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Physics Letters A

Normal modes for electromagnetically induced transparency in the presence of off-resonance transitions

I. E. Mazets, Boris G. Matisov, Elena Cerboneschi, E. Arimondo

Published May 1, 1997• 9 citations
Publisher
DOI
10.1016/s0375-9601(97)00180-1

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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.

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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.

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The theoretical results on the study of the evolution of electromagnetically induced transparency probe pulses with frequency modulation on the input surface of the active medium and possible frequency modulation of the control field are presented. It was shown that the presence of a sufficiently large frequency modulation of the input probe pulse (an instantaneous frequency offset of the order of an inhomogeneous line width resonant with the probe field) does not lead to the mode structure destruction of this field inside the active medium. At the same time, the transparency of the medium for the probe field is noticeably reduced, but it remains quite large. With frequency modulation of the control radiation, the mode regime of the probe field propagation is realized at least as long as the deviation of the frequency of the control field is less than half the width of the line of the probe quantum transition. However, the transparency of the medium for the probe field decreases in comparison with the case of the absence of frequency modulation. The analysis is carried out for the Ʌ-scheme of inhomogeneously broadened quantum transitions between the 3P0, 3P01 and 3P2 levels of the 208Pb isotope.

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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.
The theoretical results on the study of the evolution of electromagnetically induced transparency probe pulses with frequency modulation on the input surface of the active medium and possible frequency modulation of the control field are presented. It was shown that the presence of a sufficiently large frequency modulation of the input probe pulse (an instantaneous frequency offset of the order of an inhomogeneous line width resonant with the probe field) does not lead to the mode structure destruction of this field inside the active medium. At the same time, the transparency of the medium for the probe field is noticeably reduced, but it remains quite large. With frequency modulation of the control radiation, the mode regime of the probe field propagation is realized at least as long as the deviation of the frequency of the control field is less than half the width of the line of the probe quantum transition. However, the transparency of the medium for the probe field decreases in comparison with the case of the absence of frequency modulation. The analysis is carried out for the Ʌ-scheme of inhomogeneously broadened quantum transitions between the 3P0, 3P01 and 3P2 levels of the 208Pb isotope.