GRATING COUPLING TO SURFACE PLASMA-WAVES .2. INTERACTIONS BETWEEN 1ST-ORDER AND 2ND-ORDER COUPLING

For grating periods larger than the excitation wavelength, multiple-grating orders couple incident optical radiation to the surface plasma waves (SPW's) characteristic of the metal-air interface. For a grating period that is an integral multiple of the wave vector of these surface modes, two resonances become degenerate in coupling angle. There are also permitted diffraction orders at this coupling angle. The vicinity of this multiple-mode coupling resonance, where several free-space electromagnetic modes, as well as two surface modes, are coupled by different orders of a grating, is known as a minigap region. Not surprisingly, the response surface displays complex dependences on frequency, angle, and grating profile. A detailed experimental and theoretical study is presented of the optical response at 633 nm in the (+1, -2) minigap region for Ag films deposited on photolithographically defined 870-nm-period gratings. Measurements of both the 0-order reflectance and the -1-order diffraction are presented for a wide progression of grating depths. The SPW resonances depend on the grating depth, and this variation is used to tune through the minigap region for a fixed wavelength and period. Similar measurements are presented for a single grating as a function of wavelength through the minigap region. In both measurements the 0-order response shows only a single broad minimum as the resonances approach degeneracy, while the -1-order diffraction shows clearly defined momentum gaps. A simple theoretical model based on the Rayleigh hypothesis is presented that gives a good qualitative picture of the response. The response surfaces are sensitive to the grating profile, and detailed modeling requires inclusion of higher-order grating components.