Self-Imaging in Homogeneous Optical Waveguides

Abstract

When an object is placed against one end of an optical waveguide, a real optical image (self-image) of it may be formed at the other end under certain conditions (Fig. 1). In wave-optical terms, these conditions require the phase differences ψjk=(βj−βk)L between any two excited modes at the end of the guide to be integral multiples of 2π. Here, βj denotes the propagation constant of the j-th mode, and L is the length of the guide. Under these conditions, the interference of the modes in the exit plane of the waveguide is the same as in the entrance plane, and a real image is formed. While it is long known that such an image transmission is possible with guides having a square-law index profile, the imaging property has recently also been demonstrated for planar guides with homogeneous refractive index.1,2 The planar guide provides only one-dimensional (line ↔ line) imaging in the same sense as a cyclindrical lens. The corresponding two-dimensional (point ↔ point) imaging is possible with dielectric guides of rectangular or square cross-section. In the present paper, these self-imaging processes in guides of homogeneous index are discussed theoretically, and experimental results are presented illustrating this phenomenon.