Probing Optical Losses and Dispersion of Fully Guided Waves through Critical Evanescent Coupling

Surface waves such as plasmon, exciton, or phonon polaritons as well as guided modes supported by various planar structures attract particular attention due to their capability of capturing and carrying the optical signals in two- and one-dimensional systems. An important characteristic of such waves is their dispersion $\omega ({{k}_{x}},{{k}_{y}})$, which can be designed on demand by nanostructuring of planar layered systems to obtain photonic crystal slabs and metasurfaces. Engineering the dispersion of surface waves gives rise to such exciting optical effects as transition from positive to negative refraction or from elliptic to hyperbolic dispersion, self-collimation, and diffraction-free propagation of surface waves. Along with the real part of the wave vector responsible for the phase of a propagating surface wave, a crucially important parameter for the applications is its propagation length that is related to the intrinsic losses of the mode. We propose an experimental approach allowing for the extraction of the full complex dispersion of optical surface waves and guided modes. The method relies on angle-resolved attenuated total internal reflection spectroscopy. In such a setup, scanning the air gap between the sample and a solid immersion lens yields controllable tuning of the coupling between the surface waves and the free space. In the experiment, we identify the regime of critical coupling of light to waveguide modes of a planar silicon slab and use it to extract their intrinsic losses and thus the propagation lengths in a broad spectral range. Our approach is a powerful tool for studies of light and hybrid light-matter surface waves of various kinds and may find its applications in the development of on-chip optoelectronic and nanophotonic devices.