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In the paper The extraordinary optical transmission through subwavelenth hole arrays by T. W. Ebbesen it is shown at particular wavelength there is a peak observed in zero order transmission spectrum. I am not understanding what exactly this zero order transmission spectrum means?

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Likely, the "zero order transmission spectrum" naming comes from considering the hole array as a transmission grating.

(Illustration of the different orders of a transmission grating here, for example.)

The zero order is just the beam that goes straight through the hole array with no deviation.

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