Abstract

The analytic spectral transmittance of lattice-form and birefringent interleaver filters are revealed to be equivalent mathematically. The corresponding relationship between structural parameters of the two kinds of interleaver filters is also presented. With this mathematical equivalence relationship, we can easily obtain the optimum circuit parameters for designing a lattice-form interleaver filter by using the structural parameters of birefringent interleaver filter obtained by a simple numerical method developed by us recently instead of the complex algorithm based on scattering matrix factorization. More choice of structural parameters with any required spectral transmittance (channel spacing, flatness, isolation and ripple) can be obtained using this method when compared with results presented in references.

© 2003 Optical Society of America

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References

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  1. Bob Shine and Jerry Bautista, “Interleavers make high-channel-count system economical,” Lightwave 8, 140–144 (2000).
  2. Benjamin B. Dingel and Tasashi Aruga, “Properties of a novel noncascaded type, easy-to-design, ripple-free optical bandpass filter,” J. Lightwave Technol. 17, 1461–1469 (1999).
    [CrossRef]
  3. Ding-wei Huang, Tsung-hsuan Chiu, and Yinchieh Lai, “Arrayed waveguide grating DWDM interleaver,” Conference on Optical fiber Communication 2001, WDD80 (2001)
  4. W.H. Loh, F.Q. Zhou, and J.J. Pan, “Novel design for sampled grating-based multiplexers-demultiplexers,” Opt. Lett.1999,  24, 1457–1459.
    [CrossRef]
  5. W. J. Carlsen and C. F. Buhrer, “Flat passband birefringent wavelength-division multiplexers,” Electron. Lett. 23, 106–107 (1987).
    [CrossRef]
  6. M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
    [CrossRef]
  7. M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
    [CrossRef]
  8. T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).
  9. K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2002).
    [CrossRef]
  10. A. Yariv and P. Yeh, Optical waves in crystals (John Wiley & Sons, New York, 1984), pp. 121–148.
  11. E. O. Ammann., “Synthesis of optical birefringent networks,” in Progress in optics IX,E. Wolf ed. (North-Holland, Amsterdam, 1971), pp. 123–177.
  12. Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).
  13. B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
    [CrossRef]
  14. K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
    [CrossRef]
  15. Yuan P. Li and C. H. Henry, “Silica-based optical integrated circuits,” IEE Pro. -Optoelectronics, 143, 263–280 (1996).
    [CrossRef]
  16. A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems (2nd ed.), (Prentice-Hall, New Jersey, 1997), pp. 191–195.

2003 (1)

Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).

2002 (2)

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2002).
[CrossRef]

2000 (2)

Bob Shine and Jerry Bautista, “Interleavers make high-channel-count system economical,” Lightwave 8, 140–144 (2000).

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

1999 (2)

1996 (1)

Yuan P. Li and C. H. Henry, “Silica-based optical integrated circuits,” IEE Pro. -Optoelectronics, 143, 263–280 (1996).
[CrossRef]

1995 (1)

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[CrossRef]

1987 (1)

W. J. Carlsen and C. F. Buhrer, “Flat passband birefringent wavelength-division multiplexers,” Electron. Lett. 23, 106–107 (1987).
[CrossRef]

1984 (1)

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
[CrossRef]

Ammann, E. O.

E. O. Ammann., “Synthesis of optical birefringent networks,” in Progress in optics IX,E. Wolf ed. (North-Holland, Amsterdam, 1971), pp. 123–177.

Arai, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

Aruga, Tasashi

Bautista, Jerry

Bob Shine and Jerry Bautista, “Interleavers make high-channel-count system economical,” Lightwave 8, 140–144 (2000).

Buhrer, C. F.

W. J. Carlsen and C. F. Buhrer, “Flat passband birefringent wavelength-division multiplexers,” Electron. Lett. 23, 106–107 (1987).
[CrossRef]

Carlsen, W. J.

W. J. Carlsen and C. F. Buhrer, “Flat passband birefringent wavelength-division multiplexers,” Electron. Lett. 23, 106–107 (1987).
[CrossRef]

Chiba, T.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

Chiu, Tsung-hsuan

Ding-wei Huang, Tsung-hsuan Chiu, and Yinchieh Lai, “Arrayed waveguide grating DWDM interleaver,” Conference on Optical fiber Communication 2001, WDD80 (2001)

Dingel, Benjamin B.

Goodman, J. W.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
[CrossRef]

Henry, C. H.

Yuan P. Li and C. H. Henry, “Silica-based optical integrated circuits,” IEE Pro. -Optoelectronics, 143, 263–280 (1996).
[CrossRef]

Hibino, Y.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

Himeno, A.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

Huang, Ding-wei

Ding-wei Huang, Tsung-hsuan Chiu, and Yinchieh Lai, “Arrayed waveguide grating DWDM interleaver,” Conference on Optical fiber Communication 2001, WDD80 (2001)

Jinguji, K.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2002).
[CrossRef]

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[CrossRef]

Kawachi, M.

