TY - JOUR

T1 - Solitary waves, steepening and intial collapse in the Maxwell-Lorentz system

A1 - Sørensen,Mads Peter

A1 - Brio,Moysey

A1 - Webb,Garry

A1 - Moloney,Jerome V.

AU - Sørensen,Mads Peter

AU - Brio,Moysey

AU - Webb,Garry

AU - Moloney,Jerome V.

PY - 2002

Y1 - 2002

N2 - We present a numerical study of Maxwell's equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion relation reveals various asymptotic regimes such as Schrödinger and KdV branches. Existence of soliton-type solutions in the Schrödinger regime and light bullets containing few optical cycles together with dark solitons are illustrated numerically. Envelope collapse regimes of the Schrödinger equation are compared to the full system and an arrest mechanism is clearly identified when the spectral width of the initial pulse broadens beyond the applicability of the asymptotic behavior. We show that beyond a certain threshold the carrier wave steepens into an infinite gradient similarly to the canonical Majda–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities.

AB - We present a numerical study of Maxwell's equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion relation reveals various asymptotic regimes such as Schrödinger and KdV branches. Existence of soliton-type solutions in the Schrödinger regime and light bullets containing few optical cycles together with dark solitons are illustrated numerically. Envelope collapse regimes of the Schrödinger equation are compared to the full system and an arrest mechanism is clearly identified when the spectral width of the initial pulse broadens beyond the applicability of the asymptotic behavior. We show that beyond a certain threshold the carrier wave steepens into an infinite gradient similarly to the canonical Majda–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities.

KW - Nonlinear optics; Vector Maxwell's equations; Solitary waves; Initial collapse

UR - http://www.imm.dtu.dk/pubdb/p.php?2997

JO - Physica D

JF - Physica D

VL - 170

SP - 287

EP - 303

ER -