Abstract

Metasurfaces have found broad applicability in free-space optics, while its potential to tailor guided waves remains barely explored. By synergizing the Jones matrix model with generalized Snell’s law under the phase-matching condition, we propose a universal design strategy for versatile on-chip mode-selective coupling with polarization sensitivity, multiple working wavelengths, and high efficiency concurrently. The coupling direction, operation frequency, and excited mode type can be designed at will for arbitrary incident polarizations, outperforming previous technology that only works for specific polarizations and lacks versatile mode controllability. Here, using silicon-nanoantenna-patterned silicon-nitride photonic waveguides, we numerically demonstrate a set of chip-scale optical couplers around 1.55 μm, including mode-selective directional couplers with high coupling efficiency over 57% and directivity about 23 dB. Polarization and wavelength demultiplexer scenarios are also proposed with 67% maximum efficiency and an extinction ratio of 20 dB. Moreover, a chip-integrated twisted light generator, coupling free-space linear polarization into an optical vortex carrying 1 orbital angular momentum (OAM), is also reported to validate the mode-control flexibility. This comprehensive method may motivate compact wavelength/polarization (de)multiplexers, multifunctional mode converters, on-chip OAM generators for photonic integrated circuits, and high-speed optical telecommunications.

© 2020 Chinese Laser Press

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D. Marpaung, J. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Photonics 13, 80–90 (2019).
[Crossref]

Y. Hu, X. Luo, Y. Chen, Q. Liu, X. Li, Y. Wang, N. Liu, and H. Duan, “3D-integrated metasurfaces for full-colour holography,” Light: Sci. Appl. 8, 86 (2019).
[Crossref]

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[Crossref]

Y. Zhang, Z. Li, W. Liu, Z. Li, H. Cheng, S. Chen, and J. Tian, “Spin-selective and wavelength-selective demultiplexing based on waveguide-integrated all-dielectric metasurfaces,” Adv. Opt. Mater. 7, 1801273 (2019).
[Crossref]

Y. Meng, F. Hu, Z. Liu, P. Xie, Y. Shen, Q. Xiao, X. Fu, S.-H. Bae, and M. Gong, “Chip-integrated metasurface for versatile and multi-wavelength control of light couplings with independent phase and arbitrary polarization,” Opt. Express 27, 16425–16439 (2019).
[Crossref]

H.-X. Xu, G. Hu, Y. Li, L. Han, J. Zhao, Y. Sun, F. Yuan, G.-M. Wang, Z. H. Jiang, X. Ling, T. J. Cui, and C.-W. Qiu, “Interference-assisted kaleidoscopic meta-plexer for arbitrary spin-wavefront manipulation,” Light: Sci. Appl. 8, 3 (2019).
[Crossref]

H.-X. Xu, G. Hu, L. Han, M. Jiang, Y. Huang, Y. Li, X. Yang, X. Ling, L. Chen, J. Zhao, and C.-W. Qiu, “Chirality-assisted high-efficiency metasurfaces with independent control of phase, amplitude, and polarization,” Adv. Opt. Mater. 7, 1801479 (2019).
[Crossref]

H. Kwon, E. Arbabi, S. M. Kamali, M. Faraji-Dana, and A. Faraon, “Single-shot quantitative phase gradient microscopy using a system of multifunctional metasurfaces,” Nat. Photonics 13, 109–114 (2019).
[Crossref]

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8, 90 (2019).
[Crossref]

W.-Y. Tsai, Q. Sun, G. Hu, P. C. Wu, R. J. Lin, C.-W. Qiu, K. Ueno, H. Misawa, and D. P. Tsai, “Twisted surface plasmons with spin-controlled gold surfaces,” Adv. Opt. Mater. 7, 1801060 (2019).
[Crossref]

X. Liang, Y. Li, Z. Geng, and Z. Liu, “Selective transverse mode operation of a fiber laser based on few-mode FBG for rotation sensing,” Opt. Express 27, 37964–37974 (2019).
[Crossref]

W. Kong, H. Kum, S.-H. Bae, J. Shim, H. Kim, L. Kong, Y. Meng, K. Wang, C. Kim, and J. Kim, “Path towards graphene commercialization from lab to market,” Nat. Nanotechnol. 14, 927–938 (2019).
[Crossref]

S.-H. Bae, H. Kum, W. Kong, Y. Kim, C. Choi, B. Lee, P. Lin, Y. Park, and J. Kim, “Integration of bulk materials with two-dimensional materials for physical coupling and applications,” Nat. Mater. 18, 550–560 (2019).
[Crossref]

F. Peyskens, C. Chakraborty, M. Muneeb, D. V. Thourhout, and D. Englund, “Integration of single photon emitters in 2D layered materials with a silicon nitride photonic chip,” Nat. Commun. 10, 4435 (2019).
[Crossref]

