🔬 optics

Arbitrary control over multimode wave propagation for machine learning

This paper presents a two-dimensional programmable waveguide with approximately $10^4$ spatial degrees of freedom that enables arbitrary control over multimode wave propagation to perform single-pass neural network inference while offering significant improvements in device area efficiency and scaling compared to traditional discrete-component architectures.

Original authors: Tatsuhiro Onodera, Martin M. Stein, Benjamin A. Ash, Mandar M. Sohoni, Melissa Bosch, Ryotatsu Yanagimoto, Marc Jankowski, Timothy P. McKenna, Tianyu Wang, Gennady Shvets, Maxim R. Shcherbakov, Logan

Published 2026-06-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Tatsuhiro Onodera, Martin M. Stein, Benjamin A. Ash, Mandar M. Sohoni, Melissa Bosch, Ryotatsu Yanagimoto, Marc Jankowski, Timothy P. McKenna, Tianyu Wang, Gennady Shvets, Maxim R. Shcherbakov, Logan G. Wright, Peter L. McMahon

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to solve a complex puzzle, like recognizing a handwritten number or identifying a spoken vowel. Usually, computers do this by passing data through a long line of tiny, separate gears and levers (discrete components). Each gear does a small job, and the data has to travel from one to the next. This takes up a lot of space and uses a lot of energy, especially as the puzzles get bigger.

The researchers in this paper built a completely different kind of machine. Instead of using a line of separate gears, they created a single, giant, programmable "sheet" of glass (a waveguide) that acts like a smart, shape-shifting lens.

Here is how their invention works, broken down into simple concepts:

1. The "Smart Sheet" vs. The "Gear Train"

Think of traditional computer chips as a train of separate train cars. To get from point A to point B, the cargo (data) has to hop from car to car. This is bulky and slow.

This new device is like a single, massive trampoline. Instead of hopping between cars, you throw a ball (a beam of light) onto the trampoline. By changing the tension and shape of the trampoline's surface, you can make the ball bounce in any specific pattern you want. The entire surface works together at once to guide the ball to its destination.

2. How Do They "Shape" the Glass?

You can't just carve this glass like a statue; once it's carved, it's stuck. The researchers needed a way to change the shape of the glass on the fly.

They used a clever trick involving light and electricity:

The Setup: They have a special sheet of glass (Lithium Niobate) sandwiched between electrodes.
The Control: They shine a pattern of green light onto the sheet from above, like a projector showing a picture.
The Magic: Wherever the green light hits, the sheet becomes slightly more conductive (like a wire). This changes the electric field inside the glass. Because of a special property of this glass, changing the electric field changes its refractive index (how much it bends light).
The Result: The projected green light pattern instantly "sculpts" the invisible landscape inside the glass. If you project a "Y" shape, the glass becomes a Y-shaped path for light. If you project a complex maze, the glass becomes a complex maze.

They can change this "sculpting" pattern about 3 times per second, allowing them to reprogram the machine instantly.

3. Doing Math with Light

The goal of the machine is to perform Machine Learning (teaching a computer to recognize patterns).

Input: They take data (like the shape of a handwritten "7") and turn it into a pattern of light beams entering the sheet.
Processing: As the light travels through the sheet, it bounces off the "sculpted" landscape they created. The light waves interfere with each other, mixing and matching in complex ways. This mixing is the math calculation.
Output: The light exits the other side. They measure how bright the light is in different spots. The brightest spot tells them the answer (e.g., "That was a 7!").

They tested this on two tasks:

Vowel Sounds: Identifying which vowel was spoken based on sound frequencies. They got it right 96% of the time.
Handwritten Digits (MNIST): Recognizing numbers from 0 to 9. They got it right 86% of the time.

4. Why Is This a Big Deal? (The "Square Root" Surprise)

Usually, if you want to make a computer that can handle bigger and bigger puzzles (more data), you have to make the machine much, much bigger. If you double the complexity, you usually need four times the space (a square relationship).

The researchers discovered something surprising with their "Smart Sheet." Because they are using the whole sheet at once (multimode interference) rather than a line of gears, the size of the machine only needs to grow by the square root of the complexity.

Analogy: If you want to build a bridge for 100 cars, a traditional design might need to be 100 units long. Their design suggests you might only need a bridge that is 10 units long (since the square root of 100 is 10) to do the same job.

This means their machine could potentially be much smaller and more energy-efficient than current optical computers, especially for very large tasks.

Summary

The team built a reprogrammable optical processor that uses a single sheet of glass to perform complex math. Instead of using thousands of tiny, separate parts, they use a projector to "draw" the math problem directly onto the glass using light. The light then solves the problem as it travels through the glass. They proved this works for recognizing sounds and numbers, and their math suggests this approach could lead to much smaller, faster, and more energy-efficient computers in the future.

Technical Summary: Arbitrary Control over Multimode Wave Propagation for Machine Learning

Problem Statement

Deep neural networks (DNNs) are increasingly constrained by the energy costs associated with their exponential growth in size, particularly the matrix-vector multiplications (MVMs) that dominate their computational load. While optical neural networks (ONNs) offer a promising alternative for energy-efficient MVMs, current integrated photonic approaches face significant scalability limits. The dominant paradigm relies on networks of discrete programmable components (e.g., Mach–Zehnder interferometers, microring resonators) connected by single-mode waveguides. This architecture suffers from two primary bottlenecks:

Routing Complexity: Integrating the $O(N^2)$ electronic control wires required for $N \times N$ matrices through the chip perimeter limits the number of controllable degrees of freedom to a few hundred.
Spatial Inefficiency: Individual optical components are bulky due to wavelength constraints and weak programmability, and substantial chip area is consumed by interconnection regions.

