Transparency induced in opals via nanometer thick conformal coating

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.


Contact points
In our consideration (Figure S1a) for the coating thickness h, the volume of the spherical cap which is lost at the contact point (shaded zone) is: The shell volume V of a core-shell sphere is: = 4 3 2 + ℎ − 2 The missed shell volume for a point contact and for 12 contacts (due to the FCC structure) compared to the core-shell sphere is shown in Fig. S1b. In the real structure the number of contact can decrease due to slight deviations in the size of the particles.
2 Figure S1. Overestimation of the volume for the motif simplified as a core-shell sphere. (a) The missed shell volume is the volume of the spherical cap with height of h. (b) The calculated in percent depending on the coating thickness ℎ for sphere radius d=172 nm for 1 contact and 12 contacts.

Transmission simulation and experimental spectra
3 Figure S2. The simulated transmittance spectra of the opal with different coating thickness h.
The PBG disappears when the coating thickness is 6 and 9 nm, and then reappears when the coating is 12 nm. 3. Band diagrams Figure S4. The band structure for the opal without (a), with a 7.5 nm (b) and 12 nm (c) conformal coating of TiO 2 . (d) The normalized amplitude function ℱ / of the FT of a spherical polystyrene core-shell particle of 172 nm diameter uncoated (black) and with a titania shell of 3 nm (purple), 6 nm (blue), 9 nm (green) and 12 nm (red) thickness adding to 5 the radius. The background material is air. The vertical black dash line indicates the Bragg peak position at ΓL and ΓX direction.
The photonic band gap will shrink and disappear also in the band diagram. Band diagram calculation takes into account all effects, but the first order approximation presented here helps to explain why the band gap and thus the reflection peak disappear. The band structure ( Figure S3) of direct opal and opal with 6 nm conformal coating is calculated by using the MPB software package from MIT (https://mpb.readthedocs.io/en/latest/). The direct opal without conformal coating ( Figure S3a) shows a larger bandgap width (defined as band gap width divided by the central frequency, Δω/ω) of 5.977% along the ΓL direction ([111] direction). When the structure is coated with a 7.5 nm TiO 2 film with a refractive index of 2.3 ( Figure S3b), the band gap width Δω/ω decreases to 0.062%. The band gap then will increase to 2.910% when the coating thickness increase to 12 nm ( Figure S3c). The band gap in the ΓL direction decreasing and then increasing with coating thickness is consistent with the first order prediction. Similarly, the band gap at ΓX direction is almost zero without coating and opens with coating deposition which also can be explained by the shift of the first zero point of the motif FT ( Figure S3d).  for 3 nm (Figure 2b) coating sample. Thus, a little index variation (∆ around 0.04) will change the structure from light reflection to transparency which can be easily tracked by a power meter for the bright or dark mode. This measurement does not require a spectrometer.