垂直腔激光器中弛豫振荡频率的优化控制

从垂直腔面发射的半导体激光器（VCSELs）的结构出发，利用增益与载流子密度的广义对数关系，借助小信号分析法，推出了直接调制情形下驰豫振荡频率的严格解析关系。分析指出，量子阱器件的光子寿命并非越短越好，欲提高VCSELs的驰豫振荡频率，除了增加注入电流，提高微分增益等基本途径外，控制器件的结构参数可使驰豫振荡频率达到极大值。同时，自发辐射因子的可控性，以及降低稳态载流子密度，也都是提高VCSELs驰豫振荡频率和拓宽调制带宽的有效措施。     

Theoretical modeling of relaxation oscillations in Er-dopedwaveguide lasers

An analysis of relaxation oscillations (λ_s~1.5 μm) in locally Er-doped optically pumped (λ_p~1.48 μm) waveguide lasers is reported. The theoretical model is based on time dependent rate equations for a quasi-two-level-system and on the equation of continuity for a gain medium. For the first time a numerically reliable simulation of the elementary properties of the laser oscillations was possible: the build-up time and decay of the relaxation oscillations, the time-dependent repetition period, the steady state signal output power and the evolution of the pump power versus time. Mathematically the problem can be characterized as a large boundary value problem, which can approximately be replaced by a stiff initial value problem of ordinary differential equations. In this report, pump- and signal evolution versus time are presented for planar Er-diffused Ti:LiNbO₃ waveguide lasers. The numerically obtained results show a good quantitatively agreement with experimental investigations     

RESEARCH ON THE RELAXATION OSCILLATOR WITH BNRT

A piecewisely linear(with three or four segments)dynamic version for relaxation oscillations in acircuit with bidirectional negative resistance transistor is studied.The circuit and dynamic equation are given andsome properties of the relaxation oscillations are discussed.Experimental results agree well with the computations,showing that the dynamic model is adequate and useful.     

Full-wave analysis of discontinuities in planar waveguides by themethod of lines using a source approach

An accurate full-wave analysis of discontinuities in shielded microwave structures by the method of lines is presented for use in microwave integrated circuit design. The input currents are derived from a sinusoidal source representation and modeled by inhomogeneous boundary conditions. Interacting discontinuities can be treated without segmentation. Inhomogeneous boundary conditions are introduced to account for the excitation. Analysis shows that in discretizing the differential operators additional source terms which result in inhomogeneous differential equations are obtained. A deterministic equation for the current distribution is derived. For higher flexibility, nonequidistant discretization is used. The scattering parameters are presented for the microstrip step discontinuity and for a single-filter structure with interacting discontinuities, namely a coupled line filter. The filter characteristics are compared with measurements. Measurements verify the filter calculations     

Nonlinear Recombination Waves in Zn-Doped Si at Fully Developed Instability

A nonlinear theory of recombination waves in semiconductors is constructed that addresses quasi-neutrality breaking in the electron–hole plasma with fully developed instability. It is established that with increasing applied electric field a recombination wave of uniform amplitude is transformed into a traveling solitary domain; the domain formation manifests itself in the transition from almost sinusoidal to relaxation oscillations of current. A formula is derived that relates the domain velocity to the properties of the material and the current–voltage characteristic of the specimen. The predicted transformation of recombination waves is verified by checking against previously obtained experimental results concerning slow recombination waves in Si specimens with Zn doping compensation. It is found that a calculated field at which relaxation oscillations arise agrees with the measured one. The frequency of relaxation oscillations is examined as a function of applied field on the basis of the theory and the experiment. The calculated characteristic is shown to be in qualitative and quantitative agreement with the measured one.     

Higher harmonics in the current oscillations in weakly coupled GaAs/AlGaAs superlattices

It is shown that the self-sustained oscillations observed in weakly coupled GaAs/AlGaAs superlattices result from the superposition of sinusoidal oscillations of several coupled oscillators. Each oscillator is a single-barrier resonant tunneling diode. The coupled oscillators form an expanded boundary of an electric-field domain under conditions of negative differential conductance.     

