We report results of angle, polarization and frequency resolved optical reflectivity measurements on fcc crystals consisting of air spheres in titania. The carefully grown crystals show excellent structural order, as confirmed by x-ray scattering and electron microscopy. The reflectivity spectra of these strongly photonic crystals show unusual features in comparison to simple Bragg diffraction of weakly photonic crystals. Over a wide range of reflection angles, the (111) Bragg peak splits into at least two peaks that show an avoided crossing. Calculated photon dispersion curves show that the multiple peaks result from band repulsions of Bloch states due to simultaneous (200) and (111) Bragg resonances [1]. Such multiple Bragg diffraction results in flat dispersion relations, and thus plays an essential role in photonic band gap formation.
In the range of the 2nd order Bragg diffraction, where a complete photonic band gap is predicted for fcc crystals with higher dielectric contrast than our materials, at least three peaks are observed with central frequencies independent of reflection angle over a wide range. Theoretical analysis allows us to assign these peaks to stop-gaps or characteristics of dispersionless bands. A significant conclusion is that reflectivity spectra can mimic the signature of a complete photonic band-gap without such a band-gap actually being present [2]. We thank Judith Wijnhoven for sample preparation, Henry Schriemer and Rudolf Sprik for discussions, and Ad Lagendijk especially for organizing HMvD's visit.
* permanent address: Department of Physics, University of Toronto, Toronto, Canada.
[1] H.M. van Driel and W.L. Vos, submitted.
[2] W.L. Vos and H.M. van Driel, submitted.