Rediscovering the waveguide beam splitter/combiner

Abstract

By establishing the relation of Talbot self-imaging effects in free space and in waveguide, we have rediscovered the self-imaging diffraction effect in waveguide with the view of Talbot effect in free-space. We have found that the diffraction theory of Talbot effect in free space do give us a set of simplified equations, that can't be obtained with the theory of multimode interference (MMI), beam propagation method, etc.. We show that simple equations for explanation of Talbot self-imaging effect in free space can be used to design the waveguide beam splitters and combiners. Thus, the heavy designing work with the previous multimode interference method can be released with the new simple equations. More importantly, new configurations of waveguide beam splitters and combiners can be designed with the simple equations. The importance of rediscovering waveguide beam splitter is that a complete new and clear physical picture can explain the complex self-imaging phenomena in waveguide, which should be highly interesting for practical applications.

Polarization-dependent Talbot effect

“…4 There are simple principles 5 governing the Talbot effect for amplitude gratings with an arbitrary opening ratio. Since the self-imaging effect in a waveguide is essentially the same as the self-imaging effect in free space, so the simple principles for free space 6 can also be applied to explain the results in a waveguide, which are usually obtained by the multimode interference method, the beam propagation method, etc. The Talbot effect is well explained by the scalar Fresnel integral method, 5 which does not take into account the polarization effect.…”