Abstract

In this work, thermo-optic tunable 4 × 4 cascaded multimode interference based integrated optical waveguide switching matrices are designed and fabricated using photopolymer lightwave circuits. The materials of the waveguide core and cladding are fluorinated epoxy-terminated copolycarbonate and polymethylmethacrylate, respectively. The driving power that controls matrices for binary encoding of different optical switching states are simulated and analyzed. The measured insertion loss of the actual chip is < 7.1 dB and the maximum crosstalk in adjacent channels is <−30 dB. The switching time is approximately 220 μs and the extinction ratio is obtained as 21.5 dB. This flexible encoding technique can be applied for achieving optical code-division multiple-access network coders.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref] [PubMed]

2018 (5)

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Y. Tian, J. Qiu, Z. Huang, Y. Qiao, Z. Dong, and J. Wu, “On-chip integratable all-optical quantizer using cascaded step-size MMI,” Opt. Express 26(3), 2453–2461 (2018).
[Crossref] [PubMed]

V. Kumar and V. Priye, “3-D Multilayer S-Bend Silicon WaveguideOptical Interconnect,” IEEE Photonics Technol. Lett. 30(11), 1040–1043 (2018).
[Crossref]

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

A. Inoue and Y. Koike, “Low-Noise Graded-Index Plastic Optical Fiber for Significantly Stable and Robust Data Transmission,” J. Lightwave Technol. 36(24), 5887–5892 (2018).
[Crossref]

2017 (6)

M. Nikoufard, M. K. Alamouti, and S. Pourgholi, “Multimode Interference Power-Splitter Using InP-Based Deeply Etched Hybrid Plasmonic Waveguide,” IEEE Trans. NanoTechnol. 16(3), 477–483 (2017).
[Crossref]

K. J. Miller, K. A. Hallman, R. F. Haglund, and S. M. Weiss, “Silicon waveguide optical switch with embedded phase change material,” Opt. Express 25(22), 26527–26536 (2017).
[Crossref] [PubMed]

H.-D. Kenchington Goldsmith, M. Ireland, P. Ma, N. Cvetojevic, and S. Madden, “Improving the extinction bandwidth of MMI chalcogenide photonic chip -based MIR nullinginterferometers,” Opt. Express 25(14), 16813–16824 (2017).
[Crossref] [PubMed]

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

G. Fan, R. Orobtchouk, B. Han, Y. Li, and H. Li, “8 x 8 wavelength router of optical network on chip,” Opt. Express 25(20), 23677–23683 (2017).
[Crossref] [PubMed]

J. Liu and L. Tao, “Influence of Parametric Uncertainties on Narrow Width Bandpass Optical Filter of Prism Pair Coupled Planar Optical Waveguide,” IEEE J. Quantum Electron. 53(3), 6200105 (2017).
[Crossref]

2016 (7)

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Z. Wu, J. Li, D. Ge, F. Ren, P. Zhu, Q. Mo, Z. Li, Z. Chen, and Y. He, “Demonstration of all-optical MDM/WDM switching for short-reach networks,” Opt. Express 24(19), 21609–21618 (2016).
[Crossref] [PubMed]

D. Melati, A. Waqas, A. Alippi, and A. Melloni, “Wavelength and composition dependence of the thermo-optic coefficient for InGaAsP-based integrated waveguides,” J. Appl. Phys. 120(21), 213102 (2016).
[Crossref]

Z. Zhang and N. Keil, “Thermo-optic devices on polymer platform,” Opt. Commun. 362, 101–114 (2016).
[Crossref]

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

2015 (6)

N. Dupuis, B. G. Lee, A. V. Rylyakov, D. M. Kuchta, C. W. Baks, J. S. Orcutt, D. M. Gill, W. M. J. Green, and C. L. Schow, “Modeling and Characterization of a Nonblocking4 × 4 Mach–Zehnder Silicon Photonic Switch Fabric,” J. Lightwave Technol. 33(20), 4329–4337 (2015).
[Crossref]

M. Safari, C. Shafai, and L. Shafai, “X-Band Tunable Frequency Selective Surface UsingMEMS Capacitive Loads,” IEEE Trans. Antenn. Propag. 63(3), 1014–1021 (2015).
[Crossref]

