Dynamic analysis of radiation and side-mode suppression in asecond-order DFB laser using time-domain large-signal traveling wavemodel

In this paper, we have developed a relatively simple algorithm to calculate the large-signal dynamic response of DFB lasers by solving the time-dependent coupled wave equations directly in the time domain. The spontaneous emission noise, longitudinal variations of carrier (hole burning) and photon densities as well as that of the refractive index are taken into consideration. To demonstrate the power of this straightforward algorithm, the model shows how the side-mode suppression ratio in devices with high κL and a λ/4: phase shift is significantly affected by the radiation in the second-order DFB laser. The time-dependent radiation pattern in grating-coupled surface-emitting lasers is also calculated for the first time     

Spontaneous emission model of surface-emitting DFB semiconductorlasers

A general spontaneous emission model is developed for surface-emitting (SE) distributed feedback (DFB) semiconductor lasers. The frequency distribution of spontaneous emission noise below lasing threshold and the spontaneous emission rate in lasing operation are formulated by using a transfer matrix method combined with the Green's function method. The effective linewidth enhancement factor is obtained from this model in terms of the elements of the transfer matrix. By way of example, the author applies the formulation to a standard SE DFB laser, and a SE λ/4-shifted DFB laser with a distributed Bragg reflector (DBR) mirror. In particular, the author analyzes the below-threshold spectrum, the threshold current density, the differential quantum efficiency, and the spectral linewidth of these lasers     

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     

Transfer-matrix formulation of spontaneous emission noise of DFBsemiconductor lasers

A unified formulation of the spontaneous emission noise in semiconductor DFB (distributed feedback) lasers is presented by using a transfer-matrix approach. Analytical expressions for the noise power per unit frequency bandwidth below threshold and the spontaneous emission rate into the lasing mode are obtained based on the Green's function method. Three DFB laser structures are analyzed: (1) a standard DFB structure with facet reflectivities, (2) a multisection DFB structure composed of n sections which models a phase-shifted DFB laser and a multielectrode (tunable) DFB laser, and (3) a periodic layered DFB structure which models a surface-emitting DFB laser. It is shown that the spontaneous emission noise of a complicated DFB laser structure can be calculated easily by the transfer matrix of each section of the structure and its derivative to frequency     

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     

Amplified spontaneous emission model for quantum-well distributedfeedback lasers

An amplified spontaneous emission model for quantum-well (QW) distributed feedback (DFB) lasers is presented, which takes into account local spontaneous emission, stimulated emission, and real refractive index change which are calculated from the Fermi-Dirac occupancy functions in a self-consistent manner. The local-normal-mode transfer-matrix method is used, which allows a coupling of the local DFB effect with the local QW spontaneous emission and gain. As an example, an analysis is given of a partly gain-coupled DFB laser with periodically etched QWs, which has a large discontinuity of spontaneous emission and gain in high- and low-corrugation regions. It is shown that the side-mode suppression improves with the increase of the number of etched QW's, due to the carrier-density-dependent gain-coupling     

Analysis of the phase-amplitude coupling factor and spectrallinewidth of distributed feedback and composite-cavity semiconductorlasers

A Green's function approach to the analysis of semiconductor lasers is formulated in a form suitable for complex cavity structures. Both the spontaneous emission rate and the effective phase-amplitude coupling factor can be accurately evaluated. For distributed-feedback (DFB) lasers, the spontaneous emission rate is strongly dependent on both the facet reflectivities and the grating coupling coefficients. The effective phase-amplitude coupling factor depends on the wavelength detuning from the gain maximum. The calculated linewidth of DFB lasers differs considerably from previous calculated results and gives better agreement with experimental results. For composite-cavity lasers, the frequency dependence of the equivalent reflectivity has a strong impact on the phase-amplitude coupling factor and the spontaneous emission rate. Distributed Bragg reflector (DBR) lasers are investigated as an example of a composite-cavity structure     

Analysis of the spontaneous emission rate of multiple-phase-shift distributed feedback semiconductor lasers

A general expression for the spontaneous emission rate of multiple-phase-shift DFB semiconductor lasers is given using the transfer matrix based on the Green's function method. The spontaneous emission rate for coupled phase-shift DFB lasers is calculated.<>     

A new large-signal dynamic model for multielectrode DFB lasersbased on the transfer matrix method

A large-signal dynamic model capable of modeling the transient behavior of the output power and wavelength of multielectrode DFB lasers is described. The key feature of the model is the use of a modified form of the transfer matrix method. Other features are the inclusion of spontaneous emission, longitudinal spatial hole burning, and nonlinear gain in the model. Results from the model demonstrate the important role played by longitudinal spatial hole burning in the chirping of DFB lasers and the limited use of tunability in controlling chirp     

A probability-amplitude transfer matrix model fordistributed-feedback laser structures

