Abstract
We investigated the spectral properties of a new class of nanostructured artificial composite materials with tailored electromagnetic response, i.e. negative refractive index materials, also known as "left-handed" metamaterials. We analyzed structures incorporating both ordinary positive index media and negative refractive index metamaterials where the interface may be graded to an arbitrary degree. Utilizing a modified version of the Rosen-Morse function, we derived analytical expressions for the field intensity and spectral reflection and transmission through a graded interface between positive and negative index materials. We compared our results to numerical solutions obtained using the transfer matrix technique. .
Highlights
Negative refractive index metamaterials (NRM) 1, known as left-handed metamaterials (LHM) are artificial composites structured at subwavelength level, furnishing a negative value of refractive index in a certain wavelength range
Any realistic structures containing positive and negative index materials are likely to have a graded profile instead of an abrupt one. These have been extensively studied – e.g. Ramakrishna described a metamaterial lens composed of gradient index media 7
We calculated the transmission of our gradient index structure described by (4) both by using (6) and (10) and numerically, utilizing the transfer matrix method (TMM) 12
Summary
Negative refractive index metamaterials (NRM) 1, known as left-handed metamaterials (LHM) are artificial composites structured at subwavelength level, furnishing a negative value of refractive index in a certain wavelength range. Approximate analytical solutions of the Helmholtz equation for the electric field in conventional materials in the case of graded refractive index were done for some special gradient index profiles (e.g. linear or exponential dependences) 12. In this paper we solve the Helmholtz equation for a structure with a graded interface between negative and positive refractive index region utilizing a modified version of the Rosen-Morse dependence. In this way we obtain an analytical solution applicable for different practical situations of graded index metamaterial-containing structures. We utilized the transfer matrix technique to numerically determine the transmittance of graded structures in order to compare it with the analytical solution
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