Bloch surface eigenstates within the radiation continuum

Chia Wei Hsu; Bo Zhen; Song-Liang Chua; Steven G Johnson; John D Joannopoulos; Marin Soljačić

doi:10.1038/lsa.2013.40

Go to Nature Website

Your Location：

Home >

Browse articles >

Bloch surface eigenstates within the radiation continuum

Original Articles

- Bloch surface eigenstates within the radiation continuum
- Light: Science & Applications Vol. 2, Issue 3-4, (2013)
- Affiliations：
  
  1.Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
  2.Department of Physics, Harvard University, Cambridge, MA 02138, USA
  3.Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Author bio：
  
  M Soljačić, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Email: soljacic@mit.edu
- Funds：
- DOI：10.1038/lsa.2013.40
  CLC：
- Published：2013-12，
  
  Published Online：19 July 2013，
  
  Received：13 November 2012，
  
  Revised：11 January 2013，
  
  Accepted：26 February 2013
- Accepted：
Scan QR Code
Hsu, C. W. et al. Bloch surface eigenstates within the radiation continuum. Light: Science & Applications, 2, e84 (2013).
DOI：

Hsu, C. W. et al. Bloch surface eigenstates within the radiation continuum. Light: Science & Applications, 2, e84 (2013). DOI： 10.1038/lsa.2013.40.

摘要

Abstract

From detailed numerical calculations

we demonstrate that in simple photonic crystal structures

a discrete number of Bloch surface-localized eigenstates can exist inside the continuum of free-space modes. Coupling to the free space causes the surface modes to leak

but the forward and back-reflected leakage may interfere destructively to create a perfectly bound surface state with zero leakage. We perform analytical temporal coupled-mode theory analysis to show the generality of such phenomenon and its robustness from variations of system parameters. Periodicity

time-reversal invariance

two-fold rotational symmetry and a perfectly reflecting boundary are necessary for these unique states.

关键词

Keywords

bound state in continuumembedded eigenvaluephotonic crystalsurface mode

references

Joannopoulos JD, Johnson SG, Winn JN, Meade RD.Photonic Crystals: Molding the Flow of Light.Princeton, NJ: Princeton University Press, 2008.

Meade RD, Brommer KD, Rappe AM, Joannopoulos JD. Electromagnetic Bloch waves at the surface of a photonic crystal.Phys Rev B1991;44: 10961–10964..

Tsakmakidis KL, Hermann C, Klaedtke A, Jamois C, Hess O. Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability.Phys Rev B2006;73: 085104..

Robertson WM, Arjavalingam G, Meade RD, Brommer KD, Rappe AMet al. Observation of surface photons on periodic dielectric arrays.Opt Lett1993;18: 528–530..

Ishizaki K, Noda S. Manipulation of photons at the surface of three-dimensional photonic crystals.Nature2009;460: 367–370..

Moreno E, García-Vidal FJ, Martín-Moreno L. Enhanced transmission and beaming of lightviaphotonic crystal surface modes.Phys Rev B2004;69: 121402..

Kramper P, Agio M, Soukoulis CM, Birner A, Müller Fet al. Highly directional emission from photonic crystal waveguides of subwavelength width.Phys Rev Lett2004;92: 113903..

von Neumann J, Wigner E. Über merkwürdige diskrete Eigenwerte.Phys Z1929;30: 465–467..

Hislop PD, Sigal IM.Introduction to Spectral Theory: With Applications to Schrödinger Operators.New York: Springer-Verlag, 1996.

Stillinger FH, Herrick DR. Bound states in the continuum.Phys Rev A1975;11: 446–454..

Friedrich H, Wintgen D. Interfering resonances and bound states in the continuum.Phys Rev A1985;32: 3231–3242..

Naboko SN. Dense point spectra of Schrödinger and Dirac operators.Theor Math Phys1986;68: 646–653..

Simon B. Some Schrödinger operators with dense point spectrum.Proc Amer Math Soc1997;125: 203–208..

Moiseyev N. Suppression of Feshbach resonance widths in two-dimensional waveguides and quantum dots: a lower bound for the number of bound states in the continuum.Phys Rev Lett2009;102: 167404..

Krüger H. On the existence of embedded eigenvalues.J Math Anal Appl2012;395: 776..

Zhang JM, Braak D, Kollar M. Bound states in the continuum realized in the one-dimensional two-particle Hubbard model with an impurity.Phys Rev Lett2012;109: 116405..

Paddon P, Young JF. Two-dimensional vector-coupled-mode theory for textured planar waveguides.Phys Rev B2000;61: 2090–2101..

Pacradouni V, Mandeville WJ, Cowan AR, Paddon P, Young JFet al. Photonic band structure of dielectric membranes periodically textured in two dimensions.Phys Rev B2000;62: 4204–4207..

Ochiai T, Sakoda K. Dispersion relation and optical transmittance of a hexagonal photonic crystal slab.Phys Rev B2001;63: 125107..

Fan S, Joannopoulos JD. Analysis of guided resonances in photonic crystal slabs.Phys Rev B2002;65: 235112..

Shipman SP, Venakides S. Resonant transmission near nonrobust periodic slab modes.Phys Rev E2005;71: 026611..

Plotnik Y, Peleg O, Dreisow F, Heinrich M, Nolte Set al. Experimental observation of optical bound states in the continuum.Phys Rev Lett2011;107: 183901..

Lee J, Zhen B, Chua S, Qiu W, Joannopoulos JDet al. Observation and differentiation of unique high-Qoptical resonances near zero wave vector in macroscopic photonic crystal slabs.Phys Rev Lett2012;109: 067401..

