Abstract

This paper presents an infinite impulse response (IIR) structure for designing a three-port optical interleaver. With the proposed IIR structure, the spectral responses of the interleaver can be designed in two steps to achieve simultaneously three channels of identical but 2π/3 shifted passband transmissions. Compared with a three-port finite impulse response (FIR) interleaver, the proposed IIR interleaver is superior in several aspects: it uses only two 3×3 couplers, it provides a better form factor and has an improved side-lobe suppression. Simulation results are given to demonstrate the effectiveness of the proposed IIR interleaver design scheme.

© 2005 Optical Society of America

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References

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  3. A. V. Oppenheim and R. W. Schafter, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, 1975).
  4. A. Jazairy, Wavelength-tunable fiber optic MEMs scanning Fabry-Perot interferometer (Mich. Ann Arbor, UMI, 2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. S. K. Sheem, �??Optical fiber interferometers with [3�?3] directional couplers: analysis,�?? J. Appl. Phys. 52, 3865-3872 (1981).
    [CrossRef]
  14. Y. H. Chew, T. T. Tjhung, and F. V. C. Mendis, �??Performance of single- and double-ring resonators using 3�?3 optical fiber coupler,�?? IEEE J. Lightwave Technol. 11, 1998-2008 (1993).
    [CrossRef]
  15. C. K. Madsen and G. Lenz, �??Optical all-pass filters for phase response design with applications for dispersion compensation,�?? IEEE Photon. Technol. Lett. 10, 994-996 (1998).
    [CrossRef]
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  17. L. P. Ghislain, R. Sommer, R. J. Ryall, R. M. Fortenberry, D. Derickson, P. C. Egerton, M. R. Kozlowski, D. J. Poirier, S. DeMange, L. F. Stokes, and M. A. Scobey, �??Miniature Solid Etalon Interleaver,�?? in NFOEC�??2001, (Baltimore, MD, 2001), pp. 1397-1403.
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    [CrossRef]

IEEE J. Lightwave Technol.

K. Jinguji and M. Oguma, �??Optical half-band filters,�?? IEEE J. Lightwave Technol. 18, 252-259 (2000).
[CrossRef]

Y. H. Chew, T. T. Tjhung, and F. V. C. Mendis, �??Performance of single- and double-ring resonators using 3�?3 optical fiber coupler,�?? IEEE J. Lightwave Technol. 11, 1998-2008 (1993).
[CrossRef]

IEEE Photon. Technol. Lett.

C. K. Madsen and G. Lenz, �??Optical all-pass filters for phase response design with applications for dispersion compensation,�?? IEEE Photon. Technol. Lett. 10, 994-996 (1998).
[CrossRef]

Q. J.Wang, Y. Zhang and Y. C. Soh, �??Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings,�?? IEEE Photon. Technol. Lett. 17, 387-389 (2005).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, �??All-fiber 3�?3 interleaver design with flat-top passband,�?? IEEE Photon. Technol. Lett. 16, 168-170 (2004).
[CrossRef]

C. K. Madsen, �??Efficient architecture for exactly realizing optical filters with optium bandpass designs,�?? IEEE Photon. Technol. Lett. 10, 1136-1138 (1998).
[CrossRef]

C. H. Hsieh, R. Wang, Z. 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, 242-244 (2003).
[CrossRef]

J. Appl. Phys.

S. K. Sheem, �??Optical fiber interferometers with [3�?3] directional couplers: analysis,�?? J. Appl. Phys. 52, 3865-3872 (1981).
[CrossRef]

NFOEC

L. P. Ghislain, R. Sommer, R. J. Ryall, R. M. Fortenberry, D. Derickson, P. C. Egerton, M. R. Kozlowski, D. J. Poirier, S. DeMange, L. F. Stokes, and M. A. Scobey, �??Miniature Solid Etalon Interleaver,�?? in NFOEC�??2001, (Baltimore, MD, 2001), pp. 1397-1403.

OFC

S. Cao, C. Lin, C. Yang, E. Ning, J. Zhao, and G.Barbarossa, �??Birefringent Gires-Tournois interferometer (BGTI) for DWDM interleaving,�?? in OFC, (Anaheim, CA, 2002), pp. 395-396.

Opt. Commun.

Q. J. Wang, Y. Zhang and Y. C. Soh, �??Design of spectrum equalization filter for SLED light source,�?? Opt. Commun. 229, 223-231 (2003).
[CrossRef]

Opt. Lett.

SPIE Photonics West

J. C. Chon, B. Jian, and J. R. Bautista, �??High capacity and high speed DWDM and NWDM optical devices for telecom and datacom applications,�?? in SPIE Photonics West 2001, (San Jose CA, 2001), 4289-06.

Other

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: a signal processing approach (John Wiley & Sons, New York, 1999).

G. Keiser, Optical fibre communications (3rd Edition, McGraw-Hill, 2000).

A. V. Oppenheim and R. W. Schafter, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, 1975).

A. Jazairy, Wavelength-tunable fiber optic MEMs scanning Fabry-Perot interferometer (Mich. Ann Arbor, UMI, 2000).

S. K. Mitra and J. F. Kaiser, Handbook for Digital Signal Processing (Wiley, New York, 1993).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Proposed configuration of IIR three-port interleaver; (b) Schematic configuration of the proposed interleaver.

Fig. 2.
Fig. 2.

(a) Power spectra of three outputs of the designed three-port IIR interleaver; (b) Power spectrum and group delay of the proposed IIR interleaver in one typical channel.

