Research Project: Doğrusal Olmayan Saçilma Kuramı, Doğrusal Olmayan Spektral Tekillikler Ve Tek Yönlü Görünmezlik
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Contributors
Funders
ID
TB.00222
Authors
Mostafazadeh, Ali
Faculty Member
Publications
Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity
(Elsevier Science Bv, 2017) Mostafazadeh, Ali; Oflaz, Neslihan; Department of Mathematics; Yes; College of Sciences
We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.
Blowing up light: a nonlinear amplification scheme for electromagnetic waves
(Optical Society of America (OSA), 2018) Ghaemidizicheh, Hamed; Hajizadeh, Sasan; Mostafazadeh, Ali; Department of Mathematics; Department of Physics; Graduate School of Sciences and Engineering; Yes; College of Sciences; GRADUATE SCHOOL OF SCIENCES AND ENGINEERING
We use the blow-up solutions of nonlinear Helmholtz equations to introduce a nonlinear resonance effect that is capable of amplifying electromagnetic waves of a particular intensity. To achieve this, we propose a scattering setup consisting of a Kerr slab with a negative (defocusing) Kerr constant placed to the left of a linear slab in such a way that a left-incident coherent transverse electric wave with a specific incidence angle and intensity realizes a blow-up solution of the corresponding Helmholtz equation whenever its wavenumber k takes a certain critical value, k(*). For k = k(*), the solution blows up at the right-hand boundary of the Kerr slab. For k < k(*), the setup defines a scattering system with a transmission coefficient that diverges as (k - k(*))(-4) for k -> k(*). By tuning the distance between the slabs, we can use this setup to amplify coherent waves with a wavelength in an extremely narrow spectral band. For nearby wavelengths, the setup serves as a filter. Our analysis makes use of a nonlinear generalization of the transfer matrix of the scattering theory as well as properties of unidirectionally invisible potentials.
Spectral singularities and tunable slab lasers with 2D material coating
(Optical Society of America (OSA), 2020) Mostafazadeh, Ali; Ghaemi-Dizicheh, Hamed; Sarısaman, Mustafa; Department of Mathematics; Department of Physics; Yes; College of Sciences
We investigate linear and nonlinear spectral singularities in the transverse electric and transverse magnetic modes of a slab laser consisting of an active planar slab sandwiched between a pair of graphene or Weyl semimetal thin sheets. The requirement of the presence of linear spectral singularities gives the laser threshold condition while the existence of nonlinear spectral singularities due to an induced weak Kerr nonlinearity allows for computing the laser output intensity in the vicinity of the threshold. The presence of the graphene and Weyl semimetal sheets introduces additional physical parameters that we can use to tune the output intensity of the laser. We provide a comprehensive study of this phenomenon and report peculiarities of lasing in the transverse magnetic (TM) modes of the slab with Weyl semimetal coatings. In particular, we reveal the existence of a critical angle such that no lasing seems possible for TM modes of the slab with the smaller emission angle. Our results suggest that for TM modes with an emission angle slightly exceeding the critical angle, the laser output intensity becomes highly sensitive to the physical parameters of the coating.
Spectral singularities, threshold gain, and output intensity for a slab laser with mirrors
(Academic Press Inc., 2018) Doğan, Keremcan; Mostafazadeh, Ali; Sarısaman, Mustafa; Department of Mathematics; Department of Physics; Yes; College of Sciences
We explore the consequences of the emergence of linear and non-linear spectral singularities in TE modes of a homogeneous slab of active optical material that is placed between two mirrors. We use the results together with two basic postulates regarding the behavior of laser light emission to derive explicit expressions for the laser threshold condition and output intensity for these modes of the slab and discuss their physical implications. In particular, we reveal the details of the dependence of the threshold gain and output intensity on the position and properties of the mirrors and on the real part of the refractive index of the gain material. (C) 2018 Elsevier Inc. All rights reserved.
Nonlinear spectral singularities and laser output intensity
(Iop Publishing Ltd, 2017) Ghaemidizicheh, Hamed; Mostafazadeh, Ali; Sarısaman, Mustafa; Department of Mathematics; Department of Physics; Yes; College of Sciences
The mathematical notion of spectral singularity admits a description in terms of purely outgoing solutions of a corresponding linear wave equation. This leads to a nonlinear generalization of this notion for nonlinearities that are confined in space. We examine the nonlinear spectral singularities in arbitrary transverse electric (TE) and transverse magnetic (TM) modes of a mirrorless slab laser that involves a weak Kerr nonlinearity. This provides a computational scheme for the determination of the laser output intensity I for these modes. In particular, we offer an essentially mathematical derivation of the linear-dependence of I on the gain coefficient g and obtain an explicit analytic expression for its slope. This shows that if the real part eta of the refractive index of the slab does not exceed 3, there is a lower bound on the incidence angle theta below which lasing in both its TE and TM modes requires eta to be shifted by a small amount as g surpasses the threshold gain. Our results suggest that lasing in the oblique TM modes of the slab is forbidden if the incidence (emission) angle of the TM mode exceeds the Brewster's angle.
