Abstract

A dual-resonance frequency selective surface filter in the THz range that uses bilayer modified complementary metamaterial structures is proposed in this Letter. The bandpass filter, with dual bands centered at 0.315 and 0.48 THz, uses a single crystal quartz substrate and is simulated, fabricated, and measured. To minimize the manufacturing risks of working with fragile and thin quartz substrates, efforts have been made to improve the transmission frequency response features at realizable substrate thicknesses. Experimental results from 0.1 to 0.6 THz measured by THz time-domain spectroscopy show excellent agreement with the simulation results.

© 2014 Optical Society of America

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  1. P. H. Siegel, IEEE Trans. Microwave Theor. Tech. 52, 2438 (2004).
    [CrossRef]
  2. F. C. De Lucia, IEEE MTT-S Int. Microwave Symp. Dig. 3, 1579 (2002).
  3. T. Yeh, S. Genovesi, A. Monorchio, E. Prati, F. Costa, T. Huang, and T. Yen, Opt. Express 20, 7580 (2012).
  4. C. Debus and P. H. Bolivar, “Frequency selective surfaces for high-sensitivity terahertz sensors,” in Conference on Lasers and Electro-Optics (CLEO), 2007.
  5. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef]
  6. E. Ekmekci and G. Turhan-Sayan, “Use of SRR based super-cells to obtain multiple resonances and broader frequency bands with negative effective permeability,” in IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting—Leading the Wave, AP-S/URSI, 2010.
  7. H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.
  8. Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.
  9. A. Dobroiu, C. Otani, and K. Kawase, Meas. Sci. Technol. 17, R161 (2006).
    [CrossRef]
  10. M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
    [CrossRef]
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  13. C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, in IEEE Sixth International Conference on Terahertz Electronics Proceedings (1998), p. 196.
  14. V. Hansen, H.-P. Gemuend, and E. Kreysa, in 13th International Conference on Terahertz Electronics (IRMMW-THz) (2005), pp. 209–210.
  15. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  16. M. Lu, W. Li, and E. R. Brown, Opt. Lett. 36, 1071 (2011).
    [CrossRef]
  17. S. Vegesna, Y. Zhu, A. Bernussi, and M. Saed, IEEE Trans. THz Technol. 2, 441 (2012).
  18. X. Zhang, J. Gu, W. Cao, J. Han, A. Lakhtakia, and W. Zhang, Opt. Lett. 37, 906 (2012).
    [CrossRef]
  19. Y. Zhu, S. Vegesna, V. Kuryatkov, M. Holtz, M. Saed, and A. A. Bernusi, Opt. Lett. 37, 296 (2012).
    [CrossRef]
  20. H.-T. Chen, J. F. O’Hara, A. J. Taylor, and R. D. Averitt, Opt. Express 15, 1084 (2007).
    [CrossRef]
  21. H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).
  22. B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley-Interscience, 2000).
  23. J. C. Vardaxoglou, Frequency Selective Surfaces (Wiley, 1997).

2012 (4)

2011 (1)

2007 (1)

2006 (1)

A. Dobroiu, C. Otani, and K. Kawase, Meas. Sci. Technol. 17, R161 (2006).
[CrossRef]

2005 (1)

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

2004 (1)

P. H. Siegel, IEEE Trans. Microwave Theor. Tech. 52, 2438 (2004).
[CrossRef]

2003 (1)

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

2002 (1)

F. C. De Lucia, IEEE MTT-S Int. Microwave Symp. Dig. 3, 1579 (2002).

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Averitt, R. D.

H.-T. Chen, J. F. O’Hara, A. J. Taylor, and R. D. Averitt, Opt. Express 15, 1084 (2007).
[CrossRef]

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Bernusi, A. A.

Bernussi, A.

S. Vegesna, Y. Zhu, A. Bernussi, and M. Saed, IEEE Trans. THz Technol. 2, 441 (2012).

Bolivar, P. H.

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high-sensitivity terahertz sensors,” in Conference on Lasers and Electro-Optics (CLEO), 2007.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Brown, E. R.

Cao, W.

Chang, S. S.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Chen, H.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Chen, H. S.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Chen, H.-T.

Cheng, K.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Cluff, J. A.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Cole, B. E.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Costa, F.

David, R. S.

Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.

De Lucia, F. C.

F. C. De Lucia, IEEE MTT-S Int. Microwave Symp. Dig. 3, 1579 (2002).

Debus, C.

