On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: the impact of inhomogeneously broadened gain and fast carrier dynamics

We present a detailed analytical model describing the noise properties of quantum-dot (QD) optical amplifiers operating in the linear and saturated regimes. We describe the dependence of the optical noise on the main physical parameters characterizing the QD gain medium as well as on operating conditions. The optical noise at the amplifier output shows a broad-band spectrum with an incoherent spectral hole due to the gain inhomogeneity. A coherent spectral dip stemming from noise-signal nonlinear interactions is superimposed on that broad-band spectrum. The broad-band incoherent component is also calculated using an approximate model which makes use of an equivalent inhomogeneous population inversion factor. The validity of the approximation is examined in detail. We also calculate the electrical relative intensity noise and observe a spectral hole corresponding to the spectral shape of the optical noise. The most important characteristics of the optical and electrical noise spectra are determined by the degree of inhomogeneous broadening and by the fast carrier dynamics of QD amplifiers. The fast dynamics causes a very wide noise spectral hole which has important potential consequences for detection of fast data and for all optical signal processing.     

Nonlinear gain suppression in semiconductor lasers due to carrier heating

A simple model is presented for carrier heating in semiconductor lasers from which the temperature dynamics of the electron and hole distributions can be calculated. Analytical expressions for two new contributions to the nonlinear gain coefficient, in are derived, which reflect carrier heating due to stimulated emission and free carrier absorption. In typical cases, carrier heating and spectral holeburning are found to give comparable contributions to nonlinear gain suppression. The results are in good agreement with recent measurements on InGaAsP laser diodes.<>     

Bringing quantum dots up to speed [Breaking the phonon bottleneckwith high-speed modulation of quantum-dot lasers]

In this article, we will focus on the carrier relaxation time in quantum dots (QDs), its probable mechanism, and the implications for the performance characteristics of directly modulated QD lasers and other QD devices. The electron and hole bound states and general predictions of carrier capture time into them will be presented, followed by a discussion of intersubband carrier relaxation in QDs. The modulation characteristics of QD lasers as a function of temperature will be described, and these modulation results will be discussed in terms of the temperature, composition, and size dependence of the relaxation time in QDs, including possible methods for designing QDs to overcome this relaxation time barrier. Also, the performance characteristics of other possible QD devices, such as intersubband lasers and detectors, will be examined in terms of our current understanding of the relaxation time in QDs     

Theoretical and Experimental Study of High-Speed Small-Signal Cross-Gain Modulation of Quantum-Dot Semiconductor Optical Amplifiers

We numerically and experimentally investigate the high-speed small-signal cross-gain modulation (XGM) characteristics of a quantum-dot (QD) semiconductor optical amplifier (SOA). From a p-doped QD SOA operating at 1.3 $mu{hbox {m}}$, high-speed small-signal XGM responses up to 40 GHz are measured from low to high injection currents and improve at high injection currents. In the numerical model, we set up about six hundred coupled rate equations, where the carrier dynamics of QD electron and hole states are considered separately and the enhanced hole occupation due to p-type doping is included. The high-speed small-signal XGM spectra are calculated at various modulation frequencies and pump-probe detunings. We identify how the two separate XGM mechanisms of total carrier density depletion (TCDD) at low injection current and spectral hole burning (SHB) at high injection current affect the high-speed small-signal XGM behavior. From the measured and calculated results, we show that high-speed small-signal XGM responses of QD SOAs can be improved by injecting more carriers to the QD excited states, which enhances high-speed XGM induced by SHB rather than by TCDD.      

