Numerical methods for computing casimir interactions

Lecture Notes in Physics

Volumn 834, Issue , 2011, Pages 175-218

  Johnson, Steven G ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960630563     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-20288-9_6     Document Type: Conference Paper

References (141)

1. Chew, W.C., Jian-Ming, J., Michielssen, E., Jiming, S.: Fast and Efficient Algorithms in Computational Electromagnetics. Artech, Norwood, MA (2001)
2. Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech, Norwood, MA (2000)
3. Volakis, J.L., Chatterjee, A., Kempel, L.C.: Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications. IEEE Press, New York (2001)
4. Zhu, Y., Cangellaris, A.C.: Multigrid Finite Element Methods for Electromagnetic Field Modelling. John Wiley and Sons, Hooboke, NJ (2006)
5. Yasumoto, K. (ed.): Electromagnetic Theory and Applications for Photonic Crystals. CRC Press, Boca Raton, FL (2005)
6. Joannopoulos, J.D., Johnson, S.G., Winn, J.N., Meade, R.D.: Photonic Crystals: Molding the Flow of Light, 2nd edn. Princeton University Press, Princeton, NJ (2008)
7. Jin, J.: The Finite Element Method in Electromagnetics, 2nd edn. Wiley, New York (2002)
8. Rao, S.M., Balakrishnan, N.: Computational electromagnetics. Curr. Sci. 77(10), 1343-1347 (1999)
9. Reid, M.T.H., Rodriguez, A.W., White, J., Johnson, S.G.: Efficient computation ofthree-dimensional Casimir forces. Phys. Rev. Lett. 103(4), 040-401 (2009)
10. Reynaud, S., Maia Neto, P.A., Lambrecht, A.: Casimir energy and geometry: Beyond the proximity force approximation. J. Phys. A: Math. Theor. 41, 164-004 (2008)
11. Rodriguez, A., Ibanescu, M., Iannuzzi, D., Capasso, F., Joannopoulos, J.D., Johnson, S.G.: Computation and visualization of Casimir forces in arbitrary geometries: Non-monotonic lateral-wall forces and failure of proximity force approximations. Phys. Rev. Lett. 99(8), 080-401 (2007)
12. Rodriguez, A., Ibanescu, M., Iannuzzi, D., Joannopoulos, J.D., Johnson, S.G.: Virtual photons in imaginary time: Computing Casimir forces in arbitrary geometries via standard numerical electromagnetism. Phys. Rev. 76(3), 032-106 (2007)
13. Rodriguez, A.W., McCauley, A.P., Joannopoulos, J.D., Johnson, S.G.: Casimir forces in the time domain: Theory. Phys. Rev. A 80(1), 012-115 (2009)
14. Emig, T., Graham, N., Jaffe, R.L., Kardar, M.: Casimir forces between arbitrary compact objects. Phys. Rev. Lett. 99, 170-403 (2007)
15. Emig, T., Hanke, A., Golestanian, R., Kardar, M.: Probing the strong boundary shape dependence of the Casimir force. Phys. Rev. Lett. 87, 260-402 (2001)
16. Emig, T., Jaffe, R.L., Kardar, M., Scardicchio, A.: Casimir interaction between a plate and a cylinder. Phys. Rev. Lett. 96, 080-403 (2006)
17. Lambrecht, A., Maia Neto, P.A., Reynaud, S.: The Casimir effect within scattering theory. New J. Phys. 8, 243 (2008)
18. Lambrecht, A., Marachevsky, V.I.: Casimir interactions of dielectric gratings. Phys. Rev. Lett. 101, 160-403 (2008)
19. Xiong, J.L., Chew, W.C.: Efficient evaluation of Casimir force in z-invariant geometries by integral equation methods. Appl. Phys. Lett. 95, 154-102 (2009)
20. Xiong, J.L., Tong, M.S., Atkins, P., Chew, W.C.: Efficient evaluation of Casimir force in arbitrary three-dimensional geometries by integral equation methods. Phys. Lett. A 374(25), 2517-2520 (2010)
