Comparison of Brillouin Light Scattering and Density of States in a Supported Layer: Analytical and Experimental Study

We provide a detailed analytical calculation of the Brillouin light scattering (BLS) intensity of a layer on a substrate, taking into account both photoelastic and moving boundary (ripple effect) mechanisms, and give a comparison between BLS intensity and density of states (DOS) to determine the dispersion curves of longitudinal guided modes in the supported layer. In particular, in the case where the mismatch between the elastic parameters of the substrate and the adsorbed layer is high, such as in a PMMA layer on a Si substrate, we derive closed-form expressions of BLS and DOS and demonstrate a simple relationship between these two quantities. A very good agreement between experimental and theoretical BLS spectra was found and compared to theoretical DOS spectra. In particular, we show that while the peaks in the DOS present a uniform behavior, the BLS spectra follows a sine cardinal (sinc) function shape around a given frequency fixed by the chosen laser wavelength. The theoretical calculation is performed within the framework of the Green's function approach.