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[CrossRef]

Kitoh, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

Lai, Yinchieh

Ding-wei Huang, Tsung-hsuan Chiu, and Yinchieh Lai, “Arrayed waveguide grating DWDM interleaver,” Conference on Optical fiber Communication 2001, WDD80 (2001)

Li, Yuan P.

Yuan P. Li and C. H. Henry, “Silica-based optical integrated circuits,” IEE Pro. -Optoelectronics, 143, 263–280 (1996).
[CrossRef]

Liu, Liren

Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).

Loh, W.H.

Moslehi, B.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
[CrossRef]

Nawab, S. H.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems (2nd ed.), (Prentice-Hall, New Jersey, 1997), pp. 191–195.

Nonen, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

Oguma, M.

K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol. 18, 252–259 (2002).
[CrossRef]

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

Ohira, K.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

Okano, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems (2nd ed.), (Prentice-Hall, New Jersey, 1997), pp. 191–195.

Pan, J.J.

Shaw, H. J.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
[CrossRef]

Shibata, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

Shine, Bob

Bob Shine and Jerry Bautista, “Interleavers make high-channel-count system economical,” Lightwave 8, 140–144 (2000).

Tur, M.

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
[CrossRef]

Uetsuka, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems (2nd ed.), (Prentice-Hall, New Jersey, 1997), pp. 191–195.

Yariv, A.

A. Yariv and P. Yeh, Optical waves in crystals (John Wiley & Sons, New York, 1984), pp. 121–148.

Yeh, P.

A. Yariv and P. Yeh, Optical waves in crystals (John Wiley & Sons, New York, 1984), pp. 121–148.

Zhang, Juan

Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).

Zhou, Changhe

Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).

Zhou, F.Q.

Zhou, Yu

Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).

Electron. Lett. (2)

W. J. Carlsen and C. F. Buhrer, “Flat passband birefringent wavelength-division multiplexers,” Electron. Lett. 23, 106–107 (1987).
[CrossRef]

M. Oguma, K. Jinguji, T. Kitoh, T. Shibata, and A. Himeno, “Flat-passband interleaver filter with 200GHz channel spacing based on planar lightwave circuit-type lattice structure,” Electron. Lett. 36, 1299–1300 (2000).
[CrossRef]

IEE Pro. -Optoelectronics, (1)

Yuan P. Li and C. H. Henry, “Silica-based optical integrated circuits,” IEE Pro. -Optoelectronics, 143, 263–280 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Hibino, “Passband-width broadening design for WDM filter with lattice-form interleaver filter and arrayed-waveguide gratings,” IEEE Photon. Technol. Lett. 14, 328–330 (2002).
[CrossRef]

J. Lightwave Technol. (3)

J. Mod. Opt. (1)

Juan Zhang, Liren Liu, Yu Zhou, and Changhe Zhou, “Flattening spectral transmittance of birefringent interleaver filter,” J. Mod. Opt. 50, 2031–2041 (2003).

Lightwave (1)

Bob Shine and Jerry Bautista, “Interleavers make high-channel-count system economical,” Lightwave 8, 140–144 (2000).

Opt. Lett. (1)

Proc. IEEE, (1)

B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, “Fiber-optic lattice signal processing,” Proc. IEEE, 72, 909–930 (1984).
[CrossRef]

Other (5)

Ding-wei Huang, Tsung-hsuan Chiu, and Yinchieh Lai, “Arrayed waveguide grating DWDM interleaver,” Conference on Optical fiber Communication 2001, WDD80 (2001)

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleving filter with Fourier transform-based MZIs,” Conference on Optical fiber Communication 2001, WB5 (2001).

A. Yariv and P. Yeh, Optical waves in crystals (John Wiley & Sons, New York, 1984), pp. 121–148.

E. O. Ammann., “Synthesis of optical birefringent networks,” in Progress in optics IX,E. Wolf ed. (North-Holland, Amsterdam, 1971), pp. 123–177.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems (2nd ed.), (Prentice-Hall, New Jersey, 1997), pp. 191–195.

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Figures (3)

Fig. 1.
Fig. 1.

Schematic configurations of (a) lattice-form interleaver filter (b) birefringent interleaver filter.

Fig. 2.
Fig. 2.

The spectral transmittance of two-stage lattice-form interleaver filters with 200 GHz channel spacing. (A) C1 =50%, C2 =68%, C3 =12% and Δl1/Δl2 =1/2. Δf1 =400GHz. (B) C1 =50%, C2 =70%, C3 =10% and Δl1/Δl2 =Δl1/(2Δl1 +λ/2). Δf 1=400GHz. (C) C1 =50%, C2 =72%, C3 =92% and Δl1/Δl2 =1/2. Δf1 =400GHz.

