Propagation of ultrashort laser pulses

The domain of ultrashort laser pulses, which duration varies from a few femtoseconds (1 fs = 10^-15 s) to some hundreds of femtoseconds, is extremely vast, and involves many researchers around the world. One can specialize in the physics of lasers, in the generation of harmonics, in fundamental experiences, etc. I have chosen to concentrate on time & frequency aspects of ultrashort pulses, with the aim of controlling their characteristics along their propagation path. This time & frequency approach is analog to the space & spatial frequency approach of the propagation of monochromatic plane waves in diffraction and scattering.

Superluminal group delay times

In collaboration with Pierre Tournois, from 1996, we have studied the physical implications of superluminal group delay times and practical means of achieving them. Our goal was to examine the causality principle of Einstein for the propagation velocity of an optical information in some extreme cases. We predicted the existence of negative group delay velocities in optical waveguides mixing metals and dielectrics [1], in which case the energy and the phase propagate in opposite directions. We discussed the existence of negative group delay times in multiple wave interferometers of the Fabry-Perot and Gires-Tournois types. Previous works had shown the theoretical and experimental existence of superluminal group delay times in dielectric mirrors. These are equivalent to Bragg reflectors with very a high index contrast, or to one dimensional photonic band-gap structures. We obtained simple and general expressions for these asymptotic superluminal group delay times, which are confirmed by experimental results [2]. We proposed a synthesis of these results through a theorem relating the group delay times on reflection from both sides of a multilayer structure to the group delay time on transmission. We also conducted numerical simulations of the propagation of ultrashort pulses through dispersive multilayered structures. The results indicate the compatibility of superluminal group delay times with a causality principle for the intensity envelope rather than for the maximum of a wave packet.

Dispersion controlled mirrors (chirped mirrors)

From 1997, I have investigated chirped mirrors with Pierre Tournois. These optical elements, invented in 1994, are dielectric mirrors that are specifically optimized for ultrashort laser pulses. Their reflection coefficient must as close as possible to 100% over the whole target bandwidth, but in addition their dispersion has to compensate for the dispersion introduced by other optical elements in the laser chain. I developed an original optimization method, based on the simulated annealing principle, that enables efficient solutions for almost arbitrary target dispersions. In order to extend the bandwidth of chirped mirrors, I proposed and patented a new structure associating several chirped mirrors optimized simultaneously such that the sum of their dispersions follows a prescribed law. Moreover, I developed a precise measurement method for the group delay time introduced by chirped mirrors [5]. I obtained a measurement precision better than 1 fs without any statistical averaging or post processing (Fig. 1).

(a)	(b)

Acousto-optic programmable filter

During the doctoral research of Frédéric Verluise, and on the basis of an invention of Pierre Tournois, we developed a acousto-optic programmable dispersive filter (AOPDF) for ultrashort pulses. The originality of the AOPDF is to make use of a quasi-collinear (in group velocity) interaction in tellurium dioxide (TeO₂) to achieve the convolution of an ultrashort pulse with an arbitrary acoustic signal. We determined a very efficient cut of TeO₂, and then studied precisely the relation between the acoustic signal and the amplitude and phase modulation of the diffracted optical wave, in the stationary phase approximation [4]. Experiments in a chirped pulse amplification (CPA) laser chain demonstrated the adaptive control of the output ultrashort pulse by way of the AOPDF fed with the measured characteristics of the output pulse [3].

References

1. P. Tournois and V. Laude, ``Negative group velocities in metal-film optical wave-guides,'' Opt. Commun. 137, 41-45 (1997).
2. V. Laude and P. Tournois, ``Superluminal asymptotic tunneling times through 1D photonic band gaps in quarter-wave-stack dielectric mirrors,'' J. Opt. Soc. Am. B 16, 194-198 (1999).
3. F. Verluise, V. Laude, J.-P. Huignard, P. Tournois, and A. Migus, ``Arbitrary dispersion control of ultrashort optical pulses using acoustic waves,'' J. Opt. Soc. Am. B 17, 138-145 (2000).
4. F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, ``Arbitrary control of phase and amplitude of ultrashort pulses with an acousto-optic programmable dispersive filter: application to pulse compression and pulse shaping,'' Opt. Lett. 25, 575-577 (2000).
5. V. Laude, "Noise analysis of the measurement of group-delay in Fourier white-light interferometric cross-correlation, " J. Opt. Soc. Am. B 19, 1001-1008 (2002).