2006
DOI: 10.1364/josab.23.001776
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Gaussian pulse dynamics in gain media with Kerr nonlinearity

Abstract: Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can e… Show more

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Cited by 14 publications
(8 citation statements)
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“…Compared to full 4D dimensional models [13], it is much faster in terms of computing time, and allows to account for the impact of beam imperfections on the level of nonlinearity easily through an M 2 beam quality factor. Although several models using the Gaussian ansatz in both space and time have already been proposed [14,15], they fail to predict the complex temporal behavior induced by nonlinear propagation, leading to pulses that cannot be described by a Gaussian ansatz in the time domain, and are therefore not appropriate in the MPC context.…”
Section: Introductionmentioning
confidence: 99%
“…Compared to full 4D dimensional models [13], it is much faster in terms of computing time, and allows to account for the impact of beam imperfections on the level of nonlinearity easily through an M 2 beam quality factor. Although several models using the Gaussian ansatz in both space and time have already been proposed [14,15], they fail to predict the complex temporal behavior induced by nonlinear propagation, leading to pulses that cannot be described by a Gaussian ansatz in the time domain, and are therefore not appropriate in the MPC context.…”
Section: Introductionmentioning
confidence: 99%
“…(2) are shown. The corresponding equations of motion [31] can be obtained from Eqs. (7), (8) and (10) by setting n = 1, α = 0 and n ′ = α ′ = 0.…”
Section: Resultsmentioning
confidence: 99%
“…(17,20) by including the transverse spatial dimensions and to consider a space-time dynamics of an oscillator. Some partial reductions of the space-time dynamics have been used in the numerical simulations (e.g., (Kalosha et al (1998))) and semi-analytical matrix formalism has been developed (Jirauschek & Kärtner (2006); Kalashnikov (2003)). Nevertheless, the space-time theory of chirped pulse oscillators is not developed to date.…”
Section: Truncation Of Phase Space: Variational Approximation and Metmentioning
confidence: 99%