G. Hu, X. Hong, K. Wang, J. Wu, H. Xu, W. Zhao, W. Liu, S. Zhang, F. Garcia-Vidal, B. Wang, P. Lu, and C.-W. Qiu, “Coherent steering of nonlinear chiral valley photons with a synthetic metasurface,” Nat. Photonics 13, 467–472 (2019).
[Crossref]

2018 (13)

C. Choi, J. Huang, H.-C. Cheng, H. Kim, A. K. Vinod, S.-H. Bae, V. O. Ozcelik, R. Grassi, J. Chae, S.-W. Huang, X. Duan, K. Kaasbjerg, T. Low, and C. W. Wong, “Enhanced interlayer neutral excitons and trions in trilayer van der Waals heterostructures,” npj 2D Mater. Appl. 2, 30 (2018).
[Crossref]

Y. Meng, S. Ye, Y. Shen, Q. Xiao, X. Fu, R. Lu, Y. Liu, and M. Gong, “Waveguide engineering of graphene optoelectronics–modulators and polarizers,” IEEE Photonics J. 10, 6600217 (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

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2016 (3)

2015 (7)

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2000 (1)

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Figures (8)

Fig. 1.
Fig. 1. (a) Metasurface concepts comparison. Propagation phase metasurface: engineered antenna geometry (lx,ly) but fixed rotation angle θ. Geometric phase metasurface: identical antennas with spatially varying orientation angle [3941]. In the Jones matrix model (two working scenarios), red or orange color-highlighted phases or polarizations represent configurable parameters, while black or gray colored parts denote given or not configurable factors. (b) The normally incident light can be directionally coupled into specific waveguide modes after consecutive interactions with the gradient metasurface. (c) Flow chart for design process (detailed in Methods section).
Fig. 2.
Fig. 2. Polarization (de)multiplexers for arbitrary elliptical polarizations. (a), (e), and (i) Device structure sketch for splitting arbitrary orthogonal polarizations (|λ+=R(π/4)·[cos(ε)|x+i×sin(ε)|y], |λ=R(π/4)·[i×sin(ε)|x+cos(ε)|y]) with three representative incident elliptical parameters ε=40°, 60°, and 80°, respectively. Accompanied forms: antenna design details (fixed antenna height: lz=1.2  μm). (b), (f), and (j) Corresponding incident polarization illustrations. (c), (g), and (k) Coupling efficiency as a function of wavelength for ε=40°, 60°, and 80°, respectively, validating that our method is applicable for arbitrary polarizations. (d), (h), and (l) Corresponding directivity spectra.
Fig. 3.
Fig. 3. (a) Device schematic of the integrated linear-polarization (de)multiplexer. Waveguide width×height=680  nm×600  nm. (b) Phase map showing the phase retardation of transmitted light as a function of antenna geometry (lx,ly) at λ=1.55  μm with fixed antenna height lz=1.2  μm. (c) Distribution of electric field component Ey in the xy plane under |y plane wave illumination (λ=1.55  μm). Antenna and waveguide profiles are marked in solid and dashed lines, respectively. (d), (e) Full-wave simulations showing the directional coupling of electric field components Ez and Ey into opposite directions under illumination of linear |x and |y polarizations, respectively. (f), (g) Vector diagram of the electric field at the left (under |x illumination) and right (|y illumination) waveguide ports , respectively, at λ=1.55  μm. (h) Corresponding electric field norm |E| distribution. (i), (j) Coupling efficiency spectra under |x and |y excitations, respectively. (k) Structure sketch for the circular-polarization (de)multiplexer. (l) Circular polarization demultiplexing: |E| distributions under incident left-handed (LCP) and right-handed circular polarization (RCP). (m) Vector diagram and |E| distribution at the right waveguide port (approximate TM00 mode) under LCP incidence (λ=1.55  μm). (n) Coupling efficiency spectrum (LCP illumination). (o) Directivity spectrum.
Fig. 4.
Fig. 4. (a) Structure for the multifunctional (de)multiplexer for circular polarizations. When working at a fixed wavelength, it functions as a spin/polarization demultiplexer, while under fixed incident polarizations it works as a wavelength demultiplexer/color router. (b), (c) Coupling efficiency spectrum under LCP and RCP illumination, respectively. (d)–(f) Similar to (a)–(c) but for device working for linear polarizations. The shape difference between the curves in (e) and (f) can be ascribed to the discrepancy of spatial modal overlap η under different incident polarizations.
Fig. 5.