21. Rahi, S.J., Emig, T., Jaffe, R.L., Kardar, M.: Casimir forces between cylinders and plates. Phys. Rev. A 78, 012-104 (2008)
22. Rahi, S.J., Emig, T., Jaffe, R.L., Kardar, M.: Scattering theory approach to electrodynamic casimir forces. Phys. Rev. D 80, 085-021 (2009)
23. Pasquali, S., Maggs, A.C.: Numerical studies of Lifshitz interactions between dielectrics. Phys. Rev. A. 79, 020-102 (2009)
24. Maia Neto, P.A., Lambrecht, A., Reynaud, S.: Roughness correction to the Casimir force: Beyond the proximity force approximation. Euro Phys. Lett. 69, 924-930 (2005) (Pubitemid 40435923)
25. Maia Neto, P.A., Lambrecht, A., Reynaud, S.: Casimir energy between a plane and a sphere in electromagnetic vacuum. Phys. Rev. A 78, 012-115 (2008)
26. Kenneth, O., Klich, I.: Casimir forces in a T-operator approach. Phys. Rev. B 78, 014-103 (2008)
27. McCauley, A.P., Rodriguez, A.W., Joannopoulos, J.D., Johnson, S.G.: Casimir forces in the time domain: Applications. Phys. Rev. A 81, 012-119 (2010)
28. Casimir, H.B.G.: On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 51, 793-795 (1948)
29. Lamoreaux, S.K.: Demonstration of the Casimir force in the 0.6 to 6μm range. Phys. Rev. Lett. 78, 5-8 (1997) (Pubitemid 127651762)
30. Derjaguin, B.V., Abrikosova, I.I., Lifshitz, E.M.: Direct measurement of molecular attraction between solids separated by a narrow gap. Q. Rev. Chem. Soc. 10, 295-329 (1956)
31. Bordag, M.: Casimir effect for a sphere and a cylinder in front of a plane and corrections to the proximity force theorem. Phys. Rev. D 73, 125-018 (2006)
32. Bordag, M., Mohideen, U., Mostepanenko, V.M.: New developments in the Casimir effect. Phys. Rep. 353, 1-205 (2001) (Pubitemid 33642397)
33. Casimir, H.B.G., Polder, D.: The influence of retardation on the London-van der Waals forces. Phys. Rev. 13(4), 360-372 (1948)
34. Sedmik, R., Vasiljevich, I., Tajmar, M.: Detailed parametric study of Casimir forces in the casimir polder approximation for nontrivial 3d geometries. J. Comput. Aided Mater. Des. 14(1), 119-132 (2007) (Pubitemid 46432583)
35. Tajmar, M.: Finite element simulation of Casimir forces in arbitrary geometries. Intl. J. Mod. Phys. C 15(10), 1387-1395 (2004) (Pubitemid 40517840)
36. Jaffe, R.L., Scardicchio, A.: Casimir effect and geometric optics. Phys. Rev. Lett. 92, 070-402 (2004)
37. Hertzberg, M.P., Jaffe, R.L., Kardar, M., Scardicchio, A.: Casimir forces in a piston geometry at zero and finite temperatures. Phys. Rev. D 76, 045-016 (2007)
38. Zaheer, S., Rodriguez, A.W., Johnson, S.G., Jaffe, R.L.: Optical-approximation analysis of sidewall-spacing effects on the force between two squares with parallel sidewalls. Phys. Rev. A 76(6), 063-816 (2007)
39. Scardicchio, A., Jaffe, R.L.: Casimir effects: An optical approach I. Foundations and examples. Nucl. Phys. B 704(3), 552-582 (2005) (Pubitemid 40030594)
40. Van Enk, S.J.: The Casimir effect in dielectrics: A numerical approach. J. Mod. Opt. 42(2), 321-338 (1995)
41. Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1998)
42. Schaubert, D.H., Wilton, D.R., Glisson, A.W.: A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies. IEEE Trans. Antennas Propagat. 32, 77-85 (1984)
43. Bienstman, P., Baets, R.: Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers. Opt. Quantum Electron. 33(4-5), 327-341 (2001) (Pubitemid 32672461)
44. Bienstman, P., Baets, R.: Advanced boundary conditions for eigenmode expansion models. Opt. Quantum Electron. 34, 523-540 (2002) (Pubitemid 34699215)
