Cite as: H. Ren et al., Science 10.1126/science.aaf1112 (2016).

REPORTS

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Optical multiplexing using physical dimensions of light in-cluding space (1), frequency (2), brightness (3), color (1, 4), polarization (1, 5, 6), mode (7) and lifetime (8) has played a crucial role in the age of information technologies for high-definition displaying (3–5), high-capacity data storage (1, 6), high-speed communications (7), and high-sensitive biologi-cal sensing (8). As one of the most fundamental physical properties in both classical and quantum optics, angular momentum (AM) of light including spin angular momen-tum (SAM) possessed by circularly-polarized light and or-bital angular momentum (OAM) manifested by the helical wavefront of light has emerged as a physically-orthogonal multiplexing approach to high-capacity optical communica-tions ranging from free-space (9) to compact optical fibers (10). However, macroscale interference-based detection methods through hologram-coding (9, 10) or phase-shifting (11, 12) of AM carrying beams have imposed a fundamental physical limit to realize such a principle at a chip-scale foot-print.

The advance of strong light-confinement nanophotonic approaches has been a major propellant of miniaturized optical circuits to harness AM of light. The chip-scale gener-ation and transmission of AM carrying beams on silicon-integrated circuits have been realized through whispering-gallery-mode resonators (13) and resonant micro-ring fibers (10). However, these approaches are resonant in nature, leading to a narrow bandwidth down to several nanometers. Surface plasmon polaritons (SPPs) capable of strong light confinements have long been pursued to overcome the size limitation of nanophotonic devices, and hence potentially

facilitate the chip-scale multiplexing of SAM through the SAM-distinguishing nanostructures (14–18). Even though the OAM generators mediated by SPPs have been demon-strated either through digitalized metasurfaces with a heli-cal phase (19) or geometric metasurfaces based on spin-orbit interaction (20), the extrinsic nature of OAM (21) with heli-cal wavefronts restricts its detection to a phase-sensitive interference-based method through a holographic metasur-face (22), which inevitably degrades the perceptive devices for on-chip applications.

The concept of our on-chip non-interference AM multi-plexing of broadband light is illustrated in Fig. 1. Without losing the generality, co-axially-superposed AM carrying beams with four selected AM modes of l0 = –4, s = –1 (AM1), l0 = –2, s = –1 (AM2), l0 = +2, s = +1 (AM3) and l0 = +4, s = +1 (AM4) (Fig. 1A) propagate through a NRA multiplexing unit consisting of shallow nano-grooves and the spatially-shifted mode-sorting nano-ring slits with different sizes (Fig. 1B and fig. S1A). The nano-groove structures act as the metal-dielectric interfaces to convert the AM modes carried by photons into SPPs and to spatially route the excited plas-monic AM modes to the locations of nano-ring slits. A set of AM carrying beams of l0 = ±1, ±2, ±3, ±4 and s = ±1 (fig. S2) can be adopted to excite a range of plasmonic AM modes (determined by total AM L= l0 + s + ls, where ls is the geo-metrical topological charge arising from the nano-grooves) with a distinguished spatial separability from the structure depicted in fig. S1A. The formation of the spatial separabil-ity by nano-grooves provides a physical ground for AM mode sorting. As a result of the distinctive AM mode-sorting

On-chip noninterference angular momentum multiplexing of broadband light Haoran Ren,1 Xiangping Li,1,2 Qiming Zhang,1,3 Min Gu1,3* 1Centre for Micro-Photonics and CUDOS, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia. 2Institute of Photonics Technology, Jinan University, Guangzhou, China. 3Artificial-Intelligence Nanophotonics Laboratory, School of Science, RMIT University, Melbourne, VIC 3001, Australia.

*Corresponding author. Email: min.gu@rmit.edu.au

Angular momentum division has emerged as a physically-orthogonal multiplexing method in high-capacity optical information technologies. However, the typical bulky elements used for information retrieval from the overall diffracted field based on the interference method imposes a fundamental limit toward realizing on-chip multiplexing. We demonstrate non-interference angular momentum multiplexing using a mode-sorting nano-ring aperture with a chip-scale footprint as small as 4.2 × 4.2 μm2, where nano-ring slits exhibit a distinctive outcoupling efficiency on tightly-confined plasmonic modes. The non-resonant mode-sorting sensitivity and scalability of our approach enable on-chip parallel multiplexing over a bandwidth of 150 nm in the visible wavelength range. The results offer the possibility of ultrahigh-capacity and miniaturized nanophotonic devices harnessing angular momentum division.

