Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

Alberto Patiño-Vanegas (1) , Pierre-Emmanuel Durand (1) , Eric Fogret (1) , Pierre Pellat-Finet (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

Domaines: Optique [physics.optics]

Alberto Patiño-Vanegas, Pierre-Emmanuel Durand, Eric Fogret, Pierre Pellat-Finet. Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms. RIAO-OPTILAS 2010, Lima, Peru : VII Reunión Iberoamericana de Óptica (RIAO) & X Encuentro de Óptica, Láseres y Aplicaciones (OPTILAS), Sep 2010, Lima, Peru. pp.1-13, ⟨10.1088/1742-6596/274/1/012108⟩. ⟨hal-00908069⟩