Gain saturation in semiconductor lasers: Theory and experiment

The semiconductor stimulated gain saturation model of Zee has been extended using reasonable approximations to obtain an analytical solution for the gain saturation process in PbSnTe and to determine the limit to single mode power directly from the gain expression, the intraband relaxation time, and device and material parameters. The theoretical results are compared with experimental observations for single transverse mode cavity narrow stripe buried heterostructure PbSnTe lasers. Those results are interpreted in terms of an intraband relaxation time on the order of2 times 10^{-12}s in the temperature range 20-80 K.     

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     

The temperature dependence of the threshold current of GaInAsP/InP DH lasers

The temperature dependence of the threshold current of GaInAsP/InP lasers was considered in terms of linear gain, loss, and carder lifetime. The linear gain was calculated taking into account electronic intraband relaxation effects. The carrier lifetime, intraband relaxation time, loss in the active region, and dipole moment, all of which determine the threshold condition, were estimated from the experiments. The main loss mechanism which determines the temperature dependence of the differential quantum efficiency appears to be the absorption due to transitions between the split-off and heavy-hole valence bands. The temperature dependence of the theoretical threshold current Ithcalculated in terms of these parameters was compared with the measured results and reasonable agreement was obtained.     

Analysis of vertical-cavity surface-emitting laser multimodebehavior

This paper investigates problems associated with multimode oscillation in vertical-cavity surface-emitting lasers (VCSELs). The multimode rate equations for transverse mode were formulated. These equations take into account carrier diffusion and gain nonuniformity in the lateral direction. It was shown that multimode transverse mode excitation is due to carrier spatial hole burning, but many factors affect the number of lasing modes. The role of gain nonuniformity distribution, carrier diffusion, and modal loss compared with mirror loss in a cavity were demonstrated by numerical solution of the multimode rate equations     

多量子阱半导体激光器的瞬态响应特性分析

根据光增益与载流子密度的对数关系,在受激发射速率中分别引入了增益饱和项和载流子复合项,通过适应于多量子阱激光器的速率方程,从理论上证明了短腔结构存在与阈值电流最小值对应的最佳阱数。给出了多量子阱激光器的瞬态呼应特性的直接仿真结果及相图,分析了注入电流、阱数和腔长对其激射阈值、开关延误时间、弛豫振荡频率和光输出等能量的影响。     

Measurement of gain saturation coefficient of a DFB laser forlasing mode control by orthogonal polarization light

The frequency response of a 1.55-μm distributed feedback (DFB) laser is measured by injecting light which has an orthogonal polarization to the laser's lasing mode. The injected light, termed as orthogonal polarization light, is carefully selected to not couple to the lasing mode by adjusting its polarization to be orthogonal to that of the lasing mode and by setting its wavelength slightly different from that of the lasing mode. The wavelength of the orthogonal polarization light, however, is set within the range where the laser's active layer has a gain. The gain saturation coefficients for the lasing light are estimated to be 4.7×10^-23 cm² and that by the injected orthogonal polarization light (almost the same wavelength as the lasing mode) are 3.7×10^-23 cm², respectively     

Finite time of carrier energy relaxation as a cause of optical-power limitation in semiconductor lasers

It is shown that the reason why the maximum attainable optical power in semiconductor lasers is limited is the finite time of carrier energy relaxation via scattering by nonequilibrium optical phonons in the quantum-well active region. The power and spectral characteristics of semiconductor lasers are studied experimentally at high excitation levels (up to 100 kA/cm²) in pulsed lasing mode (100 ns, 10 kHz). As the drive current increases, the maximum intensity of stimulated emission tends to a constant value (“saturates”), and the emitted power increases owing to extension of the spectrum to shorter wavelengths. The intensity saturation is due to limitation of the rate of stimulated recombination, caused by a finite time of the electron energy relaxation via scattering by polar optical phonons. It is found that the broadening of the stimulated emission spectrum is related to an increase in carrier concentration in the active region, which enhances the escape of electrons into the waveguide layers. As the drive current increases, the carrier concentration in the waveguide reaches its threshold value and there appears an effective channel of current leakage from the active region. The experiment shows that the appearance of a band of waveguide lasing correlates with a sharp drop in the differential quantum efficiency of a semiconductor laser.     

