Research Project: Spektral Tekillikler ve Optik Sistemlerdeki Uygulamaları
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Contributors
Funders
ID
TB.00066
Authors
Mostafazadeh, Ali
Faculty Member
Publications
Semiclassical analysis of spectral singularities and their applications in optics
(American Physical Society (APS), 2011) Mostafazadeh, Ali; Department of Mathematics; Department of Physics; Yes; College of Sciences
Motivated by possible applications of spectral singularities in optics, we develop a semiclassical method of computing spectral singularities. We use this method to examine the spectral singularities of a planar slab gain medium whose gain coefficient varies due to the exponential decay of the intensity of the pumping beam inside the medium. For both singly and doublypumped samples, we obtain universal upper bounds on the decay constant beyond which no lasing occurs. Furthermore, we show that the dependence of the wavelength of the spectral singularities on the value of the decay constant is extremely mild. This is an indication of the stability of optical spectral singularities.
Perturbative analysis of spectral singularities and their optical realizations
(American Physical Society (APS), 2012) Mostafazadeh, Ali; Rostamzadeh, Saber; Department of Mathematics; Yes; College of Sciences
We develop a perturbative method of computing spectral singularities of a Schrodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as antilasing. We use our general results to establish the exactness of the nth-order perturbation theory for an arbitrary complex potential consisting of n delta functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.
Nonlinear spectral singularities for confined nonlinearities
(American Physical Society (APS), 2013) Mostafazadeh, Ali; Department of Mathematics; Yes; College of Sciences
We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrodinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex delta-function potential that is subject to a general confined nonlinearity.
Spectral singularities and whispering gallery modes of a cylindrical gain medium
(American Physical Society (APS), 2013) Mostafazadeh, Ali; Sarısaman, Mustafa; Department of Mathematics; Yes; College of Sciences
Complex scattering potentials can admit scattering states that behave exactly like a zero-width resonance. Their energy is what mathematicians call a spectral singularity. This phenomenon admits optical realizations in the form of lasing at the threshold gain, and its time-reversal is responsible for antilasing. We study spectral singularities and whispering gallery modes (WGMs) of a cylindrical gain medium. In particular, we introduce a class of WGMs that support a spectral singularity and, as a result, have a divergent quality factor. These singular gallery modes (SGMs) are excited only if the system has a positive gain coefficient, but typically the required gain is extremely small. More importantly, given any amount of gain, there are SGMs requiring smaller gain than this amount. This means that, in principle, the system lacks a lasing threshold. Furthermore, the abundance of these modes allows for configurations where a particular value of the gain coefficient yields an effective excitation of two distant SGMs. This induces lasing at two different wavelengths.
Spectral singularities in the surface modes of a spherical gain medium
(American Physical Society (APS), 2013) Mostafazadeh, Ali; Sarısaman, Mustafa; Department of Mathematics; Yes; College of Sciences
We study the surface modes of a homogenous spherical gain medium and provide a comprehensive analytic treatment of a special class of these modes that supports spectral singularities. Because the latter have a divergent quality factor, we call them the singular gallery modes. We show that they can be excited using arbitrarily small amounts of gain, and as a result, the system lacks a lasing threshold, effectively. This shows that we can realize spectral singularities in the surface modes of extremely small spherical samples with modest amounts of gain. We also examine the possibility of exciting singular gallery modes with different wavelengths using the same amount of gain. This corresponds to the situation where the system undergoes simultaneous lasing at different wavelengths.
