Abstract

A new GeS2-based chalcohalide glass was synthesized by the melt-quenching technique for nonlinear optical applications. A large glass-forming region was defined, and a wide infrared transmission was measured. Marked optical third-order nonlinearity was measured (n27.5×10-5 cm2/GW), making this glass one of the best candidates for ultrafast nonlinear optical applications. All-optical switching in the second telecommunication window (λ=1.31 μm) by control of the optical pulse intensity in a twin-core-fiber directional coupler was numerically modeled, and a crossover length of 9.25 mm was calculated.

© 1998 Optical Society of America

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References

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  1. M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
    [CrossRef]
  2. E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719–724 (1989).
    [CrossRef]
  3. M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2332 (1993).
    [CrossRef]
  4. S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
    [CrossRef]
  5. R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
    [CrossRef]
  6. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
    [CrossRef] [PubMed]
  7. G. I. Stegeman and R. H. Stolen, “Waveguides and fibers for nonlinear optics,” J. Opt. Soc. Am. B 6, 652–662 (1989).
    [CrossRef]
  8. M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
    [CrossRef]
  9. S. M. Jensen, “Analysis of nonlinear dual-core waveguides for switching operation,” IEEE J. Quantum Electron. QE-18, 1580–1588 (1982).
    [CrossRef]
  10. C. Yeh, “All-optical switching,” in Applied Photonics (Academic, San Diego, Calif., 1994), pp. 248–274.
  11. D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
    [CrossRef]
  12. H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
    [CrossRef]
  13. D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and thermal characteristics of Pr3+-doped GeS2- based chalcohalide glasses,” J. Non-Cryst. Solids 196, 314–319 (1996).
    [CrossRef]
  14. J. Heo, A. Sugitani, and J. D. Mackenzie, “New sulphide glasses in the ZrS2–K2S–GeS2 system,” J. Mater. Sci. Lett. 9, 29–35 (1990).
    [CrossRef]
  15. D. Marchese, “GeS2-based glasses for optical amplifiers and nonlinear optical devices,” M. Phil. thesis (Brunel University, Uxbridge, UK, 1995), pp. 54–91.
  16. P. Chandler, L. Zhang, and P. D. Townsend, “Optical waveguides formed by ion implementation,” Solid State Phenom. 27, 129–162 (1992).
    [CrossRef]
  17. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
    [CrossRef]
  18. M. D. Feit and J. A. Fleck, “Propagating beam interpretation of optical fiber cross coupling,” J. Opt. Soc. Am. 71, 1437–1443 (1981).

1997 (1)

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

1996 (2)

D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and thermal characteristics of Pr3+-doped GeS2- based chalcohalide glasses,” J. Non-Cryst. Solids 196, 314–319 (1996).
[CrossRef]

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

1994 (1)

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

1993 (1)

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2332 (1993).
[CrossRef]

1992 (2)

P. Chandler, L. Zhang, and P. D. Townsend, “Optical waveguides formed by ion implementation,” Solid State Phenom. 27, 129–162 (1992).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

1991 (1)

M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

1990 (2)

J. Heo, A. Sugitani, and J. D. Mackenzie, “New sulphide glasses in the ZrS2–K2S–GeS2 system,” J. Mater. Sci. Lett. 9, 29–35 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

1989 (3)

1987 (1)

S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
[CrossRef]

1982 (1)

S. M. Jensen, “Analysis of nonlinear dual-core waveguides for switching operation,” IEEE J. Quantum Electron. QE-18, 1580–1588 (1982).
[CrossRef]

1981 (1)

M. D. Feit and J. A. Fleck, “Propagating beam interpretation of optical fiber cross coupling,” J. Opt. Soc. Am. 71, 1437–1443 (1981).

Andrejco, M. J.

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
[CrossRef]

Asobe, M.

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2332 (1993).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

Chandler, P.

