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Perturbed nonlinear Schr??dinger dynamical wave equation with Kerr media in nonlinear optics via optical solitons
摘要： In this paper, we have presented the analytical analysis of integrable perturbed nonlinear Schr¨odinger (PNLSE) equation with third-order dispersion (TOD) in Kerr media using our newly proposed technique, extended modi?ed auxiliary equation mapping method. By the implementation of this technique, we have obtained a variety of some new families and more general form of exact traveling wave solutions including triangular-type solutions, periodic and doubly periodic-like solutions, combined soliton-like solutions, kink and anti-kink type soliton-like solutions using three parameters which is the key di?erence of our newly proposed method. PNLSE is a well-known governing model to study the propagation of optical solitons in nonlinear optical ?bers and other telecommunication networks with a type of Kerr law nonlinearity. This particular type of nonlinearity originates when a light wave in an optical ?ber is subjected to nonlinear responses. For graphical representation of our newly found results, we have presented them with detailed dynamical physical representation using Mathematica 10.4 to explain in a more e?cient manner the behavior of di?erent physical structures of solutions. Also, the computational work and e?ciency of the method demonstrate the reliability, straightforwardness, and simplicity of the technique for solving other nonlinear complicated partial di?erential equations.
关键词： mathematical methods,Mathematical physics,perturbed NLSE,optical solitons
更新于2025-09-23 15:21:01
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Derivation and Experimental Verification of the near-field 2D and 3D optical intensities from a finite-size light emitting diode (LED)
摘要： We derive the near-field light intensity distributions of an inorganic LED on its surface and in volumetric space. Our closed-form solution for 3D intensity distribution for a finite-size LED is consistent with Lambert’s Cosine Law, which provides the 3D intensity distribution for an infinitesimal, flat light source. We also derive the formula for the 2D intensity distribution on a diode surface showing its similarity to a Gaussian function, which is typically used to approximate the surface light intensity profile for an LED and a laser diode. Our 2D intensity distribution function produces light propagation similar to the Gaussian beam propagation in space. However, unlike the Gaussian approximation, our formula invariably produces this behavior without assuming the refractive index inside the diode follows a quadratic function of the transverse spatial domains. Our 2D and 3D spatial intensity formulas in near-field for LEDs offer a unique way to calculate the peak intensity that occurs at the center of the flat LED source. We demonstrate, as expected, that the peak intensity increases with the size of the LED source as well as the brightness of each radiative electron-hole pair, which is a function of the drive current and quantum efficiency of the LED.
关键词： Near-field Photometry,Optical Waveguides,Display,Optical Wave Propagation,Closed-Form Solutions,and Lighting.,Lasers,Light Emitting Diodes,Mathematical Physics
更新于2025-09-16 10:30:52