High speed quantum-well lasers and carrier transport effects

Carrier transport can significantly affect the high-speed properties of quantum-well lasers. The authors have developed a model and derived analytical expressions for the modulation response, resonance frequency, damping rate, and K factor to include these effects. They show theoretically and experimentally that carrier transport can lead to significant low-frequency parasitic-like rolloff that reduces the modulation response by as much as a factor of six in quantum-well lasers. They also show that, in addition, it leads to a reduction in the effective differential gain and thus the resonance frequency, while the nonlinear gain compression factor remains largely unaffected by it. The authors present the temperature dependence data for the K factor as further evidence for the effects of carrier transport     

Effects of carrier transport on relative intensity noise and critique of K factor predictions of modulation response

The maximum possible intrinsic modulation bandwidth in semiconductor lasers is conventionally written in terms of the K factor. Although this is often sufficient in bulk lasers, it is usually not true in quantum well lasers where carrier transport can significantly affect the high speed properties. Analytical expressions are presented, which include the effects of carrier transport, for the modulation response and the relative intensity noise in quantum well lasers. It is shown that in the presence of significant transport effects, the K factor is not an accurate measure of the maximum possible intrinsic modulation bandwidth.<>     

Reduced effective differential gain in diode lasers due toconfinement factor modulation

A reduced effective differential gain is shown to arise in diode lasers by including the modulation of the confinement factor with carrier density. This effective differential gain, not the material gain, is the parameter determined from conventional measurements of the differential gain. This term is in addition to the static reduction in confinement factor with carrier density, and can significantly reduce the resonance frequency and modulation bandwidth for lasers with short cavities and thin active layers     

Modulation resonance enhancement in SCH quantum-well lasers with anexternal Bragg reflector

The modulation response of a semiconductor laser can be enhanced by coupling it to an external cavity with frequency-selective feedback. This creates a comb of transmission bands where the modulation response is high, at the cavity round-trip frequency and its harmonics. In a previous publication, we related the bandwidths of these bands to the material and structural parameters of a bulk laser. We showed that a nonzero linewidth enhancement factor together with a nonzero intermediate facet reflectivity lead to deep nulls close to the peaks of these transmission bands. This suggests that quantum-well (QW) lasers, which have a low linewidth enhancement factor, may give a better performance than bulk lasers. To test this hypothesis, we have extended our analysis to model QW lasers coupled to a fiber grating. Carrier transport, carrier heating, intraband carrier fluctuations, and nonparabolic band structures are considered. We show that electron carrier transport and amplitude-phase coupling in the separate-confinment-heterostructure (SCH) layer contribute to the nulls in the modulation response. Therefore, the apparent advantage of having a reduced linewidth enhancement factor that we found in our previous analysis cannot be fully realized by using QW lasers     

Novel design scheme for high-speed MQW lasers with enhanceddifferential gain and reduced carrier transport effect

We present a theoretical analysis exploring the optimum design of high-speed multiple-quantum-well (MQW) lasers for 1.55-μm operation. Various combinations of well and barrier materials are examined for lattice-matched, strained-layered (SL), and strain-compensated (SC) MQW lasers with InGaAsP and InGaAlAs barriers. The gain characteristics are investigated for these MQW lasers with various barrier bandgap wavelengths and are used to evaluate the modulation characteristics based on the carrier dynamics model which includes a set of Poisson, continuity, and rate equations. The importance of band engineering aimed at simultaneously reducing the carrier transport effect and enhancing the differential gain is described. It is shown that SC-MQW lasers with InGaAlAs barriers have an advantage in reducing the density of states in the valence band by reducing the overlap integral between the heavy- and light-hole wave functions, which effect has previously been discarded as a minor correction in designing conventional InGaAsP-based MQW lasers. Furthermore, the hole transport rate across the barriers can be drastically reduced in SC-MQW lasers due to the reduced effective barrier height for the holes. Based on this novel design scheme, a 3-dB bandwidth approaching 70 GHz is expected for 20-well SC-MQW lasers with InGaAlAs barriers as a result of both the large differential gain and reduced transport effect     

垂直腔激光器中弛豫振荡频率的优化控制

从垂直腔面发射的半导体激光器（VCSELs）的结构出发，利用增益与载流子密度的广义对数关系，借助小信号分析法，推出了直接调制情形下驰豫振荡频率的严格解析关系。分析指出，量子阱器件的光子寿命并非越短越好，欲提高VCSELs的驰豫振荡频率，除了增加注入电流，提高微分增益等基本途径外，控制器件的结构参数可使驰豫振荡频率达到极大值。同时，自发辐射因子的可控性，以及降低稳态载流子密度，也都是提高VCSELs驰豫振荡频率和拓宽调制带宽的有效措施。     

A quantitative comparison of the classical rate-equation model withthe carrier heating model on dynamics of the quantum-well laser: therole of carrier energy relaxation, electron-hole interaction, and Augereffect

