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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling

Electromagnetically induced transparency in the case of elliptic polarization of interacting fields

Oleg M. Parshkov

Published Apr 26, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2309645

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Quantum Electronics•Nov 12, 2018•7 citations
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 numerical simulation results of disintegration effect of linear polarized shot probe pulses of electromagnetically induced transparency in the counterintuitive superposed linear polarized control field are presented. It is shown, that this disintegration occurs, if linear polarizations of interacting pulses are not parallel or mutually perpendicular. In case of weak input probe field the polarization of one probe pulse in the medium is parallel, whereas the polarization of another probe pulse is perpendicular to polarization direction of input control radiation. The concerned effect is analogous to the effect, which must to take place when short laser pulse propagates along main axes of biaxial crystal because of group velocity of normal mod difference. The essential difference of probe pulse disintegration and linear process in biaxial crystal is that probe pulse preserves linear polarization in all stages of propagation. The numerical simulation is performed for scheme of degenerated quantum transitions between 3P0 , 3P01 and 3P2 energy levels of 208Pb isotope.
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.
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.
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 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.
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.