Spectral and mode characteristics of InAsSbP/InAsSb/InAsSbP lasers in the spectral region near 3.3 µm

The characteristic features of the continuous-wave lasing spectra near 3.3 μm of multimode InAsSbP/InAsSb/InAsSbP double-heterostructure diode lasers are shown. The observation of mode switching to longer and shorter wavelengths at cryogenic temperatures is reported. It is shown that suppression of the longitudinal side modes closest to the main mode results in large mode jumps in energy during mode tuning by current. The characteristics which were observed are explained by gain spectrum inhomogeneity due to spectral hole burning in narrow-gap semiconductors. The intraband charge-carrier relaxation times in the active region are estimated. Fiz. Tekh. Poluprovodn. 39, 1139–1144 (September 1998)     

Optical bistability in an L-band dual-wavelength erbium-doped fiber laser with overlapping cavities

The authors investigate the optical bistability in an L-band dual-wavelength erbium-doped fiber (EDF) laser with overlapping cavities. The bistable input-output hysteresis behavior of the two lasing wavelengths evolves in antiphase. The bistable region is tens of milliwatts wide. The bistability is essentially due to the homogeneous saturable absorption of EDF. The cross-gain saturation causes the bistabilities of the two lasing lines to evolve in antiphase with respect to each other. The gain clamping effect helps to widen the bistable region, which may be controlled by the cavity loss and by the EDF length.     

Continuous-wave lasing of hybrid lasers

The continuous-wave (CW) lasing of hybrid lasers, which contain a broad-band inhomogeneously broadened laser medium and a narrow-band homogeneously broadened laser medium in a single cavity, is analyzed theoretically. The interactions of the laser modes and two gain media are solved self-consistently using the coupled rate equations. The spectral, gain, and power characteristics under different gain conditions are simulated. It is shown that a small gain from a second narrowband laser medium can effectively shape the lasing spectrum and improve the spectral concentration of the hybrid laser. The total saturated gain profile of the hybrid laser is relatively smooth, due to saturation of the gain of the narrow-band medium to a smaller and below-threshold level     

A multimode rate-equation analysis for semiconductor lasers applied to the direct intensity modulation of individual longitudinal modes

A multimode rate-equation model, including the effects of carrier diffusion, gain saturation, and mode coupling gain, has been developed. This model has been used to analyze the direct intensity modulation of individual longitudinal modes in a channeled-substrate-planar laser (Hitachi HLP 1400). The carrier diffusion is shown to reduce the intensity modulation of all longitudinal modes by the same fixed factor, while the gain saturation and mode coupling modify the intensity modulation by a factor that is spectrally dependent relative to the main-mode frequency. The gain saturation and mode coupling also modify the frequency dependence of the intensity modulation of each individual mode in relation to the mode power. These features have been experimentally confirmed.     

Transmission performance of chirp-controlled signal by usingsemiconductor optical amplifier

We examine the fiber transmission performance of the optical signal whose chirp is controlled by utilizing phase modulation in semiconductor optical amplifier (SOA) with both simulations and experiments. This chirp control technique converts a positive chirp created by electroabsorption (EA) modulator into negative chirp, which reduces the waveform degradation due to the chromatic dispersion in transmission over standard single-mode fiber (SMF). It also provides an optical gain that is sufficient to compensate the insertion loss of the EA modulator. We investigate how the chirp control is affected by the input power to the SOA and the carrier lifetime of the SOA. As the SOA input power increases, the negative chirp becomes large, while the waveform is largely distorted due to gain saturation. However, the waveform distortion at high SOA input powers can be shaped by using a frequency discriminator. The acceleration of the carrier lifetime also reduces the waveform distortion due to gain saturation. We demonstrate that the chirp control technique is effective even for a high bit rate optical signal up to 10 Gb/s, when the carrier lifetime is expedited by optical pumping     

Effect of gain and index nonlinearities on single-mode dynamics insemiconductor lasers

The finite intraband relaxation time in semiconductor lasers leads to gain saturation at high laser powers. The nonperturbative solution of the single-mode density-matrix equations shows that both the optical gain and the refractive index become intensity dependent as a result of intraband relaxation dynamics. Gain and index nonlinearities are included in the rate equations, and how the modulation response and noise characteristics of semiconductor lasers are affected by such nonlinearities is studied. The intensity dependence of the frequency and the damping rate of relaxation oscillations leads to a fundamental limit imposed on the small-signal modulation bandwidth; the analysis provides an expression for the ultimate modulation bandwidth in terms of the material parameters     

Effects of carrier heating on laser dynamics-a Monte Carlo study

The static and dynamic properties of semiconductor quantum-well (QW) lasers have traditionally been analyzed by using rate equations that couple cold carriers to photons in the lasing cavity. This assumption of cold carriers, however, has often been disputed because it does not account for heating due to carrier relaxation, hot phonon effects, and spectral hole burning. All these processes affect laser performance significantly by modifying the gain because gain depends on carrier temperature as well as spectral broadening. In this paper, we study the carrier dynamics of QW lasers using a Monte Carlo method and conclude that hot carrier effects in semiconductor lasers are important and need to be considered for the analysis and design of semiconductor lasers     

