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

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 strained wurtzite GaN quantum-well lasers

We present a comprehensive model for the calculation of the bandedge profile of both the In/sub 1-x/Ga/sub x/As/sub y/P/sub 1-y/ and In/sub 1-x-y/Ga/sub x/Al/sub y/As 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.

Theory and experiment of In/sub 1-x/Ga/sub x/As/sub y/P/sub 1-y/ and In/sub 1-x-y/Ga/sub x/Al/sub y/As long-wavelength strained quantum-well lasers

We have studied experimentally and theoretically the spontaneous emission from 1.3- and 1.5-/spl mu/m compressively strained InGaAsP multiple-quantum-well lasers in the temperature range 90-400 K to determine the variation of carrier density n with current I up to threshold. We find that the current contributing to spontaneous emission at threshold I/sub Rad/ is always well behaved and has a characteristic temperature T/sub 0/ (I/sub Rad/)/spl ap/T, as predicted by simple theory. This implies that the carrier density at threshold is also proportional to temperature. Below a breakpoint temperature T/sub B/, we find I /spl alpha/ n/sup Z/, where Z=2. And the total current at threshold I/sub th/ also has a characteristic temperature T/sub 0/ (I/sub th/)/spl ap/T, showing that the current is dominated by radiative transitions right up to threshold. Above T/sub B/, Z increases steadily to Z/spl ap/3 and T/sub 0/ (I/sub th/) decreases to a value less than T/3. This behavior is explained in terms of the onset of Auger recombination above T/sub B/; a conclusion supported by measurements of the pressure dependence of I/sub th/. From our results, we estimate that, at 300 K, Auger recombination accounts for 50% of I/sub th/ in the 1.3-/spl mu/m laser and 80% of I/sub th/ in the 1.5-/spl mu/m laser. Measurements of the spontaneous emission and differential efficiency indicate that a combination of increased optical losses and carrier overflow into the barrier and separate confinement heterostructure regions may further degrade T/sub 0/ (I/sub th/) above room temperature.

The temperature dependence of 1.3- and 1.5-/spl mu/m compressively strained InGaAs(P) MQW semiconductor lasers

We propose and analyze a strain-balanced GezSn1-z-SixGeySn1-x-y multiple-quantum-well (MQW) laser. By incorporating a proper amount of -Sn into Ge, a direct-bandgap GeSn alloy can be realized to achieve population inversion in the direct conduction band. The introduction of compressive strain into the GeSn QW can effectively modify the valence band structure to reduce the threshold carrier density. We calculate the electronic band structure and the polarization-dependent optical gain of the strained GezSn1-z-SixGeySn1-x-y MQW laser taking into account the effect of the L-conduction bands. We also present our waveguide design for index guidance and calculate the optical confinement factors of various regions. Our calculation indicates that the modal gain can reach the threshold condition and lead to lasing action.

Strain-Balanced ${\rm Ge}_{z}{\rm Sn}_{1-z}\hbox{--}{\rm Si}_{x}{\rm Ge}_{y}{\rm Sn}_{1-x-y}$ Multiple-Quantum-Well Lasers

Amplified spontaneous emission spectroscopy is used to extract the gain and refractive index spectra systematically. We obtain the gain and differential gain spectra using the Hakki-Paoli method. The refractive index profile, the induced change in refractive index by an incremental current, and the linewidth enhancement factor are measured from the Fabry-Perot peaks and the current-induced peak shifts in the amplified spontaneous emission spectra. The measured optical gain and refractive index are then compared with our theoretical model for strained quantum-well lasers. We show that a complete theoretical model for calculating the electronic band structure, the optical constant, and the linewidth enhancement factor agrees very well with the experiment. Our approach demonstrates that amplified spontaneous emission spectroscopy can be a good diagnostic tool to characterize laser diodes, extract the optical gain and index profiles, and confirm material parameters such as the strained quantum-well band structure parameters for a semiconductor structure under carrier injection.

Amplified spontaneous emission spectroscopy in strained quantum-well 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.

Theory and experiment on the amplified spontaneous emission from distributed-feedback lasers

A consistent method to characterize the temperature dependence of bulk InGaAsP semiconductor laser diodes is presented. Independent measurements of the gain and spontaneous emission spectra are conducted, and the spectra are calibrated using their fundamental relationship. This procedure will provide a unique approach to extract precise values for laser diode parameters such as quasi-Fermi level separation, peak modal gain, and total loss. The radiative and nonradiative current densities can then be calculated as a function of temperature and injection current. By comparing the measured data with a theoretical model, the carrier density is calculated. Important phenomena contributing to the strong temperature dependence of long-wavelength bulk InGaAsP/InP lasers are highlighted.

Analysis of temperature sensitivity in semiconductor lasers using gain and spontaneous emission measurements

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).

J. Minch

Papers

Theory and experiment of In/sub 1-x/Ga/sub x/As/sub y/P/sub 1-y/ and In/sub 1-x-y/Ga/sub x/Al/sub y/As long-wavelength strained quantum-well lasers

Amplified spontaneous emission spectroscopy in strained quantum-well lasers

Theory and experiment on the amplified spontaneous emission from distributed-feedback lasers

Analysis of temperature sensitivity in semiconductor lasers using gain and spontaneous emission measurements

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