1 April 2000 Ž . Optics Communications 176 2000 365–372 www.elsevier.comrlocateroptcom Simulation of light propagation in planar-integrated free-space optics Markus E. Testorf ) , Michael A. Fiddy UniÕersity of Massachusetts-Lowell, Dept. Electrical and Computer Eng., One UniÕersity AÕe., Lowell, MA 01854, USA Received 30 September 1999; accepted 19 January 2000 Abstract A Fourier transform based beam propagation method is described to simulate light propagation in planar-integrated free space optics. Wide angle beam propagation is modified to minimize the required space-bandwidth product and the required computational load with suitable coordinate transforms. To model diffraction at perfectly conducting and dielectric surfaces the extended Kirchhoff approximation is employed. This model accounts for diffraction effects in typical configurations of planar integrated optics, where the thin element approximation fails to provide an accurate description. q 2000 Elsevier Science B.V. All rights reserved. PACS: 42.25.Bs; 42.82.Gw; 42.40.My Keywords: Planar integrated free space optics; Extended Kirchhoff approximation; Beam propagation method 1. Introductions Planar integrated micro-optics is an advantageous wx packaging scheme for free space optics 1 . It pro- vides the possibility to integrate 3D micro-optical systems monolithically within the 2D geometry of a transparent plane parallel substrate. Planar-integrated optics is based on the idea of distributing optical elements, either refractive or diffractive on the sur- faces of the substrate. The light signal is coupled into the substrate and propagates along a folded optical axis between the surfaces of the substrate. Many ) Corresponding author. Tel.: q 1-978-934-3395; fax: q 1-978- 934-3027; e-mail: testorf@galileo.eng.uml.edu applications of planar optics have been proposed and demonstrated including integrated imaging systems w x wx 2,3 and optical interconnects 4 . Since the monolithic structure of a planar-optical system cannot be changed after fabrication a thor- ough design is essential to ensure a proper perfor- mance of the system. An important aspect of the design is an accurate simulation of the light propaga- tion through the optical system. Although many design aspects of planar-integrated optics can be wx investigated with ray-tracing 3 , an evaluation of the system performance usually requires knowledge about diffraction effects. Often, it is preferable to simulate the wavefront propagation directly, rather than to reconstruct the complex amplitude distribu- tion from a ray-tracing analysis. This is particularly the case, if the system contains diffractive optical Ž . elements DOEs and the properties of the system 0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0030-4018 00 00522-8