Vol. 171

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2021-10-22

Calculations of Bands and Band Field Solutions in Topological Acoustics Using the Broadband Green's Function-KKR-Multiple Scattering Method

By Leung Tsang, Tien-Hao Liao, and Shurun Tan
Progress In Electromagnetics Research, Vol. 171, 137-158, 2021
doi:10.2528/PIER21081706

Abstract

In this paper, we apply the BBGF-KKR-MST (Broadband Green's function-KKR-Multiple Scattering Theory) to calculate Band Structures and Band Field Solutions in topological acoustics. A feature of BBGF is that the lattice Green's functions are broadband, and the transformations to cylindrical waves are calculated rapidly for many frequencies for speedy calculation of the determinant of the KKR equation. For the two bands of interest, only 5 cylindrical waves are sufficient so that the dimension of the eigenvalue matrix equation is only 5. The CPU time requirement, including setup and using MATLAB on a standard laptop, is 5 milliseconds for a band eigenvalue. Using the eigenvalue and the scattered field eigenvector, the field in the cell is calculated by higher order cylindrical waves. The exciting field of higher order cylindrical waves requires only 11 coefficients to represent the band field solutions in the cell. Comparisons are made with the results of the volume integral equation method and the commercial software COMSOL. The BBGF-KKR-MST method is significantly faster.

Citation


Leung Tsang, Tien-Hao Liao, and Shurun Tan, "Calculations of Bands and Band Field Solutions in Topological Acoustics Using the Broadband Green's Function-KKR-Multiple Scattering Method," Progress In Electromagnetics Research, Vol. 171, 137-158, 2021.
doi:10.2528/PIER21081706
http://www.jpier.org/PIER/pier.php?paper=21081706

References


    1. Wang, Z., Y. D. Chong, J. D. Joannopoulos, and M. Soljacic, "Reflection-free one-way edge modes in a gyromagnetic photonic crystal," Phys. Rev. Lett., Vol. 100, 013905, 2008.

    2. Yang, Z., F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, "Topological acoustics," Phys. Rev. Lett., Vol. 114, 114301, 2015.

    3. Xue, H., Y. Yang, G. Liu, F. Gao, Y. Chong, and B. Zhang, "Realization of an acoustic third-order topological insulator," Phys. Rev. Lett., Vol. 122, 244301, June 2019.

    4. Ao, X., Z. Lin, and C. T. Chan, "One way edge modes in a magneto-optical honeycomb photonic crystal," Phys. Rev. B, Vol. 80, 033105, 2009.

    5. Feng, Z., S. Tan, L. Tsang, and E. Li, "Band characterization of topological photonic crystals using the broadband Green's function technique," Optics Express, Vol. 28, No. 19, 27223, 2020.

    6. Ho, K. M., C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett., Vol. 65, 3152-3155, 1990.

    7. Leung, K. M. and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett., Vol. 65, 2646-2649, 1990.

    8. Plihal, M. and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B, Vol. 44, 8565-8571, 1991.

    9. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press, 2011.

    10. Fan, S., P. R. Villeneuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Vol. 54, 11245-11251, 1996.

    11. Zhao, R., G. D. Xie, M. L. N. Chen, Z. Lan, Z. Huang, and W. E. I. Sha, "First-Princip calculation of Chern number in gyrotropic photonic crystals," Optics Express, Vol. 28, 4638, 2020.

    12. Nicolet, A., S. Guenneau, C. Geuzainec, and F. Zollaa, "Modelling of electromagnetic waves in periodic media with finite elements," Journal of Comp. and Appl. Math., Vol. 168, 321-329, 2004.

    13. Jin, J. M., Finite Element Method in Electromagnetics, 3rd Ed., Wiley, 2014.

    14. Korringa, J., "On the calculation of the energy of a Bloch wave in a metal," Physica, Vol. 13, 392-400, 1947.

    15. Kohn, W. and N. Rostoker, "Solution of the Schrodinger Equation in periodic lattices with an application to metallic lithium," Phys. Rev., Vol. 94, 1111-1120, 1954.

