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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

New arXiv preprint

22 Aug 2024: We just posted some exciting new results from the Optical Theory Group to arXiv. Specifically, we demonstrate a novel perturbation theory based on generalised Wigner-Smith operators. This provides a powerful tool for describing resonance shifts and broadening in open non-Hermitian systems. We also have another work in the pipeline to expand the domain of validy of the presented theory, so watch this space for more updates.

CLEO Pacific Rim 2024

9 Aug 2024: Matthew has just got back from CLEO Pacific Rim, held in Incheon, South Korea. He was honoured to be asked to give a tutorial talk on digital molecular analytics at the conference, where he also presented on our latest random matrix theory results. Whilst in South Korea, Matthew also attended the NTU-Yonsei Workshop on Photonics and Quantum Applications. It was great to meet many new colleagues from around Asia and beyond and even to catch up with a few surprise old friends as well.

New PhD Student - Sulagna Dutta

1 Aug 2024: The start of term has quickly come back around and this semester brings a new IGP PhD student, Sulagna Dutta, to the group to whom we extend a very warm welcome. Sulagna got her BSc from St Xaviers College, Kolkata and holds a MSc and MTech from Calcutta University and IIT Delhi respectively. Her project will focus on various aspects of polarised light in scattering media and how it can be leveraged for imaging.

Recent publications

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Abstract : Resonances of open non-Hermitian systems are associated with the poles of the system scattering matrix. Perturbations of the system cause these poles to shift in the complex frequency plane. In this work, we introduce a novel method for calculating shifts in scattering matrix poles using generalized Wigner-Smith operators. We link our method to traditional cavity perturbation theory and validate its effectiveness through application to complex photonic networks. Our findings underscore the versatility of generalized Wigner-Smith operators for analyzing a broad spectrum of resonant systems and provides new insight into resonant properties of non-Hermitian systems.

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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" Phys. Rev. E 110, 015308 (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.

Funding

Our research is supported by generous funding from:

Microsoft Research
IDMxS
NTU
Ministry of Education