Comprehensive study on the concept of spectral-domain reflection and refraction

Space-time duality and time-to-frequency mapping bring a lot of analogies. We apply the concept of optical reflection and refraction, for the first time, to the spectral domain. The optical reflection and refraction phenomena are addressed in the spectral domain across a dispersion discontinuity boundary, where a weak probe pulse is co-propagating with a strong perpendicularly polarized parabolic pulse. The total internal reflection behavior in the spectral domain is analytically determined. Our results can complete the theory of the optical wave confinement in the spatial, temporal and spectral domains, which can be a guide for spectrum engineering and characterization.