多量子阱的声子喇曼散射理论

<正> 近年来多量子阱的声子喇曼散射,在实验方面已有许多富有成果的工作。为了提供系统的理论基础,推动实验的进一步深入,我们系统地研究了多量子阱喇曼散射的微观理论。本文将介绍理论的部分内容,侧重说明理论基础和讨论区别于体材料最具特色的一些结果。 在微观理论中,最便于表征喇曼散射的是喇曼张量(以下具体讨论Stokes散射):     

Differential Gain and Gain Compression in Quantum-Dot Lasers

The dynamics of optical gain in semiconductor quantum dots (QDs) is investigated. Simple analytical expressions are derived, which directly connect the laser dynamical response to capture and intradot relaxation rates. The effect of hole spreading in the valence band and spectral hole burning in the QD ensemble is also quantitatively assessed. The analysis shows that intradot relaxation constitutes the main limitation in the dynamics and points to possible routes towards the improvement of QD lasers     

Rate Equations for 1.3-$mu$ m Dots-Under-a-Well and Dots-in-a-Well Self-Assembled InAs–GaAs Quantum-Dot Lasers

A rate-equation model, in which three discrete quantum-dot (QD) energy levels are assumed and all possible relaxation paths and carrier transport in the GaAs barrier are considered, is presented to analyze the steady-state performance of 1.3 mum undoped and doped dots-under-a-well (DUW) and dots-in-a-well (DWELL) InAs-GaAs QD lasers. DWELL QD lasers have higher saturation value of QD level occupation probabilities and characteristic temperature (T₀) than that of DUW QD lasers due to the improvement of hole confinement. The p-doped QD laser shows lower threshold current density than n-doped QD laser at the same threshold condition, and the T₀ of n-doped DWELL laser is higher than that of p-doped DWELL laser at room temperature. Optimized QD layer number of DUW and DWELL QD lasers with different QD density is discussed     

Linewidth Enhancement Factor of Quantum-Dot Optical Amplifiers

The linewidth enhancement (alpha-) factor of quantum-dot (QD) semiconductor optical amplifiers in the small signal gain and nonlinear regimes is theoretically investigated. A microscopic polarization equation and a wave equation are used to model subpicosecond pulse propagation in the nonlinear regime. In addition, a population equation that takes into account spectral hole burning and carrier heating effects is used. A novel approach to obtain the alpha-factor from the output pulse amplitude and phase in the dynamic nonlinear regime is presented. An in-depth study reveals that the presence of excited states (ES) limits the alpha-factor to values greater than 1 except when the energy separation between the ground state and ES is large. The alpha-factor dependence on QD inhomogeneous broadening, carrier density, carrier temperature, energy level separation, and input pulse energy is analyzed. We find that these can change the alpha-factor considerably. In particular, the alpha-factor increases with increasing input pulse energy and can be greater than 10 for input pulse energies larger than the amplifier's input pulse saturation energy. In the light of our calculations, the optimum device engineering required to obtain a low alpha-factor is discussed     

Internal efficiency of semiconductor lasers with a quantum-confined active region

We discuss in detail a new mechanism of nonlinearity of the light-current characteristic (LCC) in heterostructure lasers with reduced-dimensionality active regions, such as quantum wells (QWs), quantum wires (QWRs), and quantum dots (QDs). It arises from: 1) noninstantaneous carrier capture into the quantum-confined active region and 2) nonlinear (in the carrier density) recombination rate outside the active region. Because of 1), the carrier density outside the active region rises with injection current, even above threshold, and because of 2), the useful fraction of current (that ends up as output light) decreases. We derive a universal closed-form expression for the internal differential quantum efficiency /spl eta//sub int/ that holds true for QD, QWR, and QW lasers. This expression directly relates the power and threshold characteristics. The key parameter, controlling /spl eta//sub int/ and limiting both the output power and the LCC linearity, is the ratio of the threshold values of the recombination current outside the active region to the carrier capture current into the active region. Analysis of the LCC shape is shown to provide a method for revealing the dominant recombination channel outside the active region. A critical dependence of the power characteristics on the laser structure parameters is revealed. While the new mechanism and our formal expressions describing it are universal, we illustrate it by detailed exemplary calculations specific to QD lasers. These calculations suggest a clear path for improvement of their power characteristics. In properly optimized QD lasers, the LCC is linear and the internal quantum efficiency is close to unity up to very high injection-current densities (15 kA/cm/sup 2/). Output powers in excess of 10 W at /spl eta//sub int/ higher than 95% are shown to be attainable in broad-area devices. Our results indicate that QD lasers may possess an advantage for high-power applications.     

