Distortions of the pulse shape in inhomogeneous graded-index light guides

Mikhail A. Bisyarin; Ivan A. Molotkov

doi:10.1117/12.351068

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23 June 1999 Distortions of the pulse shape in inhomogeneous graded-index light guides

Mikhail A. Bisyarin, Ivan A. Molotkov

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Proceedings Volume 3609, Optical Pulse and Beam Propagation; (1999) https://doi.org/10.1117/12.351068
Event: Optoelectronics '99 - Integrated Optoelectronic Devices, 1999, San Jose, CA, United States

Abstract

Propagation of optical pulses in graded-index light guides is described under the assumption of the combined influence of large power, short duration and inhomogeneity which is supposed to be strong in the transverse and weak in the longitudinal direction. The propagation is treated as a weak nonlinear process modeled with a nonlinear wave equation. This equation is solved by means of a consistent asymptotic procedure with respect to a small parameter related to the pulse amplitude, with the second power of the parameter characterizing the weak longitudinal inhomogeneity of the graded-index light guide. A Sturm-Lionville problem, is obtained for the principal approximation to the asymptotic solution. The transverse distribution of the wave field and the phase of the high-frequency carrier are expressed through eigenfunctions and eigenvalues of this problem. For the pulse envelope the Nonlinear Schroedinger equation is derived, its coefficients depending on the longitudinal coordinate. The Cauchy's problem for this equation with the initial values of the soliton type is investigated. The conditions of persistence of the pulse shape are ascertained and for a large class of weak longitudinal inhomogeneities a distance is estimated where the pulse remains to be a solitary wave. A series of additional pulses with diminishing amplitudes where the pulse remains to be a solitary wave. A series of additional pulses with diminishing amplitudes arises as an effect of the weak longitudinal inhomogeneity. Formulae for these distortions are derived and it is shown that this effect may be eliminated for the case of a special relationship between the characteristics of inhomogeneity.

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Mikhail A. Bisyarin and Ivan A. Molotkov "Distortions of the pulse shape in inhomogeneous graded-index light guides", Proc. SPIE 3609, Optical Pulse and Beam Propagation, (23 June 1999); https://doi.org/10.1117/12.351068

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