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sensitivity by nano-ring slits, the plasmonic AM modes can be selectively coupled out through the slits that have differ-ent sizes and spatial shifts (Fig. 1C). Furthermore, the non-resonant AM mode-sorting sensitivity by the nano-ring slits enables the AM multiplexing over a broad bandwidth. As such, a large-scale NRA-structured AM multiplexing chip (NAMMC) (Fig. 1D) consisting of an array of individually-addressable NRAs, wherein NRA units are separated by the spacing larger than the diffraction-limit distance, allows for on-chip processing AM-multiplexed image in parallel through a multi-beam approach (Fig. 1E).

In terms of operation mechanism, a nano-ring slit en-closed by a concentric nano-groove (ls = 0) in a gold film is considered. The width of the nano-ring slit was fixed as 50 nm throughout this paper. A full vectorial approach for the analysis of the AM mode in the nano-ring slit was carried out (23). The calculated effective indices of eigen-AM modes of L = ±1 and L = ±3 with respect to the cut-off AM mode (fig. S3) of the nano-ring slit indicate the lower AM mode of L = ±1 can be supported by both slits but the higher AM mode of L = ±3 can only be maintained by the slit with Rin2 (red curves in Fig. 2A). Moreover, the effective index differ-ences almost keep flat in visible wavelengths, which indi-cates the non-resonant nature of AM modes supported by nano-ring slits and lays the foundation for multiplexing of broadband light.

The outcoupling (transmittance) efficiency of nano-ring slits can be determined by the mode matching between the eigen-AM mode supported by nano-ring slits (fig. S4, A to C) and the plasmonic AM mode excited from nano-grooves (fig. S4, D to F). A mode matching factor (MF) can be defined (23) to intuitively understand the distinctive AM mode-sorting selectivity by the nano-ring slits. The MF can be se-lectively maximized from its dependence on the illumina-tion wavelength and on the slit radius (fig. S4, G to I). As an example, the black curves in Fig. 2A reveal that plasmonic modes with total AM of L = ±1 and L = ±3 can be distinc-tively coupled out through nano-ring slits with Rin1 and Rin2, respectively. In addition, the theoretical analysis of the fun-damental symmetries in nanophotonics (24, 25) provides physical insights into the NRA exhibiting the distinctive sensitivity on total AM of SPPs, which yields an additional flexibility in the subsequent chip design operating by differ-ent SAM and OAM combinations with the given total AM.

The distinctive AM mode-sorting selectivity, as defined in (23), can be experimentally verified for AM modes of L = ±1 and L = ±3 over a broad bandwidth of 150 nm in visible wavelengths (Fig. 2D). As an illustration, transmissive pat-terns of the AM beams at the wavelength of 640 nm are giv-en in fig. S5. The physical principle of the distinctive AM mode-sorting selectivity can be extended to other wave-lengths such as telecommunication bands ranging from 1.45

μm to 1.65 μm (fig. S6). The principle of the AM mode-sorting selectivity by the

nano-ring slits with different sizes can be adopted for chip-scale multiplexing of AM-superposed beams if two nano-ring slits with Rin1 and Rin2 are used concentrically. In Fig. 3, A to D, two sections of the circular nano-grooves were spa-tially-shifted in the opposite directions yielding ls = +2 and AM beams of AM1 and AM2 can excite plasmonic AM modes corresponding to L = –3 and L = –1, respectively, leading to the distinctive transmittance from the concentrically-aligned nano-ring slits. The capacity of the AM mode-sorting multiplexing can be increased by laterally shifting one of the circular nano-groove sections and the enclosed nano-ring slit in the opposite directions (Fig. 3, E to H). Us-ing this nano-groove shifting principle, AM beams with OAM modes ranging from l0 = –4 to l0 = +4 and SAM modes of s = –1 and s = +1 can be coupled out by the two spatially-shifted nano-ring slits that have different locations and sizes with the smallest footprint of 4.2 × 4.2 μm2 (fig. S7).

