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     

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     

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.<>     

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.     

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.     

Spontaneous emission, scattering, and the spectral properties ofsemiconductor diode lasers

The effect of spontaneous emission on the above-threshold spectral output of 1.3-μm semiconductor diode lasers with internal scattering centers is examined. It is found that spontaneous emission masks the effect of scattering on the spectral properties of diode lasers. The spectral output of lasers with large amounts of spontaneous emission tend to be less affected by internal scattering than lasers with small amounts of spontaneous emission     

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.<>     

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     

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     

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     

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     

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     

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     

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     

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     

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     

Distributed feedback lasers in chiral media

The combined effects of chirality and gain (or loss) on wave propagation and coupling in periodic structures is investigated here. The focus is on distributed feedback (DFB) lasers in a transversely unbounded periodic slab with spatially modulated electromagnetic parameters. The analysis uses a coupled-mode approach employing a canonical physical model of chiral materials to predict the effects of modulated chirality admittance on DFB lasers. Results for DFB laser behavior in chiral media are compared and contrasted to that in achiral media. It is found that, under certain circumstances, the electric and magnetic field coupling, which is characteristic of chiral materials, results in a lower threshold gain for DFB lasers in media with a given index of refraction and characteristic impedance. It is also found that chiral index-coupled or gain-coupled DFB lasers exhibit the same spectral mode properties as achiral DFB lasers     

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 the spectral linewidth of distributed feedback laser diodes

The spectral linewidth of distributed feedback (DFB) laser diodes is theoretically studied. Numerical calculation shows that DFB lasers with long cavity lengths and large coupling coefficients have very narrow spectral linewidth less than 1 MHz, The effects of the phase shift and mirror facets on the spectral characteristics of DFB lasers are also analyzed, It is shown that the phase-shifter further narrows the spectral linewidth of DFB lasers. Its numerical result and physical meaning are also shown.     

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.