KEYWORDS: Frequency modulation, Fermium, Transparency, Polarization, Lead, Chemical species, Radio propagation, Modulation, Control systems, Telecommunications
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.
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 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 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.
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 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 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 the nonadiabacity display in electromagnetically induced transparency are presented. The Λ scheme of degenerate and inhomogeneous quantum transitions J = 0 → J = 1 → J = 2 is examined for the cases of slow 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. If an abrupt rise of the leading edge of the input probe pulse takes place the precursor pulse arises at a probe radiation frequency and the velocity of its propagation coincides with the speed of light in vacuum.
Theoretical treatment of the effects of external pulse field on the emission and absorption of two impurity centers has been attempted. Good overlapping of emission band of one center (donor of energy) with the absorption band of another center (acceptor of energy) is assumed, so that radiative and non-radiative energy transfer may take place. Mathematical model is based on the system of reduced Maxwell equations for magnitudes of field components and Bogolubov's equations for elements of multiparticle density matrix of donor-acceptor complex. Numerical solution is obtained for NaCl:Cu, Mn and KCl:Pb,Eu crystals. These materials are differing in the value of transition dipole moment of acceptor absorption. It is low for the first medium while for KCl:Pb,Eu it is comparable to that one for the donor emission. It turns out that in the case of low value of transition dipole moment the luminescence of both components of donor-acceptor pair takes place. On the contrary, only acceptor emission exists in the case of high value of transition dipole moment of acceptor when the pump intensity is low. Simultaneous luminescence of donor and acceptor occurs when pump intensity is enough. So, in the systems of such kind the emission may be changed over from one frequency to another through the power level of pump radiation.
The problem of stationary-gained modes formation under conditions of transient double resonance inspired by 2(pi) -pulse of pump and low-intensity signal radiation is investigated. One demonstrates the possibility of different shapes stationary-gained signal pulse formation and investigates the conditions of their arising and stability. The effect of inhomogeneous broadening of spectral transition lines on the mode formation is studied too.
One consider the amplification of pulses of coherent light in the resonant three-level active media that is excited by short power pulse of coherent light according to the common-upper- level double resonance scheme. The radiation with major frequency (pump) is supposed to be stronger than one with minor frequency (signal). The self-induced transparency is supposed to be established in the pump channel. The exponential growth of stationary shape short signal pulses is studied mainly. One shows that when any described here conditions for initial signal pulse shape are meeting the stationary gained signal pulse of complicated form can be formed. The gains of these pulses are less than ones for signal pulses of quasi-hyperbolic-secant form. Therefore in the case of incomplete condition meeting the competition between the exponentially growing signal pulses with different gains and shapes leads finally to the overwhelming of signal pulse with quasi-hyperbolic-secant-shape form. The effect of inhomogeneous broadening of spectral transition lines on the parameters of signal pulses was studied too. Evaluations that were carried out for any atomic gases show that described in this paper phenomena can be produced at realistic levels of power and duration of pump and signal pulses.
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