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Optics and Spectroscopy

Numerical modeling of evolution of nano- and picosecond probe pulses of electromagnetically induced transparency

Oleg M. Parshkov, Ekaterina R. Govorenko

Published Dec 1, 2014• 3 citations
Publisher

Abstract

Results of numerical analysis of the influence of probe pulse duration on the character of its evolution under the conditions of electromagnetically induced transparency in a Λ-scheme involving degenerate quantum transitions are presented. The cases of weak and strong input probe pulses linearly polarized in the same direction as the polarized coupling radiation, along with the case of linearly polarized probe radiation and circularly polarized coupling radiation, are considered. Calculations showed that the regime of weak probe radiation is most favorable for formation of a short probe pulse with a duration of about 1 ns and pulse shape that does not change substantially upon pulse propagation. However, even in this case, picosecond probe pulses experience considerable deformation of their shape and loss of power. Considerable changes of the pulse shape in the case of a strong probe pulse occur already when the pulse duration approaches 1 ns. This circumstance can limit the response time of prospective devices based on the effect of electromagnetically induced transparency.

DOI
10.1134/s0030400x14120182

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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.

Optics and Spectroscopy•Sep 1, 2017•1 citation
Results of numerical analysis of the influence of probe pulse duration on the character of its evolution under the conditions of electromagnetically induced transparency in a Λ-scheme involving degenerate quantum transitions are presented. The cases of weak and strong input probe pulses linearly polarized in the same direction as the polarized coupling radiation, along with the case of linearly polarized probe radiation and circularly polarized coupling radiation, are considered. Calculations showed that the regime of weak probe radiation is most favorable for formation of a short probe pulse with a duration of about 1 ns and pulse shape that does not change substantially upon pulse propagation. However, even in this case, picosecond probe pulses experience considerable deformation of their shape and loss of power. Considerable changes of the pulse shape in the case of a strong probe pulse occur already when the pulse duration approaches 1 ns. This circumstance can limit the response time of prospective devices based on the effect of electromagnetically induced transparency.
The numerical simulation results of the probe pulse duration influence on this pulse evolution in presence of electromagnetically induced transparency are presented. We investigate the cases of weak and strong input pulses in degenerated quantum transition Λ -scheme with inhomogeneous line broadening. The linear polarizations of probe and control radiation are supposed. According to our calculations, the weak input probe pulse regime is the most favorable for formation of more than one nanosecond duration probe pulse with small varying of envelop form by its transition. The strong input probe pulse condition is disadvantageous for preservation of pulse shape when the probe pulse travels across the medium, for duration less than several nanoseconds. This circumstance imposes restriction on operating speed of the perspective equipments, principle operation of which bases on the electromagnetically induce transparency effect.
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 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 results of numerical simulation of the electromagnetically induced transparency phenomenon in the Λ scheme of degenerate quantum transitions J = 0 → J = 1 → J = 2 with Doppler broadening of spectral lines are presented for the cases of continuous and abrupt rises in the leading edge of the input probe radiation pulse. For circularly polarized radiations, it has been shown that the deviation from the condition of adiabatic sequence can lead to a separation of the probe pulse of the adiabaton into a train of subpulses. In the case of linear polarization of the input probe field and the circular polarization of the input control field, the probe radiation pulse is split into two pulses with opposite circular polarizations and a multispike structure of the envelopes. In the case of an abrupt rise in the leading edge of the input probe pulse, regardless of the peak intensity of the latter, the precursor pulse arises at a probe radiation frequency and the velocity of its propagation coincides with the speed of light in vacuum.
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.