Abstract

In this work, thermo-optic (TO) waveguide switches are designed and fabricated based on the bottom-metal-printed technique. Low-loss fluorinated polycarbonate (AF-Z-PC MA) and polymethyl methacrylate (PMMA) are used as core and cladding materials, respectively. The thermal stability and optical absorption characteristics of AF-Z-PC MA are analyzed. The optical and thermal field distributions of the TO switch are simulated. The insertion loss and extinction ratio of the device are found to be 4.5 dB and 19.8 dB, respectively, at a wavelength of 1550 nm. The on-off time of the switching chip is 80 µs. The electrical power consumption is approximately 8.8 mW. The proposed low-loss fluorinated polymer TO waveguide switch realized by bottom-metal-printed fabrication technology is suitable for large-scale integrated photonic circuit systems.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2020 (3)

Y. Yuan, J. Li, Y. Dong, and H. Miao, “UV-curable fluorinated polycarbonate polyurethane with improved surface properties,” JCT Res. 17(3), 777–783 (2020).
[Crossref]

U. Roggero and H. Hernandez-Figueroa, “Polymeric power splitters for multiplexing optical biosensors,” Opt. Laser Technol. 127, 106127 (2020).
[Crossref]

Q. Q. Song, K. X. Chen, and Z. F. Hu, “Low-Power Broadband Thermo-Optic Switch With Weak Polarization Dependence Using a Segmented Graphene Heater,” J. Lightwave Technol. 38(6), 1358–1364 (2020).
[Crossref]

2019 (4)

C. Qiu, Y. Wang, and Y. Chen, “Design and Analysis of a Novel Graphene-Assisted Silica/Polymer Hybrid Waveguide with Thermal-Optical Phase Modulation Structure,” IEEE Photonics J. 11(2), 1–10 (2019).
[Crossref]

X. B. Wang and K. S. Chiang, “Polarization-insensitive mode-independent thermo-optic switch based on symmetric waveguide directional coupler,” Opt. Express 27(24), 35385–35393 (2019).
[Crossref]

S. X. Ding, C. X. Wang, X. Y. Shi, and J. W. Zou, “Directly written photo-crosslinked fluorinated polycarbonate photoresist materials for second-order nonlinear optical (NLO) applications,” J. Mater. Chem. C 7(16), 4667–4672 (2019).
[Crossref]

D. Marpaung, J. P. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Commun. 13(2), 80–90 (2019).
[Crossref]

2018 (4)

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Q. D. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 1–14 (2018).
[Crossref]

X. Z. Zi, L. F. Wang, K. X. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
[Crossref]

2017 (2)

S. P. Wang, X. L. Feng, S. M. Gao, and Y. C. Shi, “On-chip reconfigurable optical add-drop multiplexer for hybrid wavelength/mode-division-multiplexing systems,” Opt. Lett. 42(14), 2802–2805 (2017).
[Crossref]

Z. Z. Cai, Q. X. Yu, Y. Zheng, X. Y. Shi, and X. S. Wang, “Effect of fluoro-polycarbonates containing aliphatic/aromatic segments on the characteristics of thermo-optic waveguide devices,” RSC Adv. 7(31), 19136–19144 (2017).
[Crossref]

2015 (3)

L. Y. Zhou, Z. W. Xu, X. F. Cheng, and Q. R. Huang, “An optical circuit switching network architecture and reconfiguration schemes for datacenter,” Opt. Commun. 335, 250–256 (2015).
[Crossref]

V. J. Urick, J. F. Diehl, C. E. Sunderman, J. D. McKinney, and K. J. Williams, “An optical technique for radio frequency interference mitigation,” IEEE Photonics Technol. Lett. 27(12), 1333–1336 (2015).
[Crossref]

Z. Cai, H. Yu, Y. Zhang, and M. Li, “Synthesis and characterization of novel fluorinated polycarbonate negative-type photoresist for optical waveguide,” Polymer 61, 140–146 (2015).
[Crossref]

2012 (3)

2011 (1)

Y. Song, J. Wang, M. Yan, and M. Qiu, “Efficient coupling between dielectric and hybrid plasmonic waveguides by multimode interference power splitter,” J. Opt. 13(7), 075002 (2011).
[Crossref]

