Radiating dispersive shock waves in non-local optical media

Area of Science:

• Nonlinear Optics
• Condensed Matter Physics
• Fluid Dynamics

Background:

• Coherent light beam propagation in nematic liquid crystals follows a defocusing nonlinear Schrödinger (NLS) equation.
• Dispersive shock waves (DSWs) are a known phenomenon in nonlinear wave propagation.
• Standard DSW solutions of the defocusing NLS equation exhibit specific characteristics.

Purpose of the Study:

• To analyze the step Riemann problem for light beam propagation in nematic liquid crystals.
• To investigate the unique properties of the DSW generated in this system.
• To develop an asymptotic theory for the nematic DSW and compare it with numerical simulations.

Main Methods:

• Analysis of the step Riemann problem for the governing nonlinear wave equations.
• Application of the Wentzel-Kramers-Brillouin (WKB) approximation to find the radiative wavetrain solution.
• Derivation of an asymptotic model using a Korteweg-de Vries equation with fifth-order dispersion.
• Direct numerical simulations for validation.

Main Results:

• The generated DSW exhibits positive polarity, differing from standard NLS DSWs.
• The DSW generates resonant radiation that propagates ahead of the wave.
• The velocity of the leading soliton of the DSW is determined by the classical shock velocity.
• The asymptotic theory, a fifth-order dispersive Korteweg-de Vries equation, accurately describes the radiation generation.

Conclusions:

• The nematic liquid crystal system generates a unique DSW with distinct properties.
• Resonant radiation ahead of the DSW is a key feature, explained by the derived asymptotic model.
• The study provides a theoretical framework and numerical validation for this nonlinear wave phenomenon.