Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media
01 Jul 2016-Journal of Quantitative Spectroscopy & Radiative Transfer (Elsevier)-Vol. 178, pp 158-166
TL;DR: In this paper, the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics is explored. But the authors do not consider the effect of the time-varying permittivity of the media.
Abstract: We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period τ, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell׳s equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light–matter interaction in time-varying structures.
Citations
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TL;DR: In this article, an exact mathematical framework for electromagnetic wave propagation in periodically time-modulated media, in which the permittivity is homogenous and modulated in a step-varying fashion, is presented.
Abstract: We present an exact mathematical framework for electromagnetic wave propagation in periodically time-modulated media, in which the permittivity is homogenous and modulated in a step-varying fashion. By using Hill’s equation theory, we show that this problem has analytical solutions. We connect the dispersion relation, which exhibits $k-$ gaps, with the Hill stability analysis, providing an alternative mathematical description for wave propagation in temporal crystals. Our analysis, which is exact and transposable to other kinds of waves or modulation schemes, provides general useful physical and mathematical insights, complementing the use of numerical techniques such as finite differences in the time domain, or harmonic balance schemes, with a more transparent and practical design tool. The present analytical transient mathematical analysis, in contrast with the existing frequency-domain numerical approaches, can exhibit the parametric properties of electromagnetic waves inside a time periodic medium. For this reason, it can be a useful tool for the design of active microwave and optical devices, which employ time periodic wave medium modulation to filter or parametrically amplify wave signals.
51 citations
20 Jan 2021
TL;DR: In this paper, the authors investigate the use of temporal switching to reduce signal reflections from a thin grounded slab over broader bandwidths, and develop an ab initio formalism that can model a broad class of time-switched structures.
Abstract: Wave absorption in time-invariant, passive thin films is fundamentally limited by a trade-off between bandwidth and overall thickness. In this work, we investigate the use of temporal switching to reduce signal reflections from a thin grounded slab over broader bandwidths. We extend quasi-normal mode theory to time switching, developing an ab initio formalism that can model a broad class of time-switched structures. Our formalism provides optimal switching strategies to maximize the bandwidth over which minimal reflection is achieved, showing promising prospects for time-switched nanophotonic and metamaterial systems to overcome the limits of time-invariant, passive structures.
43 citations
TL;DR: The efforts to develop the biomolecule-based synthesis of 3D chiral plasmonic materials are reviewed and the vision that as in biological systems, chirality can be programmed at the molecular level and hierarchically transferred at multiple scales to develop macroscopic chiralities is shared.
Abstract: Over the last two decades, nanophotonics, including plasmonics and metamaterials, have promised compelling opportunities for exotic control over light-matter interactions. The strong chiral light-matter interaction is a representative example. Three-dimensional (3D) chirality has existed naturally only in organic molecules and bio-organisms, but a negligible chiroptic effect was attained with these naturally occurring materials because of their small absorption cross sections. However, inspired by biological chirality, nanophotonic chiral materials have greatly expanded the design space of accessible chiroptic effects (e.g., pushing the chiral light-matter interaction to an exceptional regime, such as a broad-band circular polarizer, negative refractive index, and sensitive chiral sensing). Nevertheless, it is still a challenge to achieve precisely defined and dynamically reconfigurable chiral morphologies that further increase the chiroptic effect. Biological systems continue to inspire approaches to the design and synthesis of precisely defined 3D nanostructures. In particular, a living organism can program the evolutionary pathway of highly complexed 3D chiral morphology precisely from the molecular scale to the macroscopic scale while simultaneously enabling dynamic reconfiguration of their chirality. What if we could harness the power of biological selectivity and evolutionary capability in synthesizing chiral plasmonic materials? We envisioned that platform technology mimicking biological principles would enable control of 3D chiral structures for effective plasmonic interactions with polarized light and further impart the concept of time-dependent evolution (3D + 1D = 4D) to bring about responsive and dynamic changes in chiral plasmonics. In this Account, we review our efforts to develop the biomolecule-based synthesis of 3D chiral plasmonic materials and share the vision that as in biological systems, chirality can be programmed at the molecular level and hierarchically transferred at multiple scales to develop macroscopic chirality. Accompanied by a biomimetic time-dependent chirality of singular plasmonic nanometals, we also summarize recent achievements in the chemistry and nanophotonics communities pursuing 4D plasmonics that are closely related to our research. The biomimetic and bioinspired approaches discussed in this Account will provide new synthetic insights into implementing chiral nanomaterials and extend the range of accessible nanophotonic design. We hope that the molecular encoding approach will be useful to achieve dynamic light-matter interactions at unprecedented dimensions, time scales, and chirality.
