Abstract

A statistically optimized design method suitable for a polarization-independent and temperature-insensitive broadband waveguide coupler is proposed. By use of this method, a fluorinated polyimide waveguide 3-dB waveguide coupler for 1490 ∼ 1610 nm application is designed by optimizing polarization and temperature fluctuation. The validity of the design is verified through simulation based on the three-dimensional beam propagation method (3D-BPM), which revealed a coupling ratio of 50 ± 0.8% in a 120-nm bandwidth in the temperature range -10 to 40 °C for both orthogonal polarizations.

© 2003 Optical Society of America

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  1. A. Takagi, K. Jinguji, M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers(WINC’s) with series-tapered coupling structure,” IEEE J. Lightwave Technol. 10, 1815–1824 (1992).
    [CrossRef]
  2. A. Takagi, K. Jinguji, M. Kawachi, “Design and fabrication of broadband silicon-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum. Electron. 28, 848–855 (1992).
    [CrossRef]
  3. R. Reuter, H. Franke, C. Feger, “Evaluating polyimides as lightguide materials,” Appl. Opt. 27, 4565–4571 (1988).
    [CrossRef] [PubMed]
  4. J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
    [CrossRef]
  5. T. Kurokawa, N. Takato, Y. Katayama, “Polymer optical circuits for multimode optical fiber systems,” Appl. Opt. 19, 3124–3129 (1980).
    [CrossRef] [PubMed]
  6. D. H. Hartman, G. R. Lalk, J. W. Howse, R. R. Krchnavek, “Radiant cured polymer optical waveguides on printed circuit boards for photonic interconnection use,” Appl. Opt. 28, 40–47 (1989).
    [CrossRef] [PubMed]
  7. B. L. Booth, “Low loss channel waveguides in polymers,” IEEE J. Lightwave Technol. 7, 1445–1453 (1989).
    [CrossRef]
  8. N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).
  9. T. Matsuura, J. Kobayashi, S. Ando, T. Maruno, S. Sasaki, F. Yamamoto, “Heat-resistant flexible-film optical waveguides from fluorinated polyimides,” Appl. Opt. 38, 966–971 (1999).
    [CrossRef]
  10. J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
    [CrossRef]
  11. T. Kaino, M. Fujiki, S. Oikawa, S. Nara, “Low-loss plastic fibers,” Appl. Opt. 20, 2886–2888 (1981).
    [CrossRef] [PubMed]
  12. S. Imamura, R. Yoshimura, T. Izawa, “Polymer channel waveguides with low loss at 1.3 μm,” Electron. Lett. 27, 1342–1343 (1991).
    [CrossRef]
  13. Y. Kokubun, S. Yoneda, H. Tanaka, “Temperature-independent narrowband optical filter at 1.3 μm wavelength by an athermal waveguide,” Electron. Lett. 32, 1998–2000 (1996).
    [CrossRef]
  14. H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
    [CrossRef]
  15. K. C. Ho, C. K. Seng, “Study of polarization-dependent coupling in optical waveguide directional couplers by the effective-index method with built-in perturbation correction,” IEEE J. Lightwave Technol. 20, 1018–1026 (2002).
    [CrossRef]
  16. B. X. Chen, Y. F. Yuan, M. Iso, “Design of wide wavelength-insensitive coupler using statistical optimum method,” Acta Optica Sinica 21, 996–1000 (2001).
  17. N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).
  18. T. Nose, S. Nakahama, S. Miyata, Daigakuin Koubunshikagaku (Koudansha Scientific Co., Ltd., Tokyo, Japan, 1997).
  19. H. Nishihara, M. Haruna, T. Suhara, Optical Integrated Circuit (Ohm Co., Ltd., Tokyo, Japan, 1993).

2002

K. C. Ho, C. K. Seng, “Study of polarization-dependent coupling in optical waveguide directional couplers by the effective-index method with built-in perturbation correction,” IEEE J. Lightwave Technol. 20, 1018–1026 (2002).
[CrossRef]

2001

B. X. Chen, Y. F. Yuan, M. Iso, “Design of wide wavelength-insensitive coupler using statistical optimum method,” Acta Optica Sinica 21, 996–1000 (2001).

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

1999

1998

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

1996

Y. Kokubun, S. Yoneda, H. Tanaka, “Temperature-independent narrowband optical filter at 1.3 μm wavelength by an athermal waveguide,” Electron. Lett. 32, 1998–2000 (1996).
[CrossRef]

1995

H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
[CrossRef]

1994

N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).

