with k x = k t sin ⁡ ⁡ θ θ t and k y = k t cos ⁡ ⁡ θ θ t , where k t is the magnitude of the wave vector of the transmitted wave (so the wavenumber), θ θ t is the angle of refraction, and x ^ ^ and y ^ ^ are the unit vectors along the x axis direction and the y axis direction respectively.