# Research Projects

## 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 [1]. 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 coefficient. 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 and in particular the vector character of the field which results during the self-focussing of a pulse.

- [1]
- P. L. Kelley,
*IEEE Sel. Top. Quant. Electron.,*Vol. 6, No. 1259, 2000. - [2]
- J. M. Dudley, G. Genty, and S. Coen,
*Reviews of Modern Physics,*Vol. 78, No. 1135, 2006. - [3]
- 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.

More information: http://www.eecs.berkeley.edu/~tkg