Gain and intervalence band absorption in quantum-well lasers

The linear gain and the intervalence band absorption are analyzed for quantum-well lasers. First, we analyze the electronic dipole moment in quantum-well structures. The dipole moment for the TE mode in quantum-well structures is found to be about 1.5 times larger at the subband edges than that of conventional double heterostructures. Also obtained is the difference of the dipole moment between TE and TM modes, which results in the gain difference between these modes. Then we derive the linear gain taking into account the intraband relaxation. As an example, we applied this analysis to GaInAs/InP quantum-well lasers. It is shown that the effects of the intraband relaxation are 1) shift of the gain peak toward shorter wavelength with increasing injected carrier density even in quantum-well structures, 2) increase of the gain-spectrum width due to the softening of the profile, and 3) reduction in the maximum gain by 30-40 percent. The intervalence band absorption analyzed for quantum-well lasers is nearly in the same order as that for conventional structures. However, its effect on the threshold is smaller because the gain is larger for quantum wells than conventional ones. The characteristic temperature T0of the threshold current of GaInAs/InP multiquantum-well lasers is calculated to be about 90 K at 300 K for well width and well number of 100 Å and 10, respectively.     

A study of optical amplification in a double heterostructure GaAs device using the density matrix approach

A theoretical investigation of traveling wave light amplification in a GaAs double heterostructure device is presented in this paper. The analysis is self-consistent, semiclassical, and uses a density matrix formulation. Phenomenological constants are included to account for intraband relaxation processes, pumping, and spontaneous emission. The analysis is significantly different from previous rate equation approaches in that saturation effects are inherent in the results and phase information, important for coherent applications, is retained. Results presented for steady-state and pulsed operation include gain, pulse compression, multipulse effects, and the phase variation that occurs over the pulse time.     

Excited-State-Mediated Capture of Carriers Into the Ground State and the Saturation of Optical Power in Quantum-Dot Lasers

Excited-state-mediated capture of carriers from the waveguide into the lasing ground-state in quantum dots (QDs) is studied. Such a two-step capture places a fundamental limitation on ground-state lasing-the output power saturates at high injection currents. The saturation power is controlled by the transition time between the excited- and ground-state in a QD. The longest, cut-off transition time exists, beyond which no ground-state lasing is possible     

Transverse and longitudinal mode control in semiconductor injection lasers

Mechanisms which determine the oscillating transverse and longitudinal modes in semiconductor injection lasers are discussed in this paper. The analysis is based on the semiclassical method in which the optical field is represented by Maxwell equations and the lasing phenomenon is analyzed quantum mechanically using the density matrix formalism. Guided modes are classified by the relation between refractive index and gain-loss differences at the boundaries of the active region as normal guided mode (index guiding), active-guided mode (gain guiding), and leaky mode (anti-index guiding). The guiding loss and cutoff conditions are given for these modes. The optimum range to obtain stable fundamental transverse mode operation is discussed with respect to several guiding factors, such as width of active region, the refractive index difference, and gain-loss differences at the boundaries of the active region. Longitudinal mode behavior is discussed in terms of electron transition mechanism in semiconductor crystals. The relaxation effect of the electron wave is introduced in this model. Profiles of the saturated gain and the spatial diffusion of the electron are related to this relaxation effect. Mode competition phenomena are analyzed, and a strong gain suppression among the longitudinal modes is shown to be as an intrinsic property of semiconductor lasers. The possibility of obtaining single longitudinal mode operation is postulated. Physical influences for stable single longitudinal mode operation are discussed in terms of transverse mode control (or stripe structure), spontaneous emission, threshold current level, impurity concentration in the active region, and direct modulation. Some experimental results are also given to support these analyses.     

Theory of gain in quantum-wire lasers grown in V-grooves

Theoretical calculations of gain, refractive index change, differential gain, and threshold current for GaAs-AlGaAs quantum-wire lasers grown in V-shaped grooves are presented. The theoretical model is based on the density-matrix formalism with intraband relaxation, and the subband structure is calculated within the effective bond-orbital model. For the quantum-wire geometry treated, agreement with the observed subband spacings is found. Because of the small overlap of the optical field with the active region for a single quantum wire, lasing threshold is reached only when several subbands are filled     

The role of axially nonuniform carrier density in altering theTE-TE gain margin in InGaAsP-InP DFB lasers

Axial nonuniformities in the carrier density profile of 1.55 μm capped-mesa-buried-heterostructure distributed-feedback (CMBH-DFB) InGaAsP-InP diode lasers are discussed. This is accomplished by directly measuring the spontaneous emission at various locations in the laser optical cavity. The authors observe that the highly asymmetric optical field, inherent in DFB lasers, produces a strong longitudinal nonuniformity in the carrier density. This promotes degradation of the lasing gain margin between the dominant TE Bragg modes, which is verified through measurements of the relative shift of the lasing mode in the stopband. The reduction of gain margin is shown to cause multimode operation in devices with large optical field asymmetries. In devices with modest optical field asymmetries, the reduction of the gain margin saturates, and single mode behavior is maintained. Measurements are consistent in many respects with the predicted consequences of spatial hole burning