Validity of the unidirectional propagation model: application to laser-driven terahertz emission

J Déchard,S Skupin,L Bergé,I Thiele,P González De Alaiza Martínez,A Nguyen

doi:10.1088/2399-6528/aa8cfe

Abstract

The Unidirectional Pulse Propagation Equation (uppe) is often used to compute the forward component of ultrashort light pulses in nonlinear materials. While its accuracy has frequently been reported for many applications in ultrafast optics, its validity can be questionable for ionizing pulses, in particular in the frequency domain below the electron plasma frequency . Inaccuracy of the uppe model in this frequency range may be detrimental to, e.g., a correct description of laser-driven terahertz emission. Here we demonstrate, analytically and numerically, that over long enough propagation paths, the one-dimensional solutions of both uppe and the full wave equation match in the entire spectrum, including the spectral range . Our findings confirm the reliability of the uppe solutions for a wide class of propagation problems.

Highlights

The propagation of a scalar electromagnetic field in (1 + 1)-dimensional geometry obeys the wave equation (WE) derived from Maxwells equation [1]:¶2zE - c-2¶t2E = Q (E), (1)where E (z, t ) represents the electric field propagating along the z-axis, c is the speed of light in vacuum and Q (E) is the response function that determines the linear and nonlinear properties of the material
Unlike the WE solution, the Unidirectional Pulse Propagation Equation (UPPE) spectrum is not peaked at the plasma frequency npe » 55 THz, but it develops spectral oscillations in the region n < npe, as expected (figure 2(d))
Structural differences between the WE and UPPE solutions have been explored thanks to those analytical solutions, especially the shape of the THz spectra over mm-range propagation distances

Summary

13 December 2017

J Déchard , A Nguyen, P González de Alaiza Martínez, I Thiele, S Skupin and L Bergé. The Unidirectional Pulse Propagation Equation (UPPE) is often used to compute the forward. While its accuracy has frequently been this work must maintain attribution to the reported for many applications in ultrafast optics, its validity can be questionable for ionizing pulses, author(s) and the title of the work, journal citation in particular in the frequency domain below the electron plasma frequency wpe. UPPE model in this frequency range may be detrimental to, e.g., a correct description of laser-driven terahertz emission. Analytically and numerically, that over long enough propagation paths, the one-dimensional solutions of both UPPE and the full wave equation match in the entire spectrum, including the spectral range w wpe. Our findings confirm the reliability of the UPPE solutions for a wide class of propagation problems

Introduction

The analytical solution

Numerical results

Conclusion