Abstract

Optical interleavers based on Michelson Gires-Tournois interferometer (MGTI) with arbitrary cascaded reflectors for symmetrical or asymmetrical periodic frequency response with arbitrary duty cycles are defined as universal MGTI optical interleaver (UMGTIOI). It can significantly enhance flexibility and applicability of optical networks. A novel and simple method based on digital signal processing is proposed for the design of UMGTIOI. Different kinds of design examples are given to confirm effectiveness of the method.

© 2010 OSA

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2008

J. Song, Q. Fang, S. H. Tao, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Passive ring-assisted Mach-Zehnder interleaver on silicon-on-insulator,” Opt. Express 16(12), 8359–8365 (2008).
[CrossRef] [PubMed]

K. Jinguji and T. Yasui, “Synthesis of One-Input M-Output Optical FIR Lattice Circuits,” J. Lightwave Technol. 26(7), 853–866 (2008).
[CrossRef]

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

S. Wu, L. Chen, J. Fan, and S. Cao, “Asymmetric optical interleavers filter,” Acta Opt. Sin. 28(1), 31–35 (2008).
[CrossRef]

2007

2006

C.-h. Cheng and D. J. Goode, “Michelson Interferometer Based Interleaver Design Algorithm Based on IIR Filter Model,” Proc. SPIE 6389, 638914 (2006).
[CrossRef]

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

T. Mizuno, M. Oguma, T. Kitoh, Y. Inoue, and H. Takahashi, “Lattice-form CWDM interleave filter using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 18(15), 1570–1572 (2006).
[CrossRef]

C.-W. Lee, R. Wang, P. Yeh, and W. H. Cheng, “Sagnac interferometer based flat-top birefringent interleaver,” Opt. Express 14(11), 4636–4643 (2006).
[CrossRef] [PubMed]

J. Zhang and L. Liu, “A novel Mach-Zehnder interferometer structure for tunable optical interleaver,” Opt. Eng. 45(4), 045003 (2006).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, “Design of linear-phase two-port optical interleavers using lattice architectures,” Opt. Lett. 31(16), 2411–2413 (2006).
[CrossRef] [PubMed]

2005

C.-W. Lee, R. Wang, P. Yeh, C. H. Hsieh, and W. H. Cheng, “Birefringent interleaver with a ring cavity as a phase-dispersion element,” Opt. Lett. 30(10), 1102–1104 (2005).
[CrossRef] [PubMed]

Q. J. Wang, Y. Zhang, and Y. C. Soh, “Flat-passband 3×3 interleaving filter designed with optical directional couplers in lattice structure,” J. Lightwave Technol. 23(12), 4349–4362 (2005).
[CrossRef]

A. H. Gnauck, P. J. Winzer, and S. Chandrasekhar, “Hybrid 10/40G transmission on a 50-GHz grid through 2800 km of SSMF and seven optical add-drops,” IEEE Photon. Technol. Lett. 17(10), 2203–2205 (2005).
[CrossRef]

C. Cheng, “Asymmetrical interleaver structure based on the modified Michelson interferometer,” Opt. Eng. 44(11), 115003 (2005).
[CrossRef]

2003

J. Zhang, L. Liu, and Y. Zhou, “A tunable interleaver filter based on analog birefringent units,” Opt. Commun. 227(4-6), 283–294 (2003).
[CrossRef]

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

J. Zhang, L. Liu, and Y. Zhou, “Novel and simple approach for designing lattice-form interleaver filter,” Opt. Express 11(18), 2217–2224 (2003).
[CrossRef] [PubMed]

2001

A. Zeng and J. Chon, “Ultra-high capacity and high speed DWDM optical devices for telecom and datacom applications,” Proc. SPIE 4581, 13–20 (2001).
[CrossRef]

B. Dingel and A. Dutta, ““Photonic add-drop multiplexing perspective for next generation optical networks” (invited paper),” Proc. SPIE 4532, 394–408 (2001).
[CrossRef]

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(15), 1299–1300 (2000).
[CrossRef]

1999

1985

Cao, S.

S. Wu, L. Chen, J. Fan, and S. Cao, “Asymmetric optical interleavers filter,” Acta Opt. Sin. 28(1), 31–35 (2008).
[CrossRef]

Chandrasekhar, S.

A. H. Gnauck, P. J. Winzer, and S. Chandrasekhar, “Hybrid 10/40G transmission on a 50-GHz grid through 2800 km of SSMF and seven optical add-drops,” IEEE Photon. Technol. Lett. 17(10), 2203–2205 (2005).
[CrossRef]

Chen, J.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Chen, L.

