Our colleague Ivor Krešić has published, as the leading and corresponding author, a paper in the prestigious journal Physical Review Letters, in which nonconformal geometric deformations of two-dimensional space are related to the non-Hermitian dielectric response of optically isotropic materials. The mentioned theoretical insights were used for the design of a broadband “invisibility cloak”, which prevents the detection of a desired object by both continuous and pulsed radiation. The image from the article was selected for the cover of Physical Review Letters. The paper was published in collaboration with scientists from Greece, Israel and Austria.

Transforming space with non-Hermitian dielectrics

Ivor Krešić, Konstantinos G Makris, Ulf Leonhardt, Stefan Rotter, Physical Review Letters 128 (18), 183901  (2022).

DOI : https://doi.org/10.1103/PhysRevLett.128.183901

Transformation optics is a theoretical framework that has enabled a number of fascinating applications, of which one of the most unusual ones is the “invisibility cloak”. So far, transformation optics with isotropic materials has been limited to conformal geometric transformations, in which the angles between the lines are equal before and after the transformation (Figures 1a, b). However, in optically isotropic materials, conformal transformations leads sometimes to near-zero dielectric functions – an extreme optical response achievable only close to metamaterial resonances, which significantly limits the functionality of such optical designs. This research extends the theoretical framework of transformation optics in isotropic materials to include nonconformal transformations (Figure 1c), and shows how they necessarily lead to the occurrence of non-Hermitian dielectric responses.

Figure 1: Transforming space with non-Hermitian media. (a) The virtual coordinates, with the branch cuts of the conformal (light green) and nonconformal (dark green) Zhukovsky maps. The area of each square in the grid is 0.4 × 0.4. After the mappings, the green lines form circles, see (b) and (c), inside of which is the cloaked region (gray shaded area). The local orthogonality of the coordinate lines, a signature of conformal mapping, is present only in (b) but not in (c) (in both plots only the upper Riemann sheet is depicted).

By applying these insights to the problem cloaking, it is shown that the material condition for near-zero valued dielectric functions can be replaced by adding spatially modulated optical loss and gain to dielectric materials, via modifying the so-called Zhukovsky transformations. The materials generated by such transformations are therefore necessarily non-Hermitian, have a broadband frequency response (Figure 2), but currently have the functionality limited to a small range of incident angles. It is to be expected that nonconformal transformations in isotropic materials will be useful for a wide range of optical applications which can be achieved by nonconformal extensions of the existing designs in conformal optics.

Figure 2: Demonstration of cloaking under pulsed illumination. (a) A spatially narrow pulse incident onto the cloaking region (left) is nearly perfectly transmitted (right) when the cloak is present. (b) When the cloak is absent, there is a distortion of the pulse shape, clearly revealing the presence of the reflecting material to the outside observer. The thin black dashed line denotes the separation of the plotting regions for the incoming (left) and outgoing (right) part of the pulse evolution.