45. Willems, J., Haes, J., Baets, R.: The bidirectional mode expansion method for two dimensional waveguides. Opt. Quantum Electron. 27(10), 995-1007 (1995)
46. Moharam, M.G., Grann, E.B., Pommet, D.A., Gaylord, T.K.: Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings. J. Opt. Soc. Am. A 12, 1068-1076 (1995)
47. Moharam, M.G., Pommet, D.A., Grann, E.B., Gaylord, T.K.: Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: Enhanced transmittance matrix approach. J. Opt. Soc. Am. A 12, 1077-1086 (1995)
48. Katsenelenbaum, B.Z., Mercaderdel Río, L., Pereyaslavets, M., Sorolla Ayza, M., Thumm, M.: Theory of Nonuniform Waveguides: The Cross-Section Method (1998)
49. Christ, A., Hartnagel, H.L.: Three-dimensional finite-difference method for the analysis of microwave-device embedding. IEEE Trans. Microwave Theory Tech. 35(8), 688-696 (1987) (Pubitemid 17632218)
50. Strikwerda, J.: Finite Difference Schemes and Partial Differential Equations. Wadsworth and Brooks/Cole, Pacific Grove, CA (1989)
51. Bonnet, M.: Boundary Integral Equation Methods for Solids and Fluids. Wiley, Chichester (1999)
52. Hackbush, W., Verlag, B.: Integral Equations: Theory and Numerical Treatment. Birkhauser Verlag, Basel, Switzerland (1995)
53. Boyd, J.P.: Chebychev and Fourier Spectral Methods, 2nd edn. Dover, New York (2001)
54. Ditkowski, A., Dridi, K., Hesthaven, J.S.: Convergent Cartesian grid methods forMaxwell's equations in complex geometries. J. Comp. Phys. 170, 39-80 (2001) (Pubitemid 33658377)
55. Oskooi, A.F., Kottke, C., Johnson, S.G.: Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing. Opt. Lett. 34, 2778-2780 (2009)
56. Stratton, J.A.: Electromagnetic Theory. McGraw-Hill, New York (1941)
57. Johnson, S.G., Joannopoulos, J.D.: Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Opt. Express 8(3), 173-190 (2001)
58. Kuo, S.H., Tidor, B., White, J.: A meshless, spectrally accurate, integral equation solver for molecular surface electrostatics. ACM J. Emerg. Technol. Comput. Syst. 4(2), 1-30 (2008)
59. Sladek, V., Sladek, J.: Singular Integrals in Boundary Element Methods. WIT Press, Southampton, UK (1998)
60. Taylor, D.J.: Accurate and efficient numerical integration of weakly singular integrals in Galerkin EFIE solutions. IEEE Trans. Antennas Propagat 51, 1630-1637 (2003)
61. Tong, M.S., Chew, W.C.: Super-hyper singularity treatment for solving 3d electric field integral equations. Microwave Opt. Tech. Lett. 49, 1383-1388 (2006)
62. 3. Numerische Mathematik. 35, 315-341 (1980)
63. Rao, S.M., Wilton, D.R., Glisson, A.W.: Electromagnetic scattering by surfaces ofarbitrary shape. IEEE Trans. Antennas Propagat 30, 409-418 (1982)
64. Cai, W., Yu, Y., Yuan, XC.: Singularity treatment and high-order RWG basis functions for integral equations of electromagnetic scattering. Intl. J. Numer. Meth. Eng. 53, 31-47 (2002) (Pubitemid 34018775)
65. Trefethen, L.N., Bau, D.: Numerical Linear Algebra. SIAM, Philadelphia (1997)
66. Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)
67. Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, j., Eijkhout, V., Pozo, R., Romine, C., Vander Vorst, H.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd edn. SIAM, Philadelphia (1994)
68. Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., VanDer Vorst, H.: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia (2000)
69. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., McKenney, A.: LAPACK Users' Guide, 3rd edn. SIAM, Philadelphia (1999)
70. Duff, I.S., Erisman, A.M., Reid, J.K.: On George's nested dissection method. SIAM J. Numer. Anal. 13, 686-695 (1976)
71. Phillips, J.R., White, J.K.: A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Comput. Aided Des. 16, 1059-1072 (1997) (Pubitemid 127828689)
72. Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comp. Phys. 73, 325-348 (1987)
73. Greengard, L., Gueyffier, D., Martinsson, P.G., Rokhlin, V.: Fast direct solvers for integral equations in complex three-dimensional domains. Acta Numer 18, 243-275 (2009)
74. Milonni, P.W.: The Quantum Vacuum: An Introduction to Quantum Electrodynamics. Academic Press, San Diego (1993)
75. Cohen-Tannoudji, C., Din, B., Laloë, F.: Quantum Mechanics. Hermann, Paris (1977)
76. Strang, G.: Computational Science and Engineering. Wellesley-Cambridge Press, Wellesley, MA (2007)
77. Lamoreaux, S.K.: The Casimir force: background, experiments, and applications. Rep. Prog. Phys. 68, 201-236 (2005)
78. Ford, L.H.: Spectrum of the Casimir effect and the Lifshitz theory. Phys. Rev. A 48, 2962-2967 (1993)
79. Nesterenko, V.V., Pirozhenko, I.G.: Simple method for calculating the Casimir energy for a sphere. Phys. Rev. D 57, 1284-1290 (1998)
80. Cognola, G., Elizalde, E., Kirsten, K.: Casimir energies for spherically symmetric cavities. J. Phys. A 34, 7311-7327 (2001) (Pubitemid 33577171)
81. Boyd, J.P.: Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals. J. Sci. Comput. 2, 99-109 (1987)
82. Stroud, A.H., Secrest, D.: Gaussian Quadrature Formulas. Prentice-Hall, Englewood Cliffs, NJ (1966)
83. Piessens, R., de Doncker-Kapenga, E., Uberhuber, C., Hahaner, D.: QUADPACK: A Subroutine Package for Automatic Integration. Springer-Verlag, Berlin (1983)
84. Buhmann, S.Y., Scheel, S.: Macroscopic quantum electrodynamics and duality. Phys. Rev. Lett. 102, 140-404 (2009)
85. Gel'fand, I.M., Shilov, G.E.: Generalized Functions. Academic Press, New York (1964)
86. Milton, K.A., Wagner, J., Parashar, P., Brevek, I.: Casimir energy, dispersion, and the Lifshitz formula. Phys. Rev. D 81, 065-007 (2010)
87. Economou, E.N.: Green's Functions in Quantum Physics, 3rd edn. Springer, Heidelberg (2006)
88. Zhao, J.S., Chew, W.C.: Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies. IEEE Trans. Antennas Propagat. 48, 1635-1645 (2000) (Pubitemid 32252089)
89. Epstein, C.L., Greengard, L.: Debye sources and the numerical solution of the time harmonic Maxwell equations. Commun. Pure Appl. Math. 63, 413-463 (2009)
90. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge Univ. Press, (1992)
91. Hoye, J.S., Brevik, I., Aarseth, J.B., Milton, K.A.: What is the temperature dependence of the casimir effect? J. Phys. A: Math. Gen. 39(20), 6031-6038 (2006) (Pubitemid 43684569)
92. Rodriguez, A.W., Munday, J., Dalvit, D.A.R., Capasso, F., Joannopoulos, J.D., Johnson, S.G.: Stable suspension and dispersion-induced transition from repulsive Casimir forces between fluid-separated eccentric cylinders. Phys. Rev. Lett. 101(19), 190-404 (2008)
93. Pitaevskii, L.P.: Comment on Casimir force acting on magnetodielectric bodies in embedded in media. Phys. Rev. A 73, 047-801 (2006)
94. Munday, J., Capasso, F., Parsegian, V.A.: Measured long-range repulsive Casimir-lifshitz forces. Nature 457, 170-173 (2009)
