ABSTRACT

We have recently introduced a new modeling equation for the propagation of pulses in optical waveguides, the photon-conserving Nonlinear Schrödinger Equation (pcNLSE) which, unlike the canonical NLSE, guarantees strict conservation of both the energy and the number of photons for any arbitrary frequency-dependent nonlinearity. In this paper, we analyze some properties of this new equation in the familiar case where the nonlinear coefficient of the waveguide does not change sign. We show that the pcNLSE effectively adds a correction term to the NLSE proportional to the deviation of the self-steepening (SS) parameter from the photon-conserving condition in the NLSE. Furthermore, we describe the role of the self-steepening parameter in the context of the conservation of the number of photons and derive an analytical expression for the relation of the SS parameter with the time delay experienced by pulses upon propagation. Finally, we put forth soliton-like solutions of the pcNLSE that, unlike NLSE solitons, conserve the number of photons for any arbitrary SS parameter.

摘要

我们最近推出了一个新的用于在光波导中传播脉冲的建模方程式，即光子守恒非线性薛定ding方程（pcNLSE），与经典的NLSE不同，它保证了任意频率下能量和光子数的严格守恒依赖的非线性。在本文中，我们分析了在波导非线性系数不改变符号的常见情况下该新方程的一些性质。我们表明，pcNLSE有效地将校正项添加到NLSE中，该校正项与自增强（SS）参数与NLSE中光子保持条件的偏差成比例。此外，我们描述了在光子数量守恒的情况下自变强参数的作用，并推导了SS参数与脉冲在传播时经历的时间延迟之间关系的解析表达式。最后，我们提出了pcNLSE的类孤子解，与NLSE孤子不同，它保留了任意SS参数的光子数。