Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path

Abstract

The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefront that is converted to a planar one. As an application, three kinds of phase transformation are realized and it is found that the transformation on phase is able to realize some important properties such as phase reversal or compensation, focusing, and expanding or compressing beams, which are further confirmed by numerical simulations. The slab can be applied to realizing compact electromagnetic devices for which the values of the refractive index or the permittivity and permeability can be high or low, positive or negative, or near zero, depending on the choice of coordinate transformations.

Flat designs of impedance-matched nonmagnetic phase transformer and wave-shaping polarization splitter via transformation optics

“…As such, the virtual space ′ ′ OB C D is transformed into the physical one ′ ′ OA E D, resulting in a design with an irregular shape. To obtain a planar device, we have proposed an indirect transformation method (ITM) based on the principle of equal optical path length [22,23]: the profile of the spatial separation between the original and desired wavefronts is converted to a plane surface, i.e. from AE to BC, as shown in Fig.…”

“…This method does not depend on the symmetry of the PT. We follow the principle of equal optical path length [22,38] to attain a flat configuration and adopt a nonlinear CT to ensure the impedance match.…”

“…It is worth pointing out that this slab is also able to deflect an incident plane wave into a curved wave with a curvature radius −R i . This means that the phase transformer has a two-fold function common to phase devices [22,39,40]. The two functions are demonstrated in Fig.…”

“…Meanwhile, researchers applied TO in order to manipulate the phase to create phase transformers [18][19][20][21]. On this topic we have proposed a method of phase transformation (PT) between any two wavefronts through a compact slab [22,23]. Applying this method, the device configuration remains flat irrespective of its function.…”

“…We follow the method in Refs. [22,23] but adopt a nonlinear CT to ensure impedance matching, use a quasi-conformal CT to simplify the material parameters [35,37], and keep the dispersion relation unchanged to allow the device to become nonmagnetic [6,25]. Applying this method, a phase transformer is designed such that the wave shape and propagation direction can be changed.…”