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Physical Review

Self-Induced Transparency

S. L. McCall, Erwin Louis Hahn

Published Jul 10, 1969• 1,394 citations
Publisher

Abstract

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.

DOI
10.1103/physrev.183.457

Related papers

Coherent pulse propagation and self-induced transparency on degenerate transitions in atomic iodine

Gan Xu, Terence A. King

Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the $^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}$, $F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ and $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area---pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.

Physical Review A•Jul 1, 1984•9 citations

Two-photon self-induced transparency in a resonant medium. I. Analytical treatment

N Tan-no, Kenichi Yokoto, Humio Inaba

The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.

Journal of Physics B Atomic and Molecular Physics•Feb 21, 1975•23 citations

Optical pulse probing of coherency gradient in Λ-medium

Igor V. Kazinets, I. E. Mazets, Boris G. Matisov

Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 5, 1999•0 citations

Self-Induced Transparency in Atomic Rubidium

R. E. Slusher, H. M. Gibbs

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.

Physical Review A•Apr 1, 1972•183 citations

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

N Tan-no, Kenichi Yokoto, Humio Inaba

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.

Journal of Physics B Atomic and Molecular Physics•Feb 21, 1975•10 citations

Self-Induced Transparency Phenomena of Single-Mode Pulse Laser Propagating in a Thick Ytterbium Vapor Column

Jonghoon Yi, Hyunmin Park, Yongjoo Rhee +1 more

The variations in pulse shape of a single-mode pulse laser propagating through ytterbium (Yb) atomic medium were investigated experimentally. The laser pulse shape was changed as a function of pulse area and it could be explained well using the area theorem. When the pulse area was close to 2π, the pulse shape was transformed to a hyperbolic secant function after transmission. The transmission curve of the propagating laser vs. the pulse area demonstrated self-induced transparency phenomena well. However, the transmission was markedly reduced when the atomic density was increased above ∼4×1010 atoms/cm3. Several causes; such as collision-induced polarization relaxation, Doppler broadening, laser incoherence, and power broadening, which could induce reduced transmission, were examined. It was the incoherence of the laser that caused reduced transmission because the laser line width was broader than the Fourier-transform limit, and the absorbed energy dissipated through spontaneous emission.

Japanese Journal of Applied Physics•Mar 1, 2000•3 citations
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\ensuremathπ2\ensuremath{\pi}2\ensuremathπ 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\ensuremathπ2\ensuremath{\pi}2\ensuremathπ pulse condition can be maintained if losses caused by damping are compensated by beam focusing. In an amplifying inhomogeneously broadened medium an analytic "\ensuremathπ\ensuremath{\pi}\ensuremathπ 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\ensuremathπ2\ensuremath{\pi}2\ensuremathπ pulse outputs have been observed, and pulse areas measured in the range of 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ. 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.
Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the $^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}$, $F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ and $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area---pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.
The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
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.
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.
The variations in pulse shape of a single-mode pulse laser propagating through ytterbium (Yb) atomic medium were investigated experimentally. The laser pulse shape was changed as a function of pulse area and it could be explained well using the area theorem. When the pulse area was close to 2π, the pulse shape was transformed to a hyperbolic secant function after transmission. The transmission curve of the propagating laser vs. the pulse area demonstrated self-induced transparency phenomena well. However, the transmission was markedly reduced when the atomic density was increased above ∼4×1010 atoms/cm3. Several causes; such as collision-induced polarization relaxation, Doppler broadening, laser incoherence, and power broadening, which could induce reduced transmission, were examined. It was the incoherence of the laser that caused reduced transmission because the laser line width was broader than the Fourier-transform limit, and the absorbed energy dissipated through spontaneous emission.