Past and Present Aspects of the Self-Phase Modulation of Optical Beams
Ture K. Gustafson, P. L. Kelley and R. A. Fisher
Optical self-action effects occur when an electromagnetic field induces a refractive change in the medium through which the field propagates. The change in index of refraction then exhibits a back-action on the field so as to influence its propagation characteristics. Both spatial and temporal effects occur as discussed in the overview paper by Kelley . The influence of these nonlinear effects can be significant.
In this effort we primarily consider the consequences of the phase evolution due to the temporal variation of this self-action, known as self-phase-modulation. While initially observed in association with self-trapped filaments of light in liquids, the development of low-loss optical fibers very rapidly led to its ease of generation and predictability. Recently, the development of photonic crystal fibers [2,3] has led to a significant increase in the strength of self-action effects and numerous diverse applications have resulted.
We are in the process of reviewing the development of the discipline from the early years; in particular, its observation in self-trapped filaments and mode-locked laser pulses, to its more recent developments.
There remain several outstanding problems to be addressed. In particular we are studying a generalization of the nonlinear Schroedinger equation to include higher order linear and nonlinear diffraction terms and its influence on self-action. The self-phase modulation of repetitive pulses from mode-locked lasers, which results in an optical frequency comb, has been of recent interest. The interval and spectral linewidth depend upon the stabilization of the pulse train. To lowest order, a slippage of the optical phase with respect to the pulse amplitude results in a perturbation of the frequency interval, which can be measured experimentally. This is generally related to the first order dispersion coeffcient. Higher order dispersion, which might be anticipated to give a frequency interval which varies linearly across the comb, does not appear to be influential. The role of self-phase modulation and other self-action effects in such pulse to pulse mutual coherence phenomena is of interest.
We have recently extended this effort to include new approaches to nonlinear optical pulse propagation using a Hermite-Gaussian series representation of the pulse evolution.
- P. L. Kelley, IEEE Sel. Top. Quant. Electron., Vol. 6, No. 1259, 2000.
- J. M. Dudley, G. Genty, and S. Coen, Reviews of Modern Physics, Vol. 78, No. 1135, 2006.
- F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq, Foundations of Photonic Crystal Fibers, Imperial College Press, 2005, ISBN 1-86094-507-4.