Nonlinear Gain Coefficient Research Articles

Phase jitter control of ultrashort soliton in high-speed communication systems with nonlinear gain

An expression is derived for soliton phase jitter in soliton transmission with higher-order effects in the presence of nonlinear gain and filters. It is demonstrated that soliton phase jitter can be suppressed efficiently by nonlinear gain in addition to filters not only for long duration solitons but also for ultrashort solitons provided that the nonlinear gain coefficients satisfy specific conditions. This scheme offers an alternative means for the development of ultralong distance soliton transmission systems using differential phase-shift keying (DPSK), and exploits a robust technique to achieve a higher-speed soliton communication system using DPSK.

Self-consistent rate equations of self-assembly quantum wire lasers

We describe a detailed model for the dynamical and spectral properties of quantum dash (quantum wire assembly) lasers. We use a self-consistent semiclassical theory for a multimode laser field which interacts with an inhomogeneously broadened assembly of quantum wires via the quantum mechanical radiation-matter interaction. Our comprehensive coupled equations are spectrally resolved enabling to study accurately the effect of the gain inhomogeneity. Carrier-carrier and carrier-phonon scattering are also included. We highlight the effective capture rate which is determined by the ratio between the number of states in the reservoir and in the assembly, the energetic region into which carriers are captured and the width of the inhomogeneously broadened gain. Specifically, we demonstrate that a large number of states ratio lowers both the linear optical differential gain and the nonlinear gain coefficient. We show that gain suppression dominates when a realistic energy range into which capture takes place is considered as well as for small number of states ratios. In addition, we show that the width of the inhomogeneous broadening plays a relatively small role. We conclude that the differential gain and nonlinear damping can not be optimized simultaneously. These results point therefore to the clear advantages offered by laser structures which employ non conventional carrier injection schemes such as tunnelling barrier or n-type /spl delta/-doping regions.

Nonlinear Optical Processes in 3D-Quantized Spectrum of a Semiconductor

Two-photon and three-photon Raman scattering processes are considered. Analytical expressions are derived for the non-linear susceptibility, gain coefficient and generation threshold. It is shown that the resonant fluorescence accompanies the Raman scattering and the hot luminescence processes when the finite population of states is taken into account. Numerical evaluations show that the specification of the medium leads to low generation thresholds and high magnitudes of gain coefficients.

Polarization-dependent nonlinear gain in semiconductor lasers

We have numerically studied the nonlinear gain coefficients in terms of spectral hole burning for the optical fields in parallel and orthogonal polarizations in semiconductor lasers by solving the equation of motion for the density matrix in perturbation series. The electronic band structures and the transition matrix elements used in the calculations are obtained by diagonalizing Luttinger's Hamiltonian. In the present analysis for InGaAsP lasers, the cross-saturation coefficient for the parallel polarizations is twice as large as the self-saturation. Also, the cross-saturation coefficient for the orthogonal polarizations, which affects the polarization switching and polarization bistable operations of the laser, rests between the two. The relative magnitude of self-saturation coefficients and cross-saturation coefficients for orthogonal polarizations satisfies the condition for polarization bistable operations. We also discuss the effect of carrier heating on gain saturation coefficients.

InGaAs/AlGaInAs/InP Laser with Compressively Strained Multiquantum Well Layers for High Speed Modulation Bandwidth

The modulation frequency response of compressively strained multiquantum well (MQW) lasers grown with an InGaAs/AlGaInAs/InP heterostructure and emitting at the wavelength of 1.55 <FONT FACE="Symbol">m</font>m is presented. The laser devices processed with the mushroom-stripe buried structure present a high frequency 3 dB bandwidth above 20 GHz. The frequency response was measured with the small signal modulation technique. The logarithmic subtraction method was employed to extract the intrisic frequency response of the MQW active layer, providing the determination of important laser parameters: the differential gain, the nonlinear gain coefficient and the maximum 3 dB frequency bandwidth.

Effects of electron–hole energy transfer on the nonlinear gain coefficients in the small-signal modulation response of semiconductor lasers

The effects of energy transfer between electrons and holes on the small-signal modulation response of semiconductor lasers are theoretically investigated. We calculate the electron energy relaxation time due to electron–hole scattering from the first principle. We show that its value is comparable to the electron energy relaxation time due to the electron–LO phonon scattering with the effect of nonequilibrium LO phonons. In such a case, the nonlinear gain coefficient due to carrier heating defined in the small-signal modulation response of semiconductor lasers is no longer a simple sum of the term due to electron heating and that due to hole heating.

Carrier density depinning above threshold in semiconductor lasers: effects of carrier heating and spectral hole burning

Effects of carrier heating and spectral hole burning on the depinning of the carrier density above threshold in semiconductor lasers are theoretically investigated. The authors find that the magnitude of this depinning is proportional to the sum of the nonlinear gain coefficients due to injection heating, stimulated recombination heating, free carrier absorption heating, and spectral hole burning. The carrier heating, rather than spectral hole burning, is shown to be a dominant factor. Through the theoretical analysis, it is suggested that the comparison on the nonlinear gain coefficients measured from the small-signal modulation response and the spontaneous emission may provide an estimation on the value of the nonlinear gain coefficient due to injection heating and thus the carrier energy relaxation time in bulk semiconductor lasers.

