Moments of a pulse propagating with dispersion and damping: a phase space based approximation method

Abstract

A phase space approximation to pulse propagation has recently been developed, and has been shown to be accurate in that it preserves all spectral (wavenumber) moments as well as low order spatial moments (mean and variance) of a pulse propagating with dispersion but no damping. We investigate the effects of damping on the approximation and moments. We show that for damping that is linear with wave number, the accuracy of the approximation is unchanged from the no damping case previously considered. In addition, the spectral moments remain exact for all forms of damping. However, for arbitrary damping the spatial variance and higher spatial moments are inexact; we calculate the error up to the third-order moment. We consider both global and local moments.

Keywords:

• dispersion
• damping
• moments
• Wigner distribution

Acknowledgement

This work was supported by the Office of Naval Research (N00014-06-1-0009).