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Experimental Realization of a Reflections-Free Compact Delay Line Based on a Photonic Topological Insulator

Lai, Kueifu, Ma, Tsuhsuang, Bo, Xiao, Anlage, Steven, Shvets, Gennady·2016·Scientific Reports
DOI 10.1038/srep28453PMC PMC4921924
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Abstract

Electromagnetic (EM) waves propagating through an inhomogeneous medium are generally scattered whenever the medium’s electromagnetic properties change on the scale of a single wavelength. This fundamental phenomenon constrains how optical structures are designed and interfaced with each other. Recent theoretical work indicates that electromagnetic structures collectively known as photonic topological insulators (PTIs) can be employed to overcome this fundamental limitation, thereby paving the way for ultra-compact photonic structures that no longer have to be wavelength-scale smooth. Here we present the first experimental demonstration of a photonic delay line based on topologically protected surface electromagnetic waves (TPSWs) between two PTIs which are the EM counterparts of the quantum spin-Hall topological insulators in condensed matter. Unlike conventional guided EM waves that do not benefit from topological protection, TPSWs are shown to experience multi-wavelength reflection-free time delays when detoured around sharply-curved paths, thus offering a unique paradigm for compact and efficient wave buffers and other devices.

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Figures

Figure 1 The platform for a quantum spin-Hall photonic topological insulator (QSH PTI): a bianisotropic metawaveguide. (a) Schematic of a QSH PTI. Part of the top metal plate is removed to reveal the cylinders attached to the top plate (purple) and to the bottom plate (green), leaving a gap of thickness g to the other plate. The 2-port VNA is connected to the feeding source (yellow double arrow) and to the receiving probe (red double arrow) for transmission measurement. Top inset: geometric parameters of the PTI. Bottom inset: picture of the assembled structure showing an interface between the two the PTIs which serve as two topological claddings. (b) Calculated 1D projected PBS of the PTI with topologically non-trivial interface. Cyan area: bulk bands, gray area: a complete band gap around the doubly degenerate Dirac cones, red curve: TPSWs supported by the topologically non-trivial interface. (c) Measured transmission spectra through the bulk PTI (all rods attached to the top plate: black curve) and along the interface between two PTIs shown in Fig. 1a (red curve). The transmission is enhanced by nearly 30dB in the 5.87 < f < 6.29 GHz frequency range by the presence of the interface, indicating that the surface propagation dominates over the bulk PTI propagation. QSH PTI parameters defined in the inset: h = a = 36.8 mm, d = 0.345a = 12.7 mm, g = 0.15a = 5.5 mm.
Figure 1 The platform for a quantum spin-Hall photonic topological insulator (QSH PTI): a bianisotropic metawaveguide. (a) Schematic of a QSH PTI. Part of the top metal plate is removed to reveal the cylinders attached to the top plate (purple) and to the bottom plate (green), leaving a gap of thickness g to the other plate. The 2-port VNA is connected to the feeding source (yellow double arrow) and to the receiving probe (red double arrow) for transmission measurement. Top inset: geometric parameters of the PTI. Bottom inset: picture of the assembled structure showing an interface between the two the PTIs which serve as two topological claddings. (b) Calculated 1D projected PBS of the PTI with topologically non-trivial interface. Cyan area: bulk bands, gray area: a complete band gap around the doubly degenerate Dirac cones, red curve: TPSWs supported by the topologically non-trivial interface. (c) Measured transmission spectra through the bulk PTI (all rods attached to the top plate: black curve) and along the interface between two PTIs shown in Fig. 1a (red curve). The transmission is enhanced by nearly 30dB in the 5.87 < f < 6.29 GHz frequency range by the presence of the interface, indicating that the surface propagation dominates over the bulk PTI propagation. QSH PTI parameters defined in the inset: h = a = 36.8 mm, d = 0.345a = 12.7 mm, g = 0.15a = 5.5 mm.CC BY · PubMed Central
Figure 2 Spatial localization and topological protection of the surface waves. (a) Frequency-dependent spatial profiles of the electric field intensity measured at the end of the photonic structure. The surface mode is transversely confined to a small fraction of its wavelength. The zero of the scanning axis (y = 0) is at the interface between the two PTIs. (b) Comparison of measured transmission spectra between the straight (red curve) and the delay line (green curve) interfaces. The receiving probe is at y = 0. Inset: schematic of the interface inside the dashed white box in Fig. 1a for the straight interface (red box) and the delay line interface (green box) containing a large detour-type defect. (c) Simulated energy density at f = 6.08 GHz showing the TPSW flowing around the defect without scattering.
Figure 2 Spatial localization and topological protection of the surface waves. (a) Frequency-dependent spatial profiles of the electric field intensity measured at the end of the photonic structure. The surface mode is transversely confined to a small fraction of its wavelength. The zero of the scanning axis (y = 0) is at the interface between the two PTIs. (b) Comparison of measured transmission spectra between the straight (red curve) and the delay line (green curve) interfaces. The receiving probe is at y = 0. Inset: schematic of the interface inside the dashed white box in Fig. 1a for the straight interface (red box) and the delay line interface (green box) containing a large detour-type defect. (c) Simulated energy density at f = 6.08 GHz showing the TPSW flowing around the defect without scattering.CC BY · PubMed Central
