Twisted Two-Dimensional Material Stacks for Polarization Optics

The ability to control the light polarization state is critically important for diverse applications in information processing, telecommunications, and spectroscopy. Here, we propose that a stack of anisotropic van der Waals materials can facilitate the building of optical elements with Jones matrices of unitary, Hermitian, non-normal, singular, degenerate, and defective classes. We show that the twisted stack with electrostatic control can function as arbitrary-birefringent wave-plate or arbitrary polarizer with tunable degree of non-normality, which in turn give access to plethora of polarization transformers including rotators, pseudorotators, symmetric and ambidextrous polarizers. Moreover, we discuss an electrostatic-reconfigurable stack which can be tuned to operate as four different polarizers and be used for Stokes polarimetry.

Figure 1

The eigenview of various classes of Jones matrices constructed by twisted stack of BP and ${\mathrm{MoO}}_3$ which are represented by light gray and dark gray planes, respectively. (a)–(c) The left panels depict the two eigenvalues and the corresponding polarization ellipses of the Jones matrices of the structures shown on the right.

Figure 2

(a) The seven-layer BP and ${\mathrm{MoO}}_3$ stack to achieve (b) elliptical-birefringent QWP, (c) circular-birefringent QWP, and (d) linear-birefringent HWP. The Fermi energies for each constituent BP multilayer are listed in the order which gives the result in panels (b), (c), and (d). In (b)–(d), the circles denote the eigenstates while crosses represent $|0°⟩$ and ${\mathbf{J}}_{\mathbf{R}}|0°⟩$ to showcase the wave-plate-induced rotations in the Poincaré sphere.

Figure 3

(a) The seven-layer twisted BP stack can switch between (b) $x$-linear polarizer, (c) $y$-linear polarizer, (d) 45°-linear polarizer, and (e) right-handed circular polarizer. The Fermi energies for each constituent BP multilayer are listed in the order which gives the result in panels (b), (c), (d), and (e). In (b)–(e), the crosses represent the eigenpolarization with zero eigenvalue. (f) The polarization ellipse corresponding to input light (gray) and those measured (black) using the stack in panel (a) as Stokes polarimeter. From left to right, the input Jones vectors are $[1,0{]}^T$, $[0.7071,-0.7071{]}^T$, $[0.7071,0.7071i{]}^T$, $[0.5,0.433+0.75i{]}^T$, and $[0.2236,0.9747i{]}^T$.

Figure 4

(a) The seven-layer twisted BP stack optimized to function as two asymmetric polarizers with (b) $\mathrm{\Theta }=90°$ and (c) $\mathrm{\Theta }\sim 0°$. The eigenpolarizations in (b) are $|45°⟩$ and $|R⟩$. In (c) the eigenpolarizations are set to coalesce on $|45°⟩$. In (b) and (c), the crosses represent the eigenpolarization with zero eigenvalue. The Fermi energies for each constituent BP multilayer are listed in the order which gives the result in panels (b) and (c). In (d) and (e), the action of the non-normal polarizer in (b) and the nearly ambidextrous polarizer in (c) are visualized in forward direction, respectively. (f) and (g) are the same as (d) and (e) for backward propagation. In (d)–(g) black arrows show the propagation direction and black crosses denote blocked transmission.