2010 (2)

P. R. Hua, D. L. Zhang, and E. Y. B. Pun, “Long-period grating on strip Ti:LiNbO3 waveguide embedded in planar Ti:LiNbO3 waveguide,” IEEE Photonics Technol. Lett. 22(18), 1361–1363 (2010).
[Crossref]

G. Li, J. Wang, G. Yu, and X. Jian, “Synthesis and characterization of partly fluorinated poly(phthalazinone ether)s crosslinked by allyl group for passive optical waveguides,” Polymer 51(6), 1524–1529 (2010).
[Crossref]

2009 (3)

2008 (3)

R. Ghayour, A. N. Taheri, and M. T. Fathi, “Integrated Mach-Zehnder-based 2 × 2 all-optical switch using nonlinear two-mode interference waveguide,” Appl. Opt. 47(5), 632–638 (2008).
[Crossref]

Z. Zhen, Z. F. Zhou, Q. A. Huang, and W. H. Li, “Modeling, simulation and experimental verification of inclined UV lithography for SU-8 negative thick photoresists,” J. Micromech. Microeng. 18(12), 125017 (2008).
[Crossref]

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

2007 (1)

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

2006 (3)

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

D. X. Dai and S. L. He, “Ultrasmall overlapped arrayed-waveguide grating, based on Si nanowire waveguides for dense wavelength division demultiplexing,” IEEE J. Sel. Top. Quant. Electron. 12(6), 1301–1305 (2006).
[Crossref]

2004 (2)

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Y. O. Noh, C. H. Lee, J. M. Kim, W. Y. Hwang, and Y. H. Won, “Polymer waveguide variable optical attenuator and its reliability,” Opt. Commun. 242(4-6), 533–540 (2004).
[Crossref]

2003 (1)

J. H. Kim and R. T. Chen, “A collimation mirror in polymeric planar waveguide formed by reactive ion etching,” IEEE Photonics Technol. Lett. 15(3), 422–424 (2003).
[Crossref]

2002 (2)

B. Cakmak, “Fabrication and characterization of dry and wet etched InGaAs/InGaAsP/InP long wavelength semiconductor lasers,” Opt. Express 10(13), 530–535 (2002).
[Crossref]

H. Ma, A. K. Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: Materials, processing, and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[Crossref]

2000 (2)

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quant. 6(1), 54–68 (2000).
[Crossref]

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Aguirregabiria, M.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Aitchison, J. S.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Amro, N. A.

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

Anand, S.

Andonovic, I.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Aranburu, I.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Arroyo, M. T.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Bêche, B.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

Begou, T.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

Berganzo, J.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Binnemans, K.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Blanco, F. J.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Buhl, L. L.

Cai, Z.

Z. Cai, H. Yu, Y. Zhang, and M. Li, “Synthesis and characterization of novel fluorinated polycarbonate negative-type photoresist for optical waveguide,” Polymer 61, 140–146 (2015).
[Crossref]

Cai, Z. G.

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Cai, Z. Z.

Z. Z. Cai, Q. X. Yu, Y. Zheng, X. Y. Shi, and X. S. Wang, “Effect of fluoro-polycarbonates containing aliphatic/aromatic segments on the characteristics of thermo-optic waveguide devices,” RSC Adv. 7(31), 19136–19144 (2017).
[Crossref]

Cakmak, B.

Capmany, J.

D. Marpaung, J. P. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Commun. 13(2), 80–90 (2019).
[Crossref]

Chang, Y. J.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Chaudhari, B. S.

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Chen, B.

Chen, H.

Chen, J.

J. Chen, T. Zhang, J. Zhu, and X. Zhang, “Low-loss planar optical waveguides fabricated from polycarbonate,” Polym. Eng. Sci. 49(10), 2015–2019 (2009).
[Crossref]

Chen, K. X.

Q. Q. Song, K. X. Chen, and Z. F. Hu, “Low-Power Broadband Thermo-Optic Switch With Weak Polarization Dependence Using a Segmented Graphene Heater,” J. Lightwave Technol. 38(6), 1358–1364 (2020).
[Crossref]

X. Z. Zi, L. F. Wang, K. X. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

Chen, L.