S. Wu, L. Chen, J. Fan, and S. Cao, “Asymmetric optical interleavers filter,” Acta Opt. Sin. 28(1), 31–35 (2008).
[CrossRef]

Cheng, C.

C. Cheng, “Asymmetrical interleaver structure based on the modified Michelson interferometer,” Opt. Eng. 44(11), 115003 (2005).
[CrossRef]

Cheng, C.-h.

C.-h. Cheng and D. J. Goode, “Michelson Interferometer Based Interleaver Design Algorithm Based on IIR Filter Model,” Proc. SPIE 6389, 638914 (2006).
[CrossRef]

Cheng, W. H.

Cheng, Wood-Hi

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Chi, S.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Chon, J.

A. Zeng and J. Chon, “Ultra-high capacity and high speed DWDM optical devices for telecom and datacom applications,” Proc. SPIE 4581, 13–20 (2001).
[CrossRef]

Dingel, B.

B. Dingel and A. Dutta, ““Photonic add-drop multiplexing perspective for next generation optical networks” (invited paper),” Proc. SPIE 4532, 394–408 (2001).
[CrossRef]

Dutta, A.

B. Dingel and A. Dutta, ““Photonic add-drop multiplexing perspective for next generation optical networks” (invited paper),” Proc. SPIE 4532, 394–408 (2001).
[CrossRef]

Fan, J.

S. Wu, L. Chen, J. Fan, and S. Cao, “Asymmetric optical interleavers filter,” Acta Opt. Sin. 28(1), 31–35 (2008).
[CrossRef]

Fang, Q.

Feng, K.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Gnauck, A. H.

A. H. Gnauck, P. J. Winzer, and S. Chandrasekhar, “Hybrid 10/40G transmission on a 50-GHz grid through 2800 km of SSMF and seven optical add-drops,” IEEE Photon. Technol. Lett. 17(10), 2203–2205 (2005).
[CrossRef]

Goode, D. J.

C.-h. Cheng and D. J. Goode, “Michelson Interferometer Based Interleaver Design Algorithm Based on IIR Filter Model,” Proc. SPIE 6389, 638914 (2006).
[CrossRef]

Gu, C.

Guo, Y.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Himeno, A.

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(15), 1299–1300 (2000).
[CrossRef]

Hong, J.

Hsieh, C. H.

Hsieh, Chao-Hsing

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Huang, M.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Inoue, Y.

T. Mizuno, M. Oguma, T. Kitoh, Y. Inoue, and H. Takahashi, “Lattice-form CWDM interleave filter using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 18(15), 1570–1572 (2006).
[CrossRef]

Jinguji, K.

K. Jinguji and T. Yasui, “Synthesis of One-Input M-Output Optical FIR Lattice Circuits,” J. Lightwave Technol. 26(7), 853–866 (2008).
[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(15), 1299–1300 (2000).
[CrossRef]

Kitoh, T.

T. Mizuno, M. Oguma, T. Kitoh, Y. Inoue, and H. Takahashi, “Lattice-form CWDM interleave filter using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 18(15), 1570–1572 (2006).
[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(15), 1299–1300 (2000).
[CrossRef]

Kwong, D. L.

Lai, C.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Lee, C.-W.

Lee, Chao-Wei

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Lin, T.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Lit, J. W. Y.

Liu, L.

J. Zhang and L. Liu, “A novel Mach-Zehnder interferometer structure for tunable optical interleaver,” Opt. Eng. 45(4), 045003 (2006).
[CrossRef]

J. Zhang, L. Liu, and Y. Zhou, “Novel and simple approach for designing lattice-form interleaver filter,” Opt. Express 11(18), 2217–2224 (2003).
[CrossRef] [PubMed]

J. Zhang, L. Liu, and Y. Zhou, “A tunable interleaver filter based on analog birefringent units,” Opt. Commun. 227(4-6), 283–294 (2003).
[CrossRef]

Lo, G. Q.

Luo, B.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

McMichael, I.

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Miura, R.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Mizuno, T.

T. Mizuno, M. Oguma, T. Kitoh, Y. Inoue, and H. Takahashi, “Lattice-form CWDM interleave filter using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 18(15), 1570–1572 (2006).
[CrossRef]

Muller, J. M.

Oguma, M.

T. Mizuno, M. Oguma, T. Kitoh, Y. Inoue, and H. Takahashi, “Lattice-form CWDM interleave filter using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 18(15), 1570–1572 (2006).
[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(15), 1299–1300 (2000).
[CrossRef]

Ong, C.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Shibata, T.