95. Munday, J.N., Capasso, F.: Precision measurement of the Casimir-Lifshitz force in a fluid. Phys. Rev. A 75, 060-102 (2007)
96. Chew, W.C., Weedon, W.H.: A 3d perfectly matched medium from modified Maxwell's equations with stretched coordinates. Microwave Opt. Tech. Lett. 7(13), 599-604 (1994)
97. Zhao, L., Cangellaris, A.C.: A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation. IEEE Microwave and Guided Wave Lett. 6(5), 209-211 (1996) (Pubitemid 126541724)
98. Teixeira, F.L., Chew, W.C.: General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media. IEEE Microwave and Guided Wave Lett. 8(6), 223-225 (1998) (Pubitemid 128446297)
99. Ward, A.J., Pendry, J.B.: Refraction and geometry in Maxwell's equations. J. Mod. Opt. 43(4), 773-793 (1996) (Pubitemid 126595032)
100. Farjadpour, A., Roundy, D., Rodriguez, A., Ibanescu, M., Bermel, P., Joannopoulos, J.D., Johnson, S.G., Burr, G.: Improving accuracy by subpixel smoothing in FDTD. Opt. Letters. 31, 2972-2974 (2006)
101. Kottke, C., Farjadpour, A., Johnson, S.G.: Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods. Phys. Rev. E 77, 036-611 (2008)
102. Zhao, S.: High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces. J. Comp. Phys. 229, 3155-3170 (2010)
103. Golub, G.H., Loan, C.F.V.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore, MD (1996)
104. Trottenberg, U., Ooseterlee, C., Schüller, A.: Multigrid. Academic Press, London (2001)
105. Rengarajan, S.R., Rahmat-Samii, Y.: The field equivalence principle: Illustration of the establishment of the non-intuitive null fields. IEEE Antennas Propag. Mag. 42,122-128 (2000)
106. Schelkunoff, S.A.: Some equivalence theorems ofelectromagnetic waves. Bell Syst. Tech. J. 15, 92-112 (1936)
107. Stratton, J.A., Chu, L.J.: Diffraction theory of electromagnetic waves. Phys. Rev. 56, 99-107 (1939)
108. Love, A.E.H.: The integration of equations of propagation of electric waves. Phil. Trans. Roy. Soc. London A 197, 1-45 (1901)
109. Harrington, R.F.: Boundary integral formulations for homogeneous material bodies. J. Electromagn. Waves Appl. 3, 1-15 (1989)
110. Umashankar, K., Taflove, A., Rao, S.: Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects. IEEE Trans. Antennas Propagat 34, 758-766 (1986) (Pubitemid 16631450)
111. Medgyesi-Mitschang, L.N., Putnam, J.M., Gedera, M.B.: Generalized method of moments forthree-dimensional penetrable scatterers. J. Opt. Soc. Am. A 11, 1383-1398 (1994)
112. Trefethen, L.N.: Is Gauss quadrature better than clenshaw-curtis. SIAM Review 50, 67-87 (2008) (Pubitemid 351386904)
113. Cools, R.: Advances in multidimensional integration. J. Comput. Appl. Math 149, 1-12 (2002) (Pubitemid 35404883)
114. Cools, R.: An encyclopaedia of cubature formulas. J. Complexity 19, 445-453 (2003) (Pubitemid 36645468)
115. Berntsen, J., Espelid, T.O., Genz, A.: An adaptive algorithm for the approximate calculation ofmultiple integrals. ACM Trans. Math. Soft. 17, 437-451 (1991)
116. Atkinson, K., Sommariva, A.: Quadrature over the sphere. Elec. Trans. Num. Anal. 20, 104-118 (2005) (Pubitemid 43004331)
117. Le Gia, Q.T., Mhaskar, H.N.: Localized linear polynomial operators and quadrature formulas on the sphere. SIAM J. Num. Anal. 47, 440-466 (2008)
118. Oskooi, A.F., Roundy, D., Ibanescu, M., Bermel, P., Joannopoulos, J.D., Johnson, S.G.: Meep: A flexible free-software package for electromagnetic simulations by the FDTD method. Comp. Phys. Comm. 181, 687-702 (2010)
