from 1500 to 1600 nm. The obtained results provide an important guideline for designing fabrication-tolerant photonic integrated circuits on silicon platform, which could be applied to the prospective high-volume manufacturing and large-scale integration.

Ultra-compact silicon mode (de)multiplexer based on directional couplers with subwavelength sidewall corrugations

Asymmetrical directional couplers aided with subwavelength sidewall corrugations are used to realize ultra-compact silicon mode (de)multiplexers at C-band. Three mode (de)multiplexers with ultra-short coupling lengths of 5.6/6.5/7.7 μm are designed to enable low-loss mode conversions between TE₀ and TE_1/2/3 modes. They are then cascaded to build a four-channel mode-division-multiplexing (MDM) link. The four mode channels present minimal on-chip insertion losses of 0.2/0.7/0.7/0.9 dB at their peak wavelengths. Measured cross talk levels of the four mode channels are better than -18.0/-19.1/-16.0/-18.2 dB within the wavelength range from 1530 nm to 1580 nm.

Guided-mode based arbitrary signal switching through an inverse-designed ultra-compact mode switching device

The application of the inverse design method and free-form geometrical optimization in photonic devices endows them with highly tunable functionality and an ultra-compact footprint. In this paper, we implemented this platform to silicon photonic guided-mode manipulation and demonstrated a guided mode-based signal switching architecture. The passive signal switching mechanism is utilized so that no power consumption is needed for routing state maintenance. To solve the explosive increasing design cost in such mechanism when the switching scale is expanded, we illustrate that only a small number of mode switching devices need to be designed as the switching basis. In theory, arbitrary signal routing states can be constructed by cascading some selected basis. The required switching devices can be decreased from factorial N to N - 1 for the N channels switching. For proof of concept, we design and experimentally demonstrate the three-mode cases and the cascade method to combine any three mode-based switching devices. Experiments show that the insertion losses of TE₀ - TE₁ mode switching unit (U1), TE₁ - TE₂ mode switching units (U2), and TE₀ - TE₂ mode switching unit (U3) are less than 2.8 dB, 3.1 dB, and 2.3 dB, respectively. The demonstrated architecture has both arbitrary signal switching capability and ultra-compact footprint, which is promising in the application of mode-division multiplexing communication systems.

Compact and efficient three-mode (de)multiplexer based on horizontal polymer waveguide couplers

A compact and efficient polymer three-mode (de)multiplexer with two cascaded waveguide directional couplers fabricated on the same substrate along the horizontal direction is proposed. Three waveguides formed two couplers, where two narrower waveguides were placed on either side of the central waveguide. By optimizing the core height and width, the two couplers can ensure that the E11x mode of the two narrower waveguides are highly coupled into the E21x and E31x modes of the central waveguide at a wavelength of 1310 nm. The structural size of the fabricated three-mode (de)multiplexer using ultraviolet (UV) lithography technology is in agreement with the designed value. The fabricated device, which is 35 mm long, exhibits coupling ratios of 98.07% and 95.43% for the two couplers, respectively. The insertion losses of the three waveguides are 5.23 dB, 8.58 dB, and 14.39 dB, respectively. The device can achieve the multiplexing of three modes in two dimensions, which can increase the channel capacity of optical communication.

Optical meta-waveguides for integrated photonics and beyond

The growing maturity of nanofabrication has ushered massive sophisticated optical structures available on a photonic chip. The integration of subwavelength-structured metasurfaces and metamaterials on the canonical building block of optical waveguides is gradually reshaping the landscape of photonic integrated circuits, giving rise to numerous meta-waveguides with unprecedented strength in controlling guided electromagnetic waves. Here, we review recent advances in meta-structured waveguides that synergize various functional subwavelength photonic architectures with diverse waveguide platforms, such as dielectric or plasmonic waveguides and optical fibers. Foundational results and representative applications are comprehensively summarized. Brief physical models with explicit design tutorials, either physical intuition-based design methods or computer algorithms-based inverse designs, are cataloged as well. We highlight how meta-optics can infuse new degrees of freedom to waveguide-based devices and systems, by enhancing light-matter interaction strength to drastically boost device performance, or offering a versatile designer media for manipulating light in nanoscale to enable novel functionalities. We further discuss current challenges and outline emerging opportunities of this vibrant field for various applications in photonic integrated circuits, biomedical sensing, artificial intelligence and beyond.