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high-sensitivity terahertz sensors,” in Conference on Lasers and Electro-Optics (CLEO), 2007.

Dobroiu, A.

A. Dobroiu, C. Otani, and K. Kawase, Meas. Sci. Technol. 17, R161 (2006).
[CrossRef]

Ekmekci, E.

E. Ekmekci and G. Turhan-Sayan, “Use of SRR based super-cells to obtain multiple resonances and broader frequency bands with negative effective permeability,” in IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting—Leading the Wave, AP-S/URSI, 2010.

Fan, K.

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Fitzgerald, A. J.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Gemuend, H.-P.

V. Hansen, H.-P. Gemuend, and E. Kreysa, in 13th International Conference on Terahertz Electronics (IRMMW-THz) (2005), pp. 209–210.

Genovesi, S.

Grant, J. P.

Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.

Grzegorczyk, T. M.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Gu, J.

Han, J.

Hansen, V.

V. Hansen, H.-P. Gemuend, and E. Kreysa, in 13th International Conference on Terahertz Electronics (IRMMW-THz) (2005), pp. 209–210.

Helm, H.

C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, in IEEE Sixth International Conference on Terahertz Electronics Proceedings (1998), p. 196.

Holtz, M.

Huang, T.

Huangfu, J.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Kawase, K.

A. Dobroiu, C. Otani, and K. Kawase, Meas. Sci. Technol. 17, R161 (2006).
[CrossRef]

Kemp, M. C.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Khalid’Shimul, A.

Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.

Kim, D. S.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Kim, J. H.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Kong, J. A.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Kreysa, E.

V. Hansen, H.-P. Gemuend, and E. Kreysa, in 13th International Conference on Terahertz Electronics (IRMMW-THz) (2005), pp. 209–210.

Kuryatkov, V.

Lakhtakia, A.

Lewen, F.

C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, in IEEE Sixth International Conference on Terahertz Electronics Proceedings (1998), p. 196.

Li, W.

Lu, M.

Ma, Y.

Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.

Monorchio, A.

Munk, B. A.

B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley-Interscience, 2000).

Nahar, N. K.

V. Sanphuang, N. K. Nahar, and J. L. Volakis, in Proceedings of the 2012 IEEE National Aerospace and Electronics Conference (NAECON) (2013), pp. 38–39.

Nemat Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

O’Hara, J. F.

Otani, C.

A. Dobroiu, C. Otani, and K. Kawase, Meas. Sci. Technol. 17, R161 (2006).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Park, G. S.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Prati, E.

Ran, L. X.

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Saed, M.

Y. Zhu, S. Vegesna, V. Kuryatkov, M. Holtz, M. Saed, and A. A. Bernusi, Opt. Lett. 37, 296 (2012).
[CrossRef]

S. Vegesna, Y. Zhu, A. Bernussi, and M. Saed, IEEE Trans. THz Technol. 2, 441 (2012).

Saha, C.

Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.

Sanphuang, V.

V. Sanphuang, N. K. Nahar, and J. L. Volakis, in Proceedings of the 2012 IEEE National Aerospace and Electronics Conference (NAECON) (2013), pp. 38–39.

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Seo, M. A.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Siegel, P. H.

P. H. Siegel, IEEE Trans. Microwave Theor. Tech. 52, 2438 (2004).
[CrossRef]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

So, J. K.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Son, J. H.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

Strikwerda, A.

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Taday, P. F.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Tao, H.

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Taylor, A. J.

Tribe, W. R.

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Turhan-Sayan, G.

E. Ekmekci and G. Turhan-Sayan, “Use of SRR based super-cells to obtain multiple resonances and broader frequency bands with negative effective permeability,” in IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting—Leading the Wave, AP-S/URSI, 2010.

Vardaxoglou, J. C.

J. C. Vardaxoglou, Frequency Selective Surfaces (Wiley, 1997).

Vegesna, S.

Y. Zhu, S. Vegesna, V. Kuryatkov, M. Holtz, M. Saed, and A. A. Bernusi, Opt. Lett. 37, 296 (2012).
[CrossRef]

S. Vegesna, Y. Zhu, A. Bernussi, and M. Saed, IEEE Trans. THz Technol. 2, 441 (2012).

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Volakis, J. L.

V. Sanphuang, N. K. Nahar, and J. L. Volakis, in Proceedings of the 2012 IEEE National Aerospace and Electronics Conference (NAECON) (2013), pp. 38–39.

