Destructive interference governs the principle of operation of optical resonators. An unusual form of destructive interference was demonstrated in photonics, being associated with bound state in the continuum (BICs). BICs are formed by the destructive interference of several ordinary electromagnetic waves. In the BIC regime, an optical structure is characterized with an infinite quality factor (Q factor). For practical resonators, Q factors of BICs is high yet finite, and improve field enhancement, energy confinement, and light-matter coupling. 

In this final PhD thesis presentation, I will summarize my results on the theory and applications of optical BICs in metasurfaces and individual subwavelength nanoparticles. In the first part, I will discuss how the BIC concept can unify the description of optical properties of seemingly different metasurfaces with a broken in-plane symmetry. I will show that for nonzero asymmetry of the metasurface unit cell the BIC transforms into a high-Q quasi-BIC while the asymmetry parameter governs the magnitude of the field enhancement and the sharpness of the quasi-BIC peak in scattering. Next, I will show how the designed high-Q metasurfaces can be applied to increase efficiency of second-, third- and high-harmonic generation significantly. I will present the critical coupling concept for nonlinear asymmetric metasurfaces subjected to non-radiative losses due to scattering from surface roughnesses and radiation from the sample edges.  In the second part, I will show how quasi-BICs can form in individual subwavelength dielectric resonators due to destructive interference of several Mie modes with a similar far-field profile. I will analyse how the Q factor at the quasi-BIC regime is connected to the peculiarities of scattering. Finally, I will demonstrate that an individual dielectric nanoresonator hosting a quasi-BIC can boost nonlinear effects increasing second-harmonic generation efficiency up to several orders of magnitude. I will present the conditions for the optimal efficiency of harmonic generation including spatial and temporal structuring of pump pulse and structuring of the substrate.

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