Effective nonlinear gain in semiconductor lasers

An effective nonlinear gain is introduced for semiconductor lasers by taking into account the effect of laser structure and the associated distribution of the mode intensity along the cavity length. It should be used in the analysis of laser dynamics and noise in place of the material nonlinear gain parameter. A general expression for the effective nonlinear gain is given by using the Green's function method. The results obtained for Fabry-Perot and distributed feedback lasers show that the effective nonlinear gain could be considerably enhanced. The exact value of the enhancement factor depends on cavity parameters. Affected by the laser structure, the nonlinear gain has a different power dependence than expected from material considerations alone     

Polarization-dependent gain saturations in quantum-well lasers

Theoretical analyses of polarization-dependent optical gain saturation are given for semiconductor quantum-well (QW) lasers to investigate the conditions of polarization switching and bistable operations. Nonlinear susceptibilities, which give saturation coefficients, are obtained in the perturbative analyses of density matrices, where the relevant electronic states in the QW are calculated by diagonalizing Luttinger's Hamiltonian, thus including valence band mixing. The present formulation is applied to InGaAsP QW lasers with edge-emitting and vertical-cavity surface-emitting laser (VCSEL) structures, and the self- and cross-saturation coefficients with parallel and orthogonal optical polarizations are numerically calculated, which are compared with those of bulk lasers. For the edge-emitting case, the saturation coefficients are strongly dependent on the photon energies, and the bistable operation condition is not satisfied in the gain peak, different from a bulk laser which showed only a slight energy dependence. In a VCSEL, the saturation coefficients are also dependent on the photon energies but the bistable operation condition is always satisfied     

Effect of nonlinear gain on the bandwidth of semiconductor lasers

The effect of nonlinear gain on the frequency response of semiconductor lasers at high bias powers is analysed using the multimode rate equations. In spite of the strong damping of the relaxation oscillations due to nonlinear gain, bandwidths of over 40 GHz appear to be attainable in semiconductor lasers.     

Effect of nonlinear gain on single-frequency behaviour of semiconductor lasers

The effect of nonlinear gain on the single-frequency behaviour of semiconductor lasers is analysed using a two-mode rate-equation model. We find that the asymmetric nature of the nonlinear gain is responsible for bringing the sidemode above threshold when the power in the main mode exceeds a critical level. We obtain an analytic expression for the critical current density at which the sidemode reaches threshold and apply it to discuss the single-frequency range of distributed-feedback semiconductor lasers.     

Effects of nonlinear gain on single longitudinal mode behavior of semiconductor lasers

The effects of nonlinear gain on the single longitudinal mode are analyzed by means of multilongitudinal mode and multitransverse mode rate equations and compared with the linear gain calculations and experments. It is shown that further suppression of the third order nonlinear gain on nonlasing modes always serves to accelerate the process of the single longitudinal mode operation and that results obtained with long cavity length are entirely contrary to those where only linear gain is considered. The experiments also show that single longitudinal mode lasers with even larger output power can be realized with long cavity length; and, with further proper reduction of the stripe width, single mode (single frequency) operation can be realized. But the results obtained from both gain considerations indicate that single longitudinal mode operation will be facilitated if the active layer is not too thin and the end face reflectivity is increased.     

Effect of the nonlinear gain in semiconductor lasers on theperformance of multigigabit-per-second lightwave systems

The implications on performance of the functional form of the nonlinear gain in single-mode semiconductor lasers are studied for multigigabit-per-second, intensity-modulation, direct-detection lightwave systems. Compared to a previously used functional dependence on the photon and carrier densities, a new result due to G. Agrawal (1988) can, depending on the fiber dispersion and gain compression factor, yield quite different receiver sensitivities     

Comparison of the effects of nonlinear gain and weak opticalfeedback on the dynamics of semiconductor lasers

