We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to a rather simpler geometry, a slab waveguide. This allows us to obtain an analytical solution to the problem, revealing rich physical insights. We identify various conditions that govern the SHG efficiency. Importantly, our analysis demonstrates that apart from the mode-matching condition, phase-matching condition is relevant even for this sub-wavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.
We study second-harmonic generation (SHG) arising from surface nonlinearity at a metal-dielectric interface using a spectral decomposition method. Since our method avoids the need to consider the generalized boundary condition across the metal-dielectric interface in the presence of a perpendicular surface source, we retrieve the known discontinuity of the tangential component of the electric field (E 2ω ) for a general geometry, based on a purely mathematical argument. Further, we reaffirm the standard convention of the implementation of this condition, namely, that the surface dipole source radiates as if placed outside the metal surface for arbitrary geometries. We also study and explain the spectral dependence of the discontinuity of the tangential component of the electric field at second harmonic. Finally, we note that the default settings of the commercial numerical package COMSOL Multiphysics fail to account for the E 2ω -discontinuity. We provide a simple recipe that corrects the boundary condition within these existing settings.
We study a critically coupled system [Opt. Lett. 32, 1483 (2007)] with a Kerr nonlinear spacer layer. Nonlinearity is shown to inhibit null scattering in a critically coupled system at low powers. However, a system detuned from critical coupling can exhibit near-complete suppression of scattering by means of nonlinearity-induced changes in refractive index. Our studies reveal clearly an important aspect of critical coupling as a delicate balance in both the amplitude and the phase relations, while a nonlinear resonance in dispersive bistability concerns only the phase.
We study coherent perfect absorption (CPA) of light in a Kerr nonlinear metal-dielectric composite medium, illuminated from the opposite ends. Elementary symmetry considerations reveal that equality of the incident light intensities is a prerequisite to ensure CPA in both linear and nonlinear systems for specific system parameters. We also derive the sufficient conditions for having CPA. We further show that while CPA in a linear system is insensitive to the incident power level, that in a nonlinear system can be achieved only for discrete intensities with interesting hysteretic response. Our unified formulation of CPA and waveguiding identifies them as opposite scattering phenomena. We further investigate light-induced CPA in on-and off-resonant systems.
We study theoretically a PT -symmetric saturable balanced gain-loss system in a ring cavity configuration. The saturable gain and loss are modeled by two-level medium with or without population inversion. We show that the specifics of the spectral singularity can be fully controlled by the cavity and the atomic detuning parameters. The theory is based on the mean-field approximation as in standard theory of optical bistability. Further, in the linear regime we demonstrate the regularization of the singularity in detuned systems, while larger input power levels are shown to be adequate to limit the infinite growth in absence of detunings. c 2017 Optical Society of America OCIS codes: 230.4555, 190.1450, 130.4815 In recent years there has been a great deal of interest in spectral singularities in non-Hermitian systems, especially in PT (parity-time) symmetric systems [1][2][3][4][5][6]. Such singularities with diverging scattered amplitudes (in reflection and transmission) were initially studied because of fundamental interest. A great deal of research has been devoted to understand the origin and the nature of these singularities and also the mechanism to regularize the infinities, since real systems cannot support such divergence. Indeed, no realistic system can ever support the infinite growth and such growing amplitudes will eventually render the response of the medium nonlinear. It was further understood that a dispersive Kerr nonlinearity is inadequate to regularize the singularity [7]. It was shown recently that regularization can be achieved by an all-order saturation mechanism in a balanced gainloss system [8]. In addition to the fundamental interest in PT -symmetric systems, there have been few attempts to find some basic applications in photonics [9][10][11][12][13][14]. But any application would require a thorough control of the singularities. In this paper we show that such a control can be achieved if the gain and the loss media are kept in separate cavities with an overall feed-back provided by a third cavity. A similar ring cavity configuration with saturable absorbers was studied earlier in the context of demonstrating remarkable flexibility in the multi-stable response [15]. Here we exploit the same flexibility albeit with a replacement of the saturable absorber with a saturable gain medium in one of the cavities. The balanced loss and gain cavities with identical parameters form the core of the PT -symmetric system. We first investigate the linear response which clearly shows the singularity for a perfectly tuned system as reported by others [2]. We show how PT -symmetry is violated and these are regularized by introduction of the atomic and the cavity detunings leading to poles in scattered amplitudes away from the real axis. We then look at the nonlinear response which reiterates the earlier findings that saturable nonlinearity is able to limit the infinite growth. We further report on the bistable response and the nonreciprocity in transmission [8] which can lead to switching and optical...
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