We show that optical beams propagating in path-averaged zero-index photonic crystal superlattices can have zero phase delay. The nanofabricated superlattices consist of alternating stacks of negative index photonic crystals and positive index homogeneous dielectric media, where the phase differences corresponding to consecutive primary unit cells are measured with integrated Mach-Zehnder interferometers. These measurements demonstrate that at path-averaged zero-index frequencies the phase accumulation remains constant and equal to zero despite the increase in the physical path length. We further demonstrate experimentally that these superlattice zero- bandgaps remain invariant to geometrical changes of the photonic structure and have a center frequency which is deterministically tunable. The properties of the zero- gap frequencies, optical phase, and effective refractive indices are well described by detailed experimental measurements, rigorous theoretical analysis, and comprehensive numerical simulations.
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The authors thank R. Chatterjee for helpful discussions and Ayse Selin Kocaman for the preparation of figures. The authors also acknowledge funding support from a NSF CAREER Award (0747787), NSF ECCS (1102257), DARPA InPho and the EPSRC (EP/G030502/1). Electron-beam nanopatterning was carried out at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences (contract no. DE-AC02-98CH10886). The authors acknowledge the use of the UCL Legion High Performance Computing Facility and associated support services in the completion of this work.
The authors declare no competing financial interests.
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Kocaman, S., Aras, M., Hsieh, P. et al. Zero phase delay in negative-refractive-index photonic crystal superlattices. Nature Photon 5, 499–505 (2011). https://doi.org/10.1038/nphoton.2011.129
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