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NONLINEAROPTICALEFFECTSINSPONTANEOUSAND STIMULATED EMISSIONFROM EXCITEDTWO-BANDINTRINSIC SEMICONDUCTOR (Invited paper)

Vladislav Cheltsov, Russian Federation

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Thebasic results oftheoretical nonperturbative analysis ofspontaneous andstimulated emission from two-band excited intrinsic interacting with asingle modeofradiation field inalossless micro-cavity arepresented. Theself-consistent dynamics ofthecoupled system semiconductor + single moderadiation field, accompanied withspontaneous andstimulated emission wasinvestigated asdependent oftheinitial level ofthe excitation ofsemiconductor inthepresence initially ofthephysical field vacuum. Calculations havebeen carried out withthehelpofthecommutation version oftheevolution method without introducing explicitly thephonon mechanisms. Theinitial non-equilibrium electron andholepopulations inthebands havebeensupposed tobe created byultra-short laser pulses anddescribed bytheFermi-Dirac quasi-equilibrium distributions withthegiven chemical potentials. Theinteraction between theelectron-hole subsystem andthemodefield hasbeenadopted tobe switched onsuddenly. Thecalculations haveshownthat depending ontheinitial excitation level ofelectron-hole subsystem three states ofthemodefield arerealized: theequilibrium Bose-Einstein photon distribution with nonzero chemical potential; thequasi-equilibrium distribution withtheaverage number ofphotons equal tounitand accompanied with their fluctuations, andfinally, thestate ofphoton avalanche. Thefirst regime takes theplace when thecoefficient ofthelight amplification isnegative. Then, theequilibrium between theelectron-hole subsystem and arising photons exists until theaverage number reaches theunit. Fornegative and=1theequilibrium still exists but isaccompanied withfield fluctuations. Finally, whenthesteady growth arises thelower butstable values are established. Theself-consistent spontaneous andstimulated emission fromanexcited intrinsic two-band confined inamicro-cavity andcoupled toasingle resonance field modehave beeninvestigated with thehelp ofthecommutation version ofevolution operator (1,2) method in theinteraction representation. Phonons werenotintroduced directly into theHamiltonian but through theinitial Fermi-Dirac distributions forelectrons andholes inthebands. Ithasbeen suggested that theelectron-hole subsystem isexcited byanultra-short laser pulses. Sothedynamics ofphoton emission hasbeentraced through times shorter thenthe characteristic relaxation time caused bythephonon mechanism. Theinitial state ofelectron-hole andmodefield subsystems hasbeenadopted tobepresented with asuperposition It>= ({ne,h,m,},t=0) {nh}> .m>