Chen, R. B.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Chen, R. T.

J. H. Kim and R. T. Chen, “A collimation mirror in polymeric planar waveguide formed by reactive ion etching,” IEEE Photonics Technol. Lett. 15(3), 422–424 (2003).
[Crossref]

Chen, Y.

C. Qiu, Y. Wang, and Y. Chen, “Design and Analysis of a Novel Graphene-Assisted Silica/Polymer Hybrid Waveguide with Thermal-Optical Phase Modulation Structure,” IEEE Photonics J. 11(2), 1–10 (2019).
[Crossref]

Cheng, X. F.

L. Y. Zhou, Z. W. Xu, X. F. Cheng, and Q. R. Huang, “An optical circuit switching network architecture and reconfiguration schemes for datacenter,” Opt. Commun. 335, 250–256 (2015).
[Crossref]

Chiang, K. S.

X. B. Wang and K. S. Chiang, “Polarization-insensitive mode-independent thermo-optic switch based on symmetric waveguide directional coupler,” Opt. Express 27(24), 35385–35393 (2019).
[Crossref]

X. Z. Zi, L. F. Wang, K. X. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

Q. D. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 1–14 (2018).
[Crossref]

W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
[Crossref]

Chow, C. W.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Chua, S. J.

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Crean, G.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Dai, D. X.

D. X. Dai and S. L. He, “Ultrasmall overlapped arrayed-waveguide grating, based on Si nanowire waveguides for dense wavelength division demultiplexing,” IEEE J. Sel. Top. Quant. Electron. 12(6), 1301–1305 (2006).
[Crossref]

Dalton, L. R.

H. Ma, A. K. Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: Materials, processing, and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[Crossref]

Diehl, J. F.

V. J. Urick, J. F. Diehl, C. E. Sunderman, J. D. McKinney, and K. J. Williams, “An optical technique for radio frequency interference mitigation,” IEEE Photonics Technol. Lett. 27(12), 1333–1336 (2015).
[Crossref]

Ding, S. X.

S. X. Ding, C. X. Wang, X. Y. Shi, and J. W. Zou, “Directly written photo-crosslinked fluorinated polycarbonate photoresist materials for second-order nonlinear optical (NLO) applications,” J. Mater. Chem. C 7(16), 4667–4672 (2019).
[Crossref]

Disawal, S.

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

Doerr, C. R.

Dong, Y.

Y. Yuan, J. Li, Y. Dong, and H. Miao, “UV-curable fluorinated polycarbonate polyurethane with improved surface properties,” JCT Res. 17(3), 777–783 (2020).
[Crossref]

Drakos, A.

Dupuis, N.

Eldada, L.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quant. 6(1), 54–68 (2000).
[Crossref]

Elghanian, R.

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

Elizalde, J.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Fathi, M. T.

Feng, X. L.

Fitzgerald, E. A.

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Fragala, J.

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

Gao, S. M.

Gardner, R. D.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Gaviot, E.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

Ghayour, R.

Goullet, A.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

Grossard, N.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

Gu, C. S.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Guo, B. S.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Hamoudi, A.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

He, S. L.

Y. C. Shi, S. Anand, and S. L. He, “Design of a polarization insensitive triplexer using directional couplers based on submicron silicon rib waveguides,” J. Lightwave Technol. 27(11), 1443–1447 (2009).
[Crossref]

D. X. Dai and S. L. He, “Ultrasmall overlapped arrayed-waveguide grating, based on Si nanowire waveguides for dense wavelength division demultiplexing,” IEEE J. Sel. Top. Quant. Electron. 12(6), 1301–1305 (2006).
[Crossref]

Hernandez-Figueroa, H.

U. Roggero and H. Hernandez-Figueroa, “Polymeric power splitters for multiplexing optical biosensors,” Opt. Laser Technol. 127, 106127 (2020).
[Crossref]

Hu, Z. F.

Hua, P. R.