Fractional-order Wien-bridge oscillator

The classical Wien-bridge sinusoidal oscillator is studied, when both of the capacitors of the oscillator acquire a fractional order. Accordingly, the Wien oscillator is described by a set of fractional-order nonlinear differential equations. It is shown that sinusoidal oscillations are preserved but the phase-shift between the waveforms of the two state variables and the frequency of oscillation both depend on the fractional-order, leading to a significant advantage over the integer-type Wien oscillator. Findings are validated via numerical simulations     

LSA relaxation oscillations in a waveguide iris circuit

Large-signal computer simulations of GaAs LSA relaxation oscillations in an X-band waveguide iris circuit are presented. The study is focused on a particular oscillator and a realistic model of an experimental circuit is used. However, the results are typical for other LSA relaxation oscillators. Basic features of the microwave circuit, characteristic voltage and current waveshapes, frequency tuning with bias voltage, and oscillator starting transients are discussed. The RF output power is shown to build up in less than ten cycles. Circuit optimization for high dc to RF conversion efficiency is discussed and circuit data for nearly 30 percent efficiency are given. Finally, efficiency degradation is discussed when doping gradients are present, and effciencies of 15 and 10 percent appear possible for doping gradients as high as 20 and 60 percent, respectively. Hence, the LSA relaxation mode is shown to be less sensitive to doping gradients than the sinusoidal LSA mode.     

Large amplitude operation of the nonlinear oscillator

A two-parameter oscillator equation is obtained from the inverse tangent approximation to the amplifier function. The equation accounts for the exponential wave shape of relaxation oscillations, which cannot be explained by van der Pol's equation.     

Bias circuit oscillations in Gunn devices

A theoretical and experimental study of low-frequency oscillations in the bias circuit of short (nominally 12 µ) Gunn devices is presented. Sinusoidal oscillations and relaxation oscillations including damped sinusoids and exponentially decaying pulses have been observed. The frequency, pulse width, and repetition rate are adjustable with bias voltage, bias circuit impedance, and the impedance of the microwave circuit. This behavior, as well as the conditions for stable bias, is explained in terms of an average terminal i-v characteristic for those devices which exhibit a terminal current drop. The oscillation amplitude is determined by the shape of this i-v curve. Pulses have been observed with subnanosecond rise times, peak voltages of 35 volts and adjustable pulse widths ranging from 3 to 200 ns for typical driver pulse widths of 100 to 500 ns. The sinusoidal frequencies were adjustable in the range of 300 to 550 MHz. The microwave output was in X-band and was self modulated by the bias circuit oscillations. The measured waveforms agree well with theory.     

Spectral signature of relaxation oscillations in semiconductorlasers

A novel and relatively simple expression is given for the optical spectrum of a single-mode semiconductor laser which, due to the presence of relaxation oscillations, consists of a strong central line with a broad weak sideband at each side. The coupling between phase and amplitude fluctuations is included in this derivation and is shown to result in an asymmetry between the relaxation oscillation sidebands. This asymmetry can be used to determine the linewidth enhancement factor. Using optical heterodyne detection, the spectrum of a Fabry-Perot-type AlGaAs laser has been measured as a function of output power. Information on the dynamics of the relaxation oscillations was thus obtained. The power dependence of the frequency and damping of the relaxation oscillations allowed the spontaneous lifetime and the dependence of the gain on both carrier density (differential gain) and intensity (gain saturation) to be separately determined     

碲镉汞深能级载流子弛豫时间的皮秒泵浦-探测研究

采用皮秒泵浦-探测方法研究了碲镉汞材料中非平衡载流子动力学过程,发现其差分透射强度在经过饱和之后出现一个负的极小值,归结为深能级的再吸收过程.采用速率方程模型,并引入两个深能级弛豫时间常数,很好地拟合了差分透射强度的延时曲线.两个深能级弛豫时间常数的存在意味着同时存在两种不同类型的深能级,揭示了碲镉汞材料中深能级特性的...     

Transition from the lowest linewidth mode operation to coherencecollapse in a semiconductor laser with feedback from a distant reflector

The influences of optical feedback from a distant reflector on single-mode semiconductor laser operation are analyzed theoretically. The stable operation in the lowest linewidth mode and the feedback parameter for the onset of coherence collapse are systematically derived. In the feedback regime for the lowest linewidth mode operation, the laser principally operates at the emission frequency of the solitary laser at the beginning of the operation with the feedback. It is shown exactly by asymptotic analysis of the equation for the field phase in the semiconductor cavity considering the time-lag of the feedback that the laser comes to operate in the lowest linewidth mode. In the lowest linewidth mode operation, the laser is stably phase-locked to the feedback. In the semiconductor cavity, the field amplitude and the field phase oscillate in almost the same phase in the fluctuation modes related to the relaxation oscillations, In the lowest linewidth mode operation, the phase oscillations enhance the amplitude oscillations through the feedback-action's dependence upon the phase difference between the field in the semiconductor cavity and the feedback. Thus, the damping of the relaxation oscillations decreases with further increased feedback and the transition to the coherence collapse occurs     

