Strain-dependence of the gain saturations in InGaAsP/InP quantum-well gain media

Numerical analyses of polarization-dependent optical gain saturations are given for quantum-well (QW) lasers in the presence of strain in the well regions in order to investigate the strain dependence of polarization-bistable operations. Gain saturation coefficients are obtained from nonlinear susceptibilities calculated in the perturbative analyses of density matrices. Band dispersions and dipole matrix elements, which are put into the density matrices, are calculated by diagonalizing Luttinger's Hamiltonian, including valence band mixing. The strain induces a change in band dispersions and wavefunctions, leading to strain-dependent saturation coefficients. The self-saturation coefficients and the cross-saturation coefficients (with orthogonal optical polarizations) pertinent to InGaAsP/InP QW vertical-cavity surface-emitting lasers are calculated. We find that the relative magnitudes of self- and cross-saturation coefficients are strongly dependent on the strain; in the presence of compressive strain, the cross-saturation coefficients are larger than the self-saturation in the wide range of the linear gain spectra, especially in the vicinity of the gain peak, indicating that the compressively strained structure is more favorable for the polarization-bistable operations.     

Optical gain in a strained-layer quantum-well laser

The optical gain and the refractive index change of a uniaxially stressed GaAs-Al₂Ga_1-xAs quantum-well laser is studied theoretically using the multiband effective mass theory (k -p method) and density matrix formalism with intraband relaxations. It is found that uniaxial strain of the quantum well substantially alters the subband structures and the optical gain of the quantum-well laser. In particular, the gain of the TM mode increases while the gain of the TE mode decreases with increasing stress. Thus, the threshold current either decreases or increases with the stress, depending on whether the laser is operating in a TM or TE mode     

Optical gain of strained wurtzite GaN quantum-well lasers

A theory for the electronic band structure and the free-carrier optical gain of wurtzite-strained quantum-well lasers is presented. We take into account the strain-induced band-edge shifts and the realistic band structures of the GaN wurtzite crystals. The effective-mass Hamiltonian, the basis functions, the valence band structures, the interband momentum matrix elements, and the optical gain are presented with analytical expressions and numerical results for GaN-AlGaN strained quantum-well lasers. This theoretical model provides a foundation for investigating the electronic and optical properties of wurtzite-strained quantum-well lasers.     

Optical gain of interdiffused InGaAs-As and AlGaAs-GaAs quantumwells

We have analyzed theoretically the effects of interdiffusion on the gain, differential gain, linewidth enhancement factor, and the injection current density of In_0.2Ga_0.8As-GaAs and Al_0.3Ga_0.7As-GaAs quantum-well (QW) lasers. We have calculated the electron and hole subband structures including the effects of valence band mixing and strains. The optical gain is then calculated using the density matrix approach. Our results show that the gain spectrum can be blue-shifted without an enormous increase in the injected current density. Imposing an upper limit (416 A·cm^-2) on the injection current density for a typical laser structure, we find that the InGaAs-GaAs and AlGaAs-GaAs QW lasers can be blue-shifted by 24 and 54 mn, respectively. Our theoretical results compare well with the tuning ranges of 53 and 66 meV found for AlGaAs-GaAs QWs in some experiments. This indicates that the interdiffusion technique is useful for the tuning of laser operation wavelength for multiwavelength applications     

光抽运垂直外腔面发射激光器的增益特性数值模拟

为了深入研究光抽运垂直外腔面发射激光器的增益特性,以InGaAs/GaAs应变量子阱系统为例,建立了将带隙、带边不连续性计算和带结构计算系统结合起来的完整体系,考虑在应变影响下能带及波函数的混合效应。利用有限差分法对含6×6 Luttinger-Kohn哈密顿量的有效质量方程精确求解,得到了InGaAs/GaAs应变量子阱导带、价带的能带结构和包络函数,然后选用Lorentzian线形函数,数值模拟了量子阱的材料增益谱和自发辐射谱。最后讨论了阱宽、载流子浓度、温度等因素对量子阱材料增益的影响,为光抽运垂直外腔面发射激光器的优化设计提供了理论依据。     

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.     

