Abstract
Gratings with complex multilayer strips are studied under inclined incident light. Great interest in these gratings is due to applications as input/output tools for waveguides and as subwavelength metafilms. The structured strips introduce anisotropy in the effective parameters, providing additional flexibility in polarization and angular dependences of optical responses. Their characterization is challenging in the intermediate regime between subwavelength and diffractive modes. The transition between modes occurs at the Wood's anomaly wavelength, which is different at different angle of incidence. The usual characterization with an effective film using permittivity ε and permeability μ has limited effectiveness at normal incidence but does not apply at inclined illumination, due to the effect of periodicity. The optical properties are better characterized with effective medium strips instead of an effective medium layer to account for the multilayer strips and the underlying periodic nature of the grating. This approach is convenient for describing such intermediate gratings for two types of applications: both metafilms and the coupling of incident waves to waveguide modes or diffraction orders. The parameters of the effective strips are retrieved by matching the spectral-angular map at different incident angles.
Highlights
There are two different applications of gratings in general
The spectral position of the magnetic resonance has been previously demonstrated to be a result of the effective width of the grating [20], though the normal incidence transmission local minima provide a baseline of sorts to determine the spectral locations for both ε x and μy
We demonstrate a new approach for retrieving the effective optical properties of the structured strips of a metamaterial grating
Summary
There are two different applications of gratings in general. First is a diffraction tool with a period larger than the wavelength, and second is as an engineered film with controlled material parameters.The second type of application requires substantially subwavelength gratings, so that in some ranges of wavelengths and angles they can be described by the effective parameters of a uniform film.For those ranges of wavelengths and angles there are no detectable non-zero diffraction orders.One-dimensional gratings consisting of stacked metal-dielectric strips are investigated for their ability to provide magnetic as well as electric resonances [1,2,3,4]. The second type of application requires substantially subwavelength gratings, so that in some ranges of wavelengths and angles they can be described by the effective parameters of a uniform film. For those ranges of wavelengths and angles there are no detectable non-zero diffraction orders. One-dimensional gratings consisting of stacked metal-dielectric strips are investigated for their ability to provide magnetic as well as electric resonances [1,2,3,4] Such resonances are located in the visible spectrum due to the size of the unit cell—less than 0.5 μm. It follows from Maxwell’s equations that the transmission and reflection coefficients for the effective film depend on both the product and the
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