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Physical Review Letters

Self-Induced Transparency of Degenerate Transitions with Thermally Equilibrated Levels

Alfred Zembrod, Th. Gruhl

Published Aug 9, 1971• 54 citations
Publisher

Abstract

Pulse propagation in S${\mathrm{F}}_{6}$ has been investigated using 200-nsec pulses of a C${\mathrm{O}}_{2}$ laser. Operating at $\ensuremath{\lambda}=10.53$ \ensuremath{\mu}m ($P14$ transition) we have observed a breakup of the pulse envelope, an oscillatory energy transmission, and an energy-dependent pulse delay. We interpret our data in terms of the existing theory of self-induced transparency; the corresponding Bloch-type equations were derived assuming thermal equilibrium between rotational $M$ sublevels.

DOI
10.1103/physrevlett.27.287

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Investigation of Pulse Delay in Self-Induced Transparency

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This paper gives the details of pulse delay in self-induced transparency in S${\mathrm{F}}_{6}$ with a C${\mathrm{O}}_{2}$ laser at 10.5915 \ensuremath{\mu}. Results show that the propagation of intense C${\mathrm{O}}_{2}$ laser pulses in S${\mathrm{F}}_{6}$ can be described by self-induced transparency.

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We have investigated the self-induced transparency effect in ruby over a range of input energies which range from linear absorption to full transparency. The transmission, pulse delay, and pulse broadening were studied as a function of input energy. The transition region is narrower than that found in similar studies of the C${\mathrm{O}}_{2}$/S${\mathrm{F}}_{6}$ system; this is consistent with predictions based on ensembles of two-level systems. Included are the first pulse-delay and pulse-broadening curves to be obtained for the ruby system.

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Self-induced transparency on the 1.15-μm line of neon

W. Krieger, P. E. Toschek

Self-induced transparency in an absorbing neon discharge has been observed on the nonresonance transition $2{s}_{2}(J=1)\ensuremath{-}2{p}_{4}(J=2)$. Since linearly polarized light pulses excite two dipole moments differing by only 18%, the absorber is virtually nondegenerate and superior in simplicity to molecular absorbers. Light pulses, generated from the output of a cw single-frequency 1.15-\ensuremath{\mu}m He-Ne laser oscillator by a pulsed Ne laser amplifier, were transmitted through the absorber. Comparison of the oscilloscope traces of input and output pulses indicated the occurrence of pulse retardation, peak amplification, and pulse breakup. Complete pulse reshaping to the predicted hyperbolic-secant envelope has been observed. The periodicity of transmission versus pulse power, which provides direct evidence of optical nutation, is in agreement with the results of a pulse-area-pulse-energy model.

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Effect of Resonant Collisions on the Propagation of a Self-Induced Transparency Pulse in SF6

C. H. Wang

Effect of the SF6 pressure on self-induced transparency (SIT) in SF6 was investigated systematically. The study consists of measuring the shape, width, delay time, and intensity of the transmitted pulse (which is a SIT pulse at low SF6 pressure) as a function of SF6 pressure P. The SIT pulse was induced by the nonlinear interaction of a 20-nsec P(20) CO2 laser pulse with the SF6. A theory which includes the homogeneous broadening mechanism was developed for the pulse delay time. For a stationary propagating pulse, it was found that the pulse delay time is related nonlinearly to Q (the ratio of the transiently energy stored energy density to the rate of change of the energy flux density of the field). From the interpretation of the experimental results, it was concluded that, for P>100 μ, the SF6-SF6 resonant collision makes a significant contribution to the departure from SIT. The effect of level degeneracies associated with the high angular momentum of the involved resonant vibrational states is also discussed.

The Journal of Chemical Physics•May 1, 1972•2 citations
Pulse propagation in SF6{\mathrm{F}}_{6}F6​ has been investigated using 200-nsec pulses of a CO2{\mathrm{O}}_{2}O2​ laser. Operating at \ensuremathλ=10.53\ensuremath{\lambda}=10.53\ensuremathλ=10.53 \ensuremath{\mu}m (P14P14P14 transition) we have observed a breakup of the pulse envelope, an oscillatory energy transmission, and an energy-dependent pulse delay. We interpret our data in terms of the existing theory of self-induced transparency; the corresponding Bloch-type equations were derived assuming thermal equilibrium between rotational MMM sublevels.
This paper gives the details of pulse delay in self-induced transparency in SF6{\mathrm{F}}_{6}F6​ with a CO2{\mathrm{O}}_{2}O2​ laser at 10.5915 \ensuremath{\mu}. Results show that the propagation of intense CO2{\mathrm{O}}_{2}O2​ laser pulses in SF6{\mathrm{F}}_{6}F6​ can be described by self-induced transparency.
We have investigated the self-induced transparency effect in ruby over a range of input energies which range from linear absorption to full transparency. The transmission, pulse delay, and pulse broadening were studied as a function of input energy. The transition region is narrower than that found in similar studies of the CO2{\mathrm{O}}_{2}O2​/SF6{\mathrm{F}}_{6}F6​ system; this is consistent with predictions based on ensembles of two-level systems. Included are the first pulse-delay and pulse-broadening curves to be obtained for the ruby system.
The propagation of two pulses in a three-level absorber is treated by using Maxwell's equations and an effective "two-photon Bloch equations" which are analogous to the one-photon Bloch equations, except for two-photon coupling and frequency shifts. I derive relaxation-dependent shifts in the equilibrium $2n\ensuremath{\pi}$ Lorentzian pulses. Part of these shifts depends on weighted time integrals of harmonics of the area and hence remove the propagation degeneracy of pulses having equal areas but different shapes. Absorption of small-area pulses is studied as a function of absorption length, input energies, and relaxation, and it is found that a local enhancement in the transmission occurs as a function of the absorption length.
Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the $^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}$, $F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ and $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area---pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.
Self-induced transparency in an absorbing neon discharge has been observed on the nonresonance transition $2{s}_{2}(J=1)\ensuremath{-}2{p}_{4}(J=2)$. Since linearly polarized light pulses excite two dipole moments differing by only 18%, the absorber is virtually nondegenerate and superior in simplicity to molecular absorbers. Light pulses, generated from the output of a cw single-frequency 1.15-\ensuremath{\mu}m He-Ne laser oscillator by a pulsed Ne laser amplifier, were transmitted through the absorber. Comparison of the oscilloscope traces of input and output pulses indicated the occurrence of pulse retardation, peak amplification, and pulse breakup. Complete pulse reshaping to the predicted hyperbolic-secant envelope has been observed. The periodicity of transmission versus pulse power, which provides direct evidence of optical nutation, is in agreement with the results of a pulse-area-pulse-energy model.
Effect of the SF6 pressure on self-induced transparency (SIT) in SF6 was investigated systematically. The study consists of measuring the shape, width, delay time, and intensity of the transmitted pulse (which is a SIT pulse at low SF6 pressure) as a function of SF6 pressure P. The SIT pulse was induced by the nonlinear interaction of a 20-nsec P(20) CO2 laser pulse with the SF6. A theory which includes the homogeneous broadening mechanism was developed for the pulse delay time. For a stationary propagating pulse, it was found that the pulse delay time is related nonlinearly to Q (the ratio of the transiently energy stored energy density to the rate of change of the energy flux density of the field). From the interpretation of the experimental results, it was concluded that, for P>100 μ, the SF6-SF6 resonant collision makes a significant contribution to the departure from SIT. The effect of level degeneracies associated with the high angular momentum of the involved resonant vibrational states is also discussed.