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Physical Review A

Experimental Investigation of Self-Induced Transparency and Pulse Delay in Ruby

Irvin M. Asher

Published Jan 1, 1972• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.5.349

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Physical Review•Jul 10, 1969•1,394 citations
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.
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.
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.
A computer simulation of recent self-induced-transparency experiments in ruby demonstrates the general appropriateness of a previously derived two-level model for a wide range of attenuator temperatures. The only significant deviation is a sharper rise in the experimental delay curve. The temperature dependence of the homogeneous phase relaxation ${T}_{2}^{\ensuremath{'}}$ was introduced by including a "direct" phonon transition process in our program. The parameters for best fit provide ${{T}^{\ensuremath{'}}}_{2}\ensuremath{\simeq}50$ nsec for $T\ensuremath{\simeq}0$ \ifmmode^\circ\else\textdegree\fi{}K, which emphasizes the importance of phase-memory effects in low-temperature atomic-coherence experiments in ruby.
Two types of nonlinear transmission of light pulses associated with phase modulation are observed in experiments connected with self-induced transparency (SIT) in ruby. Anomalous pulse-power transmission is observed to be an order of magnitude greater than linear transmission during the condition of zero-area pulse propagation, where the inhomogeneous line spectral width is greater than the applied pulse spectral width. For application of a pulse off-resonance by the order of a linewidth, nonlinear transmission occurs in which a type of "precursor" phase-modulated signal appears ahead of a developing SIT pulse. The precursor pulse velocity is greater than the SIT pulse velocity, but less than the background velocity of light in the medium.
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.
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.