Effect of spatial dispersion on the shape of a light pulse propagating through a quantum well

The reflection, transmission, and absorption of a symmetric electromagnetic pulse are calculated. The carrier frequency of the pulse is close to the frequency of direct interband transitions in a quantum well (QW). The QW energy levels are assumed to be discrete, with two closely spaced excited levels being taken into account. The QW width is assumed to be sufficiently large and comparable to the light wavelength corresponding to the pulse carrier frequency. In this case, the dependence of the momentum matrix element for the interband transition on the light wave vector should be taken into account. The refractive indices of the QW and barriers are assumed to be equal. The problem is solved for an arbitrary relation between the radiative and non-radiative lifetimes of the excited electronic states. It is shown that spatial dispersion considerably affects the shapes of the reflected and transmitted pulses. The greatest changes occur in the case where the inverse radiative lifetime is close to the difference between the frequencies of the interband transitions considered.     

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.     

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.     

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.     

Reflection and absorption of light by a wide quantum well with two closely spaced excitation levels

The spectra of reflection and absorption of monochromatic light by semiconductor quantum wells whose width is comparable to the wavelength of exciting radiation are calculated. The case of resonance with two closely spaced excited levels is considered. These levels can arise as a result of splitting of the electron-hole pair energy due to the magnetopolaron effect when the quantum well is placed in a strong magnetic field directed perpendicular to the plane of the quantum well. It is demonstrated that, in wide quantum wells, unlike in narrow quantum wells, the reflectance and absorptance of light depend on the quantum-well width. The theory is applicable at any reciprocal ratio of the radiative lifetime to the nonradiative lifetime of electronic excitations.     

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.     

Nonradiative and radiative Förster energy transfer between quantum dots

We theoretically study nonradiative and radiative energy transfer between two localized quantum emitters, a donor (initially excited) and an acceptor (receiving the excitation). The rates of nonradiative and radiative processes are calculated depending on the spatial and spectral separation between the donor and acceptor states and for different donor and acceptor lifetimes for typical parameters of semiconductor quantum dots. We find that the donor lifetime can be significantly modified only due to the nonradiative Förster energy transfer process at donor–acceptor separations of approximately 10 nm (depending on the acceptor radiative lifetime) and for the energy detuning not larger than 1–2 meV. The efficiency of the nonradiative Förster energy transfer process under these conditions is close to unity and decreases rapidly with an increase in the donor–acceptor distance or energy detuning. At large donor–acceptor separations greater than 40 nm, the radiative corrections to the donor lifetime are comparable with nonradiative ones but are relatively weak.     

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.     

Radiative and nonradiative recombination times in semiconducting films

The radiation emitted spontaneously by a semiconductor which has been excited for a very short time decays exponentially with a time constant that depends on the recombination rate of electrons and holes. This recombination rate is the combination of radiative and nonradiative transition rates between conduction and valence bands of the semiconductor. The radiative recombination rate depends on the density of states of the electromagnetic field, which can be made to be dependent on the geometry. In this paper, we report on the dependence of the fluorescence lifetime upon the thickness of active thin films. For systems in which the radiative recombination rate is dominant over the nonradiative ones, the total recombination time can be changed by suitable modifications of the thickness of the film. In this situation, the nonradiative rate can be evaluated. We present experimental results for the case of cadmium sulphide (CdS) thin films.     

Photoprocesses with the sub-Doppler spectral selectivity excited by the monochromatic optical pulse in a thin gas cell

The method of sub-Doppler spectroscopy is theoretically elaborated, which is based on the specific dynamics of a number of optically excited atomic particles (atoms or molecules) of a rarefied gas medium in a thin cell after the action of the resonance pulse of the monochromatic radiation. Corresponding calculations are carried out on the basis of density matrix equations for the resonance optical transition between Zeeman degenerate ground and excited quantum levels of particles in case of the linear polarization of the laser pulse at its normal incidence on the cell. The situation is considered when the radiative lifetime of the excited level is much more than the characteristic transit time of particles between nearest plane-parallel walls of the cell. Then the distribution of a number of excited particles versus the pulse frequency detuning narrows in the process of particles collisions with walls of the cell after action of the laser pulse. The factor of such a narrowing (in comparison with the Doppler broadening of the spectral line of the resonance transition) may be more than the ratio of the characteristic transverse size of the thin gas cell to its inner thickness. We discuss possible use of given sub-Doppler resonances (of the number of excited particles) in the high-resolution spectroscopy and also in high-selective processes of photo-ionization and photo-dissociation, especially, for isotope (or isomer) separation and detection of rare (in particular single) atoms or molecules of a gas medium.     

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.     

Donor binding energy and radiative life time of exciton in a strained InGaN/GaN quantum wire

Donor binding energies of positively and negatively charged impurities in a strained InGaN/GaN cylindrical quantum wire are investigated. The interband optical transition with and without the exciton is computed as a function of wire radius. The exciton oscillator strength and the exciton lifetime for radiative recombination as a function of wire radius have been computed.     

Quantum vacuum radiation spectra from a semiconductor microcavity with a time-modulated vacuum Rabi frequency

We develop a general theory of the quantum vacuum radiation generated by an arbitrary time modulation of the vacuum Rabi frequency of an intersubband transition in a doped quantum well system embedded in a planar microcavity. Both nonradiative and radiative losses are included within an input-output quantum Langevin framework. The intensity and the spectral signatures of the extra-cavity emission are characterized versus the modulation properties. For realistic parameters, the photon pair emission is predicted to largely exceed the blackbody radiation in the mid and far infrared. For strong and resonant modulation a parametric oscillation regime is achievable.     

