Chiral slab thickness measurement using weak value amplification

Abstract

A method is provided for determining a thickness L of a chiral slab that refracts incident linearly polarized light into right (+) and left (−) circularly polarized beams. The method includes disposing the slab in an achiral medium, determining values of translation coefficients γ, determining values for refraction angle differences (θ−θ), selecting pre- and post selection states |ψand |ψ, projecting an emitted light beam through said achiral medium into the chiral slab a small established angle of incidence θ, varying slab egress phase angles β, determining said pointer mean valuex, calculating weak value A, and calculating the thickness as The achiral medium has an established index of refraction n. The translation coefficients γestablish refraction translation differences (γ−γ). The pre-selection state |ψestablishes pre-selection alignment angle to satisfy Φ=π/4. The post-selection state |ψestablishes post-selection alignment angle to satisfy χ=Φ−ε and 0<ε<<1. The slab egress phase angles βare adjusted until pointer mean valuexattains one of a maximum for (γ−γ)>0 or else a minimum for (γ−γ)<0. In various exemplary embodiments, the weak value is approximated as