半导体相移分布反馈激光器模式及调制相应特性的研究--牛顿-矢量方法的应用

给出了适于分析DFB激光器稳态特性的数值模型和分析振幅及频率调制响应特性的解析模型.研究了3相移DFB激光器的调制响应特性,并提出了一种能够快速精确得到DFB激光器多个模式解的新方法--矢量牛顿法.该方法将稳定的矢量法与精确的牛顿法结合,保证了求解质量.实践表明该方法非常适合于求解高度非线性方程的多解问题.用此方法,研究了3相移及简单DFB激光器的纵向光子浓度分布,纵模及调制响应特性.结果表明,3相移DFB具有与简单的DFB激光器同样好的调制响应特性,相移的引入在一定程度上抑制了纵向空间烧孔效应,并且有利于DFB激光器的单模输出.     

半导体相移分布反馈激光器模式及调制相应特性的研究--牛顿-矢量方法的应用

给出了适于分析DFB激光器稳态特性的数值模型和分析振幅及频率调制响应特性的解析模型.研究了3相移DFB激光器的调制响应特性,并提出了一种能够快速精确得到DFB激光器多个模式解的新方法--矢量牛顿法.该方法将稳定的矢量法与精确的牛顿法结合,保证了求解质量.实践表明该方法非常适合于求解高度非线性方程的多解问题.用此方法,研究了3相移及简单DFB激光器的纵向光子浓度分布,纵模及调制响应特性.结果表明,3相移DFB具有与简单的DFB激光器同样好的调制响应特性,相移的引入在一定程度上抑制了纵向空间烧孔效应,并且有利于DFB激光器的单模输出.     

Dynamic properties of push-pull DFB semiconductor lasers

Using the spatially dependent multimode rate equations, we present a systematic study of small-signal dynamics of push-pull DFB lasers. The various spatial effects such as the longitudinal spatial hole burning, nonlinear gain compression, side-mode contribution, and push-pull modulation are all analyzed in a self-consistent manner. With the closed form expressions for the AM and FM responses, we show explicitly that the resonance frequency and the first cut-off frequency of push-pull DFB lasers are determined by the frequency spacing and the threshold gain difference between the lasing mode and its closest antisymmetric side mode, respectively. Numerical results reveal that a high modulation speed with a very low frequency chirp can be achieved with the push-pull DFB lasers     

Traveling wave analysis of semiconductor lasers: modulationresponses, mode stability and quantum mechanical treatment of noisespectra

We present a traveling wave analysis of a general class of semiconductor lasers, which includes multisection DFB/DBR lasers and gain-coupled DFB lasers. The analysis leads to new semianalytic expressions for the small-signal IM and FM modulation responses, the intensity and FM noise spectra, and the linewidth. The expressions are given in terms of solutions to four coupled linear homogeneous differential equations and can easily be evaluated numerically. We also derive a stability parameter σ, for which σ<0 indicates that the mode is unstable with respect to small-scale fluctuations. The noise spectra are derived from semiclassical calculations as well as from calculations based on quantized fields, and we discuss the limitations of the semiclassical approach. The formalism of the quantum mechanical treatment has a built-in relationship between the relative intensity noise and the noise of the injection current. This relationship is discussed and illustrated by numerical examples     

Transfer-matrix theory of the modulation and noise of multielementsemiconductor lasers

A general theory of the modulation response and noise of multielement semiconductor lasers is presented based on a transfer-matrix method combined with the Green's function method. An arbitrary laser structure is represented by an assemblage of stacked layers, each of which is assumed to have uniform carrier density and noise sources. A rate equation for the electric field envelope, with which analytical expressions for the small-signal modulation response and the intensity and FM noise are derived in terms of the transfer matrix elements, is derived. The theory can be applied to DFB (distributed feedback) and DBR (distributed Bragg reflector) lasers, coupled-cavity lasers, multielectrode lasers, vertical-cavity stacked-layer lasers, and Fabry-Perot lasers. One of the main advantages of this theory is that the longitudinal cavity effect is incorporated by a simple multiplication and summation of the transfer matrices corresponding to the individual laser segments     

Precise measurement of semiconductor laser chirp using effect ofpropagation in dispersive fiber and application to simulation oftransmission through fiber gratings

Measurements of small-signal intensity modulation from direct-modulated distributed feedback (DFB) semiconductor lasers after propagation in dispersive fiber have previously been used to extract intrinsic laser chirp parameters such as linewidth enhancement factor and crossover frequency. Here, we demonstrate that the simple rate equations do not satisfactorily account for the frequency response of real DFB lasers and describe some experimental techniques that conveniently determiner the precise laser chirp. Implications for simulation of high-speed lightwave systems are also considered     

Static, dynamic, and noise analysis of multisection DFB lasersusing frequency-domain transmission line model

