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Journal of the Optical Society of America B

Continuous-wave self-deflection effect in sodium vapor

Grover A. Swartzlander, Huimin Yin, A. E. Kaplan

Published Jul 1, 1989• 52 citations
Publisher

Abstract

Observations of the self-deflection effect for an asymmetrical continuous-wave laser beam in sodium vapor are described, and comparisons based on theoretical calculations are made. A self-bending angle as large as eight diffraction widths was recorded, and strong attenuation of the on-axis radiation due to self-bending was measured. At ~200°C the self-deflection angle increased linearly with beam power, and we determined that (n2)max ≃ −10−7 cm2/W for intensities below 220 W/cm2. While numerical calculations, based on an inhomogeneously broadened two-level system, predict strong saturation of the self-bending effect, we observed only moderate saturation.

DOI
10.1364/josab.6.001317

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 22, 1988•0 citations
Observations of the self-deflection effect for an asymmetrical continuous-wave laser beam in sodium vapor are described, and comparisons based on theoretical calculations are made. A self-bending angle as large as eight diffraction widths was recorded, and strong attenuation of the on-axis radiation due to self-bending was measured. At ~200°C the self-deflection angle increased linearly with beam power, and we determined that (n2)max ≃ −10−7 cm2/W for intensities below 220 W/cm2. While numerical calculations, based on an inhomogeneously broadened two-level system, predict strong saturation of the self-bending effect, we observed only moderate saturation.
We report the first observations of the cw self-bending effect1 using an asymmetrical laser beam propagating in sodium vapor and discuss some concerns of practical and physical importance. The laser frequency was detuned below the D2 resonance until the maximum self-bending angle was observed. At ~200°C the nonlinear refractive index was found to be predominantly Kerrlike (Δn ≃ n 2 I) at experimental peak intensities up to ~220 W/cm2. This result is inconsistent with our numerical calculations of the saturation of the anomalous dispersion that includes power-broadened hole-burning of an inhomogeneously broadened two-level system,2 which predicts strong saturation of Δn. By analyzing either the self-deflection angle or the intensity at a single point in the far-field region as the input power was varied, we were able to determine that n2 ≃ − 10 − 7 cm2/W. Self-deflection angles as large as 5.9 mrad or eight times the diffraction angle were observed, which is more than enough for some useful applications such as resonatorless optical bistability, optical switching, and interconnecting, nonlinear optical coupling, and radiation protection, the latter of which we have demonstrated.
Two intersecting laser beams of orthogonal circular polarization near resonant to the homogeneously broadened D1 transition of Na vapor were observed to deflect each other upon contact. The experimental results are in good agreement with calculations based on a model which includes diffraction and a local nonlinear atomic susceptibility wihch fully takes into account saturation and optical pumping effects. The contact deflection (or ``bouncing'') was also observed when both beams were tuned to the atomic resonance frequency.
We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3 2{\mathrm{}}^{2}2S1/2{S}_{1/2}S1/2​,F=2--3 2{\mathrm{}}^{2}2P3/2{P}_{3/2}P3/2​,F=3 transition. The intensity profile of the deflected beam was measured at different laser power levels and for different laser polarizations. Calculations using a constant force derived from a two-level atom yield deflections which are too large. The results of more realistic simulation calculations agree very well with the measured deflection. Those calculations incorporate the atomic-beam spatial and velocity distributions as well as the laser frequency distribution and polarization state. Optical pumping, loss of atoms to the nonresonant F=1 ground state, and Doppler shifting of the atoms out of resonance are all considered, as also are the statistics and angular distributions of the spontaneous photons.
A circularly polarized laser beam propagating through sodium vapor is shown to be deflected by the inhomogeneous magnetic field from a nearby electric current-carrying thin wire aligned parallel to the beam. The effect arises from the refractive index gradient induced by magnetic-field-modified optical pumping. The experimentally observed beam deflection is in good agreement with predictions from a $J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2\ensuremath{\leftrightarrow}J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ model for the full four-dimensional spatialtemporal evolution of the interaction between radiation field and atoms. The time of order 100 ns needed for the beam to switch between undeflected and deflected positions is determined by the average Larmor precession period and is 2 orders of magnitude shorter than the optical pumping time.
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.
Four wave mixing (FWM) performance of sodium vapor was investigated in the strong pump regime (I»I at) necessary to achieve good phase conjugate reflectivity, R. Reflectivities >230% were observed using narrowband CW pump powers less than 1 W. Degenerate FWM spectral response was measured with R as a parameter, and shown to depend on self-focusing effects at higher R. The field of view of the sodium FWM was determined under narrowband high R conditions and found to behave as expected, except for nearly collinear geometries. Faith-ful imaging through a severe optical aberration was demonstrated at moderate R, but experimental observations and analysis indicate potential fidelity problems at large R. Reflect-ivity and field of view were also measured for wideband (2 GHz) laser pumping.