The influence of nonlinear gain and optical feedback on the dynamics of single-mode semiconductor lasers are numerically investigated based on the Lang and Kobayashi model. It is well known that the nonlinear gain tends to stabilize the dynamics, while the optical feedback tends to increase the instabilities. In this paper, we study the behavior of the attractors when the feedback level k and the gain saturation coefficient ε vary and show that the effects of these parameters are surprisingly opposite. For example, we find that the route to chaos that the external cavity modes follow for increasing k is reversed for increasing ε in an almost identical manner. When the feedback increases the modes follow the usual quasi-periodic route and turn into torus. If k continues to increase, the torus become chaotic attractors as the result of several period-doubling bifurcations or a third Hopf bifurcation. Further increase of k causes the chaotic attractors to lose stability, Contrarily, if the value of the parameter ε is increased, the attractors recover their stability and reverse the route becoming simple torus again. If ε is increased further, the torus reverse the quasi-periodic route and turn into stable modes again. We also find that on the contrary to k, the parameter ε enhances the stability region of an attractor. We show that the feedback level above which a limit cycle emerges from a stable mode, the feedback level above which a torus emerges from a limit cycle, and the feedback level above which a chaotic attractor loses stability are all increasing functions of ε     

Theoretical gain of strained-layer semiconductor lasers in thelarge strain regime

The theoretical gain of strained-layer semiconductor lasers is analyzed in the large strain regime based on the density-matrix method, taking into account the modification of both the valence bands and the transition dipole moments. The wave functions for the valence-band states for an arbitrary wave vector at the Γ point in the presence of stain are derived from diagonalization of the strain Hamiltonian using the original wave functions obtained from the k-p method. These wave functions are then used to obtain the dipole moment matrix elements at the band edges, which are found to be independent of the wave vector     

Nonlinear gain coefficients in semiconductor lasers: effects ofcarrier heating

Nonlinear gain coefficients due to the effects of carrier heating are derived from the rate equations of carrier energy transfer in semiconductor lasers. We find that, in the modulation responses of semiconductor lasers, stimulated recombination heating will affect the resonant frequency and damping rate in a same form as the effects of spectral hole burning, while free carrier absorption heating will only affect the damping rate. The effects of injection heating and nonstimulated recombination heating are also discussed. The carrier energy relaxation time is calculated from first principles by considering the interactions between carriers and polar optical phonons, deformation potential optical phonons, deformation potential acoustic phonons, piezoelectric acoustic phonons. At the same time, the hot phonon effects associated with the optical phonons are evaluated because their negligible group velocity and finite decay time. We show that the carrier-polar longitudinal optical phonon interaction is the major channel of carrier energy relaxation processes for both electron and holes. We also point out the importance of the longitudinal optical phonon lifetime in evaluating the carrier energy relaxation time. Neglecting the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time, this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficients due to carrier heating. The effects of spectral hole burning, stimulated recombination heating, and free carrier absorption heating on limiting the modulation bandwidth in semiconductor lasers are also discussed     

Nonlinear gain suppression in semiconductor lasers due to carrier heating

A simple model is presented for carrier heating in semiconductor lasers from which the temperature dynamics of the electron and hole distributions can be calculated. Analytical expressions for two new contributions to the nonlinear gain coefficient, in are derived, which reflect carrier heating due to stimulated emission and free carrier absorption. In typical cases, carrier heating and spectral holeburning are found to give comparable contributions to nonlinear gain suppression. The results are in good agreement with recent measurements on InGaAsP laser diodes.<>     

Linewidth enhancement factor and nonlinear gain in ZnSesemiconductor lasers

We have investigated the effects of the Coulomb interaction on the optical gain and the refractive index of ZnSe semiconductor lasers. The Coulomb interaction increases the differential gain, leading to a decrease of the threshold carrier density. Its influence on the linewidth enhancement factor and the nonlinear gain coefficient is relatively small because it increases both the gain and the refractive index simultaneously. We have compared the linewidth enhancement factor α and the nonlinear gain coefficient ϵ for ZnSe and GaAs lasers with the effects of the Coulomb interaction taken into account. For typical values of total cavity losses, the values of α and ϵ are higher for ZnSe lasers compared with GaAs lasers     

