Asymptotic solutions of nonlinear differential-difference equations describing the lasing dynamic... more Asymptotic solutions of nonlinear differential-difference equations describing the lasing dynamics with a negative feedback are obtained. Periodic lasing regimes with a complex relaxational structure are shown to be possible in such lasers. The phenomenon of multistability, i.e., the co-existence of a great number of structurally different and structurally similar attractors, is analytically described. Asymptotic characteristics of lasing regimes (pulse shape and radiation pulsation frequency) are found and the domains in the parameter space and the initial conditions for their realization are determined for all types of solution. The chaotic dynamics following the sequence of period-doubling bifurcations is also numerically determined.
ABSTRACT A theoretical analysis is made of the appearance of high-frequency pulsations in a linea... more ABSTRACT A theoretical analysis is made of the appearance of high-frequency pulsations in a linear laser with constant losses. Nonlinear differential equations with a variable parameter are used for the radiation density and gain of the active medium. It is shown that the high-frequency self-modulation is to the delay of the action on the active medium of the radiation arriving from different points in the laser. The dependence of the period and depth of modulation on the laser parameters is obtained. The results of analytic investigations are compared with computer calculations.
Generalized Semiconductor Bloch Equations are derived with using the fluctuation-dissipation theo... more Generalized Semiconductor Bloch Equations are derived with using the fluctuation-dissipation theorem. Four operator expectation values like density-density correlators are calculated with account of coherent memory effects. Interactions with mixed plasmon-phonons modes and excitonic effects are taken into account. Comparison with different other theoretical approaches is provided. Numerical calculations of the spontaneous radiation produced by interband multiplasmon recombination of electron-hole pairs
... dynamic properties of a laser LA Kotomtseva, NA Loiko, and AM Samson Institute of Physics, Ac... more ... dynamic properties of a laser LA Kotomtseva, NA Loiko, and AM Samson Institute of Physics, Academy of Sciences of the Belorussian SSR, Minsk (Submitted July 10,1981) Kvantovaya Elektron. (Moscow) 9, 1384-1389 (July 1982) ... For OJ 0.7 a T/T, it 0,2 OJ T/T, FIG. ...
... 1985 DEVELOPMENT OF IRREGULAR AUTO-OSCILLATIONS IN A NONLINEAR SYSTEM WITH LAGGING LA KOTOMTS... more ... 1985 DEVELOPMENT OF IRREGULAR AUTO-OSCILLATIONS IN A NONLINEAR SYSTEM WITH LAGGING LA KOTOMTSEVA, NA LOIKO and AM SAMSON Institute of ... achieved gain K and depending on the spectral properties of the medium, given by b [7]. (D1 = oj - gr, Fi = `pi ...
Quasi-classical equations are used to study the effects of frequency detuning on the generation o... more Quasi-classical equations are used to study the effects of frequency detuning on the generation of HF pulsations in a ring laser. It is shown that detuning leads to a significant change in the temporal characteristics of emission. Consideration is given to conditions for the development of pulsations with frequencies not less than the intermode beat frequency.
A stability analysis is performed for a system of quasi-classical equations and a system of rate ... more A stability analysis is performed for a system of quasi-classical equations and a system of rate equations describing the operation of a traveling-wave ring laser with a saturable absorber. The rate equations take into account both distributed and lumped losses. Regions of stability are determined for undamped pulsations with a repetition interval equal to or smaller by an integer than the radiation circulation time in the cavity. The results of the analysis are confirmed by numerical solution of the initial systems of equations for parameter values appropriate to a dye laser.
A unidirectional ring laser with a nonlinear element with losses depending on the density of the ... more A unidirectional ring laser with a nonlinear element with losses depending on the density of the radiation generated at the preceding instant is examined. The possibility of generating stable reproducible sequences of subnanosecond pulses is theoretically demonstrated. Differential equations with a delay argument for the radiation density and the gain coefficient are applied to the analysis of the problem. The dependence of the period of the high-frequency pulsations on the system parameters is obtained with the determining factor found to be the delay time of the reaction of the nonlinear element to the radiation field. The conditions for the optimization of the high-frequency pulsations up to their degeneration into a series of short pulses are given. The results of a numerical simulation of the generation process are provided.
Specific features of the generation of a sequence of short pulses by a traveling-wave ring laser ... more Specific features of the generation of a sequence of short pulses by a traveling-wave ring laser with a nonlinear delayed-action element in the presence of counterpropagating fluxes of radiation are considered. Periods of the high frequency pulsations are given as a function of the reciprocal arrangement of the laser cavity elements.
