Source: Principles of Nano-Optics, for Lukas Novotny and Bert Hecht.
The equations above represent the electric field in the second medium when a light hit a surface and the condition of TIR (total internal reflection) is satisfied. Actually this is what called Evanescent field. The point is if I want to calculate the gradient force on a particle in this field, F(gradient)=0.5a*gradient|E|^2, where "a" is the Polarizability and "E" is the electric field. How does the gradient force hold in y- direction? If I make the derivative of the field in y direction it will vanish according to the equation above because there is no variable y that exist in the equation in y axis, on another hand how I read in some articles that they say the gradient force is exist in y direction but with no explanation or derivation!