Designing Devices for Wave-Vector Manipulation Using a Transformation-Optics Approach

Abstract

A transformation optics approach was used to derive a general method for designing electromagnetic devices able to manipulate the wave vectors in the specific manner required by the functionality of the device. While the wave paths inside the device remain of a secondary importance the wave vectors are gradually changed in the desired way by choosing the appropriate coordinate transformation. The proposed method was applied to design both converging and diverging flat lenses. Computer simulations revealed the focusing ability of a converging flat lens designed using the proposed technique.

Optical imaging system based on transformation-optics lenses

“…Considering the z-axis as the optical axis of the proposed system, the transformation media of the lenses used to build up the device are generated by functions which transform only the z coordinate of the original space, z→z/h(x, y) through the transformation function h(x, y), while the x and y coordinates remain unaltered. Giloan et al [20] described in detail the steps leading to the retrieval of the transformation function which generates the medium of a converging lens embedded in the free space, i.e. relative permittivity and permeability are equal to unity.…”

“…In the study of this optical device, of particular interest, are the transmission coefficients at these interface planes. Giloan et al [20] derived the following expression of the transmission coefficient at the output interface P i of the device as a function of α angle…”

“…where E t and E i are the transmitted respective incident electric field intensity at P i interface. Following the same steps described in [20], the following equation is obtained for the transmission coefficient at the input interface of the device where ρ is the thickness to focal distance ratio. Equation (5), which describes the total transmission of the system, shows that for higher angle α the optical rays are poorly transmitted.…”

“…Control upon the wave vectors is required when designing focusing or defocusing devices. Recently, a general method was proposed for designing both converging and diverging flat lenses made of media that perform specific coordinate transformations [20]. The permittivity and permeability tensors of the transformation media constituting these unconventional lenses are retrieved from the transformation functions which alter the coordinates of the original space.…”

“…The permittivity and permeability tensors of the transformation media constituting these unconventional lenses are retrieved from the transformation functions which alter the coordinates of the original space. A lens of this type provides a perfect convergence for a light beam propagating parallel to the optical axis of the lens [20]. In this theoretical study, we propose an optical imaging system, based on two converging transformation-optics inspired flat lenses, which provides magnified images for sub-wavelength features.…”