Plate and prism is transparent optical element which is usually used in optical system. Usually, we apply ray tracing to handle the simulation of prism. However, because of the approximation of ray tracing, the modeling is far from rigorous, which will have trouble in accurate optical experiment. In our research, we set up a rigorous modeling method to handle field propagation through plate and prism. Here we apply the new tracing method, which is called field tracing, instead of ray tracing.
Tracing the field through each surface, the rigorous output field after the component is calculated. We also set up two methods to trace an arbitrary incident field after one surface Σ:

  1. 1. Calculate the field on the intersection surface, which is also the surface Σ, from incident beam. Then apply Fresnel equation to calculate the transmitted or reflected field, which is also on the surface Σ. Next, calculate the field on the intersection surface which is perpendicular to the propagation direction. Finally, propagate the field to next working surface by rigorous propagation method.
  2. 2. The same procedure with last method to calculate the transmitted and reflected field on the surface Σ. Then propagate the field in Fourier domain to the next working surface.

Till now we can handle plate and prism with incidence of chromatic field and obtain a rigorous output field. Here we give one example of handling dispersion prism in figure 1 and figure 2.

Mathematical model of dispersion
Figure 1: Mathematical model of dispersion prism and distribution of two fields on output plane

Input five unequal weighted fields
Figure 2: (a) Input five unequal-weighted fields with different wavelengths. (b) Output field set after propagation for a proper distance.