Effects of nonlinear gain on mode-hopping in semiconductor laserdiodes

A systematic and comprehensive analysis of longitudinal mode-hopping, due to nonlinear gain, and its influence on the design criteria of transverse-mode-controlled semiconductor laser diodes are presented. An existing nonlinear model, which was derived using a density matrix formalism, has been extended in this paper to generate the nonlinear gain coefficient matrix. Properties of the nonlinear gain coefficient matrix, which describes the interaction among cavity modes, are discussed. Using the new nonlinear gain in the steady-state multimode rate equations, conventional Fabry-Perot (FP) and short cavity Fabry-Perot (SFP) semiconductor laser diodes have been numerically simulated. Design issues such as cavity length, cavity volume, facet reflectivity, spontaneous emission factor, mode wavelength, intraband relaxation time, linewidth enhancement factor, and laser structure are also discussed. It is shown that increasing the injection current causes the lasing mode to jump to longer wavelengths. Furthermore, increasing the spontaneous emission factor reduces the dynamic range of laser operation without mode-hopping, and vice versa for short cavity. It has been also shown that the carrier density in the active region shifts to higher values (i.e., experiences a kink) at the onset of mode-hopping. Finally, the total modal gain (linear and nonlinear) competes as the injection current increases     

Asymmetric gain induced by longitudinal spatial carrier burning in semiconductor lasers

Nonlinear gain caused by dielectric corrugation resulting from the cavity standing wave of a lasing mode in semiconductor lasers is investigated using the perturbation approach. The results show that the nonlinear gain spectrum is asymmetric when the linewidth enhancement factor alpha not=0, and the possibility of single mode operation is greater at alpha =0.<>     

Theory of optical gain and threshold properties of semiconductor lasers

The theory of optical gain in highly doped semiconductors employed for semiconductor lasers is developed based on the Green function approach. With the help of the analytical expression obtained for optical gain, the threshold properties of semiconductor lasers and their dependence on concentration of doping impurities and on temperature are studied. Results of numerical calculations of threshold characteristics for the most interesting cases are presented.     

Dielectric grating induced by cavity standing wave as a newexplanation of origin of nonlinear gain in semiconductor diode lasers

The nonlinear gain due to induced index and gain grating caused by the cavity standing wave is analysed using coupled-mode equations. The grating coupling coefficient is calculated using the rate equation with an ambipolar diffusion term. The self-consistent solution of the coupling coefficient and the optical field indicate the existence of a nonlinear gain term with a surprisingly large magnitude. This gain nonlinearity is shown to contribute significantly to the modulation damping factor of semiconductor diode lasers     

The gain and carrier density in semiconductor lasers understeady-state and transient conditions

The carrier distribution functions in a semiconductor crystal in the presence of a strong optical field are obtained. These are used to derive expressions for the gain dependence on the carrier density and on the optical intensity-the gain suppression effect. A general expression for high-order nonlinear gain coefficients is obtained. This formalism is used to describe the carrier and power dynamics in semiconductor lasers above and below threshold in the static and transient regimes     

Phase dampings of optical dipole moments and gain spectra in semiconductor lasers

Homogeneous broadenings and gain spectra in semiconductor lasers have been theoretically estimated, involving non-Markovian relaxation processes. The estimated spontaneous emission spectrum is in fair agreement with the observed one for a GaAlAs laser. The advantages of the present model, compared to conventional Lorentzian and delta-function models, are discussed.     

包括增益压缩因子的半导体激光器行波速率方程

对包含增益压缩因子的半导体激光器（ＬＤ）的稳态速率方程组进行了求解，得到了隐函数形式的解析解，并以此讨论了增益压缩因子对某些ＬＤ稳态特性的影响。     

Effect of gain nonlinearities on the dynamic response ofsingle-mode semiconductor lasers

The effect of gain nonlinearities on the dynamic response is studied using a nonperturbative form of the nonlinear gain in the signal-mode rate equation. The nonperturbative form is different from that used previously and leads to qualitative and quantitative differences in the intensity dependence of the important dynamic parameters such as the frequency and the damping rate for relaxation oscillations. The results are important for the design of high-speed semiconductor lasers and suggest that the new form of the nonlinear gain should be used for modeling the modulation response in both the small-signal and large-signal regimes     

Polarization-dependent gain due to signal-signal Raman interaction in low-PMD fiber

We study polarization-dependent gain (PDG) due to signal-signal Raman interaction (SSRI). We find that SSRI-induced PDG can be significant when the fiber polarization-mode dispersion (PMD) is low. If the PMD from the discrete optical components is also small, the accumulated PDG grows almost linearly with the number of the span.