1. Semiconductor Laser Diodes 2. Basic Concepts 3. Free-Carrier Theory 4. Coulomb Effects 5. Many-Body Gain 6. Band Mixing and Strain in Quantum Wells 7. Semiclassical laser Theory 8. Multimode Operation 9. Quantum Theory of the Laser 10. Propagation Effects 11. Beyond Quasiequilibrium Theory, Appendices A-e, Index

Semiconductor-Laser Physics

We present a simple, yet powerful method for calculating nonlinear pulse propagation and pulse interaction in active semiconductor waveguides. The model is based on the density matrix equations, which under realistic operation conditions are shown to lead to an accurate description of the material gain, that includes the dynamics of carrier heating and spectral-hole burning (SHB). A very general and compact description of the amplifier dynamics in terms of an integral equation is derived. The model is used to analyze saturation effects in short pulse amplification and nondegenerate four-wave mixing. An analytical expression for the four-wave mixing response is derived, which extends previous results to the case of short and intense pulses. Saturation of the four-wave mixing signal is shown to be strongly pulsewidth dependent due to ultrafast gain dynamics, and self-phase modulation is shown to give excessive broadening of the conjugate pulse. Finally, the impacts on the noise characteristics are calculated and shown to explain recent experimental results.

Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers

Subpicosecond gain and index nonlinearities in InGaAsP diode lasers

The merging of continuous wave laser-based precision optical-frequency metrology with mode-locked ultrafast lasers has led to precision control of the visible and near-infrared frequency spectrum produced by mode-locked lasers. Such a phase-controlled mode-locked laser forms the foundation of a "femtosecond optical-frequency comb generator" with a regular comb of sharp lines with well-defined frequencies. For a comb with sufficiently broad bandwidth, it is now straightforward to determine the absolute frequencies of all of the comb lines. This ability has revolutionized optical-frequency metrology, synthesis, and optical atomic clocks. Precision femtosecond optical-frequency combs also have a major impact on time-domain applications, including carrier-envelope phase stabilization, synthesis of a single pulse from two independent lasers, nonlinear spectroscopy, and passive amplifiers based on empty external optical cavities. The authors first review the frequency-domain description of a mode-locked laser and the connection between the carrier-envelope phase and the frequency spectrum to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical-frequency metrology and synthesis and optical atomic clocks are discussed. This is followed by discussions of time-domain experiments.

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Optical frequency combs: from frequency metrology to optical phase control

Four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) is an important tool for frequency conversion and fast optical switching in all-optical communication networks. We review the main applications of SOAs as nonlinear optical components. Concentrating on FWM, we define general parameters that are of relevance for signal processing applications. We show, how basic experiments and general simulation procedures can be used to determine optimum operating conditions for the intended applications. Besides a comprehensive investigation of FWM among continuous waves, we present new experimental results on FWM with picosecond optical pulses. A comparison of both reveals a different behavior and demonstrates that new optimization criteria and advanced theoretical models have to be applied for the case of short optical pulses. Moreover, we discuss the possibility to extract the dynamical SOA parameters from our experiments.

Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching

We present detailed derivation of our new model for femtosecond pulse amplification in semiconductor laser amplifiers. The various dynamic nonlinear terms of gain compression and associated self-phase modulation are derived semiphenomenologically, and are discussed physically. Included are the effects of carrier depletion, carrier heating and spectral hole-burning, as well as linear and two photon absorption and the instantaneous nonlinear index. Additionally, we account for dynamically changing gain curvature and slope. We apply the theory to strong signal cross-phase-cross-gain modulation experiments with /spl sim/500 fs pulses in a broad area GaAs amplifier and show that the model accurately describes the observed complex phenomena. We also present experimental results on single beam strong signal amplification in two different quantum-well amplifiers using 150-200 fs duration pulses. For such pulse lengths, carrier heating becomes an integrating nonlinearity and its self-phase modulation is similar to that due to carrier depletion. Additionally, since the pulse spectrum is broad, the gain slope and curvature shift and narrow it. The resultant spectral distortions are very different than observed (and modeled) earlier for the /spl sim/500 fs pulses. The model is again able to correctly describe the evolution of these ultrashort pulses, indicating that it remains valid, even though pulse durations approach the intraband relaxation time.

