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Physical Review A

Sharp-Line Self-Induced Transparency

H. M. Gibbs, R. E. Slusher

Published Dec 1, 1972• 62 citations
Publisher

Abstract

Self-induced transparency (SIT) has been observed under the conditions of sharp-line absorption, i.e., with an inhomogeneous absorption width only one-fourth the spectral width of the pulse. A 5-nsec pulse from a $^{202}\mathrm{Hg}$ ii laser intersected perpendicularly an atomic beam of natural rubidium. The beam slits reduced the Doppler absorption width to about 30 MHz. A particular resolved ${M}_{\mathrm{I}}$ transition of $^{85}\mathrm{Rb}$ was scanned into coincidence with the laser pulse by a 75-KOe magnetic field. With peak absorption depths of 3-6, nonlinear transmission, pulse delays, pulse breakup, and peak amplification were seen and found to be in excellent agreement with sharp-line computer solutions of the Maxwell-Bloch equations. The experimental realization of the sharp-line SIT is of interest because analytical formulas for pulse evolutions are more plentiful and because sharp-line SIT might permit compression of picosecond pulses.

DOI
10.1103/physreva.6.2326

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Self-Induced Transparency in Atomic Rubidium

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Self-induced transparency has been studied in detail experimentally for a simple two-level atomic absorption. A Hg II laser pulse is used at resonance with the ${D}_{1}$ line of Rb. This system eliminates many previous experimental problems such as nonuniform wave fronts and degenerate off-resonant absorbers. Nonlinear transmission, pulse delays, pulse breakup, peak amplification, incoherent-decay effects, off-resonance effects, and focusing effects have been observed. Quantitative comparison with theory is obtained by computer solutions which include the incoherent decay and optical-pulse shapes of the Hg-Rb system. Good agreement is obtained with the theory of McCall and Hahn. Pulse compression by an order of magnitude is obtained by focusing in the resonant absorber. The theory predicting preferred pulse widths and velocities proposed by Davidovich and Eberly is discussed and found inappropriate for the Hg-Rb and other similar systems.

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Above a critical power threshold for a given pulse width, a short pulse of coherent traveling-wave optical radiation is observed to propagate with anomalously low energy loss while at resonance with a two-quantum-level system of absorbers. The line shape of the resonant system is determined by inhomogeneous broadening, and the pulse width is short compared to dissipative relaxation times. A new mechanism of self-induced transparency, which accounts for the low energy loss, is analyzed in the ideal limit of a plane wave which excites a resonant medium with no damping present. The stable condition of transparency results after the traversal of the pulse through a few classical absorption lengths into the medium. This condition exists when the initial pulse has evolved into a symmetric hyperbolic-secant pulse function of time and distance, and has the area characteristic of a "$2\ensuremath{\pi}$ pulse." Ideal transparency then persists when coherent induced absorption of pulse energy during the first half of the pulse is followed by coherent induced emission of the same amount of energy back into the beam direction during the second half of the pulse. The effects of dissipative relaxation times upon pulse energy, pulse area, and pulse delay time are analyzed to first order in the ratio of short pulse width to long damping time. The analysis shows that the $2\ensuremath{\pi}$ pulse condition can be maintained if losses caused by damping are compensated by beam focusing. In an amplifying inhomogeneously broadened medium an analytic "$\ensuremath{\pi}$ pulse area" solution is presented in the limit of a sharp leading edge of the pulse. The dynamics of self-induced transparency are studied for the particular effects of Doppler velocities upon a resonant gas. The analysis of transparency for random orientations of dipole moments associated with degenerate rotational states yields modified forms of self-induced transparency behavior, which indicates a finite pulse energy loss as a function of distance in some cases. The effect of self-induced transparency on the photon echo is considered. Experimental observations of self-induced transparency have been made in a ruby sample at resonance with a pulsed ruby-laser beam. Single and multiple $2\ensuremath{\pi}$ pulse outputs have been observed, and pulse areas measured in the range of $2\ensuremath{\pi}$. The experimental results are compared with the predictions of the ideal-plane-wave theory. Deviations from the ideal-plane-wave theory are discussed. An analysis is made of the effect of a transverse mode of the propagating beam upon the transparency properties of the pulse.

