Penetration of a symmetric light pulse through a wide quantum well

The reflection, transmission, and absorption of a symmetric electromagnetic pulse whose carrier frequency is close to the frequency of the interband transition in a quantum well are calculated. The energy levels in the quantum well are assumed to be discrete, and one excited level is taken into account. Consideration is given to the case of a sufficiently wide quantum well when the pulse wavelength corresponding to the carrier frequency is comparable to the quantum well width and when allowance should be made for the dependence of the matrix element of the interband transition on the photon wave vector. The calculations are performed with due regard for the difference between the refractive indices of the material of the quantum well and the barrier at an arbitrary ratio of the reciprocal radiative to nonradiative lifetimes of the excited level of the electronic system. It is demonstrated that the inclusion of the spatial dispersion and the difference in the refractive indices most strongly affects the reflection of the electromagnetic pulse, because the reflection due to interband transitions in the quantum well is accompanied by an additional reflection from the quantum well boundaries. Compared to the previously considered model, the most radical changes in the reflection are observed in the case when the reciprocal nonradiative lifetime of the excited state is substantially longer than the reciprocal radiative lifetime.     

Resonant transmission of an electromagnetic pulse through a quantum well

The reflectance, transmittance, and absorbance of a symmetric electromagnetic pulse with a carrier frequency close to the frequency of direct interband transitions in a quantum well are calculated. The energy levels in the quantum well are assumed to be discrete, and two closely spaced excited levels are taken into account. The theory holds true for quantum wells of an arbitrary width at which the quantum confinement is retained. The calculations are performed with due regard for the difference between the refractive indices of the quantum well and the barriers. In this case, there appears an additional reflection from the quantum-well boundaries. The additional reflection results in a substantial change in the shape of the reflected pulse as compared to that characteristic of a homogeneous medium. The reflection from the quantum-well boundaries disappears at specific ratios between the carrier frequency of the exciting pulse and the quantum-well width.     

The role of spatial dispersion of an electromagnetic wave in its penetration through a quantum well

The theory of light penetration through a quantum well in a strong magnetic field perpendicular to the well plane is developed under the conditions where interband transitions occur in the well. The light wavelength is assumed to be comparable to the well width. The relationships for the reflection, absorption, and transmission are derived with due regard for the spatial dispersion of a monochromatic light wave and the difference between the refractive indices of the quantum well and the barrier. The normal incidence of light with respect to the well plane is considered, and one excited level is taken into account. It is demonstrated that the above two factors most strongly affect the reflection, because the reflection from the well boundaries appears in addition to the reflection caused by interband transitions in the quantum well. The most radical changes in the reflection are observed in the case when the reciprocal radiative lifetime of the excited state in the quantum well is short compared to the reciprocal nonradiative lifetime. In the range of large well widths, the applicability of the theory is limited by the existence condition of quantum well levels.     

Effect of the anomalous dispersion on the optical characteristics of a quantum well

The frequency dependence of the optical characteristics of a quantum well (reflectance, transmittance, and absorbance) in the vicinity of the interband resonance transitions is studied for the case of two closely spaced excited levels. A wide quantum well in a strong magnetic field directed perpendicular to the surface of the quantum well and an incident monochromatic wave are considered. Allowances are made both for the difference in the refractive indices of the barriers and the quantum well and for the spatial dispersion of the light wave. It is shown that, at long radiative lifetimes of the excited states (as compared to the nonradiative lifetimes), the frequency dependence of the light reflectance near the resonance interband transitions is primarily determined by a curve similar to that of the anomalous dispersion of the refractive index. As the lifetimes level off, the contribution of this curve decreases and becomes negligible when the lifetime ratio reverses. It is also shown that the transmittance and absorbance of light do not exhibit a frequency dependence resembling the anomalous dispersion.     

Transient intraband light absorption by quantum dots: Pump-probe spectroscopy

We have developed a theory of a transient intraband light absorption by semiconductor quantum dots. This absorption plays an important role in the two-pulse pump-probe method, which enables determining the energy relaxation rates of electron-hole excited states. We have considered all possible schemes of this process wherein the carrier frequency of optical pump pulses is close to the resonance with the interband transition of the quantum-dot electronic subsystem, while the carrier frequency of probe pulses is resonant to the intraband transition. For ensembles of identical and size-distributed quantum dots, the probe pulse energy absorption induced by the pump pulse is analyzed in relation to the delay time between the pulses. We have found that, under certain conditions, this dependence can be described by a single, two, or three exponentials. The exponents of the exponentials are proportional to the energy relaxation rates of electron-hole excited states.     