L. Pelliccia, F. Cacciamani, P. Farinelli, and R. Sorrentino, “High-Tunable Waveguide Filters Using OhmicRF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 63(10), 3381–3390 (2015).
[Crossref]

N. Vahabisani and M. Daneshmand, “Monolithic Millimeter-Wave MEMSWaveguide Switch,” IEEE Trans. Microw. Theory Tech. 63(2), 340–351 (2015).
[Crossref]

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

L. Yang, Y. Xia, F. Zhang, Q. Chen, J. Ding, P. Zhou, and L. Zhang, “Reconfigurable nonblocking 4-port silicon thermo-optic optical router based on Mach-Zehnder optical switches,” Opt. Lett. 40(7), 1402–1405 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (1)

C.-D. Truong, D.-H. Tran, T.-A. Tran, and T.-T. Le, “3×3 Multimode interference optical switches using electro-optic effects as phase Shifters,” Opt. Commun. 292, 78–83 (2013).
[Crossref]

2012 (1)

M. Jelinek, “Functional planar thin film optical waveguide lasers,” Laser Phys. Lett. 9(2), 91–99 (2012).
[Crossref]

2011 (1)

R. S. Tucker, “Green optical communications-Part II Energy limitations in network,” IEEE J. Sel. Top. Quantum Electron. 17(2), 261–274 (2011).
[Crossref]

Alamouti, M. K.

M. Nikoufard, M. K. Alamouti, and S. Pourgholi, “Multimode Interference Power-Splitter Using InP-Based Deeply Etched Hybrid Plasmonic Waveguide,” IEEE Trans. NanoTechnol. 16(3), 477–483 (2017).
[Crossref]

Alippi, A.

D. Melati, A. Waqas, A. Alippi, and A. Melloni, “Wavelength and composition dependence of the thermo-optic coefficient for InGaAsP-based integrated waveguides,” J. Appl. Phys. 120(21), 213102 (2016).
[Crossref]

Baks, C. W.

Cacciamani, F.

L. Pelliccia, F. Cacciamani, P. Farinelli, and R. Sorrentino, “High-Tunable Waveguide Filters Using OhmicRF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 63(10), 3381–3390 (2015).
[Crossref]

Cai, Z.

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Chen, C.

Chen, J.

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

Chen, Q.

Chen, Z.

Chu, W.-S.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Cui, Y.

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Cui, Z.

Cvetojevic, N.

Daneshmand, M.

N. Vahabisani and M. Daneshmand, “Monolithic Millimeter-Wave MEMSWaveguide Switch,” IEEE Trans. Microw. Theory Tech. 63(2), 340–351 (2015).
[Crossref]

Dangel, R.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Ding, J.

Dong, Z.

Du, Q.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Dupuis, N.

Etlinger, G.

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Fan, G.

Farinelli, P.

L. Pelliccia, F. Cacciamani, P. Farinelli, and R. Sorrentino, “High-Tunable Waveguide Filters Using OhmicRF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 63(10), 3381–3390 (2015).
[Crossref]

Follonier, S.

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Gartmann, T. E.

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Ge, D.

Gill, D. M.

Green, W. M. J.

Haglund, R. F.

Hallman, K. A.

Han, B.

Han, C.

He, Y.

He, Z.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Heub, S.

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Horst, F.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Hu, G.

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Huang, Z.

Inoue, A.

Ireland, M.

Jelinek, M.

M. Jelinek, “Functional planar thin film optical waveguide lasers,” Laser Phys. Lett. 9(2), 91–99 (2012).
[Crossref]

Jubin, D.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Kehl, F.

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Keil, N.

Z. Zhang and N. Keil, “Thermo-optic devices on polymer platform,” Opt. Commun. 362, 101–114 (2016).
[Crossref]

Kenchington Goldsmith, H.-D.

Kim, J.-W.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Kim, K.-J.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Koike, K.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Koike, Y.

A. Inoue and Y. Koike, “Low-Noise Graded-Index Plastic Optical Fiber for Significantly Stable and Robust Data Transmission,” J. Lightwave Technol. 36(24), 5887–5892 (2018).
[Crossref]

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Kuchta, D. M.

Kumar, V.

V. Kumar and V. Priye, “3-D Multilayer S-Bend Silicon WaveguideOptical Interconnect,” IEEE Photonics Technol. Lett. 30(11), 1040–1043 (2018).
[Crossref]

La Porta, A.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Le, T.-T.