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Self-induced transparency and soliton formation in ruby: simulations and experiment (Conference Presentation)

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Formation of optical solitons in self-induced transparency (SIT) regime, where light pulses propagate virtually without loss in nominally strongly absorbing medium, is one of the most striking coherent transient phenomena in optics. Here we study experimentally and by numeric simulations how a square shape pulse gradually transforms into a smooth sech shape pulse of well-defined pulse area, depending on the parameters such as the pulse amplitude, duration, propagation distance etc. The SIT experiments for circularly polarized light are performed in the R1−3∕2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of BIIc = 4.5 T, which corresponds to effective absorption coefficient, αL =14.5. In such a magnetic field and temperature range, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a very long decoherence (phase memory) time, TM = 50 μs. We show, in good quantitative agreement with the simulations, how SIT soliton is formatted and how this results in extremely slow pulse peak propagation velocity of ∼300 m∕s, which is to date, the slowest pulse propagation ever observed in a SIT experiment. We also show that for accurate quantitative description of the observed SIT and soliton pulse shapes, the simulations need to account for variation of the incident pulse amplitude across the beam spatial profile. Potential implications of the SIT effect on classical- and quantum information storage will be discussed.

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Effects of Degeneracy on Self-Induced Transparency

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Self-Induced Transparency in Resonant Medium.

Hidetoshi Nakano, Yuzo Ishida

Self-induced transparency (SIT) is a kind of coherent transient phenomena in two-level atomic system. The optical pulse with an area that is an integer multiple of 2π, which causes SIT in an absorber, is stable and a kind of soliton. Thus SIT is expected to be useful in pulse compression and pulse shaping. In this paper, we discuss some problems in experiments of SIT and surveys the experimental results of SIT. It is also described the recent experimental results of coherent nonlinear pulse propagation in BiI3 crystal using tunable sub-picosecond pulses.