Gradient-probability-driven discrete search algorithm for on-chip photonics inverse design

The inverse-designed photonic device, with the characteristics of high performance and ultra-high compactness, is suitable for on-chip photonics applications. The gradient-based algorithms have high convergence efficiency. However, they depend on the continuous independent variable, so they cannot be directly applied to the pixel-based discrete search methods. In this paper, we propose a gradient-probability-driven discrete search (GPDS) algorithm for photonics inverse design. The algorithm establishes a connection between the gradient and the discrete value set by introducing the method of probability sampling. As an intrinsic discrete search algorithm in which the values of pixels are selected from a finite number of the discrete set, no additional discretization process is needed. Compared with the traditional brute-force search (BFS) method and traditional gradient method, the probability sampling process of our proposed GPDS algorithm can improve device performance efficiently and provide better stability to the initial states. We illustrate several component designs which are commonly used in the silicon photonics platform, and the results show that the algorithm can achieve high-performance structures within fewer iterations and has the ability of multi-objective optimization. With good flexibility and manufacturing-friendly geometry control, the algorithms are potential to be a powerful tool in solving multi-objective problems.

Ultra-compact reconfigurable device for mode conversion and dual-mode DPSK demodulation via inverse design

The mode multiplexing/de-multiplexing devices are key components for mode-division multiplexing (MDM) technology. Here, we propose an ultra-compact and reconfigurable mode-conversion device via inverse design, which can selectively implement multichannel mode conversion controlled by input phase shifts (Δφ). The device can transform input TE₀ (TE₁) mode to TE₄ (TE₃) mode at Δφ=0, or from TE₀ (TE₁) to TE₁ (TE₂) at Δφ=π spanning the wavelength range of 1525-1565 nm. We further demonstrate an integrated monolithic module based on the mode conversions to directly demodulate the dual-mode difference phase shift keying (DPSK) signal which significantly reduces the device size and benefits for future dense integrations in MDM systems.

Compact silicon three-mode multiplexer by refractive-index manipulation on a multi-mode interferometer

Mode-division multiplexing can scale the capacity of optical communications and optical interconnects. We demonstrate an ultra-compact and fabrication-error tolerant silicon three-mode multiplexer by shallowly etching rectangular trenches on a multi-mode interferometer. Depending on the selected input port, the TE₀ mode is converted to the eigenmodes of the bus waveguide. These modes are coupled to each other owing to the refractive-index perturbation induced by the shallow trenches and finally converted to a selected spatial mode at the output. A three-mode multiplexing device is experimentally demonstrated with a footprint of 2.00 × 17.05 µm². The bandwidths for the three channels are >70 nm with crosstalk values below -10 dB.

Inverse Design for Silicon Photonics: From Iterative Optimization Algorithms to Deep Neural Networks

Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario.

Compact silicon-photonic mode-division (de)multiplexer using waveguide-wrapped microdisk resonators

We experimentally demonstrate, to the best of our knowledge, the first microdisk-based silicon-photonic mode-division (de)multiplexer circuit, which is compatible with wavelength-division multiplexing for high aggregate bandwidth on-chip optical communications. This circuit uses waveguide-wrapped microdisk resonators, featuring low levels of intermodal crosstalk and insertion loss within an ultracompact footprint. In addition, the proposed device presents an increased free spectral range, allowing for 530 combined data channels. Furthermore, the microdisk structure naturally supports vertically oriented depletion-type pn junctions, which have been shown to reach subfemtojoule-per-bit modulation efficiencies. The high modulation efficiency, compactness, and wide free spectral range of waveguide-wrapped microdisk resonators present the potential for higher bandwidth and lower energy consumption in next-generation data processing and communication applications.

Broadband and compact silicon mode converter designed using a wavefront matching method

A broadband and compact TE0-TE1 mode converter for a mode division multiplexing system designed using a wavefront matching method is realized. We present the first experimental demonstration of a silicon waveguide device designed by a wavefront matching method. In order to achieve broadband operation of the silicon mode converter, seven wavelengths are considered in its optimization process. The designed silicon mode converter is fabricated via a standard complementary metal-oxide-semiconductor technology, which enables low-cost mass production. Measurements performed using the fabricated mode converter correlate strongly with the calculated results.