Intersubband Absorption in Terahertz Lasers Based on Optically Pumped Quantum Well Structures

We study the effects of microscopic dynamics of electrons on the intersubband optical absorption in terahertz lasers based on optically pumped quantum wells (THz-OPQW). The ensemble Monte Carlo method is used to include different electron scattering mechanisms in the calculation, so that the dependence of intersubband absorption lineshape on microscopic dynamics of electrons can be easily investigated. We find that electron-electron scattering is the dominant factor to determine the absorption linewidth. The real distributions of hot electrons are included to study the temporal changes of the spectra lineshape. Our findings show that the dependence of spectral lineshape on electron population essentially results from the electron scattering and the non-Fermi electron energy distribution.     

Rate equation model for nonequilibrium operating conditions in aself-organized quantum-dot laser

A nonequilibrium rate equation model is presented and analyzed for the self-organized quantum dot (QD) laser. The model assumes the QD zero dimensional levels are coupled to a thermal electron distribution in the wetting layer through reservoir rate equations. By including the energy dependence of the wetting layer reservoir versus temperature, the model accounts for the spectral narrowing of the gain with increasing temperature, the negative temperature coefficient of the lasing threshold, and a reduction of the spectral hole burning with increasing temperature, all found experimentally in QD lasers     

Modeling and simulation of InAs/GaAs quantum dot lasers

Based on the analysis of carrier dynamics in quantum dots (QDs), the numerical model of InAs/GaAs QD laser is developed by means of complete rate equations. The model includes four energy levels and among them three energy levels join in lasing. A simulation is conducted by MATLAB according to the rate equation model we obtain. The simulation results of PI characteristic, gain characteristic and intensity modulation response are reasonable. Also, the relations between the left facet reflectivity of laser cavity and threshold current as well as modulation bandwidth are studied. It is indicated that the left facet reflectivity increasing can result in reduced threshold current and improved modulation bandwidth, which is in accordance with experimental results. The internal mechanism of QD lasers is fully described with the rate equation model, which is helpful for QD lasers research.     

Ultrafast Electronic Dynamics in Unipolar n-Doped InGaAs–GaAs Self-Assembled Quantum Dots

The dynamics of electron capture and relaxation in an n-doped quantum-dot (QD) infrared detector structure are studied directly in the time domain using ultrafast intraband-pump-interband-probe differential transmission spectroscopy. Femtosecond midinfrared pulses are used to excite electrons from the doped QDs into the conduction band continuum, and the complete electron distribution functions are monitored as a function of time using an interband probe. Because only electrons are excited and no holes are present, the electron-hole scattering which dominates the relaxation in bipolar systems is not present, and the measurement yields the electron dynamics exclusively. Excitation-dependent electron capture times were measured from 40 to <10 ps with increasing pump intensity. Intradot inter-level relaxation times were observed to be ~100 ps, driven by Auger-type electron-electron scattering. Nanosecond-scale dynamics in the n=1 state were also observed and attributed to transport effects. Our results indicate that the phonon bottleneck in the QDs is circumvented by Auger scattering; nevertheless, the electron dynamics in the unipolar device are found to be slower than those observed in bipolar systems, which confirms the significance of the holes in the carrier relaxation in bipolar devices. The results also support the improved operation of QD infrared photodetectors relative to quantum-well-based devices     