Two different treatments of spontaneous emission in distributed-feedback (DFB) lasers were found in the literature, but adequate explanations for the different treatments were not found. Using an approach that allows comparison of the two different treatments of spontaneous emission, we show that the different treatments can lead to different spectral predictions. The difference in spectral predictions is negligible in Fabry-Perot lasers and index-coupled DFB lasers. However, in truncated-well gain-coupled DFB lasers, the difference between the two treatments is noticeable, and one treatment is markedly better at fitting to data. The treatment that best fits the data is also the treatment that makes sense quantum-mechanically     

Side-mode suppression mechanism of gain-coupled DFB lasers with periodically etched quantum wells

The effect of the gain and index coupling on the side-mode suppression ratio (SMSR) is studied for gain-coupled DFB lasers with periodically etched quantum wells. An accurate expression for the SMSR based on the amplified spontaneous emission model is used with the local-normal-mode transfer-matrix method. The mechanism for the strong single-mode stability of the gain-coupled DFB lasers is explained by the difference between the effective gain and loss of the Bloch waves in the grating structures. This new view clearly shows the advantage of the gain-coupled DFB lasers in terms of single-mode stability.     

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     

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     

Above-threshold analysis of second-order circular-grating DFBlasers

The behavior of second-order circular-grating DFB lasers in the above-threshold regime are analyzed. The formulation uses the standing wave method for treating lasers with second-order gratings. The effects of spontaneous emission and the variation of carrier and photon densities in the radial direction are included in a self-consistent fashion in the model. In particular, we examine the output power emitted from the surface of the laser, the near-field, and the far-field pattern of the laser as a function of the injected current     

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.     

Global excess spontaneous emission factor of semiconductor laserswith axially varying characteristics

An expression of the excess spontaneous emission factor of semiconductor lasers having axially varying characteristics has been derived, using a classical treatment for the contribution of spontaneous emission to the laser's noise figure. Although the analysis is focused on semiconductor laser structures, including DFB lasers, the expression obtained can be applied with minor changes to other standing-wave laser geometries. This global excess spontaneous emission factor, accounting for transverse as well as longitudinal effects, is relevant even for laser structures wherein the longitudinal and lateral field distributions are mutually coupled. In this situation, this factor is not equivalent to the product of Petermann's excess noise factor and a longitudinal correction factor accounting for outcoupling losses     

Microscopic evaluation of spontaneous emission- and Auger-processes in semiconductor lasers

A fully microscopic approach is used to compute the losses in semiconductor lasers due to spontaneous emission and Auger recombination. The model is based on the semiconductor-Bloch equations and generalized quantum-Boltzmann type scattering equations in the second Born-Markov approximation. As input the theory only needs the structural layout and fundamental bulk-bandstructure parameters. It is demonstrated that such a comprehensive model that calculates gain/absorption, spontaneous emission and Auger processes on the same microscopic level can reliably predict these usually dominant loss processes. Examples of the results are compared to measurements on lasers in the 1.3-1.5 /spl mu/m range demonstrating very good agreement without empirical fitting.     

Analysis of below-threshold spectrum and linewidth of surface-emitting lambda /4-shifted DFB lasers with DBR mirror

The frequency distribution of spontaneous emission noise below lasing threshold and the spectral linewidth in lasing operation are analysed for surface-emitting lambda /4-shifted distributed feedback (DFB) lasers consisting of alternating active and passive layers with a distributed Bragg reflector (DBR) mirror.<>     

Above-Threshold Spectrum of the Radiation Field in Surface-Emitting DFB Lasers

This paper addresses the above-threshold analysis of the amplified spontaneous emission spectrum of the radiation field in surface-emitting distributed feedback (DFB) lasers with a second-order grating. To the best of the authors' knowledge, this paper is the first report in this regard. The analysis takes advantage of the time- and frequency-domain approaches. The essence of this method is obtaining the spectrum of the laser power using the fields in the frequency domain, whereas the above-threshold carrier distribution inside the cavity is obtained by the finite-difference time-domain approach. The use of this approach can be justified by the fact that the wave equations in the time and frequency domains are related by the Fourier transform. Applying this method to the surface-emitting DFB lasers with a second-order grating, the authors will demonstrate that excitation of the radiation field by the interference between the counter-propagating waves inside the cavity provides additional filtering mechanism, which makes the side-mode suppression ratio of the power emitted from the surface different than that from the edge. More importantly, it is shown that the interesting features of a properly designed quarter-wave phase-shifted surface-emitting DFB lasers with a second-order grating can be exploited in the design of transmitters for optical communications     

Intensity noise characteristics of erbium-doped distributed-feedback fiber lasers

We present an experimental and theoretical investigation into the low-frequency intensity noise characteristics of erbium-doped distributed feedback (DFB) fiber lasers. The intensity noise characteristics of six nonidentical erbium-doped DFB fiber lasers are presented along with the characteristics of the grating and doped fibers. An analytical model has been used to predict the intensity noise generated in a linear fiber laser and explain the observed noise characteristics. Overall we find good agreement between our analytical model and observations. In particular, we find the intensity noise at frequencies close to the relaxation oscillation frequency significantly elevated due to excess noise from either spontaneous emission or cavity loss modulation. These results can be used to optimize the fiber laser design for sensor applications.