The density-matrix theory of semiconductor lasers with relaxation broadening model is finally established by introducing theoretical dipole moment into previously developed treatments. The dipole moment is given theoretically by the k . p method and is calculated for various semiconductor materials. As a result, gain and gain-suppression for a variety of crystals covering wide wavelength region are calculated. It is found that the linear gain is larger for longer wavelength lasers and that the gain-suppression is much larger for longer wavelength lasers, which results in that single-mode operation is more stable in long-wavelength lasers than in shorter-wavelength lasers, in good agreement with the experiments.

Density-matrix theory of semiconductor lasers with relaxation broadening model - Gain and gain-suppression in semiconductor lasers

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

There are three nonlinear mechanisms that can lead to filamentation in broad-area semiconductor lasers: gain-saturation-induced changes in the refractive index through the linewidth-enhancement factor, self-focusing due to heat-induced index changes, and self-defocusing through intensity-dependent index changes in the cladding layer. We present a theoretical model to analyze these mechanisms and their relative roles in destabilizing the laser output. We find that there exists a critical value for the linewidth-enhancement factor below which broad area lasers are stable for wide stripe widths (as wide as 250 /spl mu/m) and high pumping levels (as high as 20 times threshold). We also find that broad-area lasers are less susceptible to filamentation through self-defocusing and show how an intensity-dependent index in the cladding layer may be used to suppress filamentation caused by the linewidth-enhancement factor.

Nonlinear mechanisms of filamentation in broad-area semiconductor lasers

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

The traveling-wave equations of four-wave mixing in semiconductor amplifiers are solved analytically including saturation of the amplifier. Excellent agreement is obtained with numerical solutions of the traveling-wave equations. The analytical model is used to analyze a highly nondegenerate four-wave mixing experiment in a bulk semiconductor amplifier. >

Four-wave mixing in traveling-wave semiconductor amplifiers

All optical frequency converters are key devices for new-conception optical networks A theoretical model is presented to evaluate performances of frequencies converters based on highly nondegenerate four-wave mixing (FWM) in semiconductor amplifiers Conversion efficiency and noise performances are evaluated in generic saturation conditions and compared with experimental results >

Efficiency and noise performance of wavelength converters based on FWM in semiconductor optical amplifiers

We present a computer simulator of semiconductor optical amplifiers. The nonlinear input-output response of the device is characterized in terms of a complex gain, representing the accumulated gain and wavevector change of the propagating field across the active waveguide. We account for the gain saturation induced by stimulated recombination and by the perturbation of the carrier quasi-equilibrium distribution within the bands. A rigorous elimination of the spatial coordinate allows us to reduce the description of the amplifier dynamics to the solution of a set of ordinary differential equation for the complex gain. If the waveguide internal loss is negligible, the spatial inhomogeneity of the complex gain is implicitly yet exactly taken into account by the reduced model. The accuracy of the reduced model is the same for models based on the direct solution of the set of partial differential equations describing the interaction between the optical field and the active semiconductor waveguide, but the model is computationally much simpler. To preserve the input-output characteristics of the model, we include the amplified spontaneous emission noise in the device description by an equivalent signal applied to the device input and amplified by the saturated gain. At the expense of a minor increase of the program complexity, the waveguide internal loss may also be included. We report on the comparison between the output of the simulator and the results of four-wave mixing experiments in various pump-signal configurations. Good agreement is obtained.

A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers

Four-wave mixing in semiconductor optical amplifiers is used to produce wavelength conversion. We report an extended study on the dependence of efficiency and noise on device length, pump power, operation wavelength and conversion interval. The use of longer active regions is a good way to obtain performance as good as requested by the most advanced telecommunication systems.

Four-wave mixing in semiconductor optical amplifiers: a practical tool for wavelength conversion

Very high four-wave mixing (FWM) efficiency and signal-to-background ratio (SBR) are obtained in a 1.5-mm-long bulk semiconductor optical amplifier. The FWM efficiency is measured to be 5 dB at 1-THz pump-signal detuning, which is the highest value reported to date. With a pump power of -1.4 dBm, the SBR is in excess of 20 dB in a bandwidth of 12.5 GHz, for a pump-signal detuning range as large as 2 THz and the efficiency is under the same conditions larger than -1 dB for a pump-signal detuning range as large as 1 THz. These results make FWM an attractive method for practical wavelength conversion. Some low-detuning measurements show a maximum efficiency around 8 GHz.

S. Scotti

Papers

Four-wave mixing in traveling-wave semiconductor amplifiers

Efficiency and noise performance of wavelength converters based on FWM in semiconductor optical amplifiers

A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers

Four-wave mixing in semiconductor optical amplifiers: a practical tool for wavelength conversion

Low-noise and very high-efficiency four-wave mixing in 1.5-mm-long semiconductor optical amplifiers