The type of slow light waveguides described in the previous section is only one example of what are also called zero-dispersion waveguides: the disper- sion of the basic W1 waveguide is flattened by playing on the coupling be- tween two modes, which is varied simply by introducing small modifications to the first rows of holes. Early examples of this type of approach involved narrowing the waveguide width (W0.x) to improve the dispersion [69, 84] but, in real devices, narrower waveguides are usually associated with higher scattering loss [74], as the optical mode has greater overlap with the air holes.
As already mentioned, the most common approaches to flatten the mode dispersion rely on the alteration of the first rows of holes by changing their radius [65,87] (Fig. 2.9a) or position, either along the normal [28] (Fig. 2.6a) or the longitudinal [66,88] (Fig. 2.9b) direction. These three mechanisms all achieve similar delay-bandwidth products [89], but for practical applications
the holes position can be controlled more accurately [30] than the radius [90], because the hole size is influenced by many parameters during the fabrication process.
Other examples, mainly numerical, of zero-dispersion techniques that have been proposed in the literature involve introducing high-index pillars inside the holes [91], or infiltrating them with liquid [92] or other dielec- tric material [93]. Some authors proposed breaking the symmetry of the waveguide [94, 95] so that the dispersion can be controlled through an anti- crossing of the even mode with the odd mode. Other proposals involve alter- ing the basic lattice itself, for instance by using elliptical [96] or even ring- shaped [97] holes, or by changing the lattice from triangular to oblique [98]. A second type of approach to suppress higher-order dispersion in slow light devices is that of dispersion-compensated structures: instead of de- signing the waveguide with a flattened dispersion curve, a dispersive slow light waveguide is followed by one with opposite dispersion, so that the two compensate each other. The transition from one waveguide type to the other is not abrupt but smooth, and it is obtained by chirping one of the design parameters — usually the hole radius — along the device, resulting in a gradual shift of the band diagram [99, 100]. Dispersion-compensated devices usually do not consist of a single waveguide, but of two parallel waveguides, coupled to each other. In some early studies, the two parallel waveguides were designed to exhibit opposite dispersion [101–103], but one important requirement was for the waveguides to match exactly their band edges, making the final device very sensitive to fabrication tolerances.
A more established design makes use of two identical coupled waveguides (Fig. 2.9c): the resulting even super-mode exhibits an inflection point in the dispersion curve, providing slow light [104] (Fig. 2.9d, left). This method of dispersion engineering is again based on the interaction of two modes, but in this case the two original modes belong to two separate waveguides. By chirping of the hole radius along the propagation direction, the inflection point is gradually shifted in frequency (Fig. 2.9d, middle and right), broad- ening the slow light condition [67,86], and different wavelengths are therefore slowed down in different regions of the device. This type of structure has been very successfully employed to demonstrate tunable slow light devices by introducing an additional thermally-controlled variable chirp [85, 105, 106], as we will discuss in more detail in Chapter 3.
The design of chirped photonic crystal coupled waveguides, however, is more complicated than for the simple zero-dispersion structures, as it requires optimisation of many parameters. In addition, while this approach is very suitable for delay devices, it cannot be employed for enhancement of nonlinear effects: the structure itself is bigger than a single W1 waveguide and, due to the initial dispersion, which is then later recovered, an optical pulse is broadened, rather than compressed, in space. In fact, suppression of optical nonlinearities has been highlighted as a positive feature of these
2.2 Slow light in photonic crystal waveguides
Figure 2.10: Examples of CROWs (from [107]). (a) Schematic of a generic CROW. (b) Design of a CROW based on width-modulated cavities. (Reprinted by permis- sion from Macmillan Publishers Ltd: Nature Photonics [107], copyright 2008.)
devices [25], which is desirable when employing slow light structures for linear applications.
Finally, the third type of approach that has been proposed for achieving structural slow light in photonic crystals is the use of a sequence of coupled cavities (coupled resonators optical waveguide, CROW, Fig. 2.10): as light propagates through the structure, it is localised at each cavity, introducing a time delay [108]. Numerous works have reported studies on the dispersion of these slow light waveguides, both theoretical/numerical [109–112] and experimental [113–116]. The most impressive demonstrations of CROWs in photonic crystals are probably those reported by Notomi and co-workers (Fig. 2.10b), who realised large arrays of up to 100 [107] and 200 [117] ultrahigh-Qcavities, which were also employed to demonstrate enhancement of nonlinear effects such as four-wave mixing [117].
One issue of CROWs in photonic crystals, however, is that the regular spacing of the cavities introduces a second periodicity on the lattice, cor- responding to an additional folding of the bands in the k-space, and as a consequence light can easily couple to the radiation modes above the light line [25]. More importantly, the precise control of both the inter-cavity coupling and the optical resonances of each cavity (which should be iden- tical) at the same time is a huge challenge in photonic crystals, once again due to disorder and non-idealities introduced during the fabrication pro- cess [118]: even in some of the best reported results [107], oscillations in the transmission band on the order of 20–30 dB are unavoidable. This type of slow light structures is therefore probably more suited for use with ring resonators [119–122], where the control of individual resonances is more straightforward and reliable [123] than in photonic crystals.
Figure 2.11: Schematic of the standard fabrication steps for photonic crystal wave- guides. (a) The SOI substrate. (b) The e-beam resist ZEP is spun on the sample. (c) The photonic crystal pattern is defined on the ZEP layer through e-beam writ- ing. (d) The pattern is transferred from the ZEP mask to the silicon layer through the dry-etch process RIE. (e) The ZEP mask is removed. (f) The silica layer is re- moved by wet-etch in HF solution, releasing the silicon photonic crystal membrane.