اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLimits of the uni-directional pulse propagation approximation
263
0
0.0
(
0
)
تأليف
P. Kinsler
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the uni-directional approximation used in many pulse propagation models. Results from numerical simulations support the theoretical predictions, and reveal the nature of the coupling between forward and backward waves.
قيم البحث
اقرأ أيضاً
I calculate the limitations on the widely-used forward-only (uni-directional) propagation assumption by considering the effects of transverse effects (e.g. diffraction). The starting point is the scalar second order wave equation, and simple predicti
ons are made which aim to clarify the forward-backward coupling limits on diffraction strength. The result is unsurprising, being based on the ratio of transverse and total wave vectors, but the intent is to present a derivation directly comparable to a recently published emph{nonlinearity} constrained limits on the uni-directional approximation [Kinsler, J. Opt. Soc. Am. B (2007)].
I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a) Maxwells
equations, (b) directional fields, and (c) the second order wave equation. While Maxwells equations simulators are the most general, directional field methods can give significant computational and conceptual advantages. Factorizations of the second order wave equation complete the set by being the simplest to understand. One important conclusion is that that envelope methods based on forward-only directional field propagation has made the traditional envelope methods (such as the SVEA, and extensions) based on the second order wave equation utterly redundant.
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order
propagation equation using a minimum of approximations and a straightforward factorization mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a single uni-directional first order wave equation by means of a simple slow evolution approximation, where the optical pulse changes little over the distance of one wavelength. It also also allows a direct term-to-term comparison of an exact bi-directional theory with the approximate uni-directional theory.
Generically, spectral statistics of spinless systems with time reversal invariance (TRI) and chaotic dynamics are well described by the Gaussian Orthogonal ensemble (GOE). However, if an additional symmetry is present, the spectrum can be split into
independent sectors which statistics depend on the type of the groups irreducible representation. In particular, this allows the construction of TRI quantum graphs with spectral statistics characteristic of the Gaussian Symplectic ensembles (GSE). To this end one usually has to use groups admitting pseudo-real irreducible representations. In this paper we show how GSE spectral statistics can be realized in TRI systems with simpler symmetry groups lacking pseudo-real representations. As an application, we provide a class of quantum graphs with only $C_4$ rotational symmetry possessing GSE spectral statistics.
We demonstrate a new design principle for unidirectionally invisible non-Hermitian structures that are not only invisible for one specific wavelength but rather for a broad frequency range. Our idea is based on the concept of constant-intensity waves
, which can propagate even through highly disordered media without back-scattering or intensity variations. Contrary to already existing invisibility studies, our new design principle requires neither a specific symmetry (like $mathcal{PT}$-symmetry) nor periodicity, and can thus be applied in a much wider context. This generality combined with broadband frequency stability allows a pulse to propagate through a disordered medium as if the medium was entirely uniform.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
