Abstract

An optical effect analogous to electromagnetically induced transparency (EIT) is observed in nanoscale plasmonic resonator systems. The system consists of a slot cavity as well as plasmonic bus and resonant waveguides, where the phase-matching condition of the resonant waveguide is tunable for the generation of an obvious EIT-like coupled resonator-induced transparency effect. A dynamic theory is utilized to exactly analyze the influence of physical parameters on transmission characteristics. The transparency effect induced by coupled resonance may have potential applications for nanoscale optical switching, nanolaser, and slow-light devices in highly integrated optical circuits.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  2. R. W. Boyd and D. J. Gauthier, Nature 441, 701 (2006).
    [CrossRef] [PubMed]
  3. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
    [CrossRef]
  4. Y. Zhang, S. Darmawan, L. Tobing, T. Mei, and D. Zhang, J. Opt. Soc. Am. B 28, 28 (2011).
    [CrossRef]
  5. X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
    [CrossRef] [PubMed]
  6. Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
    [CrossRef] [PubMed]
  7. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
    [CrossRef]
  8. K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
    [CrossRef] [PubMed]
  9. W. Barnes, A. Dereux, and T. Ebbesen, Nature 424, 824(2003).
    [CrossRef] [PubMed]
  10. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
    [CrossRef] [PubMed]
  11. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
    [CrossRef]
  12. G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97, 057402 (2006).
    [CrossRef] [PubMed]
  13. H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, Opt. Express 19, 2910 (2011).
    [CrossRef] [PubMed]
  14. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, Appl. Phys. Lett. 85, 5833 (2004).
    [CrossRef]
  15. S. Yang, W. Chen, R. Nelson, and Q. Zhan, Opt. Lett. 34, 3047 (2009).
    [CrossRef] [PubMed]
  16. I. D. Leon and P. Berini, Nat. Photonics 4, 382 (2010).
    [CrossRef]
  17. J. Park, H. Kim, and B. Lee, Opt. Express 16, 413 (2008).
    [CrossRef] [PubMed]
  18. A. Boltasseva, S. Bozhevolnyi, T. Nikolajsen, and K. Leosson, J. Lightwave Technol. 24, 912 (2006).
    [CrossRef]
  19. F. Hu, H. Yi, and Z. Zhou, Opt. Lett. 36, 1500 (2011).
    [CrossRef] [PubMed]
  20. A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102(2007).
    [CrossRef]
  21. H. Lu, X. Liu, D. Mao, L. Wang, and Y. Gong, Opt. Express 18, 17922 (2010).
    [CrossRef] [PubMed]
  22. Z. Han and S. Bozhevolnyi, Opt. Express 19, 3251 (2011).
    [CrossRef] [PubMed]
  23. B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
    [CrossRef] [PubMed]
  24. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Chap. 7.
  25. J. Zhou, D. Mu, J. Yang, W. Han, and X. Di, Opt. Express 19, 4856 (2011).
    [CrossRef] [PubMed]
  26. X. S. Lin and X. G. Huang, Opt. Lett. 33, 2874 (2008).
    [CrossRef] [PubMed]
  27. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

2011 (5)

2010 (3)

H. Lu, X. Liu, D. Mao, L. Wang, and Y. Gong, Opt. Express 18, 17922 (2010).
[CrossRef] [PubMed]

I. D. Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

2009 (2)

X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

S. Yang, W. Chen, R. Nelson, and Q. Zhan, Opt. Lett. 34, 3047 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (2)

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102(2007).
[CrossRef]

2006 (6)

R. W. Boyd and D. J. Gauthier, Nature 441, 701 (2006).
[CrossRef] [PubMed]

A. Boltasseva, S. Bozhevolnyi, T. Nikolajsen, and K. Leosson, J. Lightwave Technol. 24, 912 (2006).
[CrossRef]

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[CrossRef]

G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
[CrossRef]

2004 (2)

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

2003 (1)

W. Barnes, A. Dereux, and T. Ebbesen, Nature 424, 824(2003).
[CrossRef] [PubMed]

2000 (1)

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

1984 (1)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Chap. 7.

Barnes, W.

W. Barnes, A. Dereux, and T. Ebbesen, Nature 424, 824(2003).
[CrossRef] [PubMed]

Berini, P.

I. D. Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

Boltasseva, A.

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, Nature 441, 701 (2006).
[CrossRef] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Bozhevolnyi, S.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[CrossRef]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[CrossRef]

Chang, H.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chen, W.

Chong, C.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Darmawan, S.

Dereux, A.

W. Barnes, A. Dereux, and T. Ebbesen, Nature 424, 824(2003).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Di, X.

Ebbesen, T.