Fig. 5. (a) Device structure sketch for the waveguide-integrated mode-selective directional coupler. A left single-row antenna array (namely TE00 antennas) is applied to excite left-propagating TE00 mode. Double rows of identical antenna arrays (namely TE10 antennas) with dislocations of Δx0.5  μm in the x direction and Δy0.8  μm in the y direction. Accompanied form: detailed design parameters. (b) Electric field component Ey distribution along middle waveguide plane under the illumination of |y polarized plane wave. (c) Antenna near fields (see Methods). Left and middle panels: Ey and Ex distributions for an lx×ly=0.2  μm×0.4  μm antenna (θ = 0°) placed at waveguide center (as TE00 antennas). Right panel: Ez distribution along the center plane between two TE10 antennas (m=4 for upper and lower groups). (d) Electric field distributions for ideal TE00 (Ey), TM00 (Ex), and TE10 (Ey) modes. (e) Calculated output |Ey| distributions for the left (upper panel) and right (lower panel) waveguide ports accordingly. (f) Corresponding vector diagram of output electric fields at waveguide ports, agreeing well with TE00 and TE10 modes. (g) Device structure (with antenna design parameters) launching left-propagating TM11 mode with two rows of dislocated antennas (upper and lower groups). Right panel: simulated output |Ez| distribution at the left waveguide port at λ=1.55  μm. (h) Design schematic for the directional coupler to selectively excite TM20 mode (with three antenna rows). Antenna center coordinates: ymid=0, yup=ylow=0.7  μm. Right panel: |Ez| distribution at the left waveguide port (λ=1.55  μm).
Fig. 6.
Fig. 6. (a) Device schematic for chip-integrated OAM generator: directional coupling normally incident linearly y-polarized plane wave into right-propagating optical vortex beam. (b) Top view of the device with design parameters manifested in the accompanied forms. Δx20.415  μm and Δy0.8  μm. (c) Working principle illustration: combining TE01 and TE10 modes with π/2 phase difference can theoretically produce a helically phased vortex field with topological charge =+1. Upper panels: |Ey| distributions for ideal TE01, TE10 and mixed OAM modes accordingly. Lower panels: corresponding phase distributions. (d) Calculated output electric field |Ey| distributions when only the TE01 antennas exist (left panel), only TE10 antennas exist (middle panel), and both TE01 and TE10 antennas exist (right panels). Right most panel: corresponding (to the right panel) phase distribution at waveguide right port showing OAM+1 mode. White lines denote waveguide profile. (e), (f) Coupling efficiency and mode purity spectra when only the TE01 (left panel) or TE10 (right panel) antennas are present accordingly. (g) Calculated output OAM1 mode [|Ey| and phase (|Ey|)] distributions after re-arranging the relative locations of the TE01 and TE10 antennas in the x direction. (h), (i) Output vortex beam [instantaneous Ey and phase (Ey) at λ=1.45  μm] with =+1 and =1, respectively, after exiting waveguide right port with a propagation distance of 2 μm in free space.
Fig. 7.
Fig. 7. Analysis on the impact of different light sources for the device in Fig. 4(a). (a)–(c) Coupling efficiency spectrum under the excitation of different (RCP) light sources: (a) diffracting plane wave (plane wave trimmed by a rectangular aperture: x×y=8  μm×0.6  μm); (b), (c) focused Gaussian beams by a thin lens with circular (lens numerical aperture NA=0.2) and elliptical light spot (after beam transformation with lens NA=0.6), respectively. Insets: illumination condition sketch showing the relative size of the light spot and antenna array (see Methods). (d) Comparison of coupling directivity spectra.
Fig. 8.
Fig. 8. (a) Illustration of fabrication (fab) error on antenna geometry. (b)–(d) Coupling efficiency spectra for device shown in Fig. 3(a) with random (independent) fabrication errors Δlx, Δly obeying normal distributions N(0,102), N(0,202), and N(5,102), respectively. (e) Comparison of directivity spectrum. (f) Sketch of an antenna cell with random fabrication error on geometry (Δlx,Δly, unit: nm) and rotation angle (Δθ, unit: °). (g)–(i) Coupling efficiency curves for the device in Fig. 3(k) with (g) Δlx,ΔlyN(0,102), (h) Δlx,ΔlyN(0,202), and (i) ΔθN(0,102), respectively. (j) Directivity comparison. (k) Misalignment illustration of the whole antenna array(s) on a waveguide with positive Δym. (l), (m) Coupling efficiency spectra for the device in Fig. 4(a) with misalignments Δym=+100  nm and 100  nm, respectively. (n), (o) Comparisons of directivity spectra for the devices in Figs. 3(a) and 5(a) with different values of Δym.

Equations (7)

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(ntsinθtnisinθi)k0=neffk0=Δφd·sign(Δφd),
J(m,n)=[eiφ+(m,n)|(λ+)*,eiϕ(m,n)|(λ+)*]·[|λ+,|λ]1.
{Δφ0d=neff|λ=λ1·k0Δφ02πd=neff|λ=λ2·k0,
minlx,ly{max{|φxdesignφxsimulation|,|φydesignφysimulation|}}.
J=[jxxjxyjxyjyy]=R(θ)[eiφx00eiφy]R(θ),
[jxx,jxy]T=[[|κ,|λ]T]1·[λ1,κ1]Tandjyy=jxx·exp(2ijxy),
η|Eantenna(x,y,z)·Emode*(x,y,z)dydz|2(|Eantenna(x,y,z)|2dydz)·(|Emode(x,y,z)|2dydz).

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