P. R. Hua, D. L. Zhang, and E. Y. B. Pun, “Long-period grating on strip Ti:LiNbO3 waveguide embedded in planar Ti:LiNbO3 waveguide,” IEEE Photonics Technol. Lett. 22(18), 1361–1363 (2010).
[Crossref]

Huang, Q. A.

Z. Zhen, Z. F. Zhou, Q. A. Huang, and W. H. Li, “Modeling, simulation and experimental verification of inclined UV lithography for SU-8 negative thick photoresists,” J. Micromech. Microeng. 18(12), 125017 (2008).
[Crossref]

Huang, Q. D.

Q. D. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 1–14 (2018).
[Crossref]

Huang, Q. R.

L. Y. Zhou, Z. W. Xu, X. F. Cheng, and Q. R. Huang, “An optical circuit switching network architecture and reconfiguration schemes for datacenter,” Opt. Commun. 335, 250–256 (2015).
[Crossref]

Hunter, D. K.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Hwang, W. Y.

Y. O. Noh, C. H. Lee, J. M. Kim, W. Y. Hwang, and Y. H. Won, “Polymer waveguide variable optical attenuator and its reliability,” Opt. Commun. 242(4-6), 533–540 (2004).
[Crossref]

Jen, A. K. Y.

H. Ma, A. K. Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: Materials, processing, and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[Crossref]

Jézéquel, G.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet, G. Jézéquel, and E. Gaviot, “Marcatili's extended approach: Comparison to semi-vectorial methods applied to pedestal waveguide design,” J. Opt. A: Pure Appl. Opt. 10(5), 055310 (2008).
[Crossref]

Jian, X.

G. Li, J. Wang, G. Yu, and X. Jian, “Synthesis and characterization of partly fluorinated poly(phthalazinone ether)s crosslinked by allyl group for passive optical waveguides,” Polymer 51(6), 1524–1529 (2010).
[Crossref]

Jiang, S. J.

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Jin, W.

W. Jin and K. S. Chiang, “Three-dimensional long-period waveguide gratings for mode-division-multiplexing applications,” Opt. Express 26(12), 15289–15299 (2018).
[Crossref]

Q. D. Huang, K. S. Chiang, and W. Jin, “Thermo-optically controlled vertical waveguide directional couplers for mode-selective switching,” IEEE Photonics J. 10(6), 1–14 (2018).
[Crossref]

Kewell, A.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Kim, J. H.

J. H. Kim and R. T. Chen, “A collimation mirror in polymeric planar waveguide formed by reactive ion etching,” IEEE Photonics Technol. Lett. 15(3), 422–424 (2003).
[Crossref]

Kim, J. M.

Y. O. Noh, C. H. Lee, J. M. Kim, W. Y. Hwang, and Y. H. Won, “Polymer waveguide variable optical attenuator and its reliability,” Opt. Commun. 242(4-6), 533–540 (2004).
[Crossref]

Krueger, J.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Lee, C. H.

Y. O. Noh, C. H. Lee, J. M. Kim, W. Y. Hwang, and Y. H. Won, “Polymer waveguide variable optical attenuator and its reliability,” Opt. Commun. 242(4-6), 533–540 (2004).
[Crossref]

Li, B. J.

B. J. Li, S. J. Chua, E. A. Fitzgerald, B. S. Chaudhari, S. J. Jiang, and Z. G. Cai, “Intelligent integration of optical power splitter with optically switchable cross-connect based on multimode interference principle in SiGe/Si,” Appl. Phys. Lett. 85(7), 1119–1121 (2004).
[Crossref]

Li, G.

G. Li, J. Wang, G. Yu, and X. Jian, “Synthesis and characterization of partly fluorinated poly(phthalazinone ether)s crosslinked by allyl group for passive optical waveguides,” Polymer 51(6), 1524–1529 (2010).
[Crossref]

Li, J.

Y. Yuan, J. Li, Y. Dong, and H. Miao, “UV-curable fluorinated polycarbonate polyurethane with improved surface properties,” JCT Res. 17(3), 777–783 (2020).
[Crossref]

Li, M.

Z. Cai, H. Yu, Y. Zhang, and M. Li, “Synthesis and characterization of novel fluorinated polycarbonate negative-type photoresist for optical waveguide,” Polymer 61, 140–146 (2015).
[Crossref]

Li, W. H.

