Abstract
Self-assembled periodic structures out of monodisperse spherical particles, so-called opals, are a versatile approach to obtain 3D photonic crystals. We show that a thin conformal coating of only several nanometers can completely alter the reflection properties of such an opal. Specifically, a coating with a refractive index larger than that of the spherical particles can eliminate the first photonic band gap of opals. To explain this non-intuitive effect, where a nm-scaled coating results in a drastic change of optical properties at wavelengths a hundred times bigger, we split the permittivity distribution of the opal into a lattice function convoluted with that of core-shell particles as a motif. In reciprocal space, the Bragg peaks that define the first Brillouin zone can be eliminated if the motif function, which is multiplied, assumes zero at the Bragg peak positions. Therefore, we designed a non-monotonic refractive index distribution from the center of the particle through the shell into the background and adjusted the coating thickness. The theory is supported by simulations and experiments that a nanometer thin TiO2 coating via atomic layer deposition (ALD) on synthetic opals made from polystyrene particles induces nearly full transparency at a wavelength range where the uncoated opal strongly reflects. This effect paves the way for sensing applications such as monitoring the thicknesses growth in ALD in-situ and in real time as well as measuring a refractive index change without spectral interrogation.
Highlights
Photonic crystals (PhCs) are periodic dielectric structures[1,2,3,4,5,6]
By using the Ewald sphere construction we have shown that the scattered power P from a scattering volume increases proportionally to the square of the absolute value of Fourier transform (FT) of Δε(→r ) integrated over the Ewald sphere surface (ESS)[9,10,21]:
{Δε(→r )}(→k ) ks[2] g (θ)d2k wwahveerveeIc0toisrsthaendinftoernusnitpyoolaf rtihzeedinlicgihdtegn(tθp)la=ne(1w+avecoosf2θli)g/h2t.,Tθhieslethnegtahnogfle→kbineitswdeeefninsecdaattsenreefdfω/kcs, and input where ω is kin the frequency and c is the speed is shifted from the origin of of light in vacuum and→neff the reciprocal space by −kin and effective refractive index of the opal. has a radius ks
Summary
Photonic crystals (PhCs) are periodic dielectric structures[1,2,3,4,5,6]. The periodic modulation of the dielectric leads to the appearance of a photonic band gap (PBG), which prohibits the propagation of light within certain wavelength region in certain or all directions. The shift of the PBG with the change of the effective refractive index can be used for sensing applications[8,11,12,13,14,15]. In this case the PBG is not just shifted by the refractive index change, but switched on and off This effect allows sensing without the need for spectrally selective sources, but by probing broadband transmission or reflection from the opal. When the first-zero position of the motif FT falls on the first peak position of the lattice FT, this peak will be eliminated and the bandgap will vanish The consequence of this is that the opal changes its optical property from reflecting to transmitting in the specified wavelength range.
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