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CRC Press eBooks

Slow and Fast Light in Semiconductors

Jacob B. Khurgin, R.S. Tucker

Published Oct 8, 2018• 0 citations
Publisher

Abstract

Coherent population oscillation (CPO) is a successful method used to implement semiconductorbased slow light using the coherent pump-probe effect. The first demonstration was carried out in semiconductormultiple quantumwells (MQWs) [1-3] soon after the experimental demonstration of slow light in ruby crystal [4,5]. Later, slow light based on CPO in semiconductor QWs and quantum dots (QDs)was also successfully demonstrated at room temperature [6-10], and the slow-light regime was soon extended to the corresponding fast-light regime in semiconductor gainmedia [11-17] using a semiconductor optical amplifier (SOA) alone or combined with an electroabsorbtion (EA) section. The basicworking principle of slow light based onmost pump-probe schemes is to decrease the group velocity vg using the sharp variation of the refractive index ∂n′/∂ω within a narrow frequency range: vg = c ng = c n′ + ω ∂n′ , (2.1) where ng = n′ + ω∂n′/∂ω is the group index n′ is the real part of the refractive index n For the CPO case, the required sharp variation of the refractive index originates from the population oscillation induced by the pump and probe signals applied to a two-level system, as indicated in Figure 2.1. The induced population oscillation generates a new polarization component and changes the susceptibility and thus the refractive index experienced by the signal. In semiconductor quantum structures, this two-level system can be the heavy-hole (HH) exciton [1-3,6,18] of QWs and QDs, or the valence and conductionground states of QDs [18,19]. In principle, as long as the optical transition between the two states is dipole-allowed, the slow light based on CPO can be implemented.

