Diffractive optical
elements (DOEs) are useful across a wide variety of applications
such as laser beam focusing, communication, and other optical
devices. Currently, DOEs are being considered as potential solutions
to a number of optical design problem that are difficult or impossible
to solve with the conventional refractive and reflective elements.
In the last decades, the scalar diffraction theory, based on a
simplification of Maxwell's equations, were usually developed
to model the diffractive optical elements. However, the polarization
between the vector components of the electromagnetic field is
neglected. While the size of diffractive optical elements is comparable
to the wavelength of illumination, scalar diffractive theory is
not valid, and more rigorous models of diffraction must be used.
In theory, Maxwell's equation can precisely determine the diffracted
field of any diffractive structure. In practice, it is not possible
to obtain exact solutions for the majority of cases. Thus, the
solutions of Maxwell's equations have to be calculated numerically.
Various approaches are developed to solve the electromagnetic
equations.
