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     

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.<>     

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     

A tool to calculate the linewidth of complicated semiconductor lasers

A theory of the low-frequency phase fluctuations in the output of a semiconductor laser due to spontaneous emission is developed. The theory can be used as a tool to numerically calculate the linewidth of complicated laser structures, e.g., by use of the transfer matrix formulation. The results for the single Fabry-Perot laser are shown to be in exact agreement with the most accurate treatments published so far. Results are then presented for both DFB and F-P lasers with external optical feedback showing how the linewidth varies with the threshold gain, with the coupling coefficient, and with the external feedback conditions.     

Parameter extraction from DFB lasers by means of a simpleexpression for the spontaneous emission spectrum

A simple expression for the amplified spontaneous emission from a laser biased below lasing threshold is applied to semiconductor laser parameter extraction. We demonstrate that accurate measurement of the coupling coefficient for distributed feedback (DFB) lasers with phaseshifts and end reflections is a practical possibility. It is also shown that the used expression, for a reciprocal device, can be derived directly from the wave equation using the Green's function     

Thermal annealing effect on organic semiconducting polymer laser with an external holographic grating feedback layer

Thermal annealing effect on an organic distributed feedback (DFB) laser excited from a semiconducting polymer gain layer, poly(2-methoxy-5-(2’-ethyl-hexyloxy)-p-phenyl-envinylene) (MEH-PPV), is reported. The morphology, absorption and photoluminescence (PL) spectral characteristics of the MEH-PPV film annealed at different temperatures were analyzed. The amplified spontaneous emission (ASE), the optical gain and loss coefficients were also investigated. The organic lasing behaviors including threshold, energy conversion efficiency and polarization state in a DFB laser device were studied. The results show that the optical properties of the organic semiconducting laser can be enhanced by thermal annealing effect. The single mode laser emission at 622.4 nm with lower lasing threshold 0.2 μJ/pulse and higher energy conversion efficiency 6.71% was achieved with thermal annealing at 120 °C. The thermal annealing treatment decreases laser threshold and increases laser energy conversion efficiency dramatically, which shows the potential in ultra-low cost organic semiconducting polymer DFB lasers.     

Theory and experiment on the amplified spontaneous emission fromdistributed-feedback lasers

The amplified spontaneous emission (ASE) of a strained quantum-well distributed feedback (DFB) laser biased below laser threshold is used to extract the gain and refractive index spectra in a systematic manner. A modified Hakki-Paoli method is used to obtain the gain and differential gain spectra. The refractive index change due to carrier injection is obtained from the shift of the Fabry-Perot peaks in the ASE spectrum. The measured ASE spectrum, gain, refractive index change, and linewidth enhancement factor are then compared with our theoretical model for strained quantum-well lasers. Our model takes into account the realistic band structure and uses the material and quantum-well dimensions directly in the calculation of the electronic and optical properties. The theory agrees very well with the experiment     

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     

Analysis of surface-emitting λ/4-shifted DFB lasers with adistributed Bragg reflector

Threshold current density and differential quantum efficiency are analyzed for a surface emitting (SE) λ/4-shifted distributed feedback (DFB) laser consisting of alternating active and passive layers with a distributed Bragg reflector (DBR). It is shown that the threshold current density can be reduced by using the DFB action induced by alternating active and passive layers in the active region of the SE DFB laser structure, as compared to SE DBR lasers with a homogeneous active region. It is also shown that the differential quantum efficiency of the DFB laser with a DBR can be higher than that of conventional DBR lasers without increasing the threshold current density     

Study of wavelength shift in InGaAs/InAlGaAs QW DFB lasers based onlaser parameters from a comparison of experiment and theory

Experimental data of InGaAs/InAlGaAs quantum well distributed feedback (DFB) lasers such as spectra, under continuous and pulsed biasing, relative intensity noise and linewidth, are compared with the results of model calculations based on a transfer matrix method. Using experimental data of different lasers, a set of physical DFB laser parameters was determined. We succeeded in describing all the experimental data of different lasers by the same set. The determined parameter set was further applied to study the influence of facet properties on the wavelength shift of DFB lasers. We found a very strong dependence of the wavelength tunability on the end facet phases. The wavelength shift varies by a factor up to three between different end facet phases and coatings. This is crucial for the yield of, for example, tunable multisection DFB lasers with an envisaged large tuning range     

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.     

Transfer-matrix analysis of the intensity and phase noise ofmultisection DFB semiconductor lasers

A general small-signal model for the intensity and phase noise spectra of multisection distributed feedback (DFB) semiconductor lasers is developed by using the transfer-matrix approach based on the Green's function method. The spontaneous emission enhancements due to nonuniform longitudinal field distribution and the effective amplitude-phase coupling effect (the effective linewidth enhancement factor) are taken into account in the formulation. Analytical expressions for the spectra of the relative intensity noise and the FM noise of the main mode in the multimode operation are presented by using the transfer functions in a flow-graph representation. Facet reflectivities and external optical feedback are included in the model. The effects of the grating coupling coefficient, the random grating-phase at the facets, the phase-shift position, the external optical feedback, and the side mode on the noise spectra are analyzed systematically for a λ/4-shifted DFB laser     

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     

The design assessment of λ/4 phase-shifted DFB laserstructures

A detailed nonlinear model of the performance of single-frequency laser structures operating both below and above threshold is discussed. Arbitrary series combinations of uniform pitch grating, linearly-chirped pitch grating and plane guide sections can be analyzed-taking longitudinal-mode spatial hole burning into account. The material properties of each section of a device structure can be specified. The output power from each end of the laser and the emission wavelength, and the longitudinal intensity, carrier density, and relative permittivity profiles are predicted as a function of drive current above threshold for each lasing mode. The linewidth is also estimated while allowing for the nonuniform longitudinal distribution of spontaneous emission into the mode in a physical manner. The model was used to provide the data with which to trade off the numerous interacting performance parameters of a λ/4 phase-shifted DFB (distributed-feedback) laser. The design options are then summarized     

Low-threshold 1.5 mu m DFB laser grown by GSMBE

GaInAsP 1.5 mu m DFB lasers with a low threshold current (17 mA) have been grown by gas source molecular beam epitaxy (GSMBE) in a two-step epitaxial process. The lasers exhibit single-mode emission for emitted power in excess of 10 mW with side mode suppression ratio of 40 dB and spectral linewidth of 15 MHz. In addition the dispersion of the lasing wavelength has been found to be as low as 1.7 nm.<>     

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.<>     

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     

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     

Linewidth enhancement factor of 1.3 mu m InGaAsP/InP strained-layer multiple-quantum-well DFB lasers

The linewidth enhancement factor alpha in a 1.3 mu m InGaAsP/InP strained-layer multiple-quantum-well (SL-MQW) distributed feedback (DFB) laser has been evaluated from the relation between the frequency and intensity modulation indexes, and the spontaneous emission spectra below threshold current. It is demonstrated that the measured alpha -parameter of a 1.3 mu m SL-MQW DFB laser is about two, and is much smaller than that in a conventional bulk DFB laser. From the resonance frequency dependence on the output power, it is concluded that this reduction of the alpha -parameter originates in the increased differential gain. The reduction of wavelength chirping, as a result the low alpha -parameter, was experimentally confirmed for the SL-MQW DFB laser.<>