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Журнал технической физики

Короткие импульсы нормальных мод электромагнитно индуцированной прозрачности

Oleg M. Parshkov

Published Jan 1, 2019• 0 citations
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Abstract

AbstractThe process of propagation of short probe pulses of electromagnetically induced transparency has been analyzed theoretically in the case of elliptically polarized control radiation. As a model of a resonant medium, a Λ scheme of quantum transitions between the $$^{3}{{P}_{0}}$$ , $$^{3}P_{1}^{0}$$ , and $$^{3}{{P}_{2}}$$ degenerate levels of the ^208Pb isotope has been used. The situation in which the probe radiation is rather weak compared to the control radiation has been examined. In this case, the field of the probe pulse can be represented as a sum of the fields of two elliptically polarized pulses that propagate in the medium independently of one another without changing their polarization state, which makes it possible to interpret them as nonstationary normal modes. Numerical simulation has shown that the structure of normal modes depends on the ratio of the width of the spectrum of the input probe pulse to the Doppler frequency broadening of the quantum transition that is resonant to the probe field. If this ratio is small, each mode in the medium is a single pulse similar to the input probe pulse. Under these conditions, the propagation of each normal mode in the medium can be fairly well characterized by the group velocity depending on the intensity and the state of polarization of the control radiation. As this ratio increases, normal modes in the medium initially acquire the shape of a regular decaying train of pulses, and then their structure becomes chaotic. The described evolution is accompanied by an increase in the energy absorption of the probe radiation by the medium and by a significant deterioration in the applicability of the notion of group velocity for describing the propagation process of normal modes.

