Application of the conservation of etendue theorem for 2-D subdomains of the phase space in nonimaging concentrators

The conservation of etendue for general 2-D bundles of rays (not necessarily coplanar) is examined (a 2-D bundle of rays is that whose rays are distinguishable by giving each one two parameters). This is one of the integral invariants of Poincaré and it is directly related to the Lagrange invariant. The application of this theorem to selected 2-D bundles of rays crossing an arbitrary cylindrical concentrator gives us a relationship between the maximum geometrical concentration of a cylindrical concentrator and the angular field of view which is more restrictive than the general one (i.e., the relationship is valid for an arbitrary concentrator) when the collector is surrounded by a refractive medium.