Z. Zhen, Z. F. Zhou, Q. A. Huang, and W. H. Li, “Modeling, simulation and experimental verification of inclined UV lithography for SU-8 negative thick photoresists,” J. Micromech. Microeng. 18(12), 125017 (2008).
[Crossref]

Ma, H.

H. Ma, A. K. Y. Jen, and L. R. Dalton, “Polymer-based optical waveguides: Materials, processing, and devices,” Adv. Mater. 14(19), 1339–1365 (2002).
[Crossref]

Marpaung, D.

D. Marpaung, J. P. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Commun. 13(2), 80–90 (2019).
[Crossref]

Marsh, J. H.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Mayora, K.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

McKinney, J. D.

V. J. Urick, J. F. Diehl, C. E. Sunderman, J. D. McKinney, and K. J. Williams, “An optical technique for radio frequency interference mitigation,” IEEE Photonics Technol. Lett. 27(12), 1333–1336 (2015).
[Crossref]

McLaughlin, A. J.

R. D. Gardner, I. Andonovic, D. K. Hunter, A. Hamoudi, A. J. McLaughlin, J. S. Aitchison, and J. H. Marsh, “Multi-gigabit WDM optical networking for next generation avionics system communications,” Opt. Laser Eng. 33(4), 277–297 (2000).
[Crossref]

Miao, H.

Y. Yuan, J. Li, Y. Dong, and H. Miao, “UV-curable fluorinated polycarbonate polyurethane with improved surface properties,” JCT Res. 17(3), 777–783 (2020).
[Crossref]

Moynihan, S.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Noh, Y. O.

Y. O. Noh, C. H. Lee, J. M. Kim, W. Y. Hwang, and Y. H. Won, “Polymer waveguide variable optical attenuator and its reliability,” Opt. Commun. 242(4-6), 533–540 (2004).
[Crossref]

Orphanoudakis, T. G.

Pun, E. Y. B.

P. R. Hua, D. L. Zhang, and E. Y. B. Pun, “Long-period grating on strip Ti:LiNbO3 waveguide embedded in planar Ti:LiNbO3 waveguide,” IEEE Photonics Technol. Lett. 22(18), 1361–1363 (2010).
[Crossref]

Qiu, C.

C. Qiu, Y. Wang, and Y. Chen, “Design and Analysis of a Novel Graphene-Assisted Silica/Polymer Hybrid Waveguide with Thermal-Optical Phase Modulation Structure,” IEEE Photonics J. 11(2), 1–10 (2019).
[Crossref]

Qiu, F.

Qiu, M.

Y. Song, J. Wang, M. Yan, and M. Qiu, “Efficient coupling between dielectric and hybrid plasmonic waveguides by multimode interference power splitter,” J. Opt. 13(7), 075002 (2011).
[Crossref]

Redmond, G.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Roggero, U.

U. Roggero and H. Hernandez-Figueroa, “Polymeric power splitters for multiplexing optical biosensors,” Opt. Laser Technol. 127, 106127 (2020).
[Crossref]

Ruano-Lopez, J. M.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Shacklette, L. W.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quant. 6(1), 54–68 (2000).
[Crossref]

Shi, X. Y.

S. X. Ding, C. X. Wang, X. Y. Shi, and J. W. Zou, “Directly written photo-crosslinked fluorinated polycarbonate photoresist materials for second-order nonlinear optical (NLO) applications,” J. Mater. Chem. C 7(16), 4667–4672 (2019).
[Crossref]

Z. Z. Cai, Q. X. Yu, Y. Zheng, X. Y. Shi, and X. S. Wang, “Effect of fluoro-polycarbonates containing aliphatic/aromatic segments on the characteristics of thermo-optic waveguide devices,” RSC Adv. 7(31), 19136–19144 (2017).
[Crossref]

Shi, Y. C.

Shile, R.

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

Song, Q. Q.

Song, Y.

Y. Song, J. Wang, M. Yan, and M. Qiu, “Efficient coupling between dielectric and hybrid plasmonic waveguides by multimode interference power splitter,” J. Opt. 13(7), 075002 (2011).
[Crossref]

Spring, A.

