Observation of Slowly Varying Envelope Approximation Breakdown by Comparison between the Extended Finite-Difference Time-Domain Method and the Beam Propagation Method for Ultrashort-Laser-Pulse Propagation in a Silica Fiber

Abstract

Conventionally, the beam propagation method (BPM) for solving the generalized nonlinear Schrödinger equation (GNLSE) including the slowly varying envelope approximation (SVEA) has been used to describe ultrashort-laser-pulse propagation in an optical fiber. However, if the pulse duration approaches the optical cycle regime (<10 fs), this approximation becomes invalid. Consequently, it becomes necessary to use the finite difference time domain method (FDTD method) for solving the Maxwell equation with the least approximation. In order to both experimentally and numerically investigate nonlinear femtosecond ultrabroad-band-pulse propagation in a silica fiber, we have extended the FDTD calculation of Maxwell's equations with nonlinear terms to that including all exact Sellmeier-fitting values. We compared the results of this extended FDTD method with the solution of the BPM that includes the Raman response function, which is the same as in the extended FDTD method, up to fifth-order dispersion with the SVEA, as well as with the experimental results for nonlinear propagation of a 12 fs laser pulse in a silica fiber. Furthermore, in only the calculation, pulse width was gradually shortened from 12 fs to 7 fs to 4 fs to observe the breakdown of the SVEA in detail. Moreover, the soliton number N was established as 1 or 2. To the best of our knowledge, this is the first observation of the breakdown of the SVEA by comparison between the results of the extended FDTD and the BPM calculations for the nonlinear propagation of an ultrashort (<12 fs) laser pulse in a silica fiber.