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Reciprocal transmittances and reflectances: An elementary proof
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Image of Fig. 1.
Fig. 1.

Reciprocal configurations. (a) and (b) show reciprocal configurations for transmission. in (a) denotes the transmittance for the incident wavevector . in (b) is defined similarly. The reciprocal relation is . (a) and (c) are reciprocal for reflection. in (a) is the reflectance for the incident wavevector and in (c) for . The reciprocal relation is .

Image of Fig. 2.
Fig. 2.

Schematic drawing of two currents and the electric fields induced by . The curves denote the position where the currents exist.

Image of Fig. 3.
Fig. 3.

Schematic drawing of reciprocal configuration for transmission. The object has an arbitrary periodic structure, which is asymmetric along the axis. Currents induce electric fields .

Image of Fig. 4.
Fig. 4.

Schematic configuration for reciprocal reflection. The object has an arbitrary periodic structure, which consists of asymmetric unit cells. The currents yield electric fields .

Image of Fig. 5.
Fig. 5.

(a) Schematic drawing of metallic grating profile modeled from AFM images. The periodicity is . The dotted lines show the unit cells in which the ratio is Au:air:Au:air=3:1:4:5. The thicknesses of Au, Cr, and the quartz substrate are , , and , respectively. (b) Numerically calculated spectra for incidence of (upper panel) and (lower panel) of TM polarization. In both panels the reflectance (upper solid line) and absorption (dotted line) are plotted using the left axis, while the transmittance (lower solid line) uses the right axis. (c) Measured transmittance spectra, corresponding to the transmittance spectra in (b).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Reciprocal transmittances and reflectances: An elementary proof