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

Theoretical results on wave mixing in traveling-wave semiconductor laser amplifiers are presented. Starting from rather general density-matrix equations, including the effects of carrier-density pulsations, carrier heating, and spectral-hole burning, we derive equations capable of treating the range from nearly degenerate to highly nondegenerate four-wave mixing. The equations are solved numerically, and comparison to published experimental results is made. The theoretical results explain different experimental results, which have been taken to support either the role of spectral-hole burning or that of carrier heating in mediating wave mixing under highly nondegenerate conditions. >

Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning

Recent progress in optical time-division-multiplexed (TDM) transmission technologies is reviewed including optical short pulse generation, time-division multiplexing/demultiplexing, timing extraction, and waveform measurement. The latest 400-Gbit/s transmission experiments based on optical signal processing are presented and the possibility of terabit/second TDM transmission is discussed.

Ultrahigh-speed optical time-division-multiplexed transmission technology based on optical signal processing

This paper reviews the recent progress of quantum-dot semiconductor optical amplifiers developed as ultrawideband polarization-insensitive high-power amplifiers, high-speed signal regenerators, and wideband wavelength converters. A semiconductor optical amplifier having a gain of > 25 dB, noise figure of 20 dBm, over the record widest bandwidth of 90 nm among all kinds of optical amplifiers, and also having a penalty-free output power of 23 dBm, the record highest among all the semiconductor optical amplifiers, was realized by using quantum dots. By utilizing isotropically shaped quantum dots, the TM gain, which is absent in the standard Stranski-Krastanow QDs, has been drastically enhanced, and nearly polarization-insensitive SOAs have been realized for the first time. With an ultrafast gain response unique to quantum dots, an optical regenerator having receiver-sensitivity improving capability of 4 dB at a BER of 10-9 and operating speed of > 40 Gb/s has been successfully realized with an SOA chip. This performance achieved together with simplicity of structure suggests a potential for low-cost realization of regenerative transmission systems.

Quantum-Dot Semiconductor Optical Amplifiers

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

Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect. >

Observation of highly nondegenerate four-wave mixing in 1.5 mu m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient

The differential gain and the linewidth enhancement factor of 1.5- mu m multiple-quantum-well (MQW) active layers were measured with and without biaxially compressive strain as functions of the wavelength and the carrier density. These parameters of the strained MQW layer reveal stronger carrier-density dependence than those of the unstrained MQW layer. Most significantly, an anomalous increase in the linewidth enhancement factor is observed at high carrier densities. These characteristics are explained by a simple theoretical analysis. >

T.-P. Lee

Papers

Observation of highly nondegenerate four-wave mixing in 1.5 mu m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient

Differential gain and linewidth enhancement factor of 1.5- mu m multiple-quantum-well active layers with and without biaxially compressive strain