Frequency Vectoralization and Frequency Birefringence

In view of momentum continuity at a temporal slab, it is shown that instantaneous switching of an isotropic medium to an anisotropic medium offers the incident frequency a directional property- a counterintuitive process which is called frequency vectoralization. By expressing the dispersion diagrams before and after the temporal transition, a general analogy between spatial and temporal interfaces is given and the concept of frequency birefringence, i.e. double frequency jump, will be explained. Furthermore, it will be shown that an anisotropic temporal interface diffracts a monochromatic beam in both the spatial and spectral domains.