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.

Comparison between Finite-Difference Time-Domain Method and Experimental Results for Femtosecond Laser Pulse Propagation

“…This is the first observation of the DFWM with IPM by FDTD. Furthermore, we compared the extended FDTD method (Nakamura et al, 2002b), (Nakamura et al, 2004b), with experimental results (Xu et al, 1999) for nonlinear propagation with the IPM effect of two-color sub-picosecond laser pulses in a silica fiber that have different initial delays between the two pulses. To the best of our knowledge, this is the first comparison between FDTD calculation and experimental results for nonlinear propagation with the IPM effect of twocolor 120 fs laser pulses in a silica fiber.…”

Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber

“…To test the solution under consideration, which describes the propagation of a highpower ultrashort pulse in polarization-maintaining optical fiber, we performed the simulation for the experimental conditions described in detail [60][61][62][63][64][65][66]. According to the experiment's description, a Ti: sapphire femtosecond laser with a mode-locking and a center wavelength of 798 nm generated pulses with a duration of 12 fs and a peak power of 175 kW.…”

“…A comparison of the simulation results obtained using the proposed algorithm and the known algorithm [54,55] is carried out. The results of a comparison of the data obtained by simulations using the proposed algorithm with the experimental data described in detail in [58][59][60][61][62][63][64] are presented.…”

Fast single-mode characterization of optical fiber by finite-difference time-domain method

“…In fact, to demonstrate the goodness of the BPM method, it has been compared with the FDTD [8]. However, the BPM method has a drawback: If the pulse duration approaches the optical cycle regime (as in our case), the BMP method is not appropriate, and therefore, it becomes necessary to use the FDTD method [8].…”