The Review of Laser Engineering•Jan 1, 1992•0 citations
Self-induced transparency (SIT) has been observed under the conditions of sharp-line absorption, i.e., with an inhomogeneous absorption width only one-fourth the spectral width of the pulse. A 5-nsec pulse from a 202Hg^{202}\mathrm{Hg}202Hg ii laser intersected perpendicularly an atomic beam of natural rubidium. The beam slits reduced the Doppler absorption width to about 30 MHz. A particular resolved MI{M}_{\mathrm{I}}MI​ transition of 85Rb^{85}\mathrm{Rb}85Rb was scanned into coincidence with the laser pulse by a 75-KOe magnetic field. With peak absorption depths of 3-6, nonlinear transmission, pulse delays, pulse breakup, and peak amplification were seen and found to be in excellent agreement with sharp-line computer solutions of the Maxwell-Bloch equations. The experimental realization of the sharp-line SIT is of interest because analytical formulas for pulse evolutions are more plentiful and because sharp-line SIT might permit compression of picosecond pulses.
Self-induced transparency has been studied in detail experimentally for a simple two-level atomic absorption. A Hg II laser pulse is used at resonance with the D1{D}_{1}D1​ line of Rb. This system eliminates many previous experimental problems such as nonuniform wave fronts and degenerate off-resonant absorbers. Nonlinear transmission, pulse delays, pulse breakup, peak amplification, incoherent-decay effects, off-resonance effects, and focusing effects have been observed. Quantitative comparison with theory is obtained by computer solutions which include the incoherent decay and optical-pulse shapes of the Hg-Rb system. Good agreement is obtained with the theory of McCall and Hahn. Pulse compression by an order of magnitude is obtained by focusing in the resonant absorber. The theory predicting preferred pulse widths and velocities proposed by Davidovich and Eberly is discussed and found inappropriate for the Hg-Rb and other similar systems.
Above a critical power threshold for a given pulse width, a short pulse of coherent traveling-wave optical radiation is observed to propagate with anomalously low energy loss while at resonance with a two-quantum-level system of absorbers. The line shape of the resonant system is determined by inhomogeneous broadening, and the pulse width is short compared to dissipative relaxation times. A new mechanism of self-induced transparency, which accounts for the low energy loss, is analyzed in the ideal limit of a plane wave which excites a resonant medium with no damping present. The stable condition of transparency results after the traversal of the pulse through a few classical absorption lengths into the medium. This condition exists when the initial pulse has evolved into a symmetric hyperbolic-secant pulse function of time and distance, and has the area characteristic of a "$2\ensuremath{\pi}$ pulse." Ideal transparency then persists when coherent induced absorption of pulse energy during the first half of the pulse is followed by coherent induced emission of the same amount of energy back into the beam direction during the second half of the pulse. The effects of dissipative relaxation times upon pulse energy, pulse area, and pulse delay time are analyzed to first order in the ratio of short pulse width to long damping time. The analysis shows that the $2\ensuremath{\pi}$ pulse condition can be maintained if losses caused by damping are compensated by beam focusing. In an amplifying inhomogeneously broadened medium an analytic "$\ensuremath{\pi}$ pulse area" solution is presented in the limit of a sharp leading edge of the pulse. The dynamics of self-induced transparency are studied for the particular effects of Doppler velocities upon a resonant gas. The analysis of transparency for random orientations of dipole moments associated with degenerate rotational states yields modified forms of self-induced transparency behavior, which indicates a finite pulse energy loss as a function of distance in some cases. The effect of self-induced transparency on the photon echo is considered. Experimental observations of self-induced transparency have been made in a ruby sample at resonance with a pulsed ruby-laser beam. Single and multiple $2\ensuremath{\pi}$ pulse outputs have been observed, and pulse areas measured in the range of $2\ensuremath{\pi}$. The experimental results are compared with the predictions of the ideal-plane-wave theory. Deviations from the ideal-plane-wave theory are discussed. An analysis is made of the effect of a transverse mode of the propagating beam upon the transparency properties of the pulse.
Formation of optical solitons in self-induced transparency (SIT) regime, where light pulses propagate virtually without loss in nominally strongly absorbing medium, is one of the most striking coherent transient phenomena in optics. Here we study experimentally and by numeric simulations how a square shape pulse gradually transforms into a smooth sech shape pulse of well-defined pulse area, depending on the parameters such as the pulse amplitude, duration, propagation distance etc. The SIT experiments for circularly polarized light are performed in the R1−3∕2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of BIIc = 4.5 T, which corresponds to effective absorption coefficient, αL =14.5. In such a magnetic field and temperature range, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a very long decoherence (phase memory) time, TM = 50 μs. We show, in good quantitative agreement with the simulations, how SIT soliton is formatted and how this results in extremely slow pulse peak propagation velocity of ∼300 m∕s, which is to date, the slowest pulse propagation ever observed in a SIT experiment. We also show that for accurate quantitative description of the observed SIT and soliton pulse shapes, the simulations need to account for variation of the incident pulse amplitude across the beam spatial profile. Potential implications of the SIT effect on classical- and quantum information storage will be discussed.
The self-induced transparency solution of the Bloch-Maxwell equations is found in the case of inhomogeneously broadened resonant atomic lines and a host medium with a Kerr-type nonlinearity in the index of refraction. The characteristic feature of the solution is that the atomic functions are not factorized. The time dependence of the pulse phase is different from that in the case of a sharp atomic line. In addition to the known term quadratic in the pulse envelope, it contains a term increasing in time, attaining a maximum at the trailing edge of the pulse, and rapidly decreasing afterwards. The average carrier frequency is proportional to the square of the spectral width of the atomic line divided by the squared width of the pulse. A satisfactory solution is found by modulation of the center of the Lorentz distribution function of the purely resonant solutions. It is shown that in the presence of the inhomogeneous broadening the problem cannot be solved by a linear perturbation expansion with respect to the Kerr constant. This method leads to divergencies near the trailing edge of the pulse.
Self-induced transparency (SIT) is a kind of coherent transient phenomena in two-level atomic system. The optical pulse with an area that is an integer multiple of 2π, which causes SIT in an absorber, is stable and a kind of soliton. Thus SIT is expected to be useful in pulse compression and pulse shaping. In this paper, we discuss some problems in experiments of SIT and surveys the experimental results of SIT. It is also described the recent experimental results of coherent nonlinear pulse propagation in BiI3 crystal using tunable sub-picosecond pulses.