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(15), 1299–1300 (2000).
[CrossRef]

Soh, Y.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Soh, Y. C.

Song, J.

Takahashi, H.

T. Mizuno, M. Oguma, T. Kitoh, Y. Inoue, and H. Takahashi, “Lattice-form CWDM interleave filter using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 18(15), 1570–1572 (2006).
[CrossRef]

Tao, S. H.

van de Stadt, H.

Wang, Q.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Wang, Q. J.

Wang, R.

Wang, Ruibo

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Wei, C.

M. Huang, J. Chen, K. Feng, C. Wei, C. Lai, T. Lin, and S. Chi, “210-km bidirectional transmission system with a novel four-port interleaver to facilitate unidirectional amplification,” IEEE Photon. Technol. Lett. 18(1), 172–174 (2006).
[CrossRef]

Wei, L.

Wen, Zhiqing James

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Winzer, P. J.

A. H. Gnauck, P. J. Winzer, and S. Chandrasekhar, “Hybrid 10/40G transmission on a 50-GHz grid through 2800 km of SSMF and seven optical add-drops,” IEEE Photon. Technol. Lett. 17(10), 2203–2205 (2005).
[CrossRef]

Wu, S.

S. Wu, L. Chen, J. Fan, and S. Cao, “Asymmetric optical interleavers filter,” Acta Opt. Sin. 28(1), 31–35 (2008).
[CrossRef]

Yang, M.

Yasui, T.

Yeh, P.

Yeh, Pochi

Chao-Hsing Hsieh, Ruibo Wang, I. McMichael, Pochi Yeh, Chao-Wei Lee, Wood-Hi Cheng, and Zhiqing James Wen, “Flat-top interleavers using two Gires-Tournois etalons as phase-dispersion mirrors in a Michelson interferometer,” IEEE Photon. Technol. Lett. 15(2), 242–244 (2003).
[CrossRef]

Yu, M. B.

Zeng, A.

A. Zeng and J. Chon, “Ultra-high capacity and high speed DWDM optical devices for telecom and datacom applications,” Proc. SPIE 4581, 13–20 (2001).
[CrossRef]

Zhang, J.

J. Zhang and L. Liu, “A novel Mach-Zehnder interferometer structure for tunable optical interleaver,” Opt. Eng. 45(4), 045003 (2006).
[CrossRef]

J. Zhang, L. Liu, and Y. Zhou, “Novel and simple approach for designing lattice-form interleaver filter,” Opt. Express 11(18), 2217–2224 (2003).
[CrossRef] [PubMed]

J. Zhang, L. Liu, and Y. Zhou, “A tunable interleaver filter based on analog birefringent units,” Opt. Commun. 227(4-6), 283–294 (2003).
[CrossRef]

Zhang, Y.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, “Design of linear-phase two-port optical interleavers using lattice architectures,” Opt. Lett. 31(16), 2411–2413 (2006).
[CrossRef] [PubMed]

Q. J. Wang, Y. Zhang, and Y. C. Soh, “Flat-passband 3×3 interleaving filter designed with optical directional couplers in lattice structure,” J. Lightwave Technol. 23(12), 4349–4362 (2005).
[CrossRef]

Zhou, M.

M. Zhou, Q. Wang, B. Luo, Y. Guo, C. Ong, Y. Zhang, Y. Zhang, Y. Soh, and R. Miura, “Performance improvement and wavelength reuse in millimeter-wave radio-over-fiber links incorporating all-fiber optical interleaver,” Opt. Commun. 281(9), 2572–2581 (2008).
[CrossRef]

Zhou, Y.

J. Zhang, L. Liu, and Y. Zhou, “A tunable interleaver filter based on analog birefringent units,” Opt. Commun. 227(4-6), 283–294 (2003).
[CrossRef]

J. Zhang, L. Liu, and Y. Zhou, “Novel and simple approach for designing lattice-form interleaver filter,” Opt. Express 11(18), 2217–2224 (2003).
[CrossRef] [PubMed]

Acta Opt. Sin.

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of an MGTI interleaver.

Fig. 2
Fig. 2

Amplitudes at reflectors i and i-1 out of a stack of multi-reflectors.

Fig. 3
Fig. 3

Digital filter model.

Fig. 4
Fig. 4

Schematic diagram of zero and pole locations.

Fig. 5
Fig. 5

Pole/zero plot.

Fig. 6
Fig. 6

Output spectrum.

Fig. 7
Fig. 7

Zoomed spectra in the pass-band of Fig. 6.

