Researcher:
Ghaemidizicheh, Hamed

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PhD Student

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Hamed

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Ghaemidizicheh

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Ghaemidizicheh, Hamed

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2017 - 20182

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Researcher Of Publications: search.filters.isAuthorOfPublication.325d8773-39dd-4a0a-b0c5-61801f7a0046

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    Nonlinear spectral singularities and laser output intensity
    (Iop Publishing Ltd, 2017) N/A; Department of Mathematics; Department of Mathematics; Ghaemidizicheh, Hamed; Mostafazadeh, Ali; Sarısaman, Mustafa; PhD Student; Faculty Member; Researcher; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; College of Sciences; N/A; 4231; 217652
    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.
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    Blowing up light: a nonlinear amplification scheme for electromagnetic waves
    (Optical Society of America (OSA), 2018) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Ghaemidizicheh, Hamed; Hajizadeh, Sasan; Faculty Member; PhD Student; Department of Mathematics; Department of Physics; Graduate School of Sciences and Engineering; 4231; N/A; N/A
    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.