Bloch surface eigenstates within the radiation continuum

Light: Science and Applications

Volumn 2, Issue JULY, 2013, Pages

  Hsu, Chia Wei ^a,b   Zhen, Bo ^a   Chua, Song Liang ^a   Johnson, Steven G ^a   Joannopoulos, John D ^a   Soljačić, Marin ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Bound state in continuum; Embedded eigenvalue; Photonic crystal; Surface mode

Indexed keywords

EID: 84880399856     PISSN: None     EISSN: 20477538     Source Type: Journal    
DOI: 10.1038/lsa.2013.40     Document Type: Article

References (54)

1. Joannopoulos JD, Johnson SG, Winn JN, Meade RD. Photonic Crystals: Molding the Flow of Light. Princeton, NJ: Princeton University Press, 2008.
2. Meade RD, Brommer KD, Rappe AM, Joannopoulos JD. Electromagnetic Bloch waves at the surface of a photonic crystal. Phys Rev B 1991; 44: 10961-10964.
3. Tsakmakidis KL, Hermann C, Klaedtke A, Jamois C, Hess O. Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability. Phys Rev B 2006; 73: 085104.
4. Robertson WM, Arjavalingam G, Meade RD, Brommer KD, Rappe AM et al. Observation of surface photons on periodic dielectric arrays. Opt Lett 1993; 18: 528-530.
5. Ishizaki K, Noda S. Manipulation of photons at the surface of three-dimensional photonic crystals. Nature 2009; 460: 367-370.
6. Moreno E, García-Vidal FJ, Martín-Moreno L. Enhanced transmission and beaming of light via photonic crystal surface modes. Phys Rev B 2004; 69: 121402.
7. Kramper P, AgioM, Soukoulis CM, Birner A, Mü ller F et al.Highly directional emission from photonic crystal waveguides of subwavelength width. Phys Rev Lett 2004; 92: 113903.
8. von Neumann J, Wigner E.U? ber merkwü rdige diskrete Eigenwerte. Phys Z 1929; 30: 465-467.
9. Hislop PD, Sigal IM. Introduction to Spectral Theory: With Applications to Schrödinger Operators. New York: Springer-Verlag, 1996.
10. Stillinger FH, Herrick DR. Bound states in the continuum. Phys Rev A 1975; 11: 446- 454.
11. Friedrich H, Wintgen D. Interfering resonances and bound states in the continuum. Phys Rev A 1985; 32: 3231-3242.
12. Naboko SN. Dense point spectra of Schrödinger and Dirac operators. Theor Math Phys 1986; 68: 646-653.
13. Simon B. Some Schrödinger operators with dense point spectrum. Proc Amer Math Soc 1997; 125: 203-208.
14. 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 Lett 2009; 102: 167404.
15. Krü ger H. On the existence of embedded eigenvalues. J Math Anal Appl 2012; 395: 776.
16. Zhang JM, Braak D, Kollar M. Bound states in the continuum realized in the onedimensional two-particle Hubbard model with an impurity. Phys Rev Lett 2012; 109: 116405.
17. Paddon P, Young JF. Two-dimensional vector-coupled-mode theory for textured planar waveguides. Phys Rev B 2000; 61: 2090-2101.
18. Pacradouni V, Mandeville WJ, Cowan AR, Paddon P, Young JF et al. Photonic band structure of dielectric membranes periodically textured in two dimensions. Phys Rev B 2000; 62: 4204-4207.
19. Ochiai T, Sakoda K. Dispersion relation and optical transmittance of a hexagonal photonic crystal slab. Phys Rev B 2001; 63: 125107.
20. Fan S, Joannopoulos JD. Analysis of guided resonances in photonic crystal slabs. Phys Rev B 2002; 65: 235112.
21. Shipman SP, Venakides S. Resonant transmission near nonrobust periodic slab modes. Phys Rev E 2005; 71: 026611.
22. Plotnik Y, Peleg O, Dreisow F, Heinrich M, Nolte S et al. Experimental observation of optical bound states in the continuum. Phys Rev Lett 2011; 107: 183901.
23. Lee J, Zhen B, Chua S, Qiu W, Joannopoulos JD et al. Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs. Phys Rev Lett 2012; 109: 067401.
24. Čtyroký J. Photonic bandgap structures in planar waveguides. J Opt Soc Am A 2001; 18: 435-441.
25. Kawakami S. Analytically solvable model of photonic crystal structures and novel phenomena. J Lightwave Technol 2002; 20: 1644.