State-filling and magneto-photoluminescence of excited states in InGaAs/GaAs self-assembled quantum dots

We present the first radiative lifetime measurements and magneto-photoluminescence results of excited states in InGaAs/GaAs semiconductor self-assembled quantum dots. By increasing the photo-excitation intensity, excited state interband transitions up ton= 5 can be observed in the emission spectrum. The dynamics of the interband transitions and the inter-sublevel relaxation in these zero-dimensional energy levels lead to state-filling of the lower-energy states, allowing the quasi-Fermi level to be raised by more than 200 meV due to the combined large inter-sublevel spacing and the low density of states. The decay time of each energy level obtained under various excitation conditions is used to evaluate the inter-sublevel thermalization time. Finally, the emission spectrum of the dots filled with an average of about eight excitons is measured in magnetic fields up to 13 Tesla. The dependences of the spectrum as a function of carrier density and magnetic field are compared to calculations and interpreted in terms of coherent many-exciton states and their destruction by the magnetic field.     

Mathematical modeling of the population dynamics of “dark” states of a three-level system

Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (??dark??). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.     

Dynamics of spontaneous radiation of atoms scattered by a resonance standing light wave

The scattering of atoms by a resonance standing light wave is considered under conditions when the lower of two resonance levels is metastable, while the upper level rapidly decays due to mainly spontaneous radiative transitions to the nonresonance levels of an atom. The diffraction scattering regime is studied, when the Rabi frequency is sufficiently high and many diffraction maxima are formed due to scattering. The dynamics of spontaneous radiation of an atom is investigated. It is shown that scattering slows down substantially the radiative decay of the atom. The regions and characteristics of the power and exponential decay are determined. The adiabatic and nonadiabatic scattering regimes are studied. It is shown that the wave packets of atoms in the metastable and resonance excited states narrow down during scattering. A limiting (minimal) size of the wave packets is found, which is achieved upon nonadiabatic scattering in the case of a sufficiently long interaction time.     

Effect of surface defects on radiative interband recombination in silicon nanocrystals highly doped with hydrogen-like impurities

The role of surface defects at the Si nanocrystal boundary during the process of interband radiative recombination is studied in the case in which nanocrystals are doped with hydrogen-like impurities with shallow energy levels. It is shown that, in the case of a nonpassivated surface with a large number of dangling bonds, the rate of radiative transitions in nanocrystals doped with donors can be larger than that in nondoped crystallites. On the other hand, doping with acceptors leads to a decrease in the rate of transitions. In the case of a completely passivated surface, the recombination rate remains almost unchanged irrespective of the type of dope.     

The photon angle dependence of photoemission from a Cu(100) crystal

The symmetry properties of direct interband transitions are shown to have important consequences for angle-resolved u.v. photoemission. Predictions are made regarding the photon incidence angle dependence of Ar I (11.7 eV) excited photoemission from a Cu(100) single crystal surface, and these are shown to be in close agreement with the experimental results.     

Pulsed and monochromatic excitation of semiconductor quantum wells under the conditions of quantum confinement

The reflectance and absorbance of light by quantum wells whose width is comparable to the light wavelength have been calculated. The difference in the refractive indices of the materials of the quantum well and the barriers has been taken into account. Pulsed irradiation with an arbitrary shape of the exciting pulse has been considered, and the existence of two closely spaced discrete excitation levels has been assumed. This pair of levels can correspond to two magnetopolaron states in a quantizing magnetic field directed perpendicular to the plane of the quantum well. The ratio between the magnitudes of nonradiative and radiative dampings of electronic excitations is arbitrary. The final results have been obtained without invoking the approximation in which the Coulomb interaction of electrons and holes is negligible.     

Generation of low-frequency radiation by dense hot plasma under pondermotive action of a short laser pulse

The theory of the generation of low-frequency radiation under the pondermotive action of a femtosecond laser pulse on dense hot plasma is developed. It is shown that, at fairly high plasma temperatures, when electron-electron collisions are rare and the low-frequency field is excited under conditions of the anomalous skin effect, the generation efficiency can be close to maximal. The optimal generation conditions are achieved if the carrier frequency of the laser pulse is close to the plasma frequency and the pulse is tightly focused. Under irradiation by pulses with durations of tens to hundreds femtoseconds, terahertz radiation is generated in a broad angular range.     