Femtosecond self- and cross-phase modulation in semiconductor laser amplifiers

We present a phenomenological model of subpicosecond pulse evolution in semiconductor laser amplifiers, which includes carrier heating effect, gain dispersion, gain saturation, and three kinds of self-phase modulations (SPM). The results obtained from this model are applied to and found to agree very well with experimental measurements of spectral distortions and time-resolved gain on a semiconductor laser amplifier with 460-fs and 2-ps input pulses. The device parameters that are used to match the experimental results are within a reasonable range, either suggested by previous experiments or by published calculations, The results show that the evolution of the pulses and their spectra is sensitively dependent on the input pulse shape and on a variety of time domain and frequency domain amplitude and phase shaping effects. Matching the theory to the experimental data suggests that among the possible causes of the carrier heating two-photon absorption (TPA) is the most important. This effect of TPA needs to be included to properly account for the observed dependence of the carrier heating gain reduction on the pulse length. By examining separately the contribution of the corresponding terms, we also prove the importance of SPM due to the carrier heating and to the instantaneous nonlinear index in shaping the output spectrum. We compare our model with Agrawal's theory, which is valid for pulses of tens of picosecond duration, and find large differences for subpicosecond pulses. For 2-ps pulses, on the other hand, the differences are fewer and less dramatic. The good agreement of the new model with experiments will now allow diagnostics and predictions of pulse evolution in semiconductor optical amplifiers from the picosecond to the subpicosecond range. >

Subpicosecond pulse amplification in semiconductor laser amplifiers: theory and experiment

We describe the generation of femtosecond high power optical pulses using hybrid passive-active mode-locking techniques. Angle stripe geometry GaAs/AlGaAs semiconductor laser amplifiers are employed in an external cavity including prisms and a stagger-tuned quantum-well saturable absorber. An identical amplifier also serves as an optical power amplifier in a stretched pulse amplification and recompression sequence. After amplification and pulse compression this laser system produces 200 fs, 160 W peak power pulses. We discuss and extend our theory, and supporting phenomenological models, of picosecond and subpicosecond optical pulse amplification in semiconductor laser amplifiers which has been successful in calculating measured spectra and time-resolved dynamics in our amplifiers. We have refined the theory to include a phenomenological model of spectral hole-burning for finite intraband thermalization time. Our calculations are consistent with an intra-band time of approximately 60 fs. This theory of large signal subpicosecond pulse amplification will be an essential tool for understanding the mode-locking dynamics of semiconductor lasers and for analysis of high speed multiple wave-length optical signal processing and transmission devices and systems based on semiconductor laser amplifiers.

Femtosecond hybrid mode-locked semiconductor laser and amplifier dynamics

The evolution of ultrashort pulses in semiconductor laser amplifiers is modeled, including the effects of gain dispersion, slow and fast carrier dynamics, and self-phase modulation, which includes an instantaneous response (n2). The temporal and spectral evolution of 2-ps and 500-fs pulses differ considerably. This is due mainly to saturation caused by the fast (heating) dynamics and to the phase modulation by n2.

Time- and spectral-domain evolution of subpicosecond pulses in semiconductor optical amplifiers.

Recent experimental progress in high power modelocked semiconductor lasers together with the discovery of subpicosecond time scale gain and index dynamics in semiconductor amplifiers has underscored the need for an improved theory of amplification in these devices that correctly accounts for TeraHertz bandwidths and high intensities The authors present an improved and more general version of their theoretical model for femtosecond pulse amplification in a SLA that includes the influence of finite intraband relaxations time Comparison of calculation with a sequence of experiments on an angle stripe geometry SLA show excellent agreement and give parameter values that are all reasonable and also give information on the underlying physics The propagation of the pulse in the SLA is described by a nonlinear equation for the time domain pulse envelope which includes both intensity and phase shaping effects as well the rapid gain and phase dynamics which have been observed through pump-probe experiments >

Y.H. Chang

Papers

Femtosecond self- and cross-phase modulation in semiconductor laser amplifiers

Subpicosecond pulse amplification in semiconductor laser amplifiers: theory and experiment

Femtosecond hybrid mode-locked semiconductor laser and amplifier dynamics

Time- and spectral-domain evolution of subpicosecond pulses in semiconductor optical amplifiers.

Subpicosecond pulse amplification in semiconductor laser amplifiers