Consequently, existing chips support vector sizes ( $N$ ) far below the threshold ( $N \gtrsim 1000$ ) required for optics to demonstrate a clear energy-efficiency advantage over electronics. The central challenge addressed by this work is how to create a photonic chip with a programmable refractive-index distribution $n(x, z)$ that avoids the integration complexity of electronic wiring while enabling arbitrary control over wave propagation.

Methodology

The authors introduce and demonstrate a 2D-programmable waveguide, a device that treats the entire chip as a continuous, reprogrammable substrate rather than a collection of discrete elements.

Device Architecture and Operating Principle

The device consists of a lithium niobate (LiNbO $_3$ ) slab waveguide sandwiched between a conductive silicon substrate (acting as a ground electrode) and a gold electrode. A photoconductive layer (silicon-rich silicon nitride) is deposited on top of the waveguide.

Refractive Index Modulation: The device utilizes photoconductive gain to induce a spatially varying refractive index change, $\Delta n(x, z)$ . An oscillating bias voltage (up to 1000 V) is applied across the electrodes. When a patterned light projection illuminates the photoconductor, its impedance drops locally, increasing the electric field within the underlying LiNbO $_3$ waveguide.
Electro-Optic Effect: The increased electric field induces a local change in the refractive index via the Pockels effect in the lithium niobate.
Programmability: By projecting arbitrary light patterns onto the device, the authors can sculpt the refractive index distribution across approximately $10^4$ spatial degrees of freedom (a $9 \text{ mm} \times 1 \text{ mm}$ area with $9 \mu\text{m} \times 9 \mu\text{m}$ resolution). The system updates the entire distribution at a rate of 3 Hz.

Training and Machine Learning Implementation

To perform machine learning tasks, the device is trained to map input optical fields to output intensity distributions that correspond to classification labels.

Encoding: Input data vectors are amplitude-encoded into spatial Gaussian modes at the input facet.
Propagation: The light propagates through the programmable waveguide, governed by the paraxial wave equation (Eq. 1 in the paper), where the refractive index profile acts as the trainable weights.
Readout: The output intensity is measured and binned into spatial regions corresponding to class labels.
Training Algorithm: The authors employ physics-aware training, a hybrid in-situ–in-silico backpropagation algorithm. The forward pass is performed physically by the device, while the backward pass (gradient calculation) is computed using a differentiable digital model of the wave propagation. This model was refined with data-driven parameters to account for experimental non-idealities, enabling efficient training despite the large parameter count.

Key Contributions

Demonstration of a 2D-Programmable Waveguide: The authors successfully fabricated and operated a device with $\sim 10,000$ programmable spatial degrees of freedom, capable of arbitrary refractive index sculpting via parallel electro-optic modulation.
High-Dimensional Neural Network Inference: The device performed neural network inference on benchmark tasks with input vectors up to 49 dimensions (MNIST handwritten digits) and 12 dimensions (vowel classification) in a single pass, without digital pre- or post-processing of the linear transformation.
Scaling Analysis: The paper provides theoretical and numerical evidence suggesting that 2D-programmable waveguides offer a superior scaling law for device length compared to discrete component architectures. While traditional approaches often require device length scaling as $N$ (or $N^2$ area), the authors argue that for multimode interference, the required length scales as $\sqrt{N}$ for a given refractive index modulation strength.

Experimental Results

Vowel Classification: The device was trained to classify 7 spoken vowels from a 12-dimensional input vector of formant frequencies. After 300 epochs (approx. 1 hour), the system achieved a 96% test accuracy. The trained refractive index profile evolved from a uniform state to a complex pattern resembling inverse-designed photonic structures.
MNIST Handwritten Digit Classification: The device was trained to classify downsampled 7 $\times$ 7 MNIST images (49-dimensional input) into 10 classes. After 10 epochs (approx. 10 hours), the system achieved 86% test accuracy. This result is comparable to a single-layer digital neural network with a $49 \times 10$ matrix (which achieves 90% on the same downsampled task), demonstrating that the complex multimode wave propagation can effectively perform high-dimensional linear transformations.
Device Performance: The maximum refractive index modulation achieved was approximately $\Delta n \approx 10^{-3}$ . The device exhibited low propagation loss (< 1 dB/cm) and operated with less than 1 mW of electrical power dissipation across the active area.

Significance and Claims

The paper claims that this work represents a significant step toward overcoming the spatial and scalability limits of current integrated photonic neural networks.

Space Efficiency: By replacing discrete components with a continuous, programmable substrate, the device achieves a more space-efficient architecture. The authors note that their prototype supports input dimensions larger than any previously reported on-chip optical neural network based on discrete components.
Energy Efficiency Potential: The work highlights a theoretical path toward the "break-even point" where optical MVMs outperform electronic ones in energy efficiency (estimated at $N \approx 1000$ ). The demonstrated $\sqrt{N}$ scaling for device length suggests that 2D-programmable waveguides could enable all-optical matrix-vector multipliers with dimensions exceeding this threshold, potentially making hybrid neural network architectures (analog optics for linear operations, electronics for non-linearities) energy-competitive.
Reconfigurability: Unlike inverse-designed devices which are fixed after fabrication, this device is fully reconfigurable. The authors suggest this capability could extend beyond machine learning to solving integral equations, combinatorial optimization, and serving as a reconfigurable platform for studying bound states in the continuum and topological photonics.

The authors remain modest regarding the current limitations, acknowledging that the experimental prototype operated in a regime where light was effectively unguided in the transverse direction, and that the current $\Delta n$ and update rates are constrained by material properties and the photoconductive layer design. However, they posit that the demonstrated principle of arbitrary multimode control opens new avenues for optical computing.