Fig. 8
Fig. 8

Output intensity spectra of the five schemes in different orders. (a) Output intensity spectra of five schemes.(b) Zoomed intensity spectra of pass-band. (c) Zoomed intensity spectra of stop-band.

Fig. 9
Fig. 9

pole/zero plot.

Fig. 10
Fig. 10

Output intensity spectrum of asymmetrical interleavers.

Fig. 11
Fig. 11

Output intensity spectra for two output ports obtained with different schemes. (a) wide port, (b)narrow port.

Fig. 12
Fig. 12

Output intensity spectra of four different duty cycles obtained with same structure. (a)duty cycle 1:3, (b)duty cycle 1:4, (c)duty cycle 1:5, (d)duty cycle 1:6.

Fig. 13
Fig. 13

Output intensity spectra with duty cycle 1:4 obtained with three different structures. (a) wide port, (b) narrow port.

Fig. 14
Fig. 14

Passband width at 1 dB (a) and steepness (b) plotted against N for third-order interleavers.

Fig. 15
Fig. 15

The output intensity spectra when the design parameters deviated from ideal value. (a) R 1 1 and R 1 2 deviated by 0, −1% and 1% respectively. (b) d 1 1 deviated by 0, −10−8 m and 10−8 m respectively.(c) d 1 2 deviated by 0, −10−8 m and 10−8 m respectively. (d) ΔL deviated by 0, −10−8 m and 10−8 m respectively.

Tables (6)

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Table 1 Design parameters for the 3 different spectra corresponding to the lines in Figs. 6 and 7.

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Table 2 Parameters of five schemes.

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Table 3 Passband bandwidth ratio for different configurations.

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Table 4 Design parameters for different duty cycles.

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Table 5 Parameters of three different structures.

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Table 6 Performance of output spectrum of third-order interleavers.

Equations (14)

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

( E i + E i ) = 1 t i [ e i ϕ i r i e i ϕ i r i e i ϕ i e i ϕ i ] ( E i 1 + E i 1 ) ,
E i E i + = r i e j ϕ i + e j ϕ i ( E i 1 E i 1 + ) e j ϕ i + r i e j ϕ i ( E i 1 E i 1 + ) = e j Θ ,
H 1 = 1 2 { exp [ j ( Θ 1 + 4 π L 1 / λ ) ] + exp [ j ( Θ 2 + 4 π L 2 / λ ) ] } ,
H 2 = 1 2 { exp [ j ( Θ 1 + 4 π L 1 / λ ) ] exp [ j ( Θ 2 + 4 π L 2 / λ ) ] } ,
H 1 = 1 2 exp ( i 4 π L 2 / λ ) [ exp ( i Θ 1 ) exp ( i 4 π Δ L / λ ) + exp ( i Θ 2 ) ] ,
H 2 = 1 2 exp ( i 4 π L 2 / λ ) [ exp ( i Θ 1 ) exp ( i 4 π Δ L / λ ) exp ( i Θ 2 ) ] ,
H 1 ( z ) = 1 2 [ A 1 ( z ) z Δ L d + A 2 ( z ) ] ,
H 2 ( z ) = 1 2 [ A 1 ( z ) z Δ L d A 2 ( z ) ] .
| H ( e j ω ) 1 | = | e j ω z 1 | | e j ω z 1 * | | e j ω z 0 | | e j ω p 1 | | e j ω p 1 * | | e j ω p 0 | .
| H 1 ( e j π 2 ) | = | H 1 ( e j π 2 ) | = | ± i ± 1 | / 2 = 2 / 2.
H 1 ( z ) = 1 2 [ r 1 1 + z p 11 1 + r 1 1 z p 11 z q + r 1 2 + z p 21 1 + r 1 2 z p 21 ] ,
H 2 ( z ) = 1 2 [ r 1 1 + z p 11 1 + r 1 1 z p 11 z q r 1 2 + z p 21 1 + r 1 2 z p 21 ] .
H 1 ( z ) = 1 2 [ r 2 1 r 1 1 z p 12 + r 2 1 r 1 1 z p 11 + z ( p 11 + p 12 ) 1 + r 2 1 r 1 1 z p 12 r 1 1 z p 11 r 2 1 z ( p 11 + p 12 ) z q + r 1 2 + z p 21 1 r 1 2 z p 21 ] ,
H 2 ( z ) = 1 2 [ r 2 1 r 1 1 z p 12 + r 2 1 r 1 1 z p 11 + z ( p 11 + p 12 ) 1 + r 2 1 r 1 1 z p 12 r 1 1 z p 11 r 2 1 z ( p 11 + p 12 ) z q r 1 2 + z p 21 1 r 1 2 z p 21 ] .

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