Transverse magneto-optical Kerr effect enhanced at the bound states in continuum

We calculate theoretically the transverse magneto-optical Kerr effect (TMOKE) in the periodically patterned waveguide made from a diluted magnetic semiconductor. It is demonstrated that the TMOKE is resonantly enhanced when the incident wave is in resonance with the bound state in continuum, arising when the quality factor of the waveguide mode increases due to the far-field interference. Our results uncover the potential of all-dielectric and semiconductor nanostructures for resonant magneto-optics.