Filamentation Dynamics and Few-cycle Pulse Generation using Filaments

When a high energy femtosecond laser beam propagates through a transparent medium with a peak power exceeding the critical power for self-focusing filamentation can occur. Filamentation is characterized by a dynamic interplay between Kerr-induced self-focusing and dispersion, diffraction, and plasma generation. Loosely focusing <50 fs pulses containing a few millijoules of energy in air results in the generation of an extended (2-3 times the Rayleigh range) low-density plasma channel ~100 micrometers in diameter. In this region (the "filament") dramatic pulse reshaping occurs, resulting in dramatic pulse shortening and white-light continuum generation. In conjunction with the high pulse intensity in the filament channel (1013-1014 Wcm-2) these characteristics make femtosecond laser filaments an interesting tool for spectroscopy.

In the Levis laboratory we study the dynamic temporal and spectral structures that occur during filament propagation in order to rigorously characterize the filament as a spectroscopic tool and also to better understand the filamentation process itself. A particular challenge to studying filamentation is the high intensity of the pulse in the filament channel, which prohibits the use of many standard techniques for pulse characterization. We have developed several methods for circumventing this challenge, allowing us to directly measure a pulse as it undergoes filamentary propagation.

Life-cycle of a laser filament:

Laser pulse reshaping during filamentary propagation in the gas phase is driven primarily by the spatio-temporal dynamics arising from the interplay of self-focusing and defocusing induced by plasma generation in the medium. Self-focusing sharpens the profile of the laser pulse profile in space and time, both shortening the pulse duration and increasing the energy density of the pulse on the propagation axis. Eventually, this leads to high enough intensity to ionize the medium, generating free electrons that defocus the rear part of the pulse and halting the focusing process. Once plasma generation is halted, the rear part of the pulse can re-focus again, sharply localizing a significant portion of the pulse energy in space and time. This pulse shortening is accompanied by continuum generation as a result of the inverse relationship between pulse duration and frequency content. Ultimately, the peak power of the laser pulse drops below the critical power required for self-focusing due to diffraction and dispersion, halting the filamentation process.

Figure after Couairon and Mysyrowicz, Phys. Rep. 411, 47-189 (2007)

Tracking Filamentation dynamics in air through impulsive Raman excitation

The intrinsic pulse shortening that occurs during filamentation can lead to coherent excitation of molecules present in the propagation medium. When a laser pulse is shorter than the characteristic time scale of a Raman-active molecular mode (vibrational or rotational), intrapulse Raman scattering induces a macroscopic change in the medium as all of the molecules move in phase. Subsequently probing the coherently excited medium with a narrowband laser pulse imprints sidebands at the Raman-shifted frequency of the excited mode. Thus, by measuring which modes have been excited it is possible to extract information about the pulse shape and structure. Recording the Raman spectrum at different points along the filament can then provide information about the pulse propagation dynamics.

The adjacent figure shows such a series of measurements recorded for a 40 fs, 2 mJ pulse focused by an f = 2-m lens in air, along with the fluorescence profile of the filament. Nitrogen (τvib=14.3 fs), oxygen (τvib=21.5 fs), and water (τvib=9.1 fs) Raman lines appear successively along the filament, demonstrating pulse shortening. After initial pulse shortening (inferred by the increase in the oxygen and nitrogen signals before ~200 cm), we see evidence of pulse splitting in the oscillatory motion of the oxygen and nitrogen signals. Finally, efficient pulse shortening occurs in the second filamnetation cycle and is accompanied by continuum generation (integrated continuum spectrum plotted as dotted black line).

-Odhner et al., Physical Review Letters 105, 125001 (2010)

Phase and Amplitude characterization of a filamentary pulse

The sparse sampling of Raman lines in air and the necessity of directly measuring the pulse spectrum in the filament make the use of impulsive Raman scattering for complete retrieval of the temporal and spectral phase and amplitude of the filamentary pulse extremely challenging. An attractive alternative is to adapt a standard pulse measurement technique, frequency-resolved optical gating (FROG), for application to pulse measurement in laser filaments. In FROG, a reference laser pulse acts as the gate and the time-dependent signal generated by the interaction between the test and reference pulses in a nonlinear medium can be iteratively retrieved to recover the phase and amplitudes of the electric fields generating the signal, provided the reference pulse and the nonlinearity are known.

To measure the filament pulse dynamics, we have implemented a transient grating cross-correlation variant of FROG (TG-XFROG) in which two beams generate a laser-induced grating in a noble gas jet (acting as the instantaneous third-order nonlinear medium required for the measurement) and the filamentary pulse diffracts off of the grating and can be measured without introducing any optical elements into the filament path. The figure at right shows the measured and retrieved TG-XFROG traces, along with the pulse spectrum and temporal intensity profile of a 1.5-mJ, 50 fs pulse during filamentary propagation (255 cm from the f = 207 cm lens used to focus the pulse).

-Odhner et al., Opt. Lett. 37, 1775 (2012)

 

Levis Group, Department of Chemistry, Temple University, Beury Hall 244, 1901 N. 13th Street, Philadelphia, PA 19122    Tel: 215-204-5241     Fax: 215-204-6179
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