DOI
10.1201/9781315219059-7

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Coherent population oscillation (CPO) is a successful method used to implement semiconductorbased slow light using the coherent pump-probe effect. The first demonstration was carried out in semiconductormultiple quantumwells (MQWs) [1-3] soon after the experimental demonstration of slow light in ruby crystal [4,5]. Later, slow light based on CPO in semiconductor QWs and quantum dots (QDs)was also successfully demonstrated at room temperature [6-10], and the slow-light regime was soon extended to the corresponding fast-light regime in semiconductor gainmedia [11-17] using a semiconductor optical amplifier (SOA) alone or combined with an electroabsorbtion (EA) section. The basicworking principle of slow light based onmost pump-probe schemes is to decrease the group velocity vg using the sharp variation of the refractive index ∂n′/∂ω within a narrow frequency range: vg = c ng = c n′ + ω ∂n′ , (2.1) where ng = n′ + ω∂n′/∂ω is the group index n′ is the real part of the refractive index n For the CPO case, the required sharp variation of the refractive index originates from the population oscillation induced by the pump and probe signals applied to a two-level system, as indicated in Figure 2.1. The induced population oscillation generates a new polarization component and changes the susceptibility and thus the refractive index experienced by the signal. In semiconductor quantum structures, this two-level system can be the heavy-hole (HH) exciton [1-3,6,18] of QWs and QDs, or the valence and conductionground states of QDs [18,19]. In principle, as long as the optical transition between the two states is dipole-allowed, the slow light based on CPO can be implemented.
Coherent population oscillations (CPO) in quantum dots (QDs) have been utilized in this article to achieve slow and fast light effects in a semiconductor optical amplifier. These phenomena have been achieved based on a pump-probe scheme and tuning the input current source. Coupled rate equations have been developed to determine the carrier dynamics and occupation probabilities. The effects of barrier, wetting layer and excited state densities have been included for CPO phenomenon occurring between the ground states. A quantum disc model embedded in another disc has been assumed for modeling the QDs and density matrix elements are used to obtain induced polarization at the signal frequency after determining the energy states and state probabilities. Tunable absorption dip, corresponding refractive index variation and group index, exhibit widely tunable slow and fast light characteristics by changing the bias condition.
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.
We develop a model for slow light based on the coherent population oscillation of quantum dots at room temperature. With the absorption dip and corresponding variation of the refractive index due to the coherent population beating induced by the pump and probe signal, quantum dots can be used as a slow-light medium. Our theoretical model matches the experimental results very well. We also experimentally and theoretically demonstrate that both the forward-bias injection current and reverse-bias voltage can change the group index in a semiconductor quantum-dot waveguide. Our results indicate that quantum-dot devices can be potentially used as electrically and optically controllable slow light devices
We develop a theoretical model for slow light using excitonic population oscillation in a semiconductor quantum well. In a two-level system, if the resonant pump and the signal have a difference frequency within the range of inverse of the carrier lifetime, coherent population beating at this frequency will be generated. We analyze the excitonic population oscillation using an atomiclike model extended from semiconductor Bloch equations for both spin subsystems of the excitonic population and the electrical polarization density. The two spin subsystems are coupled by the excitation-induced dephasing rate, which depends on the net population difference in conduction and heavy hole quantized bands and the population exchange due to flip of the spins of electrons or holes. We present our theoretical results for the absorbance, the refractive index spectra, and the slowdown factor due to population oscillation at various pump intensities, and show very good agreement with experimental data. It is shown that a slowdown factor of $3.12\ifmmode\times\else\texttimes\fi{}{10}^{4}$ has been achieved for a semiconductor quantum-well structure. We also obtain analytical solutions from our theory and account for different response behaviors of the signal when its polarization is either parallel or orthogonal to that of the pump, which has also been confirmed by experiments.
Coherent population oscillations (CPO), an ubiquitous mechanism inducing slow and fast light (SFL), is present in any active medium provided that a strong optical beam saturates this medium. Thus, CPO must be present in any single frequency laser since the oscillating beam acts as a strong pump which saturates the active medium. This effect could be observed using an external probe whose angular frequency is detuned with respect to the oscillating mode, by less than the inverse of the population inversion lifetime. This effect should be visible in the laser excess noise, using the spontaneous emission present in the non-lasing side longitudinal modes of a single-frequency laser as probe of the CPO effect. Class-A vertical external cavity surface emitting semiconductor lasers (VECSELs) [1] recently developed for their low noise characteristics make them perfectly suited for the observation of CPO induced SFL in their noise spectrum. The single-frequency laser used in our experiment is a VECSEL which operates at ∼ 1 µm. We focus on the excess noise due to the beat notes between the laser line and the spontaneous emission noise at neighboring longitudinal mode frequencies [2,3]. At the pthFSR frequency pΔ, the noise spectrum is thus the sum of two Lorentzian peaks due to the beat notes of the lasing mode with the corresponding sidebands (pthand −pthmodes). When the pumping rate is increased, we found experimentally that the excess noise consists of two peaks separated by δf = fp− f−p∼ 100 kHz (inset of Fig.1(a)). This frequency shift is given by: δf ≈ ν0Lmover L+n0Lm(δnp+δn−p), where n0 is the bulk refractive index of the semiconductor structure, L and Lmare the length of the cavity and the gain medium respectively. δn±pare the modifications of the refractive index of the structure experienced by the ±p side modes and induced by the dispersion associated with the CPO effect. In a semiconductor active medium, thanks to the Bogatov effect [4], the dispersion is not an odd function of the frequency detuning with respect to ½0. Thus, δnp≠ −δn−pand the two beat note frequencies fpand f−pcorresponding to the p and −p modes occur at slightly different frequencies, as evidenced by the double peak of Fig.1(a). This CPO induced index modification can be derived from the gain medium rate equation including the phase-intensity coupling coefficient α (Henry's factor) that is responsible for the Bogatov effect. This CPO effect is also responsible for the modification of the refractive index seen by the side modes which modifies the round-trip phase accumulated by each side mode Fig.1(b). Notice also that since the cavity FSR Δ is sufficiently large that we are probe the wings of the dispersion profile of Fig.1(b), i. e., in the slow light regime. In conclusion, we experimentally evidenced the existence of intracavity slow light effects in a laser induced by the CPO mechanism. These effects are probed by the laser spontaneous emission noise present in the non lasing modes.
We demonstrate room-temperature slow light that is electrically and optically controllable by using a quantum-dot (QD) semiconductor optical amplifier (SOA) at zero and low bias below the transparency current. The absorption spectrum of the QD SOA exhibits a spectral dip with a corresponding group-index dispersion and group delay owing to coherent population oscillation caused by the interaction of pump and probe laser light near resonance of the first heavy-hole-conduction-state transition. At an optical pump power of approximately 0.3 mW inside the single-mode waveguide without current injection, a group-index change of 3.0 with a bandwidth of 2 GHz was measured. This group-index change can be controlled by injection of electrical current and by changing the optical pump power.