    16. Leung, K. M. and Y. Qiu, "Multiple-scattering calculation of the two-dimensional photonic band structure," Phys. Rev. B, Vol. 48, 7767-7771, 1993.

    17. Foldy, L. L., "The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers," Phys. Rev., Vol. 67, 107-119, 1945.

    18. Lax, M., "Multiple scattering of waves," Rev. Mod. Phys., Vol. 23, 287-310, 1951.

    19. Liu, Z., C. T. Chan, P. Sheng, A. L. Goertzen, and J. H. Page, "Elastic wave scattering by periodic structures of spherical objects: Theory and experiment," Phys. Rev. B, Vol. 62, 2446-2457, 2000.

    20. Tsang, L., C. E. Mandy, and K. H. Ding, "Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell's equations," Optics Letters, Vol. 17, 314-316, 1992.

    21. Tse, K. K., L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, "Multiple scattering of waves by dense random distribution of sticky particles for applications in microwave scattering by terrestrial snow," Radio Science, Vol. 42, 2007.

    22. Chen, H. F., Q. Li, L. Tsang, C. C. Huang, and V. Jandhyala, "Analysis of a large number of vias and differential signaling in multilayered structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, 818-829, 2003.

    23. Tsang, L., H. F. Chem, C. C. Huang, and V. Jandhyala, "Methods for modeling interactions between massively coupled multiple vias in multilayered electronic packaging structures,", US patent, Number 7149666, 2006.

    24. Mishchenko, M. I., L. D. Travis, and A. A. Laci's, Multiple Scattering of Light by Particles, Radiative Transfer and Coherent Backscattering, Cambridge University Press, 2006.

    25. Mishchenko, M. I., L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, "Multiple scattering by random particulate media: Exact 3D results," Optics Express, Vol. 15, 2822-2836, 2007.

    26. Waterman, P. C. and R. Truell, "Multiple scattering of waves," Journal of Mathematical Physics, Vol. 2, 512-537, 1961.

    27. Faulkner, J. S., G. Malcolm, and Y. Wang, Multiple Scattering Theory, Electronic Structure of Solids, IOP Press, 2018.

    28. Lai, Y., Z. Q. Zhang, C.H. Chan, and L. Tsang, "Gap structures and wave functions of classical waves in large-sized two-dimensional quasiperiodic structures," Phys. Rev. B, Vol. 74, 054305, 2006.

    29. Van Hove, M. A. and S. Y. Tong, "Surface crystallography by LEED: Theory, computation and structural results," Springer Theory in Chemical Physics, 1979.

    30. Xu, M.-L., J. J. Barton, and M. A. Van Hove, "Electron scattering by atomic chains: Multiple-scattering effects," Phys. Rev. B, Vol. 39, 8275, 1989.

    31. Gavaza, G. M., Z. X. Yu, L. Tsang, C. H. Chan, S. Y. Tong, and M. A. van Hove, "Efficient calculation of electron diffraction for the structural determination of nanomaterials," Phys. Rev. Lett., Vol. 97, 055505/1-4, 2006.

    32. Lubatsch, A. and R. Frank, "Self-consistent quantum field theory for the characterization of complex random media by short laser pulses," Phys. Rev. Res., Vol. 2, 013324, 2020.

    33. Chan, C. H. and L. Tsang, "A sparse-matrix canonical-grid method for scattering by many scatterers," Microwave and Optical Technology Letters, Vol. 8, 114-118, 1995.

    34. Yang, Z., F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, "Topological acoustics," Phys. Rev. Lett., Vol. 114, 114301, 2015.

    35. Xue, H., Y. Yang, G. Liu, F. Gao, Y Chong, and B. Zhang, "Realization of an acoustic third-order topological insulator," Phys. Rev. Lett., Vol. 122, 244301, 2019.