P. Chandler, L. Zhang, and P. D. Townsend, “Optical waveguides formed by ion implementation,” Solid State Phenom. 27, 129–162 (1992).
[CrossRef]

DeLong, K. W.

Ewen, P. J. S.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Feit, M. D.

M. D. Feit and J. A. Fleck, “Propagating beam interpretation of optical fiber cross coupling,” J. Opt. Soc. Am. 71, 1437–1443 (1981).

Fleck, J. A.

M. D. Feit and J. A. Fleck, “Propagating beam interpretation of optical fiber cross coupling,” J. Opt. Soc. Am. 71, 1437–1443 (1981).

Friberg, S. R.

S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
[CrossRef]

Fujiwara, S.

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

Hajto, E.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Heo, J.

J. Heo, A. Sugitani, and J. D. Mackenzie, “New sulphide glasses in the ZrS2–K2S–GeS2 system,” J. Mater. Sci. Lett. 9, 29–35 (1990).
[CrossRef]

Hirao, K.

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

Jensen, S. M.

S. M. Jensen, “Analysis of nonlinear dual-core waveguides for switching operation,” IEEE J. Quantum Electron. QE-18, 1580–1588 (1982).
[CrossRef]

Jha, A.

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and thermal characteristics of Pr3+-doped GeS2- based chalcohalide glasses,” J. Non-Cryst. Solids 196, 314–319 (1996).
[CrossRef]

Kakarantzas, G.

D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and thermal characteristics of Pr3+-doped GeS2- based chalcohalide glasses,” J. Non-Cryst. Solids 196, 314–319 (1996).
[CrossRef]

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

Kanamori, T.

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2332 (1993).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

Kanbara, H.

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

Kar, A. K.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Kosa, T.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Kubodera, K.

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2332 (1993).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

Lines, M. E.

M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

Mackenzie, J. D.

J. Heo, A. Sugitani, and J. D. Mackenzie, “New sulphide glasses in the ZrS2–K2S–GeS2 system,” J. Mater. Sci. Lett. 9, 29–35 (1990).
[CrossRef]

Marchese, D.

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and thermal characteristics of Pr3+-doped GeS2- based chalcohalide glasses,” J. Non-Cryst. Solids 196, 314–319 (1996).
[CrossRef]

Mizrahi, V.

Nasu, H.

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

Oliver, M. K.

S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
[CrossRef]

Owen, A. E.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Rangel-Rojo, R.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

Saifi, M. A.

Samson, B.

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

Silberg, Y.

S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
[CrossRef]

Stegeman, G. I.

Stolen, R. H.

Sugitani, A.

J. Heo, A. Sugitani, and J. D. Mackenzie, “New sulphide glasses in the ZrS2–K2S–GeS2 system,” J. Mater. Sci. Lett. 9, 29–35 (1990).
[CrossRef]

Tanaka, K.

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

Townsend, P. D.

P. Chandler, L. Zhang, and P. D. Townsend, “Optical waveguides formed by ion implementation,” Solid State Phenom. 27, 129–162 (1992).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

Vogel, E. M.

E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719–724 (1989).
[CrossRef]

Wang, J.

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

Wherrett, B. S.

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Zhang, L.

P. Chandler, L. Zhang, and P. D. Townsend, “Optical waveguides formed by ion implementation,” Solid State Phenom. 27, 129–162 (1992).
[CrossRef]

Appl. Phys. Lett. (2)

H. Kanbara, S. Fujiwara, K. Tanaka, H. Nasu, and K. Hirao, “Third-order nonlinear optical properties of chalcogenide glasses,” Appl. Phys. Lett. 70, 325–327 (1997).
[CrossRef]

S. R. Friberg, Y. Silberg, M. K. Oliver, and M. J. Andrejco, “Ultrafast all-optical switching in a twin-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135–1137 (1987).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2332 (1993).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760–766 (1990).
[CrossRef]

S. M. Jensen, “Analysis of nonlinear dual-core waveguides for switching operation,” IEEE J. Quantum Electron. QE-18, 1580–1588 (1982).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

