Many physical phenomena create colour: spectrally selective light absorption by pigments and dyes1,2, material-specific optical dispersion3 and light interference4,5,6,7,8,9,10,11 in micrometre-scale and nanometre-scale periodic structures12,13,14,15,16,17. In addition, scattering, diffraction and interference mechanisms are inherent to spherical droplets18, which contribute to atmospheric phenomena such as glories, coronas and rainbows19. Here we describe a previously unrecognized mechanism for creating iridescent structural colour with large angular spectral separation. Light travelling along different trajectories of total internal reflection at a concave optical interface can interfere to generate brilliant patterns of colour. The effect is generated at interfaces with dimensions that are orders of magnitude larger than the wavelength of visible light and is readily observed in systems as simple as water drops condensed on a transparent substrate. We also exploit this phenomenon in complex systems, including multiphase droplets, three-dimensional patterned polymer surfaces and solid microparticles, to create patterns of iridescent colour that are consistent with theoretical predictions. Such controllable structural colouration is straightforward to generate at microscale interfaces, so we expect that the design principles and predictive theory outlined here will be of interest both for fundamental exploration in optics and for application in functional colloidal inks and paints, displays and sensors.
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All relevant data generated or analysed for this study are included in this published article (and its Supplementary Information files).
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L.D.Z., A.E.G., C.H.M., A.P.S. and S.C. acknowledge support from the Department of Materials Science and Engineering, the Department of Chemistry, and the Materials Research Institute at The Pennsylvania State University. S.N. and M.K. were supported in part by the US Army Research Office through the Institute for Soldier Nanotechnologies at MIT, under contract number W911NF-13-D-0001. A.E.G., S.N., M.K. and L.D.Z. acknowledge support by the National Science Foundation’s CBET programme on “Particulate and Multiphase Processes” under grant numbers 1804241 and 1804092. C.H.M. acknowledges support from the Thomas and June Beaver Fellowship and A.P.S. received support from the Office of Science Engagement at The Pennsylvania State University. Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc. for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in this paper do not necessarily represent the view of the US Department of Energy or the United States Government.
Nature thanks Kenneth Chau, Lorne Whitehead and the other anonymous reviewer(s) for their contribution to the peer review of this work.
A.E.G., S.N., M.K. and L.D.Z. are named as inventors on a provisional patent application pertaining to this work (US 62/765,032).
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Extended Data Fig. 1 Transparent, polymeric hemispheres printed with multiphoton lithography display iridescence.
a, Schematic of the geometry of the hemispheres. b, Scanning electron micrograph of the polymeric hemispheres. Scale bar, 10 µm. c, Reflection optical micrograph of the transparent hemispheres. Scale bar, 20 µm. d, Macroscopic Canon EOS Rebel T6 DSLR photographs of the hemisphere array as viewed by rotating the camera around the sample under a constant illumination angle. Scale bar, 1 mm.
Extended Data Fig. 2 Material dispersion in biphasic droplets does not fully account for the colour separation.
a, Refractive index as a function of wavelength for each of the droplet materials. Water and heptane are both more dispersive than perfluorohexane27,28. b, Ray-tracing diagram through the droplet, where the red phase is heptane and the grey phase is perfluorohexane. Ray trajectories were determined for a large number of rays, with different refractive index values for each wavelength. Outgoing rays were binned according to angle and wavelength and for each (θ, φ) pixel the spectrum was converted to colour, yielding c, the colour separation diagram due to material dispersion. Binning was only necessary for the ray-tracer data taking into account the curved upper interface of the droplets. Nothing is binned in the analytical interference model that was used to explain the observed effects. The only colour separation is a small amount of blue, where total internal reflection just starts (because the critical angle for blue light is smaller than that of red light). d, Experimental iridescent colour distribution from a similar droplet geometry for comparison. Scale bar, 20 mm.
Extended Data Fig. 3 Flat-sided polygonal segments printed with multiphoton lithography display iridescence.
The number of sides in the polygon serves to limit the maximum possible number of total internal reflections (diagram at left) that light can undergo for a given illumination angle. Shown are Canon EOS Rebel T6 DSLR photographs of the reflected colour distributions produced by the method described in Fig. 2a. The light input direction is provided as θ and the dome was photographed from two viewing angles. Each polygon had a base width of 20 µm. Scale bar, 1 cm.
Extended Data Fig. 4 Effect of droplet size and illumination angle on the reflected colour distribution from biphasic droplets.
a, The iridescence of monodisperse heptane–perfluorohexane droplets with varying diameter but consistent morphology was investigated. The top row shows optical micrographs of a droplet from each sample. Scale bar, 100 μm. The bottom row shows photographs of the angular colour distribution pattern as viewed from θ = 0° with an illumination angle of θ = 35°. b, Optical micrograph (far left) of an example biphasic droplet containing heptane and perfluorohexane (scale bar, 50 µm) and photographs of the angular colour distributions as viewed from θ = 0° when the illumination angle is altered, as shown (scale bar, 1 cm).
This file contains a Supplementary Discussion. Includes the full derivations of: the analytical description of the interference phenomenon in 2D, ray density for a given light trajectory, extension of the theoretical description to 3D spherical concave optical interfaces, quantitative angle measurements from the experimentally determined angular color distributions, converting spectra into colors, and comparison with Finite-Difference Time-Domain simulation. Nine supplementary figures are included.
Biphasic droplets display iridescence. DSLR video showing how the perceived color of the biphasic perfluorohexane and heptane droplets (as in Figure 1a) changes as a function of viewing direction under a constant illumination angle. Scale, 1 cm.
Water droplets condensed onto a polystyrene Petri dish reflect iridescent color. Warm water in a Petri dish condenses onto the lid, revealing macroscopic structural coloration that changes as the droplets grow in size and dispersity. Scale, 1 cm.
Change in refractive index contrast affects the reflected color. As methanol evaporates off of an array of printed solid transparent hemispheres (Extended Data Figure 1, refractive index = 1.56) the reflected colors change, showing the dynamic effect of varying refractive index contrast. Scale, 500 µm.
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Goodling, A.E., Nagelberg, S., Kaehr, B. et al. Colouration by total internal reflection and interference at microscale concave interfaces. Nature 566, 523–527 (2019). https://doi.org/10.1038/s41586-019-0946-4
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