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Physical Review A

Propagation of a Cavity-Dumped C O2 Laser Pulse through S F6

Peter K. Cheo, C. H. Wang

Published Feb 1, 1970• 21 citations
Publisher

Abstract

Coherent interactions between short C${\mathrm{O}}_{2}$ laser pulses and a resonant absorbing S${\mathrm{F}}_{6}$ gas medium have been examined carefully, using a laser cavity-dumped rectangular pulse with a width of 20 nsec and input intensities from 10 to ${10}^{4}$ W/${\mathrm{cm}}^{2}$. Parameters studied included the width, shape, and delay time of the transmitted pulse after propagation through several absorption lengths of S${\mathrm{F}}_{6}$ cell. In addition to these measurements, we have observed two new phenomena, namely, optical free induction decay and edge echo, which are induced by this short rectangular C${\mathrm{O}}_{2}$ laser input pulse. Results indicate that although level degeneracy in S${\mathrm{F}}_{6}$ may be involved, the simple two-level model can account qualitatively for most observed phenomena, with the exception that the observed shape of a $2\ensuremath{\pi}$ pulse deviates significantly from the symmetric hyperbolic-secant function predicted by the simple two-level theory. In the $\ensuremath{\pi}$ pulse region, we have demonstrated that the free-induction-decay tail can be valuable for studies of atomic and molecular collision processes.

DOI
10.1103/physreva.1.225

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The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous S${\mathrm{F}}_{6}$ excited by pulses of C${\mathrm{O}}_{2}$ laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions ($P$ and $R$ branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions ($Q$ branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.

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When an intense and short laser pulse or a fast-switching-on/off laser field interacts with a resonant absorbing medium, several optical coherent transient effects can be observed, including the self-induced transparency effect, photon echo effect, optical nutation effect, and the optical free induction decay effect. The study of these effects enables us to gain a deeper understanding of the coherent transient interaction of an intense pulsed or rapidly switched optical field with the resonant medium, and to measure the magnitude of the dipole-moment matrix elements, relaxation parameters, and spectral broadening mechanisms of the investigated materials. On the other hand, these optical coherent transient effects can also be applied for developing special techniques of optical pulse delay, pulse reshaping, and optical pulse manipulation.

Oxford University Press eBooks•Oct 30, 2014•0 citations
Coherent interactions between short CO2{\mathrm{O}}_{2}O2​ laser pulses and a resonant absorbing SF6{\mathrm{F}}_{6}F6​ gas medium have been examined carefully, using a laser cavity-dumped rectangular pulse with a width of 20 nsec and input intensities from 10 to 104{10}^{4}104 W/cm2{\mathrm{cm}}^{2}cm2. Parameters studied included the width, shape, and delay time of the transmitted pulse after propagation through several absorption lengths of SF6{\mathrm{F}}_{6}F6​ cell. In addition to these measurements, we have observed two new phenomena, namely, optical free induction decay and edge echo, which are induced by this short rectangular CO2{\mathrm{O}}_{2}O2​ laser input pulse. Results indicate that although level degeneracy in SF6{\mathrm{F}}_{6}F6​ may be involved, the simple two-level model can account qualitatively for most observed phenomena, with the exception that the observed shape of a 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ pulse deviates significantly from the symmetric hyperbolic-secant function predicted by the simple two-level theory. In the \ensuremathπ\ensuremath{\pi}\ensuremathπ pulse region, we have demonstrated that the free-induction-decay tail can be valuable for studies of atomic and molecular collision processes.
Strong and short coherent pulses of electromagnetic radiation propagate through extended absorbing media with anomalously low absorption, they are delayed and reshaped. This article presents experimental results and calculations for propagation of 10.6-\ensuremath{\mu} wavelength pulses through gaseous SF6{\mathrm{F}}_{6}F6​. The degeneracy of overlapping levels of SF6{\mathrm{F}}_{6}F6​ in that spectral region is important, and enables us to use a simple model to describe observed phenomena. We assume a continuous distribution of dipole moments. Results are particularly interesting in two regimes of excitation. One corresponds to very strong excitation and \ensuremath{\sim}20 absorption lengths in the medium: Pulses sharpen at their leading edge, while their front part gets absorbed. The other pertains to much lower excitation and only 2 absorption lengths: Reradiation can be distinguished and long delays result which qualitatively resemble the behavior of a two-level system in self-induced transparency. Fairly conclusive agreement is obtained between a previous theoretical treatment of a homogeneously broadened multilevel medium and experiment. The agreement is substantiated by computer calculations. In three Appendixes we present the observation of focusing effects, the theory of an experiment related to transient nutation, and some remarks on photon-echo polarization experiments in optically thick media.
Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in SF6{\mathrm{F}}_{6}F6​ using a pulsed CO2{\mathrm{O}}_{2}O2​ laser operated on the 10.4-\ensuremath{\mu} m branch. A pulse width of 1.2 nsec was used to reduce effects of collisional relaxation. Data are also presented for pulse widths of 140 nsec. At high-energy fluences (\ensuremath{\sim}0.1 J/cm2{\mathrm{cm}}^{2}cm2) pulse breakup is observed and is believed to arise from multiple-photon effects. The data obtained with the short pulse width are compared to a four-level saturable-absorber model where excellent agreement is obtained when pump absorption is included. The qualitative behavior of DFWM due to dispersion is also demonstrated in the wings of the SF6{\mathrm{F}}_{6}F6​ absorption spectrum. Peak reflectivities of 38% were readily obtained. In addition contributions due to a coherent three-level nonlinearity are presented showing a contribution equal to the measured saturable contribution.
Photon echoes following two pulses of CO2{\mathrm{O}}_{2}O2​ laser radiation incident on SF6{\mathrm{F}}_{6}F6​ gas have been observed. Homogeneous relaxation times for SF6{\mathrm{F}}_{6}F6​ colliding with SF6{\mathrm{F}}_{6}F6​, He, Ne, and H2{\mathrm{H}}_{2}H2​ are shown to be easily measurable from the decay of photon-echo amplitude.
The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous SF6{\mathrm{F}}_{6}F6​ excited by pulses of CO2{\mathrm{O}}_{2}O2​ laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions (PPP and RRR branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions (QQQ branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.
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.
When an intense and short laser pulse or a fast-switching-on/off laser field interacts with a resonant absorbing medium, several optical coherent transient effects can be observed, including the self-induced transparency effect, photon echo effect, optical nutation effect, and the optical free induction decay effect. The study of these effects enables us to gain a deeper understanding of the coherent transient interaction of an intense pulsed or rapidly switched optical field with the resonant medium, and to measure the magnitude of the dipole-moment matrix elements, relaxation parameters, and spectral broadening mechanisms of the investigated materials. On the other hand, these optical coherent transient effects can also be applied for developing special techniques of optical pulse delay, pulse reshaping, and optical pulse manipulation.