I doing an experiment now.
My structure has 700nm periodicity.
The surface of the unit structure is sloped at 45 degrees from the normal incidence angle.
My laser is 500 nm.
I can expect there will be diffraction.
I wonder if the geometrical optics can be applicable for my case?
Or just I need to consider the diffraction?
I am asking this question because I have something that I can not explain.
It depends on what you mean by whether "geometrical optics can be applicable".
Geometric optics will work fine with a system with a grating like the one you mention, although you need to know the rules for calculating the directions and strengths of the transmitted / reflected rays. There are three main points to heed here:
In general, several separate rays will emerge from the incidence of one ray;
Their directions are governed by the Bragg Resonance Condition.
Their relative strengths are governed by the actual shape of the periodic structure: these are related to the amplitudes of the components in the Fourier series describing the periodic index variation.
The reason that geometric optics works well here is that a ray stands for essentially a plane wave i.e. a wavefront that has minimal aberration over length scales that are typically much longer than the length scales in the grating you mention. Plane waves incident on a grating give rise to a set of plane waves, one for each integer solution in the Bragg resonance law.
