We performed spectroscopic ellipsometry measurements of the specular and off-specular reflections of a one-dimensional polymethyl methacrylate grating on a Au-coated glass substrate and analyzed the data with efficient theoretical modeling. Very good agreement is obtained between calculation and experiment for both specular and off-specular reflections. It is found that the resonance peak of the off-specular reflection is much sharper than specular reflection at a wavelength that matches the condition for exciting the interface (surface plasmon) mode. When different media are used as the ambient, we found that the off-specular reflection near the surface-plasmon resonance can give significant enhancement in detection sensitivity compared with the corresponding specular reflection. This study may open a new way for biosensing. To analyze the data, we also developed a method to compute quasi-photonic band structures for periodic structures with frequency-dependent complex dielectric constants.