**2.2.1 Material-based slow light generation**

Within material-based methods, the exploitation of atomic resonances was the first to be discovered. Dramatic modifications of the velocity of light are often based on this principle. Highly dispersive media present extreme values of the group velocity and thus they are well

Nonetheless, from the point of view of practical applications, a more useful figure of merit (FOM) than the absolute value of the group velocity itself is the number of pulse widths that can be delayed by the system. This FOM is given by the delay-bandwidth product, being the bandwidth inversely proportional to the duration of the pulse, and it gives an idea of the information storage capacity of the system (Boyd & Narum, 2007). The delay-bandwidth product is limited by two major impediments: the pulse distortion, mainly caused by group velocity dispersion, and the propagation loss. These two factors present different origin and significance for each slow-light approach but it is a common feature to all of them that higher delays come at the expense of bandwidth reductions and, usually, of higher loss.

**Slow light techniques** 

**Electromagnetic induced transparency Coherent Population Oscillation** 

**Brillouin / Raman Scattering** 

**Metamaterials** 

**Plasmonics** 

**Engineered Structures Material-based** 

In Fig. 2 we present a classification of the different approaches to slow light.

Fig. 2. Classification of the proposed approaches to slow light

**2.2.1 Material-based slow light generation** 

How to control something that has no mass and no electric charge? These fundamental properties make the task of stopping light very challenging. However, far from being intimidated, science community has dedicated a great number of research efforts to 'trap' light. More specifically, these efforts try, not to store the photons, but the information that

In Fig. 2 slow light techniques have been separated into two subclasses: those based in modifying the waveguide dispersion by using engineered structures, such as gratings, photonic crystals or micro-ring resonators; and those based upon the change of material dispersion to large and positive values involving the use and modification of properties

Within material-based methods, the exploitation of atomic resonances was the first to be discovered. Dramatic modifications of the velocity of light are often based on this principle. Highly dispersive media present extreme values of the group velocity and thus they are well

inherent to the material, e.g. the transmission spectrum or the scattering effects.

**2.2 Techniques to achieve slow light** 

**Photonic Crystals** 

**Micro-ring resonators** 

**Cascaded Gratings / Moiré Pattern**

they carry.

suited for realizing this kind of systems, as in electromagnetically induced transparency (EIT), and coherent population oscillations (CPO). EIT and CPO have been used to create narrow transparency windows in absorbing materials. These techniques, not only allow making controllable the degree of slowing (or speeding), but they also alleviate other important issues related to strong atomic resonances: excessive absorption and dispersion.

The electromagnetically induced transparency is a quantum effect that permits the propagation of light through a medium otherwise opaque. In (Hau et al., 1999), the extremely low speed of light of 17 ms-1 was achieved by exploiting this technique. The biggest disadvantages of EIT arise because the method has a highly limited operation bandwidth owing to its narrow transparency window and to higher-order dispersion effects. Moreover EIT relies on delicate interference between two quantum amplitudes and thus the presence of collisions or any other dephasing effect can destroy the interference. On the face of it, EIT requires cryogenic temperatures and atomic media, preventing its practical use.

The quantum coherence technique of coherent population oscillations is studied as an alternative to EIT, due to its larger bandwidth and because it is highly insensitive to dephasing effects. The CPO method relies on creating a spectral hole due to population oscillations. Slow light propagation with a group velocity as low as 57.5m/s was observed employing CPO at room temperature in a ruby crystal (Bigelow et al., 2003). However, significant delays can only be achieved for signals of a few kb/s.

More recently, stimulated Brillouin and Raman scattering have also been proposed as material-based methods for slowing light. Brillouin scattering arises from the interaction of light with propagating density waves or acoustic phonons. Raman scattering arises from the interaction of light with the vibrational or rotational modes of the molecules in the scattering medium. The main advantage of these techniques is that they make use of optical fibers, which is an unmatched medium in terms of low attenuation levels. They are very adequate to provide practical moderate delays as in (Gonzalez-Herraez et al., 2005). Unluckily, Brillouin presents a limited bandwidth due to its narrow gain linewidth while Raman presents reduced slow-light efficiency.

The innovative realm of metamaterials has also been explored for developing photonic buffers. Metamaterials are artificial composites with dramatically different electromagnetic properties. The most noticeable approach to storing light in metamaterials is presented in (Tsakmakidis & Hess, 2007). So far, this theoretical approach is unfeasible due to the material losses, and, difficulty of fabrication in a light wavelength scale.

Recently, novel approaches to slow light based on plasmonics have been proposed, as in (Søndergaard & Bozhevolnyi, 2007). The main argument for using plasmonics is that it overcomes the diffraction limit affecting photonics, i.e. surface plasmon polaritons (SPPs) enable focusing light in nanoscale while photonics is size-limited to a wavelength scale. The main limitation to plasmonics today is that plasmons tend to dissipate after only a few millimetres. For sending data longer distances, the technology would need a great breakthrough. SPPs are also very sensitive to surface roughness and they are difficult to excite efficiently, although some "tricks" (e.g. Kretschmann geometry) have been already proposed for their excitation.

Photonic Band Gap Engineered Materials for Controlling the Group Velocity of Light 59

To illustrate the use of optical buffers, Fig.3 shows the schematics of a proposed design for an OPS core router. Optical packets are wavelength-demultiplexed and immediately tapped: a copy of the packet is passed to the control subsystem while the other copy must remain "stored" in the optical domain. This latter copy must be released as soon as control decisions are made to ensure efficiency. Once the packets have been optically switched to the

Not so obvious applications arise from the slow-light-based enhancement of light-matter interaction. Two facts explain this effect: on the one hand, slowly travelling photons are more likely to interact with the surrounding matter simply because it takes longer for them to go through it; on the other hand, at the very moment a light pulse enters a slow light device, its leading edge starts propagating at extraordinarily low speeds while the rest of the pulse is still propagating at normal velocities. This fact generates an accordion effect that implies spatial pulse compression and consequently an increase of local energy density and nonlinear effects. In Fig. 4 one of our simulations serves to illustrate the pulse compression and energy density increase suffered by a gaussian pulse entering in a photonic crystal slow

Optical sensing, especially biosensing, is one of the application fields most benefitted from the strengthening of light-matter interaction, since its principle relies on identifying substance changes on the basis of light-matter relations. Higher standards of sensitivity and resolution are enabled by the use of slow light in sensing devices (Biallo et al., 2007; Pedersen et al., 2008). Fig. 5 illustrates the concept of optical biosensing using a slow-light photonic crystal waveguide to improve sensitivity to the biomarkers bounded to its surface. Distributed Raman amplification is one of the nonlinear systems benefiting from slow light, with an expected efficiency improvement by a factor of 66.000 (McMillan et al., 2006). In quantum optics, as another example, slowing light down provides a mean to achieve sufficiently long storage time of quantum states to enable quantum operations (Dutton et al. 2004). Finally, it is worth to mention the role that slow light may play at improving the conversion efficiency of next generation solar cells. It is well known that recent thin film and organic photovoltaic (PV) technologies lack of a sufficient solar light-to-electrical energy conversion efficiency. By making photons travel slower within the active zone of the PV cell,

Fig. 4. Slow light photonic crystal waveguide (bottom inset), and transverse magnetic field

component of the optical wave (top inset) to illustrate pulse compression

appropriate output, optical buffers are needed to resolve possibly arising collisions.

light region from a conventional ridge waveguide.

up to a 50% increase in photon absorption (El Daif et al., 2010).