Figure 3 Properties of the guided modes of a topologically trivial waveguide produced by removing one row of rods. The waveguide shown in the orange box in the inset of (b) is classified as topologically trivial because the bulk modes of the claddings possess a vanishing Chern index. The center frequency GHz of the topologically trivial bandgap is considerably lower than that of the topologically nontrivial bandgap GHz shown in Fig. 1. (a) Calculated 1D projected PBS: bulk bands of the claddings (cyan area), a complete band gap (gray area), and the dispersion curve of the TTGW (orange lines). (b) Orange box inset: straight waveguide, blue box inset: bent waveguide. Black curve: transmission spectrum through the bulk of the claddings (i.e. a row of rods is not removed). Transmission drop in the 1.8 < f < 3.9 GHz range indicates the complete bandgap. Near-perfect spectrally-flat transmission (orange curve) through the straight waveguide indicates reveals TTGWs in the 3.0 < f < 3.9 GHz range. Transmission through the bent waveguide (blue curve) is negligible for all frequencies except at GHz, GHz, and GHz corresponding to Fabry-Perot resonances of the defect. High transmission at is enabled by multiple bounces of the TTGW inside the defect. (c) Frequency-dependent spatial profiles of the electric field intensity measured at the end of the photonic structure. Spatially confined guided modes are observed in three narrow frequency bands.
Figure 3 Properties of the guided modes of a topologically trivial waveguide produced by removing one row of rods. The waveguide shown in the orange box in the inset of (b) is classified as topologically trivial because the bulk modes of the claddings possess a vanishing Chern index. The center frequency GHz of the topologically trivial bandgap is considerably lower than that of the topologically nontrivial bandgap GHz shown in Fig. 1. (a) Calculated 1D projected PBS: bulk bands of the claddings (cyan area), a complete band gap (gray area), and the dispersion curve of the TTGW (orange lines). (b) Orange box inset: straight waveguide, blue box inset: bent waveguide. Black curve: transmission spectrum through the bulk of the claddings (i.e. a row of rods is not removed). Transmission drop in the 1.8 < f < 3.9 GHz range indicates the complete bandgap. Near-perfect spectrally-flat transmission (orange curve) through the straight waveguide indicates reveals TTGWs in the 3.0 < f < 3.9 GHz range. Transmission through the bent waveguide (blue curve) is negligible for all frequencies except at GHz, GHz, and GHz corresponding to Fabry-Perot resonances of the defect. High transmission at is enabled by multiple bounces of the TTGW inside the defect. (c) Frequency-dependent spatial profiles of the electric field intensity measured at the end of the photonic structure. Spatially confined guided modes are observed in three narrow frequency bands.CC BY · PubMed Central
Figure 4 Photonic time delay lines based on detour-type defects. Top: schematics of stacking two defects along the photonic waveguides. The second defect is placed at a distance Δx = 16a after the first defect. Green arrows: transmitted, orange arrows: reflected EM waves. (a) Two compact detours (red line) produce twice the delay time of the one (black line), with no decrease in the bandwidth for TPSWs. (b) In contrast, two detour-type defects in a topologically trivial waveguide reduces the operational bandwidth because of the reflections of TTGWs. While the peak delay is almost doubled by the second defect, the bandwidth is reduced to less than half of the original value. The resultant delay-bandwidth product N = Δfτ, which determines the number of electromagnetic pulses that can be buffered by a delay line, does not increase by the addition of the second defect.
Figure 4 Photonic time delay lines based on detour-type defects. Top: schematics of stacking two defects along the photonic waveguides. The second defect is placed at a distance Δx = 16a after the first defect. Green arrows: transmitted, orange arrows: reflected EM waves. (a) Two compact detours (red line) produce twice the delay time of the one (black line), with no decrease in the bandwidth for TPSWs. (b) In contrast, two detour-type defects in a topologically trivial waveguide reduces the operational bandwidth because of the reflections of TTGWs. While the peak delay is almost doubled by the second defect, the bandwidth is reduced to less than half of the original value. The resultant delay-bandwidth product N = Δfτ, which determines the number of electromagnetic pulses that can be buffered by a delay line, does not increase by the addition of the second defect.CC BY · PubMed Central
Figure 5 Photonic delay line applications based on QSH PTI. Top half: the relative phases extracted from the transmission spectra of straight path and defect; bottom half: the time delays of delay line application on the platforms of (a) TPSWs and (b) TTGWs. Note that the time delays for the TTGWs can be negative around the Fabry-Perot (FP) resonances of the detour20. Negative time delays are not observed for the detoured TPSWs because topological protection against backscattering prevents FP resonances.
Figure 5 Photonic delay line applications based on QSH PTI. Top half: the relative phases extracted from the transmission spectra of straight path and defect; bottom half: the time delays of delay line application on the platforms of (a) TPSWs and (b) TTGWs. Note that the time delays for the TTGWs can be negative around the Fabry-Perot (FP) resonances of the detour20. Negative time delays are not observed for the detoured TPSWs because topological protection against backscattering prevents FP resonances.CC BY · PubMed Central

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Research works printed but not linked: 24

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Metadata

Authors
Lai, K., Ma, T., Bo, X., Anlage, S., & Shvets, G.
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2016-06-27
Volume
6
Issue
1
ISSN
2045-2322
DOI
10.1038/srep28453
PMC
PMC4921924
Cited by
70
References
11
Language
en
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