This review presents results of the analysis of the semiclassical equations of lasers in the appr... more This review presents results of the analysis of the semiclassical equations of lasers in the approximation of slow envelopes for plane waves. A description is given of instabilities leading to the formation of regular and chaotic regimes due to coherent or incoherent interaction and inhomogeneities in the longitudinal distribution of gain and losses in the resonator. Regimes with regular and chaotic dynamics are analyzed for the examples of a traveling-wave ring laser with a brightening filter and a laser with counterpropagating waves.
A theoretical analysis is made of the dynamics of a laser with the loss factor dependent on the d... more A theoretical analysis is made of the dynamics of a laser with the loss factor dependent on the density of the output radiation passing through an external feedback loop. Asymptotic solutions are obtained of differential–difference equations describing such a laser. The existence of multistable states representing a set of periodic regimes is demonstrated. The regions of existence of pulsations of radiation with different frequencies, amplitudes, and profiles are found and the initial conditions facilitating the appearance of these pulsations are identified. Chaotization of the dynamics of the system via a sequence of period-doubling bifurcations is predicted. Studies are made of the statistical properties of the resultant strange attractor.
Theoretical results are presented which show that a delay-effect intracavity nonlinear element ca... more Theoretical results are presented which show that a delay-effect intracavity nonlinear element can be used to control the temporal pattern of the generation of picosecond pulses. This element makes it possible to regulate the development of nutational oscillations and leads to the generation of stable picosecond pulses in lasers based on various active media. Example results are presented for a traveling-wave ring laser.
ABSTRACT A theoretical investigation is made of the dynamics of the interaction of light with a b... more ABSTRACT A theoretical investigation is made of the dynamics of the interaction of light with a bistable system formed by a thin film and a feedback mirror. The dependence of the dynamics on the ratio of the relaxation time of a two-level medium to the delay associated with the transmission of light from the film to the mirror and back again is determined. The reasons and conditions for the appearance of regular pulsations and of more complex dynamics are found.
It is demonstrated that the Hopf spatiotemporal modes can build stable resonant triads in an opti... more It is demonstrated that the Hopf spatiotemporal modes can build stable resonant triads in an optical pattern-forming system with delay. The resonant Hopf triads correspond to dissipative structures in the form of drifting patterns of rhombic, hexagonal, or rhomboidal symmetry. Multistability of different patterns is found in numerical simulations.
Asymptotic solutions of nonlinear differential-difference equations describing the lasing dynamic... more Asymptotic solutions of nonlinear differential-difference equations describing the lasing dynamics with a negative feedback are obtained. Periodic lasing regimes with a complex relaxational structure are shown to be possible in such lasers. The phenomenon of multistability, i.e., the co-existence of a great number of structurally different and structurally similar attractors, is analytically described. Asymptotic characteristics of lasing regimes (pulse shape and radiation pulsation frequency) are found and the domains in the parameter space and the initial conditions for their realization are determined for all types of solution. The chaotic dynamics following the sequence of period-doubling bifurcations is also numerically determined.
ABSTRACT A theoretical analysis is made of the appearance of high-frequency pulsations in a linea... more ABSTRACT A theoretical analysis is made of the appearance of high-frequency pulsations in a linear laser with constant losses. Nonlinear differential equations with a variable parameter are used for the radiation density and gain of the active medium. It is shown that the high-frequency self-modulation is to the delay of the action on the active medium of the radiation arriving from different points in the laser. The dependence of the period and depth of modulation on the laser parameters is obtained. The results of analytic investigations are compared with computer calculations.
Generalized Semiconductor Bloch Equations are derived with using the fluctuation-dissipation theo... more Generalized Semiconductor Bloch Equations are derived with using the fluctuation-dissipation theorem. Four operator expectation values like density-density correlators are calculated with account of coherent memory effects. Interactions with mixed plasmon-phonons modes and excitonic effects are taken into account. Comparison with different other theoretical approaches is provided. Numerical calculations of the spontaneous radiation produced by interband multiplasmon recombination of electron-hole pairs
... dynamic properties of a laser LA Kotomtseva, NA Loiko, and AM Samson Institute of Physics, Ac... more ... dynamic properties of a laser LA Kotomtseva, NA Loiko, and AM Samson Institute of Physics, Academy of Sciences of the Belorussian SSR, Minsk (Submitted July 10,1981) Kvantovaya Elektron. (Moscow) 9, 1384-1389 (July 1982) ... For OJ 0.7 a T/T, it 0,2 OJ T/T, FIG. ...