A novel frequency-domain transmission line model for multisection distributed feedback (DFB) lasers is developed. The characteristic impedances of active periodic structures are derived. A multisection DFB laser is described as a transmission line network, with each section represented by a transmission lint segment with a corresponding characteristic impedance. Static, dynamic, and noise analysis of multisection DFB lasers is demonstrated. The reflections at the junctions between sections are evaluated more accurately. The resonant condition of the equivalent transmission line network, instead of cumbersome Wronskian, is used to reformulate the rate equations. The diffusion coefficient of Langevin noise terms of any two different positions is solved for the first time, resulting in a more accurate noise analysis of multisection semiconductor lasers. Analytical expressions of the dynamic responses and noise properties of multisection DFB semiconductor lasers are derived     

Modulation characteristics of tunable DFB/DBR lasers with one ortwo passive tuning sections

Calculation of the small-signal modulation characteristics of tunable distributed-feedback (DFB) and distributed Bragg reflector (DBR) lasers requires rate equations for the photon number, the phase of the electric field, and the carrier densities. Here, the rate equation for the photon number and phase is derived from an optical transmission-line model. Examples of the frequency- and intensity-modulation characteristics of a phase-tunable DFB laser are presented. The modulation responses exhibit the well-known relaxation resonance if either of the drive currents is modulated, but the possibility of complete removal of the resonance peak together with a perfect cancellation of spurious intensity modulation is also demonstrated. The frequency-modulation response then assumes a simple low-pass character with a cutoff frequency determined by the carrier lifetime in the passive tuning section. The importance of choosing the proper bias conditions is emphasized     

Simulation of DFB semiconductor lasers incorporating thermaleffects

Static and dynamic thermal processes are incorporated into the modeling and simulation of DFB lasers. Analytical expressions for AM/FM responses considering both carrier and thermal effects are obtained. The self-consistency of this model is verified by comparing with experiment. Thermal effects on the laser performance such as L-I characteristics, lasing wavelength chirp, small signal AM/FM and large signal modulation responses are examined. It is noted that there is a trade-off between static and dynamic thermal wavelength chirps     

Chirp reduction of directly modulated semiconductor lasers at 10Gb/s by strong CW light injection

The influence of strong light injection on the reduction of the dynamical linewidth broadening of directly current-modulated semiconductor lasers at high bit rates is theoretically investigated and experimentally verified for 10 Gb/s NRZ pseudorandom modulation with a large current swing of 40 mA pp. Significant chirp reduction and single-mode operation are observed for bulk DFB, quantum well DFB lasers at 10 Gb/s and a weakly coupled bulk DFB laser at 8 Gb/s, so that an improvement of the transmission performance using standard monomode fibers in the 1.55 μm low-loss wavelength region can be achieved for all these laser types, where dispersion otherwise causes severe penalties for long-haul transmission. The properties of injection-locked bulk DFB and quantum well DFB lasers with respect to high bit rate modulation have been systematically studied by the use of the rate equation formalism. A dynamically stable locking range of more than 30 GHz under modulation has been found for both laser types with injection ratios higher than 0.5     

Basic analysis of AR-coated, partly gain-coupled DFB lasers: thestanding wave effect

A theoretical analysis of distributed feedback (DFB) lasers with mixed gain and index coupling (partly gain-coupled DFB) is given for perfect antireflection (AR) coatings. Analytical expressions for the threshold gain, facet loss, and the relative depth of the standing wave pattern are derived. At the same time the importance of the standing wave effect and its consideration by coupled mode equations is shown. For purely gain-coupled DFB lasers, simple expressions for the effective linewidth enhancement factor and the longitudinal spontaneous emission factor are derived. In addition, various approximations describing the performance of purely gain-coupled DFB lasers are given     

Transfer-matrix dynamic model of partly gain-coupled 1.55 μm DFBlasers with a strained-layer MQW active grating

A dynamic model for partly gain-coupled 1.55 μm MQW DFB lasers consisting of etched strained-layer multiquantum wells is presented. For the modulation and noise characteristics of DFB lasers, analytical expressions which take into account both the longitudinal distribution of laser parameters and carrier transport effects are derived for the first time using the transfer-matrix method. As a numerical example, the relaxation oscillation frequency is compared to experimental results, and reasonable agreements are obtained between the theory and experiment     

FM response of InGaAsP buried heterostructure distributed feedbacklasers and their applications in incoherent FSK systems

Measurements are reported of the frequency modulation (FM) response of InGaAsP buried heterostructure distributed feedback (DFB) lasers and the system performance of a 1.7-Gb/s and 622-Mb/s incoherent frequency-shift-keyingn (FSK) system using these lasers. The measured lasers include 1.55-μm conventional DFB lasers and quarter-wave shifted DFB lasers. The thermal dips in the FM response of quarter-wave shifted DFB lasers usually occur at the lower frequencies, compared with that of conventional (250-μm-long) DFB lasers. A receiver sensitivity of -32.5 dBm (-39.5 dBm) for a 1.7-GB/s (622-Mb/s) incoherent frequency-shift-keying (FSK) system was achieved using a quarter-wave shifted DFB laser     

