Abstract

An easy method for designing filters with equalized passband ripples of a given magnitude is proposed. The filter, which is made of two dielectric materials, comprises coupled half-wavelength resonators and multilayer mirrors. The filter design begins with the synthesis of the multimaterial filter prototype whose mirrors consist of quarter-wavelength layers. Optimal refractive indices of the layers in the prototype are obtained by a special optimization based on universal rules. The thicknesses of the mirrors’ layers in the final filter are computed using derived formulas. A design procedure example for silicon–air bandpass filters with a fractional bandwidth of 1% is described.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Macleod, Thin-Film Optical Filters (CRC Press, 2010).
  2. G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).
  3. B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Dokl. Phys. 59, 73 (2014).
    [CrossRef]
  4. S. Dasgupta, S. Mandal, and C. Bose, International Conference on Communications, Devices and Intelligent Systems (IEEE, 2012), pp. 184–187.
  5. S. Yu and J. Zhang, Asia Communications and Photonics Conference and Exhibition, Technical Digest (CD) (Optical Society of America, 2009), Vol. 7630, paper TuV5.
  6. A. Baldycheva, V. A. Tolmachev, T. S. Perova, Y. A. Zharova, E. V. Astrova, and K. Berwick, Opt. Lett. 36, 1854 (2011).
    [CrossRef]
  7. P. G. Verly, Proc. SPIE 5250, 378 (2004).
  8. P. Baumeister, Opt. Express 9, 652 (2001).
    [CrossRef]
  9. P. Baumeister, Appl. Opt. 42, 2407 (2003).
    [CrossRef]
  10. B. A. Belyaev and V. V. Tyurnev, 16th International Crimean Conference Microwave and Telecommunication Technology (CriMiCO, 2006) Vol. 2, pp. 517–519.
  11. A. Thelen, Design of Optical Interference Coatings (McGraw Hill, 1989), Section 3.1.
  12. K. C. Gupta, R. Garg, and R. Chadha, Computer-Aided Design of Microwave Circuits (Artech House, 1981).
  13. B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Russ. Phys. J. 56, 1378 (2014).
    [CrossRef]
  14. W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).
  15. N. Kaizer, Appl. Opt. 41, 3053 (2002).
    [CrossRef]
  16. B. T. Sullivan, G. A. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, Appl. Opt. 39, 157 (2000).
    [CrossRef]

2014 (2)

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Dokl. Phys. 59, 73 (2014).
[CrossRef]

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Russ. Phys. J. 56, 1378 (2014).
[CrossRef]

2012 (1)

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

2011 (1)

2004 (1)

P. G. Verly, Proc. SPIE 5250, 378 (2004).

2003 (1)

2002 (1)

2001 (1)

2000 (1)

Akiyama, T.

Astrova, E. V.

Baldycheva, A.

Baumeister, P.

Belyaev, B. A.

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Russ. Phys. J. 56, 1378 (2014).
[CrossRef]

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Dokl. Phys. 59, 73 (2014).
[CrossRef]

B. A. Belyaev and V. V. Tyurnev, 16th International Crimean Conference Microwave and Telecommunication Technology (CriMiCO, 2006) Vol. 2, pp. 517–519.

Berwick, K.

Bose, C.

S. Dasgupta, S. Mandal, and C. Bose, International Conference on Communications, Devices and Intelligent Systems (IEEE, 2012), pp. 184–187.

Chadha, R.

K. C. Gupta, R. Garg, and R. Chadha, Computer-Aided Design of Microwave Circuits (Artech House, 1981).

Chan, C. C. S.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Clarke, G. A.

Danner, A. J.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Dasgupta, S.

S. Dasgupta, S. Mandal, and C. Bose, International Conference on Communications, Devices and Intelligent Systems (IEEE, 2012), pp. 184–187.

Deng, J.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Dobrowolski, J. A.

Garg, R.

K. C. Gupta, R. Garg, and R. Chadha, Computer-Aided Design of Microwave Circuits (Artech House, 1981).

Gupta, K. C.

K. C. Gupta, R. Garg, and R. Chadha, Computer-Aided Design of Microwave Circuits (Artech House, 1981).

Howe, L.

Jia, W.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Jones, E. M.

G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).

Kaizer, N.

Kikuchi, K.

Li, X.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (CRC Press, 2010).

Mandal, S.