Stavdas, A.

Sunderman, C. E.

V. J. Urick, J. F. Diehl, C. E. Sunderman, J. D. McKinney, and K. J. Williams, “An optical technique for radio frequency interference mitigation,” IEEE Photonics Technol. Lett. 27(12), 1333–1336 (2015).
[Crossref]

Taheri, A. N.

Tang, T. T.

Tijero, M.

J. M. Ruano-Lopez, M. Aguirregabiria, M. Tijero, M. T. Arroyo, J. Elizalde, J. Berganzo, I. Aranburu, F. J. Blanco, and K. Mayora, “A new SU-8 process to integrate buried waveguides and sealed microchannels for a Lab-on-a-Chip,” Sens. Actuators, B 114(1), 542–551 (2006).
[Crossref]

Tseng, M. C.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Urick, V. J.

V. J. Urick, J. F. Diehl, C. E. Sunderman, J. D. McKinney, and K. J. Williams, “An optical technique for radio frequency interference mitigation,” IEEE Photonics Technol. Lett. 27(12), 1333–1336 (2015).
[Crossref]

Van Deun, R.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

von Papen, G.

S. Moynihan, R. Van Deun, K. Binnemans, J. Krueger, G. von Papen, A. Kewell, G. Crean, and G. Redmond, “Organo-lanthanide complexes as luminescent dopants in polymer waveguides fabricated by hot embossing,” Opt. Mater. 29(12), 1798–1808 (2007).
[Crossref]

Wang, C. X.

S. X. Ding, C. X. Wang, X. Y. Shi, and J. W. Zou, “Directly written photo-crosslinked fluorinated polycarbonate photoresist materials for second-order nonlinear optical (NLO) applications,” J. Mater. Chem. C 7(16), 4667–4672 (2019).
[Crossref]

Wang, J.

Y. Song, J. Wang, M. Yan, and M. Qiu, “Efficient coupling between dielectric and hybrid plasmonic waveguides by multimode interference power splitter,” J. Opt. 13(7), 075002 (2011).
[Crossref]

G. Li, J. Wang, G. Yu, and X. Jian, “Synthesis and characterization of partly fluorinated poly(phthalazinone ether)s crosslinked by allyl group for passive optical waveguides,” Polymer 51(6), 1524–1529 (2010).
[Crossref]

Wang, L. F.

X. Z. Zi, L. F. Wang, K. X. Chen, and K. S. Chiang, “Mode-selective switch based on thermo-optic asymmetric directional coupler,” IEEE Photonics Technol. Lett. 30(7), 618–621 (2018).
[Crossref]

Wang, S. P.

Wang, X. B.

Wang, X. S.

Z. Z. Cai, Q. X. Yu, Y. Zheng, X. Y. Shi, and X. S. Wang, “Effect of fluoro-polycarbonates containing aliphatic/aromatic segments on the characteristics of thermo-optic waveguide devices,” RSC Adv. 7(31), 19136–19144 (2017).
[Crossref]

Wang, Y.

C. Qiu, Y. Wang, and Y. Chen, “Design and Analysis of a Novel Graphene-Assisted Silica/Polymer Hybrid Waveguide with Thermal-Optical Phase Modulation Structure,” IEEE Photonics J. 11(2), 1–10 (2019).
[Crossref]

Williams, K. J.

V. J. Urick, J. F. Diehl, C. E. Sunderman, J. D. McKinney, and K. J. Williams, “An optical technique for radio frequency interference mitigation,” IEEE Photonics Technol. Lett. 27(12), 1333–1336 (2015).
[Crossref]

Won, Y. H.

Y. O. Noh, C. H. Lee, J. M. Kim, W. Y. Hwang, and Y. H. Won, “Polymer waveguide variable optical attenuator and its reliability,” Opt. Commun. 242(4-6), 533–540 (2004).
[Crossref]

Xu, Z. W.

L. Y. Zhou, Z. W. Xu, X. F. Cheng, and Q. R. Huang, “An optical circuit switching network architecture and reconfiguration schemes for datacenter,” Opt. Commun. 335, 250–256 (2015).
[Crossref]

Yan, M.

