The optical properties of the micro-structured surface and also the theoretical models to describe them depend very much on the relation between the period Л of the grating and the wavelength X of the incident radiation. Therefore, a classification of gratings defined by the period-to-wavelength relation is very helpful (Fig. 1).

effective medium theories rigorous diffraction theories rigorous diffraction theories photonic band structure calculation rigorous diffraction theories extended sea ar diffraction theories

geometrical optics (ray tracing)

If Л << X then the microstructured regions can by regarded as an effective media. They lead to a modification of reflection and transmission at the boundary air to material but not to a modification of the propagation direction of the radiation (Fig. 1). Only the zero-order diffracted wave is propagating and the wavelength dependence of the optical properties is small in this case. The effective refractive indices of this effective media depend on the refractive indices of the two media in the structured region and on the volume fractions of each of the media. Such subwavelength gratings can be used for antireflective surfaces or for polarisation sensitive devices.

If Л = X then resonance effects dominate and result in a strong wavelength dependence of the optical properties. It is possible to achieve high diffraction efficiencies in a specific dif­fraction order just due to the fact that only few diffracted waves propagate. The optical properties of such gratings have in general to be modelled by using rigorous diffraction theory, i. e. by solving Maxwell equations numerically [16]. Gratings in the resonance re­gion have mainly been used for spectral filtering but also for radiation deflection due to the high diffraction efficiencies which can be achieved.

If Л >> X then many diffracted orders propagate. The distribution of the diffraction efficien­cies depends very much on the structure profile. For very large ratios Л/X the optical properties of the surface-relief grating can derived by means of geometrical optics be­cause this is an approximation which holds for X ^ 0. The grating then represents an array of prisms, lenses, etc. which can be modelled to some extend by using ray tracing meth­ods. For ratios Л/X even as large as 100, the ray tracing method is not sufficiently accurate in many cases. Then, extended scalar approaches or rigorous diffraction theory has to be applied. Surface-relief gratings with a large ratio Л/X are particularly suited for light re­directing elements.