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Thebasic results oftheoretical nonperturbative analysis ofspontaneous andstimulated emission from two-band excited intrinsic interacting with asingle modeofradiation field inalossless micro-cavity arepresented. Theself-consistent dynamics ofthecoupled system semiconductor + single moderadiation field, accompanied withspontaneous andstimulated emission wasinvestigated asdependent oftheinitial level ofthe excitation ofsemiconductor inthepresence initially ofthephysical field vacuum. Calculations havebeen carried out withthehelpofthecommutation version oftheevolution method without introducing explicitly thephonon mechanisms. Theinitial non-equilibrium electron andholepopulations inthebands havebeensupposed tobe created byultra-short laser pulses anddescribed bytheFermi-Dirac quasi-equilibrium distributions withthegiven chemical potentials. Theinteraction between theelectron-hole subsystem andthemodefield hasbeenadopted tobe switched onsuddenly. Thecalculations haveshownthat depending ontheinitial excitation level ofelectron-hole subsystem three states ofthemodefield arerealized: theequilibrium Bose-Einstein photon distribution with nonzero chemical potential; thequasi-equilibrium distribution withtheaverage number ofphotons equal tounitand accompanied with their fluctuations, andfinally, thestate ofphoton avalanche. Thefirst regime takes theplace when thecoefficient ofthelight amplification isnegative. Then, theequilibrium between theelectron-hole subsystem and arising photons exists until theaverage number reaches theunit. Fornegative and=1theequilibrium still exists but isaccompanied withfield fluctuations. Finally, whenthesteady growth arises thelower butstable values are established. Theself-consistent spontaneous andstimulated emission fromanexcited intrinsic two-band confined inamicro-cavity andcoupled toasingle resonance field modehave beeninvestigated with thehelp ofthecommutation version ofevolution operator (1,2) method in theinteraction representation. Phonons werenotintroduced directly into theHamiltonian but through theinitial Fermi-Dirac distributions forelectrons andholes inthebands. Ithasbeen suggested that theelectron-hole subsystem isexcited byanultra-short laser pulses. Sothedynamics ofphoton emission hasbeentraced through times shorter thenthe characteristic relaxation time caused bythephonon mechanism. Theinitial state ofelectron-hole andmodefield subsystems hasbeenadopted tobepresented with asuperposition It>= ({ne,h,m,},t=0) {nh}> .m>
The basic results of theoretical nonperturbative analysis of spontaneous and stimulated emission from two-band excited intrinsic semiconductor interacting with a single mode of radiation field in a lossless micro-cavity are presented. The self-consistent dynamics of the coupled system ''semiconductor + single mode radiation field", accompanied with spontaneous and stimulated emission was investigated as dependent of the initial level of the excitation of semiconductor in the presence initially of the physical field vacuum. Calculations have been carried out with the help of the commutation version of the evolution method without introducing explicitly the phonon mechanisms. The initial non-equilibrium electron and hole populations in the bands have been supposed to be created by ultra-short laser pulses and described by the Fermi-Dirac quasi-equilibrium distributions with the given chemical potentials. The interaction between the electron-hole subsystem and the mode field has been adopted to be switched on suddenly. The calculations have shown that depending on the initial excitation level of electron-hole subsystem three states of the mode field are realized: the equilibrium Bose-Einstein photon distribution with nonzero chemical potential; the quasi-equilibrium distribution with the average number of photons equal to unit and accompanied with their fluctuations, and finally, the state of photon avalanche. The first regime takes the place when the coefficient of the light amplification is negative. Then, the equilibrium between the electron-hole subsystem and arising photons exists until the average number reaches the unit. For negative and =1 the equilibrium still exists but is accompanied with field fluctuations. Finally, when the steady growth arises the lower but stable values are established
The behavior of a single mode of radiation field coupled to an excited two band intrinsic semiconductor has been investigated with the help of the commutator version of evolution operator method. As dependent on the excitation level three states of the field has been shown to exist: the equilibrium with the number of photons determined by the Bose–Einstein distribution with nonzero chemical potential; the quasi-equilibrium with the average number of photons equal to unity and accompanied by fluctuations; the state of photon avalanche.
The dynamics of electrons and holes in semiconductors and semiconductor heterostructures have been extensively discussed in the literature, and are governed by their mutual Coulomb interaction, by their interaction with lattice vibrations (phonons) and by their radiative recombination (for an overview see e.g. Ref. [1]). A powerful technique to study the carrier dynamics in semiconductors utilizes short optical pulses to photoexcite electrons from the valence to the conduction band (i.e. to create electron-hole pairs) that subsequently relax until the photon energy stored in the medium is dissipated and the system has recovered the thermal equilibrium. The dynamics of the carriers photoexcited by the short optical pulse can be followed by monitoring two main optical observables: the interband population difference and the induced polarization. Both quantities decay with time after the photoexcitation due to the carrier dynamics. While the induced polarization (which is an ensemble average over many photoexcited dipole moments) is sensitive to scattering events that break the phase relationship among the individual dipoles and/or with the light field creating them (dephasing processes), the population difference is sensitive only to events that change the energy state of the carriers. Transient coherent optical spectroscopy addresses the time-evolution of the induced polarization in the time-regime during and immediately following the photoexcitation by a short laser pulse, in which the photoexcited dipoles have retained a defined phase relationship among each other and with the exciting coherent radiation.
An electron-hole system in a direct-gap semiconductor that is coherently excited by a high-intensity laser is investigated. The stationary state of the system in the presence of laser field is described by Bogolyubov quasiparticles. Using a mean-field approximation, we derive a set of basic equations including electron-electron, hole-hole, and electron-hole screened Coulomb interactions. The screening effects are incorporated self-consistently on the basis of a quasistatic random-phase approximation. The stationary state has a fixed chemical potential and is controlled by the frequency of the laser field. By numerical analysis of the basic equations, we show that a resonatorless bistability occurs; that is, an electron-hole pair-density bistability with respect to the excitation energy is shown to be caused by many-body effects via the screened Coulomb interaction. We clarify how the stationary state changes its entity depending on the frequency and intensity of the laser field, and how such a characteristic behavior is observed in optical spectra of probe light.
The nonperturbative theory of the cooperative spontaneous emission from a two level atom trapped in one-dimentional damped nanocavity with a single resonance mode is presented. The time-dependent spectral properties and nonlinear dynamics of a separate photon emission by the micro-molecular-like system "excited atom coupled to a resonance decaying mode" have been analyzed. The investigation has been carried out by solving the Schrödinger equation in the interaction picture with the help of the Green functions method in the Heitler-Ma's form. The formalism was supplemented with the novel algorithm in operating causal singular functions and with fundamentals of the theory of quasi-stationary systems. The proposed theory accounts automatically of both reabsorptions of emitted photon and its simultaneous escaping out of the cavity. Solutions of the wave equation were found without using intermediate virtual states and series expansions. In accordance with the theory of quasi-stationary systems the field of mode decaying exponentially in the empty nanocavity was represented with the Lorenz-shaped packet of stationary photonic states (quasi-modes). The electro-dipolar interaction between the atom and the mode field was adopted to be switched on suddenly. The expressions and plots of emission probabilities spectral densities together with photon emission probability dynamics as functions of time for various ratios Γ/4g of photon escaping rate Γ and coupling constant g are presented. For Γ/4g <1 the transient emission spectrum reveals the presence of two symmetrical side-bands and of the central peak, the latter decaying in time at the rate ∝ Γ/2 so that the final spectrum is a doublet. In this case the photon emission probability is described by decaying oscillations. On the contrary for Γ/4g ≥ 1 the spectrum is a singlet and the emission occurs in exponentially decaying ways.
A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by