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     

Design and optimization of strained-layer-multiquantum-well lasersfor high-speed analog communications

We report on how the contributions from spatial hole burning, gain suppression, and relaxation oscillations to the chirp and harmonic distortion of SL-MQW DFB lasers can be calculated and minimized. It is shown how, by taking into account the specific properties of strained-layer-multiquantum-well (SL-MQW) lasers, simple solutions of the rate equations point the way to a chirp reduction and an increase of the useful bandwidth for analog communications. In such lasers, the absorption is only weakly dependent on the carrier density and therefore the harmonic distortion at lower modulation frequencies is mainly caused by spatial hole burning. Our numerical simulations indicate that in many cases this distortion is seduced by the same measures that reduce the chirp and increase the bandwidth     

High-power single-mode operation in DFB and FP lasers usingdiffused quantum-well structure

Distributed feedback (DFB) and Fabry-Perot (FP) semiconductor lasers with step and periodic interdiffusion quantum-well structures are proposed for high-power single-longitudinal-mode operation. It is shown that the phase-adjustment region formed by the diffusion step (i.e., step change in optical gain and refractive index) counteracts the influence of spatial hole burning, especially for DFB lasers with large coupling-length products biased at high injection current. Furthermore, it is found that with careful design of the diffusion grating (i.e., grating period and amount of diffusion extent) of FP lasers, side-mode suppression ratio can be enhanced and threshold current density can be minimized to a satisfied level     

Improved performance of AR-coated DFB lasers for the introductionof gain coupling

Antireflection (AR)-coated distributed-feedback (DFB) lasers with both gain- and index-coupled distributed feedback are studied numerically with respect to mode losses, mode suppression, and spatial hole burning. The mode losses and the spatial hole burning decrease with increasing gain coupling, while the mode suppression increases. It is shown that a large improvement in performance can already be obtained for small fractions of gain coupling     

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     

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     

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     

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     

Semiclassical model of semiconductor laser noise and amplitudenoise squeezing. II. Application to complex laser structures

For pt.I see ibid., vol.33, no.11, p.2097-2104 (1997). We present noise studies of distributed feedback (DFB) laser structures, where spatial hole burning (SHB) plays a key role performed using the model described in part I of this paper with particular emphasis on the influence of SHB, on the coupling coefficient κL, and on the laser facet reflectivities. These structures exhibit high amplitude noise and the possible noise reduction is strongly reduced compared to Fabry-Perot structures. Distributed Bragg reflector (DBR) lasers are better candidates even if their performances are also strictly determined by SHB and the loss in the Bragg reflector. Finally, limitations due to gain suppression are demonstrated for such complex lasers structures. We conclude on the optimum laser structure for amplitude squeezed states generation     

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     

Dynamic and noise properties of tunable multielectrodesemiconductor lasers including spatial hole burning and nonlinear gain

A general formalism based on the Green's function method is given for multielectrode semiconductor lasers. The effects of both spatial hole burning and nonlinear gain are included in this formalism. An effective nonlinear gain is introduced by taking into account the influence of the laser structure and the associated distribution of the mode intensity along the cavity length and the frequency and intensity modulation properties of multielectrode semiconductor lasers are studied. A general linewidth expression which includes contributions from spontaneous emission and carrier shot noise is given. It is found that the effective α-factor affecting the linewidth is in general different from its counterpart affecting modulation and injection locking properties due to spatial hole burning and nonlinear gain. The linewidth due to various contributions is calculated for both uniform intensity distributed lasers and phase-shifted distributed feedback (DFB) lasers     

Influence of the carrier density dependence of the absorption onthe harmonic distortion in semiconductor lasers

It is shown that the carrier density dependence of the absorption can result in a significant increase of the harmonic distortion caused by gain suppression or by spatial hole burning in distributed-feedback (DFB)-lasers. This carrier density dependence of the absorption is often neglected in theoretical studies, but the author found that it may result in a dominant contribution to the second-order distortion in the AM response, especially at high output powers. The distortion then mainly depends on material parameters such as differential gain, differential absorption and the gain suppression method     

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     

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     

Second- and third-order harmonic distortion in DFB lasers

The second- and third-order harmonic distortion in distributed feedback (DFB) lasers is simulated using a time domain large signal dynamic model. The effects of the longitudinal spatial hole burning, nonlinear gain, spontaneous emission, and current leakage are included in the model. Composite second-order (CSO) and composite triple beat (CTB) are calculated for an 80 channel 60-540 MHz system with 3% modulation depth in each channel. The simulation results are compared with the experimental harmonic distortion measurements     

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     

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     

Analytical formulation of distortion and chirp in CATV DFB lasersincluding spatial hole burning

Analytical formulas for distortions permitting the calculation of composite second order (CSO) and composite triple beat (CTB) in distributed feedback (DFB) laser diodes are given, including gain compression and longitudinal spatial hole burning (LSHB). An improved chirp expression including both effects is also proposed. Gain compression is compared to LSHB over the CATV band: LSHB effects on distortion and chirp are found to be dominant in actual CATV lasers. Nonmonotonous behavior (dips) function of frequency and bias current is verified in second- and third-order distortions in agreement with recent results     

An accurate rate-equation description for DFB lasers and someinteresting solutions

Starting from the coupled-wave equations, we have derived an alternative set of rate equations which are valid for most single-section distributed feedback (DFB) lasers. These rate equations are in many respects more useful than the conventional rate equations and have also been used to derive the influence of spatial hole burning on characteristics such as the chirp, the linewidth, or the harmonic distortion. Numerical results are presented for a DFB laser with both facets cleaved, AR-coated, and for a λ/4-shifted DFB laser     

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