A study of first-order Talbot resonators is presented. The general conditions for Talbot effect in <i>ABCD</i> systems are determined. These conditions are applied to the computation of the diffraction overlapping coefficients between array Gaussian emitters in a general first-order Talbot resonator. Relations on the ray-transfer matrix to generate the symmetric and the totally antisymmetric supermodes of the array are derived. These relations generalize the free-space, round-trip lengths of 1/2 and 1/4 of the Talbot distance. A new type of resonator based on a plano–convex gradient-index rod is proposed.
© 2003 Optical Society of America
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(110.0110) Imaging systems : Imaging systems
(140.3410) Lasers and laser optics : Laser resonators
(230.5750) Optical devices : Resonators
Carlos R. Fernández-Pousa, María Teresa Flores-Arias, Carmen Bao, María Victoria Pérez, and Carlos Gómez-Reino, "Talbot conditions, Talbot resonators, and first-order systems," J. Opt. Soc. Am. A 20, 638-643 (2003)