In this paper, a quantitative theoretical comparison of the classical rate-equation model with the carrier heating model for large signal dynamic response of 1.5-μm InGaAs-InGaAsP single-mode quantum-well (QW) lasers Is performed. The contributions of carrier energy relaxation, electron-hole interaction, and Auger effect to the nonlinear gain are inspected in detail by a numerical comparison of the two models at room temperature (293 K) and low temperature (50 K). It can be shown that contribution of the carrier heating to the nonlinear gain coefficient is proportional to an effective carrier energy relaxation time, and the contribution of the electron-hole energy exchange time shows a nonlinear relation. Furthermore, the influence of Auger heating on the modulation dynamics is also considered and is found to be indescribable by a single phenomenological nonlinear gain coefficient. The dependence of the nonlinear gain coefficient on the laser emission wavelength of distributed feedback lasers is also demonstrated quantitatively for the first time     

Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser

This paper describes a circuit modeling technique for directly modulated narrow-stripe semiconductor lasers with strong carrier confinement and index guiding. It is shown that diffusion damping of the modulation response, due to a nonuniform electron density distribution in the active layer, can be accounted for in terms of an equivalent optical gain saturation. Based on this equivalence, a small-signal ac circuit model of a narrow-stripe laser is derived. The model can be used to determine the intensity modulation and frequency modulation response characteristics of a packaged device.     

Effective differential gain and modulation bandwidth reduction inquantum well lasers due to confinement factor modulation

A mechanism that may reduce the effective differential gain due to the modulation of the confinement factor with carrier density in quantum-well lasers is described. This mechanism may limit modulation bandwidth for quantum-well lasers with high threshold carrier density and narrow confining layer     

A small-signal analysis of the modulation response of high-speedquantum-well lasers: effects of spectral hole burning, carrier heating,and carrier diffusion-capture-escape

We present a small-signal analysis of the modulation response by simultaneously considering the effects of spectral hole burning, carrier heating, and carrier diffusion capture-escape. An explicit form of the small-signal modulation response is obtained and the nonlinear gain coefficients associated with each physical process are defined. Further simplifications in our results will give analytical forms for calculating the resonant frequency and damping rate of the modulation response. One of the simplified versions of our results is shown to agree with previous investigations. The effects of the carrier dephasing time, energy relaxation time, and diffusion-capture-escape times on the high-speed performance of QW lasers are theoretically investigated     

Effect of linear gain saturation on small-signal dynamics of MQWDFB lasers

The linear gain saturation effect is shown to be important in determining the dynamics of multiple-quantum-well (MQW) distributed-feedback (DFB) lasers. A more realistic logarithmic dependence of material gain on carrier density is assumed in a comprehensive MQW DFB laser model. It is found through simulation that because of the linear gain saturation, the interplay between modal gain and differential gain leads to an optimal κL for maximum small-signal modulation bandwidth in λ/4-shifted MQW DFB lasers     

High-speed modulation of long-wavelength In1-xGaxAsyP1-y andIn1-x-yGaxAlyAs strained quantum-welllasers

In_1-xGa_xAs_1-yP_y quantum-well (QW) lasers with compressive strain and In_1-x-yGa_xAl_yAs QW lasers with two strain types (compressively strained and lattice matched) for 1.55-μm telecommunication applications are investigated both in the steady-state and high-speed microwave modulation schemes. Under steady-state electric bias, the gain and intrinsic loss are measured based on the well-known Hakki-Paoli method from below threshold to threshold. The photon lifetime is obtained from this measurement. A comprehensive theoretical gain model with realistic band structure, including valence band mixing and many-body effects, is then used to fit the experimentally obtained modal gain profiles and extract the carrier density and, therefore, the differential gain. In the high-speed microwave modulation scheme, the experimental modulation response curves are fitted by the theory and parameters such as the differential gain and K factor are obtained. The differential gain agrees very well with the value obtained from the steady-state direct optical gain measurement. The comparison of two material systems will be important to design high-bandwidth high-performance semiconductor lasers in order to meet requirements of 1.55-μm telecommunication applications     

Dynamic properties of partly gain-coupled 1.55-μm DFB lasers

The lasing characteristics and dynamic properties of partly gain-coupled 1.55-μm DFB lasers with a gain corrugation in the strained-layer MQW active region are presented. Narrow spectral linewidth, which is associated with the low linewidth enhancement factor, was experimentally measured. By analyzing data from RIN measurements, the damping rate, the damping factor, the intrinsic bandwidth and the effective differential gain were obtained. From the small-signal frequency response, a measured 3 dB bandwidth of 22 GHz at 10 mW output power was achieved. The high bandwidth is believed to be related to the high differential gain, resulting from the combination of longitudinal gain and index-coupling mechanisms and the reduction of the carrier transport time, which is due to an efficient lateral carrier injection along the longitudinal interface. Experimental results show that under 10 Gbit/s pseudorandom NRZ modulation, the devices have small wavelength chirp and clear eye openings making them suitable for long haul and high bit-rate applications     

Measurement and characterization of laser chirp ofmultiquantum-well distributed-feedback lasers

Measurements of relative intensity noise and modulation response, before and after propagation in optical fiber, of the output field of multiquantum-well distributed-feedback (MQW-DFB) lasers are used to determine the influence of the intraband damping mechanisms, the DFB structure and the carrier transport and carrier capture into the QWs on the laser chirp. The power dependence of the linewidth enhancement factor is shown to explain the saturation of the laser linewidth at high optical powers     