Based on the AM mode-sorting principle, we can achieve on-chip multiplexing of multiple AM modes (Fig. 4). Here, we used two concentric double nano-ring slits (Fig. 4A and fig. S1D) to selectively couple out the AM beams of AM1, AM2, AM3 and AM4, which can be straightforwardly evi-denced by their distinctive transmissive patterns in the far-field region (fig. S8). As such, chip-scale AM multiplexing by dynamically switching on individual AM beams can be di-rectly observed at different wavelengths (Fig. 4B and fig. S9) with a modal crosstalk as low as –17 dB (Fig. 4C).

The broadband feature of the non-interference AM mul-tiplexing by the chip-scale NRA can enable a multiplexing chip constructed by an array of NRAs, the NAMMC, to carry out both AM- and wavelength-division multiplexing in par-allel. The NAMMC consisting of an array of 8 by 8 NRA units was fabricated (Fig. 4D) and illuminated by an array of 8 by 8 multi-beams carrying well-defined SAM and OAM (23) (figs. S10 and S11). Consequently, Fig. 4E shows the ex-perimentally-reconstructed AM- and wavelength-coded im-ages (with 100 by 100 pixels) which were built into a piece at a time through the dynamic area-by-area coding method (23). In addition, we show that the NAMMC is also capable of displaying the AM-coded image by simultaneously ad-dressing the four AM information channels (fig. S12).

Although in bulky optics, OAM multiplexing is outper-formed by conventional multiplexing techniques in terms of multiplexing capacity, OAM multiplexing outperforms other techniques in nanoscale systems with a small space-bandwidth product (26). The AM mode-sorting sensitivity of the NRAs can be in general extended to other nano-groove systems with different ls (figs. S13 and S14) and to multiple concentric nano-ring slits. This generalization can be advan-tageous for the further reduction of the footprint of NRAs

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while multiplexing optical beams with more AM modes is demanded. The non-interference operating principle in NRAs removes the requirement of bulky interference-based optics and the associated non-resonance nature can largely increase the multiplexing capacity in conjunction with the wavelength-division multiplexing in a broad band. The large-scale NAMMC can be further integrated with chip-scale AM generators and thereby could offer compact on-chip AM applications in optical communication, infor-mation display, data storage and data encryption.

REFERENCES AND NOTES 1. P. Zijlstra, J. W. M. Chon, M. Gu, Five-dimensional optical recording mediated by

surface plasmons in gold nanorods. Nature 459, 410–413 (2009). Medline doi:10.1038/nature08053

2. N. J. Karl, R. W. Mckinney, Y. Monnai, R. Mendis, D. M. Mittleman, Frequency-division multiplexing in the terahertz range using a leaky-wave antenna. Nat. Photonics 9, 717–720 (2015). doi:10.1038/nphoton.2015.176

3. H. Yun, S. Y. Lee, K. Hong, J. Yeom, B. Lee, Plasmonic cavity-apertures as dynamic pixels for the simultaneous control of colour and intensity. Nat. Commun. 6, 7133 (2015). Medline doi:10.1038/ncomms8133

4. R. Deng, F. Qin, R. Chen, W. Huang, M. Hong, X. Liu, Temporal full-colour tuning through non-steady-state upconversion. Nat. Nanotechnol. 10, 237–242 (2015). Medline doi:10.1038/nnano.2014.317

5. X. Li, H. Ren, X. Chen, J. Liu, Q. Li, C. Li, G. Xue, J. Jia, L. Cao, A. Sahu, B. Hu, Y. Wang, G. Jin, M. Gu, Athermally photoreduced graphene oxides for three-dimensional holographic images. Nat. Commun. 6, 6984 (2015). Medline doi:10.1038/ncomms7984

6. X. Li, T. H. Lan, C. H. Tien, M. Gu, Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam. Nat. Commun. 3, 998 (2012). Medline doi:10.1038/ncomms2006

7. L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, M. Lipson, WDM-compatible mode-division multiplexing on a silicon chip. Nat. Commun. 5, 3069 (2014). Medline doi:10.1038/ncomms4069