C.-D. Truong, D.-H. Tran, T.-A. Tran, and T.-T. Le, “3×3 Multimode interference optical switches using electro-optic effects as phase Shifters,” Opt. Commun. 292, 78–83 (2013).
[Crossref]

Lee, B. G.

Lee, H.-J.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Lee, H.-K.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Li, H.

Li, J.

Li, M.

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Li, X.

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

Li, Y.

G. Fan, R. Orobtchouk, B. Han, Y. Li, and H. Li, “8 x 8 wavelength router of optical network on chip,” Opt. Express 25(20), 23677–23683 (2017).
[Crossref] [PubMed]

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Li, Z.

Z. Wu, J. Li, D. Ge, F. Ren, P. Zhu, Q. Mo, Z. Li, Z. Chen, and Y. He, “Demonstration of all-optical MDM/WDM switching for short-reach networks,” Opt. Express 24(19), 21609–21618 (2016).
[Crossref] [PubMed]

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

Liang, L.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Liu, J.

J. Liu and L. Tao, “Influence of Parametric Uncertainties on Narrow Width Bandpass Optical Filter of Prism Pair Coupled Planar Optical Waveguide,” IEEE J. Quantum Electron. 53(3), 6200105 (2017).
[Crossref]

Liu, P.

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Lu, L.

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

Ma, P.

Madden, S.

Meier, N.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Melati, D.

D. Melati, A. Waqas, A. Alippi, and A. Melloni, “Wavelength and composition dependence of the thermo-optic coefficient for InGaAsP-based integrated waveguides,” J. Appl. Phys. 120(21), 213102 (2016).
[Crossref]

Melloni, A.

D. Melati, A. Waqas, A. Alippi, and A. Melloni, “Wavelength and composition dependence of the thermo-optic coefficient for InGaAsP-based integrated waveguides,” J. Appl. Phys. 120(21), 213102 (2016).
[Crossref]

Merkel, T. C.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Mikeš, F.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Miller, K. J.

Mo, Q.

Nikoufard, M.

M. Nikoufard, M. K. Alamouti, and S. Pourgholi, “Multimode Interference Power-Splitter Using InP-Based Deeply Etched Hybrid Plasmonic Waveguide,” IEEE Trans. NanoTechnol. 16(3), 477–483 (2017).
[Crossref]

Ning, Y. Q.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Niu, X.

Noh, Y.-O.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Offrein, B. J.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Oh, M.-C.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Okamoto, Y.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Orcutt, J. S.

Orobtchouk, R.

Pelliccia, L.

L. Pelliccia, F. Cacciamani, P. Farinelli, and R. Sorrentino, “High-Tunable Waveguide Filters Using OhmicRF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 63(10), 3381–3390 (2015).
[Crossref]

Pourgholi, S.

M. Nikoufard, M. K. Alamouti, and S. Pourgholi, “Multimode Interference Power-Splitter Using InP-Based Deeply Etched Hybrid Plasmonic Waveguide,” IEEE Trans. NanoTechnol. 16(3), 477–483 (2017).
[Crossref]

Priye, V.

V. Kumar and V. Priye, “3-D Multilayer S-Bend Silicon WaveguideOptical Interconnect,” IEEE Photonics Technol. Lett. 30(11), 1040–1043 (2018).
[Crossref]

Qiao, Y.

Qin, L.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Qiu, J.

Rakshit, J. K.

J. N. Roy and J. K. Rakshit, “Design of micro-ring resonator-based all-optical logic shifter,” Opt. Commun. 312, 73–79 (2014).
[Crossref]

Ren, F.

Roy, J. N.

J. N. Roy and J. K. Rakshit, “Design of micro-ring resonator-based all-optical logic shifter,” Opt. Commun. 312, 73–79 (2014).
[Crossref]

Rylyakov, A. V.

Safari, M.

M. Safari, C. Shafai, and L. Shafai, “X-Band Tunable Frequency Selective Surface UsingMEMS Capacitive Loads,” IEEE Trans. Antenn. Propag. 63(3), 1014–1021 (2015).
[Crossref]

Schow, C. L.

Seifried, M.

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

Seo, J.-K.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Shafai, C.

