Abstract

Spin-polarized directive coupling of light associated with the photonic quantum spin-Hall effect (QSHE) is a nanoscale phenomenon based on strong spin–orbit interaction that has recently attracted significant attention. Herein, we discuss the experimental manifestation of QSHE intrinsic in the Bloch waves associated with a bound state in the continuum (BIC) of a dielectric photonic crystal metasurface (PhCM). We show numerically that BICs in nanoscale PhCMs have photonic spin angular momentum density transverse to the orbital momentum not only at the interfaces but also inside the confining dielectric medium. Then, we experimentally demonstrate that the fundamental Bloch waves of the BIC mode, macroscopically amplified on resonance, propagate along the symmetry axes of the PhCM obeying spin-momentum locking also at normal incidence, i.e., with no symmetry breaking. This BIC-enhanced spin-directive coupling of light may enable versatile implementations of spin-optical structures, paving the way for novel photonic spin multiplatform devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

W. Chen, Y. Chen, and W. Liu, “Singularities and poincaré indices of electromagnetic multipoles,” Phys. Rev. Lett. 122, 153907 (2019).
[Crossref]

F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13, 390–396 (2019).
[Crossref]

S. Romano, G. Zito, S. N. Lara Yépez, S. Cabrini, E. Penzo, G. Coppola, I. Rendina, and V. Mocella, “Tuning the exponential sensitivity of a bound-state-in-continuum optical sensor,” Opt. Express 27, 18776–18786 (2019).
[Crossref]

2018 (6)

S. Romano, A. Lamberti, M. Masullo, E. Penzo, S. Cabrini, I. Rendina, and V. Mocella, “Optical biosensors based on photonic crystals supporting bound states in the continuum,” Materials 11, 526 (2018).
[Crossref]

S. Romano, G. Zito, S. Torino, G. Calafiore, E. Penzo, G. Coppola, S. Cabrini, I. Rendina, and V. Mocella, “Label-free sensing of ultralow-weight molecules with all-dielectric metasurfaces supporting bound states in the continuum,” Photon. Res. 6, 726–733 (2018).
[Crossref]

Y. Zhang, A. Chen, W. Liu, C. W. Hsu, B. Wang, F. Guan, X. Liu, L. Shi, L. Lu, and J. Zi, “Observation of polarization vortices in momentum space,” Phys. Rev. Lett. 120, 186103 (2018).
[Crossref]

H. M. Doeleman, F. Monticone, W. den Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12, 397–401 (2018).
[Crossref]

S. Romano, G. Zito, S. Managò, G. Calafiore, E. Penzo, S. Cabrini, A. C. De Luca, and V. Mocella, “Surface-enhanced Raman and fluorescence spectroscopy with an all-dielectric metasurface,” J. Phys. Chem. C 122, 19738–19745 (2018).
[Crossref]

K. Koshelev, A. Bogdanov, and Y. Kivshar, “Meta-optics and bound states in the continuum,” Sci. Bull. 64, 836–842 (2018).
[Crossref]

2017 (5)

A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541, 196–199 (2017).
[Crossref]

J. Gomis-Bresco, D. Artigas, and L. Torner, “Anisotropy-induced photonic bound states in the continuum,” Nat. Photonics 11, 232–236 (2017).
[Crossref]

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6, 51–70 (2017).
[Crossref]

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
[Crossref]

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11, 763 (2017).
[Crossref]

2016 (4)

T. Van Mechelen and Z. Jacob, “Universal spin-momentum locking of evanescent waves,” Optica 3, 118–126 (2016).
[Crossref]

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, “Photonic spin-controlled multifunctional shared-aperture antenna array,” Science 352, 1202–1206 (2016).
[Crossref]

R. Gansch, S. Kalchmair, P. Genevet, T. Zederbauer, H. Detz, A. M. Andrews, W. Schrenk, F. Capasso, M. Loncar, and G. Strasser, “Measurement of bound states in the continuum by a detector embedded in a photonic crystal,” Light Sci. Appl. 5, e16147 (2016).
[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

2015 (6)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

V. Mocella and S. Romano, “Giant field enhancement in photonic resonant lattices,” Phys. Rev. B 92, 155117 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref]

K. Y. Bliokh, F. Rodrguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

2014 (7)

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

2013 (6)

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
[Crossref]

2012 (1)

V. Liu and S. Fan, “S4: a free electromagnetic solver for layered periodic structures,” Comp. Phys. Commun. 183, 2233–2244 (2012).
[Crossref]

2011 (3)

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19, 26132–26149 (2011).
[Crossref]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

2005 (1)

C. L. Kane and E. J. Mele, “z2 topological order and the quantum spin Hall effect,” Phys. Rev. Lett. 95, 146802 (2005).
[Crossref]

2002 (1)

S. Fan and J. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[Crossref]

1985 (1)

H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32, 3231 (1985).
[Crossref]

1929 (1)

J. von Neumann and E. P. Wigner, “Über merkwürdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen,” Phys. Z. 30, 465–467 (1929).

Aiello, A.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Albrecht, B.

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Allen, L.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (CRC Press, 2003).

Alonso, M. A.

Altug, H.

F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13, 390–396 (2019).
[Crossref]

Alù, A.

H. M. Doeleman, F. Monticone, W. den Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12, 397–401 (2018).
[Crossref]

Andrews, A. M.

