Optical Thouless pumping transport and nonlinear switching in a topological low-dimensional discrete nematic liquid crystal array

Pawel S. Jung, Midya Parto, Georgios G. Pyrialakos, Hadiseh Nasari, Katarzyna Rutkowska, Marek Trippenbach, Mercedeh Khajavikhan, Wieslaw Krolikowski, and Demetrios N. Christodoulides

Phys. Rev. A 105, 013513 – Published 12 January 2022

Abstract

We theoretically investigate a Thouless pumping scheme in the one-dimensional topological Su-Schrieffer-Heeger (SSH) model for single and multiple band-gap systems when implemented in a discrete nematic liquid crystal arrangement. For an electrically controlled SSH waveguide array, we numerically demonstrate edge-to-edge light transport at low power levels. On the other hand, at higher powers, the transport is frustrated by light-induced nonlinear defect states, giving rise to robust all-optical switching.

Received 1 November 2021
Accepted 23 December 2021

DOI:https://doi.org/10.1103/PhysRevA.105.013513

Physics Subject Headings (PhySH)

Optical solitons Topological insulators

Liquid crystals Topological materials

Nonlinear DynamicsCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Pawel S. Jung^1,2,*, Midya Parto¹, Georgios G. Pyrialakos¹, Hadiseh Nasari^1,3, Katarzyna Rutkowska ², Marek Trippenbach⁴, Mercedeh Khajavikhan^1,3,5, Wieslaw Krolikowski^6,7, and Demetrios N. Christodoulides¹

¹CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA
²Faculty of Physics, Warsaw University of Technology, Warsaw, Poland
³Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
⁴Faculty of Physics, University of Warsaw, Warsaw, Poland
⁵Department of Physics & Astronomy, Dornsife College of Letters, Arts, & Sciences, University of Southern California, Los Angeles, California 90089, USA
⁶Laser Physics Centre, Research School of Physics, Australian National University, Canberra, ACT 0200, Australia
⁷Science Program, Texas A&M University at Qatar, Doha, Qatar

^*pawel.jung@ucf.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 105, Iss. 1 — January 2022

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The schematic of the Su-Schrieffer-Heeger model for trans-polyacetylene host and its potential implementation in a discrete liquid-crystal platform. (a) Chemical form showing the two-site unit-cell structure (A and B) with the carbon defect marked with a dashed circle. The tight-binding model representation of hopping electrons with strength $t_{A}$ and $t_{B}$ is shown at the bottom. (b) The bar plot on the right represents the wave function $ψ$ for the edge state with the inset depicting the full band structure. The planar liquid-crystal cell with ITO electrodes as a platform for the SSH model where $d$ represents the cell thickness, $w$ and $w_{d}$ are the electrode thicknesses, and $d_{1}, d_{2}$ are the distances between electrodes is shown in panels (c) and (d).
Reuse & Permissions
Figure 2
The SSH model in a discrete NLC platform based on thirteen waveguides operating at $λ = 1.55 μ m$ induced through the biasing with the voltage of (a) 0.94 V and (b) 1.15 V applied to the electrodes. The left panels show the refractive index distribution in the $x y$ plane. In the middle panel the numerically extracted band structures for two configurations are presented. The right panels in (a) and (b) depict the optical field distribution of the topological states in the $x y$ plane and the cross sections at $x = 0$ of the edge modes together with the refractive index distributions. The parameters used in this design are $w = 2 μ m, w_{d} = 2.35 μ m, d = 2 μ m, d_{1} = 6.8 μ m, d_{2} = 4 μ m, n_{glass} = 1.45$ , NLC $n_{o} = 1.5158, n_{e} = 1.6814, K = 8.15 pN$ .
Reuse & Permissions
Figure 3
The topological Thouless pumping scheme in a discrete NLS platform. (a) The schematic shape of the ITO electrodes are shown for $w = 2 μ m$ and $w_{d} = 2.35 μ m$ . Every second electrode counting from the upper side changes linearly its position along the $z$ direction between $\pm 1.4 μ m$ from the central point where the distance between electrodes is equal ( $d_{1} = d_{2} = 5.4 μ m$ ). The middle panel shows schematically the two varying couplings coefficients $κ_{1}$ and $κ_{2}$ in a coupling paths. The bottom panel depicts the slowly varying refractive index distribution in $z$ after applying a finite voltage, forming 13 waveguide arrays. For lower biasing voltage (0.94 V) these waveguides are single-moded while they support two modes for higher bias (1.15 V). (b) The left panel depicts the numerically extracted evolution of the linear spectrum of the system as a function of distance $z$ (a full cycle of the Thouless pump with the topologically protected state is marked in red). The right panels show that the input topological edge mode adiabatically switches between states, during linear evolution, before returning to its initial state at the output when the structure is induced at 0.94 V. (c) The analogical full cycle of the Thouless pump scheme but this time apply for a topological edge mode consisting of the second-order states (1.15 V).
Reuse & Permissions
Figure 4
The field evolution in a two-level all-optical switching arrangement that utilizes a topological Thouless pumping scheme with broken chiral symmetry. (a) Evolution of an excited topological edge mode with optical power of 0.1 mW. (b) Nonlinear propagation with the same excitation conditions and input power 16 mW. (c) A threshold all-optical switching based on the ratio between the output power confined in the first two waveguides ( $P_{12}$ ) to the total input power ( $P$ ).
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information