Y. Song, J. Wang, M. Yan, and M. Qiu, “Efficient coupling between dielectric and hybrid plasmonic waveguides by multimode interference power splitter,” J. Opt. 13(7), 075002 (2011).
[Crossref]

Yao, J. P.

D. Marpaung, J. P. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Commun. 13(2), 80–90 (2019).
[Crossref]

Yeh, C. H.

C. H. Yeh, C. S. Gu, B. S. Guo, Y. J. Chang, C. W. Chow, M. C. Tseng, and R. B. Chen, “Hybrid free space optical communication system and passive optical network with high splitting ratio for broadcasting data traffic,” J. Opt. 20(12), 125702 (2018).
[Crossref]

Yokoyama, S.

Yu, F.

Yu, G.

G. Li, J. Wang, G. Yu, and X. Jian, “Synthesis and characterization of partly fluorinated poly(phthalazinone ether)s crosslinked by allyl group for passive optical waveguides,” Polymer 51(6), 1524–1529 (2010).
[Crossref]

Yu, H.

Z. Cai, H. Yu, Y. Zhang, and M. Li, “Synthesis and characterization of novel fluorinated polycarbonate negative-type photoresist for optical waveguide,” Polymer 61, 140–146 (2015).
[Crossref]

Yu, Q. X.

Z. Z. Cai, Q. X. Yu, Y. Zheng, X. Y. Shi, and X. S. Wang, “Effect of fluoro-polycarbonates containing aliphatic/aromatic segments on the characteristics of thermo-optic waveguide devices,” RSC Adv. 7(31), 19136–19144 (2017).
[Crossref]

Yuan, Y.

Y. Yuan, J. Li, Y. Dong, and H. Miao, “UV-curable fluorinated polycarbonate polyurethane with improved surface properties,” JCT Res. 17(3), 777–783 (2020).
[Crossref]

Zhang, D. L.

P. R. Hua, D. L. Zhang, and E. Y. B. Pun, “Long-period grating on strip Ti:LiNbO3 waveguide embedded in planar Ti:LiNbO3 waveguide,” IEEE Photonics Technol. Lett. 22(18), 1361–1363 (2010).
[Crossref]

Zhang, H.

H. Zhang, N. A. Amro, S. Disawal, R. Elghanian, R. Shile, and J. Fragala, “Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching,” Appl. Surf. Sci. 253(4), 1960–1963 (2006).
[Crossref]

Zhang, T.

J. Chen, T. Zhang, J. Zhu, and X. Zhang, “Low-loss planar optical waveguides fabricated from polycarbonate,” Polym. Eng. Sci. 49(10), 2015–2019 (2009).
[Crossref]

Zhang, X.

J. Chen, T. Zhang, J. Zhu, and X. Zhang, “Low-loss planar optical waveguides fabricated from polycarbonate,” Polym. Eng. Sci. 49(10), 2015–2019 (2009).
[Crossref]

Zhang, Y.

Z. Cai, H. Yu, Y. Zhang, and M. Li, “Synthesis and characterization of novel fluorinated polycarbonate negative-type photoresist for optical waveguide,” Polymer 61, 140–146 (2015).
[Crossref]

Zhen, Z.

Z. Zhen, Z. F. Zhou, Q. A. Huang, and W. H. Li, “Modeling, simulation and experimental verification of inclined UV lithography for SU-8 negative thick photoresists,” J. Micromech. Microeng. 18(12), 125017 (2008).
[Crossref]

Zheng, Y.

Z. Z. Cai, Q. X. Yu, Y. Zheng, X. Y. Shi, and X. S. Wang, “Effect of fluoro-polycarbonates containing aliphatic/aromatic segments on the characteristics of thermo-optic waveguide devices,” RSC Adv. 7(31), 19136–19144 (2017).
[Crossref]

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Figures (12)