DOI
10.21883/os.2019.04.47520.304-18

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Quantum Electronics•Oct 31, 2017•3 citations
AbstractThe process of propagation of short probe pulses of electromagnetically induced transparency has been analyzed theoretically in the case of elliptically polarized control radiation. As a model of a resonant medium, a Λ scheme of quantum transitions between the 3P0^{3}{{P}_{0}}3P0​ , 3P10^{3}P_{1}^{0}3P10​ , and 3P2^{3}{{P}_{2}}3P2​ degenerate levels of the ^208Pb isotope has been used. The situation in which the probe radiation is rather weak compared to the control radiation has been examined. In this case, the field of the probe pulse can be represented as a sum of the fields of two elliptically polarized pulses that propagate in the medium independently of one another without changing their polarization state, which makes it possible to interpret them as nonstationary normal modes. Numerical simulation has shown that the structure of normal modes depends on the ratio of the width of the spectrum of the input probe pulse to the Doppler frequency broadening of the quantum transition that is resonant to the probe field. If this ratio is small, each mode in the medium is a single pulse similar to the input probe pulse. Under these conditions, the propagation of each normal mode in the medium can be fairly well characterized by the group velocity depending on the intensity and the state of polarization of the control radiation. As this ratio increases, normal modes in the medium initially acquire the shape of a regular decaying train of pulses, and then their structure becomes chaotic. The described evolution is accompanied by an increase in the energy absorption of the probe radiation by the medium and by a significant deterioration in the applicability of the notion of group velocity for describing the propagation process of normal modes.
The process of propagation of short probe pulses of electromagnetically induced transparency has been analyzed theoretically in the case of elliptically polarized control radiation. As a model of a resonant medium, a Λ scheme of quantum transitions between the 3P0^{3}{{P}_{0}}3P0​ , 3P10^{3}P_{1}^{0}3P10​ , and 3P2^{3}{{P}_{2}}3P2​ degenerate levels of the 208Pb isotope has been used. The situation in which the probe radiation is rather weak compared to the control radiation has been examined. In this case, the field of the probe pulse can be represented as a sum of the fields of two elliptically polarized pulses that propagate in the medium independently of one another without changing their polarization state, which makes it possible to interpret them as nonstationary normal modes. Numerical simulation has shown that the structure of normal modes depends on the ratio of the width of the spectrum of the input probe pulse to the Doppler frequency broadening of the quantum transition that is resonant to the probe field. If this ratio is small, each mode in the medium is a single pulse similar to the input probe pulse. Under these conditions, the propagation of each normal mode in the medium can be fairly well characterized by the group velocity depending on the intensity and the state of polarization of the control radiation. As this ratio increases, normal modes in the medium initially acquire the shape of a regular decaying train of pulses, and then their structure becomes chaotic. The described evolution is accompanied by an increase in the energy absorption of the probe radiation by the medium and by a significant deterioration in the applicability of the notion of group velocity for describing the propagation process of normal modes.
The results of analytical and numerical analysis of propagation of short probe pulses of electromagnetically induced transparency in the case of control field elliptic polarization are presented. The situation is explored, when the probe field is weak comparison with control radiation. Then the probe pulse in the medium is a sum of two elliptically polarized pulses, which travel without interaction among themselves and have invariable states of polarization. This fact permits to term these pulses nonstationary elliptically polarized normal modes. Numerical simulation shown, that normal mode structure is determined by the ratio of spectral width of input probe pulse to spectral width of quantum transition, which is resonant to probe emission. When this relation is small, each mode in the medium is the pulse similar to input probe pulse. If this relation is large, the mode envelopes are distorted, when mode pulses travel in the medium. In this case, probe pulse absorption increases considerably. The theoretical investigation is performed for the  -scheme of degenerate quantum transitions between 3P0 , 3P10 and 3P2 energy levels of 208Pb isotope.
The conclusions of a theoretical study of the dependence of the characteristics of the phenomenon of electromagnetically induced transparency on the pulse intensity of the input probe radiation under elliptical polarization of laser fields have been reported. The analysis has been carried out for the Ʌ-scheme of inhomogeneously broadened quantum transitions between the levels 3P0{}^{3}{{P}_{0}}3P0​ , 3P10{}^{3}P_{1}^{0}3P10​ , and 3P2{}^{3}{{P}_{2}}3P2​ of the 208Pb isotope. The cases of resonance, i.e., the coincidence of the frequencies of the probe and control fields with the central frequencies of the corresponding quantum transitions, and quasi-resonance, when such a coincidence occurs only up to the line width of the corresponding quantum transition, have been considered. It has been shown that in these cases there is a tendency for the input probe radiation to split into pulses with different polarization characteristics. If the input probe radiation is weak enough, these pulses have constant polarization characteristics and are normal mode pulses. In the case of a higher power of the input probe radiation, the pulses into which it splits in the medium are not normal mode pulses, but their polarization characteristics fluctuate near the values inherent in normal modes. At the same time, the phase modulation of the probe field is present at all stages of its propagation in the medium. It has been shown that the transparency of the medium for the probe field decreases with increasing intensity of the input probe radiation. However, it is sufficiently large if the polarization characteristics of the input probe radiation coincide with those for the normal mode, the major axis of the polarization ellipse of which is parallel to the major axis of the control field polarization ellipse.
The results of a theoretical study of the evolution of powerful elliptically polarized probe nanosecond pulses of electromagnetically induced transparency are presented. The analysis was carried out for the Ʌ-scheme of inhomogeneously broadened quantum transitions between degenerate levels of the 208Pb isotope. The cases of resonance and quasiresonance are considered under the assumption that the input probe and control radiation have no phase modulation. It is shown that at a higher power of the input probe radiation, the pulses, into which it decays in the medium, are not pulses of normal modes, but their polarization characteristics fluctuate around the values inherent in normal modes, arising at a weak input probe radiation. In the case of a powerful input probe pulse, the phase modulation of the probe field is present at all stages of its propagation in the medium. It is shown that with an increase in the intensity of the input probe radiation, the transparency of the medium for the probe field decreases. However, it is large enough if the polarization characteristics of the input probe radiation coincide with those for normal modes of the parallel type.
The effect of separation of linearly polarized short probe pulses of electromagnetically induced transparency in the field of linearly polarized coupling radiation is modeled numerically. It is shown that the input-probe pulses polarized parallel or perpendicular to the input-probe field propagate in the medium without changing the state of their polarization. If the input-probe radiation is weak compared to the coupling radiation, then the probe field inside the medium is the sum of two independently propagating linearly polarized normal modes, which are excited by the projections of the input-probe pulse onto the direction of polarization of the coupling radiation and onto the perpendicular direction, respectively. The normal modes have the same phase velocities, but different velocities of their real envelopes. This circumstance leads to the rotation of the plane of polarization of the total probe field at short distances and to its separation into two pulses with mutually perpendicular directions of polarization at long distances. At a high intensity of the probe radiation, the input-probe pulse decays into pulses the planes of polarization of which are not mutually perpendicular. Under these conditions, it is impossible to represent the probe radiation as a sum of normal modes. The modeling is performed in the scheme of degenerate quantum transitions between states of levels 3 P 0, 3 P 1 0, and 3 P 2 of isotope 208Pb taking into account the Doppler broadening of spectral lines.
We report the results of numerical simulation of the evolution of a weak elliptically polarised input probe pulse in the case of electromagnetically induced transparency in the field of elliptically polarised control light. It is shown that the electric field strength of any input probe pulse can be represented as a sum of the electric field strengths of two subpulses whose polarisation ellipses have the same constant eccentricities and mutually perpendicular directions of the major axes, one of these axes being parallel to the major axis of the polarisation ellipse of the control light. The directions of rotation of the electric field strength vectors of subpulses are mutually opposite. Subpulses move with different velocities in a medium, which leads to their spatial separation. In the propagation of subpulses, their polarisation characteristics (eccentricities and directions of major axes of polarisation ellipses) remain unchanged. At any stage of evolution, including the instants of significant spatial overlapping of subpulses, the intensity of the probe light in the medium is the sum of their intensities. Consequently, these subpulses are nonstationary mutually orthogonal elliptically polarised normal modes of the probe field whose existence is related to the medium anisotropy caused by the control field. The simulation is carried out for a scheme of degenerate quantum transitions between 3 P 0 , 3 P 1 0 and 3 P 2 levels of the 208 Pb isotope, taking into account the Doppler broadening of the spectral lines under the assumption that the probe field has a higher frequency than the control field.