M. Safari, C. Shafai, and L. Shafai, “X-Band Tunable Frequency Selective Surface UsingMEMS Capacitive Loads,” IEEE Trans. Antenn. Propag. 63(3), 1014–1021 (2015).
[Crossref]

Shafai, L.

M. Safari, C. Shafai, and L. Shafai, “X-Band Tunable Frequency Selective Surface UsingMEMS Capacitive Loads,” IEEE Trans. Antenn. Propag. 63(3), 1014–1021 (2015).
[Crossref]

Shi, Z.

Shin, J.-S.

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

Sorrentino, R.

L. Pelliccia, F. Cacciamani, P. Farinelli, and R. Sorrentino, “High-Tunable Waveguide Filters Using OhmicRF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 63(10), 3381–3390 (2015).
[Crossref]

Sun, X.

Tao, L.

J. Liu and L. Tao, “Influence of Parametric Uncertainties on Narrow Width Bandpass Optical Filter of Prism Pair Coupled Planar Optical Waveguide,” IEEE J. Quantum Electron. 53(3), 6200105 (2017).
[Crossref]

Tian, Y.

Tran, D.-H.

C.-D. Truong, D.-H. Tran, T.-A. Tran, and T.-T. Le, “3×3 Multimode interference optical switches using electro-optic effects as phase Shifters,” Opt. Commun. 292, 78–83 (2013).
[Crossref]

Tran, T.-A.

C.-D. Truong, D.-H. Tran, T.-A. Tran, and T.-T. Le, “3×3 Multimode interference optical switches using electro-optic effects as phase Shifters,” Opt. Commun. 292, 78–83 (2013).
[Crossref]

Truong, C.-D.

C.-D. Truong, D.-H. Tran, T.-A. Tran, and T.-T. Le, “3×3 Multimode interference optical switches using electro-optic effects as phase Shifters,” Opt. Commun. 292, 78–83 (2013).
[Crossref]

Tscharner, N. S. R. U.

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Tucker, R. S.

R. S. Tucker, “Green optical communications-Part II Energy limitations in network,” IEEE J. Sel. Top. Quantum Electron. 17(2), 261–274 (2011).
[Crossref]

Vahabisani, N.

N. Vahabisani and M. Daneshmand, “Monolithic Millimeter-Wave MEMSWaveguide Switch,” IEEE Trans. Microw. Theory Tech. 63(2), 340–351 (2015).
[Crossref]

Wang, B.

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Wang, F.

Wang, L. J.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Wang, X.

Waqas, A.

D. Melati, A. Waqas, A. Alippi, and A. Melloni, “Wavelength and composition dependence of the thermo-optic coefficient for InGaAsP-based integrated waveguides,” J. Appl. Phys. 120(21), 213102 (2016).
[Crossref]

Weiss, S. M.

Wu, J.

Wu, Z.

Xia, Y.

Yang, H.

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Yang, L.

Yun, B.

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Zhang, D.

Zhang, D. M.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Zhang, F.

Zhang, H.

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Zhang, K.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Zhang, L.

Zhang, X.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Zhang, Z.

Z. Zhang and N. Keil, “Thermo-optic devices on polymer platform,” Opt. Commun. 362, 101–114 (2016).
[Crossref]

Zheng, C. T.

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

Zheng, P.

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

Zheng, Y.

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Zhou, L.

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

Zhou, P.

Zhu, P.

IEEE J. Quantum Electron. (1)

J. Liu and L. Tao, “Influence of Parametric Uncertainties on Narrow Width Bandpass Optical Filter of Prism Pair Coupled Planar Optical Waveguide,” IEEE J. Quantum Electron. 53(3), 6200105 (2017).
[Crossref]

IEEE J. Sel. Top Quant. (1)

R. Dangel, A. La Porta, D. Jubin, F. Horst, N. Meier, M. Seifried, and B. J. Offrein, “Polymer Waveguides Enabling Scalable Low-Loss Adiabatic Optical Coupling for Silicon Photonics,” IEEE J. Sel. Top Quant. 24, 8200211 (2018).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. S. Tucker, “Green optical communications-Part II Energy limitations in network,” IEEE J. Sel. Top. Quantum Electron. 17(2), 261–274 (2011).
[Crossref]

IEEE Photonics J. (2)

L. Lu, L. Zhou, Z. Li, X. Li, and J. Chen, “Broadband 4×4 Nonblocking SiliconElectrooptic Switches Based onMach–Zehnder Interferometers,” IEEE Photonics J. 7(1), 7800108 (2015).
[Crossref]

