Local wavevector - Knowlpedia

For the factor $e^{i\Psi(t,x)}$ , the local wavevector is

k(t,x)=\nabla_x\Psi(t,x).

If $\Psi=\kappa\Phi$ with constant $\kappa$ , then $k=\kappa\nabla\Phi$ . The gradient points normally to the local constant-phase surfaces where it is nonzero.

Plane waves and conventions

For $e^{i(k_0\cdot x-\omega t)}$ , the wavevector is the constant $k_0$ . In the convention $e^{2\pi i\xi\cdot x}$ , it is $2\pi\xi$ . Thus a Fourier frequency measured in cycles per unit length and an angular wavevector differ by $2\pi$ .