# An Introduction to Nonlinear Integrated Photonics: Structures and Devices
## 2 Integrated Photonic Structures
### Microresonators and Photonic Crystals  
During recent decades, the fast growth of micro-scale fabrication techniques has enabled successful demonstration of various types of microphotonic devices; special attention  
Figure 1: Schematic representation of various channel waveguides. Adapted from [63] under Creative Commons License 3.0.  
has been addressed to microcavities [66; 67], such as whispering gallery modes resonators (WGMR) and photonic crystals (PhC) [68; 69], which combine small modal volume with very high optical quality factor (Q). In these microphotonic devices, due to their reduced size, photons are trapped in small volumes close to the diffraction limit for sufficiently long times so that these photons strongly interact with the host material, creating enhanced nonlinear effect and significant reduction in their power threshold [66; 67; 68; 69]. WGMRs have shown high mode stability and ultra-high-quality factors Q, up to \(10^{11}\). These resonators are excellent platforms for fundamental and applied studies of nonlinear processes due to their long photon lifetimes (temporal confinement) and their small mode volumes (spatial confinement) [70; 71; 72; 73; 74]. Temporal and spatial confinement have made possible optical frequency conversion with low-power continuous-wave (CW) lasers with powers ranging from micro-watts to milliwatts. However, the high circulating intensities inside a WGMR are not a sufficient condition for efficient harmonic generation, parametric, and hyper-parametric oscillations: these phenomena require fulfilling phase and mode matching and energy conservation conditions [75; 71]. Figure 2 shows different types of optical microcavities. It must be underlined that, even if more difficult to integrate in a compact structure, microspherical resonators play an important role in nonlinear photonics [70; 71; 76]. Photonic crystals provide an excellent building block for photonic integrated circuits and for enhancing a variety of nonlinear optical processes as well [77; 78; 79; 80; 81]. A strong advantage of PhC cavities with ultra-small-mode volume V\({}_{\rm m}\) is that quality factors can be relaxed while still achieving excellent Q/V\({}_{\rm m}\) values; despite the fact that the quality factor is inversely proportional to the linewidth of the cavity, both high-bandwidth and low-threshold all-optical processes can be realized in a single system. Integration issues, of course, must be considered in the case of PhCs as well, especially for 3D structures [80]. Figure 3 shows the design of a dispersion-engineered slow-light photonic crystal waveguide (PhCW); the blue circles represent the air-holes in a standard single-line defect (W1) PhCW with a lattice constant a, while the red circles represent the engineered air-holes, with radius decreasing from R to R2 and horizontally shifted from the dashed circles by \(\Delta\)X [81]. Guided waves can also result from coupling between an electromagnetic field and resonance related to material properties. For example, plasma resonance associated with the electron gas in a metal can be coupled to an electromagnetic field via the interaction between the field and the charges, leading to surface plasmon. These surface waves, propagating along the dielectric-conductor interface, are evanescently confined in the perpendicular  
Figure 2: Different types of optical microcavities: (**a**) micro-ring resonator, (**b**) micro-toroid resonator, (**c**) micro-sphere resonator. Adapted from [76] under Creative Commons License 3.0.  
direction due to very shallow penetration of the electromagnetic field into the metal. Plasmonic waveguiding allows breaking the diffraction limit of light, opening possibilities for subwavelength light confinement. To increase integration density and compactness of photonic structures, many different geometries of plasmonic waveguide have been investigated in recent years, including interferometers and ring resonators [82] and periodic metal structures [83].