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     

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     

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     

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     

Linewidth enhancement for DFB lasers due to longitudinal field dependence in the laser cavity

To calculate the linewidth for an index-guided semiconductor laser, one usually neglects a correction factor for the spontaneous emission rate, which is introduced by the longitudinal field distribution within the laser cavity. For FabryPerot lasers with cleaved facets the correction factor is small. However, for DFB lasers this correction factor may become quite significant, yielding a linewidth enhancement for DFB laser diodes.     

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     

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     

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.     

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     

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     

Large-signal dynamic model of the DFB laser

A computer model is proposed to analyze the characteristics of distributed feedback (DFB) lasers. The model is based on time-dependent coupled wave equations, with spontaneous emission taken into account. In order to avoid uncertain phase factors in spontaneous emission, a method of converting field equations to power equations in a matrix format before computation is introduced. The steady-state LI curve and transient response to the pulse excitation are calculated in the λ/4 phase-shifted DFB lasers. The longitudinal variations of the carrier and photon densities as well as of the refractive index are considered in the model     

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     

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 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     

The symmetry of the amplified spontaneous emission spectrum incomplex-coupled DFB lasers

We present relations between facet reflections and coupling coefficient for the amplified spontaneous emission (ASE) spectrum of a complex-coupled, an index-coupled, and a gain-coupled distributed feedback (DFB) laser to have a mirror image with respect to the Bragg wavelength. We show that the ASE spectrum of a complex-coupled DFB laser cannot be symmetric in general with respect to the Bragg wavelength. The index-coupled and gain-coupled DFB lasers can have symmetric ASE spectrum for some values of the phase of the facet reflection coefficient that are determined     

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.<>     

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     

Nondegenerate four-wave mixing efficiencies in DFB laser wavelengthconverters

The salient parameters affecting nondegenerate four-wave-mixing (FWM) conversion efficiency in distributed-feedback (DFB) laser wavelength converters are examined analytically. Both the maximum attainable, and typical gain saturated, FWM efficiencies are derived. Typical DFB lasers cannot achieve maximum conversion efficiency due to gain saturation, while laser-amplifier combinations potentially can. The ratio of efficiency to spontaneous emission noise is also addressed, where it is found that this ratio increases quadratically with net unsaturated gain     

Nonlinear dynamics in directly modulated multiple-quantum-welllaser diodes

A theoretical and experimental analysis of the nonlinear dynamics of Fabry-Perot (FP) and distributed feedback (DFB) multiple-quantum-well (MQW) laser diodes is presented. The analysis is performed under single-tone and two-tone direct modulation. In the FP laser, we observe period doubling and in the DFB laser both period doubling and period tripling are identified. Period doubling is found over a wide range of modulation frequencies in both lasers. The reason for this wide modulation frequency range is attributed to the large relaxation frequencies found in MQW laser diodes. The spontaneous emission factor is measured for both FP and DFB lasers. The dependencies of period doubling on output power and RF input power level are also analyzed. The nonlinear dynamics of the laser are found to be enhanced when modulated under two-tone modulation. Numerical simulations carried out show good agreement with the measured results     

Mechanism for high singlemode stability of gain-coupled DFB laserswith periodically etched quantum wells

The sidemode suppression ratio of gain-coupled DFB lasers with periodically etched quantum wells is analysed by a more accurate model for amplified spontaneous emission. It is shown that the periodic etching of quantum wells is very effective for providing a high side-mode suppression. The mechanism for the high singlemode stability is explained by the effective modal gain. which has an enhancement at the longer wavelength side of the Bragg stopband