Development of a model of the interaction of light with nano-holes in thin metal films
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We develop an analytical electromagnetic model of a conducting film perforated by slits with subwavelength slit width and periodicity. We use a plane wave expansion methodology to calculate the reflected and transmitted fields diffracted by the conducting grating, with the exception that the sub-wavelength periodicity means that the diffracted field is composed of non-propogating surface waves rather than plane waves. We label the non-propogating surface waves evanescent diffracted waves EDWs. We show how the collection of all EDWs present can be treated as an effective medium described by an impedance and that the reflectance and transmittance of a plane wave incident on the grating can be calculated as if the plane wave where interacting with an effective medium. We find that depending on slit depth this effective medium allows for transmittances of 100% even when slit width is so narrow that it is negligable compared to slit periodicity. Thus our analytical model reproduces the extraordinary optical transmission reported in the literature. We show that the EDWs on either side of the grating also act like mirrors coupling to a standing wave in the grating with the result that slit depth determines whether transmission is high or low. We find that when the effective permittivity of the effective medium created by the EDWs is equal to the permittivity of the metal film then the EDWs collectively become a surface plasmon. We also find that except for films with no absorption the state in which EDWs are also a surface plasmon corresponds to low transmittance not high transmittance and thus surface plasmons appear to hinder rather than help transmittance for a grating composed of slits. We also develop an FDTD model of Maxwell's equations which reproduces the predictions of our analytical model. We further develop our analytical electromagnetic model of conducting gratings to also include the situation in which a planar conducting lens is placed under the grating. We demonstrate that such a lens can create a near-field focusing effect that enables sub-wavelength imaging so that incident light can produce a periodic intensity pattern in a substrate with periodic feature less than the wavelength of the incident light. We show that this sub-wavelength imaging is possible with or without surface plasmons being present.
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