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Chiral slab thickness measurement using weak value amplification

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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 |ψi and |ψj, projecting an emitted light beam through said achiral medium into the chiral slab a small established angle of incidence θ0, varying slab egress phase angles β±, determining said pointer mean value x, calculating weak value Aw, and calculating the thickness as L=〈x〉Re⁢⁢Aw. The achiral medium has an established index of refraction n0. The translation coefficients γ± establish refraction translation differences (γ+−γ−). The pre-selection state |ψi establishes pre-selection alignment angle to satisfy Φ=π/4. The post-selection state |ψj establishes post-selection alignment angle to satisfy χ=Φ−ε and 0<ε<<1. The slab egress phase angles β± are adjusted until pointer mean value x attains 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 Aw≈γ+-γ-+2⁢⁢ɛ⁢⁢γ-2⁢⁢sin⁢⁢ɛ≈γ+-γ-2⁢⁢ε.

Parks, Allen D.
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Sensors and Measurement
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Grant time: 
1,254 days
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