Let us consider a plane wave which has only E_x component and propagating along z . Since the plane wave will have no variation along the plane perpendicular to z i.e., xy plane, . The Helmholtz's equation (6.2) reduces to,

.........................................................................(6.3)

    The solution to this equation can be written as

............................................................(6.4)

     are the amplitude constants (can be determined from boundary conditions).