Inverse design of a single-step-etched ultracompact silicon polarization rotator

We propose and experimentally demonstrate a novel ultracompact silicon polarization rotator based on equivalent asymmetric waveguide cross section in only single-step etching procedure for densely integrated on-chip mode-division multiplexing system. In the conventional mode hybridization scheme, the asymmetric waveguide cross section is employed to excite the hybridized modes to realize high performance polarization rotator with compact footprint and high polarization extinction ratio. However, the fabrication complexity severely restricts the potential application of asymmetric waveguide cross section. We use inverse-designed photonic-crystal-like subwavelength structure to realize an equivalent asymmetric waveguide cross section, which can be fabricated in only single-step etching process. Besides, a theory-assisted inverse design method based on a manually-set initial pattern is employed to optimize the device to improve design efficiency and device perform. The fabricated device exhibited high performance with a compact footprint of only 1.2 × 7.2 µm², high extinction ratio (> 19 dB) and low insertion loss (< 0.7 dB) from 1530 to 1590 nm.

Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnects

Mode-division multiplexing (MDM) technology has drawn tremendous attention for its ability to expand the link capacity within a single-wavelength carrier, paving the way for large-scale on-chip data communications. In the MDM system, the signals are carried by a series of higher-order modes in a multi-mode bus waveguide. Hence, it is essential to develop on-chip mode-handling devices. Silicon-on-insulator (SOI) has been considered as a promising platform to realize MDM since it provides an ultra-high-index contrast and mature fabrication processes. In this paper, we review the recent progresses on silicon integrated nanophotonic devices for MDM applications. We firstly discuss the working principles and device configurations of mode (de)multiplexers. In the second section, we summarize the multi-mode routing devices, including multi-mode bends, multi-mode crossings and multi-mode splitters. The inverse-designed multi-mode devices are then discussed in the third section. We also provide a discussion about the emerging reconfigurable MDM devices in the fourth section. Finally, we offer our outlook of the development prospects for on-chip multi-mode photonics.

Ultra-compact high efficiency and low crosstalk optical interconnection structures based on inverse designed nanophotonic elements

In this paper, we combine inverse design concept and direct binary search algorithm to demonstrate three ultra-compact high efficiency and low crosstalk on-chip integrated optical interconnection basic devices in the entire wavelength range of 1,400-1600 nm based on silicon-on-insulator platform. A 90-degree waveguide bend with a footprint of only 2.4 × 2.4 μm² is designed, whose transmission efficiency up to 0.18 dB. A waveguide crossing with a footprint of only 2.4 × 2.4 μm² is designed, which can provide insertion loss of less than 0.5 dB and crosstalk (CL) of lower than - 19 dB. A same direction waveguide crossing with footprint of only 2.4 × 3.6 μm² is designed, which can provide the insertion loss of less than 0.56 dB and the crosstalk of lower than - 21 dB. Then, we use them to form several ultra-compact optical interconnect basic structures and performed the simulation calculation. They overall achieve high performance. This will significantly improve the integration density.

Inverse-designed arbitrary-input and ultra-compact 1 × N power splitters based on high symmetric structure

Based on high symmetric structure, we propose the arbitrary-input and ultra-compact 1 × 2 and 1 × 3 power splitters by utilizing inverse design method. These devices can realize the functionality of power splitting, when the optical field is launched from arbitrary port. The shapes of their structures are 3.8 μm-wide regular hexagon and 4.0 μm-wide regular octagon, respectively. By utilizing 3D fine difference time domain solutions, the simulated results indicate that the excess loss of the 1 × 2 power splitter is less than 1.5 dB from 1,500 to 1,600 nm, and the excess loss and crosstalk of the 1 × 3 power splitter are less than 1.9 dB and lower than − 15.5 dB over 100 nm bandwidth at the centered wavelength of 1,550 nm respectively. In addition, the tolerances to fabrication errors are also investigated.

Ultra-compact and efficient 1 × 2 mode converters based on rotatable direct-binary-search algorithm

In this paper, we innovatively demonstrate a rotatable direct-binary-search algorithm. Based on this unique inverse design method, the coupling region of nanophotonic device can be realized with multi-shape and multi-rotation pixels. In addition, the novel 1× 2 mode converters with multipurpose design goals on a 220 nm-thick top silicon-on-insulator platform are proposed by utilizing this enhanced algorithm, which can simultaneously achieve power splitting and mode conversion. By 3D fine difference time domain solutions, the 1 × 2 mode converter that converts TE₀ mode into TE₁, with a footprint of 2.7 µm × 2.4 µm, exhibits the excess loss of 0.1 - 0.2 dB (TE₁ mode), crosstalk of lower than -20.6 dB (TE₀ mode) and reflection loss of lower than -19.5 dB (TE₀ mode) from 1500 nm to 1600 nm. The 1 × 2 mode converter that transforms TE₀ into TE₂ occupies the footprint of 3.6 µm × 3 µm. The excess loss is 0.3 - 0.4 dB (TE₂ mode) in the wavelength range of 1500 - 1600 nm. The crosstalks are lower than -17.5 dB (TE₁ mode) and -25.1 dB (TE₀ mode), and the reflection loss is lower than -18.3 dB (TE₀ mode). Besides, the fabrication tolerances caused by both expansion or contraction of etched pattern contour and round corner effect are also investigated.

