Gap-Acoustic Solitons: Slowing and Stopping of Light

Tasgal, Richard S.; Shnaiderman, R.; Band, Yehuda B.

doi:10.1007/978-3-642-16549-8_3

Cited by 1 publication

(3 citation statements)

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“…The Maxwell equations can be used to obtain the following nonlinear wave equation for the electric field [1,2,4,15]: The electric field E is treated as a superposition of monochromatic constituents with different frequencies and wavevectors centered at their central values 0 ω and 0 k . We limit ourself only to considering the propagation of the electric field in an arbitrary direction, say Oz (usually chosen as the direction of 0 ), k so we can write ( ) …”

Section: Ii1 General Pulse Propagation Equation In the Nonlinear DImentioning

confidence: 99%

“…Some additional terms describing the delayed response of the medium should be included in the expression (13). This delayed response is related to the reduced Raman scattering on the molecules of the medium [15,20]. Using the Lorentz atomic model in the adiabatic approximation [1,15,17] we can present the nonlinear susceptibility of the medium in the form [3,17]:…”

Section: Xxxx T T T T T Tmentioning

confidence: 99%

“…We have recently developed a powerful method of deriving a general equation for short-duration intense pulses [8,14,15]. This method is based on a consistent and mathematically rigorous expansion of the nonlinear wave equation, which treats the nonlinear processes involved in the problem as perturbations.…”

Section: Introductionmentioning

confidence: 99%

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Propagation of Ultrashort Pulses in a Nonlinear Medium

Van¹,

Thuan²,

Goldstein³

et al. 2010

CMST

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Abstract:In this paper, using a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in [8] we study in the specific case of Kerr media. An obtained ultrashort pulse propagation equation which is called Generalized Nonlinear Schrödinger Equation usually has a very complicated form and looking for its solutions is usually a "mission impossible". Theoretical methods to solve this equation are effective only for some special cases. As an example we describe the method of a developed elliptic Jacobi function expansion. Several numerical methods of finding approximate solutions are simultaneously used. We focus mainly on the following methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for soliton propagation and interacting high order solitons. We consider also an interesting phenomenon: the collapse of solitons.

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Section: Ii1 General Pulse Propagation Equation In the Nonlinear DImentioning

confidence: 99%