R. Gansch, S. Kalchmair, P. Genevet, T. Zederbauer, H. Detz, A. M. Andrews, W. Schrenk, F. Capasso, M. Loncar, and G. Strasser, “Measurement of bound states in the continuum by a detector embedded in a photonic crystal,” Light Sci. Appl. 5, e16147 (2016).
[Crossref]

Andrews, D. L.

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge University, 2012).

Artigas, D.

J. Gomis-Bresco, D. Artigas, and L. Torner, “Anisotropy-induced photonic bound states in the continuum,” Nat. Photonics 11, 232–236 (2017).
[Crossref]

Arvelo, E. R.

F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13, 390–396 (2019).
[Crossref]

Babiker, M.

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge University, 2012).

Bahari, B.

A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541, 196–199 (2017).
[Crossref]

Bai, B.

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

Banzer, P.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (CRC Press, 2003).

Bekshaev, A. Y.

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic layout of the PhCM. The experimental sample consists of a square lattice of period a of cylindrical air holes etched in a silicon nitride (Si3N4) thin film. The silicon nitride film covers all the surface of the supporting quartz substrate (SiO2), which has thickness 120 μm. The patterned area is 1mm2. (b) Scanning electron microscopy images of the patterned area (inset has sizes of 1 μm). (c) Spin-momentum locking scheme at the boundaries: the evanescent decay direction κ in the positive and negative z half spaces locks the relative transverse spin s and phase-propagation orientation k. (d) Transmittance spectra of the system close to normal incidence showing resonances with a progressively higher Q- factor. (e) Diverging Q-factor of the mode approaching normal incidence, corresponding to ω2a/2πc=a/λ0.6762 in panel (d).
Fig. 2.
Fig. 2. RCWA numerical analysis of the electromagnetic field at the BIC and input SAM dependence. A TM-like BIC mode obtained for h=144nm is represented in the unit cell. The top row refers to results obtained for RCP, whereas the second row to LCP excitation. (a), (b). The vector map of the field E (uniform magnitude for clarity of representation) shows its character of surface wave and reveals the intriguing behavior of the field excited by opposite circularly polarized input plane waves with opposite orientation of the electric field point by point in (a) and (b). The colormap is associated with magnetic field intensity |H|2. The tight confinement produces a significant transverse SAM not only at the interfaces but also inside the nanoscale slab, which locks the propagation direction of the wave along the x axis depending on the helicity of the input plane wave as can be seen by comparing top and bottom Poynting vector maps in the zx plane (c), (d) (arrow length is proportional to the vector magnitude). Because of symmetry, an analogous behavior of directional Poynting vector flow occurs also in the z cross section along y axis (zy plane). The colormap is associated with the energy density. In particular, the relative orientation of SAM and Poynting vector can be seen in detail in (e) and (f) (arrow length imposed uniform for better visual inspection for both vectors). It is worth emphasizing that the energy density is much weaker at the interface of the PhC cell with air (top region) as shown in panels (c) and (d); thus, the SAM average z-axis projection (Sz) is that represented by the arrows in (e) and (f). The input spin (scheme on the left) matches the average Sz of the mode. Since this is transverse to the Poynting vector, as visible in the insets, spin-momentum locking occurs.
Fig. 3.
Fig. 3. Phenomenology of the redirection effect at the BIC. (a) Schematic layout of the experimental setup. The input beam polarization Ei (initially || x^) is controlled by means of a half-wave plate (HWP) and a quarter-wave plate (QWP). At the BIC frequency, light is redirected at θr=π/2 along the PhC axes of symmetry. (b) Normal incidence transmission spectrum of a PhCM designed to support a BIC in the visible range. Two modes are visible: λ1 corresponds to a near-BIC regime, whereas λ2 to a conventional leaky mode. (c) At the BIC wavelength λ1, the normally incident light is experimentally redirected along the PhC symmetry axes (LCP input in figure). The inset of the spectrum in (b) shows the far-field spectral profile of the redirected beam of wavevector kR collected from the side. (d) At λ2, there is no detectable redirection effect at any input polarization (LCP input in figure).
Fig. 4.
Fig. 4. Asymmetric spin–orbit behavior at the BIC (θi=0°). (a) General layout of the far-field characterization with the PhCM axes parallel to the laboratory reference system. (b) Intensity of the side waves outcoupled from the PhCM measured as function of the QWP angle β for input s and p polarization for θi=0°. The experimental points show a macroscopic chiral behavior The solid lines are the curves obtained with the model fit, which show an excellent agreement with the data. (c) The chiral parameters resulting from the fit are indicated in Table 1: S/P indicates that the values are, respectively, refereed to s-pol or p-pol of (b).
Fig. 5.
Fig. 5. Chiral behavior with broken symmetry excitation (θi=0.03°) and geometric phase effect. (a) Intensity of the redirected bottom side wave measured as function of the QWP angle β for input s and p polarization. Measurements were carried out at θi=0.03°. Top panels report the case ϕ0=0°, whereas bottom panels the case ϕ0=30°. (b) Table 2 reports the fit parameters with a chiral directivity η close to 1. S/P indicates that the values are respectively referred to s-pol or p-pol of (a).

Equations (1)

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I(vj)=c+|Ew+(vj)|2+c|Ew(vj)|2+cz|Ewz(vj)|2,