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Scattering resonances for a three-dimensional subwavelength hole

Author

Listed:
  • Maryam Fatima

    (Auburn University)

  • Junshan Lin

    (Auburn University)

Abstract

This work aims to investigate scattering resonances and the field amplification at resonant frequencies for a subwavelength hole of width $$\varepsilon $$ ε embedded in a sound hard slab. We apply the integral equation approach and asymptotic analysis to derive the asymptotic expansions of scattering resonances and quantitatively analyze the corresponding field amplifications. It is shown that the complex-valued scattering resonances attain imaginary parts of order $$O(\varepsilon ^2)$$ O ( ε 2 ) . The field enhancement inside the hole and in the far field is of order $$O({1/\varepsilon ^2})$$ O ( 1 / ε 2 ) at the resonant frequencies, which is much stronger the enhancement order in the two-dimensional subwavelengt hole of the same width.

Suggested Citation

  • Maryam Fatima & Junshan Lin, 2021. "Scattering resonances for a three-dimensional subwavelength hole," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-25, August.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:4:d:10.1007_s42985-021-00111-w
    DOI: 10.1007/s42985-021-00111-w
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    References listed on IDEAS

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    1. T. W. Ebbesen & H. J. Lezec & H. F. Ghaemi & T. Thio & P. A. Wolff, 1998. "Extraordinary optical transmission through sub-wavelength hole arrays," Nature, Nature, vol. 391(6668), pages 667-669, February.
    2. Sang-Hyun Oh & Hatice Altug, 2018. "Performance metrics and enabling technologies for nanoplasmonic biosensors," Nature Communications, Nature, vol. 9(1), pages 1-5, December.
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