Relaxation instabilities in high-perveance electron beams

Spurious low-frequency oscillations similar to those reported by Cutler have been observed in the form of large amplitude modulation of both the RF output and the collector current of klystrons utilizing high-perveance electron beams. This modulation, which appears typically as sawtooth-like relaxation oscillations with frequencies ranging from 10 cps to 100 kc, was observed to occur spontaneously only if the operating pressure was lower than a critical threshold (approx 1 times 10^{-7}mm Hg). Experiments are described which were designed to investigate this phenomenon using dc beam testers. Evidence is presented which indicates that the oscillations are due to a relaxation back and forth between two possible solutions to Poisson's equation which both satisfy all boundary conditions. One of the possible solutions corresponds to the existence of a virtual cathode within the beam, resulting in a partial reflection of electrons. Experimental evidence indicates that positive ions play an important role in triggering the relaxation. Both theoretical and experimental evidence are presented which point to relaxation instabilities of the type described as a potential hazard in utilizing depressed collector operation for improved efficiency of high-perveance microwave tubes. The same potential hazard exists in the use of periodic electrostatic focusing.     

Theoretical investigation of the second-order harmonic distortionin the AM response of 1.55 μm F-P and DFB lasers

Numerical calculations of the second-order harmonic distortion in the amplitude modulation-response of Fabry-Perot, and distributed feedback (DFB) lasers are presented, and the influence of several nonlinearities, such as longitudinal spatial hole burning, gain suppression, and relaxation oscillations are considered. This analysis is valid for modulation frequencies ranging from a few megahertz to well beyond the resonance frequency of the relaxation oscillation. The distortion of Fabry-Perot lasers for which the effects of spontaneous emission and gain suppression can be clearly illustrated is investigated. The distortion of DFB lasers where the emphasis is on the influence of spatial hole burning and its combination with other nonlinearities is discussed. Various effects are discussed     

A temperature-stable RC transistor oscillator

Generation of stable sinusoidal oscillations of fairly good waveform has been realized in a basic multivibrator circuit by optimizing load and coupling elements and introducing an amplitude defining mechanism with the use of emitter coupling. The resulting differential operation introduces an inherent tendency of self-compensation against changes of active circuit parameters, and the frequency remains practically independent of temperature change even though transistors are used.     

Analysis of the response of lasers to external signal injection

The rate equation including the injection term was extended and solved numerically. The relation between the peak photon number in the onset of relaxation oscillations of lasers and the injected photon number is shown. The step response of the CW laser to the external signal injection and the reshaping property of the laser for the distorted optical pulse are reported.     

On crosstalk and noise in an optical amplifier with gain clamping by vertical laser field

We have calculated the transient behavior and noise figure of a semiconductor optical amplifier (SOA) with the gain clamped by a vertical cavity laser (VCL). The characteristic behavior of the more conventional gain-clamped SOAs and SOAs with no gain-clamping is also studied and compared with the vertically gain-clamped amplifier. The calculations are based on a numerical stochastic rate equation model including several forward- and backward-propagating channels that are coupled to the vertical laser field through the active medium. The noise model takes into account the input noise, randomly amplified spontaneous emission, and random gain. Numerical simulations have been carried out to study the relaxation oscillations, crosstalk, and noise in a system with a strong input signal switched on and off while observing the output signals, VCL photon density, and carrier density. Results show that the VCL field captures most of the disturbances, in agreement with available experimental data.     

Characteristics of negative-resistance nonsinusoidal oscillators

This paper discusses the general characteristics of negative-resistance oscillators for which the voltage waveform across the active device consists not only of the fundamental voltage component but also of substantial harmonic voltage components. It is shown that a stability criterion, equivalent to that described by Kurokawa for sinusoidal voltage oscillators, must be satisfied at each frequency. The waveform components are derived from the fact that, when oscillating, the diode dynamic admittance at each frequency must always be equal to the negative of the load admittance at that frequency. The analysis is applied to two different practical circuits which give rise to LSA relaxation oscillations and good agreement is obtained between theory and experiment.     

Transient response of a thin wire to a moving charged particle

The transient current on a thin wire induced by a charged particle moving parallel to the wire axis is studied. An explicit analytical solution for the induced current is obtained by utilizing the natural-mode method in conjunction with the method of asymptotic expansion. It is found that the solution can be split into two parts: one part consists of damped sinusoidal oscillations and the other exhibits quasistatic-like behavior. Numerical results are presented and compared with some selected results obtained directly by numerically solving a spacetime domain integral equation for the induced wire current.