Abstract

An elegant method to design a Michelson interferometer based interleaver using a classic infinite impulse response (IIR) filter such as Butterworth, Chebyshev, and elliptic filters as a starting point are presented. The proposed design method allows engineers to design a Michelson interferometer based interleaver from specifications seamlessly. Simulation results are presented to demonstrate the validity of the proposed design method.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Cao, J. Chen, J. N. Damask, C. R. Doerr, L. Guiziou, G. Harvey, Y. Hibino, H. Li, S. Suzuki, K.-Y. Wu, and P. Xie, “Interleaver Technology: Comparisons and Applications Requirement,” J. Lightwave Technol.22(1), 281–289 (2004).
    [CrossRef]
  2. K.-Y. Wu and J.-Y. Liu, “Switchable Wavelength Router” US Patent No. 5,694,233.
  3. B. B. Dingel and T. Aruga, “Properties of a Novel Noncascaded Type, Easy-to-Design, Ripple-Free Optical Bandpass Filter,” J. Lightwave Technol.17(8), 1461–1469 (1999).
    [CrossRef]
  4. C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
    [CrossRef]
  5. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (John Wiley & Sons, 1999.)
  6. C. K. Madsen, “General IIR Optical Filter Design for WDM Applications Using All-Pass Filters,” J. Lightwave Technol.18(6), 860–868 (2000).
    [CrossRef]
  7. J. Zhang and X. Yang, “Universal Michelson Gires-Tournois Interferometer Optical Interleaver Based On Digital Signal Processing,” Opt. Express18(5), 5075–5088 (2010).
    [CrossRef] [PubMed]
  8. S. K. Mitra, Digital Signal Processing: a Computer-Based Approach, 4th ed. (McGraw-Hill, 2011.)
  9. MathWorks Document Center, “tf2ca,” http://www.mathworks.com/help/dsp/ref/tf2ca.html
  10. H. van de Stadt and J. M. Muller, “Multimirror Fabry-Perot Interferometers,” J. Opt. Soc. Am. A2(8), 1363–1370 (1985).
    [CrossRef]
  11. C.-H. Cheng, “Asymmetrical Interleaver Structure Based on the Modified Michelson Interferometer,” Opt. Eng.44(11), 115003 (2005).
    [CrossRef]
  12. H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
    [CrossRef]
  13. J. X. Li and K. X. Chen, “An Interleaver with Arbitrary Passband Width Ratio Based on Hybrid Structure of Microring and Mach-Zehnder Interferometer,” J. Lightwave Technol.31(10), 1538–1543 (2013).
    [CrossRef]
  14. P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

2013 (2)

P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

J. X. Li and K. X. Chen, “An Interleaver with Arbitrary Passband Width Ratio Based on Hybrid Structure of Microring and Mach-Zehnder Interferometer,” J. Lightwave Technol.31(10), 1538–1543 (2013).
[CrossRef]

2012 (1)

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

2010 (1)

2005 (1)

C.-H. Cheng, “Asymmetrical Interleaver Structure Based on the Modified Michelson Interferometer,” Opt. Eng.44(11), 115003 (2005).
[CrossRef]

2004 (1)

2003 (1)

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

2000 (1)

1999 (1)

1985 (1)

Aruga, T.

Cao, S.

Chen, J.

Chen, K. X.

Cheng, C.-H.

C.-H. Cheng, “Asymmetrical Interleaver Structure Based on the Modified Michelson Interferometer,” Opt. Eng.44(11), 115003 (2005).
[CrossRef]

Cheng, W.-H.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Damask, J. N.

Dingel, B. B.

Doerr, C. R.

Guiziou, L.

Harvey, G.

Hibino, Y.

Hsieh, C.-H.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Lee, C.-W.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Li, H.

Li, J. X.

Lu, H.-W.

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

Luo, G.-W.

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

Madsen, C. K.

McMichael, I.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Muller, J. M.

Pena, J. M. S.

P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

Perez, I.

P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

Pinzon, P. J.

P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

Suzuki, S.

van de Stadt, H.

Vazquez, C.

P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

Wang, R.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Wei, Y.

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

Wen, Z. J.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Wu, K.-J.

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

Wu, K.-Y.

Xie, P.

Yang, X.

Yeh, P.

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

Zhang, B.-G.

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

Zhang, J.