Fig. 1.
Fig. 1. The specific synthesis process and molecular structure of the AF-Z-PC MA polymer.
Fig. 2.
Fig. 2. Thermal stability and optical transmission loss of AF-Z-PC-MA. (a) DSC test curves, (b) TGA test curves, (c) the UV-vis-NIR absorbance spectrum.
Fig. 3.
Fig. 3. AF-Z-PC MA thin film physical properties. (a) Refractive index of AF-Z-PC MA thin film measured by ellipsometer and (b) surface morphology of AF-Z-PC MA thin film scanned by AFM.
Fig. 4.
Fig. 4. Structural diagrams of the optical waveguide TO switch. (a) 3D schematic diagram of the waveguide chip; (b) 2D cross-sectional structure of the waveguide chip.
Fig. 5.
Fig. 5. Relationships (a) between N1 and core layer thickness b; (b) between N2 and core layer thickness b; (c) mode birefringence between ΔN1 and b for TE0 and TM0 modes.
Fig. 6.
Fig. 6. The mode profile distributions of waveguide core and cladding layers simulated by the COMSOL Multiphysics software. (a) TM0 and TE0 fundamental optical modes in the waveguide core region, (b)-(d) TM−1 surface plasmon polariton (SPP) mode, TE0 mode, and TM1 optical mode in the waveguide cladding regions.
Fig. 7.
Fig. 7. Optical and thermal field simulation results. (a) Optical field distribution state; (b) thermal field distribution state; (c) on-state before thermal modulation; (d) off-state after thermal modulation.
Fig. 8.
Fig. 8. Preparation process for bottom-metal-printed waveguide TO switch.
Fig. 9.
Fig. 9. Micrographs of the waveguide TO switch. (a) and (b) images of the waveguide splitting segments and electrode (×50); (c) and (d) images of the waveguide input and branch sections (×1200).
Fig. 10.
Fig. 10. (a) Coupling test photograph of the waveguide chip, (b) output near-infrared field image captured by CCD camera.
Fig. 11.
Fig. 11. Actual performances of the waveguide chip. (a) Waveguide propagation loss measured by the cut-back measurement method, (b) output optical power intensity of the waveguide TO switch.
Fig. 12.
Fig. 12. TO switch on-off time curves at 1550 nm.

Tables (1)

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Table 1. Performances comparison with previously reported polymer TO switch chips.

Equations (5)

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k 0 b ( n 1 2 N 1 2 ) 1 2 = n π + a r c t a n n 1 2 n 2 2 ( N 1 2 n 2 2 ) 1 2 ( n 1 2 N 1 2 ) 2 1 + a r c t a n n 1 2 n 3 2 ( N 1 2 n 3 2 ) 1 2 δ 3 ( n 1 2 N 1 2 ) 1 2 ( n = 0 , 1 , 2 , )
δ 3 = 1 + ε 3 ( N 1 2 n 4 2 ) 1 2 ε 4 ( N 1 2 n 3 2 ) 1 2 ε 3 ( N 1 2 n 4 2 ) 1 2 + ε 4 ( N 1 2 n 3 2 ) 1 2 exp [ 2 k 0 ε 3 ( N 1 2 n 3 2 ) 1 2 h ] 1 ε 3 ( N 1 2 n 4 2 ) 1 2 ε 4 ( N 1 2 n 3 2 ) 1 2 ε 3 ( N 1 2 n 4 2 ) 1 2 + ε 4 ( N 1 2 n 3 2 ) 1 2 exp [ 2 k 0 ε 3 ( N 1 2 n 3 2 ) 1 2 h ] ε 3 = n 3 2 k 3 2 , ε 4 = n 4 2
k 0 b ( n 1 2 N 2 2 ) 1 2 = n π + a r c t a n n 1 2 n 2 2 ( N 2 2 n 2 2 ) 1 2 ( n 1 2 N 2 2 ) 1 2   + a r c t a n n 1 2 n 4 2 ( N 2 2 n 4 2 ) 1 2 ( n 1 2 N 2 2 ) 1 2 ( n = 0 , 1 , 2 , )
k 0 w ( N 1 2 N 2 ) 1 2 = m π + 2 a r c t a n N 1 2 ( N 2 N 2 2 ) 1 2 N 2 2 ( N 1 2 N 2 ) 1 2 ( m = 0 , 1 , 2 , )
L o s s   ( i n s e r t i o n )   =   L o s s   ( c o u p l i n g )   +   α ×   L