Fig 1 Conventional and topological 3-dB couplers.
Published:31 August 2024,
Published Online:16 July 2024,
Received:16 November 2023,
Revised:19 June 2024,
Accepted:26 June 2024
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3-dB couplers, which are commonly used in photonic integrated circuits for on-chip information processing, precision measurement, and quantum computing, face challenges in achieving robust performance due to their limited 3-dB bandwidths and sensitivity to fabrication errors. To address this, we introduce topological physics to nanophotonics, developing a framework for topological 3-dB couplers. These couplers exhibit broad working wavelength range and robustness against fabrication dimensional errors. By leveraging valley-Hall topology and mirror symmetry, the photonic-crystal-slab couplers achieve ideal 3-dB splitting characterized by a wavelength-insensitive scattering matrix. Tolerance analysis confirms the superiority on broad bandwidth of 48 nm and robust splitting against dimensional errors of 20 nm. We further propose a topological interferometer for on-chip distance measurement, which also exhibits robustness against dimensional errors. This extension of topological principles to the fields of interferometers, may open up new possibilities for constructing robust wavelength division multiplexing, temperature-drift-insensitive sensing, and optical coherence tomography applications.
Photonic integrated circuits provide an efficient platform for optical interconnection
Topological nanophotonics, a recently flourishing research field that combines the topological physics with nanophotonics
In this work, we utilize VPCs to develop a topological 3-dB coupler. We thoroughly investigate the operational principles of such topological couplers and discover a scattering matrix insensitive to wavelength, resulting in the ideal 3-dB power splitting. This broadband and robust splitting ratio is achieved through the combination of valley-Hall topology and mirror symmetry. The 3-dB power splitting supports a wide wavelength range around 1550 nm and exhibits tolerance to dimensional errors, as compared to the case of conventional DCs. To further demonstrate its functionality, we propose an on-chip Michelson-like interferometer by utilizing the aforementioned topological coupler. We experimentally validate its capability of extracting length differences and demonstrate its robustness against dimensional errors. These findings highlight the resilience of the splitting ratio and the potential of realizing broadband and fabrication-tolerant topological 3-dB couplers in a wide variety of applications such as sensing, information processing, and optical coherence tomography.
Consider a conventional 3-dB coupler, such as DC, consists of four ports [labeled with ①-④ in
Fig 1 Conventional and topological 3-dB couplers.
a, b Beam splitting in (a) a conventional 3-dB directional coupler and (b) a topological 3-dB coupler composed of two different VPCs. The numbers in circles label four different ports. Light input from port 1 is divided into ports 3 and 4. The inset shows the splitting ratio as a function of wavelength, in which the dash lines represent the cases with dimensional errors. The 3 dB splitting is achieved at only one single wavelength λ1 for the conventional coupler. In contrast, the topological coupler achieves the ideal 3-dB splitting in a broadband wavelength even when dimensional errors are introduced. The white arrows with crosses indicate that no backscattering to port 1 and no straight transmission to port 2 are allowed. c Structures of Edge21 and Edge12 which are constructed with VPC1 and VPC2. Structural parameters such as s1, s2 and a are marked. The black (gray) arrows denote the propagation directions of edge modes at K (K') valleys, respectively. d Hz field within the topological 3-dB coupler when the light is incident from port 1. No backscattering and no through transmission are observed due to the inter-valley scattering suppression. The incident light is divided equally into two output ports, resulting in the 3-dB splitting
Utilizing the two distinct edges, we design a topological coupler capable of achieving ideal 3-dB splitting. The device consists of a harpoon-shaped structure formed by connecting two different edges, resulting in four ports (
1
The derivation of each element of the scattering matrix is detailed in Supplementary Section C.
We note that the scattering matrix described above represents the ideal 3-dB splitting over a broad bandwidth that determined by the operation range of valley edge modes. The scattering matrix is derived from topology and symmetry, which are independent to wavelength and are always valid in the range of topological edge modes in band gap. Since no additional wavelength condition is required, the matrix elements are wavelength-independent in this range. Therefore, the 3-dB splitting can be achieved in the operation range of edge modes. This remarkable characteristic is protected by the nontrivial valley-Hall topology and the mirror symmetry of the structure.
In this section, we present the experimental investigation of the topological 3-dB coupler. The topological couplers are fabricated on the SOI platform using a top-down nanofabrication process [see Methods for fabrication details]. The optical microscope image of the whole sample, including topological coupler, strip waveguides and grating couplers, is shown in
Fig 2 Broadband 3-dB splitting of the topological coupler.
a Optical micrograph of the fabricated topological 3-dB coupler. b Scanning electron microscope (SEM) images of the splitting junction between two topologically distinct VPCs (i.e. VPC1 and VPC2). c, d Experimental splitting ratio spectra of the fabricated topological 3-dB coupler when light is incident from different ports. e, f Far-field images taken from an optical microscope system for inputting light of 1550 nm from (e) port 1 and (f) port 3. The dashed boxes and numbers 1–4 in circles denote the grating couplers for four ports. The red arrows denote the input ports
To confirm the broadband and robust 3-dB splitting performance in experiment, a fiber-to-waveguide alignment system is set up to image the light energy output from the grating couplers and to measure the transmission spectra [see Methods for the optical measurement setup].
