Uday K. Khankhoje

Bio: Uday K. Khankhoje is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Inverse problem & Inverse scattering problem. The author has an hindex of 10, co-authored 46 publications receiving 285 citations. Previous affiliations of Uday K. Khankhoje include University of Southern California & California Institute of Technology.

Embedding Deep Learning in Inverse Scattering Problems

Abstract: In this paper, we introduce a deep-learning-based framework to solve electromagnetic inverse scattering problems. This framework builds on and extends the capabilities of existing physics-based inversion algorithms. These algorithms, such as the contrast source inversion, subspace-optimization method, and their variants face a problem of getting trapped in false local minima when recovering objects with high permittivity. We propose a novel convolutional neural network architecture, termed the contrast source network, that learns the noise space components of the radiation operator. Together with the signal space components directly estimated from the data, we iteratively refine the solution and show convergence to the correct solution in cases where traditional techniques fail without any significant increase in computational time. We also propose a novel multiresolution strategy that helps in producing high resolution solutions without any significant increase in computational costs. Through extensive numerical experiments, we demonstrate the ability to recover high permittivity objects that include homogeneous, heterogeneous, and lossy scatterers.

Inverse Scattering Using a Joint $L1-L2$ Norm-Based Regularization

Abstract: Inverse scattering problems suffer from ill-posedness and ill-conditioning, necessitating the use of regularization methods to get meaningful solutions. Commonly used regularizations are $L2$ norm based, but these generate over-smooth solutions. We propose a regularization method using both the $L1$ and $L2$ norms to obtain sharp object boundaries, while also achieving good interior reconstruction of the object permittivity. Knowledge about the permittivity can also be used as a priori information. The applicability of the method is demonstrated on synthetically generated data for two-dimensional (2-D) microwave imaging using the Born-iterative method (BIM). The optimization routine systematically estimates all parameters, while minimizing the cost function. Different objects chosen to represent realistic features have been considered to evaluate the performance. The reconstructed images indicate that the method can produce accurate object localization, shape identification, and good permittivity estimation.

Modelling and Fabrication of GaAs Photonic-Crystal Cavities for Cavity Quantum Electrodynamics

Abstract: In this paper, we present recent progress in the growth, modelling, fabrication and characterization of gallium arsenide (GaAs) two-dimensional (2D) photonic-crystal slab cavities with embedded indium arsenide (InAs) quantum dots (QDs) that are designed for cavity quantum electrodynamics (cQED) experiments. Photonic-crystal modelling and device fabrication are discussed, followed by a detailed discussion of different failure modes that lead to photon loss. It is found that, along with errors introduced during fabrication, other significant factors such as the presence of a bottom substrate and cavity axis orientation with respect to the crystal axis, can influence the cavity quality factor (Q). A useful diagnostic tool in the form of contour finite-difference time domain (FDTD) is employed to analyse device performance.

GaAs Photonic Crystal Slab Nanocavities: Growth, Fabrication, and Quality Factor

Abstract: In an effort to understand why short wavelength (~1000 nm) GaAs-based photonic crystal slab nanocavities have much lower quality factors (Q) than predicted (and observed in Si), many samples were grown, fabricated into nanocavities, and studied by atomic force, transmission electron, and scanning electron microscopy as well as optical spectroscopy. The top surface of the AlGaAs sacrificial layer can be rough even when the top of the slab is smooth; growth conditions are reported that reduce the AlGaAs roughness by an order of magnitude, but this had little effect on Q. The removal of the sacrificial layer by hydrogen fluoride can leave behind a residue; potassium hydroxide completely removes the residue, resulting in higher Qs.

Computation of Radar Scattering From Heterogeneous Rough Soil Using the Finite-Element Method

Abstract: A 2-D vector-element-based finite-element method (FEM) is used to calculate the radar backscatter from 1-D bare rough soil surfaces which can have an underlying heterogeneous substrate. Monte Carlo simulation results are presented for scattering at L-band (λ = 0.24 m). For homogeneous soils with rough surfaces, the results of FEM are compared with the predictions of the small perturbation method. In the case of heterogeneous substrates, soil moisture (and, hence, soil permittivity) is assumed to vary as a function of depth. In this case, the results of FEM are compared with those of the transfer matrix method for flat soil surfaces. In both cases, a good agreement is found. For homogeneous rough soils, it is found that polarimetric radar backscatter and copolarized phase difference have a nonlinear relationship with soil moisture. Finally, it is found that the nature of the soil moisture variation in the top few centimeters of the soil has a strong influence on the backscatter and, hence, on the inferred soil moisture content.

The Quantum Theory of Light

Abstract: (b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

Regularization Of Inverse Problems

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QED: The Strange Theory of Light and Matter

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Physics-informed neural networks for inverse problems in nano-optics and metamaterials.

Abstract: In this paper, we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the finite element method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.