Abstract
Throughout optics and photonics, phase is normally controlled via an optical path difference. Although much less common, an alternative means for phase control exists: a geometric phase (GP) shift occurring when a light wave is transformed through one parameter space, e.g., polarization, in such a way as to create a change in a second parameter, e.g., phase. In thin films and surfaces where only the GP varies spatially—which may be called GP holograms (GPHs)—the phase profile of nearly any (physical or virtual) object can in principle be embodied as an inhomogeneous anisotropy manifesting exceptional diffraction and polarization behavior. Pure GP elements have had poor efficiency and utility up to now, except in isolated cases, due to the lack of fabrication techniques producing elements with an arbitrary spatially varying GP shift at visible and near-infrared wavelengths. Here, we describe two methods to create high-fidelity GPHs, one interferometric and another direct-write, capable of recording the wavefront of nearly any physical or virtual object. We employ photoaligned liquid crystals to record the patterns as an inhomogeneous optical axis profile in thin films with a few μm thickness. We report on eight representative examples, including a GP lens with F/2.3 (at 633 nm) and 99% diffraction efficiency across visible wavelengths, and several GP vortex phase plates with excellent modal purity and remarkably small central defect size (e.g., 0.7 and 7 μm for topological charges of 1 and 8, respectively). We also report on a GP Fourier hologram, a fan-out grid with dozens of far-field spots, and an elaborate phase profile, which showed excellent fidelity and very low leakage wave transmittance and haze. Together, these techniques are the first practical bases for arbitrary GPHs with essentially no loss, high phase gradients (∼rad/μm), novel polarization functionality, and broadband behavior.
Highlights
Phase shifts in light waves are ordinarily produced via an optical path difference (OPD) known as a dynamic phase effect
These two techniques in principle enable the embodiment of nearly any phase change as a GP holograms (GPHs)
We offer three reasons supporting “geometric phase” as the proper name beyond simple semantics: First, the diversity of terminology for the same photonic effect is evidence of at least some confusion on the physics fundamental to them all, hindering effective comparison and dissemination; second, this name all at once provides the clearest distinction for a general audience from conventional holograms and from polarization holograms, of which GPH is a distinct subclass; and third, only the three output waves in Eq (1) are possible in all embodiments of inhomogeneous pure geometric phase, including all those other than anisotropy (e.g., Refs. [2,7,10,15,33])
Summary
Phase shifts in light waves are ordinarily produced via an optical path difference (OPD) known as a dynamic phase effect. In elements wherein only the GP varies spatially, exceptional diffraction and polarization behavior arises— most strikingly, they can theoretically produce nearly any wavefront variation and produce its conjugate just by changing input polarization [Fig. 1(a)]. This should be possible with 100% efficiency [13,16], e.g., when a birefringent layer has half-wave retardation, since the desired phase profile is encoded in the optical axis orientation [Fig. 1(b)]. We set forth that the class of pure GP elements is most properly designated GP holograms (GPHs), wherein attenuation and dynamic phase are homogenous
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