Pure strain effect on differential gain of strained InGaAsP/InPquantum-well lasers

The effect of pure strain on the differential gain of strained InGaAsP/InP quantum-well lasers (QWLs) is analyzed on the basis of the valence band structures calculated by k×p theory. By using an InGaAsP quaternary compound as an active layer, it becomes possible to study the relationship between the differential gain and strain (both tensile and compressive) when both the quantum-well thickness and the emission wavelength are kept constant. It is shown that the tensile strain not only reduces the density of states in the valence band but also increases the energy spacings between the first two valence subbands. It is concluded that tensile strain has a more pronounced impact on the improvement of differential gain in InP-based, strained QWLs as compared with compressive strain     

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     

Dispersion-induced ultrafast pulse reshaping in 1.55-/spl mu/m InGaAs-InGaAsP optical amplifiers

Using the Foreman effective mass Hamiltonian, the electronic structure of the valence band and the interband dipole matrix elements in In/sub x/Ga/sub 1-x/As-In/sub y/Ga/sub 1-y/As/sub z/P/sub 1-z/ quantum-well optical amplifiers are calculated, taking into account the valence band mixing and the biaxial strain. The optical field of the amplified pulse is calculated by solving the wave equation with the computed polarization as a source term. A novel wavelet transform is introduced in analyzing the pulse chirp imposed by the optical amplifier. In the linear propagation regime, the spectrum of the amplified pulse can be either red-shifted or blue-shifted with respect to its initial center frequency, depending on the local gain dispersion spanned by the pulse spectrum. The output pulse shape can be retarded or advanced, depending on the local gain and group velocity dispersion. Furthermore, an initially unchirped pulse centered in the tail of the gain spectrum is significantly reshaped after propagating 600 /spl mu/m, and its spectrum is broadened and distorted considerably. In the spectral region where both gain and group velocity change rapidly, the frequency chirp for a linearly chirped input pulse is significantly weakened after propagation.     

Nonlinear gain effects due to carrier heating and spectralholeburning in strained-quantum-well lasers

The authors present numerical results for the nonlinear gain effects due to carrier heating and spectral holeburning in 50 Å strained In_xGa_1-xAs/Al_0.3Ga_0.7 As quantum-well lasers. Calculations are performed on the basis of a 4×4 matrix system consisting of the usual Kohn-Luttinger Hamiltonian and a strain Hamiltonian for the valence band structure. In addition, the authors perform a small-signal analysis based on four dynamic equations for the photon density, carrier density, and two supplementary equations for the electron and hole energy densities to obtain information about nonlinear gain coefficients. The results indicate that the nonlinear gain is enhanced with the strain mainly due to the rapid increase of the carrier heating effect as the carrier density at the lasing threshold decreases, and that carrier heating is about five times as important compared to spectral holeburning     

Envelope function calculations of linear and nonlinear opticalgains in a strained-layer quantum-well laser

The linear and nonlinear optical gain of strained-layer InGaAs-AlGaAs quantum well (QW) lasers are studied theoretically, with band mixing effects taken into account. Effects of the biaxial compressive strain of the InGaAs-AlGaAs QW on the band structure are investigated by solving for the Pikus-Bir Hamiltonian. The biaxial compressive strain separates the HH and the LH subbands by pulling down the HH subbands and pushing the LH subbands away from the valence band edge. Since the C-HH transition is dominated by the TE polarization, it is expected that the TE mode gain would be substantially larger than the TM mode gain. The gain and the gain-suppression coefficient are calculated from the complex optical susceptibility obtained by the density matrix formalism. Optical output power is calculated by solving the rate equations for the stationary states with nonlinear gain suppression. The calculated L-I characteristics shows reasonable agreement with the experimental data     

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     

Theory and experiment of In1-xGaxAsyP1-y andIn1-x-yGaxAlyAs long-wavelengthstrained quantum-well lasers

