Breakthrough in optical computing: Seeing through the “invisible”

Researchers have discovered a method for decoding “scrambled” information using light transmitted through a scattering medium such as ground glass, with potential applications in optical computing and machine learning. The research team demonstrated that the optical input-output response of a nonlinear scattering medium can be represented by a third-order tensor, providing a new approach for logic gates and optical encoding.

Decoding the optical response of nonlinear scattering media: A leap towards highly scalable physical operators.

Is it possible to see through a scattering medium like ground glass? Traditionally, this was considered impossible. When light passes through an opaque substance, the information carried in the light becomes “cluttered”, almost undergoing a complex encoding process.

Recently, a remarkable scientific breakthrough by Professor Choi Wonshik’s group from the IBS Center for Molecular Spectroscopy and Dynamics (IBS CMSD) revealed a method to take advantage of this phenomenon in the fields of electronics. optical mathematics and machine learning.

Since 2010, several previous studies have attempted to exploit information lost by scattering media, such as biological tissue, using mathematics. This is often done using optical operators such as linear scattering matrices, which can be used to determine the input-output relationship of photons as they undergo scattering.

This topic is a key research interest of Professor Choi’s group from IBS CMSD, which has published numerous works combining both hardware- and software-based adaptive optics for tissue imaging. Some of their work has been demonstrated with new types of microscopes that can see through highly opaque scattering media, such as mouse skulls, as well as perform deep 3D imaging of tissues.

The nonlinear scattering medium, as shown in (a), exhibits nonlinear scattering and modulation through nonlinear nanoparticles, making its response impossible to describe using a linear matrix. normally. To measure the nonlinear response, a nonlinear second-harmonic interference system, as shown in (b), was developed. Source: Institute of Basic Sciences

However, things become much more complicated when nonlinearity enters the equation. If the scattering medium produces nonlinear signals, it can no longer be simply represented by a linear matrix because the superposition principle is violated. Furthermore, measuring nonlinear input-output characteristics becomes a difficult challenge, posing a demanding stage for research.

Unraveling the mystery of nonlinear scattering media

This time, Professor Choi’s team achieved another scientific breakthrough. They became the first to discover that the input-output optical response of a nonlinear scattering medium could be determined by a third-order tensor, as opposed to a linear matrix.

A cubic tensor is a mathematical object used to represent relationships between three sets of data. Simply put, it is a series of numbers arranged in a three-dimensional structure. Tensor is a generalization of scalar (zeroth order tensor), vector (1st order tensor) and matrix (2nd order tensor) and is commonly used in various fields of mathematics, physics and engineering to describe Describe physical quantities and their relationships.

The information of light scattered and modulated by the nonlinear scattering medium changes randomly, making it difficult to reconstruct the original information, as shown in the right figure of (a). This can be called optical encryption. However, by knowing the input-output response characteristics, it is possible to reconstruct the original information from the random output blob, as in (b). This process can be thought of as decoding encrypted information. With only linear response characteristics that do not involve cross terms, it is not possible to reconstruct the information accurately, as shown in (c). Source: Institute of Basic Sciences

To demonstrate this, the team used a medium consisting of barium titanate nanoparticles, which produces a nonlinear second harmonic generation (SHG) signal due to the inherent asymmetric properties of barium titanate. These SHG signals appear as the square of the input electric field through a second harmonic process, causing cross terms when multiple input channels are activated simultaneously, breaking the principle of linear superposition . The researchers devised and experimentally validated a new theoretical framework involving these diagonal terms in a cubic tensor.

To illustrate this, the researchers measured cross-terms by isolating the difference between the output electric field generated when the two input channels are activated simultaneously and when each channel is activated separately. . This requires an additional 1,176 measurements to be established by combining two independent input channels, even with only 49 input channels.

“The effort required to detect cross terms from weak nonlinear signals is significant,” said Dr. Moon Jungho, lead author of the study.

Real-world applications are liberating

The tensor obtained from the nonlinear scattering medium has a higher rank than the matrix of the linear scattering medium, indicating its potential as a scalable physical operator. The team demonstrated this through real-world implementations of nonlinear optical encryption and all-optical logic gates.

First, the team successfully demonstrated that nonlinear scattering media can be used for optical encryption. When specific image information is input to the medium, the output second harmonic signal is displayed as a random pattern, like a series of encoding processes.

(a) Nonlinear optical logic circuit implemented using digital phase conjugation method with nonlinear scattering medium. By using the phase conjugate field of the crossover term (c), it is possible to create an AND gate (b) that focuses light only when both input channels are active at the same time. Since all nonlinear input-output responses are captured, it is also possible to implement a multichannel AND gate as in (d). Source: Institute of Basic Sciences

Conversely, by performing the inverse operation of the third-order tensor representation of the second harmonic, the original input information can be retrieved through the decoding process. Using the inverse operation of the tensor input-output response, they decoded the original signals from a randomly encrypted SHG signal, providing enhanced security compared to standard optical encryption. standard using linear scattering media.

Furthermore, the integration of digital phase conjugation allowed the researchers to show all-optical AND logic gates that only activate when two specific input channels are activated simultaneously. This approach offers potential advantages over silicon-based logic, including reduced power consumption and the possibility of light-speed parallel processing.

This research is expected to open new frontiers in the field of optical computing and machine learning. “In the growing field of all-optical machine learning, nonlinear optical layers are key in enhancing model performance. We are currently investigating how our research can be integrated into the field,” said Professor Choi.

Reference: “Scattering tensor measurement of turbulent nonlinear media” by Jungho Moon, Ye-Chan Cho, Sungsam Kang, Mooseok Jang and Wonshik Choi, July 31, 2023, Natural physics.
DOI: 10.1038/s41567-023-02163-8

The research was funded by the Institute of Basic Sciences.