The coloration of some butterflies, Pachyrhynchus weevils, and many chameleons are notable examples of natural organisms employing photonic crystals to produce colorful patterns. Despite advances in nanotechnology, we still lack the ability to print arbitrary colors and shapes in all three dimensions at this microscopic length scale. Here, we introduce a heat-shrinking method to produce 3D-printed photonic crystals with a 5x reduction in lattice constants, achieving sub-100-nm features with a full range of colors. With these lattice structures as 3D color volumetric elements, we printed 3D microscopic scale objects, including the first multi-color microscopic model of the Eiffel Tower measuring only 39 µm tall with a color pixel size of 1.45 µm. The technology to print 3D structures in color at the microscopic scale promises the direct patterning and integration of spectrally selective devices, such as photonic crystal-based color filters, onto free-form optical elements and curved surfaces.
We use beam tracing --- implemented with a newly-written code, Scotty --- and the reciprocity theorem to derive a model for the linear backscattered power of the Doppler Backscattering (DBS) diagnostic. Our model works for both the O-mode and X-mode in tokamak geometry (and certain regimes of stellarators). We present the analytical derivation of our model and its implications on the DBS signal localisation and the wavenumber resolution. To determine these two quantities, we find that it is the curvature of the field lines and the magnetic shear that are important, rather than the curvature of the cut-off surface. We also provide an explicit formula for the hitherto poorly-understood quantitative effect of the mismatch angle. Consequently, one can use this model to correct for the attenuation due to mismatch, avoiding the need for empirical optimisation. This is especially important in spherical tokamaks, since the magnetic pitch angle is large and varies both spatially and temporally.
A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al., Plasma Phys. Control. Fusion 49 1019 (2007) ) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wavenumber k ⊥ selected by the Doppler backscattering (DBS) signal. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a non-separable power law spectrum in wavenumber space, leading to a power law dependence of the radial correlation length with binormal wavenumber l r ∽ C k ⊥ α (α ≈ 1) which agrees with the inverse proportionality relationship between the measured l r and k ⊥ in experiments (Fernández-Marina et al., Nucl. Fusion 54 072001 (2014) ). This new insight indicates that RCDR characterizes the eddy aspect ratio in the perpendicular plane to the magnetic field. It also motivates future use of a non-separable turbulent spectrum to quantitatively interpret RCDR and potentially other turbulence diagnostics. The radial correlation length is only measurable when the radial resolution at the cutoff location Wn satisfies Wn < l r, while the measurement becomes dominated by Wn for Wn ≥ l r. This suggests that l r is likely inaccessible for electron-scale DBS measurements (k ⊥ρs > 1). The effect of Wn on ion-scale radial correlation lengths could be non-negligible.
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