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.
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.
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.
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 theoretical investigation results of disintegration effect of elliptic polarized shot probe pulses of electromagnetically induced transparency in the counterintuitive superposed elliptic polarized control field and in weak probe field approximation are presented. It is shown that this disintegration occurs because the probe field in the medium is the sum of two normal modes, which correspond to elliptic polarized pulses with different speeds of propagation. The polarization ellipses of normal modes have equal eccentricities and mutually perpendicular major axes. Major axis of polarization ellipse of one normal mode is parallel to polarization ellipse major axis of control field, and electric vector of this mode rotates in the opposite direction, than electric vector of the control field. The electric vector other normal mode rotates in the same direction that the control field electric vector. The normal mode speed of the first type aforementioned is less than that of the second type. The polarization characteristics of the normal mode depend uniquely on the polarization characteristics of elliptic polarized control field and remain changeless in the propagation process. The theoretical investigation is performed for Λ-scheme of degenerated quantum transitions between 3P0, 3P10 and 3P2 energy levels of 208Pb isotope.
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 , 3P10 , and 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 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.
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.