Interaction of frequency modulated light pulses with rubidium atoms in a magneto-optical trap

The spatial displacement of the ⁸⁵Rb atoms in a Magneto-Optical Trap (MOT) under the influence of series of frequency modulated light pulse pairs propagating opposite to each other is measured as a function of the time elapsed after the start of the pulse train, and compared with the results of simulations. Adiabatic excitation and consecutive de-excitation take place between the ground 5²S_1/2 (F=3) and the 5²P_3/2 (F'=2, 3, 4) excited levels as the result of the interaction. The displacement of the ⁸⁵Rb atoms is calculated as the solution of simple equation of motion where the expelling force is that arising from the action of the frequency modulated light pulses. The restoring and friction forces of the MOT are taken into account also. The system of Bloch equations for the density matrix elements is solved numerically for transitions between six working hyperfine levels of the atom interacting with the sequence of the frequency modulated laser pulses. According to these simulations, the momentum transferred by one pulse pair is always smaller than the expected 2ħk, (1) where ħ is the Plank constant and k=2π/λ where λ is the wavelength, (2) having a maximum value in a restricted region of variation of the laser pulse peak intensity and the chirp.     

Determination of carrier density dependent lifetime and quantum efficiency in semiconductors with a photoluminescence method (application to InGaAsP/InP heterostructures)

The light beam of a laser is focussed near the surface of a semiconductor sample. Thereby the excitation rate can be controlled precisely assuming a Gaussian intensity distribution of the beam. Measuring the recombination light intensity yields the quantum efficiency of the sample. By sinusoidal modulation of the excitation light and measurement of the resulting phase shift of the recombination light, the carrier density dependent lifetime is obtained. By evaluation of measured internal quantum efficiency and phase shift, Auger and radiative recombination coefficients are determined. The analysis takes into account the carrier density dependence of the radiative coefficient and shows that for most experimental conditions carrier diffusion can be neglected. In this case the analysis can be performed without numerical integration. Application of the method to quaternary InGaAsP material yielded values for Auger coefficient and radiative coefficients in accordance with published results.     

Pulsed Optical Pumping as a Tool for the Determination of Population Mechanisms of Excited States in a Low-Pressure Mercury Discharge

Experiments are described in which a low-pressure mercury discharge is irradiated with a dye-laser pulse tuned resonant to one of the 6 3P-7 3S1 mercury transitions. The effects of this optical pumping process are monitored via fluorescence on many mercury transitions. The sign and time behavior of each fluorescence signal are different, and are determined by one or more of the following processes: a) radiative decay of the 7 3S1 level; b) a change in electron-impact excitation rate from the ground state induced by the optogal-vanic effect (OGE). This OGE results from the population redistribution in the 6 3P levels after radiative decay of the 7 3S1 level; c) a change in electron-impact excitation rate from the 6 3P levels; and d) a change in 6 3P-6 3P collisional excitation rate. It is demonstrated that the signal and time behavior of the fluorescence signals induced by the pulsed optical pumping process can be used to determine the population mechanism(s) of excited states qualitatively.     

控制光和信号光频差对太赫兹光非对称解复用器性能的影响

讨论了半导体光放大器中的带间效应，及载流子热效应、谱烧孔效应、双光子吸收以及超快非线性折射等带内效应对半导体光放大器的动态特性的影响，讨论了两种情况：1)保持控制光波长不变而改变信号光频率，2)保持控制光和信号光频率相同而同时改变它们的频率下半导体光放大器的增益、相位动态特性以及太赫兹光非对称解复用器的开关窗口特性。数值结果表明，为了得到较为平坦而窄的开关窗口，控制光波长应与信号光波长相同，且其与半导体光放大器增益谱中心波长的差值应该大一些。     

Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

Parametric frequency transformation in a superconducting waveguide line with an integrated Josephson oscillator

The parametric frequency division in a coplanar waveguide line with an integrated single-contact rf SQUID (Josephson oscillator) is discussed. It is assumed that the oscillator is excited by pump pulses whose carrier frequency can be a multiple of the plasma frequency of the oscillator. It is shown that the Josephson oscillator excited at the pump frequency can induce frequency division by emitting subharmonics that are multiples of the fundamental frequency (fractional resonances). Parameters for which parametric frequency transformation occurs are determined. The possible generalization of this effect to the quantum case in which correlated microwave photons (entangled photon states) can be generated is discussed.     

Optical band gap width in GaAs in megagauss magnetic fields

The band gap width in GaAs in magnetic fields of up to 10 MG is calculated using a five-band kp model. The selection rules for interband electron transitions in strong magnetic fields are found, and the dependences of the interband transition probabilities on a magnetic field are calculated. The electronic spectra calculated in the five-band model are compared with those calculated in the Kane model and in the tight-coupling approximation. The calculations are shown to agree with experimental data if the contribution from the density-of-states tails and excitonic effects to light absorption is taken into account.