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

Rational design of an integrated directional coupler for wideband operation

We consider a design procedure for directional couplers for which the coupling length is approximately wavelength-independent over a wide bandwidth. We show analytically that two coupled planar waveguides exhibit a maximum in the coupling strength, which ensures both wideband transmission and minimal device footprint. This acts as a starting point for mapping out the relevant part of phase space. This analysis is then generalized to the fully three-dimensional geometry of rib waveguides using an effective medium approximation. This forms an excellent starting point for fully numerical calculations and leads to designs with unprecedented bandwidths and compactness.

Integrating inverse design and partially etched platform: an ultra-compact polarization splitter and rotator as an example

Silicon photonics devices benefit greatly from a partially etched platform and inverse design. Herein, we propose a bi-layer polarization splitter and rotator with a topology pattern and demonstrate it on a silicon-on-insulator platform. Our device exhibits a significantly reduced physical footprint of only 2µm×6µm, compared to traditional directional couplers and tapered waveguides. The device accomplishes the functions of polarization conversion and separation in such a compact design without redundant tapered or bending waveguides. The tested minimum insertion loss with the fabrication batch reaches 0.57 and 0.67 dB for TE and TM modes, respectively. The TE mode demonstrates a wider bandwidth and lower ILs than the TM modes, averaging around 1 dB from 1530 to 1565 nm. The M modes exhibit approximately 2 dB ILs at the same wavelength range, decreasing to about 1 dB between 1565 and 1580 nm. Improved designs and fabrication conditions strongly suggest the potential for further performance enhancement in the device. This successful initiative validates the exceptional performance resulting from the integration of the partially etched platform and inverse design, providing valuable insights for future photonic integrated device designs.

Design of compact and low-loss S-bends by CMA-ES

We employ the covariance matrix adaptation evolution strategy (CMA-ES) algorithm to design compact and low-loss S-bends on the standard silicon-on-insulator platform. In line with the CMA-ES-based approach, we present experimental results demonstrating insertion losses of 0.041 dB, 0.025 dB, and 0.011 dB for S-bends with sizes of 3.5 µm, 4.5 µm, and 5.5 µm, respectively, which are the lowest insertion losses within the footprint range smaller than approximately 30 µm2. These outcomes underscore the remarkable performance and adaptability of the CMA-ES to design Si photonics devices tailored for high-density photonic integrated circuits.

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 design of an ultra-compact dual-band wavelength demultiplexing power splitter with detailed analysis of hyperparameters

Inverse design has been widely studied as an efficient method to reduce footprint and improve performance for integrated silicon photonic (SiP) devices. In this study, we have used inverse design to develop a series of ultra-compact dual-band wavelength demultiplexing power splitters (WDPSs) that can simultaneously perform both wavelength demultiplexing and 1:1 optical power splitting. These WDPSs could facilitate the potential coexistence of dual-band passive optical networks (PONs). The design is performed on a standard silicon-on-insulator (SOI) platform using, what we believe to be, a novel two-step direct binary search (TS-DBS) method and the impact of different hyperparameters related to the physical structure and the optimization algorithm is analyzed in detail. Our inverse-designed WDPS with a minimum feature size of 130 nm achieves a 12.77-times reduction in footprint and a slight increase in performance compared with the forward-designed WDPS. We utilize the optimal combination of hyperparameters to design another WDPS with a minimum feature size reduced to 65 nm, which achieves ultra-low insertion losses of 0.36 dB and 0.37 dB and crosstalk values of -19.91 dB and -17.02 dB at wavelength channels of 1310 nm and 1550 nm, respectively. To the best of our knowledge, the hyperparameters of optimization-based inverse design are systematically discussed for the first time. Our work demonstrates that appropriate setting of hyperparameters greatly improves device performance, throwing light on the manipulation of hyperparameters for future inverse design.

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.

Modified variational autoencoder for inversely predicting plasmonic nanofeatures for generating structural color

We apply a modified variational autoencoder (VAE) regressor for inversely retrieving the topological parameters of the building blocks of plasmonic composites for generating structural colors as per requirement. We demonstrate results of a comparison study between inverse models based on generative VAEs as well as conventional tandem networks that have been favored traditionally. We describe our strategy for improving the performance of our model by filtering the simulated dataset prior to training. The VAE- based inverse model links the electromagnetic response expressed as the structural color to the geometrical dimensions from the latent space using a multilayer perceptron regressor and shows better accuracy over a conventional tandem inverse model.

An Integrated Optical Circuit Architecture for Inverse-Designed Silicon Photonic Components

In this work, we demonstrate a compact toolkit of inverse-designed, topologically optimized silicon photonic devices that are arranged in a "plug-and-play" fashion to realize many different photonic integrated circuits, both passive and active, each with a small footprint. The silicon-on-insulator 1550-nm toolkit contains a 2 × 2 3-dB splitter/combiner, a 2 × 2 waveguide crossover, and a 2 × 2 all-forward add-drop resonator. The resonator can become a 2 × 2 electro-optical crossbar switch by means of the thermo-optical effect, phase-change cladding, or free-carrier injection. For each of the ten circuits demonstrated in this work, the toolkit of photonic devices enables the compact circuit to achieve low insertion loss and low crosstalk. By adopting the sophisticated inverse-design approach, the design structure, shape, and sizing of each individual device can be made more flexible to better suit the architecture of the greater circuit. For a compact architecture, we present a unified, parallel waveguide circuit framework into which the devices are designed to fit seamlessly, thus enabling low-complexity circuit design.

