Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields

We study phase-matching conditions for high-order harmonic generation as well as high-order sum- and difference-frequency mixing processes in strong laser fields, using a graphical approach described in Balcou et al (1997 Phys. Rev. A 55 3204-10). This method is based on the analysis of the different quantum paths that contribute, with different phase properties, to the single-atom response. We propose a simple numerical method to disentangle the quantum paths contributing to the generation process. We present graphical maps of the phase matching around the laser focus, which allow one to predict the geometries that optimize the conversion efficiency of the process considered. The method is applied to the study of sum- and difference-frequency mixing processes. The qualitative predictions of the graphical phase-matching approach are confirmed by numerical propagation calculations

Which group velocity of light in a dispersive medium?

The interaction between a light pulse, traveling in air, and a generic linear, non-absorbing and dispersive structure is analyzed. It is shown that energy conservation imposes a constraint between the group velocities of the transmitted and reflected light pulses. It follows that the two fields propagate with group velocities depending on the dispersive properties of the environment (air) and on the transmission properties of the optical structure, and are one faster and the other slower than the incident field. In other words, the group velocity of a light pulse in a dispersive medium is reminiscent of previous interactions. One example is discussed in detail.Comment: To be submitted on PR

High-order Harmonic-generation In Rare-gases With An Intense Short-pulse Laser

We present experimental studies of high-order harmonic generation in the rare gases performed with a short-pulse titanium sapphire laser operating at 794 nm in the 10(14)-10(15) W/cm2 range. The harmonic yields generated in neon and in argon are studied for all orders as a function of the laser intensity. They vary first rather steeply, in the cutoff region, then much more slowly in the plateau region, and, finally, they saturate when the medium gets ionized. The dependence of the high-order harmonic cutoff with the laser intensity in neon and argon is found to be lower than that predicted in single-atom theories. We observe high-order harmonics in argon and xenon (up to the 65th and 45th, respectively) at 10(15) W/cm2, which we attribute to harmonic generation from ions. We also show how the harmonic and fundamental spectra get blueshifted when the medium becomes ionized

On a universal photonic tunnelling time

We consider photonic tunnelling through evanescent regions and obtain general analytic expressions for the transit (phase) time $\tau$ (in the opaque barrier limit) in order to study the recently proposed ``universality'' property according to which $\tau$ is given by the reciprocal of the photon frequency. We consider different physical phenomena (corresponding to performed experiments) and show that such a property is only an approximation. In particular we find that the ``correction'' factor is a constant term for total internal reflection and quarter-wave photonic bandgap, while it is frequency-dependent in the case of undersized waveguide and distributed Bragg reflector. The comparison of our predictions with the experimental results shows quite a good agreement with observations and reveals the range of applicability of the approximated ``universality'' property.Comment: RevTeX, 8 pages, 4 figures, 1 table; subsection added with a new experiment analyzed, some other minor change

Measurement of Superluminal optical tunneling times in double-barrier photonic bandgaps

Tunneling of optical pulses at 1.5 micron wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated. Tunneling time measurements as a function of barrier distance show that, far from the resonances of the structure, the transit time is paradoxically short, implying Superluminal propagation, and almost independent of the distance between the barriers. These results are in agreement with theoretical predictions based on phase time analysis and also provide an experimental evidence, in the optical context, of the analogous phenomenon expected in Quantum Mechanics for non-resonant superluminal tunneling of particles across two successive potential barriers. [Attention is called, in particular, to our last Figure]. PACS nos.: 42.50.Wm, 03.65.Xp, 42.70.Qs, 03.50.De, 03.65.-w, 73.40.GkComment: LaTeX file (8 pages), plus 5 figure

Plasma-Induced Frequency Chirp of Intense Femtosecond Lasers and Its Role in Shaping High-Order Harmonic Spectral Lines

We investigate the self-phase modulation of intense femtosecond laser pulses propagating in an ionizing gas and its effects on collective properties of high-order harmonics generated in the medium. Plasmas produced in the medium are shown to induce a positive frequency chirp on the leading edge of the propagating laser pulse, which subsequently drives high harmonics to become positively chirped. In certain parameter regimes, the plasma-induced positive chirp can help to generate sharply peaked high harmonics, by compensating for the dynamically-induced negative chirp that is caused by the steep intensity profile of intense short laser pulses.Comment: 5 pages, 5 figure

Strongly dispersive transient Bragg grating for high harmonics

We create a transient Bragg grating in a high-harmonic generation medium using two counterpropagating pulses. The Bragg grating disperses the harmonics in angle and can diffract a large bandwidth with temporal resolution limited only by the source size. © 2010 Optical Society of America

Possibility of the tunneling time determination

We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We propose a model of time measurements. The model provides a procedure for calculation of the asymptotic tunneling and reflection times. The model also demonstrates the impossibility of determination of the time the tunneling particle spends under the barrier. Examples for delta-form and rectangular barrier illustrate the obtained results.Comment: 8 figure

Negative group delay for Dirac particles traveling through a potential well

The properties of group delay for Dirac particles traveling through a potential well are investigated. A necessary condition is put forward for the group delay to be negative. It is shown that this negative group delay is closely related to its anomalous dependence on the width of the potential well. In order to demonstrate the validity of stationary-phase approach, numerical simulations are made for Gaussian-shaped temporal wave packets. A restriction to the potential-well's width is obtained that is necessary for the wave packet to remain distortionless in the travelling. Numerical comparison shows that the relativistic group delay is larger than its corresponding non-relativistic one.Comment: 10 pages, 5 figure