Fig. 3.
Fig. 3.

Comparison between one channel power spectrum of the proposed IIR three-port interleaver and that of the FIR interleaver proposed in [12].

Fig. 4.
Fig. 4.

Interleaver responses with the design parameters bearing ±5% fabrication deviations.

Tables (2)

Tables Icon

Table 1. Order of z -k , Numerator Amplitude Expansion Coefficients, Denominator Amplitude Expansion Coefficients, and Circuit Parameters for 12th Order IIR Three-Port Interleaver.

Tables Icon

Table 2. Expressions of the Coefficients of aij(1) , aij(2) , aij(3) , bj(1) , bj(2) , bj(3) , cj(1) , cj(2) , cj(3) , d (1), d (2), and d (3).

Equations (20)

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( E 1 o E 2 o E 3 o ) = ( γ δ δ δ γ δ δ δ γ ) ( E 1 I E 2 I E 3 I ) = M ( κ ) ( E 1 I E 2 I E 3 I )
S i ( z 3 ) = e j ϕ 1 , i t i e j ϕ 1 , i z 3 1 t i e j ϕ 1 , i z 3
D ( z ) = ( z S 1 ( z 3 ) 0 0 0 S 2 ( z 3 ) 0 0 0 z 1 S 3 ( z 3 ) )
( E 1 o E 2 o E 3 o ) = M ( κ 2 ) D ( z ) M ( κ 1 ) ( E 1 I E 2 I E 3 I ) .
H 1 ( z ) = γ 1 γ 2 z S 1 ( z 3 ) + δ 1 δ 2 S 2 ( z 3 ) + δ 1 δ 2 z 1 S 3 ( z 3 )
H 2 ( z ) = γ 1 δ 2 z S 1 ( z 3 ) + δ 1 γ 2 S 2 ( z 3 ) + δ 1 δ 2 z 1 S 3 ( z 3 )
H 3 ( z ) = γ 1 δ 2 z S 1 ( z 3 ) + δ 1 δ 2 S 2 ( z 3 ) + δ 1 γ 2 z 1 S 3 ( z 3 )
H 1 ( z ) 2 = H 2 ( z e j 2 π 3 ) 2 = H 3 ( z e j 4 π 3 ) 2
H 1 ( z ) κ 1 = 2 π 9 , κ 2 = 4 π 9 = e j 2 π 3 H 2 ( z e j 2 π 3 ) κ 1 = 2 π 9 , κ 2 = 4 π 9 = H 3 ( z e j 4 π 3 ) κ 1 = 2 π 9 , κ 2 = 4 π 9
S i ( z 3 ) = S i ( ( z e j 2 π 3 ) 3 ) = S i ( ( z e j 4 π 3 ) 3 ) for i = 1 , 2 , 3
H 1 ( z ) 2 = i = 1 2 j = 1 2 a ij ( 1 ) z 2 j 2 i S i ( z 3 ) S j * ( z 3 ) + j = 1 2 b j ( 1 ) z 3 2 j S j ( z 3 ) + j = 1 2 c j ( 1 ) z 2 j 3 S j * ( z 3 ) + d ( 1 )
H 2 ( z e j 2 π 3 ) 2 = i = 1 2 j = 1 2 a ij ( 2 ) z 2 j 2 i S i ( z 3 ) S j * ( z 3 ) + j = 1 2 b j ( 2 ) z 3 2 j S j ( z 3 ) + j = 1 2 c j ( 2 ) z 2 j 3 S j * ( z 3 ) + d ( 2 )
H 3 ( z e j 4 π 3 ) 2 = i = 1 2 j = 1 2 a ij ( 3 ) z 2 j 2 i S i ( z 3 ) S j * ( z 3 ) + j = 1 2 b j ( 3 ) z 3 2 j S j ( z 3 ) + j = 1 2 c j ( 3 ) z 2 j 3 S j * ( z 3 ) + d ( 3 )
H 1 ( z ) κ 1 = 2 π 9 , κ 2 = 4 π 9 = e j 2 π 3 H 2 ( ze j 2 π 3 ) κ 1 = 2 π 9 , κ 2 = 4 π 9 = H 3 ( ze j 4 π 3 ) κ 1 = 2 π 9 , κ 2 = 4 π 9
max ( H 1 ( e jw ) w = π 2 H 1 ( e jw ) w = π 2 )
{ H 1 ( e jw ) w = π 2 ϕ 1 , 1 = H 1 ( e jw ) w = π 2 ϕ 1 , 2 = H 1 ( e jw ) w = π 2 ϕ 1 , 3 = 0 H 1 ( e jw ) w = π 2 t 1 = H 1 ( e jw ) w = π 2 t 2 = H 1 ( e jw ) w = π 2 t 3 = 0
A 1 = A 1 * A 2 = A 2 * A 3 = A 3 *
B 1 = B 1 * B 2 = B 2 * B 3 = B 3 *
arg ( e j ϕ 1 , i ( 1 + t i e j ϕ 1 , i ) 2 ) = ϕ 1 , i 2 arctan t i sin ϕ 1 , i 1 + t i sin ϕ 1 , i = β + 2 k π
arg ( 1 e 2 j ϕ 1 , i ( 1 + t i e j ϕ 1 , i ) 2 ) = ϕ 1 , i + π 2 2 arctan t i sin ϕ 1 , i 1 + t i sin ϕ 1 , i = β + 2 k π + π 2

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