Analysis of the carrier-induced FM response of DFB lasers:theoretical and experimental case studies

A comprehensive analysis of the carrier-induced FM response of DFB lasers is given. Experimentally it is found that the FM response can sometimes vary strongly from chip to chip. In a number of cases anomalies either as a function of frequency or as a function of bias are observed. Theoretically, a dynamic model which includes spectral as well as longitudinal spatial hole burning is presented. The main feature of the model is that local variations of the Bragg wavelength caused by hole burning are rigorously and self-consistently taken into account. By comparing the experimental results with theoretical calculations, it is shown that in DFB lasers, spatial hole burning is an important phenomenon. The model confirms that the dynamic (FM) behavior can vary from DFB chip to DFB chip. The model shows that spatial hole burning is indeed the dominant factor which induces the anomalies that are found experimentally in the FM response     

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.     

Design of index-coupled DEB lasers with reduced longitudinalspatial hole burning

Methods for reducing or eliminating longitudinal spatial hole burning in antireflection-coated, index-coupled distributed feedback (DFB) lasers are discussed. It is shown that elimination of spatial hole burning in DFB lasers can be achieved by the introduction of well-chosen variations of coupling strength and/or internal absorption in the longitudinal direction. It is shown that a theoretical laser structure with uniform power can always be obtained by choosing two arbitrary functions. The authors describe some of the more basic solutions with uniform power. Practical approximations of these structures, their numerical modeling, and some methods to fabricate them are presented     

Analysis of external optical feedback on distributed-feedbacksemiconductor lasers above threshold

An analysis of external optical feedback based on distributed-feedback (DFB) semiconductor lasers above threshold is presented. It is based on a numerical model taking into account the longitudinal spatial hole burning (SHB) effect, which has been recently known to be an important phenomenon for DFB lasers above threshold. Numerical results for a typical index-coupled quarter-wave-shifted (QWS) DFB laser with a moderate coupling coefficient (κL=3) are given. It was found that the SHB effect can affect the sensitivity to feedback for DFB lasers above threshold     

Dynamics of index coupled DFB lasers with minimal spatial holeburning

Spatial hole burning in quarter-wave phase-shifted DFB lasers can be significantly reduced by spatially varying the coupling coefficient in the longitudinal direction. For such a laser, time dependent spatial hole burning is examined using a large signal dynamic model established earlier. The transient power changes, frequency chirp during gain switching and side mode suppression ratio at steady state are also simulated     

A transfer matrix method based large-signal dynamic model formultielectrode DFB lasers

A large-signal dynamic model capable of modeling the transient behavior of the output power and wavelength of multielectrode DFB lasers is described here. The key feature of the model is the use of a modified form of the transfer matrix method resulting in a time-dependent implementation of this technique. Other features are the inclusion of longitudinal spatial hole burning and nonlinear gain in the model. The versatility of the model is demonstrated in an analysis of the response of a two-electrode DFB laser under large-signal direct current modulation which illustrates the important role played by longitudinal spatial hole burning. The limited use of wavelength tunability in controlling chirp is also demonstrated. However, a scheme to improve the damping mechanism through nonuniform excitation called backbiasing is proposed. Finally, wavelength switching is demonstrated using the model     

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     

Stabilization of the longitudinal mode against spatial hole burningin λ/4-shifted DFB lasers by quantum size effect

A novel method for stabilizing the spectral properties of λ/4-shifted distributed-feedback (DFB) lasers against the longitudinal spatial hole burning by using the quantum size effect in MQW structures is proposed and demonstrated experimentally and theoretically. The effect of the longitudinal spatial hole burning on the spectral behavior is shown to be determined by the α parameter, not by the differential index or by the optical confinement in the active layer. The reduction of the α parameter is found to be very effective in suppressing the spectral instabilities induced by the longitudinal spatial hole burning     

Large-signal dynamic behavior of distributed-feedback lasersincluding lateral effects

The large-signal behavior of DFB lasers is analyzed, including lateral as well as longitudinal variations in carrier density, photon density, and refractive index. The effective index method and other approximations are used to reduce the complex three-dimensional problem to one dimension. The coupled wave and carrier rate equations are then solved in a self-consistent manner. Lateral spatial carrier hole burning and lateral diffusion are found to affect the relaxation oscillation frequency and damping rate of DFB lasers, depending on their detailed structure. The effective time-averaged linewidth enhancement factor is also affected. In symmetric AR-coated λ/4 phase-shifted lasers the side mode suppression ratio can be deteriorated significantly by lateral spatial hole burning when kL is large     

Linearity and third-order intermodulation distortion in DFBsemiconductor lasers

This paper presents a systematic investigation of the third-order intermodulation distortion characteristics in distributed feedback (DFB) semiconductor lasers. The influence of several nonlinearities, such as longitudinal spatial hole burning, gain compression, and relaxation oscillation, is considered. Detailed analysis shows that it is possible to make different nonlinearities cancel one another to give a low intermodulation distortion by choosing the appropriate DFB structure and beat conditions. Specifically, conditions for cancellation between spatial hole burning and gain compression nonlinearities are introduced     

Self-consistent analysis of side-mode suppression in gain-coupledDFB semiconductor lasers