IEEE Photon. J. (1)

P. J. Pinzon, C. Vazquez, I. Perez, and J. M. S. Pena, “Synthesis of Asymmetric Flat-Top Birefringent Interleaver Based on Digital Filter Design and Genetic Algorithm,” IEEE Photon. J.5(3), 7100113 (2013).

IEEE Photon. Technol. Lett. (1)

C.-H. Hsieh, R. Wang, Z. J. Wen, I. McMichael, P. Yeh, C.-W. Lee, and W.-H. Cheng, “Flat-Top Interleavers Using Two Gires-Tournois Etalons as Phase-Dispersive Mirrors in a Michelson Interferometer,” IEEE Photon. Technol. Lett.15(2), 242–244 (2003).
[CrossRef]

J. Lightwave Technol. (4)

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

Opt. Commun. (1)

H.-W. Lu, K.-J. Wu, Y. Wei, B.-G. Zhang, and G.-W. Luo, “Study of all-fiber asymmetric interleaver based on two-stage cascaded Mach–Zehnder Interferometer,” Opt. Commun.285(6), 1118–1122 (2012).
[CrossRef]

Opt. Eng. (1)

C.-H. Cheng, “Asymmetrical Interleaver Structure Based on the Modified Michelson Interferometer,” Opt. Eng.44(11), 115003 (2005).
[CrossRef]

Opt. Express (1)

Other (4)

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (John Wiley & Sons, 1999.)

K.-Y. Wu and J.-Y. Liu, “Switchable Wavelength Router” US Patent No. 5,694,233.

S. K. Mitra, Digital Signal Processing: a Computer-Based Approach, 4th ed. (McGraw-Hill, 2011.)

MathWorks Document Center, “tf2ca,” http://www.mathworks.com/help/dsp/ref/tf2ca.html

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

(a) The Michelson interferometer based interleaver (L is the distance between the coupler and Fabry-Perot interferometers) (b) doubly-complementary transfer function pair consists of parallel APFs.

Fig. 2
Fig. 2

A (N + 1)-mirror Fabry-Perot interferometer.

Fig. 3
Fig. 3

Output spectra of symmetric interleaver based on (a) elliptic filter (b) Chebyshev filter (c) Butterworth filter.

Fig. 4
Fig. 4

Output spectra of asymmetric interleaver based on (a) elliptic filter (b) Chebyshev filter (c) Butterworth filter.

Tables (2)

Tables Icon

Table 1 Fabry-Perot Interferometer Reflectivity of 3 Symmetric Interleaver Designs

Tables Icon

Table 2 Fabry-Perot Interferometer Reflectivity of 3 Asymmetric Interleaver Designs

Equations (9)

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

[ E i + E i ]= z 0.5 t i [ z 1 r i r i z 1 1 ][ E i+1 + E i+1 ]
t i = (1 r i 2 ) .
[ E 1 + E 1 ]= z 0.5N t 1 t 2 t N [ z 1 r 1 r 1 z 1 1 ][ z 1 r N r N z 1 1 ][ E N+1 + E N+1 ] = z 0.5N t 1 t 2 t N [ A N B N C N D N ][ E N+1 + E N+1 ]
H N (z)= E 1 E 1 + = Num N (z) Den N (z) = C N D N r N+1 A N B N r N+1 = C N D N A N B N =( r 1 z N ++1 z N ++ r 1 )
[ A N B N C N D N ]=[ z 1 r 1 r 1 z 1 1 ][ A N1 B N1 C N1 D N1 ]=[ z 1 A N1 r 1 C N1 z 1 B N1 r 1 D N1 r 1 z 1 A N1 +C N1 r 1 z 1 B N1 +D N1 ]
H N (z)= Num N (z) Den N (z) = C N D N A N B N = r 1 Z 1 ( A N1 B N1 )+( C N1 D N1 ) Z 1 ( A N1 B N1 ) r 1 ( C N1 D N1 )
H N1 (z)= Num N1 (z) Den N1 (z) = C N1 D N1 A N1 B N1
Den N1 (z)= Num N (z) r 1 + Den N (z) ( r 1 2 +1) z 1
H'(z)= Num N ' (z) Den N ' (z) = 1+ d 1 z 1 ++ d N1 z (N1) +d N Z N d N + d N1 z 1 ++ d 1 z (N1) + Z N

Metrics