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Reproduction in free space of fields confined by 3-dimensional optical waveguides

Abstract It is shown by using the Fresnel-Kirchhoff diffraction theory and the method of images that a scalar field confined by a 3-dimensional optical waveguide can be generated in free space by a suitable light source. In the method the boundaries of a waveguide are replaced by virtual sources. This allows one to present the wave guiding as the interference and diffraction of multiple light beams produced in free space by the guide equivalent source (Fresnel waveguide). Thus, the scalar optics of a 3-dimensional waveguide is presented as the free-space beam optics. The method is illustrated by construction of the Fresnel sources for the triangular, rectangular and hexagonal waveguides. The numerical examples demonstrate the diffraction-free and self-imaging propagation in the free-space of the eigenmodes of the Fresnel rectangular-waveguide.