Development of a model of the interaction of light with nano-holes in thin metal films
- Publication Type:
- Thesis
- Issue Date:
- 2008
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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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