During the processes of nanofabrication, fabrication errors are inevitable, including dimensional error, sidewall roughness, defects and dislocations. Dimensional error is common for the fabrication of topological 3-dB coupler, corresponding to variations of
Fig 3 Tolerance analysis of the topological and conventional 3-dB couplers.
a, c Schematic of the dimensional errors and the corresponding radiation patterns of far-field microscope images in (a) topological couplers and (c) conventional directional couplers. The patterns are collected from the grating couplers of port 3 and port 4, when light of 1550 nm is input from port 1. The green dashed boxes denote the grating couplers. b, d Measured splitting ratio spectra for (b) topological couplers and (d) conventional couplers with different dimensional errors when inputting light from port 1. The orange regions in (b and d) represent the range where that splitting ratio for all three cases keeps within (3 ± 0.6) dB. The region spans from 1533 nm to 1581 nm in b and only 0.3 nm (from 1551.43 nm to 1551.73 nm) in (d)
In addition to the demonstration of the principles of topological physics, another important goal in topological nanophotonics is to achieve robust optical functionality even in the presence of fabrication errors. To verify this capability, we utilize the topological 3-dB coupler to construct an on-chip Michelson-like interferometer. The schematic in
Fig 4 Distance measurement with topological interferometers.
a Structure and operation principle of the topological interferometer. Middle: Illustration of the topological interferometer constructed by the 3-dB topological coupler and a pair of DBRs that placed at the end of the reference and measuring arms. The red arrows represent the forward propagating waves, while the blue arrows represent those reflected by the DBRs. The inset shows the SEM image of DBR. Left: SEM image of the coupling region of port 1. Right: SEM image of the coupling region of port 2. The coupling regions are designed to reduce the insertion loss of photonic crystal waveguides. b Transmission spectrum of topological interferometer in the C band. The red arrows show the extinction ratio. c Extinction ratio spectra of topological interferometer. The operation range from 1530 nm to 1583 nm is colored in orange, where the extinction ratio is > 20 dB. d Distance measurement with dimensional errors. The magnitude for certain length difference represents the intensity of light beams experiencing corresponding length difference in two arms. The magnitude is normalized by the zero-length-difference value, which represents the average of transmission spectrum
This interferometer design can be used to carry out distance measurements. For example, in
2
Owing to the wavelength-dependent nature of the waveguide mode dispersion (i.e., Δϕ is a function of wavelength), the transmission spectrum of port 2 exhibits periodic dips (
Furthermore, the length difference between two waveguides can be extracted by applying Fourier transform on the transmission spectrum. After introducing the dispersion of strip waveguide, we can obtain the length difference from the peak position of Fourier transform result [see details in Supplementary Section H]. In
We have designed and realized a topological coupler that maintains a 3-dB splitting ratio over a broad wavelength range, even in the presence of common dimensional errors during practical fabrication processes. The underlying principle of the 3-dB splitting origins from the valley-Hall topology and mirror symmetry, which we have theoretically elucidated by deriving a wavelength-insensitive scattering matrix. The tolerance analysis confirmed the robustness of the topological 3-dB coupler against dimensional errors, as compared to the conventional directional couplers (DCs). Furthermore, the proposed topological coupler was utilized to construct an on-chip interferometer capable of extracting the length difference between two arms. The interferometer exhibits remarkable resilience to dimensional errors, which is crucial for practical applications. This finding gives a systematic analysis on the advantages offered by topologically-protected edge modes and explicitly demonstrates the crucial performance of photonic structures. The proposal of topological splitting structure paves the way for the development of practical on-chip nanophotonic devices with topological protection. For example, the length difference measurement function can be applied in optical coherence tomographs and frequency modulated continuous wave LiDARs. To do this, the insertion loss between photonic crystals and strip waveguides should be further reduced to improve the signal-noise ratio of nanophotonic topological devices. The inverse design is anticipated to be applied for improving the performance of topological devices. In addition, the bandwidth and the footprint of topological coupler can be optimized based on the properties of topological valley edge modes [see details in Supplementary Sections G and I]. Based on VPCs, various kinds of on-chip photonic devices have been realized, such as asymmetric splitters
The transmission spectra and field distributions in our devices were simulated using Ansys Lumerical FDTD software, utilizing the finite-difference time-domain (FDTD) method. The band structures and eigen modes of VPCs were calculated using the eigenmode solver of MIT Photonic Bands (MPB)
We fabricated the experimental sample on a silicon-on-insulator (SOI) wafer, with a 220 nm-thick silicon top layer and a 3 μm-thick buried oxide layer. The pattern of the devices was defined using electron-beam lithography (Vistec EBPG 5200 +). Inductively coupled plasma etching technique (SPTS DRIE-I) was employed to transfer the pattern onto the silicon layer. The strip waveguides, photonic crystals, and distributed Bragg reflectors (DBRs) were etched to a depth of 220 nm, while the grating couplers was etched to a depth of 70 nm. Finally, a silica upper-cladding layer was deposited on top of the silicon layer.
For the measurements of transmission spectra and far-field images, three tunable continuous-wave lasers (Santec TSL-550/710) were utilized to cover the wavelength range from 1260 nm to 1640 nm. The incident light was launched into a fiber and then coupled to the input waveguide using a grating coupler. After passing through the devices based on VPCs, the output light was either coupled into a fiber or emitted into free space via grating couplers. To get the transmission spectra, the output light coupled to the fiber was detected by an optical power meter (Santec MPM-210). For obtaining far-field images, the output light emitted into free space was collected by a varifocal microscope objective and then imaged using an InGaAs CCD camera (Xenics Bobcat-640-GigE).
This work was supported by National Key Research and Development Program of China (Grant No. 2022YFA1404304), National Natural Science Foundation of China (Grant Nos. 62035016, 12274475, 12074443, 62105200), Guangdong Basic and Applied Basic Research Foundation (Grant Nos. 2023B1515040023, 2023B1515020072), Fundamental Research Funds for the Central Universities, Sun Yat-sen University (23lgbj021, 23ptpy01).
The authors declare that all data supporting the findings of this study are available within the paper and its Supplementary Information files.
The authors declare no competing interests.
Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41377-024-01512-3.
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