Performance comparison of gain-coupled and index-coupled DFBsemiconductor lasers

Comprehensive numerical simulations with the transmission-line laser model (TLLM) are used to compare the behavior of gain-coupled DFB lasers with index-coupled DFB lasers fabricated from identical materials. These simulations compare slope efficiency, threshold current, spectra, small-signal modulation bandwidth, maximum-intrinsic modulation bandwidth, large-signal transient response and chirp, relative-intensity-noise (RIN) spectra, and feedback sensitivity for coherence collapse. In most cases gain-coupled lasers with additional index coupling have better performance than index-coupled lasers for a given material. However, high-coupling factor index-coupled lasers do have lower threshold currents, lower RIN levels, and lower sensitivity to external feedback than gain-coupled lasers, although spatial hole burning in these devices can be disadvantageous     

Feedback sensitivity and coherence collapse threshold of semiconductor DFB lasers with complex structures

A general method for evaluating the feedback sensitivity of semiconductor lasers is proposed based on Green's functions approach. The rate equations derived in this paper generalize works already published to any type of laser cavities such as those with axially varying parameters. The variation of the lasing frequency occurring under external optical feedback is then used to predict the coherence collapse threshold. The approach is validated for conventional DFB lasers by comparing the calculated feedback sensitivity with those obtained from analytical expressions. Both feedback sensitivity and coherence collapse thresholds are then calculated and analyzed for DFB lasers with a chirped grating. A remarkable agreement on the critical feedback level between simulations and measurements is obtained for all the lasers under study.     

Empirical formulas for design and optimization of 1.5 μmInGaAs/InGaAsP strained-quantum-well lasers

The effects of strain and number of quantum wells on optical gain, differential gain, and nonlinear gain coefficient in 1.55-μm InGaAs/InGaAsP strained-quantum-well lasers are theoretically investigated. Well-approximated empirical expressions are proposed to model these effects. Using these formulas, one can easily and accurately predict the performance of a laser diode for a given structure. Therefore, these empirical formulas are useful tools for design and optimization of strained quantum well lasers. As a general design guideline revealed from the empirical formulas, the threshold current is reduced with the compressive strain, and the modulation bandwidth is most efficiently increased with the number of wells     

Effective linewidth enhancement factor and spontaneous emissionrate of DFB lasers with gain coupling

A field rate equation governing the noise and dynamic properties of a DFB (distributed feedback) laser with gain coupling is presented. Analytic expressions for the effective linewidth enhancement factor and spontaneous emission rate are derived. It is shown numerically that the linewidth contribution from spontaneous emission can be substantially reduced in DFB lasers with gain coupling     

Stability and dynamic properties of multi-electrode laser diodesusing a Green's function approach

In DFB (distributed feedback) lasers, the shape of the longitudinal intensity and carrier density distributions changes above threshold as a result of spatial hole burning. The longitudinally distributed coupling of spontaneous emission into the lasing mode also plays an important role for the noise properties. The authors demonstrate how both effects can be included in a dynamic analysis. They extend their previously developed theory for multielectrode lasers to enable calculation of stability properties as well as small-signal modulation responses and noise spectra. The theory is used to study global and local stability of the stationary solutions (modes). The numerical results for several laser structures are presented. It is shown that symmetric DFB lasers are likely to exhibit pitchfork bifurcations in their static tuning characteristics as the current is increased. The authors discuss how the presence or proximity of such instabilities can affect the modulation and noise properties, and in particular, the spectral linewidth     

Extraction of gain parameters for truncated-well gain-coupled DFBlasers

An amplified spontaneous emission transfer matrix model for prediction of the subthreshold spectral output of distributed-feedback (DFB) lasers was developed and fitted to the spectra of truncated-well gain-coupled DFB lasers using a least-squares-fitting algorithm. Modal gains for the high- and low-gain segments of the truncated-well DFB lasers were extracted, and their evolution as a function of injection current was examined. Results explain the tendency for the truncated-well gain coupled DFB lasers to have higher yields of single-frequency lasers and larger sidemode suppression ratios than are expected from simple considerations     

1064-nm DFB laser diode modules applicable to seeder for pulse-on-demand fiber laser systems

Semiconductor DFB (Distributed feedback) laser diodes with an operating wavelength of 1064 nm, which is suitable for pulse-on-demand fiber laser, have been developed. The stable performance of CW and nanosecond/picosecond pulsed operation is reviewed. By applying gain-switching operation with a simple direct modulation technique, 50-ps pulse generation with a stable spectral single-mode property was obtained. For the efficient amplification of the obtained 50-ps pulse, a monolithic semiconductor optical amplifier (SOA) was integrated into the DFB lasers. An improved peak power of 300 mW at 50-ps pulse was observed with limited optical noise injection when the synchronous modulation technique of the DFB and the SOA was employed. Short cavity lasers showed a high-frequency response compared to the original DFB lasers and achieved a short pulse width of 13 ps by standard gain-switched operation.