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Physical Review

Transmission of Coherent Optical Pulses in Gaseous S F6

C. K. Rhodes, A. Szöke

Published Aug 5, 1969• 79 citations
Publisher

Abstract

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 S${\mathrm{F}}_{6}$. The degeneracy of overlapping levels of S${\mathrm{F}}_{6}$ 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.

DOI
10.1103/physrev.184.25

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

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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.

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Photon Echoes in Gases

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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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Two-photon self-induced transparency in a resonant medium. II. Transient pulse behaviour

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For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.

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Degenerate four-wave mixing in a resonant homogeneously broadened system

Duncan G. Steel, Richard C. Lind, Jenny Lam

Detailed measurements have been made of degenerate four-wave mixing (DFWM) in a resonant homogeneously broadened gas. The measurements were performed in S${\mathrm{F}}_{6}$ using a pulsed C${\mathrm{O}}_{2}$ 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/${\mathrm{cm}}^{2}$) 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 S${\mathrm{F}}_{6}$ 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.

Physical Review A•May 1, 1981•49 citations
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.
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 $2\ensuremath{\pi}$ 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.
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.
The influence of degeneracy on coherent pulse propagation in an inhomogeneously broadened attenuator is examined by computer calculations, and the connection with self-induced transparency in a nondegenerate system is described. Specific modifications that arise in a degenerate system are the development of pulse shapes characteristic of the degeneracy, the association of a finite loss with propagation, a reduction of pulse delay times, and the suppression of pulse separation of multi-$2\ensuremath{\pi}$ pulses. Additionally, results of calculations pertaining to experiments on pulse propagation in SF6{\mathrm{F}}_{6}F6​ are presented which indicate two basically different phenomena. One corresponds to delay phenomena qualitatively similar to nondegenerate self-induced transparency, while the other is a coherent saturation effect generally characteristic of degenerate media. The computed results fully substantiate our earlier experimental findings.
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.
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.
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.