L. Liang, K. Zhang, C. T. Zheng, X. Zhang, L. Qin, Y. Q. Ning, D. M. Zhang, and L. J. Wang, “N × NReconfigurable Nonblocking Polymer/Silica Hybrid Planar Optical Switch Matrix Based on Total-Internal-Reflection Effect,” IEEE Photonics J. 9(4), 4904711 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

V. Kumar and V. Priye, “3-D Multilayer S-Bend Silicon WaveguideOptical Interconnect,” IEEE Photonics Technol. Lett. 30(11), 1040–1043 (2018).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

M. Safari, C. Shafai, and L. Shafai, “X-Band Tunable Frequency Selective Surface UsingMEMS Capacitive Loads,” IEEE Trans. Antenn. Propag. 63(3), 1014–1021 (2015).
[Crossref]

IEEE Trans. Microw. Theory Tech. (2)

L. Pelliccia, F. Cacciamani, P. Farinelli, and R. Sorrentino, “High-Tunable Waveguide Filters Using OhmicRF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 63(10), 3381–3390 (2015).
[Crossref]

N. Vahabisani and M. Daneshmand, “Monolithic Millimeter-Wave MEMSWaveguide Switch,” IEEE Trans. Microw. Theory Tech. 63(2), 340–351 (2015).
[Crossref]

IEEE Trans. NanoTechnol. (1)

M. Nikoufard, M. K. Alamouti, and S. Pourgholi, “Multimode Interference Power-Splitter Using InP-Based Deeply Etched Hybrid Plasmonic Waveguide,” IEEE Trans. NanoTechnol. 16(3), 477–483 (2017).
[Crossref]

J. Appl. Phys. (1)

D. Melati, A. Waqas, A. Alippi, and A. Melloni, “Wavelength and composition dependence of the thermo-optic coefficient for InGaAsP-based integrated waveguides,” J. Appl. Phys. 120(21), 213102 (2016).
[Crossref]

J. Lightwave Technol. (2)

J. Mater. Chem. C Mater. Opt. Electron. Devices (1)

Z. Cai, B. Wang, Y. Zheng, M. Li, Y. Li, C. Chen, D. Zhang, Z. Cui, and Z. Shi, “Novel fluorinated polycarbonate negative-type photoresists for thermo-optic waveguide gate switch arrays,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(3), 533–540 (2016).
[Crossref]

Laser Phys. Lett. (1)

M. Jelinek, “Functional planar thin film optical waveguide lasers,” Laser Phys. Lett. 9(2), 91–99 (2012).
[Crossref]

Opt. Commun. (5)

Z. Zhang and N. Keil, “Thermo-optic devices on polymer platform,” Opt. Commun. 362, 101–114 (2016).
[Crossref]

M.-C. Oh, W.-S. Chu, J.-S. Shin, J.-W. Kim, K.-J. Kim, J.-K. Seo, H.-K. Lee, Y.-O. Noh, and H.-J. Lee, “Polymeric optical waveguide devices exploiting special properties of polymer materials,” Opt. Commun. 362, 3–12 (2016).
[Crossref]

J. N. Roy and J. K. Rakshit, “Design of micro-ring resonator-based all-optical logic shifter,” Opt. Commun. 312, 73–79 (2014).
[Crossref]

H. Yang, P. Zheng, P. Liu, G. Hu, B. Yun, and Y. Cui, “Design of polarization-insensitive 2×2 multimode interference coupler based on double strip silicon nitride waveguides,” Opt. Commun. 410, 559–564 (2018).
[Crossref]

C.-D. Truong, D.-H. Tran, T.-A. Tran, and T.-T. Le, “3×3 Multimode interference optical switches using electro-optic effects as phase Shifters,” Opt. Commun. 292, 78–83 (2013).
[Crossref]

Opt. Express (7)

C. Chen, X. Niu, C. Han, Z. Shi, X. Wang, X. Sun, F. Wang, Z. Cui, and D. Zhang, “Monolithic multi-functional integration of ROADM modules based on polymer photonic lightwave circuit,” Opt. Express 22(9), 10716–10727 (2014).
[Crossref] [PubMed]

