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Frontiers in Optics

Why Do Coherent Population Oscillations (CPOs) Lead to Slow Light When the Laser Linewidth Exceeds the Width of the CPO Transparency Window?

Giovanni Piredda, Robert W. Boyd

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We derive coherent population oscillations (CPO) from the rate equations, showing that it is possible to slow down light using CPO even if the laser linewidth exceeds the width of the CPO transparency window.
DOI
10.1364/ls.2006.ltuj3

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Several groups have recently reported the observation of slow light propagation speeds based on the process of coherent population oscillations (CPO) under conditions such that the laser line width exceeds the width of the CPO transparency window. We explain this apparently paradoxical result by noting that the CPO effect is sensitive only to intensity variations of the incident laser field that occur on time scales comparable to or shorter than the population relaxation time of the material medium. Laser linewidths are associated primarily with phase fluctuations or with intensity fluctuations on much shorter time scales.
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), 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.