Ultra-compact reflective mode converter based on a silicon subwavelength structure

Mode converters play an essential role in mode-division multiplexing systems. A reflective mode converter (RMC), which is utilized to accomplish the mode conversion in the contra-propagation process, can fold the optical path and realize the mode exchange in an optical network. In this paper, we propose and experimentally demonstrate an RMC based on a silicon subwavelength structure. It can convert the input fundamental mode (${\text{TE}_0}$TE₀) into the first-order mode (${\text{TE}_1}$TE₁) in a ${2.0}\;\unicode{x00B5} \text{m} \times {2.0}\;\unicode{x00B5} \text{m}$2.0µm×2.0µm footprint. The simulated insertion loss and cross talk are lower than 0.6 dB and $ - {20.3}\;\text{dB}$-20.3dB in 1525-1565 nm. Experimental results verify the functionality of the device. The measured insertion loss and cross talk are lower than 2.2 dB and $ - {16.2}\;\text{dB}$-16.2dB. To further prove the generality of the methodology, we design another two RMCs realizing the mode conversion functions of ${\text{TE}_0}$TE₀ to ${\text{TE}_2}$TE₂ and ${\text{TE}_0}$TE₀ to ${\text{TE}_3}$TE₃ modes. The simulated insertion losses are lower than 1.1 dB and 1.8 dB.

State-of-the-Art and Perspectives on Silicon Waveguide Crossings: A Review

In the past few decades, silicon photonics has witnessed a ramp-up of investment in both research and industry. As a basic building block, silicon waveguide crossing is inevitable for dense silicon photonic integrated circuits and efficient crossing designs will greatly improve the performance of photonic devices with multiple crossings. In this paper, we focus on the state-of-the-art and perspectives on silicon waveguide crossings. It reviews several classical structures in silicon waveguide crossing design, such as shaped taper, multimode interference, subwavelength grating, holey subwavelength grating and vertical directional coupler by forward or inverse design method. In addition, we introduce some emerging research directions in crossing design including polarization-division-multiplexing and mode-division-multiplexing technologies.

Ultrasmall broadband wavelength and polarization router based on hybrid waveguide of monolithic-LiNbO3

The nanoscale wavelength and polarization router, which can simultaneously separate wavelength and polarization modes, is an essential component of on-chip nanophotonic devices. Here, an on-chip wavelength and polarization router is realized experimentally based on a three-layer hybrid waveguide of Au-SiO₂-LiNbO₃ etched with asymmetric nano-cavities. The central area size of the device is only 1.60×1.96  μm². A broad operation band covers from 500 nm to 1150 nm with low cross talk of under 10 dB. The monolithic-LiNbO₃is introduced for the first time, to the best of our knowledge, to on-chip multichannel wavelength and polarization routers. This work plays a key role for dense chip integration, visible light displays, and communications, and can inspire LiNbO₃-based nanophotonic devices.

Silicon Mode-Selective Switch via Horizontal Metal-Oxide-Semiconductor Capacitor Incorporated With ENZ-ITO

A silicon mode-selective switch (MSS) is proposed by using a horizontal metal-oxide-semiconductor (MOS) capacitor incorporated with the epsilon-near-zero (ENZ) indium-tin-oxide (ITO). The carrier concentration of the double accumulation-layers in ITO can be adjusted via the applied gate-voltage to achieve the desired switching state. The MOS-type mode of the central MOS-capacitor based triple-waveguide coupler is introduced and optimised by using the full-vectorial finite element method to switch the "OFF" and "ON" states. The thickness of the accumulation layer and the optimal design are studied by using the 3D full-vectorial eigenmode expansion method. The optimised quasi-TE₀ and quasi-TE₁ modes based MSSes are with the extinction ratios of 28.52 dB (19.05 dB), 37.29 dB (17.8 dB), and 37.29 dB (23.7 dB), at "OFF" ("ON") states for the accumulation-layer thicknesses of 1.5, 5.0, and 10.0 nm, respectively. The operation speed can achieve to be 6.3 GHz, 6.2 GHz, and 6.2 GHz for these three accumulation-layer thicknesses, respectively. The performance of the proposed MSS with a 2.5 V gate-voltage is also studied for preventing the oxide breakdown. The proposed MSS can be applied in the mode-division-multiplexing networks for signal switching and exchanging.

