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Physical Review A

Microwave EPR self-induced transparency

S. B. Grossman, Erwin Louis Hahn

Published Dec 1, 1976• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.14.2206

Related papers

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

Aleksander K. Rebane, Hans Riesen, Steffen Ganschow +3 more

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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Self-Induced Transparency in Acoustic Paramagnetic Resonance

N. S. Shiren

Experiments on the propagation of microwave ultrasonic pulses through a resonant absorber are described. The principal features of self-induced transparency as described by McCall and Hahn for light pulses are observed. Quantitative measurements of pulse delay, output pulse width, energy, and area are in fair agreement with a calculation by Hopf which accounts approximately for the effect of the single reflection present in most of the experiments. Multiply reflected pulses exhibited linearly cumulative delay times, indicating constant reduced velocity during successive traversals through the absorber. Coherence-induced pulse breakup is shown to be a possible explanation of the pulse distortion and modulation observed in acoustic-paramagnetic-resonance experiments on ${\mathrm{Fe}}^{2+}$.

Physical review. B, Solid state•Oct 1, 1970•108 citations

Self-Induced Transparency

S. L. McCall, Erwin Louis Hahn

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.

Physical Review•Jul 10, 1969•1,394 citations

Effects of spatial dispersion on Self--induced transparency in two--level media

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We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - $x=ω/ω_0$. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of $x$. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.

arXiv:1909.01393•Sep 3, 2019•0 citations

Phase-modulation propagation effects in ruby

Jean‐Claude Diels, Erwin Louis Hahn

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.

Physical Review A•Dec 1, 1974•30 citations

Analytical studies of ultrashort optical pulse propagation in a resonant absorbing medium

C. T. Lee

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.

•Aug 1, 1974•0 citations
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.
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.
Experiments on the propagation of microwave ultrasonic pulses through a resonant absorber are described. The principal features of self-induced transparency as described by McCall and Hahn for light pulses are observed. Quantitative measurements of pulse delay, output pulse width, energy, and area are in fair agreement with a calculation by Hopf which accounts approximately for the effect of the single reflection present in most of the experiments. Multiply reflected pulses exhibited linearly cumulative delay times, indicating constant reduced velocity during successive traversals through the absorber. Coherence-induced pulse breakup is shown to be a possible explanation of the pulse distortion and modulation observed in acoustic-paramagnetic-resonance experiments on Fe2+{\mathrm{Fe}}^{2+}Fe2+.
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.
We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - x=ω/ω0x=ω/ω_0x=ω/ω0​. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of xxx. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.
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.
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.