Spectra of gain, absolute refractive index, and wave-guideconfinement factor of strained single quantum-well GaInP laser fromspontaneous emission

Both unamplified and amplified spontaneous emission was measured from a compressively-strained single quantum-well GaInP laser. By using a novel and self-consistent technique briefly described in the text, the data were used to systematically determine the gain-peak energy, quasi-Fermi level separation, intrinsic optical loss, absolute refractive index, and optical waveguide confinement factor and gain, including the dispersion of refractive index for a given current. During this process, there is no need for a knowledge of parameters that are difficult to experimentally check with enough accuracy. Furthermore, the effect of dispersion of the refractive index on the optical waveguide confinement factor is discussed     

Measurement of semiconductor laser gain and dispersion curvesutilizing Fourier transforms of the emission spectra

A new technique for the measurement of semiconductor laser gain and dispersion spectra is presented. The technique is based on an analysis of the subthreshold emission spectrum by Fourier transforms. Applications of this method to AlGaInP-based interband laser diodes and mid-infrared intersubband quantum cascade lasers are discussed. A good agreement between the measured dispersion of the refractive index and tabulated values in the literature was found     

Substrate Modes of (Al,In)GaN Semiconductor Laser Diodes on SiC and GaN Substrates

In semiconductor laser diodes layers with high refractive index can act as parasitic waveguides and cause severe losses to the optical mode propagating in the longitudinal direction. For (Al,In)GaN laser diodes, the parasitic modes are typically caused by the SiC or GaN substrate or buffer layers, hence the name substrate modes. A set of four different experiments shows the effect of substrate modes in the near-field (the most direct evidence of substrate modes), as side lobes in far-field, oscillations of the optical gain spectra, and as dependency of threshold current on n-cladding thickness. We derive several basic properties of the substrate modes by simple estimates. For a quantitative analysis we employ a 2-D finite element electromagnetic simulation tool. We simulate periodic variations in the cavity gain spectrum that explain the measurements in terms of absolute value and oscillation amplitude. We show that it is necessary to include the refractive index dispersion in order to get the correct period of the gain oscillations. Furthermore, we use the simulations to optimize the laser diode design with respect to substrate mode losses within the constraints given, e.g., by growth conditions     

Group delay and α-parameter measurement of 1.3 μmsemiconductor traveling-wave optical amplifier using the interferometricmethod

The group delay dispersion and the linewidth broadening factor (α-parameter) are measured for a 1.3-μm semiconductor traveling-wave optical amplifier (TWA) using a newly developed interferometric method. By Fourier transforming an interferometric cross-correlation signal, both the optical phase and the gain are simultaneously obtained in the entire gain bandwidth. The group delay spectrum is evaluated from the frequency derivative of the phase, and by selecting an appropriate interval for the interferometer scan, a refractive index dispersion of ~ 3.2 fs/nm is separated from the dispersion caused by Fabry-Perot resonance. From the phase and gain change with injection current, the α-parameter spectrum is evaluated, and the results indicate a strong dependence on wavelength     

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.     

Wavelength chirp and dependence of carrier temperature on currentin MQW InGaAsP-InP lasers

In this paper, we derive a relation between the wavelength chirp and carrier temperature in semiconductor lasers. The coefficient relating the change in carrier temperature and chirp is expressed in terms of the temperature derivative of the optical gain, and two parameters describing the variation of refractive index produced by the variation of optical gain due to change of carrier quasi-Fermi level separation or carrier temperature. We have measured these parameters for MQW InGaAsP lasers, Using this data, we estimated the rate of the temperature increase with current above threshold in these devices, which is 0.13 K/mA     

Theory and experiment on the amplified spontaneous emission fromdistributed-feedback lasers

The amplified spontaneous emission (ASE) of a strained quantum-well distributed feedback (DFB) laser biased below laser threshold is used to extract the gain and refractive index spectra in a systematic manner. A modified Hakki-Paoli method is used to obtain the gain and differential gain spectra. The refractive index change due to carrier injection is obtained from the shift of the Fabry-Perot peaks in the ASE spectrum. The measured ASE spectrum, gain, refractive index change, and linewidth enhancement factor are then compared with our theoretical model for strained quantum-well lasers. Our model takes into account the realistic band structure and uses the material and quantum-well dimensions directly in the calculation of the electronic and optical properties. The theory agrees very well with the experiment     

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.     

Minimal group refractive index dispersion and gain evolution in ultra-broad-band quantum cascade lasers

The group refractive index dispersion in ultra-broad-band quantum cascade (QC) lasers has been determined using Fabry-Perot spectra obtained by operating the lasers in continuous wave mode below threshold. In the wavelength range of 5-8 /spl mu/m, the global change of the group refractive index is as small as +8.2 /spl times/ 10/sup -3/ /spl mu/m/sup -1/. Using the method of Hakki and Paoli (1975), the subthreshold gain of the lasers has furthermore been measured as a function of wavelength and current. At the wavelength of best performance, 7.4 /spl mu/m, a modal gain coefficient of 16 cm/spl middot/kA/sup -1/ at threshold and a waveguide loss of 18 cm/sup -1/ have been estimated. The gain evolution confirms an earlier assumption that cross-absorption restricted laser action to above 6 /spl mu/m wavelength.     

Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers

A theoretical and experimental study of the optical gain, refractive index change, and linewidth enhancement factor (LEF) of a p-doped quantum-dot (QD) laser is reported. These parameters are measured by injecting an external pump, which induces cross-gain and cross-phase modulation. A comprehensive theoretical model for the optical gain and refractive index change of InAs QD lasers is introduced with the quasi-equilibrium approximation of carrier distribution. 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. We match the experimental data with the theoretical results when the thermal effect is isolated by an additional pulsed current measurement. We also calculate theoretically the optical gain, refractive index change, and LEF of an undoped QD laser of the same structure except the absence of p-type doping. We show that the differential gain and LEF of the p-doped QD laser are improved compared with those of the undoped QD laser due to the reduced transparency carrier density.     

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     

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     

Gain, refractive index, and /spl alpha/-parameter in InGaAs-GaAs SQW broad-area lasers

Gain, refractive index, and the linewidth enhancement factor, or /spl alpha/-parameter, are measured in broad-area InGaAs-GaAs single-quantum-well semiconductor lasers using below-threshold amplified spontaneous emission spectra and a far-field filtering technique. The /spl alpha/ parameter is shown to increase dramatically with increasing carrier density and wavelength. Modes propagating in the transparent substrate of the lasers are shown to have a significant influence on the measured value of /spl alpha/.     

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.     

Dispersion of the group velocity refractive index in GaAs double heterostructure lasers

The dispersion of the refractive index corresponding to the group velocityn*_{1}has been measured as a function of wavelength. It is obtained from the longitudinal mode spacing of GaAs buried heterostructure lasers at threshold. The dependence ofn*_{1}on wavelength contains an approximately constant term due to the refractive index n1and a strongly dispersive component due to-lambda (partialn_{1}/ partiallambda). For a given spectral bandwidth, the dispersion ofn*_{1}causes a temporal broadening of a pulse as it passes through the medium. This dispersive effect is shown to contribute to the width of 0.65 ps long pulses obtained recently from mode locked semiconductor lasers. By reducing the length of the laser, the dispersive effect is reduced and it is suggested that pulses as short as 10^-13s should be obtainable from such mode locked semiconductor lasers.     

Measurement of gain spectrum for semiconductor lasers utilizing integrations of product of emission spectrum and a phase function over one mode interval

A technique based on the integration of the product of amplified spontaneous emission spectrum and a phase function over one mode interval is proposed for measuring the gain spectrum for Fabry-Perot semiconductor lasers, and a gain correction factor related to the response function of the optical spectrum analyzer (OSA) is obtained for improving the accuracy of the measured spectrum. Gain spectra with a difference less than 1.3 cm/sup -1/ from 1500 to 1600 nm are obtained for a 250-/spl mu/m-long semiconductor laser at an OSA resolution of 0.06, 0.1, 0.2, and 0.5 nm. The corresponding gain correction factor is about 9 cm/sup -1/ at a resolution of 0.5 nm. The gain spectrum measured at a resolution of 0.5 nm has the same accuracy as that obtained by the Hakki-Paoli method at a resolution of 0.06 nm for a laser with a mode interval of 1.3 nm.     

High-power single-mode operation in DFB and FP lasers usingdiffused quantum-well structure

Distributed feedback (DFB) and Fabry-Perot (FP) semiconductor lasers with step and periodic interdiffusion quantum-well structures are proposed for high-power single-longitudinal-mode operation. It is shown that the phase-adjustment region formed by the diffusion step (i.e., step change in optical gain and refractive index) counteracts the influence of spatial hole burning, especially for DFB lasers with large coupling-length products biased at high injection current. Furthermore, it is found that with careful design of the diffusion grating (i.e., grating period and amount of diffusion extent) of FP lasers, side-mode suppression ratio can be enhanced and threshold current density can be minimized to a satisfied level     

Joint time-frequency measurements of modelocked semiconductor diodelasers and dynamics using frequency-resolved optical gating

Joint time-frequency ultrafast measurements using frequency-resolved optical gating (FROG) have been used to provide a fundamental understanding of: (1) ultrashort pulse propagation in semiconductor optical amplifiers; (2) the modelocking dynamics in external cavity semiconductor diode lasers; and (3) correlated multiple-wavelength generation from mode locked semiconductor lasers. The pulse shaping and chirping effects measured by FROG are shown to be attributed to intracavity gain and saturable absorbing dynamics, as well as group velocity dispersion. In addition, the intracavity gain dynamics show a regime of transient unsaturated gain, which can be exploited to allow phase-correlated multiple-wavelength modelocked operation from a single-stripe external-cavity semiconductor diode laser. In this case, FROG techniques are used to understand the underlying mechanisms involved in the phase correlation process     

Four-wave mixing and optical modulation in a semiconductor laser

There is a direct connection between nearly degenerate four-wave mixing in a semiconductor laser and optical modulation in the laser field. It can be understood using a model of an unlocked, optically injected laser, which emphasizes the effect of the laser resonator on the optical interactions. This model correctly describes the observed spectral characteristics and their dependence on the intrinsic parameters of the semiconductor laser. This is used to develop a simple and accurate technique using a single experimental setup for the parasitic-free characterization of the intrinsic laser parameters, including the relaxation resonance frequency, the total relaxation rate, the nonlinear relaxation rate, and the linewidth enhancement factor. Other parameters, such as the spontaneous carrier lifetime, the photon lifetime, the differential and nonlinear gain parameters, and the K factor, are determined from the power dependencies of these parameters. This technique requires only two CW lasers closely matched in wavelength and is applicable to semiconductor lasers of any wavelength and any dynamic bandwidth     

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