Resonance Properties of Dielectric Diffraction Gratings
Abstract
The guidedmode resonance characteristics of dielectric diffraction gratings are studied by means of the rigorous coupledwave 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 coupledwave 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 wellknown 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 coupledwave 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), surfacerelief waveguide gratings, and multiplylayered gratings. It is found that unslanted dielectriclayer 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 doubleresonance 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 guidedmode 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 narrowline filters and highefficiency switches.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......123W
 Keywords:

 WAVEGUIDE GRATINGS;
 DIFFRACTION GRATINGS;
 Physics: Optics; Engineering: Electronics and Electrical; Physics: Electricity and Magnetism