TY - JOUR
T1 - Asymptotic analysis of weakly nonlinear Bessel-Gauß beams
AU - Graf, Tobias
AU - Moloney, Jerome
AU - Venkataramani, Shankar
N1 - Funding Information:
This research was supported by AFOSR MURI , “Mathematical Modeling and Experimental Validation of Ultrashort Nonlinear Light–Matter Coupling associated with Filamentation in Transparent Media”, grant FA9550-10-1-0561 . We also thank Professors Moysey Brio, Miroslav Kolesik, and Per Jakobsen for fruitful discussions.
PY - 2013/1/15
Y1 - 2013/1/15
N2 - In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schrödinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.
AB - In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schrödinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.
KW - Amplitude equations
KW - Conical waves
KW - Multiple scales
KW - Nonlinear Schrödinger equation
KW - Uniform estimates
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U2 - 10.1016/j.physd.2012.09.004
DO - 10.1016/j.physd.2012.09.004
M3 - Article
AN - SCOPUS:84870062239
VL - 243
SP - 32
EP - 44
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1
ER -