S. Dasgupta, S. Mandal, and C. Bose, International Conference on Communications, Devices and Intelligent Systems (IEEE, 2012), pp. 184–187.

Matsumoto, A.

Matthaei, G. L.

G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).

Osborne, N.

Perova, T. S.

Ranger, M.

Reid, B. P. L.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Shabanov, V. F.

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Russ. Phys. J. 56, 1378 (2014).
[CrossRef]

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Dokl. Phys. 59, 73 (2014).
[CrossRef]

Song, Y.

Sullivan, B. T.

Taylor, R. A.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw Hill, 1989), Section 3.1.

Tolmachev, V. A.

Tyurnev, V. V.

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Dokl. Phys. 59, 73 (2014).
[CrossRef]

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Russ. Phys. J. 56, 1378 (2014).
[CrossRef]

B. A. Belyaev and V. V. Tyurnev, 16th International Crimean Conference Microwave and Telecommunication Technology (CriMiCO, 2006) Vol. 2, pp. 517–519.

Verly, P. G.

P. G. Verly, Proc. SPIE 5250, 378 (2004).

Wang, X.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Wu, H.

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Young, L.

G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).

Yu, S.

S. Yu and J. Zhang, Asia Communications and Photonics Conference and Exhibition, Technical Digest (CD) (Optical Society of America, 2009), Vol. 7630, paper TuV5.

Zhang, J.

S. Yu and J. Zhang, Asia Communications and Photonics Conference and Exhibition, Technical Digest (CD) (Optical Society of America, 2009), Vol. 7630, paper TuV5.

Zharova, Y. A.

Appl. Opt. (3)

Dokl. Phys. (1)

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Dokl. Phys. 59, 73 (2014).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Photo. Nano. Fund. Appl. (1)

W. Jia, J. Deng, B. P. L. Reid, X. Wang, C. C. S. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, Photo. Nano. Fund. Appl. 10, 447 (2012).

Proc. SPIE (1)

P. G. Verly, Proc. SPIE 5250, 378 (2004).

Russ. Phys. J. (1)

B. A. Belyaev, V. V. Tyurnev, and V. F. Shabanov, Russ. Phys. J. 56, 1378 (2014).
[CrossRef]

Other (7)

S. Dasgupta, S. Mandal, and C. Bose, International Conference on Communications, Devices and Intelligent Systems (IEEE, 2012), pp. 184–187.

S. Yu and J. Zhang, Asia Communications and Photonics Conference and Exhibition, Technical Digest (CD) (Optical Society of America, 2009), Vol. 7630, paper TuV5.

H. A. Macleod, Thin-Film Optical Filters (CRC Press, 2010).

G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).

B. A. Belyaev and V. V. Tyurnev, 16th International Crimean Conference Microwave and Telecommunication Technology (CriMiCO, 2006) Vol. 2, pp. 517–519.

A. Thelen, Design of Optical Interference Coatings (McGraw Hill, 1989), Section 3.1.

K. C. Gupta, R. Garg, and R. Chadha, Computer-Aided Design of Microwave Circuits (Artech House, 1981).

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 (3)

Fig. 1.
Fig. 1.

Frequency response of the filter prototype (a) after and (b) before optimization. Here, S 21 and S 11 are reflection and transmission, respectively. Solid curves in (a) refer to the equalized ripple response (Chebyshev response) that is required and dotted curves refer to the flat-top response (Butterworth response) that is the alternative passband.

Fig. 2.
Fig. 2.

Schematic sketch of the designed silicon–air filter.

Fig. 3.
Fig. 3.

Computed frequency responses of the designed filter and its prototype.

Equations (4)

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

( n H 2 + n L 2 ) tan 2 θ H i tan θ L i = 2 n H n L ,
sin 2 θ H i cos θ L i + ( n L n H cos 2 θ H i n H n L sin 2 θ H i ) sin θ L i = n i n H .
tan 2 θ H i = ( n H 2 + n L 2 ) 2 ( n H 2 n i 2 ) 2 + 4 n H 2 ( n H 4 n L 2 n i 2 ) ( n i 2 n L 2 ) ( n H 2 + n L 2 ) ( n H 2 n i 2 ) 2 ( n H 4 n L 2 n i 2 ) ,
cot θ L i = n H 2 + n L 2 2 n H n L tan ( 2 θ H i ) .

Metrics