Efficient computation of equifrequency surfaces and density of states in photonic crystals using Dirichlet-to-Neumann maps

Journal of the Optical Society of America B: Optical Physics

Volumn 28, Issue 8, 2011, Pages 1837-1843

  Liu, Victor ^a   Fan, Shanhui ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

DENSITY OF STATE; DIRICHLET-TO-NEUMANN MAP; EFFICIENT COMPUTATION; EFFICIENT METHOD; EQUI-FREQUENCY SURFACE; GROUP VELOCITIES; ITS EFFICIENCIES; NONLINEAR EIGENVALUE PROBLEM; UNIT CELLS;

PHOTONIC CRYSTALS;

EID: 79961094110     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.28.001837     Document Type: Article

References (34)

1. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000). (Pubitemid 32367242)
2. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Allangle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
3. X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
4. D. Pustai, S. Shi, C. Chen, A. Sharkawy, and D. Prather, "Analysis of splitters for self-collimated beams in planar photonic crystals," Opt. Express 12, 1823-1831 (2004).
5. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, "Deepsubwavelength focusing and steering of light in an aperiodic metallic waveguide array," Phys. Rev. Lett. 103, 033902 (2009).
6. P. Russel and T. Birks, "Hamiltonian optics of nonuniform photonic crystals," J. Lightwave Technol. 17, 1982-1988 (1999). (Pubitemid 30518937)
7. Y. A. Urzhumov and D. R. Smith, "Transformation optics with photonic band gap media," Phys. Rev. Lett. 105, 163901 (2010).
8. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
9. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals (Princeton Univ. Press, 2008).
10. Z. Jacob, I. Smolyaninov, and E. Narimanov, "Broadband Purcell effect: Radiative decay engineering with metamaterials," ar- Xiv:0910.3981v2 (2009).
11. Z. Yu, A. Raman, and S. Fan, "Fundamental limit of nanophotonic light trapping in solar cells," Proc. Natl. Acad. Sci. USA 107, 17491-17496 (2010).
12. M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, "Enhanced photonic band-gap confinement via van Hove saddle point singularities," Phys. Rev. Lett. 96, 033904 (2006).
13. G. Gilat and L. J. Raubenheimer, "Accurate numerical method for calculating frequency-distribution functions in solids," Phys. Rev. 144, 390-395 (1966).
14. G. Lehmann and M. Taut, "On the numerical calculation of the density of states and related properties," Phys. Status Solidi B 54, 469-477 (1972).
15. J. Hama, M. Watanabe, and T. Kato, "Correctly weighted tetrahedron method for k-space integration," J. Phys. Condens. Matter 2, 7445 (1990).
16. R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, "Density of states functions for photonic crystals," Phys. Rev. E 69, 016609 (2004).
17. C. J. Pickard and M. C. Payne, "Extrapolative approaches to brillouin-zone integration," Phys. Rev. B 59, 4685-4693 (1999).
18. E. Moreno, D. Erni, and C. Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Phys. Rev. B 65, 155120 (2002).
19. J. Yuan and Y. Y. Lu, "Photonic bandgap calculations with Dirichlet-to-Neumann maps," J. Opt. Soc. Am. A 23, 3217-3222 (2006). (Pubitemid 46023817)
20. Y. Huang, Y. Y. Lu, and S. Li, "Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps," J. Opt. Soc. Am. B 24, 2860-2867 (2007).
21. Z. Hu and Y. Y. Lu, "Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps," Opt. Express 16, 17383-17399 (2008).
22. V. Liu, Y. Jiao, D. A. B. Miller, and S. Fan, "Design methodology for compact photonic crystal based wavelength division multiplexers," Opt. Lett. 36, 591-593 (2011).
23. Z. Hu and Y. Y. Lu, "Improved bends for two-dimensional photonic crystal waveguides," Opt. Commun. 284, 2812-2816 (2011).
24. J. Yuan, Y. Y. Lu, and X. Antoine, "Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps," J. Comp. Phys. 227, 4617-4629 (2008).
25. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. Sterke, and A. A. Asatryan, "Photonic band structure calculations using scattering matrices," Phys. Rev. E 64, 046603 (2001).
26. Z.-Y. Li and L.-L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003).
27. T. S. Newman and H. Yi, "A survey of the marching cubes algorithm," Comput. Graph. 30, 854-879 (2006). (Pubitemid 44573407)
28. J.-D. Boissonnat and S. Oudot, "Provably good sampling and meshing of surfaces," Graph. Models 67, 405-451 (2005). (Pubitemid 41329184)
29. A. Quarteroni, Numerical Mathematics (Springer, 2000).
30. G. Strang, Linear Algebra and Its Applications (Harcourt Brace Jovanovich, 1988).
31. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, 3rd ed. (Society for Industrial and Applied Mathematics, 1999).
32. A. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, no. 105 in Other Titles in Applied Mathematics, 2nd ed. (SIAM, 2008).
33. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a plane wave basis," Opt. Express 8, 173-190 (2001).
34. K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998). (Pubitemid 128603426)