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.     

Influence of Mg Composition on Optical Properties of Exciton Confinement in Strained Wurtzite ZnO/MgxZn1-xO Cylindrical Quantum Dots

Based on the effective-mass approximation and variational approach, excitonic optical properties are investigated theoretically in strained wurtzite (WZ) ZnO/Mg_xZn_1-xO cylindrical quantum dots (QDs) for four different Mg compositions: x=0.08, 0.14, 0.25, and 0.33, with considering a three-dimensional carrier confinement in QDs and a strong built-in electric field effect due to the piezoelectricity and spontaneous polarization. The ground-state exciton binding energy, the interband emission wavelength, and the radiative lifetime as functions of the QD structural parameters (height and radius) are calculated in detail. The computations are performed in the case of finite band offset. Numerical results elucidate that Mg composition has a significant influence on the exciton states and optical properties of ZnO/Mg_xZn_1-xO QDs. The ground-state exciton binding energy increases with increasing Mg composition and the increment tendency is more prominent for small height QDs. As Mg composition increases, the interband emission wavelength has a blue-shift if the dot height L<3.5 nm, but the interband emission wavelength has a red-shift when L>3.5 nm. Furthermore, the radiative lifetime increases rapidly with increasing Mg composition if the dot height L>3 nm and the increment tendency is more prominent for large height QDs. The physical reason has been analyzed in depth.     

Influence of an electric field on the magnetoabsorption in a field of resonant laser radiation

The frequency dependence of the coefficient of interband magnetoabsorption of a weak electromagnetic wave propagating in a constant electric field and in a field of resonant laser radiation at a frequency equal to the cyclotron frequency (infrared magnetic resonance) is calculated. The specific features observed in interband absorption of the electromagnetic wave in a uniform electric field are considered for the case in which the frequency of laser radiation is equal to the confinement frequency in a parabolic quantum well (infrared quantum-well resonance).     

Influence of Mg Composition on Optical Properties of Exciton Confinement in Strained Wurtzite ZnO/Mg_x Zn_(1-x) O Cylindrical Quantum Dots

Based on the effective-mass approximation and variational approach, excitonic optical properties are investigated theoretically in strained wurtzite (WZ) ZnO/Mg x Zn 1-x O cylindrical quantum dots (QDs) for four different Mg compositions: x = 0.08, 0.14, 0.25, and 0.33, with considering a three-dimensional carrier confinement in QDs and a strong built-in electric field effect due to the piezoelectricity and spontaneous polarization. The ground-state exciton binding energy, the interband emission wavelength, and the radiative lifetime as functions of the QD structural parameters (height and radius) are calculated in detail. The computations are performed in the case of finite band offset. Numerical results elucidate that Mg composition has a significant influence on the exciton states and optical properties of ZnO/Mg x Zn 1 x O QDs. The ground-state exciton binding energy increases with increasing Mg composition and the increment tendency is more prominent for small height QDs. As Mg composition increases, the interband emission wavelength has a blue-shift if the dot height L 3.5 nm, but the interband emission wavelength has a red-shift when L 3.5 nm. Furthermore, the radiative lifetime increases rapidly with increasing Mg composition if the dot height L 3 nm and the increment tendency is more prominent for large height QDs. The physical reason has been analyzed in depth.     

Thin-film electroluminescent devices excited by a linearly rising voltage

The average and instantaneous luminances of a thin-film electroluminescent device (TFELD) are determined as functions of the voltage rise time by solving kinetic equations for the concentration of excited emission centers in the electroluminescent layer of the device. It is shown theoretically and experimentally that the dependences of the average and peak luminances, the external and internal quantum yield, the energy yield, and the luminous efficacy as functions of the voltage rise time all have a maximum, and the position of that maximum depends on the frequency of the driving voltage. The calculated and experimental dependences make it possible to determine the main parameters of the electroluminescence process: the collisional excitation cross section for the emission centers, the concentration of emission centers, and the transition probability of the emission centers to an excited state, as well as the radiative and nonradiative recombination probabilities of these and other centers. Zh. Tekh. Fiz. 69, 58–63 (February 1999)     

Photon emission during intraband tunneling through quantum well structures

Radiative transitions associated with intraband electron tunneling through DC biased quantum well structures are analyzed theoretically. Spontaneous emission and stimulated emission of photons within the quantum well structure are calculated and estimates are made of the radiative transition rate in comparison with the damping loss. The absence of an inherent long wavelength emission cutoff is in contrast with interband transition devices and suggests applications of intraband transition devices as far infrared or microwave sources.     

The quantum yield of a metallic nanoantenna

The local-field factor and quantum yield of a metallic nanoantenna are studied to identify its enhancement of an emitter’s emission within the feed gap. For simplicity, a two-dimensional model, an Au nanoantenna with an emitter at the center, is studied. The electromagnetic field is solved by a set of surface integral equations. An incident plane wave irradiating the nanoantenna is modeled to simulate the excitation of the emitter by illuminating light, and the local-field factor is used to evaluate the amplification of the electric field in the feed gap of the metallic nanoantenna. Once the emitter becomes excited, a model of an electric dipole interacting with the nanoantenna is used for calculating the radiative and nonradiative powers to obtain the quantum yield of the excited emitter in the presence of the nanoantenna. The numerical results of quantum yield indicate that an Au nanoantenna acts as a low-pass filter for the emission of the emitter. Moreover, the smaller the feed gap, the larger the local-field factor but the less the quantum yield. PACS 78.67.-n; 33.80.-b; 33.50.-j; 42.30.-d; 42.50.Hz; 81.07.Pr