Resonance Properties of Dielectric Diffraction Gratings

The guided-mode resonance characteristics of dielectric diffraction gratings are studied by means of the rigorous coupled-wave theory. These resonances occur in waveguide gratings that are periodic structures sufficiently thin to possess distinct, discrete waveguide modes when surrounded by regions of lower average permittivity. For weakly modulated waveguide gratings, the coupled-wave equations are close to being decoupled to a set of unmodulated slab waveguide equations. Therefore, an explicit connection of the waveguide wavenumbers to the grating parameters is obtained. It is shown that the well-known wavenumber condition of a guided wave in an ordinary slab waveguide may then be used to predict approximately the range of the incident angle, the incident wavelength, or grating period that corresponds to the resonances in each spectral order. Furthermore, the eigenvalue equation of a slab waveguide can be used to estimate the locations of the resonances. It is also shown that the transverse field equation describing the field distribution across waveguide structures can be used to express the ratio of the complex amplitudes of the spectral orders on the grating boundaries. The waveguide equation approach holds for small permittivity modulation. As the magnitude of the permittivity modulation is reduced, the resonances become sharper. When the modulation amplitude increases, the locations and shapes of the resonances must be described in detail by the rigorous coupled-wave theory with the connection to the unmodulated slab waveguide of decreased value. The cases studied in this work include planar dielectric waveguide gratings (TE and TM polarization), surface-relief waveguide gratings, and multiply-layered gratings. It is found that unslanted dielectric-layer diffraction gratings at the first Bragg condition or normal incidence can exhibit complete energy exchange between the forward and backward propagating zeroth orders. For rectangular gratings, a double-resonance behavior is found. Physically, for all cases studied, it is seen that the evanescent spectral orders correspond to waveguide modes of the unmodulated slab waveguide. The guided-mode resonances induced in the evanescent waves couple to the external propagating diffracted orders as clearly visualized in the coupled -wave model. Envisioned practical applications of the guided -mode resonance phenomena include narrow-line filters and high-efficiency switches.