Data-Enhanced Deep Greedy Optimization Algorithm for the On-Demand Inverse Design of TMDC-Cavity Heterojunctions

A data-enhanced deep greedy optimization (DEDGO) algorithm is proposed to achieve the efficient and on-demand inverse design of multiple transition metal dichalcogenides (TMDC)-photonic cavity-integrated heterojunctions operating in the strong coupling regime. Precisely, five types of photonic cavities with different geometrical parameters are employed to alter the optical properties of monolayer TMDC, aiming at discovering new and intriguing physics associated with the strong coupling effect. Notably, the traditional rigorous coupled wave analysis (RCWA) approach is utilized to generate a relatively small training dataset for the DEDGO algorithm. Importantly, one remarkable feature of DEDGO is the integration the decision theory of reinforcement learning, which remedies the deficiencies of previous research that focused more on modeling over decision making, increasing the success rate of inverse prediction. Specifically, an iterative optimization strategy, namely, deep greedy optimization, is implemented to improve the performance. In addition, a data enhancement method is also employed in DEDGO to address the dependence on a large amount of training data. The accuracy and effectiveness of the DEDGO algorithm are confirmed to be much higher than those of the random forest algorithm and deep neural network, making possible the replacement of the time-consuming conventional scanning optimization method with the DEDGO algorithm. This research thoroughly describes the universality, interpretability, and excellent performance of the DEDGO algorithm in exploring the underlying physics of TMDC-cavity heterojunctions, laying the foundations for the on-demand inverse design of low-dimensional material-based nano-devices.

Inverse design of a nano-photonic wavelength demultiplexer with a deep neural network approach

In this paper, we propose a pre-trained-combined neural network (PTCN) as a comprehensive solution to the inverse design of an integrated photonic circuit. By utilizing both the initially pre-trained inverse and forward model with a joint training process, our PTCN model shows remarkable tolerance to the quantity and quality of the training data. As a proof of concept demonstration, the inverse design of a wavelength demultiplexer is used to verify the effectiveness of the PTCN model. The correlation coefficient of the prediction by the presented PTCN model remains greater than 0.974 even when the size of training data is decreased to 17%. The experimental results show a good agreement with predictions, and demonstrate a wavelength demultiplexer with an ultra-compact footprint of 2.6×2.6µm², a high transmission efficiency with a transmission loss of -2dB, a low reflection of -10dB, and low crosstalk around -7dB simultaneously.

Sensitivity Improvement of Multi-Slot Subwavelength Bragg Grating Refractive Index Sensors by Increasing the Waveguide Height or Suspending the Sensor

We present two methods of improving wavelength sensitivity for multi-slot sub-wavelength Bragg grating (MS-SW BG) refractive index sensors. The sensor structure is designed to have high optical mode confinement in the gaps between the silicon pillars whereby the surrounding medium interaction is high, thus improving the sensitivity. Further sensitivity improvements are achieved by increasing the waveguide height or suspending the sensor. The second option, sensor suspension, additionally requires supporting modifications in which case various configurations are considered. After the optimization of the parameters the sensors were fabricated. For the case of a waveguide height increase to 500 nm, the sensitivity of 850 nm/RIU was obtained; for sensor suspension with fully etched holes, 922 nm/RIU; for the case of not fully etched holes, 1100 nm/RIU; with the sensor lengths of about 10 µm for all cases. These values show improvements by 16.5%, 25%, and 50.5%, respectively, compared to the previous result where the height was fixed to 340 nm.

Ultra-compact dual-mode mode-size converter for silicon photonic few-mode fiber interfaces

Fiber couplers usually take a lot of space on photonic integrated circuits due to the large mode-size mismatch between the waveguide and fiber, especially when a fiber with larger core is utilized, such as a few-mode fiber. We demonstrate experimentally that such challenge can be overcome by an ultra-compact mode-size converter with a footprint of only 10 µm. Our device expands TE₀ and TE₁ waveguide modes simultaneously from a 1-µm wide strip waveguide to an 18-µm wide slab on a 220-nm thick silicon-on-insulator, with calculated losses of 0.75 dB and 0.68 dB, respectively. The fabricated device has a measured insertion loss of 1.02 dB for TE₀ mode and 1.59 dB for TE₁ mode. By connecting the ultra-compact converter with diffraction grating couplers, higher-order modes in a few-mode fiber can be generated with a compact footprint on-chip.

Ultra-broadband and ultra-compact polarization beam splitter based on a tapered subwavelength-grating waveguide and slot waveguide

In this work, we propose an ultra-broadband and ultra-compact polarization beam splitter (PBS) on a standard silicon-on-isolator platform. Assisted by a tapered subwavelength-grating waveguide and a slot waveguide, the working bandwidth of the directional-coupler-based PBS covers the entire O-, E-, S-, C-, L- and U-bands and the coupling length is only 4.6 µm. The insertion losses (ILs) of the device are simulated to be less than 0.8 dB and the extinction ratios (ERs) are larger than 10.9 dB at the wavelength range of 1260-1680 nm for both TE and TM polarizations. The experimental results show the average ILs are less than 1 dB for both polarizations at our measured wavelength ranges, which are consistent with the simulation results. It has the largest 1-dB bandwidth among all the reported broadband PBSs to the best of our knowledge.