37 citations
TL;DR: In this paper, the authors studied the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion and showed that the second-order nature of the dielectric function now gives rise to two shifted frequencies.
Abstract: We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-traveling in a (generally lossy) Lorentzian-like medium scatters from the temporal interface that results from an instantaneous and homogeneous abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffices to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration.
31 citations
TL;DR: In this article, a time-transitioning state matrix is proposed to study electromagnetic wave phenomena under time-varying media and points out novel physical insights connecting the energy transitions and electromagnetic modes with exceptional point physics and operator symmetries.
Abstract: In this article, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We assume a time-variation of permittivity, permeability, and conductivity, and derive the appropriate time-domain solutions based on the causality state at a past observation time. We formulate a time-transitioning state matrix and connect the unusual energy transitions of electromagnetic fields in time-varying media with the exceptional point theory. This state-matrix approach allows us to analyze further the electromagnetic waves in terms of parity and time-reversal symmetries and signify parity-time symmetric wave-states without the presence of a spatially symmetric distribution of gain and loss, or any inhomogeneities and material periodicity. This article provides a useful arsenal to study electromagnetic wave phenomena under time-varying media and points out novel physical insights connecting the resulting energy transitions and electromagnetic modes with exceptional point physics and operator symmetries.
30 citations
References
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Book•
01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
Additional excerpts
...By building a new convergent variable 1/ξ = −e−t/τ at t > 0, in fact, one can re-write the solution (25) as [58] Dt>0 (r, t) = DI0 e i(k·r−ωIt) × [ Γ (c) Γ (b− a) Γ (b) Γ (c− a) e−at/τF ( a, a+ 1− c, a+ 1− b,−e−t/τ )...
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...Equation (22) has an exact solution expressed in terms of the hypergeometric function, F (ξ) = CF (a, b, c, ξ) with C being a constant, provided that ν(2) ≡ −α−β = −ω(2) Iτ(2) to ensure the convergence of the solution when ξ = −e → 0 [58]....
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Book•
01 Jan 1960
TL;DR: In this article, the propagation of electromagnetic waves and X-ray diffraction of X rays in crystals are discussed. But they do not consider the effects of superconductivity on superconducting conductors.
Abstract: Electrostatics of conductors Static magnetic field Superconductivity The propagation of electromagnetic waves Spatial dispersion Diffraction of X rays in crystals.
12,543 citations
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03 Jul 1995
TL;DR: In this paper, the authors developed the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory, and investigated the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions.
Abstract: Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
8,188 citations
"Electromagnetic wave propagation in..." refers background in this paper
...Controlling the optical properties of photonic structures has been a topic of significant interest for last few decades both in fundamental [1, 2] and applied research [3, 4, 5]....
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TL;DR: In this method, non-linear susceptibility tensors are introduced which relate the induced dipole moment to a power series expansion in field strengths and the various experimental observations are described and interpreted in terms of this formalism.
Abstract: Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.
3,893 citations
"Electromagnetic wave propagation in..." refers background in this paper
...Controlling the optical properties of photonic structures has been a topic of significant interest for last few decades both in fundamental [1, 2] and applied research [3, 4, 5]....
[...]
...While the free-carriers are typically induced by strong pump pulses creating electron-hole pairs in semiconductors [13, 14, 15, 16], the Kerr effect arises from the non-linear (instantaneous) response of bound electrons to the applied field [1, 17, 18, 19]....
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