Optical gain and refractive index of a laser amplifier in the presence of pump light for cross-gain and cross-phase modulation

The wavelength dependent changes in optical gain and refractive index in a Fabry-Perot semiconductor optical amplifier are measured for various detunings of the pump wavelength from the quasi-Fermi level separation. The refractive index change is nearly constant over a very large wavelength range. We also present data for the linewidth enhancement factor due to optical injection. Estimates of the carrier densities and stimulated recombination rates are made using our optical gain model based on realistic band structure calculations for a strained quantum-well laser. Our results are very useful for ultra-broad-band wavelength conversion by cross-gain and cross-phase modulation (XGM, XPM).     

Characteristics measurement of gain and refractive index of traveling-wave semiconductor optical amplifier

A novel method to measure the gain and refractive index characteristics of traveling-wave semiconductor optical amplifier（TMA） is presented. In-out fiber ends of TWA are used to construct an external cavity resonator to produce big ripple on amplified spontaneous emission（ASE） spectrum. By this means,Hakki-Paoli method is adepted to obtain the gain spectra of TWA over a wide spectral range. From measured longitudinal mode spacing and peak wavelength shift due to increased bias current, we further calculate the effective refractive index and the refractive index change. Special feature of refractive index change above lasing threshold is revealed and explained.     

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     

Gain, refractive index, linewidth enhancement factor fromspontaneous emission of strained GaInP quantum-well lasers

Unamplified spontaneously emitted light was measured through openings in the top contact of GaInP strained quantum-well ridge lasers. The data was recorded over a spectral range from 1.65 to 2.25 eV for different injection currents below threshold. Hakki-Paoli gain measurements of the same devices were used to determine the quasi-Fermi level separation and the scaling constant needed to calculate the modal gain from spontaneous emission spectra. The refractive index change due to current injection and the linewidth enhancement factor were derived from this data     

Theory of Optical Gain of Ge-SixGeySn1−x−y Quantum-Well Lasers

We develop a theoretical model for optical gain of a strained Ge--Si_xGe_ySn_1-x-y quantum-well (QW) structure. By using a ternary Si_xGe_ySn_1-x-y material system as the barriers, a tensile strained germanium QW with a direct band gap for the electron and hole confinements can be realized. We show our theoretical model for the strained band structure and the polarization dependent optical gain spectrum of the tensile strained germanium QW laser taking into account the carrier occupations in both the Gamma- and L-valleys of the conduction band. Reasonable material parameters are used to estimate the transition energy, optical gain spectrum, and effects of the carrier leakage in presence of the quantized subbands     

Gain narrowing and output behavior of InP-InGaAlP tunneling injection quantum-dot-well laser

Polarization-resolved amplified spontaneous emission (ASE) and gain from tensile-strained multiple quantum wells (QWs) coupled to a single layer of compressively strained quantum dots (QDs) show interesting output characteristics. Low current injection reveals transverse electric polarized ASE from the QD ground state and QD-coupled-QW state. Additionally, transverse magnetic ASE from the QW state is observed. The modal gain of this laser shows coupled active state activation which is evident by spectral narrowing and change from QW-like to QD-like spectrum.     

Tensile-strained multiple quantum-well structures for a largerefractive index change caused by current injection

Tensile-strained multiple quantum-well (MQW) structures with camel-back shaped first valence sub-bands are proposed as structures with a large refractive index change caused by current injection. These structures have a high joint density of states at the absorption edge, and the injected carriers in the structures have a long lifetime because of separation in the k-space between electrons and holes. The refractive index change caused by current injection is calculated for camel-back InGaAs/InGaAsP strained MQW structures for 1.55 μm-wavelength light. These structures show a larger refractive index change than the other InGaAs/InGaAsP strained/unstrained MQW structures     

Spontaneous Radiative Efficiency and Gain Characteristics of Strained-Layer InGaAs–GaAs Quantum-Well Lasers

