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Applied Optics

Four-wave mixing in quantum dot semiconductor optical amplifiers

Ahmed H. Flayyih, Amin Habbeb AL-Khursan

Published May 6, 2013• 14 citations
Publisher

Abstract

The theory of four-wave mixing (FWM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is discussed by combining the QD rate equations system, the quantum-mechanical density-matrix theory, and the pulse propagation in QD SOAs including the three region of QD structure ground state (GS), excited state (ES), and wetting layer. Also, relations for differential gain, gain integral, and nonlinear susceptibility of both pump, probe, and signal pulses were discussed. Gain and differential gain have been calculated for QD structure. FWM efficiency and its components [spectral hole burning (SHB), carrier heating, and carrier density pulsation] are calculated. It is found that inclusion of ES in the formulas and in the calculations is essential since it works as a carrier reservoir for GS. It is found that QD SOA with enough capture time from ES to GS will reduce the SHB component, and so it is suitable for telecommunication applications that require symmetric conversion and independent detuning.

DOI
10.1364/ao.52.003156

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The theory of four-wave mixing (FWM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is discussed by combining the QD rate equations system, the quantum-mechanical density-matrix theory, and the pulse propagation in QD SOAs including the three region of QD structure ground state (GS), excited state (ES), and wetting layer. Also, relations for differential gain, gain integral, and nonlinear susceptibility of both pump, probe, and signal pulses were discussed. Gain and differential gain have been calculated for QD structure. FWM efficiency and its components [spectral hole burning (SHB), carrier heating, and carrier density pulsation] are calculated. It is found that inclusion of ES in the formulas and in the calculations is essential since it works as a carrier reservoir for GS. It is found that QD SOA with enough capture time from ES to GS will reduce the SHB component, and so it is suitable for telecommunication applications that require symmetric conversion and independent detuning.
The Pulse effect on the cross-gain modulation (XGM) in the quantum dot (QD) semiconductor optical amplifiers (SOAs) is investigated using the combining of the SOA power with the QD rate equations system. The QDs structure includes three regions: ground state (GS), excited state (ES) and wetting layer (WL). Thus, a set of rate equations for pump and probe signals is introduced for both steady-state and small-signal power values, which are solved numerically. The pulse shape was included in the analysis, for pump and probe signals. The theoretical results showed a good agreement with the experimental results. It was found that decreasing pulse width of pump/probe ratio is efficient to increase XGM efficiency and bandwidth.
Using a self-consistent delay-differential-equation model for the description of the nonlinear light propagation in InAs/InGaAs quantum-dot-in-a-well semiconductor optical amplifiers, we analyze the amplifier in a four-wave-mixing setup in terms of the conversion efficiency. Our model allows us to extract the hierarchy of nonlinear effects that constitute the four-wave-mixing process. We show that spectral hole burning in the quantum-dot medium facilitates wavelength conversion over a spectral detuning of several THz, whereas the effect of carrier heating and global carrier-density pulsations is found to be negligible. Furthermore we show that for high optical field amplitudes the emergence of Rabi oscillations leads to a flattening of the conversion efficiency, potentially allowing for ultra-broadband wavelength conversion and frequency comb generation.
In this work, the ultrafast gain dynamics of a quantum dot (QD)-based semiconductor optical amplifier (SOA) is modeled on the basis of semiconductor Bloch equations that include microscopically calculated nonlinear scattering rates between QD carriers and the surrounding carrier reservoir. This enables us to separately study the dynamics of electrons and holes inside the device as well as the coherent effects related to the fast polarization dynamics. We show that the optical pulse power and the dephasing time of the polarization mainly affect the gain depletion inside the active region, while the electric injection current density and thus the internal carrier dynamics influence the gain recovery. We observe that carrier–carrier scattering is the source of desynchronized behavior of electrons and holes in the recovery dynamics of QD-based SOAs. The amplification of pulse trains in the SOA predicted by our model agrees well with experimental data.
Quantum dot (QD)-based semiconductor optical amplifiers offer unique properties compared with conventional devices based on bulk or quantum well material. Due to the bandfilling properties of QDs and the existence of a nearby reservoir of carriers in the form of a wetting layer, QD semiconductor optical amplifiers may be operated in regimes of high linearity, i.e. with a high saturation power, but can also show strong and fast nonlinearities by breaking the equilibrium between discrete dot states and the continuum of wetting layer states. In this paper, we analyse the interplay of these two carrier populations in terms of a simple rate equation model. Based on the steady-state and small-signal properties of the model, we analyse and discuss the optical modulation response and the four-wave mixing properties of QD semiconductor optical amplifiers, in particular emphasizing the role of ultrafast gain dynamics.
Slow and fast light in quantum-well (QW) and quantum-dot (QD) semiconductor optical amplifiers (SOAs) using nonlinear quantum optical effects are presented.We demonstrate electrical and optical controls of fast light using the coherent population oscillation (CPO) and four wave mixing (FWM) in the gain regime of QW SOAs.We then consider the dependence on the wavelength and modal gain of the pump in QW SOAs.To enhance the tunable photonic delay of a single QW SOA, we explore a serial cascade of multiple amplifiers.A model for the number of QW SOAs in series with variable optical attenuation is developed and matched to the experimental data.We demonstrate the scaling law and the bandwidth control by using the serial cascade of multiple QW SOAs.Experimentally, we achieve a phase change of 160 • and a scaling factor of four at 1 GHz using the cascade of four QW SOAs.Finally, we investigate CPO and FWM slow and fast light of QD SOAs.The experiment shows that the bandwidth of the time delay as a function of the modulation frequency changes in the absorption and gain regimes due to the carrier-lifetime variation.The tunable phase shift in QD SOA is compared between the ground-and first excited-state transitions with different modal gains.
Summary form only given. Significant progress has been obtained on quantum dot (QD) lasers, but the possible advantages of QD amplifiers are not yet clear. We show here that a relatively slow coupling between the optically active QD carrier states and the surrounding carrier reservoir can lead to efficient gain modulation suitable for ultrafast signal processing. The basis of this property is that the process of spectral hole burning (SHB) can become very effective. We consider a traveling wave optical amplifier consisting of the dot states, which interact with the optical signal (no inhomogeneous broadening included), and the wetting layer (WL), where current is injected. Time evolution is described by two coupled rate equations. Carrier capture from WL to dots is characterized by the capture time /spl tau//sub 0/.