Weinzierl, J.

C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, in IEEE Sixth International Conference on Terahertz Electronics Proceedings (1998), p. 196.

Winnewisser, C.

C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, in IEEE Sixth International Conference on Terahertz Electronics Proceedings (1998), p. 196.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Yeh, T.

Yen, T.

Zhang, W.

Zhang, X.

X. Zhang, J. Gu, W. Cao, J. Han, A. Lakhtakia, and W. Zhang, Opt. Lett. 37, 906 (2012).
[CrossRef]

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Zhu, Y.

Y. Zhu, S. Vegesna, V. Kuryatkov, M. Holtz, M. Saed, and A. A. Bernusi, Opt. Lett. 37, 296 (2012).
[CrossRef]

S. Vegesna, Y. Zhu, A. Bernussi, and M. Saed, IEEE Trans. THz Technol. 2, 441 (2012).

IEEE MTT-S Int. Microwave Symp. Dig. (1)

F. C. De Lucia, IEEE MTT-S Int. Microwave Symp. Dig. 3, 1579 (2002).

IEEE Trans. Microwave Theor. Tech. (1)

P. H. Siegel, IEEE Trans. Microwave Theor. Tech. 52, 2438 (2004).
[CrossRef]

IEEE Trans. THz Technol. (1)

S. Vegesna, Y. Zhu, A. Bernussi, and M. Saed, IEEE Trans. THz Technol. 2, 441 (2012).

Meas. Sci. Technol. (1)

A. Dobroiu, C. Otani, and K. Kawase, Meas. Sci. Technol. 17, R161 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef]

Proc. SPIE (1)

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, Proc. SPIE 5070, 44 (2003).
[CrossRef]

Prog. Electromagn. Res. (1)

H. S. Chen, L. X. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 51, 231 (2005).

Other (11)

B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley-Interscience, 2000).

J. C. Vardaxoglou, Frequency Selective Surfaces (Wiley, 1997).

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high-sensitivity terahertz sensors,” in Conference on Lasers and Electro-Optics (CLEO), 2007.

V. Sanphuang, N. K. Nahar, and J. L. Volakis, in Proceedings of the 2012 IEEE National Aerospace and Electronics Conference (NAECON) (2013), pp. 38–39.

J. K. So, M. A. Seo, D. S. Kim, J. H. Kim, S. S. Chang, J. H. Son, and G. S. Park, in 33rd International Conference on Infrared and Millimeter Waves and the 16th International Conference on Terahertz Electronics (IRMMW-THz) (IEEE, 2008).

C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, in IEEE Sixth International Conference on Terahertz Electronics Proceedings (1998), p. 196.

V. Hansen, H.-P. Gemuend, and E. Kreysa, in 13th International Conference on Terahertz Electronics (IRMMW-THz) (2005), pp. 209–210.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

E. Ekmekci and G. Turhan-Sayan, “Use of SRR based super-cells to obtain multiple resonances and broader frequency bands with negative effective permeability,” in IEEE International Symposium on Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting—Leading the Wave, AP-S/URSI, 2010.

H. Tao, A. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, and X. Zhang, in 22nd IEEE International Conference on Micro Electro Mechanical Systems (MEMS) (2009), pp. 108–111.

Y. Ma, A. Khalid’Shimul, C. Saha, J. P. Grant, and R. S. David, in IEEE Photonics Society Winter Topicals Meeting Series (WTM) (IEEE, 2010), pp. 50–51.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Unit cell of FC. (b) Unit cell of MFC. (c) Double-layer structure of the filter.

Fig. 2.
Fig. 2.

Numerical simulation results of induced surface current and electric field distributions for (a) and (c) the FC, (b) and (d) the MFC.

Fig. 3.
Fig. 3.

Comparison of the simulated transmission of (a) FC and MFC, and (b) FC with different dimensions and MFC.

Fig. 4.
Fig. 4.

Simulated transmission of the MFC BPF with (a) different thicknesses and (b) different central circle radii.

Fig. 5.
Fig. 5.

(a) Photograph of the fabricated filter. (b) Experimental transmission spectra of the dual-resonance BPF. Dielectric separation: d=155μm. Unit cell dimensions: s=35, w=35, r1=112, r2=r1w=77, r3=60 and a=350μm.

Equations (1)

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T(ω)=t(ω)eiφ(ω)=S(ω)/R(ω),

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