We investigate bound states in the continuum (BICs) in a planar dielectric waveguide structure consisting of a gold grating on a dielectric layer with a back layer of metal. In this structure, Friedrich-Wintgen (FW) BICs caused by the destructive interference between the radiations from two waveguide modes appear near the anti-crossing point of the dispersion curves. In this study, it is revealed that the branch at which the BIC appears changes according to the polarization of the modes. Based on a temporal coupled mode theory, it is shown that the BIC branch is determined by the sign of the product of the coupling coefficients between the two waveguide modes and external radiation, which is consistent with FW theory. The signs of the coupling coefficients are estimated by the waveguidemode decomposition of the numerically obtained electric fields and are confirmed to vary depending on the polarization.

Bound states in the continuum (BICs) and exceptional points (EPs) have been the subjects of recent intensive research as they exhibit exotic phenomena that are significant for both fundamental physics and practical applications. We investigated the emergence of the Friedrich–Wintgen (FW) type BIC and the EP in a dielectric waveguide comprising a metal grating, focusing on their dependence on the grating thickness. The BIC emerges at a branch near the anti-crossing formed of the two waveguide modes, for a grating of any thickness. With the grating-thickness change, the anti-crossing gap varies and the branch at which the BIC appears flips. We show that, when the slit is single mode, the BIC appears in the vicinity of the crossing between the two waveguide modes in the empty-lattice (zero slit-width) limit, while the results satisfy the criteria for the branch at which the BIC appears in the previous reports. In addition, we find that the EP appears near the BIC in the same device only on selecting the grating thickness. The BIC and EP in the dielectric waveguide comprising a metal grating, particularly with such tunability, are expected to result in the development of functional and high-performance photonic devices in addition to being a platform for the fundamental research of non-Hermitian systems.

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