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Quantum Electronics

Normal modes of strictly resonant and quasi-resonant regimes of electromagnetically induced transparency

Oleg M. Parshkov

Published Nov 1, 2019• 2 citations
Publisher

Abstract

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.

DOI
10.1070/qel17092

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Optics and Spectroscopy•May 1, 2021•0 citations
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 investigation of the evolution of a probe pulse under electromagnetically induced transparency in the Λ -scheme of degenerated inhomogeneously broadened quantum transitions are presented. It supposed that the interacted light fields are elliptically polarized, and their influence on the medium can be either strictly resonant or quasiresonant. It is demonstrated that the probe pulse in the medium can be presented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarized fields propagating independently of each other. Due to the fact that velocities of normal mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside of the medium, each of which transfers the energy of one of the normal modes. If normal modes are not phase modulated at the input surface, then in the case of quasi-resonance they become phase modulated during propagation in the medium, whereas this does not occur in the case of strict resonance. The total probe field, which is the sum of normal modes, has phase modulation before it splits into the mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.
This paper presents an analytical study of the formation of normal modes of probe light for electromagnetically induced transparency in a lambda system of quantum transitions between 3 P 0 , and 3 P 2 levels in the case of an elliptically polarised control field and inhomogeneous broadening. The normal modes are elliptically polarised waves with identical polarisation ellipse eccentricities but different electric vector rotation directions. The mode eccentricities are only determined by the control field polarisation ellipse eccentricity. The major axis of the polarisation ellipse of one of the normal modes is parallel to the major axis of the control light polarisation ellipse, whereas the major axis of the polarisation ellipse of the other normal mode is perpendicular to it. The former type of mode has a higher group velocity than does the latter type of mode, and both velocities depend on control light polarisation ellipse eccentricity and intensity. Probe light with an arbitrary elliptical polarisation is the sum of normal modes which propagate independently of each other. Since the modes differ in group velocity, a probe pulse entering the medium splits into two components, each of which is a normal mode. The fraction of energy in each normal mode depends only on polarisation characteristics of coupled fields and is independent of their intensity. The bibliography includes 27 references.
Abstract We report the results of an analytical and numerical analysis of the evolution of nanosecond probe pulses in the case of electromagnetically induced transparency in the Λ-scheme of degenerate quantum transitions. It is assumed that the probe and control fields at the active medium input are elliptically polarised, and one of them is phase modulated. It is shown analytically that probe radiation in a medium is the sum of two normal modes propagating independently of each other. Because the group velocities of normal mode pulses are different, a single probe pulse entering the medium decays inside the medium into separate pulses, each of which transfers the energy of one of the normal modes. Numerical simulations have shown that with a sufficiently large phase modulation, normal modes, whose intensity on the input surface is described by a bell-shaped curve, turn into trains of subpulses in the medium. Phase modulation of the input field has practically no effect on the group propagation velocities of normal modes, but it reduces the transparency of the medium for probe radiation.
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.
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.