The propagation of waves in waveguide gratings with a double-negative film but double-positive cover and substrate is studied. Perturbation theory is used to derive expressions that approximate the transverse and longitudinal coupling coefficients for coupling between various transverse-magnetic guided modes in a three-layer waveguide with a rectangular grating profile at the film–cover interface. An analytical method is then used to draw the coupling coefficients’ curves as functions of the film thickness. The curves of the waveguide gratings with double-negative material film differ significantly from that of the conventional waveguide gratings and those with a double-negative cover. Numerical results show that the obtained coupling coefficients are much higher than those of conventional waveguide gratings. Waveguide gratings with double-negative film possess a number of unusual properties. We show that the fundamental mode does not exist and the first-order mode is confined within a narrow film thickness range and cannot couple to any other modes. The coexistence of both the longitudinal and transverse coupling coefficients with the same order of magnitude, double degeneracy of the modes, and double degeneracy of the coupling coefficients near the cutoff are other unusual properties of the proposed structure