C. Chen, X. Niu, C. Han, Z. Shi, X. Wang, X. Sun, F. Wang, Z. Cui, and D. Zhang, “Reconfigurable optical interleaver modules with tunable wavelength transfer matrix function using polymer photonics lightwave circuits,” Opt. Express 22(17), 19895–19911 (2014).
[Crossref] [PubMed]

Z. Wu, J. Li, D. Ge, F. Ren, P. Zhu, Q. Mo, Z. Li, Z. Chen, and Y. He, “Demonstration of all-optical MDM/WDM switching for short-reach networks,” Opt. Express 24(19), 21609–21618 (2016).
[Crossref] [PubMed]

H.-D. Kenchington Goldsmith, M. Ireland, P. Ma, N. Cvetojevic, and S. Madden, “Improving the extinction bandwidth of MMI chalcogenide photonic chip -based MIR nullinginterferometers,” Opt. Express 25(14), 16813–16824 (2017).
[Crossref] [PubMed]

G. Fan, R. Orobtchouk, B. Han, Y. Li, and H. Li, “8 x 8 wavelength router of optical network on chip,” Opt. Express 25(20), 23677–23683 (2017).
[Crossref] [PubMed]

K. J. Miller, K. A. Hallman, R. F. Haglund, and S. M. Weiss, “Silicon waveguide optical switch with embedded phase change material,” Opt. Express 25(22), 26527–26536 (2017).
[Crossref] [PubMed]

Y. Tian, J. Qiu, Z. Huang, Y. Qiao, Z. Dong, and J. Wu, “On-chip integratable all-optical quantizer using cascaded step-size MMI,” Opt. Express 26(3), 2453–2461 (2018).
[Crossref] [PubMed]

Opt. Lett. (1)

Polym. Adv. Technol. (1)

Y. Okamoto, Q. Du, K. Koike, F. Mikeš, T. C. Merkel, Z. He, H. Zhang, and Y. Koike, “New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes,” Polym. Adv. Technol. 27(1), 33–41 (2016).
[Crossref]

Sens. Actuators B Chem. (1)

F. Kehl, G. Etlinger, T. E. Gartmann, N. S. R. U. Tscharner, S. Heub, and S. Follonier, “Introduction of an angle interrogated, MEMS-based, opticalwaveguide grating system for label-free biosensing,” Sens. Actuators B Chem. 226, 135–143 (2016).
[Crossref]

Other (1)

http://www.microchem.com/Prod-SU82000.htm .

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Figures (14)

Fig. 1
Fig. 1 Molecular structure and absorption spectrum of the waveguide material (a) molecular structure of AF-Z-PC EP, (b) molecular structure of FSU-8, and (c) visible and near-infrared absorption spectrum of the waveguide material compared with commercial SU-8 2000.
Fig. 2
Fig. 2 Structural and optical characteristics of the waveguide and electrode heaters (a) cross-sectional structure of the polymer waveguide, (b) TM-mode optical field distribution for the polymer waveguide, and (c)thermal field distribution of Al electrode heater.
Fig. 3
Fig. 3 Schematic diagram of the integrated optical waveguide cascaded MMI-based switching matrix module.
Fig. 4
Fig. 4 The relationship between waveguide Neff and temperature change.
Fig. 5
Fig. 5 MMI switching unit defined (a) optimized structural parameters of the simple MMI waveguide and (b) optimal length of the electrode heater simulated.
Fig. 6
Fig. 6 Schematic diagram of the cascaded MMI-based switching matrix with specific location markers.
Fig. 7
Fig. 7 Encoding schemes of An vectors for the TO tuning transmission light field of the switching matrix.
Fig. 8
Fig. 8 Encoding schemes of Bn vectors for the TO tuning transmission light field of the switching matrix.
Fig. 9
Fig. 9 Encoding schemes of Cn vectors for the TO tuning transmission light field of the switching matrix.
Fig. 10
Fig. 10 Encoding schemes of Dn vectors for the TO tuning transmission light field of the switching matrix.
Fig. 11
Fig. 11 Actual profile micrographs of the waveguide and electrode region: (a) and (b) images of cascaded output regional and center MMI units measured by optical microscope ( × 500), (c) partial interactional regional images between the electrode heater and MMI waveguide measured by optical microscope ( × 1000), (d) SEM images of the cross-section for the input waveguide.
Fig. 12
Fig. 12 (a)Actual optical coupling testing system photograph of integrated cascaded MMI-based switching matrix chip, (b) circuit diagrams of the rectification filter circuits,(c)circuit diagrams of regulator circuits.
Fig. 13
Fig. 13 Output near-infrared fields of the chip measured by infrared CCD camera with lens ( × 80) (a) encoding group A1 and (b) encoding A2[0011], A3[1011], and A4[1111].
Fig. 14
Fig. 14 Actual performances of the chip measured (a) TO switching response curves, (b) relationship between driving electrical power and different channel output optical power, (c) relationship curves between output powers and wavelengths, and (d) insertion loss of the chip with temperature changed.

