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Physical Review A

Self-focused light propagation in a fully saturable medium: Experiment

Marla L. Dowell, Roger C. Hart, Alan Gallagher, J. Cooper

Published Mar 1, 1996• 23 citations
Publisher

Abstract

We report observations of self-focusing and filamentation, i.e., the formation of one or more self-trapped beams, of \ensuremath{\sim}3 ns laser pulses in strontium (Sr) vapor. The experimental arrangement consists of a Sr vapor cell and a pulsed neodymium-doped yttrium aluminum garnet pumped dye laser tuned to the blue of the 461 nm transition in Sr. The spatial intensity distribution of individual self-focused beams has been measured at the exit window of a vapor cell by using a magnifying lens and video camera. Measurements of power dependence, spatial distributions, and scaling behavior for filament formation are in good agreement with theory over a wide range of vapor densities, laser detunings, and laser powers. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1775

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We report observations of self-focusing and filamentation, i.e., the formation of one or more self-trapped beams, of \ensuremath{\sim}3 ns laser pulses in strontium (Sr) vapor. The experimental arrangement consists of a Sr vapor cell and a pulsed neodymium-doped yttrium aluminum garnet pumped dye laser tuned to the blue of the 461 nm transition in Sr. The spatial intensity distribution of individual self-focused beams has been measured at the exit window of a vapor cell by using a magnifying lens and video camera. Measurements of power dependence, spatial distributions, and scaling behavior for filament formation are in good agreement with theory over a wide range of vapor densities, laser detunings, and laser powers. \textcopyright{} 1996 The American Physical Society.
A comprehensive model of intense laser light propagation in a fully saturable medium is presented. This model employs the Maxwell-Bloch equations for a two-level atomic system. Light propagating through a medium creates intensity-dependent index of refraction gradients that reduce to a Kerr nonlinearity only for a weak field. When the laser detuning is positive, self-induced index gradients cause the beam to self-focus. Stationary filaments occur when self-focusing exactly balances diffraction. There exists a unique set of two-dimensional fundamental (and higher mode) solutions for which the filament transverse profile (not Gaussian in general) depends on the following quantities: density of saturable absorbers, laser detuning from resonance, laser power, and natural linewidth. (In contrast the Kerr solution does not have a unique filament diameter.) Emphasis will be placed on propagation of Gaussian incident beams; deviations from the stationary solution in either shape or power generally give rise to oscillating spatial patterns, including donutlike profiles, or beam breakup.
We report observations of conical emission from a pulsed laser beam with incident laser power, detuning, and beam diameter matched to a range of single, steady-state filaments. The beam thus propagates with nearly constant diameter through 5 cm of strontium (Sr) vapor. Emission angles $(\ensuremath{\theta})$ are imaged as the height on the input slit of a 1.5 m spectrometer; a charge-coupled device camera in the spectrometer exit plane measures energy as a function of $\ensuremath{\theta}$ and frequency. Data are reported versus laser-pulse energy, diameter and detuning, and the collisional dephasing rate. Spectrally broad, red-detuned cones are observed, but only when the laser beam is predominately self-trapped. As previously observed in experiments where the beam breaks up into multiple filaments, forward emission at the blue-detuned Rabi sideband is much weaker than at the red (cone) sideband. The cone angle is largely independent of the phase velocity of the self-trapped laser beam, which varies from the vapor to the vacuum speed. The efficiency of the cone emission shows incomplete saturation, as well as strong dependence on self-trapped filament parameters.
We report steady-state self-focusing, self-trapping, and self-defocusing of a cw dye laser beam in sodium vapor for frequencies within several Doppler widths of the DDD-line resonance transitions. We measured the variation of the beam profile as the light propagates through the vapor. We observed a 20-mW beam self-trapped in a 12-cm-long filament having a half-power diameter of 70 \ensuremath{\mu}m.
We report steady-state self-focusing, self-trapping, and self-defocusing of a cw dye laser beam in sodium vapor for frequencies within several Doppler widths of the DDD-line resonance transitions. We measured the variation of the beam profile as the light propagates through the vapor. We observed a 20-mW beam self-trapped in a 12-cm-long filament having a half-power diameter of 70 \ensuremath{\mu}m.
This study presents examples of observed optical pattern formation in which a single laser beam propagating through atomic sodium vapor without feedback develops a stable, regular transverse structure. In particular, a three-filament near-field pattern leading to a honeycomb far-field pattern occurs at intensities near the saturation intensity and at powers larger than (but of the order of magnitude of) the critical power for self-focusing. The three-filament pattern has a uniform phase profile and strongly correlated power fluctuations, which suggest that it is perhaps a quantum image. These observations are also found to be in good agreement with numerical simulations of filamentation in a two-level atomic medium.
Two years ago, the first proposal and demonstration of self-focusing optical bistability was published.1 In this paper it was shown that a self-focused beam in a nonlinear medium would exhibit hysteresis if the beam were reflected back on itself. The effect was demonstrated using a dye laser beam and Na vapor as the nonlinear medium. The optical hysteresis observed is in good qualitative agreement with a recently - published analysis of this system.2 By taking account of the saturation of the nonlinearity, more complex behavior has been predicted.2 This behavior is due to oscillations of the spot size as the self-focused beam propagates through the nonlinear medium. In this paper we report on our experimental studies of optical multistability due to these spot size oscillations.