Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces

We discuss the target space pseudoduality in supersymmetric sigma models on symmetric spaces using two different methods, orthonormal coframe and component expansion. These two methods yield similar results to the classical cases with the exception that commuting bracket relations in classical case turns out to be anticommuting ones because of the appearance of grassmann numbers. In component expansion method it is understood that constraint relations in case of non-mixing pseudoduality are the remnants of mixing pseudoduality. Once mixing terms are included in the pseudoduality relations the constraint relations disappear.Comment: 21 pages, typos correcte

Pseudoduality and Conserved Currents in Sigma Models

We discuss the current conservation laws in sigma models based on a compact Lie groups of the same dimensionality and connected to each other via pseudoduality transformations in two dimensions. We show that pseudoduality transformations induce an infinite number of nonlocal conserved currents on the pseudodual manifold.Comment: 15 pages, discussion section adde

Spectral Singularities in the Surface Modes of a Spherical Gain Medium

We study the surface modes of a homogeneous spherical gain medium and provide a comprehensive analytic treatment of a special class of these modes that support 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.Comment: 13 pages, 4 figures, 6 tables; to appear in Phys. Rev.

Euclidean Pseudoduality and Boundary Conditions in Sigma Models

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.Comment: 17 pages, v2: References added, slightly revised; To appear in Nucl. Phys.

Spectral Singularities and Whispering Gallery Modes of a Cylindrical Gain Medium

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 new 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.Comment: 12 pages, 6 figures, 3 tables; to appear in Phys. Rev.

Lasing Threshold Condition for Oblique TE and TM Modes, Spectral Singularities, and Coherent Perfect Absorption

We study spectral singularities and their application in determining the threshold gain coefficient $g^{(E/M)}$ for oblique transverse electric/magnetic (TE/TM) modes of an infinite planar slab of homogenous optically active material. We show that $g^{(E)}$ is a monotonically decreasing function of the incidence angle $\theta$ (measured with respect to the normal direction to the slab), while $g^{(M)}$ has a single maximum, $\theta_c$, where it takes an extremely large value. We identify $\theta_c$ with the Brewster's angle and show that $g^{(E)}$ and $g^{(M)}$ coincide for $\theta=0$ (normal incidence), tend to zero as $\theta\to 90^\circ$, and satisfy $g^{(E)}<g^{(M)}$ for $0<\theta<90^\circ$. We therefore conclude that lasing and coherent perfect absorption are always more difficult to achieve for the oblique TM waves and that they are virtually impossible for the TM waves with $\theta\approx\theta_c$. We also give a detailed description of the behavior of the energy density and the Poynting vector for spectrally singular oblique TE and TM waves. This provides an explicit demonstration of the parity-invariance of these waves and shows that the energy density of a spectrally singular TM wave with $\theta>\theta_c$ is smaller inside the gain region than outside it. The converse is true for the TM waves with $\theta<\theta_c$ and all TE waves.Comment: 14 pages, 3 tables, 7 figure

Pseudoduality and Complex Geometry in Sigma Models

We study the pseudoduality transformations in two dimensional N = (2, 2) sigma models on K\"ahler 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.Comment: 12 pages; typos corrected; To appear in Int. J. Geom. Meth. Mod. Phy

Lasing with Topological Weyl Semimetal

Lasing behavior of optically active planar topological Weyl semimetal (TWS) is investigated in view of the Kerr and Faraday rotations. Robust topological character of TWS is revealed by the presence of Weyl nodes and relevant surface conductivities. We focus our attention on the surfaces where no Fermi arcs are formed, and thus Maxwell equations contain topological terms. We explicitly demonstrate that two distinct lasing modes arise because of the presence of effective refractive indices which lead to the birefringence phenomena. Transfer matrix is constructed in such a way that reflection and transmission amplitudes involve $2\times2$ matrix-valued components describing the bimodal character of the TWS laser. We provide associated parameters of the topological laser system yielding the optimal impacts. We reveal that gain values corresponding to the lasing threshold display a quantized behavior, which occurs due to topological character of the system. Our proposal is supported by the corresponding graphical demonstrations. Our observations and predictions suggest a concrete way of forming TWS laser and coherent perfect absorber; and are awaited to be confirmed by an experimental realization based on our computations.Comment: 17 pages, 9 figures, 3 table

PT\mathcal{P}\mathcal{T}-Symmetric Coherent Perfect Absorber with Graphene

We investigate $\mathcal{PT}$-symmetric coherent perfect absorbers (CPAs) in the TE mode solution of a linear homogeneous optical system surrounded by graphene sheets. It is revealed that presence of graphene sheets contributes the enhancement of absorption in a coherent perfect absorber. We derive exact analytic expressions, and work through their possible impacts on lasing threshold and CPA conditions. We point out roles of each parameter governing optical system with graphene and show that optimal conditions of these parameters give rise to enhancement and possible experimental realization of a CPA laser. Presence of graphene leads the required gain amount to reduce considerably based on its chemical potential and temperature. We obtain that relation between system parameters decides the measure of CPA condition. We find out that graphene features contributing to resonance effect in graphene sheets are rather preferable to build a better coherent perfect absorber.Comment: 14 pages, 9 figure