We present a comprehensive model for the calculation of the bandedge profile of both the In_1-xGa_xAs_yP_1-y and In_1-x-yGa_xAl_yAs quantum-well systems with an arbitrary composition. Using a many-body optical gain model, we compare the measured net modal gain for both material systems with calculations from the realistic band structure including valence band mixing effects. Calibrated measurements of the side light spontaneous emission spectrum based on its fundamental relation to the optical gain spectrum give values for the radiative current density. These measurements allow us to extract the relationship between total current density and carrier density. A fit of this relation yields values for the Auger coefficient for each material system     

Anomalous in-plane polarization dependence of optical gain in compressively strained GaInAsP-InP quantum-wire lasers

In-plane polarization anisotropy of optical gain in compressively strained GaInAsP-InP quantum wire (Q-wire) lasers including elastic strain relaxation induced band mixing is studied. The interaction between two-dimensional (2-D) quantum confinement and elastic strain relaxation effects is found to be complex depending qualitatively also on the wire width. Additional valence band mixing due to strain relaxation has a strong influence on the polarization dependence of optical gain. In the absence of elastic strain relaxation, gain is the maximum for tranverse electric (TE) polarization with the electric field parallel to the wire axis (TE/sub /spl par//), in agreement with the existing theory. On the other hand, when strain relaxation is strong, contrary to the existing theory, valence band mixing causes the gain to be the maximum in TE polarization with the electric field normal to the wire axis (TE/sub /spl perp//). Moreover, Q-wire lasers without suppression of strain relaxation are more likely to exhibit ground-state lasing for TE/sub /spl perp// polarization. These results suggest that in the presence of strong strain relaxation, a laser cavity parallel to the wire axis would provide higher gain. Therefore, the appropriate orientation of the laser cavity in strained GaInAsP-InP Q-wire lasers should be decided after carefully studying the polarization dependence of gain. Our calculation also shows that strong strain relaxation causes in-plane polarization anisotropy to show complex, nonmonotonic dependence on the wire width. Consequently, in such structures, in-plane polarization anisotropy may not be regarded as a direct measure of 2-D confinement effects.     

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     

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     

Two-level description of gain and mixing susceptibilities inamplifying semiconductor materials

Optical-intensity-dependent gain and mixing susceptibilities of amplifying semiconductor materials have been calculated using the density-matrix approach. The model, which takes intraband relaxation and carrier-injection rate into account, allows for numerical computation of these susceptibilities, whatever the medium saturation is. As a simplification, an equivalent two-level system is derived which represents the gain and nearly degenerate four-wave mixing susceptibilities. Such an equivalence, which leads to the same field-induced polarization as the conventional rate equation model, also connects the two-level (or rate equation) parameters to the real characteristics of the semiconductor material     

Theoretical investigation of gain and linewidth enhancement factorfor 1.55-μm tensile strained quantum-well lasers

The performance of quantum-well laser diodes with tensile strained wells was theoretically calculated. Using 4×4 Luttinger-Kohn Hamiltonian, valence band dispersion was calculated and used for the calculation of material gain. Linewidth enhancement factor was obtained by calculating the change of refractive index due to interband transition and free carrier plasma motion. The tensile well shows smaller material and differential gain compared to the compressive strained one. But smaller linewidth enhancement factor is obtained due to the absence of free carrier plasma effect. Linewidth enhancement factor is further reduced by p-type modulation doping in the barrier     

Intraband Radiation Absorption by Holes in InAsSb/AlSb and InGaAsP/InP Quantum Wells

Microscopic analysis of intraband radiation absorption by holes with their transition to the spin-split band for InAsSb/AlSb and InGaAsP/InP semiconductor quantum wells is performed in the context of the four-band Kane model. The calculation is performed for two incident-radiation polarizations: along the crystal-growth axis and in the quantum-well plane. It is demonstrated that absorption with transition to the discrete spectrum of spin-split holes has a higher intensity than absorption with transitions to the continuous spectrum. The dependences of the intraband absorption coefficient on temperature, hole density, and quantum- well width are thoroughly analyzed. It is shown that intraband radiation absorption can be the main mechanism of internal radiation losses in lasers based on quantum wells.