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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    [CrossRef]
  3. Ding-wei Huang, Tsung-hsuan Chiu and Yinchieh Lai, �??Arrayed waveguide grating DWDM interleaver,�?? Conference on Optical fiber Communication 2001, WDD80 (2001).
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    [CrossRef]
  5. W. J. Carlsen, 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).
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    [CrossRef]
  10. A. Yariv, 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.

Electron. Lett.

W. J. Carlsen, 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

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

IEEE Photon. Technol. Lett.

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.

J. Mod. Opt.

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

Lightwave

Bob Shine, Jerry Bautista, �??Interleavers make high-channel-count system economical,�?? Lightwave 8, 140-144 (2000).

OFC 2001

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).

Opt. Lett.

Proc. IEEE

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

Progress in optics IX

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

Other

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

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

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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)

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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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