Harnessing Spectral Singularities in Non- Hermitian Cylindrical Structures

Moccia, Massimo; Castaldi, G.; Alù, Andrea; Galdi, Vincenzo

doi:10.1109/tap.2019.2927861

Cited by 17 publications

(11 citation statements)

References 71 publications

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“…Eqs. (72) and (73) are respectively known as the "reflection reciprocity" and "unitarity" relations. The latter implies that, for a real potential, R l/r and T are bounded functions.…”

Section: Spectral Singularities and Lasingmentioning

confidence: 99%

“…This involves the computation of the M 22 (k) entry of the transfer matrix and finding the values of the physical parameters of the system for which M 22 (k) has a real and positive zero k ⋆ . This method has the advantage of being applicable to lasers with a variety of geometries and special properties [60,61,62,63,64,65,66,67,68,69,70,71,73,72].…”

Section: Spectral Singularities and Lasingmentioning

confidence: 99%

“…The classical real reflectionless potentials studied in [93] are not invisible for all wavenumbers, because they do not satisfy T (k) = 1 for all k ∈ Z + . We can however use (73) to conclude that T (k) is a phase factor, i.e., there is a function τ : R → R such that T (k) = e iτ (k) . This implies that if τ (k ✶ ) in an integer multiple of 2π for some k ✶ ∈ R + , then the potential is bidirectionally invisible for k = k ✶ .…”

Section: Reflectionless and Invisible Potentialsmentioning

confidence: 99%

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Transfermatrix in scattering theory: a survey of basic properties and recent developments

Mostafazadeh¹

2020

Turk J Phys

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We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential scattering such as transfer matrix and its analyticity, multi-delta-function and locally periodic potentials, Jost solutions, spectral singularities and their time-reversal, and unidirectional reflectionlessness and invisibility. We then offer a simple derivation of the Lippmann-Schwinger equation and Born series, and discuss the Born approximation. Next, we outline a recently developed dynamical formulation of timeindependent scattering theory in one dimension. This formulation relates the transfer matrix and therefore the solution of the scattering problem for a given potential to the solution of the time-dependent Schrödinger equation for an effective non-unitary two-level quantum system. We provide a self-contained treatment of this formulation and some of its most important applications. Specifically, we use it to devise a powerful alternative to the Born series and Born approximation, derive dynamical equations for the reflection and transmission amplitudes, discuss their application in constructing exact tunable unidirectionally invisible potentials, and use them to provide an exact solution for single-mode inverse scattering problems. The latter, which has important applications in designing optical devices with a variety of functionalities, amounts to providing an explicit construction for a finite-range complex potential whose reflection and transmission amplitudes take arbitrary prescribed values at any given wavenumber.

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“…Eqs. (72) and (73) are respectively known as the "reflection reciprocity" and "unitarity" relations. The latter implies that, for a real potential, R l/r and T are bounded functions.…”

Section: Spectral Singularities and Lasingmentioning

confidence: 99%

Section: Spectral Singularities and Lasingmentioning

confidence: 99%

Section: Reflectionless and Invisible Potentialsmentioning

confidence: 99%

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Transfermatrix in scattering theory: a survey of basic properties and recent developments

Mostafazadeh¹

2020

Turk J Phys

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“…Non-Hermitian optics concepts are particularly intriguing in ENZ media, where the effects of relatively low levels of loss and/ or gain can be dramatically enhanced (30)(31)(32). For instance, recent studies have demonstrated a variety of interesting effects including tunneling (33), waveguiding (34), coherent perfect absorption (35), immunity to impurities (36), exceptional points and spectral singularities (37,38), and nonlinear and nonreciprocal effects (17).…”

mentioning

confidence: 99%

“…dealing with cylindrical non-Hermitian configurations (38,52), it has been shown that unconditional stability could be, in principle, attained by suitably tailoring the dispersion properties of the material constituents. In SI Appendix, Fig.…”

mentioning

confidence: 99%

Non-Hermitian doping of epsilon-near-zero media

Coppolaro

Moccia

Castaldi

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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In solid-state physics, “doping” is a pivotal concept that allows controlling and engineering of the macroscopic electronic and optical properties of materials such as semiconductors by judiciously introducing small concentrations of impurities. Recently, this concept has been translated to two-dimensional photonic scenarios in connection with host media characterized by vanishingly small relative permittivity (“epsilon near zero”), showing that it is possible to obtain broadly tunable effective magnetic responses by introducing a single, nonmagnetic doping particle at an arbitrary position. So far, this phenomenon has been studied mostly for lossless configurations. In principle, the inevitable presence of material losses can be compensated via optical gain. However, taking inspiration from quantum (e.g., parity−time) symmetries that are eliciting growing attention in the emerging fields of non-Hermitian optics and photonics, this suggests considering more general gain−loss interactions. Here, we theoretically show that the photonic doping concept can be extended to non-Hermitian scenarios characterized by tailored distributions of gain and loss in either the doping particles or the host medium. In these scenarios, the effective permeability can be modeled as a complex-valued quantity (with the imaginary part accounting for the gain or loss), which can be tailored over broad regions of the complex plane. This enables a variety of unconventional optical responses and waveguiding mechanisms, which can be, in principle, reconfigured by varying the optical gain (e.g., via optical pumping). We envision several possible applications of this concept, including reconfigurable nanophotonics platforms and optical sensing, which motivate further studies for their experimental validation.

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