Barrier strain influence on the high-speed properties of compressively strained InGaAsP multiquantum-well laser structures

We report on an extensive experimental study of the barrier strain influence on the high-speed properties of compressively strained quaternary (InGaAsP) multiquantum-well (MQW) lasers emitting at 1.55 /spl mu/m. In the design of strained MQW laser structure emitting at 1.55 /spl mu/m, the main effect of varying the barrier strain amount is to modify the effective well/barrier height for both electrons and holes. In this paper, it is shown experimentally from MQW structures with different barrier strain values, that a strong decrease of the nonlinear gain coefficient can be obtained when the barrier strain is reduced, leading to quantum-well (QW) laser structures with a damping coefficient (called the K-factor) as low as 0.18 ns, i.e., theoretical damping limited bandwidth as high as 50 GHz. This result appears to be qualitatively well explained by a substantial reduction of the carrier capture time to escape time ratio, due to an increase of the well/barrier offset in the conduction and valence bands.

A quantitative comparison of the classical rate-equation model with the carrier heating model on dynamics of the quantum-well laser: the role of carrier energy relaxation, electron-hole interaction, and Auger effect

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-/spl mu/m 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.

Effects of laser diode parameters on power penalty in 10 Gb/s optical fiber transmission systems

A composite tradeoff study based on the influence of key laser diode parameters on frequency chirp induced power penalty, extinction induced power penalty, the turn-on delay, and the dispersion transmission limit is presented for 10 Gb/s optical fiber transmission systems. The simulated results reveal that an optimum range of differential gain and nonlinear gain coefficient exists, and it is advantageous to set an extinction ratio that minimizes both the total power penalty and the turn-on delay. In addition, it is shown that a reduction of chirp and maximization of the dispersion transmission limit can be realized by designing the laser diode with a linewidth enhancement factor near -0.8.

A small-signal analysis of the modulation response of high-speed quantum-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.

Nonlinear gain suppression in quantum-well lasers due to carrier heating: the roles of carrier energy relaxation, electron-hole interaction, and Auger effect

The influences of carrier energy relaxation and electron-hole interaction on the nonlinear gain coefficient are detailed inspected by a numerical comparison of carrier heating model with classical rate-equation model in a large-signal analysis. It is shown that the nonlinear gain coefficient due to carrier heating is in proportion to an effective carrier energy relaxation time and has a nonlinear relation to the electron-hole energy exchange time. Accordingly, an empirical formula is deduced. In addition, the influence of Auger heating on the modulation dynamics is also considered, which can not be described by a single phenomenological nonlinear gain coefficient. Furthermore, the dependence of the nonlinear gain coefficient on the laser emission wavelength of distributed feedback laser is also demonstrated quantitatively.

Theory of lasing in a multiple-scattering medium.

In several recent experiments, isotropic lasing action was observed in paints that contain rhodamine 640 dye molecules in methanol solution as gain media and titania particles as optical scatterers. These so-called paint-on laser systems are extraordinary because they are highly disordered systems. The microscopic mechanism for laser activity and the coherence properties of light emission in this multiple-light-scattering medium have not yet been elucidated. In this paper we derive the emission intensity properties of a model dye system with excited singlet and triplet electronic energy levels, which is immersed in a multiple-scattering medium with transport mean free path l*. Using physically reasonable estimates for the absorption and emission cross section for the singlet and triplet manifolds, and the singlet-triplet intersystem crossing rate, we solve the nonlinear laser rate equations for the dye molecules. This leads to a diffusion equation for the light intensity in the medium with a nonlinear intensity-dependent gain coefficient. Using this model we are able to account for nearly all of the experimentally observed properties of laser paint reported so far when l*\ensuremath{\gg}${\ensuremath{\lambda}}_{0}$, the emission wavelength. This includes the dependence of the peak intensity of amplified emission on the mean free path l*, the dye concentration \ensuremath{\rho}, and the pump intensity characteristics. Our model recaptures the collapse of the emission linewidth at a specific threshold pump intensity and describes how this threshold intensity varies with l*. In addition, our model predicts a dramatic increase in the peak intensity and a further lowering of the lasing threshold for the strong scattering limit l*\ensuremath{\rightarrow}${\ensuremath{\lambda}}_{0}$. This suggests a striking enhancement of the characteristics of laser paint near the photon localization threshold in a disordered medium. \textcopyright{} 1996 The American Physical Society.

Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating

Nonlinear gain coefficients due to the effects of carrier heating are derived from the rate equations of carrier energy transfer in semiconductor lasers. We find that, in the modulation responses of semiconductor lasers, stimulated recombination heating will affect the resonant frequency and damping rate in a same form as the effects of spectral hole burning, while free carrier absorption heating will only affect the damping rate. The effects of injection heating and nonstimulated recombination heating are also discussed. The carrier energy relaxation time is calculated from first principles by considering the interactions between carriers and polar optical phonons, deformation potential optical phonons, deformation potential acoustic phonons, piezoelectric acoustic phonons. At the same time, the hot phonon effects associated with the optical phonons are evaluated because their negligible group velocity and finite decay time. We show that the carrier-polar longitudinal optical phonon interaction is the major channel of carrier energy relaxation processes for both electron and holes. We also point out the importance of the longitudinal optical phonon lifetime in evaluating the carrier energy relaxation time. Neglecting the finite decay time of longitudinal optical phonons will significantly underestimate the carrier energy relaxation time, this not only contradicts the experimental results but also severely underestimates the nonlinear gain coefficients due to carrier heating. The effects of spectral hole burning, stimulated recombination heating, and free carrier absorption heating on limiting the modulation bandwidth in semiconductor lasers are also discussed.

Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multi-quantum-well 1.55 μm lasers

The transverse spontaneous emission is used to characterize the gain suppression in semiconductor lasers during their operation for the first time. The carrier heating and the spectral-hole-burning are distinguished by using their different spectral behavior. The measurements show a very strong carrier heating in strained multi-quantum-well lasers which do not appear in bulk devices. Moreover, the total nonlinear gain coefficient is measured by using a modulation method; the results show a high value of ε=16.10−17 cm3 for the strained multi quantum-well laser and an usual value of ε=2.10−17 cm3 for the bulk, consistent with the measurement of gain suppression spectrum.

Semiconductor laser dynamics beyond the rate-equation approximation

Starting from the density-matrix equations, we have obtained a new set of generalized macroscopic Maxwell-Bloch equations for semiconductor lasers which can be used to study ultrafast phenomena at femtosecond time scales where the conventional rate equations are no longer valid. The band-structure details are included in these Maxwell-Bloch equations through two parameters κ and ζ which can be determined numerically by using their definitions or obtained experimentally by fitting the measured data. In the limit of ultrafast intraband relaxation (the rate-equation approximation), these equations reduce to the conventional rate equations. As an illustration of the usefulness of the new Maxwell-Bloch equations we have obtained the analytic expressions for several important laser parameters such as the differential gain, the linewidth enhancement factor and the nonlinear gain coefficient, in terms of the parameters κ and ζ when the semiconductor laser is operating continuously (the cw operation). The results obtained from these analytic expressions agree with those obtained numerically from the density-matrix equations under steady-state conditions by integrating over the density of states.

Effects of nonlinear gain on mode-hopping in semiconductor laser diodes

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. >

Nonlinear gain coefficients in semiconductor quantum-well lasers: effects of carrier diffusion, capture, and escape

Effective nonlinear gain coefficients due to the effects of carrier diffusion, capture, and escape are derived from the carrier transport equations. The quantum capture and escape processes between the confined states and the unconfined states are calculated from first principles by evaluating the carrier-polar longitudinal optical phonon interactions. The dc and ac capture times and escape times are derived from evaluating the net capture current of carriers. The differences in capture and escape times between dc and ac operating conditions are numerically investigated. We find that both dc and ac escape times are strongly dependent on the quantum well structure. This differs from the dc and ac capture times that are not sensitive to the quantum well structure. We also find that the dc escape time predicted by the classical thermionic emission theory will no longer be valid for narrow or shallow quantum wells. We show that both dc and ac capture and escape time ratios will increase as the carrier temperature and the carrier density in the quantum well increase. Therefore, we suggest that the possible cause of the resonant frequency degradation and dramatic increase in the damping rate results from the increase of the ac capture to escape time ratio by the effects of carrier heating. Two theoretical models (2N and 3N models) were used to study the effects of carrier diffusion-capture-escape on the modulation response of quantum-well lasers and a distributed model of carrier transport in quantum-well lasers is proposed. Their implications in designing high-speed quantum-well lasers are discussed. >

A method to determine the above-threshold stability of distributed feedback semiconductor laser diodes

An analysis of the above-threshold stability of distributed feedback (DFB) semiconductor laser diodes (LD's) is presented. It is based on a numerical model which takes into account effects of spatial hole burning (SHB) and the nonlinear gain coefficient. In the analysis, the Newton-Raphson (NR) technique has not been used, and no functional derivative is required. Taking into account the presence of another nonlasing mode, the single-mode stability of the DFB laser diodes is determined. The proposed model does not depend on any particular DFB structure, and hence can be applied to various DFB LD structures. Numerical results are presented for a three-phase-shift (3PS) DFB LD.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Gain nonlinearity and its temperature dependence in bulk- and quantum-well quaternary lasers

Spectrally resolved measurements of unclamped spontaneous emission above threshold in 1.3 μm InGaAsP bulk double heterostructure and compressively strained multiquantum-well lasers are analyzed using steady state rate equations. Both types of structures are characterized by nonlinear gain coefficients in the range of (2.7-3.0)×10/sup -17/ cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> at 20/spl deg/C. The nonlinear gain coefficient decreases with increasing temperature due to thermionic emission of carriers out of the active region and decreasing differential gain. The former effect was found to be more pronounced in quantum-well lasers. Excellent agreement with the rate equation based model is obtained.