1992

A. Takagi, K. Jinguji, M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers(WINC’s) with series-tapered coupling structure,” IEEE J. Lightwave Technol. 10, 1815–1824 (1992).
[CrossRef]

A. Takagi, K. Jinguji, M. Kawachi, “Design and fabrication of broadband silicon-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum. Electron. 28, 848–855 (1992).
[CrossRef]

1991

S. Imamura, R. Yoshimura, T. Izawa, “Polymer channel waveguides with low loss at 1.3 μm,” Electron. Lett. 27, 1342–1343 (1991).
[CrossRef]

1989

D. H. Hartman, G. R. Lalk, J. W. Howse, R. R. Krchnavek, “Radiant cured polymer optical waveguides on printed circuit boards for photonic interconnection use,” Appl. Opt. 28, 40–47 (1989).
[CrossRef] [PubMed]

B. L. Booth, “Low loss channel waveguides in polymers,” IEEE J. Lightwave Technol. 7, 1445–1453 (1989).
[CrossRef]

N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).

1988

1981

1980

Ando, S.

Booth, B. L.

B. L. Booth, “Low loss channel waveguides in polymers,” IEEE J. Lightwave Technol. 7, 1445–1453 (1989).
[CrossRef]

Chen, B. X.

B. X. Chen, Y. F. Yuan, M. Iso, “Design of wide wavelength-insensitive coupler using statistical optimum method,” Acta Optica Sinica 21, 996–1000 (2001).

Feger, C.

Franke, H.

Fujiki, M.

Hanawa, F.

N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).

Hartman, D. H.

Haruna, M.

H. Nishihara, M. Haruna, T. Suhara, Optical Integrated Circuit (Ohm Co., Ltd., Tokyo, Japan, 1993).

Hida, Y.

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

Ho, K. C.

K. C. Ho, C. K. Seng, “Study of polarization-dependent coupling in optical waveguide directional couplers by the effective-index method with built-in perturbation correction,” IEEE J. Lightwave Technol. 20, 1018–1026 (2002).
[CrossRef]

Howse, J. W.

Imamura, S.

S. Imamura, R. Yoshimura, T. Izawa, “Polymer channel waveguides with low loss at 1.3 μm,” Electron. Lett. 27, 1342–1343 (1991).
[CrossRef]

Inoue, Y.

H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
[CrossRef]

Iso, M.

B. X. Chen, Y. F. Yuan, M. Iso, “Design of wide wavelength-insensitive coupler using statistical optimum method,” Acta Optica Sinica 21, 996–1000 (2001).

Izawa, T.

S. Imamura, R. Yoshimura, T. Izawa, “Polymer channel waveguides with low loss at 1.3 μm,” Electron. Lett. 27, 1342–1343 (1991).
[CrossRef]

Jinguji, K.

A. Takagi, K. Jinguji, M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers(WINC’s) with series-tapered coupling structure,” IEEE J. Lightwave Technol. 10, 1815–1824 (1992).
[CrossRef]

A. Takagi, K. Jinguji, M. Kawachi, “Design and fabrication of broadband silicon-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum. Electron. 28, 848–855 (1992).
[CrossRef]

Kaino, T.

Kang, J. W.

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

Katayama, Y.

Kawachi, M.

A. Takagi, K. Jinguji, M. Kawachi, “Design and fabrication of broadband silicon-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum. Electron. 28, 848–855 (1992).
[CrossRef]

A. Takagi, K. Jinguji, M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers(WINC’s) with series-tapered coupling structure,” IEEE J. Lightwave Technol. 10, 1815–1824 (1992).
[CrossRef]

Keil, N.

N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).

Kim, J. J.

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

Kim, J. P.

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

Kim, S. J. S.

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

Kobayashi, J.

T. Matsuura, J. Kobayashi, S. Ando, T. Maruno, S. Sasaki, F. Yamamoto, “Heat-resistant flexible-film optical waveguides from fluorinated polyimides,” Appl. Opt. 38, 966–971 (1999).
[CrossRef]

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

Kokubun, Y.

Y. Kokubun, S. Yoneda, H. Tanaka, “Temperature-independent narrowband optical filter at 1.3 μm wavelength by an athermal waveguide,” Electron. Lett. 32, 1998–2000 (1996).
[CrossRef]

Krchnavek, R. R.

Kurokawa, T.

Lalk, G. R.

Lee, J. S.

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

Lee, W. Y.

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

Maruno, T.

