  While structural colors are ubiquitous in nature, saturated reds are
mysteriously absent. Hence, a longstanding problem is in fabricating
nanostructured surfaces that exhibit reflectance approaching the theoretical
limit. This limit is termed the Schrodinger red and demands sharp spectral
transitions from "stopband" to a high reflectance "passband" with total
suppression of higher-order resonances at blue and green wavelengths. Current
approaches based on metallic or dielectric nanoantennas are insufficient to
simultaneously meet these conditions. Here, for the 1st time, we designed and
fabricated tall Si nanoantenna arrays on quartz substrate to support two
partially overlapping y polarized quasi bound-state-in-the-continuum (q-BIC)
modes in the red wavelengths with sharp spectral edges. These structures
produce possibly the most saturated and brightest reds with ~80% reflectance,
exceeding the red vertex in sRGB and even the cadmium red pigment. We employed
a gradient descent algorithm with structures supporting q BIC as the starting
point. Although the current design is polarization dependent, the proposed
paradigm has enabled us to achieve the elusive structural red and the design
principle could be generalized to Schrodinger's pixels of other colors. The
design is suitable for scale up using other nanofabrication techniques for
larger area applications, such as red pixels in displays, decorative coatings,
and miniaturized spectrometers with high wavelength selectivity.
