UvA-DARE ( Digital Academic Repository ) Transmission and diffraction by photonic colloidal crystals

Content Provider	Semantic Scholar
Author	Vos, Willem L. Megens, Mischa Kats, Carlos M. Van B̈osecke, Peter
Copyright Year	1996
Abstract	We have performed optical transmission and synchrotron small-angle x-ray scattering (SAXS) experiments on colloidal crystals with optical refractive index ratios as large as possible over a wide range of volume fractions. These conditions push colloidal crystals into the regime where strong coupling of photonic crystals with light occurs. The optical transmission spectra reveal minima corresponding to stop gaps on the edges of the Brillouin zone of the photonic band structures. The positions of the optically measured stop gaps agree well with lattice spacings measured by SAXS. The stop gap in the 111 direction of crystals of polystyrene in water has a width of up to 5% of the gap frequency as a function of volume fraction, in agreement with theoretical band-structure calculations. A maximum of the relative width confirms the notion that the strength of the interaction between photonic crystals and light has an optimum as a function of volume fraction. The detailed structural information from SAXS data greatly assists in the interpretation of optical experiments on photonic crystals. Advances in colloid science have made it possible to fabricate crystalline arrays with lattice parameters comparable to the wavelength of visible light [1]. Light travelling through such crystals experiences a periodic variation of the refractive index, analogous to the periodic potential energy of an electron in an atomic crystal [2]. Therefore, the dispersion relations may be described by photonic band structures in Brillouin zones in reciprocal space (figure 1), and the crystals are called ‘photonic’. The variation of the refractive index causes a splitting of the bands at the edges of the Brillouin zone (cf. figure 1). These stop gaps appear as minima in the transmission and give rise to Bragg scattering [3]. The coupling strength between light and a photonic crystal can be expressed by a parameter 9 defined as the ratio of the optical volume per particle—the polarizability—to the physical volume per particle [4]. An exciting physical situation arises if the stop gaps overlap in all directions [5]: a complete photonic band gap appears [6], that may be used to localize light or inhibit spontaneous emission [7]. Several optical experiments have already been reported on weakly photonic colloidal crystals ( 9 < 0.05); see reference [8]. In particular, Tarhan and Watson [9] have resolved the stop bands and the dispersion curves in a colloidal single crystal. The strength of coupling9 between light and photonic crystals can be increased by using colloids with a higher refractive index and by raising the volume fraction φ of the particles. Colloidal particles with a high refractive index that are monodisperse enough to crystallize are currently being developed [10]. The effect of increased φ has been investigated in optical diffraction experiments on colloidal crystals with refractive index ratios m of the particles and the medium of up to 1.45, and 9 < 0.6 [4]. It was found that the photonic band structures result inapparentBragg spacings that strongly depend on the wavelength of 0953-8984/96/479503+05$19.50c © 1996 IOP Publishing Ltd 9503
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