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Physical Review A

Phase-modulation propagation effects in ruby

Jean‐Claude Diels, Erwin Louis Hahn

Published Dec 1, 1974• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.10.2501

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Physical Review A•Dec 1, 1976•7 citations
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.
Self-induced transparency is reported for circularly polarized light in the R1(−3/2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of B‖c=4.5 T. In such a field and temperature, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a long phase memory time, TM=50 μs, and a thousand-fold slower pulse propagation velocity of ∼300 m/s was observed, compared to the ∼300 km/s measured in the first observation of self-induced transparency (SIT) ∼50 years ago, that employed a ruby with a 500 ppm chromium concentration in zero field and at 4.2 K. To date, this is the slowest pulse propagation ever observed in a SIT experiment.
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.
The nonlinear propagation of a Q-switched ruby laser pulse in a resonant medium such as a ruby sample is experimentally investigated. The transmission characteristics obtained at the sample temperature between 25℃ to -180℃ show the nonlinearity as increasing of the input energy. This result may be qualitatively explained by the saturation effect (incoherent effect). The pulse spliting phenomenon in the transmitted pulse, which is an evidence of the ""self induced transparency (coherent effect), "" is also observed at about -80℃. These results show that the coherent and incoherent effects simultaneously occur in the ruby absorption sample.
Resonant absorption in a laser pulse can be reduced to zero if the trailing part induces stimulated emission and returns the absorbed energy back to the pulse. This kind of effect is called Self-Induced Transparency (SIT). Analytic descriptions of short pulse propagation in a resonant medium, based on Slowly Varying Envelope Approximation (SVEA) and in linear media, have been extended in studies of SIT along two principal directions: First, to improve the SVEA by introducing Short Pulse Approximation (SPA); and second, to consider the effect of nonlinear refractive index.
The waveguide propagation of a microwave magnetic field pulse at electron paramagnetic resonance (EPR) with a free radical sample of electron spins distributed along the guide displays the phenomenon of self-induced transparency (SIT). Predictions of plane-wave optical SIT are modified by summation of the magnetic-moment-microwave-field coupling over the transverse waveguide mode for specific sample geometries. Mode modified pulse area theorems are presented. Observed output pulse areas and shapes are compared with computer predictions. After pulse propagation over several absorption lengths a spontaneous zero-area pulse propagation effect is observed for a short weak input pulse with spectral width comparable to or larger than the spin-resonance linewidth. Alternating 180\ifmmode^\circ\else\textdegree\fi{} phase shifts in the pulse carrier wave, accounting for zero area, signify magnetic dipole transitions which alternate between coherent absorption and emission to some extent, and therefore anomalous pulse propagation is observed. For pulses applied off-resonance, linear and nonlinear shifts of the average carrier frequency occur toward the center of the spin resonance.