The optical gain spectra, unamplified spontaneous emission spectra, and spontaneous radiative efficiency are extracted from the measurement of amplified spontaneous emission (ASE) on a single pass, segmented contact 0.98-mum-emitting aluminum-free InGaAs-InGaAsP-GaAs quantum-well (QW) laser diode. These measurements provide a baseline for which to compare higher strain InGaAs QW lasers emitting near 1.2 mum. The peak gain-current relationship is extracted from gain spectra and the peak gain parameter go is found to agree within 25% of the value extracted using conventional cavity length analysis for 0.98-mum-emitting devices. The spontaneous radiative current is extracted using the fundamental connection between gain and unamplified spontaneous emission, which in turn gives an estimate of the amount of nonradiative recombination in this material system. The spontaneous radiative efficiency, the ratio of spontaneous radiative current to total current, at room temperature of 0.98-mum-emitting InGaAs QW laser material is found to be in the range of 40%-54%, which is 2.5-3.5 times larger than that of highly strained InGaAs QW laser emitting near lambda = 1.2 mum. Whereas the gain parameter, g₀ = dg/d(ln j), was measured to be 1130 and 1585 cm^-1 for the 0.98-mum- and 1.2-mum-emitting materials, respectively. From the calculated below threshold current injection efficiency of 75%-85%, we deduce that the internal radiative efficiency of the QW material is ~ 20% higher than the ratio of internal radiative current to external injected current extracted directly from ASE measurements.     

Power scaling in quantum-well laser amplifiers

The effects of increasing excitation on the performance of quantum-well semiconductor laser amplifiers were investigated. Amplified spontaneous emission (ASE) and gain roll over at high injected carrier densities are two limitations to the power scaling of these devices. A Rigrod analysis was used to study the effects of these limitations on the gain, ratio of signal to ASE power, and efficiency for different values of injection current, facet reflectivity, and input laser intensity. Comparisons are made with an equivalent amplifier operating with a bulk semiconductor gain medium. This analysis suggests that quantum-well semiconductor amplifier performance improves with a double-pass configuration     

Gain spectra of quantum-well lasers

The gain spectrum and its sensitivity to carrier density is calculated for a model quantum-well heterostructure semiconductor laser for a range of quantum-well widths. The gain spectra, especially for narrow wells, show better mode-to-mode gain discrimination than for the equivalent bulk laser. Good carrier confinement helps obtain this desirable feature.     

Analysis of differential gain in InGaAs-InGaAsP compressive andtensile strained quantum-well lasers and its application for estimationof high-speed modulation limit

A simplified model that furnishes an intuitive insight for the change in quantum-well (QW) laser gain due to QW strain and quantum confinement is presented. Differential gain for InGaAs-InGaAsP compressive and tensile strained multi-quantum-well (MQW) lasers is studied using the model. The comparison between the calculated and experimental results for lattice-matched and compressive strained MQW lasers shows that this model also gives quantitatively reasonable results. It is found that the variance-band barrier height strongly affects the differential gain, especially for compressively strained MQW lasers. The tensile strained MQW lasers are found to have quite high differential gain, due to the large dipole matrix element for the electron-light-hole transition, in spite of the large valence-band state density. Furthermore, a great improvement in the differential gain is expected by modulation p doping in the tensile strained MQW lasers. The ultimate modulation bandwidth for such lasers is studied using the above results     

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     

Threshold current density in strained layerInxGa1-xAs-GaAs quantum-well heterostructurelasers

The authors consider the transparency carrier density in ideal and practical strained layer In_xGa_1-xAs-GaAs quantum-well heterostructure lasers. The transparency carrier density in practical structures is then related to transparency current density using realistic values for spontaneous recombination rates. These parameters are incorporated with representative structural parameters into a nonlinear model for gain in a quantum-well laser, in order to provide a complete model for the laser threshold current density in strained layer In_xGa_1-xAs-GaAs quantum-well heterostructure lasers. These results are then compared and contrasted with experimental laser results from several laboratories     

Linewidth rebroadening due to nonlinear gain and index induced by carrier heating in strained quantum-well lasers

The carrier heating has been recently recognized as one of the main origins of nonlinear gain, in particular in strained quantum-well lasers. The asymmetry of this effect introduces a nonlinear refractive index. The joint effects of nonlinear gain and nonlinear refractive index that are both due to carrier heating together with the spatial-hole-burning give rise to an increase in the carrier density and in the linewidth enhancement factor. These effects can explain the linewidth rebroadening at high power in phase-shifted single-mode DFB lasers.     

