Vol. 142

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2013-09-27

Casimir Force for Arbitrary Objects Using the Argument Principle and Boundary Element Methods

By Phillip R. Atkins, Qi Dai, Wei E. I. Sha, and Weng Cho Chew
Progress In Electromagnetics Research, Vol. 142, 615-624, 2013
doi:10.2528/PIER13082105

Abstract

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplified derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.

Citation


Phillip R. Atkins, Qi Dai, Wei E. I. Sha, and Weng Cho Chew, "Casimir Force for Arbitrary Objects Using the Argument Principle and Boundary Element Methods," Progress In Electromagnetics Research, Vol. 142, 615-624, 2013.
doi:10.2528/PIER13082105
http://www.jpier.org/PIER/pier.php?paper=13082105

References


    1. Reid, M. T. H., A. W. Rodriguez, J. White, and S. G. Johnson, "Efficient computation of casimir interactions between arbitrary 3D objects," Phys. Rev. Lett., Vol. 103, 2009.
    doi:10.1103/PhysRevLett.103.040401

    2. Reid, M. T. H., J. White, and S. G. Johnson, "Computation of casimir interactions between arbitrary three-dimensional objects with arbitrary material properties," Phys. Rev. A, Vol. 84, 2011.
    doi:10.1103/PhysRevA.84.010503

    3. Van Kampen, N. G., B. R. A. Nijboer, and K. Schram, "On the macroscopic theory of van derWaals forces," Phys. Lett., Vol. 26A, 307, 1968.

    4. Qian, Z.-G. and W. C. Chew, "Fast full-wave surface integral equation solver for multiscale structure modeling," IEEE Trans. Antennas Propag., Vol. 57, No. 11, 3594-3601, Nov. 2009.
    doi:10.1109/TAP.2009.2023629

    5. Li, H. and M. Kardar, "Fluctuation-induced forces between rough surfaces," Phys. Rev. Lett., Vol. 67, No. 23, 3275-3278, 1991.
    doi:10.1103/PhysRevLett.67.3275

    6. Chew, W. C., M. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan & Claypool, USA, 2009.

    7. Barash, Y. S. and V. L. Ginzburg, "Electromagnetic fluctuations in matter and molecular (van-der-Waals) forces between them," Sov. Phys. Usp., Vol. 18, No. 5, 305-322, 1975.
    doi:10.1070/PU1975v018n05ABEH001958

    8. Milonni, P. W., The Quantum Vacuum: An Introduction to Quantum Electrodynamics, Academic Press, San Diego, CA, 1994.

    9. Langbein, D., "The macroscopic theory of van der Waals attraction," Solid State Comm., Vol. 12, 853-855, 1973.
    doi:10.1016/0038-1098(73)90093-8

    10. Schram, K., "On the macroscopic theory of retarded van der Waals forces," Phys. Lett., Vol. 43A, No. 3, 282-284, 1973.

    11. Lambrecht, A. and V. N. Marachevsky, "New geometries in the casimir effect: Dielectric gratings," J. Phys. Conf. Ser., Vol. 161, 1-8, 2009.

    12. Ginzburg, V. L., Theoretical Physics and Astrophysics, Pergamon Press, New York, 1979.

    13. Lamoreaux, S. K., "The casimir force: Background, experiments, and applications," Rep. Prog. Phys., Vol. 68, 201-236, 2005.
    doi:10.1088/0034-4885/68/1/R04

    14. Rosa, F. S. S., D. A. R. Dalvit, and P. Milonni, "Electromagnetic energy, absorption, and casimir forces: Uniform dielectric media in thermal equilibrium," Phys. Rev. A, Vol. 81, 033812, 2010.
    doi:10.1103/PhysRevA.81.033812

    15. Rosa, F. S. S., D. A. R. Dalvit, and P. Milonni, "Electromagnetic energy, absorption, and casimir forces. II. Inhomogeneous dielectric media," Phys. Rev. A, Vol. 84, 053813, 2011.
    doi:10.1103/PhysRevA.84.053813

    16. Sernelius, B. E., "Casimir force and complications in the Van Kampen theory for dissipative systems," Phys. Rev. B, Vol. 74, 233103, 2006.
    doi:10.1103/PhysRevB.74.233103

    17. Intravaia, F. and R. Behunin, "Casimir effect as a sum over modes in dissipative system," Phys. Rev. A, Vol. 86, 062517, 2012.
    doi:10.1103/PhysRevA.86.062517

    18. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.

    19. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, 409-418, 1982.
    doi:10.1109/TAP.1982.1142818

    20. Jiang, L. J. and W. C. Chew, "The mixed-form fast multipole algorithm for broadband electromagnetic simulations," Antennas and Propagation Society International Symposium, 180-183, 2005.

    21. Poggio, A. J. and E. K. Miller, Integral Equation Solutions of Three Dimensional Scattering Problems, R. Mittra, Ed., Permagon, Elmsford, NY, 1973.

    22. Chang, Y. and R. Harrington, "A surface formulation for characteristic modes of material bodies," IEEE Trans. Antennas Propag. , Vol. 25, 789-795, 1977.
    doi:10.1109/TAP.1977.1141685

    23. Wu, T. and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Sci., Vol. 12, No. 5, 709-718, 1977.
    doi:10.1029/RS012i005p00709

    24. Medgyesi-Mitschang, L. N., J. M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1383-1398, 1994.
    doi:10.1364/JOSAA.11.001383

    25. Chew, W. C. and L. E. Sun, "A novel formulation of the volume integral equation for electromagnetic scattering," Waves in Random and Complex Media, Vol. 19, No. 1, 162-180, 2009.
    doi:10.1080/17455030802625427

    26. Chew, W. C., J. L. Xiong, and M. A. Saville, "A matrix-friendly formulation of layered medium Green's function," IEEE Antennas Wireless Propag. Lett., Vol. 5, 490-494, 2006.
    doi:10.1109/LAWP.2006.886306