A surface plasmon resonance sensor uses a gold film on a BK7 prism illuminated at

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Condensed Matter, Materials & Soft Matter · Wave propagation and light in media

What an Instrument Can See, Ch Media that are designed: plasmons, metamaterials and photonic crystals

Problem

A surface plasmon resonance sensor uses a gold film on a BK7 prism illuminated at 633 nm633\text{ nm}, the same geometry already analysed for gold on BK7 at that wavelength. It is known that raising the index on the metal's far side from 1.0001.000 to 1.0021.002 moves the coupling angle from 43.80∘43.80^\circ to 43.92∘43.92^\circ, a shift of 0.12∘0.12^\circ for Δn=0.002\Delta n = 0.002. The sensor, still with gas on the far side of the gold, is now used to follow a vapour adsorbing on the gold that raises the near-surface index from 1.0001.000 to 1.0121.012. ((a)) Treating the angular shift as proportional to Δn\Delta n over this range, estimate the angular shift produced. ((b)) Express this index change in resonance units, where 1 RU=10−61\text{ RU} = 10^{-6} refractive index units.

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