    36. Feng, Z. and S. Tan, "Modeling reáection-free one-way edge modes using foldy-lax multiple scattering theory," 2021 International Applied Computational Electromagnetics Society Symposium (ACES), August 2021.

    37. Tsang, L., "Broadband calculations of band diagrams in periodic structures using the broadband Green's function with low wavenumber extraction (BBGFL)," Progress In Electromagnetics Research, Vol. 153, 57-68, 2015.

    38. Tsang, L. and S. Tan, "Calculations of band diagrams and low frequency dispersion relations of 2D periodic dielectric scattering using broadband Green's function with low wavenumber extraction (BBGFL)," Optics Express, Vol. 24, 945-965, 2016.

    39. Tan, S. and L. Tsang, "Band structures and modal fields in topological acoustics: An integral equation formulation," IEEE Antennas and Propagation Symposium, Atlanta, 2019.

    40. Gao, R., L. Tsang. S. Tan, and T.-H. Liao, "Band calculations using broadband Green's functions and the KKR method with applications to magneto-optics and photonic crystals," Journal of Optical Society of America B, Vol. 37, 3896-3907, 2020.

    41. Gao, R., L. Tsang, S. Tan, and T.-H. Liao, "Broadband Green's function-KKR-multiple scattering method for calculations of normalized band-field solutions in magnetic-optics crystals," Journal of Optical Society of America B, Vol. 38, 3159-3171, 2021.

    42. Tan, S. and L. Tsang, "Efficient broadband evaluations of lattice green's functions via imaginary wavenumber components extractions," Progress In Electromagnetics Research, Vol. 164, 63-74, 2019.

    43. Sanamzadeh, M. and L. Tsang, "Fast and broad band calculation of the dyadic Green's function in the rectangular cavity; An imaginary wave number extraction technique," Progress In Electromagnetic Research C, Vol. 96, 243-258, 2019.

    44. Tsang, L., J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Vol. 2: Numerical Simulations, 705, Wiley Interscience, 2001.

    45. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves, Vol. 3: Advanced Topics, 413, Wiley Interscience, 2001.

    46. Xu, X., D. Liang, L. Tsang, C. M. Andreadis, E. G. Josberger, D. P. Lettenmaier, D. W. Cline, and S. H. Yue, "Active remote sensing of snow using NMM3D/DMRT and comparison with CLPX II airborne data," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 3, No. 4, 689-697, December 2010.

    47. Huang, H., L. Tsang, A. Colliander, R. Shah, X. Xu, and S. H. Yueh, "Multiple scattering of waves by complex objects using hybrid method of T-matrix and foldy-lax equations using vector spherical waves and vector spheroidal waves," Progress In Electromagnetic Research, Vol. 168, 87-111, 2020.

    48. Gu, W., L. Tsang, A. Colliander, and S. H. Yueh, "Wave propagation in vegetation field using a hybrid method," IEEE Transactions on Antennas and Propagation, early access, 2021.

    49. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, 2007.

    50. Tan, S. and L. Tsang, "Green functions, including scatterers, for photonic crystals and metamaterials," Journal of Optical Society of America B, Vol. 34, 1450-1458, 2017.

    51. Tan, S. and L. Tsang, "Scattering of waves by a half-space of periodic scatterers using broadband Green's function," Opt. Lett., Vol. 42, No. 22, 4667-4670, November 2017.

    52. Tsang, L., K.-H. Ding, and S. Tan, "Broadband point source Green's function in a one-dimensional infinite periodic lossless medium based on BBGFL with modal method," Progress In Electromagnetics Research, Vol. 163, 51-77, 2018.

    53. Tsang, L. and S. Tan, "Full wave simulations of photonic crystals and metamaterials using the broadband green's functions,", US patent number 11,087,043, August 10, 2021.