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1 - He-Ne laser speckle
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2 - Interference fringes in a soap bubble
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3 - Fractal electron tree or Lichtenberg figure

About us

We are a theoretical research group at the School of Electrical and Electronic Engineering and the Institute for Digital Molecular Analytics and Science at Nanyang Technological University, Singapore. The group is lead by Assistant Professor Matthew R. Foreman.

Our research focuses on optical and plasmonic sensing, polarisation sensitive imaging, disordered media and electromagnetic theory. More information on some of our past and present projects can be found by visiting our Research pages.

Recent news

PhD scholarship available. July 31st application deadline.

13 May 2024: Looking for a PhD in theoretical optics, information theory or biosensing? Why not consider joining the Optical Theory Group in EEE at Nanyang Technological University in Singapore? We have a scholarship available for the January 2025 intake! The application deadline is 31st July 2024. Further details can be found here. Some available projects are listed here, but we are always open to discuss possible research with you to ensure the best fit. Please contact Matthew Foreman for further information.

New arXiv preprint

7 May 2024: We have uploaded some of our latest work to arXiv. This work reports on a dual-pool based bootstrapping approach to improve computation times when using cascaded random matrix models. We investigate the statistical biases and correlations that can be introduced through use of such a technique and show that in practical domains these are fortunately of little practical concern.

Joint ICCAS-IDMxS workshop

7 May 2024: Today we were at the ICCAS-IDMxS Joint Workshop. Thanks to everyone who joined us. There was an interesting and diverse range of talks and some stimulating discussions to follow. I look forward to the next one.

Recent publications

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N. Byrnes, G. R. W. Greaves and M. R. Foreman, "Bootstrapping cascaded random matrix models: Correlations in permutations of matrix products" arXiv , 2405.02541 (2024).

Abstract : Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for example optical scattering or electron transport, typically necessitates cascading of multiple random matrices drawn from an underlying ensemble for thin media, greatly increasing computational burden. Here we propose a dual pool based bootstrapping approach to speed up statistical studies of scattering in thick random media. We examine how potential matrix reuse in this approach can impact statistical estimates of population averages. Specifically, we discuss how both bias and additional variance in the sample mean estimator are introduced through bootstrapping. In the diffusive scattering regime, the extra estimator variance is shown to originate from samples in which cascaded transfer matrices are permuted matrix products. Through analysis of the combinatorics and cycle structure of permutations we quantify the resulting correlations. Proofs of several analytic formulae enumerating the frequency with which correlations of different strengths occur are derived. Extension to the ballistic regime is briefly considered.

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N. Byrnes and M. R. Foreman, "Random matrix theory of polarized light scattering in disordered media" Waves Random Complex Media , DOI: 10.1080/17455030.2022.2153305 (2022).

Abstract : In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering matrices automatically satisfy the physical constraints of unitarity, reciprocity and time reversal, whilst also incorporating the polarization properties of electromagnetic waves and scattering anisotropy. Our technique therefore enables statistical study of a variety of polarization phenomena, including depolarization rates and polarization-dependent scattering by chiral particles. In this vein, we perform numerical simulations for media containing isotropic and chiral spherical particles of different sizes for thicknesses ranging from the single to multiple scattering regime and discuss our results, drawing comparisons to established theory.

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H. Lee, J. Berk, A. Webster, D. Kim and M. R. Foreman, "Label-free detection of single nanoparticles with disordered nanoisland surface plasmon sensor" Nanotechnology 33, 165502 (2022).

Abstract : We report sensing of single nanoparticles using disordered metallic nanoisland substrates supporting surface plasmon polaritons (SPPs). Speckle patterns arising from leakage radiation of elastically scattered SPPs provides a unique fingerprint of the scattering microstructure at the sensor surface. Experimental measurements of the speckle decorrelation are presented and shown to enable detection of sorption of individual gold nanoparticles and polystyrene beads. Our approach is verified through bright-field and fluorescence imaging of particles adhering to the nanoisland substrate.


Our research is supported by generous funding from:

Microsoft Research
Ministry of Education