Holographic Display Étendue Expansion with a Binary π-Metasurface

The phase step of a conventional binary diffractive optical element (DOE) scales as 2π(n−1)h/λ. It is exactly π at one design wavelength and drifts away everywhere else. Any departure from π leaves an unscattered fraction |c₀(λ)|² of the light that bypasses the expander and lands as an unexpanded ghost copy of the hologram. A DOE designed for π at 520 nm leaks 7.0% at 450 nm and 11.9% at 660 nm; one designed at 660 nm leaks 51.2% of the blue.

The metasurface’s two pillar populations are dispersion-engineered so their phase difference stays within 13° of π on average over 400–700 nm in full-wave simulation, apart from a 560–595 nm resonance. The simulated zero order is 0.27%, 1.31% and 2.75% at 450, 520 and 660 nm. The DOE remains exact at its own 520 nm design point, so the metasurface’s advantage lies at the outer primaries. On the fabricated element we measure 9.1%, 7.5% and 3.5%, above simulation, but the worst channel stays below the DOE’s 11.9% and far below the 51.2% of a 660 nm design.

We ran experimental captures at s = 2 to test the fabricated metasurface expander. The 450, 520 and 660 nm channels are captured as sequential monochrome exposures through the same passive metasurface, and they reconstruct each target at matched positions. Each capture averages K = 24 separately optimized patterns per color.

The simulation propagates the same displayed patterns through the scalar model. Every hologram is optimized against the nominal π mask, so a chromatic phase step would show up only in the captures, as a ghost raising the background. Instead, the measured background contrast stays at a common fraction of the model prediction at all three primaries. Residual background haze and speckle-softened detail leave the measured composites 2 to 5 dB below simulation in color PSNR on most subjects (values are in Supplementary).