Transverse magneto-optical Kerr effect enhanced at the bound states in the 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 leaky waveguide mode increases due to far-field interference. Our results uncover the potential of all-dielectric and semiconductor nanostructures for resonant magneto-optics.