Based on a set of spatially dependent multimode rate equations derived from Maxwell's equations, a self-consistent analysis of gain-coupled distributed feedback (DFB) lasers is developed. By introducing the modal net gain into the coupled wave equations, we also obtain a closed form formula of the side-mode suppression ratio (SMSR) for DFB lasers. It is shown that, associated with the distributed feedback, the longitudinal spatial hole burning, and the nonlinear gain compression effects, gain coupling produces significant effects on the SMSR of DFB lasers     

Gain-coupled DFB lasers versus index-coupled and phase shifted DFBlasers: a comparison based on spatial hole burning corrected yield

A statistical yield analysis is presented for gain- and index-coupled distributed feedback (DFB) laser structures, allowing a comparison of their single longitudinal mode (SLM) yield capabilities. For the yield calculations, the threshold gain difference and the longitudinal spatial hole burning (SHB) are taken into account. By comparing the experimental and theoretical yield of index-coupled DFB lasers, the significance of SHB for correct yield predictions is illustrated. For the purpose of comparison, yield calculations for various λ/4-shifted DFB lasers (with low facet reflectivities) are presented. The most emphasis, however, is on partly gain-coupled DFB lasers. Estimations of practical gain coupling coefficient values for gain and for loss gratings are discussed     

CLADISS-a longitudinal multimode model for the analysis of thestatic, dynamic, and stochastic behavior of diode lasers withdistributed feedback

A computer model called CLADISS is presented for the analysis of multisection diode lasers. The model allows for the analysis of a wide variety of multisection devices with discrete or distributed internal reflections. The simulator can carry out a threshold, DC, AC, and a noise analysis. The threshold analysis determines the threshold of the various longitudinal modes of the laser. The power versus current and the wavelength versus current characteristics are found with the self-consistent DC analysis. CLADISS includes all of the longitudinal variations by dividing each laser section in many short segments. Both the optical field and carrier density are discretized according to this segmentation. To demonstrate the capabilities of CLADISS some nonlinear effects in DFB lasers are treated. Instabilities induced in the side-mode suppression ratio by spatial hole burning are considered. The effects of spatial hole burning and side modes on the FM response on the linewidth are discussed     

External feedback sensitivity of partly gain-coupled DFBsemiconductor lasers

External optical feedback sensitivity of partly gain-coupled DFB semiconductor lasers has been analyzed in above threshold operation regime. Both the longitudinal spatial hole burning and the nonlinear gain compression have been taken into account. A comparison has been made among λ/4-shifted, pure index-coupled and partly gain-coupled DFB laser diodes. Even though pure index-coupled and partly gain coupled DFB lasers exhibit similar sensitivity to external optical feedback at the threshold, however, gain grating can reduce the feedback sensitivity when the lasers operate well above the threshold specially when the κL parameter is high     

Spatial hole burning effects in distributed feedback lasers

The effects of spatial hole burning in a steady-state distributed feedback (DFB) laser are examined by numerically solving the coupled mode equations that describe the system. An approximate solution for the gain above threshold is derived and compared to the exact solution. It is shown that the self-induced grating that arises due to spatial hole burning significantly reduces the mode discrimination of index-coupled DFB lasers. This makes it difficult for these lasers to maintain single-longitudinal-mode behavior above threshold. However, it is found in addition that bulk-modulated (gain-coupled) DFB lasers do not lose their mode selectivity above threshold, indicating that these lasers may be better choices for narrow-linewidth operation     

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     

Analysis of the second- and third-order intermodulation distortionin DFB lasers including dynamic spatial hole burning effect

Analysis of second and third order intermodulation distortion characteristics of semiconductor DFB lasers is, for the first time, performed, including dynamic longitudinal spatial hole burning (LSHB) effect. We have shown theoretically that the third order intermodulation distortion can be lower than the calculated curve without LSHB effect, which is confirmed with experiments     

A tractable large-signal dynamic model-application to stronglycoupled distributed feedback lasers

The modulation characteristics of DFB semiconductor lasers have been studied using a transfer matrix method combined with an appropriate rate equation analysis. The model takes into account longitudinal mode spatial hole burning, as well as the nonuniform current injection resulting from the axially varying Fermi voltage, and can be used for the efficient simulation of static, small-signal, and large-signal dynamic properties. The program is applied to the interpretation of experimental data from a strongly coupled InGaAsP/InP DFB laser. The experimental high-frequency properties of this device are well described by the simulations     

Longitudinal spatial instability in symmetric semiconductor lasersdue to spatial hole burning

A novel type of longitudinal instability due to spatial hole burning in symmetric semiconductor laser structures (DFB lasers in particular) is examined analytically and numerically. It is shown that, at a certain output power, the gain and refractive index spatial distributions of the lasing mode become unstable. Above this output power, the modal gains and oscillation frequencies change drastically, which often causes multimode operation. A measure of the cavity stability is introduced and derived analytically for a Fabry-Perot and a single phase-shifted DFB laser. Results from numerical simulations of a multiple phase-shifted DFB laser are presented     

Analysis of linewidth of separated-electrode DFB laser diode

Presents a new linewidth formula for DFB lasers, which includes the spatial hole burning effect. The linewidth of DFB lasers with three separated electrodes is calculated in various bias conditions. The optimum bias condition is discussed to obtain a narrow linewidth.<>