Fig. 3.
Fig. 3.

The passband spectra of two-stage and three-stage lattice-form interleaver filters with 200 GHz channel spacing. (A) C1 =50%, C2 =68%, C3 =12% and Δl1/Δl2 =1/2. Δf1 =400GHz. (B) C1 =50%, C2 =70%, C3 =10% and Δl1/Δl2 =Δl1/(2Δl1 +λ/2). Δf1 =400GHz. (C) C1 =50%, C2 =72%, C3 =92% and Δl1/Δl2 =1/2. Δf1 =400GHz. (D) C1 =50%, C2 =50%, C3 =98%, C4 =2% and Δl1/Δl2/Δl3 =1/2/4. Δf1 =400GHz.. (E)C1 =50%, C2 =50%, C3 =2%, C4 =2% and Δl1/Δl2 =-1/2, Δl1/Δl3 =Δl1 /(4Δl1 -λ/2). Δf1 =400GHz.

Tables (3)

Tables Icon

Table 1. The azimuth angles of plates and analyzer when ripples is not greater than 0.3% (i.e. isolation <-25 dB) in both the passband and stopband with width of greater than 2/13 period for a birefringent interleaver filter and the coupling ratios of the directional couplers corresponding to the azimuth angles for a lattice-form interleaver filter.

Tables Icon

Table 2. The azimuth angles of plates and analyzer when ripples is not greater than 0.1% (i.e. isolation <-30dB) in both the passband and stopband with the width of greater than 1/5 period for a birefringent interleaver filter and the coupling ratios of the directional couplers corresponding to the azimuth angles for a lattice-form interleaver filter.

Tables Icon

Table 3. The azimuth angles of plates and analyzer when ripples is not greater than 1.5% (i.e. isolation < -18dB) in both the passband and stopband with the width of greater than 9/40 period for a birefringent interleaver filter and the coupling ratios of the directional couplers corresponding to the azimuth angles for a lattice-form interleaver filter.

Equations (11)

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

S i = ( cos φ i j sin φ i j sin φ i cos φ i ) .
x i = ( e j k 0 n Δ l i 0 0 1 ) = ( e j β Δ l i 0 0 1 ) ,
t i = 1 Δ f i = n ( l i , 1 l i , 2 ) c = n Δ l i c ,
T ( f ) = a 0 + a 1 cos ( 2 π · t ' 1 f ) + a 2 cos ( 2 π · t ' 2 · f ) + + a n cos ( 2 π · t ' n · f ) + ,
t 1 ' = t 1 , t 2 ' = t 2 , t 3 ' = t 1 + t 2 , t 4 ' = t 2 t 1 ,
{ a 0 = 1 2 ( 1 + cos 2 φ 1 cos 2 φ 2 cos 2 φ 3 ) a 1 = ( 1 2 ) sin 2 φ 1 sin 2 φ 2 cos 2 φ 3 a 2 = ( 1 2 ) cos 2 φ 1 sin 2 φ 2 sin 2 φ 3 a 3 = ( 1 2 ) cos 2 φ 2 sin 2 φ 1 sin 2 φ 3 a 4 = 1 2 sin 2 φ 2 sin 2 φ 1 sin 2 φ 3 .
T ' ( f ) = T 0 + T 1 cos ( 2 π γ ' 1 f ) + T 2 cos ( 2 π γ ' 2 f ) + + T n cos ( 2 π γ ' n f ) + ,
γ i = ( n i , o n i , e ) · L i c = Δ n i · L i c ,
γ 1 ' = γ 1 , γ 2 ' = γ 2 , γ 3 ' = γ 1 + γ 2 , γ 4 ' = γ 2 γ 1 ,
{ T 0 = 1 2 [ 1 + cos 2 θ 1 cos 2 ( θ 2 θ 1 ) cos 2 ( θ p θ 2 ) ] T 1 = ( 1 2 ) sin 2 θ 1 sin 2 ( θ 2 θ 1 ) cos 2 ( θ p θ 2 ) T 2 = ( 1 2 ) cos 2 θ 1 sin 2 ( θ 2 θ 1 ) sin 2 ( θ p θ 2 ) T 3 = ( 1 2 ) cos 2 ( θ 2 θ 1 ) sin 2 θ 1 sin 2 ( θ p θ 2 ) T 4 = 1 2 sin 2 ( θ 2 θ 1 ) sin 2 θ 1 sin 2 ( θ p θ 2 ) .
{ φ 1 = θ 1 φ 2 = θ 2 θ 1 φ i = θ i θ i 1 φ i + 1 = θ p θ i n Δ l i = Δ n i L i .

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