Čtyroký J. Photonic bandgap structures in planar waveguides.J Opt Soc Am A2001;18: 435–441..

Kawakami S. Analytically solvable model of photonic crystal structures and novel phenomena.J Lightwave Technol2002;20: 1644..

Watts MR, Johnson SG, Haus HA, Joannopoulos JD. Electromagnetic cavity with arbitraryQand small modal volume without a complete photonic bandgap.Opt Lett2002;27: 1785–1787..

Marinica DC, Borisov AG, Shabanov SV. Bound statesin the continuum in photonics.Phys Rev Lett2008;100: 183902..

Molina MI, Miroshnichenko AE, Kivshar YS. Surface bound states in the continuum.Phys Rev Lett2012;108: 070401..

Shipman SP, Welters A. Resonance in anisotropic layered media. In: Proceedings of 2012 International Conference on Mathematical Methods in Electromagnetic Theory; 28–30 August 2012; Kharkiv, Ukraine; IEEE: Washington, DC, USA, 2012, pp227–232.

Ursell F. Trapping modes in the theory of surface waves.Math Proc Cambridge1951;47: 347–358..

Jones DS. The eigenvalues of ∇2μ+λμ=0 when the boundary conditions are given on semi-infinite domains.Math Proc Cambridge1953;49: 668–684..

Parker R. Resonance effects in wake shedding from parallel plates: some experimental observations.J Sound Vibrat1966;4: 62..

Witsch KJ. Examples of embedded eigenvalues for the Dirichlet Laplacian in perturbed waveguides.Math Methods Appl Sci1990;12: 91–93..

Evans DV, Levitin M, Vassiliev D. Existence theorems for trapped modes.J Fluid Mech1994;261: 21–31..

Evans DV, Linton CM, Ursell F. Trapped mode frequencies embedded in the continuous spectrum.Q J Mech Appl Math1993;46: 253–274..

Groves MD. Examples of embedded eigenvalues for problems in acoustic waveguides.Math Methods Appl Sci1998;21: 479–488..

Porter R, Evans DV. Embedded Rayleigh–Bloch surface waves along periodic rectangular arrays.Wave Motion2005;43: 29..

Linton CM, McIver P. Embedded trapped modes in water waves and acoustics.Wave Motion2007;45: 16..

Capasso F, Sirtori C, Faist J, Sivco DL, Chu SGet al. Observation of an electronic bound state above a potential well.Nature1992;358: 565–567..

Shipman SP, Venakides S. Resonance and bound states in photonic crystal slabs.SIAM J Appl Math2003;64: 322–342..

Oskooi AF, Roundy D, Ibanescu M, Bermel P, Joannopoulos JDet al. Meep: a flexible free-software package for electromagnetic simulations by the FDTD method.Comput Phys Commun2010;181: 687–702..

Haus HA.Waves and Fields in Optoelectronics.Englewood Cliffs, NJ: Prentice-Hall, 1984.

FanS, Suh W, Joannopoulos JD. Temporal coupled-mode theory for the Fano resonance in optical resonators.J Opt Soc Am A2003;20: 569–572..

Ameling R, Langguth L, Hentschel M, Mesch M, Braun PVet al. Cavity-enhanced localized plasmon resonance sensing.Appl Phys Lett2010;97: 253116..

Johnson SG, Fan S, Mekis A, Joannopoulos JD. Multipole-cancellation mechanism for high-Qcavities in the absence of a complete photonic band gap.Appl Phys Lett2001;78: 3388–3390..

Vučković J, Lončar M, Mabuchi H, Scherer A. Design of photonic crystal microcavities for cavity QED.Phys Rev E2001;65: 016608..

Akahane Y, Asano T, Song B, Noda S. High-Qphotonic nanocavity in a two-dimensional photonic crystal.Nature2003;425: 944–947..

Karalis A, Johnson SG, Joannopoulos JD. Discrete-mode cancellation mechanism for high-Qintegrated optical cavities with small modal volume.Opt Lett2004;29: 2309–2311..

Johnson PB, Christy RW. Optical constants of the noble metals.Phys Rev B1972;6: 4370–4379..

Chua S, Chong Y, Stone AD, Soljacic M, Bravo-Abad J. Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances.Opt Express2011;19: 1539–1562..

Bravo-Abad J, Joannopoulos JD, Soljačić M. Enabling single-mode behavior over large areas with photonic Dirac cones.Proc Natl Acad Sci USA2012;109: 9761–9765..

Hess O, Pendry JB, Maier SA, Oulton RF, Hamm JMet al. Active nanoplasmonic metamaterials.Nat Mater2012;11: 573–584..

Le Ru EC, Etchegoin PG.Principles of Surface-Enhanced Raman Spectroscopy: and Related Plasmonic Effects.Amsterdam: Elsevier, 2009.

Lončar M, Scherer A, Qiu Y. Photonic crystal laser sources for chemical detection.Appl Phys Lett2003;82: 4648–4650..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Fiber guiding at the Dirac frequency beyond photonic bandgaps

Zero-dimensional polariton laser in a subwavelength grating-based vertical microcavity

Related Author

Wei Zhang

Erlei Wang

Fei Wen

Tianyu Yang

Qian Li

Lei Hu

Qiuping Mao

Ming Xie

Related Institution

School of Instrument Science and Opto-electronic Engineering, Hefei University of Technology

Department of Physics, University of Salford,, Manchester

Department of Polymer Science and Engineering, University of Science and Technology of China

School of Optoelectronic Information, University of Electronic Science and Technology of China

Department of Physics, University of Michigan

⁰