T. Matsuura, J. Kobayashi, S. Ando, T. Maruno, S. Sasaki, F. Yamamoto, “Heat-resistant flexible-film optical waveguides from fluorinated polyimides,” Appl. Opt. 38, 966–971 (1999).
[CrossRef]

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

Matsuura, T.

T. Matsuura, J. Kobayashi, S. Ando, T. Maruno, S. Sasaki, F. Yamamoto, “Heat-resistant flexible-film optical waveguides from fluorinated polyimides,” Appl. Opt. 38, 966–971 (1999).
[CrossRef]

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

Miyata, S.

T. Nose, S. Nakahama, S. Miyata, Daigakuin Koubunshikagaku (Koudansha Scientific Co., Ltd., Tokyo, Japan, 1997).

Nakahama, S.

T. Nose, S. Nakahama, S. Miyata, Daigakuin Koubunshikagaku (Koudansha Scientific Co., Ltd., Tokyo, Japan, 1997).

Nara, S.

Nishihara, H.

H. Nishihara, M. Haruna, T. Suhara, Optical Integrated Circuit (Ohm Co., Ltd., Tokyo, Japan, 1993).

Nose, T.

T. Nose, S. Nakahama, S. Miyata, Daigakuin Koubunshikagaku (Koudansha Scientific Co., Ltd., Tokyo, Japan, 1997).

Oda, K.

H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
[CrossRef]

Oguchi, T.

N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).

Oikawa, S.

Okamoto, K.

N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).

Reuter, R.

Sasaki, S.

T. Matsuura, J. Kobayashi, S. Ando, T. Maruno, S. Sasaki, F. Yamamoto, “Heat-resistant flexible-film optical waveguides from fluorinated polyimides,” Appl. Opt. 38, 966–971 (1999).
[CrossRef]

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

Seng, C. K.

K. C. Ho, C. K. Seng, “Study of polarization-dependent coupling in optical waveguide directional couplers by the effective-index method with built-in perturbation correction,” IEEE J. Lightwave Technol. 20, 1018–1026 (2002).
[CrossRef]

Strebel, B.

N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).

Suhara, T.

H. Nishihara, M. Haruna, T. Suhara, Optical Integrated Circuit (Ohm Co., Ltd., Tokyo, Japan, 1993).

Takagi, A.

A. Takagi, K. Jinguji, M. Kawachi, “Design and fabrication of broadband silicon-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum. Electron. 28, 848–855 (1992).
[CrossRef]

A. Takagi, K. Jinguji, M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers(WINC’s) with series-tapered coupling structure,” IEEE J. Lightwave Technol. 10, 1815–1824 (1992).
[CrossRef]

Takahashi, H.

H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
[CrossRef]

Takato, N.

N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).

T. Kurokawa, N. Takato, Y. Katayama, “Polymer optical circuits for multimode optical fiber systems,” Appl. Opt. 19, 3124–3129 (1980).
[CrossRef] [PubMed]

Tanaka, H.

Y. Kokubun, S. Yoneda, H. Tanaka, “Temperature-independent narrowband optical filter at 1.3 μm wavelength by an athermal waveguide,” Electron. Lett. 32, 1998–2000 (1996).
[CrossRef]

Toba, H.

H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
[CrossRef]

Yamamoto, F.

Yao, H. H.

N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).

Yoneda, S.

Y. Kokubun, S. Yoneda, H. Tanaka, “Temperature-independent narrowband optical filter at 1.3 μm wavelength by an athermal waveguide,” Electron. Lett. 32, 1998–2000 (1996).
[CrossRef]

Yoshimura, R.

S. Imamura, R. Yoshimura, T. Izawa, “Polymer channel waveguides with low loss at 1.3 μm,” Electron. Lett. 27, 1342–1343 (1991).
[CrossRef]

Yuan, Y. F.

B. X. Chen, Y. F. Yuan, M. Iso, “Design of wide wavelength-insensitive coupler using statistical optimum method,” Acta Optica Sinica 21, 996–1000 (2001).

Zawadzki, C.

N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).

Acta Optica Sinica

B. X. Chen, Y. F. Yuan, M. Iso, “Design of wide wavelength-insensitive coupler using statistical optimum method,” Acta Optica Sinica 21, 996–1000 (2001).

Appl. Opt.

Electron Lett.

N. Keil, H. H. Yao, C. Zawadzki, B. Strebel, “4 × 4 polymer thermo-optic directional coupler switch at 1.55 μm,” Electron Lett. 30, 1445–1453 (1989).

Electron. Lett.

