Achieving Arbitrary Control over Pairs of Polarization States Using Complex Birefringent Metamaterials

Alexander Cerjan and Shanhui Fan

Phys. Rev. Lett. 118, 253902 – Published 22 June 2017

Abstract

We demonstrate that the key to realizing arbitrary control over pairs of polarization states of light, i.e., transforming an arbitrarily polarized pair of input states to an arbitrarily polarized pair of output states, is the ability to generate pairs of states with orthogonal polarizations from nonorthogonal pairs of initial states. Then, we develop a new class of non-Hermitian metamaterials, termed complex birefringent metamaterials, which are able to do exactly this. Such materials could facilitate the detection of small polarization changes in scattering experiments as well as enable new polarization multiplexing schemes in communications networks.

Received 24 January 2017

DOI:https://doi.org/10.1103/PhysRevLett.118.253902

Physics Subject Headings (PhySH)

Birefringence Metamaterials

General Physics

Authors & Affiliations

Alexander Cerjan and Shanhui Fan

Department of Electrical Engineering, and Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

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Vol. 118, Iss. 25 — 23 June 2017

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Images

Figure 1
(a) Flow lines (yellow) depict the polarization dynamics on the Poincaré sphere when light travels along the $z$ direction through a complex birefringent material as described by Eqs. (6)–(8) with $τ = 0.81$ . Note that the shape of the flow lines depends only the value of $τ$ . The great circle containing $| 1, i ⟩$ and $| 1, 1 ⟩$ is shown in blue. The nonorthogonal eigenpolarizations of the dielectric tensor which form the axis of polarization flow are shown in red. The purple crosses show the initial nonorthogonal polarization states $| \pm θ ⟩$ which can be mapped to the orthogonal polarization states $| 1, \pm 1 ⟩$ , shown as purple circles, as described by Eqs. (1) and (2). (b) Flow lines (yellow) depict the polarization dynamics on the Poincaré sphere when traveling through a conventional birefringent material, with $τ = 0$ . The orthogonal eigenpolarizations of the dielectric tensor are shown in red.
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Figure 2
(a) Flow lines (yellow) depict the polarization dynamics on the Poincaré sphere when light travels along the $z$ direction through a complex birefringent material as described by Eqs. (6)–(8) with $τ = 1.5$ . The eigenvectors of the dielectric tensor are shown in red, with the arrow indicating the direction in which the polarization flows for $ϵ_{x y} > 0$ . (b) Flow lines (yellow) depict the polarization dynamics when light travels along the $z$ direction through a complex birefringent material as described by Eqs. (6)–(8) with $τ = 1$ . The single eigenpolarization of the system is $| 1, i ⟩$ (red).
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Figure 3
(a) Schematic of a complex birefringent metamaterial, consisting of layers of a conventional birefringent material (gray), and layers of a material containing gain (red) and loss (blue), forming a comb. The patterning of the structure is assumed to be fine enough relative to the wavelength of the light so as to be in the effective medium limit. (b) Transformation of the polarization on the Poincaré sphere of two signals through $59 μ m$ of a complex birefringent metamaterial, as shown schematically in (a). Here, for an incident light with wavelength $1.55 μ m$ , we have used calcium carbonate whose ordinary and extraordinary axes are rotated 7.47° with respect to the lab frame, yielding a dielectric tensor with $ϵ_{x x} = 2.66$ , $ϵ_{y y} = 2.19$ , $ϵ_{x y} = 0.063$ . The isotropic gain has $ϵ = 4 - 0.1 i$ , and the isotropic loss has $ϵ = 9.74 + 0.63 i$ . By forming a comb consisting of 77% gain regions and 23% loss regions, the effective dielectric tensor is anisotropic in this layer, with $ϵ_{∥} = 5.34 + 0.07 i$ and $ϵ_{∥} = 4.64 - 0.07 i$ . By using 30 nm layers of calcium carbonate, and 20 nm layers of the gain and loss, the total system constitutes a complex birefringent metamaterial with $ϵ_{x x} = 3.454 - 0.028 i$ , $ϵ_{y y} = 3.453 + 0.028 i$ , and $ϵ_{x y} = 0.038$ (see Supplemental Material [41]), which corresponds to $τ = 0.75$ . The initial signal polarizations are separated by 16.2° (cyan circles), while the final polarization states are nearly orthogonal (cyan triangles). The surrounding medium is air, $ϵ = 1$ .
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