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.
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 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 show experimentally that the effects of pulse delay and advancement usually ascribed to the "slow and fast light" under conditions of the coherent population oscillations (CPO) can be universally observed with incoherent light fields on objects with the pure-intensity nonlinearity. As a light source, we used an incandescent lamp and as objects for study, a photochromic glass and a thermochromic coating. The response of the objects to intensity modulation of the incident light reproduced in all details the commonly accepted experimental evidences of the "light with a negative group velocity" and "ultraslow light". Thus we show that observations of the pulse delay (advancement) and characteristic changes in the light intensity modulation spectrum are not enough to make conclusion about modification of the light group velocity in the medium.
The group velocity at which light pulses propagate through a dispersive material system is very different from the vacuum speed of light c, One refers to light as being "slow" for v g << c (Boyd & Gauthier, 2009) or "fast" for v g > c or v g <0 (Stenner et al, 2003 ).For v g <0, the pulse envelope appears to travel backward in the material (Gehring et al, 2006), and hence it is sometimes referred to as "backward light."The subject of slow light has caused keen interest in the past decade or more, and it is possible to control the group velocity of light pulses in the dispersive materials.Interest in slow and fast light dates back to the early days of the 20th century.Sommerfeld and Brillouin (Sommerfeld & Brillouin, 1960) were intrigued by the fact that theory predicts that v g can exceed c, which leads to apparent inconsistencies with Einstein's special theory of relativity.Experimental investigations of extreme propagation velocities were performed soon after the invention of the laser (Faxvog and et al, 1970).In 1999, Harris's group research work greatly stimulated researchers' interests, which showed that light could be slowed down to 17m/s.The result was obtained in ultra cold atom clouds with the use of electromagnetically induced transparency (EIT), which induces transparency in a material while allowing it to retain strong linear and nonlinear optical properties (Hau et al, 1999).Slow light can also be obtained through the use of the optical response of hot atomic vapors (Philips et al, 2001).These early research works require hard conditions and the slow light cannot operate in room temperature.Recently, researchers found ways to realize slow light operating in room temperature and solid-state materials, which are more suited for many practical applications, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.In this chapter, we describe some of the physical mechanisms that can be used to induce slow and fast light effects in room-temperature solids (Bigelow et al, 2003) and some of the exotic propagation effects that can thereby be observed.We also survey some applications of slow and fast light within the fields of quantum electronics and photonics. Fundamentals of slow and fast lightSlow and fast light refer to the group velocity of a light wave.The group velocity is the velocity most closely related to the velocity at which the peak of a light pulse moves through an optical dispersive material (Milonni, 2005), and is given by the standard result www.intechopen.comRecent Progress in Optical Fiber Research 82where n is the refractive (phase) index and ω is the angular frequency of the carrier wave of the light field.One refers to light as being slow light for v g << c, fast light for for v g > c, and backwards light for v g <0 or v g is negative.Extreme values of the group velocity invariably rely on the dominance of the second contribution to the group index of Equation ( 1).This contribution of course results from the frequency dependence of the refractive index, and for this reason extreme values of the group velocity are usually associated with the resonant or near-resonant response of material systems.According to this theory, slow light is expected in the wings of an absorption line and fast light is expected near line center, and the spatial dispersion, that is, the non-locality in space of the medium response, is another mechanism that can lead to slow light, as has been predicted (Kocharovskaya et al,2001) and observed (Strekalov et al, 2001).We catalogue the main methods to realize slow light in room temperature solid, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.We will describe CPO and SBS slow light in more details.
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.
There are two opposing models in the analysis of the slow transmission of light pulses through saturable absorbers. The canonical incoherent bleaching model simply explains the slow transmission by combined effects of saturation and of noninstantaneous response of the medium resulting in absorption of the front part of the incident pulse larger than that of its rear. The second model, referred to as the coherent-population-oscillations (CPO) model, considers light beams whose intensity is slightly pulse modulated and attributes the time delay of the transmitted pulse to a reduction of the group velocity. We point out some inconsistencies in the CPO model and show that the two models lie in reality on the same hypotheses, the equations derived in the duly rectified CPO model being local expressions of the integral equations obtained in the incoherent bleaching model. When intense pulses without background are used, the CPO model, based on linearized equations, breaks down. The incoherent bleaching model then predicts that the transmitted light should vanish when the intensity of the incident light is strictly zero. This point is confirmed by the experiments that we have performed on ruby with square-wave incident pulses and we show that the whole shape of the observed pulses agrees with that derived analytically by means of the incoherent bleaching model. We also determine in this model the corresponding evolution of the fluorescence light, which seems to have been evidenced in other experiments.