Optical shock waves

 

A light pulse propagating in a nonlinear medium behaves as a fluid which may experience wave breaking. At variance with what occurs for a wave along the seashore, this does not result in a breaker, but rather in a nonlinear structure known as a « dispersive shock wave », analogous to the undular bores formed at some estuaries and which can travel upriver for miles.

 

 

 

 

The undular bore consists in an initial large amplitude nonlinear wave (almost a solitary wave) followed by periodic « whelps » of decreasing amplitude which eventually degenerate in linear disturbances.

plunging breaker
undular bore: picture from the book « Mascaret, l’onde lunaire » by Antony Colas. reprinted with permission.

We describe the formation and evolution of the dispersive shock of light by means of a mathematical approach whose results compare very well with numerical simulations and experimental results. The theory yields simple asymptotic formulae for the parameters of the shock, making it possible to characterize the different types of behaviors of the light wave and to identify the best experimental situations for observing the dispersive shock.

 

The figure below represents the time evolution of a region of increased light intensity. The initial bump splits into 2 counter-propagating pulses whose leading fronts steepen, leading to wave breaking followed by the formation of two dispersive shock waves (regions of rapid nonlinear oscillations at both ends of the structure).  Details in PhysRevA.99.053819 by  M. Isoard, A. M. Kamchatnov and N. Pavloff.

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