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     

Numerical analysis of the absorption and the refractive indexchange in arbitrary semiconductor quantum-well structures

A numerical method for the analysis of the absorption spectrum and the refractive index change due to an external electric field in quantum-well structures is presented. The finite-element method and the variational method are used to obtain the subband and the exciton energies in a quantum-well structure, respectively. The absorption spectrum due to the band-to-band and the excitonic transitions is then calculated, and the refractive index change is obtained using the Kramers-Kronig relations. This method is applicable to quantum-well structures with arbitrary potential profiles made of arbitrary semiconductors, because it is based on the finite-element method in which the general boundary condition for the heterointerface is employed. The validity of the method is confirmed by comparing the computed results with the measured ones     

Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers

A theoretical and experimental study of the optical gain and the linewidth enhancement factor (LEF) of a type-I quantum-cascade (QC) laser is reported. QC lasers have a symmetrical gain spectrum because the optical transition occurs between conduction subbands. According to the Kramers-Kronig relation, a zero LEF is predicted at the gain peak, but there has been no experimental observation of a zero LEF. There are other mechanisms that affect the LEF such as device self-heating, and the refractive index change due to other transition states not involved in lasing action. In this paper, the effects of these mechanisms on the LEF of a type-I QC laser are investigated theoretically and experimentally. The optical gain spectrum and the LEF are measured using the Hakki-Paoli method. Device self-heating on the wavelength shift in the Fabry-Perot modes is isolated by measuring the shift of the lasing wavelength above the threshold current. The band structure of a QC laser is calculated by solving the Schro/spl uml/dinger-Poisson equation self-consistently. We use the Gaussian lineshape function for gain change and the confluent hypergeometric function of the first kind for refractive index change, which satisfies the Kramers-Kronig relation. The refractive index change caused by various transition states is calculated by the theoretical model of a type-I QC laser. The calculated LEF shows good agreement with the experimental measurement.     

Approximate optical gain formulas for 1.55-μm strainedquaternary quantum-well lasers

We have used an efficient analytical model to calculate the optical gain of the strained quantum-well laser of InGaAsP-InP material system. Based on the anisotropic effective mass theory, empirical formulas delineating the relations between optical gain, emission wavelength, well width and material compositions are obtained for 1.55-μm In_1-xGa_xAs_yP_1-y quaternary strained quantum-well lasers. Results show a logarithmic relation between the peak optical gain and carrier concentration for all possible material compositions of the quaternary system. We show that the logarithmic relation can be derived algebraically     

Modeling the static and dynamic behavior of quarter-wave-shiftedDFB lasers

High-coupling (grating coupling constant=3.0) phase-shifted distributed-feedback (DFB) lasers are studied using a transmission-line laser model (TTLM) which includes spatial hole burning (SHB), the material gain spectrum, refractive index dependence on carrier concentration, and random spontaneous emission. Good agreement for CW spectra is shown with other models and experimental results. Dynamic simulation of laser transients shows SHB-induced deterministic mode hopping and chirping at moderate output powers. The effects of mode hopping and chirping on system performance are studied using a laser model combined with a fiber model     

Novel technique for the systematic measurement of gain, absoluterefractive index spectra, and other parameters of semiconductor lasers

To characterize semiconductor lasers, it is often required to measure parameters such as the quasi Fermi-level separation, intrinsic optical loss, the position of the gain peak, and gain and absolute refractive index spectra. For these measurements, there are many different techniques available, but they neglect to take into account the dispersion of refractive index and cannot be used to extract the absolute refractive index spectrum. A novel technique is proposed to systematically and accurately measure all these parameters of semiconductor lasers. Compared with techniques often used, which will be briefly reviewed in the paper, this novel technique has the following advantages: (1) the determination process uses only the measured spontaneous emission spectra, without the requirement for knowledge of such parameters as intrinsic optical loss, facet reflectivity, and waveguide confinement factor, which presently are difficult to check experimentally; (2) results are obtained for each given current (for example, this technique measures intrinsic optical loss for each given current, rather than the average one over the whole current range); (3) the dispersion of refractive index is taken into account; (4) both the absolute refractive index spectrum for a given current and its change with current can be accurately measured; (5) the gain spectra and refractive index can be measured as wide as one wants; (6) the measurement accuracy is improved; and (7) no adjustable parameter or recalibration is needed