S. Imamura, R. Yoshimura, T. Izawa, “Polymer channel waveguides with low loss at 1.3 μm,” Electron. Lett. 27, 1342–1343 (1991).
[CrossRef]

Y. Kokubun, S. Yoneda, H. Tanaka, “Temperature-independent narrowband optical filter at 1.3 μm wavelength by an athermal waveguide,” Electron. Lett. 32, 1998–2000 (1996).
[CrossRef]

IEEE J. Lightwave Technol.

H. Takahashi, K. Oda, H. Toba, Y. Inoue, “Transmission characteristics of arrayed waveguide N × N wavelength multiplexer,” IEEE J. Lightwave Technol. 13, 447–455 (1995).
[CrossRef]

K. C. Ho, C. K. Seng, “Study of polarization-dependent coupling in optical waveguide directional couplers by the effective-index method with built-in perturbation correction,” IEEE J. Lightwave Technol. 20, 1018–1026 (2002).
[CrossRef]

J. W. Kang, J. P. Kim, W. Y. Lee, S. J. S. Kim, J. S. Lee, J. J. Kim, “Low-loss fluorinated poly(arylene ether sulfide) waveguides with high thermal stability,” IEEE J. Lightwave Technol. 19, 872–875 (2001).
[CrossRef]

B. L. Booth, “Low loss channel waveguides in polymers,” IEEE J. Lightwave Technol. 7, 1445–1453 (1989).
[CrossRef]

J. Kobayashi, T. Matsuura, Y. Hida, S. Sasaki, T. Maruno, “Fluorinated polyimide waveguides with low polarization-dependent loss and their applications to thermooptic switches,” IEEE J. Lightwave Technol. 16, 1024–1029 (1998).
[CrossRef]

A. Takagi, K. Jinguji, M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers(WINC’s) with series-tapered coupling structure,” IEEE J. Lightwave Technol. 10, 1815–1824 (1992).
[CrossRef]

IEEE J. Quantum. Electron.

A. Takagi, K. Jinguji, M. Kawachi, “Design and fabrication of broadband silicon-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum. Electron. 28, 848–855 (1992).
[CrossRef]

NTT RD

N. Takato, F. Hanawa, K. Okamoto, T. Oguchi, “Optical couplers using silica-based planar lightwave circuits,” NTT RD 43, 1281–1288 (1994).

Other

T. Nose, S. Nakahama, S. Miyata, Daigakuin Koubunshikagaku (Koudansha Scientific Co., Ltd., Tokyo, Japan, 1997).

H. Nishihara, M. Haruna, T. Suhara, Optical Integrated Circuit (Ohm Co., Ltd., Tokyo, Japan, 1993).

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Figures (6)

Fig. 1
Fig. 1

(a) Construction of the Mach-Zehnder interferometer waveguide coupler used in the design. (b) Cross section of directional coupler.

Fig. 2
Fig. 2

Numerical calculation for the 3-dB waveguide coupler in fluorinated polyimide for the E11x mode.

Fig. 3
Fig. 3

Numerical calculation for the 3-dB waveguide coupler in fluorinated polyimide at 20 °C.

Fig. 4
Fig. 4

Relationship between 6FDA/TFDB ratio of fluorinated polyimide and refractive indices (n TE and n TM) measured with a prism coupler at 1550 nm.

Fig. 5
Fig. 5

Variation in the refractive index of fluorinated polyimide film with temperature as determined by the prism-coupling method.

Fig. 6
Fig. 6

Results of 3-dimensional BPM simulation for a 3-dB waveguide coupler in fluorinated polyimide.

Equations (16)

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

η=|Bout|2|Aout|2+|Bout|2=a2+b2+2ab cosβΔL
a=cosπ2Lc1L1+Le1sinπ2Lc2L2+Le2,
b=sinπ2Lc1L1+Le1cosπ2Lc2L2+Le2,
Lci=Lciλ, w, t, ng, nc, si, i=1, 2
Lei=Leiλ, w, t, ng, nc, si, i=1, 2
β=βλ, w, t, ng, nc.
ng=ngλ, T,
nc=ncλ, T,
ηλ, T=50%±δη,
|δηλ, T|λ=ηλ δλ<σλ,
|δηλ, T|T=ηT δT<σT,
δη=|δηλ, T|λ+|δηλ, T|T.
Dlmn=ηlmn-Q, l=1, 2; m=1, 2,, 6; n=1,2,, 7,
δ=lmn Dlmn2, l=1, 2; m=1, 2,, 6; n=1, 2,, 7.
Lc=πβe-βo,
Le=2Lcπcos-1ηs,

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