Scattering of a short electromagnetic pulse from a Lorentz-Duffing film: theoretical and numerical analysis

TL;DR

This paper investigates the interaction of femtosecond electromagnetic pulses with Lorentz-Duffing thin films using combined theoretical and numerical methods, revealing phenomena like pulse slowing, total reflection, and nonlinear switching.

Contribution

It introduces a comprehensive analysis of pulse scattering on nonlinear Lorentz-Duffing films, combining multiple analytical approaches with numerical simulations to uncover new optical behaviors.

Findings

Pulse slowing near dielectric pole with zero group velocity.

Total reflection when spectrum is within the forbidden region.

Nonlinear switching from reflection to transparency.

Abstract

We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer; this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent.