# An Introduction to Nonlinear Integrated Photonics: Structures and Devices
## 2 Integrated Photonic Structures
### Microresonators and Photonic Crystals
However, in all cases, energy dissipation in closely spaced metal layers causes high losses, limiting the propagation length to a few micrometers. Nanophotonics is another fascinating field, investigating the light behavior on the nanometer scale and its interaction with nanometer-scale objects [84; 85; 86]. Major demand in the near future is expected for devices that should allow to control light with light in a very thin nanoscale layer or in a single nanoparticle of nonlinear material. During the past few decades, a significant number of nanomaterials have shown notable optical properties, motivating fabrication and design of nanoscale photonic devices [87; 88]. Electromagnetic metamaterials are artificial media in which subwavelength electromagnetic constituents replace atoms as the basic structural elements to control light-matter interaction. Many novel phenomena related to metamaterials are due to optical magnetism, observed in specifically designed artificial subwavelength structures, even when such structures are made of non-magnetic materials. The most popular constitutive elements of metamaterials are made of metals, where free electrons oscillate back and forth, creating effective loops of current, thus inducing an efficient magnetic response. Plasmonic nanostructures support field localization due to localized surface-plasmon resonances with multipolar electric-type characteristics. The plasmonic resonances, generally, result in high field enhancement but at the price of higher absorption losses due to free-carrier absorption and reduced optical damage thresholds [89; 90]. In order to control light-matter interactions at the nanoscale, the most disruptive strategy would be to replace metals by all-dielectric nanoparticles with high refractive index [91; 92; 93], providing fine control over the light features (amplitude, phase, and polarization). Dielectric nanoparticles support an alternative mechanism of light localization in subwavelength optical structures via low-order dipole and multipole Mie resonances [94]. They may generate a magnetic response via displacement current contribution, playing a crucial role in the realization of the unique functionalities of meta-atoms, also driving novel effects in the fields of metamaterials and nanophotonics. It can be mentioned that important steps towards ultra-compactness of photonic circuits have been made very recently via either anisotropic metamaterials [95] or photonic inverse design [96; 97; 98]. As an example, a polarization beam splitter (PBS), which is an  
Figure 3: Structure of a photonic crystal waveguide, with air holes represented by blue and red circles. Simulations were made by considering standard silicon-on-insulator air-bridge PhCW of 220 nm thickness, lattice period 400 nm, and radius R of the first air-holes row 100 nm. By adjusting the radius R2 and lattice positions \(\Delta\)X of the second air-holes rows, a very wide flat band larger than 50 nm could be obtained. Reproduced from [81] under Creative Commons License 3.0.  
important device in PICs for multiplexing and demultiplexing polarizations, was designed and fabricated on a silicon-on-insulator (SOI) platform using a directional coupler with single-mode waveguides 500 nm wide; the coupling region was designed by tailoring the anisotropic metamaterial, which was composed of identical periodic subwavelength strips. The device, with a 2.5 \(\times\) 14 \(\upmu\)m\({}^{2}\) footprint, exhibited a low insertion loss of 1 dB, high extinction ratio >20 dB, and wide operational bandwidth >80 nm [98]. There is strong interest in exploring interesting physical mechanisms to create the optical resonances in such structures, for example, using guided-mode resonances [99] and bound-states in continuum resonances [100], to enhance local electric fields and consequently amplify the nonlinear optical effects in metamaterials [12; 101; 102; 103; 104; 105]. Bound states in the continuum (BIC), experimentally observed by [PERSON] et al.