J. Am. Ceram. Soc. (1)

E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719–724 (1989).
[CrossRef]

J. Appl. Phys. (1)

M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

J. Mater. Sci. Lett. (1)

J. Heo, A. Sugitani, and J. D. Mackenzie, “New sulphide glasses in the ZrS2–K2S–GeS2 system,” J. Mater. Sci. Lett. 9, 29–35 (1990).
[CrossRef]

J. Mod. Opt. (1)

D. Marchese, G. Kakarantzas, A. Jha, B. Samson, and J. Wang, “Spectroscopic and thermal properties of GeS2-based chalcohalide glasses,” J. Mod. Opt. 43, 963–970 (1996).
[CrossRef]

J. Non-Cryst. Solids (1)

D. Marchese, G. Kakarantzas, and A. Jha, “1G4 lifetimes, optical and thermal characteristics of Pr3+-doped GeS2- based chalcohalide glasses,” J. Non-Cryst. Solids 196, 314–319 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

M. D. Feit and J. A. Fleck, “Propagating beam interpretation of optical fiber cross coupling,” J. Opt. Soc. Am. 71, 1437–1443 (1981).

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

R. Rangel-Rojo, T. Kosa, E. Hajto, P. J. S. Ewen, A. E. Owen, A. K. Kar, and B. S. Wherrett, “Near-Infrared optical nonlinearities in amorphous chalcogenides,” Opt. Commun. 109, 145–150 (1994).
[CrossRef]

Opt. Lett. (1)

Solid State Phenom. (1)

P. Chandler, L. Zhang, and P. D. Townsend, “Optical waveguides formed by ion implementation,” Solid State Phenom. 27, 129–162 (1992).
[CrossRef]

Other (2)

D. Marchese, “GeS2-based glasses for optical amplifiers and nonlinear optical devices,” M. Phil. thesis (Brunel University, Uxbridge, UK, 1995), pp. 54–91.

C. Yeh, “All-optical switching,” in Applied Photonics (Academic, San Diego, Calif., 1994), pp. 248–274.

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Figures (9)

Fig. 1
Fig. 1

Schematic of a twin-core-fiber nonlinear coupler of length L.

Fig. 2
Fig. 2

Linear refractive index versus CsI concentration, with CsI replacing either GeS2 or Ga2S3.

Fig. 3
Fig. 3

Molar volume VM versus CsI concentration, with CsI replacing either GeS2 or Ga2S3.

Fig. 4
Fig. 4

Contour lines of the signal spatial power density calculated for four consecutive cross sections of the optical switch in the cross state; Lc=0.925 cm and Iav=55.5 kW/cm2.

Fig. 5
Fig. 5

Contour lines of the signal spatial power density calculated for four consecutive cross sections of the optical switch in the bar state; Lc=0.925 cm and Iav=94.3 MW/cm2.

Fig. 6
Fig. 6

Contour lines of the signal spatial power density calculated for four consecutive cross sections of the optical switch in the split state; Lc=0.925 cm and Iav=72.0 MW/cm2.

Fig. 7
Fig. 7

Power driving characteristics of the all-optical switch.

Fig. 8
Fig. 8

Cross-over length Lc versus center core distance; Iav=55.5 MW/cm2.

Fig. 9
Fig. 9

Cross-over length Lc versus core–cladding refractive-index change Δn; ncr=2.15.

Tables (2)

Tables Icon

Table 1 Optical Parameters Measured for Compositions of Selected Glasses within the Glass-Forming Region

Tables Icon

Table 2 Most-Significant Parameters of the Twin-Core Optical Fiber Switch

Equations (5)

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

ntot[I(x, y)]=n+n2I(x, y),
αtot[I(x, y)]=α+βI(x, y),
Pc=AλLcn2,
T=λmβn2,W=Δnmaxαλm,
CT=10 log10P1(Lc)P2(Lc),

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