Topological nature of optical bound states in the continuum.

Optical bound states in the continuum (BICs) have recently been realized in photonic crystal slabs, where the disappearance of out-of-plane radiation turns leaky resonances into guided modes with infinite lifetimes. We show that such BICs are vortex centers in the polarization directions of far-field radiation. They carry conserved and quantized topological charges, defined by the winding number of the polarization vectors, which ensure their robust existence and govern their generation, evolution, and annihilation. Our findings connect robust BICs in photonics to a wide range of topological physical phenomena.

[1]  Andrea Alù,et al.  Embedded photonic eigenvalues in 3D nanostructures , 2014 .

[2]  S. Noda,et al.  Watt-class high-power, high-beam-quality photonic-crystal lasers , 2014, Nature Photonics.

[3]  M. Silveirinha.  Trapping light in open plasmonic nanostructures , 2014 .

[4]  Zhengbin Li,et al.  Analytical perspective for bound states in the continuum in photonic crystal slabs. , 2013, Physical review letters.

[5]  Steven G. Johnson,et al.  Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals , 2013, Proceedings of the National Academy of Sciences.

[6]  Steven G. Johnson,et al.  Observation of trapped light within the radiation continuum , 2013, Nature.

[7]  Steven G. Johnson,et al.  Bloch surface eigenstates within the radiation continuum , 2013, Light: Science & Applications.

[8]  A. Crespi,et al.  Observation of surface states with algebraic localization. , 2013, Physical review letters.

[9]  A. Tünnermann,et al.  Compact surface Fano states embedded in the continuum of waveguide arrays. , 2013, Physical review letters.

[10]  Wenjun Qiu,et al.  Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs. , 2012, Physical review letters.

[11]  S. Noda,et al.  Focusing properties of vector vortex beams emitted by photonic-crystal lasers. , 2012, Optics letters.

[12]  Y. Kivshar,et al.  Surface bound states in the continuum. , 2011, Physical review letters.

[13]  M. Segev,et al.  Experimental observation of optical bound states in the continuum. , 2011, Physical review letters.

[14]  A. E. Cetin,et al.  Seeing protein monolayers with naked eye through plasmonic Fano resonances , 2011, Proceedings of the National Academy of Sciences.

[15]  S. Noda,et al.  Higher-order vector beams produced by photonic-crystal lasers. , 2011, Optics express.

[16]  S. Noda,et al.  On-chip beam-steering photonic-crystal lasers , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[17]  Steven G. Johnson,et al.  Meep: A flexible free-software package for electromagnetic simulations by the FDTD method , 2010, Comput. Phys. Commun..

[18]  M. Povinelli,et al.  Resonance-enhanced optical forces between coupled photonic crystal slabs. , 2009, Optics express.

[19]  Lei Zhang,et al.  Photonic crystal geometry for organic solar cells. , 2009, Nano letters.

[20]  N. Moiseyev.  Suppression of feshbach resonance widths in two-dimensional waveguides and quantum dots: a lower bound for the number of bound states in the continuum. , 2009, Physical review letters.

[21]  Jonathan J. Wierer,et al.  III -nitride photonic-crystal light-emitting diodes with high extraction efficiency , 2009 .

[22]  Q. Zhan.  Cylindrical vector beams: from mathematical concepts to applications , 2009 .

[23]  E. Bulgakov,et al.  Bound states in the continuum in photonic waveguides inspired by defects , 2008 .

[24]  A. Borisov,et al.  Bound States in the continuum in photonics. , 2008, Physical review letters.

[25]  Viktor Malyarchuk,et al.  Enhanced fluorescence emission from quantum dots on a photonic crystal surface , 2007, Nature Nanotechnology.

[26]  F. Guinea,et al.  Existence and topological stability of Fermi points in multilayered graphene , 2006, cond-mat/0611347.

[27]  R. H. Mayer.  Optical Properties of Photonic Crystals. Springer,, K. Sakoda. Heidelberg, ISBN 3-540-20682-5 (2005), (XIV/253pp., price 107 illus, EUR 79.95, US$89.95, Hardcover) , 2006 .

[28]  D. V. Evans,et al.  Embedded Rayleigh–Bloch surface waves along periodic rectangular arrays , 2005 .

[29]  刘金明,et al.  IL-13受体α2降低血吸虫病肉芽肿的炎症反应并延长宿主存活时间[英]/Mentink-Kane MM,Cheever AW，Thompson RW，et al//Proc Natl Acad Sci U S A , 2005 .

[30]  S. Shipman,et al.  Resonant transmission near nonrobust periodic slab modes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Shanhui Fan,et al.  Analysis of guided resonances in photonic crystal slabs , 2002 .

[32]  Kazuaki Sakoda,et al.  Dispersion relation and optical transmittance of a hexagonal photonic crystal slab , 2001 .

[33]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[34]  D. V. Evans,et al.  Existence theorems for trapped modes , 1994, Journal of Fluid Mechanics.

[35]  Russell J. Donnelly,et al.  Quantized Vortices in Helium II , 1991 .

[36]  M. Berry.  The Adiabatic Phase and Pancharatnam's Phase for Polarized Light , 1987 .

[37]  Friedrich,et al.  Interfering resonances and bound states in the continuum. , 1985, Physical review. A, General physics.

[38]  N. D. Mermin,et al.  The topological theory of defects in ordered media , 1979 .

[39]  G. Stegeman.  Normal‐mode surface waves in the pseudobranch on the (001) plane of gallium arsenide , 1976 .

[40]  Petra Holtzmann,et al.  Optical Properties Of Photonic Crystals , 2016 .

[41]  J. Engelbrecht.  What is wave motion , 2015 .

[42]  Jeff F. Young,et al.  Photonic band structure of dielectric membranes periodically textured in two dimensions , 2000 .

[43]  J. Neumann,et al.  Über merkwürdige diskrete Eigenwerte , 1993 .