119. Rodriguez, A.W., McCauley, A.P., Joannopoulos, J.D., Johnson, S.G.: Theoretical ingredients of a Casimir analog computer. Proc. Nat Acad. Sci. 107, 9531-9536 (2010)
120. McCauley, A.P., Rodriguez, A.W., Johnson, S.G.: Casimir Meep wiki. http://ab-initio. mit.edu
121. Werner, G.R., Cary, J.R.: A stable FDTD algorithm for non-diagonal anisotropic dielectrics. J. Comp. Phys. 226, 1085-1101 (2007)
122. Li, H., Kardar, M.: Fluctuation-induced forces between rough surfaces. Phys. Rev. Lett. 67, 3275-3278 (1991)
123. Reid, M.T.H.: Fluctuating surface currents: A new algorithm for efficient prediction of Casimir interactions among arbitrary materials in arbitrary geometries. Ph.D. Thesis, Department of Physics, Massachusetts Institute of Technology (2010)
124. Emig, T.: Casimir forces: An exact approach for periodically deformed objects. Euro Phys. Lett. 62, 466 (2003)
125. Gies, H., Klingmuller, K.: Worldline algorithms for Casimir configurations. Phys. Rev. D 74, 045-002 (2006)
126. Gies, H., Langfeld, K., Moyaerts, L.: Casimir effect on the worldline. J. High Energy Phys. 6, 018 (2003)
127. Emig, T., Graham, N., Jaffe, R.L., Kardar, M.: Orientation dependence of Casimir forces. Phys. Rev. A 79, 054-901 (2009)
128. Waterman, P.C.: The Γ-matrix revisited. J. Opt. Soc. Am. A 24(8), 2257-2267 (2007)
129. Emig, T.: Fluctuation-induced quantum interactions between compact objects and a plane mirror. J. Stat. Mech. p. P04007 (2008)
130. Emig, T., Jaffe, R.L.: Casimir forces between arbitrary compact objects. J. Phys. A 41, 164-001 (2008)
131. Bimonte, G.: Scattering approach to Casimir forces and radiative heat transfer for nanostructured surfaces out of thermal equilibrium. Phys. Rev. A 80, 042-102 (2009)
132. McCauley, A.P., Zhao, R., Reid, M.T.H., Rodriguez, A.W., Zhao, J., Rosa, F.S.S., Joannopoulos, J.D., Dalvit, D.A.R., Soukoulis, C.M., Johnson, S.G.: Microstructure effects for Casimir forces in chiral metamaterials. Phys. Rev. B 82, 165108 (2010)
133. Marcuse, D.: Theory of Dielectric Optical Waveguides, 2nd edn. Academic Press, San Diego (1991)
134. Johnson, S.G., Bienstman, P., Skorobogatiy, M., Ibanescu, M., Lidorikis, E., Joannopoulos, J.D.: Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals. Phys. Rev. E. 66, 066-608 (2002)
135. Skorobogatiy, M., Yang, J.: Fundamentals of Photonic Crystal Guiding. Cambridge University Press, Cambridge (2009)
136. Inui, T., Tanabe, Y., Onodera, Y.: Group Theory and Its Applications in Physics. Springer, Heidelberg (1996)
137. Tinkham, M.: Group Theory and Quantum Mechanics. Dover, New York (2003)
138. Rodriguez, A.W., Woolf, D., McCauley, A.P., Capasso, F., Joannopoulos, J.D., Johnson, S.G.: Achieving a strongly temperature-dependent Casimir effect. Phys. Rev. Lett. 105, 060-401 (2010)
139. Milton, K.A.: The Casimir effect: recent controveries and progress. J. Phys. A: Math. Gen. 37, R209-R277 (2004) (Pubitemid 39332490)
140. Najafi, A., Golestanian, R.: Forces induced by nonequilibrium fluctuations: The soret-Casimir effect. Euro Phys. Lett. 68, 776-782 (2004) (Pubitemid 40014173)
141. Obrecht, J.M., Wild, R.J., Antezza, M., Pitaevskii, L.P., Stringari, S., Cornell, E.A.: Measurement of the temperature dependence of the Casimir-Polder force. Phys. Rev. Lett. 98(6), 063-201 (2007)