On the basis of the unitary transformation and the Lie algebra decomposition technology widely used in quantum mechanics, we obtain the analytical propagator for light beams propagating through an imperfect gradient-index (GRIN) waveguide. The results show that, unlike in the straight GRIN waveguide widely studied, in an imperfect GRIN waveguide, self-imagining phenomena can result in two new effects: one is a phase shift including a global one and a local one, in which the local one results in a change of direction of the light beam propagating through the imperfect GRIN waveguide; the other is a transverse shift of self-image. The transverse deviation occurring in the imperfect GRIN waveguide is also calculated.
© 2004 Optical Society of America
Kaicheng Zhu and Huiqin Tang, "Influence of imperfections in gradient-index waveguides on Talbot effects," J. Opt. Soc. Am. A 21, 187-192 (2004)