Unidirectional radiation is important for various optoelectronic applications, such as lasers, grating couplers and optical antennas. However, almost all existing unidirectional emitters rely on the use of materials or structures that forbid outgoing waves—that is, mirrors, which are often bulky, lossy and difficult to fabricate. Here we theoretically propose and experimentally demonstrate a class of resonances in photonic crystal slabs that radiate only towards one side of the slab, with no mirror placed on the other side. These resonances, which we name ‘unidirectional guided resonances’, are found to be topological in nature: they emerge when a pair of half-integer topological charges1,2,3 in the polarization field bounce into each other in momentum space. We experimentally demonstrate unidirectional guided resonances in the telecommunication regime by achieving single-side radiative quality factors as high as 1.6 × 105. We further demonstrate their topological nature through far-field polarimetry measurements. Our work represents a characteristic example of applying topological principles4,5 to control optical fields and could lead to energy-efficient grating couplers and antennas for light detection and ranging.
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The datasets generated and analysed during the current study are available from the corresponding author upon request.
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We thank L. He for discussion, V. Yoshioka for reading the manuscript and Z. Zhang for helping to conduct the experiments. C.P. was supported by the National Natural Science Foundation of China under grant number 61922004. J.J. and B.Z. were sponsored by the US Army Research Office under grant number W911NF-19-1-0087. The simulations were supported by the High-performance Computing Platform of Peking University. The project was partially supported by AFRL contract FA8650-16-D-5403 and MIT Lincoln Laboratory contract 7000371273, as well as by the Army Research Office, and was accomplished under Cooperative Agreement number W911NF-18-2-0048. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
The authors declare no competing interests.
Peer review information Nature thanks Yuri Kivshar, Mikael Rechtsman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
a, Step-by-step flow chart of the fabrication process. b, Schematics of the customized RIE process. EBL, electron-beam lithography; PECVD, plasma-enhanced chemical vapour deposition; CMP, chemical-mechanical polishing.
The setup is capable of both near- and far-field measurements. The focal lengths of lenses L2, L3, L4 and L5 are 150 mm, 100 mm, 75 mm and 75 mm, respectively. RFP, rear focal plane; PD, photodetector; Obj, objective; Pol, polarizer; Amp, amplifier; BS, beam splitter. N1 and N2 denote the movable lenses used to achive near-field imaging.
a, Experimentally extracted Qtot (blue) compared with simulation results for samples with (green) and without (red) disorder. b, Measured asymmetry ratio η (blue) compared with simulation results for samples with (green) and without (red) disorder.
An amplified spontaneous emission (ASE) source excites the resonances in the sample. Scattered light is recorded by a camera under six different combinations of a polarizer (Pol) and a QWP. The focal lengths of lenses L2, L3, L4 and L5 are 150 mm, 100 mm, 75 mm and 75 mm, respectively.
a, UGR as the merging point between two half-integer charges. b–f, Measured ellipticity ρ of the resonances in five samples with slightly different air-gap widths w, ranging from w/a = 0.399 (b) to 0.403 (f). Dark red (ρ = 1) and dark green (ρ = −1) colours indicate the locations of the LCP and RCP resonances, which are also half-integer topological charges.
a, Device performance when the air-gap widths deviate by ±2.5 nm from the perfect design. b, Device performance when the etching angle deviates by ±1° from the perfect design (grey). c, The UGR is restored if the etching angle deviates by −1° from the perfect design and the air-gap width changes to w = 365 nm.
Simulated (left) and measured (right) asymmetry ratios η for resonances close to the UGR in momentum space.
a, Asymmetry ratio η between upward and downward radiation intensities for a fixed out-coupling angle of 9°. The maximum reaches 27.7 dB near the UGR and remains high (above 10 dB) over a bandwidth of 26 nm. b, Highly directional emission is observed over a wide range of excitation wavelengths and for different out-coupling angles. The fibre-to-waveguide loss is not measured.
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Yin, X., Jin, J., Soljačić, M. et al. Observation of topologically enabled unidirectional guided resonances. Nature 580, 467–471 (2020). https://doi.org/10.1038/s41586-020-2181-4
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