26. Watts MR, Johnson SG, Haus HA, Joannopoulos JD. Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap. Opt Lett 2002; 27: 1785-1787. (Pubitemid 35328910)
27. Marinica DC, Borisov AG, Shabanov SV. Bound states in the continuum in photonics. Phys Rev Lett 2008; 100: 183902.
28. Molina MI, Miroshnichenko AE, Kivshar YS. Surface bound states in the continuum. Phys Rev Lett 2012; 108: 070401.
29. 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.
30. Ursell F. Trapping modes in the theory of surface waves. Math Proc Cambridge 1951; 47: 347-358.
31. Jones DS. The eigenvalues of =2m1lm50 when the boundary conditions are given on semi-infinite domains. Math Proc Cambridge 1953; 49: 668-684.
32. Parker R. Resonance effects in wake shedding from parallel plates: some experimental observations. J Sound Vibrat 1966; 4: 62.
33. Witsch KJ. Examples of embedded eigenvalues for the Dirichlet Laplacian in perturbed waveguides. Math Methods Appl Sci 1990; 12: 91-93. (Pubitemid 20668567)
34. Evans DV, Levitin M, Vassiliev D. Existence theorems for trapped modes. J Fluid Mech 1994; 261: 21-31. (Pubitemid 280597)
35. Evans DV, Linton CM, Ursell F. Trapped mode frequencies embedded in the continuous spectrum. Q J Mech Appl Math 1993; 46: 253-274. (Pubitemid 23694874)
36. Groves MD. Examples of embedded eigenvalues for problems in acoustic waveguides. Math Methods Appl Sci 1998; 21: 479-488. (Pubitemid 128589159)
37. Porter R, Evans DV. Embedded Rayleigh-Bloch surface waves along periodic rectangular arrays. Wave Motion 2005; 43: 29.
38. Linton CM, McIver P. Embedded trapped modes in water waves and acoustics. Wave Motion 2007; 45: 16.
39. Capasso F, Sirtori C, Faist J, Sivco DL, Chu SGet al. Observation of an electronic bound state above a potential well. Nature 1992; 358: 565-567.
40. Shipman SP, Venakides S. Resonance and bound states in photonic crystal slabs. SIAM J Appl Math 2003; 64: 322-342.
41. Oskooi AF, Roundy D, Ibanescu M, Bermel P, Joannopoulos JD et al. Meep: a flexible free-software package for electromagnetic simulations by the FDTD method. Comput Phys Commun 2010; 181: 687-702.
42. Haus HA. Waves and Fields in Optoelectronics. Englewood Cliffs, NJ: Prentice-Hall, 1984.
43. Fan S, Suh W, Joannopoulos JD. Temporal coupled-mode theory for the Fano resonance in optical resonators. J Opt Soc Am A 2003; 20: 569-572.
44. Ameling R, Langguth L, Hentschel M, Mesch M, Braun PV et al. Cavity-enhanced localized plasmon resonance sensing. Appl Phys Lett 2010; 97: 253116.
45. Johnson SG, Fan S, Mekis A, Joannopoulos JD. Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap. Appl Phys Lett 2001; 78: 3388-3390. (Pubitemid 33666768)
46. Vučković J, Lončar M, Mabuchi H, Scherer A. Design of photonic crystalmicrocavities for cavity QED. Phys Rev E 2001; 65: 016608.
47. Akahane Y, Asano T, Song B, Noda S. High-Q photonic nanocavity in a twodimensional photonic crystal. Nature 2003; 425: 944-947. (Pubitemid 37376922)
48. Karalis A, Johnson SG, Joannopoulos JD. Discrete-mode cancellation mechanism for high-Q integrated optical cavities with small modal volume. Opt Lett 2004; 29: 2309-2311.
49. Johnson PB, Christy RW. Optical constants of the noble metals. Phys Rev B 1972; 6: 4370-4379.
50. Chua S, Chong Y, Stone AD, Soljacic M, Bravo-Abad J. Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances. Opt Express 2011; 19: 1539-1562.
51. Bravo-Abad J, Joannopoulos JD, Soljač ić M. Enabling single-mode behavior over large areas with photonic Dirac cones. Proc Natl Acad Sci USA 2012; 109: 9761-9765.
52. Hess O, Pendry JB, Maier SA, Oulton RF, Hamm JM et al. Active nanoplasmonic metamaterials. Nat Mater 2012; 11: 573-584.
53. Le Ru EC, Etchegoin PG. Principles of Surface-Enhanced Raman Spectroscopy: and Related Plasmonic Effects. Amsterdam: Elsevier, 2009.
54. Lončar M, Scherer A, Qiu Y. Photonic crystal laser sources for chemical detection. Appl Phys Lett 2003; 82: 4648-4650.