Decoding the optical response of nonlinear scattering media: A leap towards highly scalable physical operators.
Is it possible to see through a scattering medium such as ground glass? Traditionally, this would be considered impossible. When light passes through an opaque substance, the information carried in the light becomes “confused”, almost as if undergoing complex encryption.
Recently, a remarkable scientific breakthrough by Professor Choi Wonshik’s team from the IBS Center for Molecular Spectroscopy and Dynamics (IBS CMSD) has revealed a method to exploit this phenomenon in the fields of optical computing and machine learning.
Since 2010, several previous studies have attempted to exploit information lost due to propagation media, such as biological tissues, using mathematics. This has typically been done by using optical operators such as linear scattering matrices, which can be used to determine the input-output ratios of photons as they undergo scattering.
This topic has been of primary research interest to Professor Choi’s team from IBS CMSD, who published many works combining both hardware- and software-based adaptive optics for tissue imaging. Some of their work was demonstrated in new types of microscopes that can see through high-opacity scattering media, such as mouse skulls, as well as perform deep 3D imaging of tissues.
But things get much more complex when nonlinearity enters the equation. If a propagation medium generates nonlinear signals, it can no longer be represented simply by a linear matrix, because the superposition principle is violated. Moreover, measuring the nonlinear input-output characteristics becomes a daunting challenge, setting a demanding stage for research.
Unraveling the mystery of non-linear propagation media
This time, Professor Choi’s team has achieved another scientific breakthrough. They were the first to discover that the optical input-output response of a nonlinear scattering medium can be defined by a third-order tensor, as opposed to a linear matrix.
The third-order tensor is a mathematical object used to represent relationships between three sets of data. Simply put, it is a set of numbers arranged in a three-dimensional structure. Tensors are generalizations of scalars (0th order tensors), vectors (1st order tensors) and matrices (2nd order tensors) and are often used in various fields of mathematics, physics and engineering to describe physical quantities and their relationships .
To demonstrate this, the team used a medium consisting of barium titanate nanoparticles, which generate nonlinear second harmonic generation (SHG) signals due to barium titanate’s inherent non-centrosymmetric properties. These SHG signals appear as a square of the input electric field through the second harmonic process, causing cross terms when multiple input channels are activated simultaneously, which disrupts the linear superposition principle. The researchers devised and experimentally validated a new theoretical framework involving these cross terms in a third-order tensor.
To illustrate this, the researchers measured cross terms by isolating the difference between the output electric fields produced when two input channels were activated simultaneously and when each channel was activated separately. This required an additional 1,176 measurements set of possible combinations of two independent input channels, even with only 49 input channels.
“The effort required to detect cross terms from weak nonlinear signals was significant,” noted Dr. Moon Jungho, the study’s lead author.
Real applications are unleashed
The tensor derived from the nonlinear scattering medium has a higher rank than linear scattering matrices, suggesting its potential as a scalable physical operator. The team demonstrated this through the real-world implementation of nonlinear optical encryption and all-optical logic gates.
First, the team successfully demonstrated that non-linear propagation media can be used for the optical encryption process. When specific image information is fed into the media, the output second harmonic wave signals appear as random patterns, similar to a series of encryption processes.
Conversely, by performing an inverse operation of the third-order tensor representation of the second harmonic wave, the original input information can be retrieved through a decryption process. Using the inverse operation of the tensor’s input-output response, they decoded original signals from randomly encoded SHG signals, offering improved security compared to standard optical encryption using linear propagation media.
Additionally, the integration of digital phase conjugation allowed the researchers to demonstrate all-optical AND logic gates that are activated only when two specific input channels are activated simultaneously. This approach offers potential advantages over silicon-based logic, including reduced power consumption and parallel processing capabilities at light speeds.
This research is expected to open up new frontiers in the fields of optical computing and machine learning. “In the growing field of all-optical machine learning, nonlinear optical layers are key to improving model performance. We are currently investigating how our research can be integrated into this field,” said Professor Choi.
Reference: “Measuring the scattering tensor of a disordered nonlinear medium” by Jungho Moon, Ye-Chan Cho, Sungsam Kang, Mooseok Jang and Wonshik Choi, 31 July 2023, Natural physics.
The study was funded by the Institute for Basic Science.
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