Researcher:
Sarısaman, Mustafa

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Mustafa

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Sarısaman

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Sarısaman, Mustafa

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2011 - 201812

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    Pseudoduality and complex geometry in sigma models
    (World Scientific Publ Co Pte Ltd, 2013) Department of Mathematics; Sarısaman, Mustafa; Researcher; Department of Mathematics; College of Sciences; 217652
    We study the pseudoduality transformations in two-dimensional N = (2, 2) sigma models on Kahler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti) holomorphic preserving mapping. This map requires that torsions related to individual spaces and riemann connection on pseudodual manifold must vanish. We also consider holomorphic isometries which puts additional constraints on the pseudoduality.
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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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    Spectral singularities of a complex spherical barrier potential and their optical realization
    (Elsevier Science Bv, 2011) N/A; Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Sarısaman, Mustafa; Faculty Member; Researcher; Department of Mathematics; College of Sciences; College of Sciences; 4231; 217652
    The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral singularities of a complex spherical barrier potential and study their realization as transverse spherical electromagnetic waves emitted by a gain medium with a spherical geometry. In particular, for a typical dye laser material, we obtain a lower bound on the size of the gain medium for the occurrence of this kind of spectral singularities.
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    Spectral singularities in the TE and TM modes of a PT-symmetric slab system: optimal conditions for realizing a CPA-laser
    (Academic Press Inc Elsevier Science, 2016) N/A; Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Sarısaman, Mustafa; Faculty Member; Researcher; Department of Mathematics; College of Sciences; College of Sciences; 4231; 217652
    Among the interesting outcomes of the study of the physical applications of spectral singularities in PT-symmetric optical systems is the discovery of CPA-lasers. These are devices that act both as a threshold laser and a coherent perfect absorber (CPA) for the same values of their physical parameters. Unlike a homogeneous slab that is made to act as a CPA, a slab CPA laser would absorb the incident waves coming from the left and right of the device provided that they have appropriate intensity and phase contrasts. We provide a comprehensive study of one of the simplest experimentally accessible examples of a CPA laser, namely a PT-symmetric optical slab system consisting of a balanced pair of adjacent or separated gain and loss components. In particular, we give a closed form expression describing the spectral singularities of the system which correspond to its CPA laser configurations. We determine the intensity and phase contrasts for the TE and TM waves that are emitted (absorbed) whenever the slab acts as a laser (CPA). We also investigate the behavior of the time-averaged energy density and Poynting vector for these waves. This is necessary for determining the optimal values of the physical parameters of the system that make it act as a CPA laser. These turn out to correspond to situations where the separation distance s between the gain and loss layers is an odd multiple of a characteristic length scale so. A curious by-product of our study is that, except for the cases where s is an even integer multiple of so, there is a critical angle of polarization beyond which the energy of the waves emitted from the lossy layer can be larger than the energy of those emitted from the gain layer.
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    Spectral singularities, threshold gain, and output intensity for a slab laser with mirrors
    (Academic Press Inc Elsevier Science, 2018) Department of Physics; Department of Mathematics; Department of Mathematics; Doğan, Keremcan; Mostafazadeh, Ali; Sarısaman, Mustafa; PhD Student; Faculty Member; Researcher; Department of Physics; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; College of Sciences; N/A; 4231; 217652
    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.
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    PublicationOpen Access
    Spectral singularities and whispering gallery modes of a cylindrical gain medium
    (American Physical Society (APS), 2013) Department of Mathematics; Mostafazadeh, Ali; Sarısaman, Mustafa; Faculty Member; Researcher; Department of Mathematics; College of Sciences; 4231; N/A
    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.
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    PublicationOpen Access
    Optical spectral singularities and coherent perfect absorption in a two-layer spherical medium
    (The Royal Society, 2012) Department of Mathematics; Mostafazadeh, Ali; Sarısaman, Mustafa; Faculty Member; Researcher; Department of Mathematics; College of Sciences; 4231; N/A
    An optical spectral singularity is a zero-width resonance that corresponds to lasing at threshold gain. Its time-reversal causes coherent perfect absorption of light and forms the theoretical basis of antilasing. In this article, we explore optical spectral singularities of a two-layer spherical medium. In particular, we examine the cases that a gain medium is coated by a thin layer of high-refractive index glass and a spherical glass covered by a layer of gain material. In the former case, the coating reduces the minimum radius required for exciting spectral singularities and gives rise to the formation of clusters of spectral singularities separated by wide spectral gaps. In the latter case, the coating leads to a doubling of the number of spectral singularities.
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    Unidirectional reflectionlessness and invisibility in the TE and TM modes of a PT-symmetric slab system
    (American Physical Society (APS), 2017) Department of Physics; Department of Mathematics; Sarısaman, Mustafa; Researcher; Department of Physics; Department of Mathematics; College of Sciences
    Unidirectional invisibility of a PT-symmetric optical system is of great interest, but challenging as well since it is infeasible to fulfill it through wide optical frequency ranges in all angular directions. Accordingly we study reflectionless and invisible patterns in the TE and TM modes of an optical slab system consisting of an adjacent or separated pair of balanced gain and loss layers with a gap. We provide a comprehensive study of one of the simplest experimentally accessible examples of a unidirectionally reflectionless and invisible PT-symmetric optical slab system. We obtain the physically optimal conditions for the realization of these phenomena. We derive analytic expressions, and show that only certain gain amounts restricted to take values between certain minimum and maximum values give rise to uni- or bidirectionally invisible configurations. The size of gap decides the measure of reflectionlessness and invisibility parameters, especially on gain value and incident angle.
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    Spectral singularities in the surface modes of a spherical gain medium
    (American Physical Society (APS), 2013) Department of Mathematics; Mostafazadeh, Ali; Sarısaman, Mustafa; Faculty Member; Researcher; Department of Mathematics; College of Sciences; College of Sciences; 4231; N/A
    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.
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    PublicationOpen Access
    Euclidean pseudoduality and boundary conditions in sigma models
    (Elsevier, 2013) Department of Mathematics; Sarısaman, Mustafa; Researcher; Department of Mathematics; College of Sciences
    We discuss pseudoduality transformations in two-dimensional conformally invariant classical sigma models, and extend our analysis to a given boundaries of world-sheet, which gives rise to an appropriate framework for the discussion of the pseudoduality between D-branes. We perform analysis using the Euclidean spacetime and show that structures on the target space can be transformed into pseudodual manifold identically. This map requires that torsions and curvatures related to individual spaces are the same when connections are Riemannian. Boundary pseudoduality imposes locality condition. (C) 2012 Elsevier B.V. All rights reserved.