8. Y. Lu, J. Zhao, R. Zhang, Y. Liu, D. Liu, E. M. Goldys, X. Yang, P. Xi, A. Sunna, J. Lu, Y. Shi, R. C. Leif, Y. Huo, J. Shen, J. A. Piper, J. P. Robinson, D. Jin, Tunable lifetime multiplexing using luminescent nanocrystals. Nat. Photonics 8, 32–36 (2014). doi:10.1038/nphoton.2013.322

9. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, A. E. Willner, Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 6, 488–496 (2012). doi:10.1038/nphoton.2012.138

10. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545–1548 (2013). Medline doi:10.1126/science.1237861

11. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, M. J. Padgett, Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 105, 153601 (2010). Medline doi:10.1103/PhysRevLett.105.153601

12. M. Mirhosseini, M. Malik, Z. Shi, R. W. Boyd, Efficient separation of the orbital angular momentum eigenstates of light. Nat. Commun. 4, 2781 (2013). Medline doi:10.1038/ncomms3781

13. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, S. Yu, Integrated compact optical vortex beam emitters. Science 338, 363–366 (2012). Medline doi:10.1126/science.1226528

14. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, M. Wegener, Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009). Medline doi:10.1126/science.1177031

15. Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, E. Hasman, Observation of optical spin symmetry breaking in nanoapertures. Nano Lett. 9, 3016–3019 (2009). Medline doi:10.1021/nl901437d

16. X. Yin, Z. Ye, J. Rho, Y. Wang, X. Zhang, Photonic spin Hall effect at metasurfaces. Science 339, 1405–1407 (2013). Medline doi:10.1126/science.1231758

17. J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, F. Capasso, Polarization-controlled tunable directional coupling of surface plasmon polaritons. Science 340, 331–334 (2013). Medline doi:10.1126/science.1233746

18. X. Zambrana-Puyalto, X. Vidal, G. Molina-Terriza, Angular momentum-induced circular dichroism in non-chiral nanostructures. Nat. Commun. 5, 4922 (2014). Medline doi:10.1038/ncomms5922

19. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, Z. Gaburro, Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science 334, 333–337 (2011). Medline doi:10.1126/science.1210713

20. M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, X. Luo, Catenary optics for achromatic generation of perfect optical angular momentum. Sci. Adv. 1, e1500396 (2015). Medline doi:10.1126/sciadv.1500396

21. A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Phys. Rev. Lett. 88, 053601 (2002). Medline doi:10.1103/PhysRevLett.88.053601

22. P. Genevet, J. Lin, M. A. Kats, F. Capasso, Holographic detection of the orbital angular momentum of light with plasmonic photodiodes. Nat. Commun. 3, 1278 (2012). Medline doi:10.1038/ncomms2293

23. Materials and methods and supplementary text are available as supplementary materials on Science Online.

24. I. Fernandez-Corbaton, X. Zambrana-Puyalto, G. Molina-Terriza, Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions. Phys. Rev. A 86, 042103 (2012). doi:10.1103/PhysRevA.86.042103

25. I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, X. Vidal, M. L. Juan, G. Molina-Terriza, Electromagnetic duality symmetry and helicity conservation for the macroscopic Maxwell’s equations. Phys. Rev. Lett. 111, 060401 (2013). Medline doi:10.1103/PhysRevLett.111.060401

26. N. Zhao, X. Li, G. Li, J. M. Kahn, Capacity limits of spatially multiplexed free-space communication. Nat. Photonics 9, 822–826 (2015). doi:10.1038/nphoton.2015.214

27. P. B. Johnson, R. W. Christy, Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972). doi:10.1103/PhysRevB.6.4370

28. M. I. Haftel, C. Schlockermann, G. Blumberg, Enhanced transmission with coaxial nanoapertures: Role of cylindrical surface plasmons. Phys. Rev. B 74, 235405 (2006). doi:10.1103/PhysRevB.74.235405

29. M. Gu, in Advanced Optical Imaging Theory (Springer, 2000), pp. 7–107. 30. H. Ren, H. Lin, X. Li, M. Gu, Three-dimensional parallel recording with a Debye

diffraction-limited and aberration-free volumetric multifocal array. Opt. Lett. 39, 1621–1624 (2014). Medline doi:10.1364/OL.39.001621

ACKNOWLEDGMENTS

We thank Xijun Li for the help on the ion beam lithography, Gedminas Gervinskas and Fatima Eftekhari from the Melbourne Centre for Nanofabrication for their fabrication efforts, Hua Lu for the technical assistance in the waveguide calculation, and Jelle Storteboom for the training of using Spectra-Physics Inspire laser system. This work was supported under the Australian Research Council Laureate Fellowship program (FL100100099). M.G. acknowledges the support from the Australian Research Council Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS) (project number CE110001018). X.L. acknowledges the support from the Australian Research Council (DE150101665). All data related to the experiments described in this manuscript are archived on a lab computer at Swinburne University of Technology.

