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Physical Review A

Observation of conical emission from a single self-trapped beam

B. D. Paul, Marla L. Dowell, Alan C. Gallagher, J. Cooper

Published Jun 1, 1999• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.59.4784

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
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 (\ensuremathθ)(\ensuremath{\theta})(\ensuremathθ) 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 \ensuremathθ\ensuremath{\theta}\ensuremathθ 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 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.
In our experiment conical emission (CE) has no wavelength shift and the same polarization as the original beam. Varying laser power, detuning, and atomic density, the images of CE were captured and analyzed. Typical far-field images are presented. Under the blue detuning condition, manifest CE patterns were observed, and under red detuning, original beam blurs due to not only to self-defocusing but also the conical pattern were observed. By comparing laser power and atomic density dependence of cone angle and theoretical curve, we could estimate spectroscopic data such as nonlinear refractive index. From the density dependence data, we get the fact that cone angle is proportional to atomic density which supports the self-phase-modulation (SPM) model. In conclusion, we observed and analyzed CE from near-resonant Sm vapor. With this simple setup, we could measure spectroscopic data.
Conical emission, redshifted from the atomic resonance, is observed when a ∼2-ps laser beam, blueshifted from resonance, propagates through potassium vapor. In contrast, no cone is visible when a 150-fs pulse is used. The 2-ps-pulse-induced cone has a unique, small, angular spread of Δθ/θ≈0.1, compared with Δθ/θ≈0.3 from other pulsed experiments, which used 25-ps–5-ns-excitation pulses. In addition, the fraction of the 2-ps-pulse power emitted in the cone reached 7.5%, far exceeding this fraction from the longer-pulse experiments. An additional, unexpected result is that the spectral width of the laser pulse is narrower, without significant intensity loss, after propagation through the vapor. The vapor densities and laser detunings that yield cones in the present experiment are similar to those from the longer-pulse experiments. Although the 2-ps-pulse spectrum partially overlaps the resonance, the cone spectrum and cone angles versus density and laser detuning are similar to those previously reported for nanosecond pulses. The fourth (blue-detuned) wave required for satisfying four-wave mixing is absent, again equivalent to what is observed in the nanosecond experiments. The physical origin of cone emission by pulsed excitation of atomic vapors is still largely unknown, and this high efficiency and narrow angular spread of a spectrally broad cone further contradicts existing models, perhaps ultimately providing a clue to a correct explanation.
There Is an ongoing interest in the conical emission resulting from the passage of a laser light tuned in the vicinity of a resonant atomic transition(1–2). We also have observed such emission in high density sodium vapor in the range of 1015 cm−3, when an intense laser radiation is blue detuned with respect to any of the D lines. This conical emission shell has half angle of a few degrees around the laser axis, is red detuned from the respective D line, is spectrally broad (3A) and is obtained in laser intensity and detunings and sodium vapor density ranges where self-focusing occurs. No symmetric blue shifted component was observed. Harter and Boyd(1) have obtained symmetrical Rabi side-band emission in the forward direction at sodium vapor density of 1014 cm−3.
Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of the breakup of the pulse into solitary waves. For an incident pulse with a transverse as well as a temporal profile, the crests and troughs of the 2-D solitary waves are curved in a time-radius plane. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum, while the curvature of the solitary waves in the time-radius plane results in a transverse spatial modulation, resulting in conical emission in the far field. These results were obtained by performing detailed numerical calculations of the time-dependent paraxial propagation of a cylindrically symmetric laser pulse through a vapor of two-level atoms. Our results can be interpreted readily in terms of optical nutation on the Bloch sphere and in terms of noncollinear phase matching through the curvature of the solitary waves rather than through additional parametrically generated waves. The cone opening angle depends on the initial transverse profile of the pulse and the process of beam breakup as well as self-focusing.