Nonlinear gain coefficients in semiconductor lasers: effects ofcarrier heating

Nonlinear gain coefficients due to the effects of carrier heating are derived from the rate equations of carrier energy transfer in semiconductor lasers. We find that, in the modulation responses of semiconductor lasers, stimulated recombination heating will affect the resonant frequency and damping rate in a same form as the effects of spectral hole burning, while free carrier absorption heating will only affect the damping rate. The effects of injection heating and nonstimulated recombination heating are also discussed. The carrier energy relaxation time is calculated from first principles by considering the interactions between carriers and polar optical phonons, deformation potential optical phonons, deformation potential acoustic phonons, piezoelectric acoustic phonons. At the same time, the hot phonon effects associated with the optical phonons are evaluated because their negligible group velocity and finite decay time. We show that the carrier-polar longitudinal optical phonon interaction is the major channel of carrier energy relaxation processes for both electron and holes. We also point out the importance of the longitudinal optical phonon lifetime in evaluating the carrier energy relaxation time. Neglecting the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time, this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficients due to carrier heating. The effects of spectral hole burning, stimulated recombination heating, and free carrier absorption heating on limiting the modulation bandwidth in semiconductor lasers are also discussed     

Fundamental second-order nonlinear distortions in analog AM CATVtransport systems based on single frequency semiconductor lasers

The author analyzes the fundamental second-order nonlinearities and their composite distortions in lightwave analog AM CATV transport systems based on single frequency semiconductor lasers. The nonlinear interaction between the photons and the electrons in the laser, the nonlinear dynamics of laser spatial hole burning, and the nonlinear interaction of fiber chromatic dispersion and laser frequency chirping are strongly dependent on the CATV carrier frequencies. The author found that the overall distortions increase for higher carrier frequencies and longer fiber spans. The distortion levels, however, are within the critical requirements for current and future CATV transport systems     

Simulation of carrier transport and nonlinearities in quantum-welllaser diodes

The two-dimensional (2-D) quantum-well (QW) laser diode simulator Minilase-II is presented in detail. This simulator contains a complete treatment of carrier dynamics including bulk transport, quantum carrier capture, spectral hole burning, and quantum carrier heating. The models used in the simulator and their connectivity are first presented. Then the simulator is used to demonstrate the effects of various nonlinear processes occurring in QW lasers. Finally, modulation responses produced by Minilase-II are compared directly with experimental data, showing good quantitative agreement     

Effects of spatial hole burning on gain switching invertical-cavity surface-emitting lasers

We present a numerical study of the effects of carrier diffusion and spatial hole-burning in vertical-cavity surface-emitting lasers under gain switching. Our model includes spatial and temporal dependences of both the optical field and the carrier density. Results show that spatial hole burning places a limit on the minimum achievable pulse width. We demonstrate that spatial hole-burning tan be avoided and shorter pulses can be obtained by using an appropriate pumping geometry. We also consider the case in which the laser operates simultaneously in two transverse modes and show that transverse-mode competition induced by spatial hole burning leads to period doubling and other interesting nonlinear behavior     

Numerical Analysis of the Frequency Chirp in Quantum-Dot Semiconductor Lasers

We present a numerical model for the analysis of the chirp dynamics of quantum-dot (QD) semiconductor laser under large signal current modulation. The model is based on the multipopulation rate equation formalism, and it includes all the peculiar characteristics of the active QD material such as the inhomogeneous broadening of the gain spectrum, the presence of an excited state confined in the QDs and the presence of nonconfined states due to the wetting layer and the barrier. In this paper the model is applied to the analysis of the chirp of two QD single-mode lasers emitting from the ground state and from the excited state, respectively. In order to make comparisons of the chirp in various operating conditions, we define some equivalent parameters for quantifying the adiabatic and transient contributions to the chirp. These parameters are then used to analyze the chirp as function of the bias current, of the modulation depth and of the modulation frequency. All the various simulation results show that the carrier accumulation in the QD states, poorly involved in the stimulated emission process and the carrier dynamics in these states, can cause a nonzero chirp under current modulation even for the ideal condition of zero linewidth enhancement factor (or -parameter) at the laser threshold.