SUPPLEMENTARY MATERIALS www.sciencemag.org/cgi/content/full/science.aaf1112/DC1 Materials and Methods Supplementary Text Figures S1 to S14 References (27–30) 18 December 2015; accepted 9 March 2016 Published online 7 April 2016 10.1126/science.aaf1112

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Fig. 1. The principle of on-chip non-interference AM multiplexing of broadband light. (A) Four selected AM beams of l0 = –4, s = –1 (AM1), l0 = –2, s = –1 (AM2), l0 = +2, s = +1 (AM3) and l0 = +4, s = +1 (AM4) are co-axially overlapped as the AM-superposed beams (l0 and s are the modal indices for OAM and SAM, respectively). (B) The schematic of a NRA multiplexing unit consisting of nano-groove structures and the mode-sorting nano-ring slits. (C) The mechanism for AM mode-sorting by nano-ring slits that have different sizes and lateral shifts. (D) The NAMMC integrated by an array of 8 by 8 NRA units. (E) Concept of on-chip processing of AM-multiplexed images over a broadband by the NAMMC.

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Fig. 2. Distinctive AM mode-sorting selectivity by a size-varying nano-ring slit. (A) The theoretically calculated effective index differences (red curves) and the MF (black curves) for the plasmonic modes with total AM of L = ±1 (solid lines) and L = ±3 (dashed lines) for nano-ring slit with Rin1 = 75 nm (upper) and Rin2 = 200 nm (lower), respectively. (B and C) The scanning electron microscopy (SEM) images of the fabricated NRAs consisting of concentric nano-grooves and nano-ring slits with the inner radii of Rin1 (see fig. S1B for 45 degree view) and Rin2 (see fig. S1C for 45 degree view), respectively. The insets are the enlarged view of the nano-ring slits with a scale bar of 100 nm. (D) The numerically-calculated (curves) and experimentally-confirmed (triangles) AM mode-sorting selectivity spectra of the AM beams of l0 = –2, s = +1 (L = –1) and l0 = +2, s = +1 (L = +3) for nano-ring slits with the inner radii of Rin1 (upper) and Rin2 (lower), respectively. The red color marks out the bandwidths (defined as the selectivity ≥ 0.1) of AM mode-sorting selectivity by nano-ring slits.

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Fig. 3. Experimental characterization of chip-scale AM multiplexing based on double concentric and spatially-shifted nano-ring slits enclosed by sections of spatially-shifted nano-grooves. (A) The SEM image of the double nano-ring slits (inset) with Rin1 and Rin2 enclosed by the two sections of shifted grooves with ls = +2. (B) The simulated total intensity distributions of the AM beams of AM1 and AM2 in the longitudinal planes of nano-ring slits. (C) The experimental far-field intensity distributions of the AM beams of AM1 and AM2 in the transverse planes. (D) The experimental cross-section plots of the far-field intensity distributions in (C) as labeled by the dashed white lines. (E to H) The counterparts of (A) to (D) but based on the spatially-shifted nano-ring slits with Rin1 and nano-grooves with ls = +2 (left) and ls = –2 (right).

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Fig. 4. Four-state AM multiplexing through a NRA unit and parallel AM- and wavelength-division multiplexing through the large-scale NAMMC. (A) The SEM image of the single NRA (see fig. S1D for 45 degree view) in the NAMMC and the two concentric double nano-ring slits (inset). (B) The experimental characterization of the four-state AM multiplexing by dynamically switching on the AM-superposed beams. The images are presented in pseudo colors. (C) Measured modal crosstalk of the four AM modes at different wavelengths. (D) The SEM image of the NAMMC. (E) The experimentally-reconstructed AM- and wavelength-coded images retrieved from the four AM modes of AM1, AM2, AM3 and AM4 (Fig. 1A) at the three different wavelengths.