All-optical photonic switch via the higher-order topological spin Hall effect

Evelyn Y. González-Ramírez, José G. Murillo-Ramírez, Óscar O. Solís-Canto, and José A. Medina-Vázquez

Phys. Rev. Applied 21, 044038 – Published 19 April 2024

Abstract

Topological photonics has established itself as a promising area for the development of photonic integrated circuits due to the robust properties of topological states. In recent years, different logical devices have been proposed to form the fundamental elements of an integrated topological photonic circuit. Despite the rapid theoretical growth of topological photonics, it still lacks experimental foundations concerning logical devices for on-chip integration. For this reason, in this work, we report the design and build of an all-optical photonic switch in a silicon slab working under the higher-order topological spin Hall effect. We have taken advantage of the gapped edge states due to the higher-order topology and combined this feature with changes in the dielectric permittivity of silicon by inducing transitions of free charge carriers. The transitions of charge carriers were realized through the incidence of electromagnetic radiation with a frequency close to the visible-ultraviolet region boundary, making the device operation entirely optical. The behavior of the constructed device has also been numerically simulated and compared with the experimental results obtained. This work contributes to the idea that photonic crystals are a powerful platform for studying topological states and paves the way for the experimental realization of integrated topological optical circuits.

Received 6 December 2023
Revised 24 February 2024
Accepted 5 April 2024

DOI:https://doi.org/10.1103/PhysRevApplied.21.044038

Physics Subject Headings (PhySH)

Integrated optics Photonic crystals Quantum spin Hall effect Spin Hall effect Symmetry protected topological states Topological effects in photonic systems

Devices for digital logic, storage & processing Topological materials

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Evelyn Y. González-Ramírez ^1,2,*, José G. Murillo-Ramírez ^1,2, Óscar O. Solís-Canto ¹, and José A. Medina-Vázquez ^1,2

¹Centro de Investigación en Materiales Avanzados S.C, Complejo Industrial Chihuahua, Miguel de Cervantes 120 C.P. 31136, Chihuahua, Chih., Mexico
²Facultad de Ingeniería, Universidad Autónoma de Chihuahua, Nuevo Campus Universitario, Circuito, Universitario S/N 31125, Chihuahua, Chih., Mexico

^*Corresponding author: evgonzalez@uach.mx

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Vol. 21, Iss. 4 — April 2024

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Images

Figure 1
Design of the HOTSH PhC. (a) Selection of unit cells UC1 and UC2 describing a triangular mesh of square air holes. (b) Photonic band diagram obtained from UC1 and UC2. Both unit cells produce the same band diagram. The gray region represents the light cone. (c) H_z magnetic field phase profiles of the photonic Bloch functions below the band gap in the HSPs for UC1 and UC2.
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Figure 2
(a) Interface formed by PhC_UC1 and PhC_UC2, creating a domain wall. (b) 10 × 1 supercell, containing the topological interface. On the right is shown the distribution of the |H_z| field in the supercell and the H_z phase distribution. The inset highlights the presence of the Poynting vector vortices visualized by green arrows. (c) Projection of the photonic band diagram obtained with the supercell designed. By means of the vortex distribution of the Poynting vectors, we found the different pseudospin configurations of the band with edge states. The blue upward arrow indicates a positive upward pseudospin and the red arrow indicates a negative downward pseudospin.
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Figure 3
(a) |H_z| field distribution calculated, corresponding to gapped edge states with pseudospin character at the topological interface of HOTSH PhC. The upper panel indicates the propagation of the edge state with a positive pseudospin, while the lower panel shows the propagation of an edge state with a negative pseudospin. (b) Topological corner design formed from two PhCs, one with trivial UC1 and the other with nontrivial UC2. (c) Eigenfrequencies computed in the HOTSH PhC with the topological corner. Both edge states and corner states are indicated. The inset shows the distribution of the |H_z| field corresponding to the corner state presented in the HOTSH PhC, highlighting the higher-order topological character. All field distributions were calculated on the silicon slab with a thickness of 0.7 µm.
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Figure 4
(a) Schematic representation of the $Si$ slab fabrication process from a box-shaped geometry. The blue-shaded regions denote the volume of material removed by FIB machining. (b) SEM micrograph of the $Si$ plate obtained by box-shaped machining. (c) SEM micrograph of the topological PhC formed with a hexagonal lattice and square air holes.
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Figure 5
(a) Representation of the experimental configuration used to measure the edge state in the HOTSH PhC. A butterfly laser diode attached to a single-mode optical fiber is coupled to an optical collimator. Subsequently, the laser beam is focused with a convergent lens to incidence on the sample. The coupled light beam travels at the interface HOTSH PhC and exits to be measured by a low-power detector. (b) A spatial scan process along the y coordinate is performed to demonstrate the existence of the edge state. The maximum coupling occurs when the laser beam approaches the interface HOTSH PhC. (c) Experimental measurement of the amplitude of coupled and guided light beam emerging from the topological PhC as a function of the spatial coordinate y in which the laser beam was swept. The red dots show the intensity of the laser beam obtained after traveling through the topological interface without the incidence of the LED pump incoherent beam. The blue dots correspond to the amplitude of coupled and guided emergent coherent light beam through the topological PhC, with the light bath provided by the pumping incoherent beam with the 400-nm LED. (d) Theoretical transmission of the coupled light beam obtained from numerical simulations where the continuous red line denotes the intensity of the laser beam of 1550 nm coming from the topological interface and without the LED pumping incoherent beam. The continuous blue curve is the transmission of the laser beam of 1550 nm coming from the topological interface under the bath of the pump light beam of the LED at 400 nm.
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Figure 6
(a) Cross-section view of the HOTSH PhC showing the E_y-field distribution of the on state of the photonic switch. Here the incoherent light source is off and no change in dielectric permittivity is generated. (b) Cross-section view of the HOTSH PhC showing the E_y-field distribution of the off state of the photonic switch. Here the incoherent light source is on and generates charge-carrier transition. (c) Plot of the photonic switch effect realized with the edge state transmission as a function of various experimental and numerically simulated mediations. (d) Comparison of the one-dimensional band-diagram projections for the HOTSH PhC with (right) and without (left) incoherent LED illumination. Here, the band shift in frequencies is shown, causing the laser frequency to no longer intersect the frequency of the gapped edge state.
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