W. Barnes, A. Dereux, and T. Ebbesen, Nature 424, 824(2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Fan, S.

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Farca, G.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, Nature 441, 701 (2006).
[CrossRef] [PubMed]

Giessen, H.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Gong, Y.

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Halas, N.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Han, W.

Han, Z.

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Chap. 7.

Hosseini, A.

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102(2007).
[CrossRef]

Hu, F.

Huang, X. G.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Kim, H.

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Kwong, D.

X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Lee, B.

Leon, I. D.

I. D. Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

Leosson, K.

A. Boltasseva, S. Bozhevolnyi, T. Nikolajsen, and K. Leosson, J. Lightwave Technol. 24, 912 (2006).
[CrossRef]

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

Lin, X. S.

Lipson, M.

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Liu, X.

Lu, H.

Luk’yanchuk, B.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Maier, S.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Mao, D.

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Massoud, Y.

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102(2007).
[CrossRef]

Mei, T.

Mu, D.

Naweed, A.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Nelson, R.

Nikolajsen, T.

A. Boltasseva, S. Bozhevolnyi, T. Nikolajsen, and K. Leosson, J. Lightwave Technol. 24, 912 (2006).
[CrossRef]

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Park, J.

Pollard, R.

G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Povinelli, M.

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Rosenberger, A. T.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[CrossRef]

Shakya, J.

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Shopova, S. I.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Tobing, L.

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Wang, L.

Wong, C.

X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Wurtz, G. A.

G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Xu, Q.

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Yang, J.

Yang, S.

Yang, X.

X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Yi, H.

Yu, M.

X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Zayats, A. V.

G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Zhan, Q.

Zhang, D.

Zhang, Y.

Zheludev, N.

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Zhou, J.

Zhou, Z.

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102(2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Mater. Today (1)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[CrossRef]

Nat. Mater. (1)

B. Luk’yanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Chong, Nat. Mater. 9, 707(2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

I. D. Leon and P. Berini, Nat. Photonics 4, 382 (2010).
[CrossRef]

Nature (3)

R. W. Boyd and D. J. Gauthier, Nature 441, 701 (2006).
[CrossRef] [PubMed]

W. Barnes, A. Dereux, and T. Ebbesen, Nature 424, 824(2003).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rev. A (2)

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, Phys. Rev. A 71, 043804 (2005).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

X. Yang, M. Yu, D. Kwong, and C. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, and A. V. Zayats, Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Other (2)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Chap. 7.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Supplementary Material (1)

» Media 1: MOV (224 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the nanoscale plasmonic resonator system.

Fig. 2
Fig. 2

(a) Evolution of transmission spectrum with the length L of resonant waveguide in the resonator system with d = 150 nm , g = 5 nm , and t = 30 nm . (b) Transmission spectra without (red dashed curve) and with (blue solid curve) resonant waveguide when L = 400 nm . (c) and (d) Field distributions of H z at the transmitted dip wavelength with L = 0 nm and induced transparency wavelength with L = 400 nm (Media 1).

Fig. 3
Fig. 3

(a) Transmission spectra at different coupling distances t with g = 5 nm , L = 400 nm , d = 150 nm , and w = w r = w c = 50 nm . (b) Evolution of transmission spectrum with Q 1 . The results are calculated by a theoretical model with assumed parameters Q i = 220 , Q 2 = 7 , θ = 0.6 , L = 400 nm , ω 0 = 2.973 × 10 15 rad / s , and σ = 0.98 .

Fig. 4
Fig. 4

(a) Transmission spectra at different lengths d in the plasmonic structures with L = 0 nm (red dashed line) and L = 400 nm (blue solid line). (b) Evolution of transmission spectrum with the refractive index n d of the resonant waveguide. The other parameters are set as d = 150 nm , g = 5 nm , t = 30 nm , and L = 250 nm .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

d a d t = ( j ω 0 ω 0 Q i ω 0 2 Q 1 ω 0 2 Q 2 ) a + S + 21 e j θ 0 ω 0 2 Q 2 + S + 11 e j θ 1 ω 0 2 Q 1 + S + 12 e j θ 2 ω 0 2 Q 1 .
S 22 = S + 21 e j θ 0 ω 0 2 Q 2 a ,
S 11 = S + 12 e j θ 1 ω 0 2 Q 1 a ,
S 12 = S + 11 e j θ 2 ω 0 2 Q 1 a .
T = | S 22 S + 21 | 2 = | j ( ω ω 0 1 ) + 1 Q i 1 2 Q 1 + 1 Q 1 1 1 δ e j φ j ( ω ω 0 1 ) + 1 Q i 1 2 Q 1 + 1 2 Q 2 + 1 Q 1 1 1 δ e j φ | 2 .
φ ( ω ) = ω Re ( n eff ) L c + θ ,

Metrics