Equations (18)

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

L π = π β 0 - β 1 4 n e f f w e m 2 3 λ 0
φ ( i , l ) = π N N 1 4 π 2 π λ 0 n e f f L m m i + π + π 4 N ( l i ) ( 2 N l + i ) ( i = 1 , 2 , ... N ) , ( l = N , N 1 , ...0 ) if i + l even  
φ ( i , l ) = π N N 1 4 π 2 π λ 0 n e f f L m m i + π + π 4 N ( l + i 1 ) ( 2 N l i + 1 ) ( i = 1 , 2 , ... N ) , ( l = N , N 1 , ...1 ) if i + l odd
φ ( 2 , 2 ) - φ ( 2,1 ) = Δ ϕ = k L e ( n T ) Δ T
A 1 = ( 0 0 0 0 0 0 0 0 0 22 22 0 0 0 0 0 0 22 0 0 ) 4 × 5 , A 2 = ( 0 0 0 0 11 11 0 0 0 0 11 0 0 0 22 0 0 11 0 0 0 0 11 0 22 22 0 0 11 0 ) 6 × 5 , A 3 = ( 8 0 0 0 11 0 0 8 0 11 14 0 0 11 0 14 0 0 11 22 ) 4 × 5 , A 4 = ( 11 0 0 11 11 ) 1 × 5 .
B 1 = ( 22 0 0 0 0 22 0 0 0 22 0 0 0 0 0 0 0 0 22 0 ) 4 × 5 , B 2 = ( 22 0 0 0 11 11 0 0 0 0 11 0 0 0 22 11 0 0 22 0 11 0 0 22 22 0 0 0 11 0 ) 6 × 5 , B 3 = ( 14 0 0 0 11 14 0 0 22 11 8 0 0 11 0 8 0 0 11 22 ) 4 × 5 , B 4 = ( 11 0 0 11 11 ) 1 × 5 .
C 1 = ( 0 0 0 0 22 0 0 0 0 0 0 22 0 22 0 0 22 0 0 0 ) 4 × 5 , C 2 = ( 0 0 0 0 11 0 11 0 22 22 0 11 0 22 0 0 11 0 0 22 0 11 0 0 0 0 22 0 11 0 ) 6 × 5 , C 3 = ( 0 8 0 22 11 0 8 0 0 11 0 14 0 11 22 0 14 0 11 0 ) 4 × 5 , C 4 = ( 0 11 0 11 11 ) 1 × 5 .
D 1 = ( 0 0 22 0 0 0 22 0 0 0 0 0 0 22 0 0 0 0 0 0 ) 4 × 5 , D 2 = ( 0 22 0 0 11 0 0 11 22 0 0 11 0 22 0 0 0 11 0 0 0 11 0 0 0 0 0 0 11 0 ) 6 × 5 , D 3 = ( 0 14 0 22 11 0 14 0 0 11 0 0 8 11 0 0 8 0 11 0 ) 4 × 5 , D 4 = ( 0 11 0 11 11 ) 1 × 5 .
F A n F = D n ,     G B n G = C n
( 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ) 4 × 4 A 1 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) 5 × 5 = D 1
( 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ) 4 × 4 B 1 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) 5 × 5 = C 1
( 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 ) 6 × 6 A 2 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) 5 × 5 = D 2
( 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 ) 6 × 6 B 2 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) 5 × 5 = C 2
( 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ) 4 × 4 A 3 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) 5 × 5 = D 3
( 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ) 4 × 4 B 3 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) 5 × 5 = C 3
A 4 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 = D 4
B 4 ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 = C 4
K 1 = ( 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 ) 4 × 4 K 2 = ( 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) 5 × 5 K 3 = ( 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 ) 6 × 6

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