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Optics and Spectroscopy

Normal modes of a probe field in the pulsed regime of electromagnetically induced transparency in a Λ-scheme of degenerate quantum transitions

Oleg M. Parshkov

Published Sep 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1134/s0030400x17090259

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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling•May 4, 2021•0 citations
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.
The evolution of radiation under conditions of electromagnetically induced transparency in the scheme of degenerate quantum transitions J = 0 → J = 1 → J = 2 in the pulsed interaction regime of the fields and with allowance for the Doppler broadening of spectral lines has been analyzed numerically. It has been shown that, if the input coupling radiation is linearly polarized, the circularly polarized input probe pulse splits in the medium into pulses with mutually perpendicular linear polarizations. The direction of polarization of one of these pulses coincides with the direction of polarization of the input coupling field. The distance that the probe pulse travels in the medium until it completely decays decreases with a decrease in both the duration of the input probe pulse and the intensity of the input coupling radiation. A change in the power of the input probe pulse hardly affects the distance required for the decay and the velocity of propagation of linearly polarized pulses in the medium. An increase in the Doppler broadening of spectral lines leads to a decrease in this distance and, simultaneously, to an increase in the energy losses of the probe radiation. Qualitative considerations that explain the physical reason for the investigated effects have been presented.
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 numerical simulation results of radiations evolution in the presence of electromagnetically induced transparency for J=0→J=1→J=2 scheme of degenerate quantum transitions are presented. The pulse regime of wave interaction with Doppler broadening spectral lines was investigated. It was indicated that when the control field is linear polarized, the input circular polarized probe pulse breaks up in the medium into pulses with mutually perpendicular linear polarizations. Polarization direction of one of these pulses coincides with the polarization direction of control fields. The distance, which probe pulse passes in the medium to its full separation, decreases, when input probe pulse duration or control field intensity decreases. The input probe pulse intensity variation almost does not influence separation distance and speed of the linear polarized probe pulses in the medium. The effects, described above, may be interpreted as the birefringence effects of electromagnetically induced transparency in the case of short probe pulse.
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.
Abstract We report the results of a theoretical study of the evolution of a probe pulse under electromagnetically induced transparency conditions in the lambda scheme of degenerate inhomogeneously broadened quantum transitions. It is assumed that the interacting fields are elliptically polarised, and their effect on the medium can be either strictly resonant or quasi-resonant. It is shown that probe light in a medium can be represented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarised fields propagating independently of each other. The major axis of the polarisation ellipse of the normal mode of the first type is parallel, and that of the second type is perpendicular to the major axis of the polarisation ellipse of the control light. Due to the fact that velocities of normal-mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside the medium, each of which transfers the energy of one of the normal modes. In the case of quasi-resonance, the splitting occurs at a shorter distance than in the case of strict resonance. If normal modes are not phase modulated at the input surface of the medium, then in the case of quasi-resonance they become phase modulated during their propagation inside the medium, whereas this does not occur in the case of strict resonance. It is shown that in the case of quasi-resonance, the phase modulation value of the mode of the second of the above types significantly exceeds that of the first type. The medium transparency for the normal mode of the first type slightly decreases with the transition from the case of strict resonance to the case of quasi-resonance, while the medium transparency for the mode of the second type decreases significantly. The total probe field, which is the sum of the normal modes, has phase modulation before it splits into mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.
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.