On-chip silicon dual-mode multiplexer via a subwavelength grating-based directional coupler and a mode blocker

An on-chip silicon dual-mode multiplexer (MUX) is proposed via a subwavelength grating (SWG)-based directional coupler and a mode blocker. The proposed mode MUX is optimized by utilizing the three-dimensional full-vectorial finite-difference time-domain-based band structure and propagation calculations. The simulated results indicate that an ultralow mode cross talk of $ - {40}\,\,{\rm dB}$-40dB at the operating wavelength of 1550 nm can be achieved by introducing a ${{\rm TE}_0}$TE₀ mode blocker. Benefiting from the triple SWG coupler, the mode-coupling strength can be significantly enhanced inside the proposed mode MUX, which can achieve a compact coupling length of 8.75 µm, a low insertion loss of 0.39 dB at 1550 nm, an ultrabroad bandwidth of 310 nm for the mode CT $ \lt - {15.0}\,\,{\rm dB}$<-15.0dB, and insensitivity to fabrication errors.

Ultra-compact low-loss 1 × 4 optical power splitter with splitting ratio of 1∶2∶4∶8 based on two-stage cascaded MMI couplers

An ultra-compact low-loss 1×4 optical power splitter with a splitting ratio of 1∶2∶4∶8 is proposed and demonstrated on a 220-nm-thick silicon-on-insulator (SOI) platform at the C band. The splitter is based on two stages of a cascaded 1×3 multimode interference (MMI) coupler and a 4×4 MMI coupler. The footprint of the device is 124.0  μm×6.4  μm, which is more compact than the traditional scheme of four-stage cascaded 1×2 MMI couplers. Phase shifters based on taper waveguides are incorporated in the device as the connection of two MMI couplers. The fabricated device exhibits a 3 dB power difference with a deviation of less than 0.88 dB from 1530 nm to 1570 nm. The average power difference is 3.14 dB at the center of the C band with an insertion loss of 1.84 dB.

Compact silicon 10-mode multi/demultiplexer for hybrid mode- and polarisation-division multiplexing system

To further increase the capacity of the optical transmission system, the hybrid mode- and polarisation-division multiplexing (MDM-PDM) technology has been proved to be an efficient approach by multiplexing dual polarisations for each orthogonal eigen mode. A hybrid (de)multiplexer [(De)MUX] is one of the most important fabrics for the hybrid MDM-PDM networks. A compact silicon 10-mode hybrid (De)MUX is proposed based on three cascaded asymmetric directional couplers (ADCs) based sections, three adiabatic tapers, and a polarisation beam splitter (PBS). The phase-matching conditions can be achieved by varying the widths of the bus waveguides for the TM modes and then by varying the widths of the access waveguides for the TE modes. The simulated results show that a compact total coupling length for TM₁ ~ TM₃ and TE₁ ~ TE₅ modes can be achieved to be 55.4 μm. In addition, the total loss of the proposed hybrid (De)MUX can be reduced benefitting from the fewer tapers compared with the conventional cascaded ADCs. The PBS is also optimised with a compact length of 7.0 μm and high extinction ratios of 32.9 dB and 15.4 dB for the TM₀ and TE₀ modes, respectively.

Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter

An ultracompact broadband dual-mode 3 dB power splitter using inverse design method for highly integrated on-chip mode (de) multiplexing system is proposed and experimentally demonstrated. A dual-mode convertor based on subwavelength axisymmetric three-branch waveguide is utilized to convert TE₀ and TE₁ to three intermediate fundamental modes. The axisymmetric topology constraint of the nanostructures enables the optimized device to achieve a strict 50:50 splitting ratio over a broad wavelength range from 1.52 to 1.60 µm. The fabricated device occupied a compact footprint of only 2.88 µm × 2.88 µm. The measured average excess losses and crosstalks for both modes were respectively less than 1.5 dB and -20 dB from 1.52 to 1.58 µm for both TE₀ and TE₁, which are consistent with the numerical simulations.