Influence of refractive index nonlinearities on modulation and noise properties of semiconductor lasers

The modulation response and the spectral linewidth of singlemode semiconductor lasers are analysed by taking into account the nonlinear gain and the nonlinear refractive index in the rate equations. It is shown that the effect of nonlinear gain and index can be included through an effective linewidth enhancement factor alpha /sub eff/ that is different for frequency modulation and for spectral linewidth. The effect of the nonlinear index is particularly strong in the case of frequency modulation where alpha /sub eff/ can become zero or even negative for lasers operating on the red side of the gain peak. In the case of laser noise, alpha /sub eff/ causes linewidth saturation but no rebroadening at high output powers. The authors' results indicate that gain and index nonlinearities are not the cause of linewidth rebroadening.<>     

Theoretical study on enhanced differential gain and extremelyreduced linewidth enhancement factor in quantum-well lasers

Low-chirp lasing operation in semiconductor lasers is addressed in a theoretical investigation of the possibility of reducing the linewidth enhancement factor (α factor) in quantum-well (QW) lasers to zero. It is shown that in reducing the α factor it is essential that lasing oscillation be around the peak of the differential gain spectrum, not in the vicinity of the gain peak. The condition for such lasing oscillation is analytically derived. The wavelength dependence of the material gain, the differential gain, and the α factor are calculated in detail taking into account the effects of compressive strain and band mixing on the valence subband structure. The effect of p-type modulation doping in compressively strained QWs is discussed. It is shown that the α factor, the anomalous dispersion part in the spectrum, crosses zero in the region of positive material gain, which makes is possible to attain virtual chirpless operation by detuning     

Microscopic simulation of the temperature dependence of static and dynamic 1.3-/spl mu/m multi-quantum-well laser performance

The temperature dependence of the performance of 1.3-/spl mu/m Fabry-Perot (FP) multiple-quantum-well (MQW) lasers is analyzed using detailed microscopic simulations. Both static and dynamic properties are extracted and compared to measurements. Devices with different profiles of acceptor doping in the active region are studied. The simulation takes into account microscopic carrier transport, quantum mechanical calculation of the optical and electronic quantum well properties, and the solution of the optical mode. The temperature dependence of the Auger coefficients is found to be important and is represented by an activated form. Excellent agreement between measurement and simulation is achieved as a function of both temperature and doping profile for static and dynamic properties of the lasers, threshold current density, and effective differential gain. The simulations show that the static carrier density, and hence the contribution to the optical gain, varies significantly from the quantum wells on the p-side of the active layer to those on the n-side. Furthermore, the modal differential gain and the carrier density modulation also vary. Both effects are a consequence of the carrier dynamics involved in transport through the MQW active layer. Despite the complexity of the dynamic response of the MQW laser, the resonance frequency is determined by an effective differential gain, which we show can be estimated by a gain-weighted average of the local differential gain in each well.     

Impedance, modulation response, and equivalent circuit ofultra-high-speed In0.35Ga0.65As/GaAs MQW laserswith p-doping

On-wafer measurements of the frequency-dependent impedance, modulation response, and RIN power spectra of ultra-high-speed p-doped In_0.35Ga_0.65As/GaAs MQW lasers are presented and analyzed. The experimental results are shown to be accurately modeled by an equivalent circuit which accounts for both the carrier transport/capture dynamics and the junction space-charge capacitance. We find that the carrier escape time out of the QW's in our laser structure is much larger. Than the carrier capture time, and therefore the interplay between carrier capture and re-emission is not affecting the high-speed modulation dynamics. On the other hand, the absolute values of both the carrier capture time and the space-charge capacitance still limit the modulation bandwidth     

Intensity dependence of the linewidth enhancement factor and itsimplications for semiconductor lasers

The linewidth enhancement factor is shown to become intensity dependent when the intraband relaxation effects responsible for nonlinear gain and index changes are incorporated in the theory of semiconductor lasers. The intensity dependence of the linewidth enhancement factor influences many laser characteristics such as the frequency chirp, the modulation response, the injection-locking range, and the phase noise. In particular, it leads to a power-independent contribution to the laser linewidth. Furthermore, for semiconductor lasers detuned to operate away from the gain peak, the nonlinear index changes can even lead to a rebroadening of the laser linewidth at high-output powers     

Importance of self-induced carrier-density modulation insemiconductor lasers

Semiconductor lasers have a built-in mechanism for modulating the carrier density at multiples of the longitudinal-mode spacing. This mechanism is believed to be relatively unimportant for solitary laser diodes since the mode spacing typically exceeds 50 GHz. A general numerical model capable of including self-saturation, cross saturation, and four-wave mixing occurring due to both interband and intraband effects is presented, and the self-induced carrier-density modulation is shown to play an important role in solitary laser diodes. In particular, it can severely degrade the gain margin and the mode-suppression ratio in single-mode semiconductor lasers when the operating current is increased. Degradation depends on the linewidth enhancement factor and the laser length and can be especially severe when the cavity length exceeds 1 mm