Вестник Саратовского государственного технического университета

Численное моделирование поляризационных эффектов при взаимодействии коротких лазерных импульсов с вырожденным 0↔1 квантовым переходом

Волков Александр Валерьянович, Oleg M. Parshkov

Published Jan 1, 2009• 0 citations

Abstract

The authors study the numerical simulation results of formation and collision of elliptical polarized solitons and breathers which created at laser radiation effects upon inhomogeneous broadening quantum jump. Such a situation is described when the sufficiently simple for experimental realization laser pulses turn into elliptic polarized breather in the medium, where each field component is breather of nondegenerate quantum jump self-induced transparency theory. It is shown that such breathers' collision is not elastic in general case: it reduces to more general forms of resonance breather-like pulses.

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Вестник Саратовского государственного технического университета

Численное моделирование поляризационных эффектов при взаимодействии коротких лазерных импульсов с вырожденным 0↔1 квантовым переходом

Волков Александр Валерьянович, Oleg M. Parshkov

Published Jan 1, 2009• 0 citations

OpenAlex

Abstract

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Polarisation effects in the formation of optical breathers at the inhomogeneously broadenedJ= 0 →J= 1 quantum transition

А. В. Волков, Oleg M. Parshkov

The formation and collisions of breathers excited by laser radiation at the inhomogeneously broadened J = 0 → J = 1 quantum transition are studied by numerical simulations in the slowly varying envelope approximation. Conditions are obtained under which laser pulses with the initial shape quite simply realised in experiments can be transformed into elliptically polarised breathers in the medium, each of the components of their field being a breather described by the theory of self-induced transparency at a nondegenerate quantum transition. It is shown that the collision of such breathers is not elastic in the general case and leads to the appearance of more general types of resonance breather-like pulses. Taking into account relaxation processes, the possibility of the formation of a breather at the 6p 2 3 P 0 → 6p7s 3 P 1 transition in the 208 Pb isotope is investigated. It is found that relaxation in some case not only causes the pulse decay but also changes the eccentricity of its polarisation ellipse.The formation and collisions of breathers excited by laser radiation at the inhomogeneously broadened J = 0 → J = 1 quantum transition are studied by numerical simulations in the slowly varying envelope approximation. Conditions are obtained under which laser pulses with the initial shape quite simply realised in experiments can be transformed into elliptically polarised breathers in the medium, each of the components of their field being a breather described by the theory of self-induced transparency at a nondegenerate quantum transition. It is shown that the collision of such breathers is not elastic in the general case and leads to the appearance of more general types of resonance breather-like pulses. Taking into account relaxation processes, the possibility of the formation of a breather at the 6p 2 3 P 0 → 6p7s 3 P 1 transition in the 208 Pb isotope is investigated. It is found that relaxation in some case not only causes the pulse decay but also changes the eccentricity of its polarisation ellipse.

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Using numerical simulations, we study propagation of ultrashort light pulses in an inhomogeneously broadened two-level medium. There are two main issues in our study. The first one concerns the transient process of self-induced transparency soliton formation, in particular, the compression of the pulse which seems to be more effective in the case of homogeneous broadening. The second question deals with the collisions of counter-propagating solitons. It is shown that the level of inhomogeneous broadening has a substantial effect on the elasticity of such collisions.Using numerical simulations, we study propagation of ultrashort light pulses in an inhomogeneously broadened two-level medium. There are two main issues in our study. The first one concerns the transient process of self-induced transparency soliton formation, in particular, the compression of the pulse which seems to be more effective in the case of homogeneous broadening. The second question deals with the collisions of counter-propagating solitons. It is shown that the level of inhomogeneous broadening has a substantial effect on the elasticity of such collisions.

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The results of numerical modeling of 0pi-pulse evolution in the medium with inhomogeneous broadening of resonant quantum transition line are presented in this paper. The main attention is devoted to phenomena related with 0pi-breather formation as in the strong resonance conditions so as in the presence of small detuning from exact resonance (quasi-resonance case). To compare with existed experimental data the numerical modeling was carried out with adequate duration of input 0pi-pulse and with taking into account of quantum transition transverse relaxation. There is founded that existed in real experiment irreversible relaxation essentially effects on evolution of pulse. So the conclusion can be made that in analyzed experiment the 0pi-breather on the stage of its transformation into many 0pi-pulse was observedThe results of numerical modeling of 0pi-pulse evolution in the medium with inhomogeneous broadening of resonant quantum transition line are presented in this paper. The main attention is devoted to phenomena related with 0pi-breather formation as in the strong resonance conditions so as in the presence of small detuning from exact resonance (quasi-resonance case). To compare with existed experimental data the numerical modeling was carried out with adequate duration of input 0pi-pulse and with taking into account of quantum transition transverse relaxation. There is founded that existed in real experiment irreversible relaxation essentially effects on evolution of pulse. So the conclusion can be made that in analyzed experiment the 0pi-breather on the stage of its transformation into many 0pi-pulse was observed

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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 ${}^{3}{{P}_{0}}$ , ${}^{3}P_{1}^{0}$ , and ${}^{3}{{P}_{2}}$ 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 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 $${}^{3}{{P}_{0}}$$ , $${}^{3}P_{1}^{0}$$ , and $${}^{3}{{P}_{2}}$$ 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.

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Oleg M. Parshkov

AbstractThe 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 $^{3}{{P}_{0}}$ , $^{3}P_{1}^{0}$ , and $^{3}{{P}_{2}}$ 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.AbstractThe 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 $$^{3}{{P}_{0}}$$ , $$^{3}P_{1}^{0}$$ , and $$^{3}{{P}_{2}}$$ 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.

Журнал технической физикиJan 1, 20190 citations

{}^{3}{{P}_{0}}

{}^{3}P_{1}^{0}

, and

{}^{3}{{P}_{2}}

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.

^{3}{{P}_{0}}

^{3}P_{1}^{0}

, and

^{3}{{P}_{2}}

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.