... 1985 DEVELOPMENT OF IRREGULAR AUTO-OSCILLATIONS IN A NONLINEAR SYSTEM WITH LAGGING LA KOTOMTS... more ... 1985 DEVELOPMENT OF IRREGULAR AUTO-OSCILLATIONS IN A NONLINEAR SYSTEM WITH LAGGING LA KOTOMTSEVA, NA LOIKO and AM SAMSON Institute of ... achieved gain K and depending on the spectral properties of the medium, given by b [7]. (D1 = oj - gr, Fi = `pi ...
Quasi-classical equations are used to study the effects of frequency detuning on the generation o... more Quasi-classical equations are used to study the effects of frequency detuning on the generation of HF pulsations in a ring laser. It is shown that detuning leads to a significant change in the temporal characteristics of emission. Consideration is given to conditions for the development of pulsations with frequencies not less than the intermode beat frequency.
A stability analysis is performed for a system of quasi-classical equations and a system of rate ... more A stability analysis is performed for a system of quasi-classical equations and a system of rate equations describing the operation of a traveling-wave ring laser with a saturable absorber. The rate equations take into account both distributed and lumped losses. Regions of stability are determined for undamped pulsations with a repetition interval equal to or smaller by an integer than the radiation circulation time in the cavity. The results of the analysis are confirmed by numerical solution of the initial systems of equations for parameter values appropriate to a dye laser.
A unidirectional ring laser with a nonlinear element with losses depending on the density of the ... more A unidirectional ring laser with a nonlinear element with losses depending on the density of the radiation generated at the preceding instant is examined. The possibility of generating stable reproducible sequences of subnanosecond pulses is theoretically demonstrated. Differential equations with a delay argument for the radiation density and the gain coefficient are applied to the analysis of the problem. The dependence of the period of the high-frequency pulsations on the system parameters is obtained with the determining factor found to be the delay time of the reaction of the nonlinear element to the radiation field. The conditions for the optimization of the high-frequency pulsations up to their degeneration into a series of short pulses are given. The results of a numerical simulation of the generation process are provided.
Specific features of the generation of a sequence of short pulses by a traveling-wave ring laser ... more Specific features of the generation of a sequence of short pulses by a traveling-wave ring laser with a nonlinear delayed-action element in the presence of counterpropagating fluxes of radiation are considered. Periods of the high frequency pulsations are given as a function of the reciprocal arrangement of the laser cavity elements.
This review presents results of the analysis of the semiclassical equations of lasers in the appr... more This review presents results of the analysis of the semiclassical equations of lasers in the approximation of slow envelopes for plane waves. A description is given of instabilities leading to the formation of regular and chaotic regimes due to coherent or incoherent interaction and inhomogeneities in the longitudinal distribution of gain and losses in the resonator. Regimes with regular and chaotic dynamics are analyzed for the examples of a traveling-wave ring laser with a brightening filter and a laser with counterpropagating waves.
A theoretical analysis is made of the dynamics of a laser with the loss factor dependent on the d... more A theoretical analysis is made of the dynamics of a laser with the loss factor dependent on the density of the output radiation passing through an external feedback loop. Asymptotic solutions are obtained of differential–difference equations describing such a laser. The existence of multistable states representing a set of periodic regimes is demonstrated. The regions of existence of pulsations of radiation with different frequencies, amplitudes, and profiles are found and the initial conditions facilitating the appearance of these pulsations are identified. Chaotization of the dynamics of the system via a sequence of period-doubling bifurcations is predicted. Studies are made of the statistical properties of the resultant strange attractor.
Theoretical results are presented which show that a delay-effect intracavity nonlinear element ca... more Theoretical results are presented which show that a delay-effect intracavity nonlinear element can be used to control the temporal pattern of the generation of picosecond pulses. This element makes it possible to regulate the development of nutational oscillations and leads to the generation of stable picosecond pulses in lasers based on various active media. Example results are presented for a traveling-wave ring laser.
ABSTRACT A theoretical investigation is made of the dynamics of the interaction of light with a b... more ABSTRACT A theoretical investigation is made of the dynamics of the interaction of light with a bistable system formed by a thin film and a feedback mirror. The dependence of the dynamics on the ratio of the relaxation time of a two-level medium to the delay associated with the transmission of light from the film to the mirror and back again is determined. The reasons and conditions for the appearance of regular pulsations and of more complex dynamics are found.
It is demonstrated that the Hopf spatiotemporal modes can build stable resonant triads in an opti... more It is demonstrated that the Hopf spatiotemporal modes can build stable resonant triads in an optical pattern-forming system with delay. The resonant Hopf triads correspond to dissipative structures in the form of drifting patterns of rhombic, hexagonal, or rhomboidal symmetry. Multistability of different patterns is found in numerical simulations.
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Papers by Natalia Loiko