Abstract

We measured the nonlinear optical susceptibility χ(3) of some Ge-Ga-Sb-S chalcogenide glasses feasible for the fabrication of highly nonlinear photonic crystal fibers. The χ(3) values of Ge17Ga4Sb10S69, Ge20Ga5Sb10S65, and Ge20Ga5Sb6S69 glasses were found to be 3.5, 2.6, and 1.8×1019m2/V2 (6.3, 4.6, and 3.2×1012esu, where “esu” stands for electrostatic unit) at the fundamental wavelength λ=1.9μm, i.e., 227, 167, and 117 times higher than that of standard silica [1.55×1021m2/V2 (2.79×1014esu)]. Their nonlinear refractive indices n2 were then obtained as 1.8, 1.3, and 1×1017m2/W (5.1, 3.7, and 2.7×1011esu). They are 78, 56, and 43% of n2=2.3×1017m2/W (7×1011esu) of the As2S3 glass used as the chalcogenide glass reference.

© 2011 Optical Society of America

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2009 (4)

2008 (1)

Y. Ohishi, “Novel photonic glasses for future amplifiers,” Glass Technol. Eur. J. Glass Sci. Technol. Part A 49, 317–328 (2008).

2007 (1)

2006 (2)

2005 (1)

2004 (2)

2002 (1)

A. Zakery, “Low loss waveguides in pulsed laser deposited arsenic sulfide chalcogenide films,” J. Phys. D 35, 2909–2913(2002).
[CrossRef]

2001 (1)

J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, L. E. Busse, P. Thielen, V. Nguyen, P. Pureza, S. Bayya, and F. Kung, “Applications of chalcogenide glass optical fibers at NRL,” J. Optoelectron. Adv. Mater. 3, 627–640 (2001).

2000 (2)

1999 (1)

E. R. Skordeva, “The dispersion energies Wemple–DiDomenico in chalcogenide films based on Ge-As(Sb)-S(Se),” J. Optoelectron. Adv. Mater. 1, 43–47 (1999).

1998 (1)

F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

1995 (1)

M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77, 5518–5523 (1995).
[CrossRef]

1994 (1)

Y. Ohishi, A. Mori, T. Kanamori, K. Fujiura, and S. Sudo, “Fabrication of praseodymium-doped arsenic sulfide chalcogenide fiber for 1.3μm fiber amplifiers,” Appl. Phys. Lett. 65, 13–15(1994).
[CrossRef]

1993 (1)

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993).
[CrossRef]

1992 (1)

Y. Kawamura and H. Iwamura, “InP/InAlAs resonant tunneling diodes grown by gas source molecular beam epitaxy,” Jpn. J. Appl. Phys. 31, L1733–L1735 (1992).
[CrossRef]

1991 (2)

J. R. Heflin, Y. M. Cai, and A. E. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2147 (1991).
[CrossRef]

H. Kobayashi and K. Kubodera, “Analysis of asymmetric fringe patterns of third‐harmonic generation in a molecular crystal,” J. Appl. Phys. 69, 3807–3810 (1991).
[CrossRef]

1990 (1)

H. Nasu, K. Kubodera, H. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794–1796 (1990).
[CrossRef]

1989 (1)

H. Kobayashi, H. Iwamura, and K. Kubodera, “Third‐harmonic generation in an AlGaAs/AlAs superlattice,” J. Appl. Phys. 65, 5202–5204 (1989).
[CrossRef]

1985 (1)

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[CrossRef] [PubMed]

1982 (1)

M. Zavetova, B. Velicky, and V. Vorlicek, “Index of refraction of the glassy As/x/Te/100-x/system,” Solar En. Mater. 8, 33–39 (1982).
[CrossRef]

1980 (1)

K. Tanaka, “Optical properties and photoinduced changes in amorphous As-S films,” Thin Solid Films 66, 271–279(1980).
[CrossRef]

1971 (1)

S. H. Wemple and M. Di Domenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Agarwal, A.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

Aggarwal, I. D.

J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, L. E. Busse, P. Thielen, V. Nguyen, P. Pureza, S. Bayya, and F. Kung, “Applications of chalcogenide glass optical fibers at NRL,” J. Optoelectron. Adv. Mater. 3, 627–640 (2001).

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S. W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–257 (2000).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2001).

Asobe, M.

M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77, 5518–5523 (1995).
[CrossRef]

Barthelemy, A.

F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Bayya, S.

J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, L. E. Busse, P. Thielen, V. Nguyen, P. Pureza, S. Bayya, and F. Kung, “Applications of chalcogenide glass optical fibers at NRL,” J. Optoelectron. Adv. Mater. 3, 627–640 (2001).

Boolchand, P.

P. Boolchand and W. J. Bresser, “The structural origin of broken chemical order in GeSe2 glass,” Philos. Mag. B 80, 1757–1772(2000).
[CrossRef]

Boudebs, G.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

L. Petit, N. Carlie, K. Richardson, A. Humeau, S. Cherukulappurath, and G. Boudebs, “Nonlinear optical properties of glasses in the system Ge/Ga-Sb-S/Se,” Opt. Lett. 31, 1495–1497(2006).
[CrossRef] [PubMed]

Boussard-Plédel, C.

Boyd, R. W.

R.W. Boyd, “The Intensity-Dependent Refractive Index” in Nonlinear Optics (Academic, 1992), Chapter 4, p. 210.

Bresser, W. J.

P. Boolchand and W. J. Bresser, “The structural origin of broken chemical order in GeSe2 glass,” Philos. Mag. B 80, 1757–1772(2000).
[CrossRef]

Brilland, L.

Bureau, B.

Busse, L. E.

J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, L. E. Busse, P. Thielen, V. Nguyen, P. Pureza, S. Bayya, and F. Kung, “Applications of chalcogenide glass optical fibers at NRL,” J. Optoelectron. Adv. Mater. 3, 627–640 (2001).

Cai, Y. M.

Carlie, N.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

L. Petit, N. Carlie, K. Richardson, A. Humeau, S. Cherukulappurath, and G. Boudebs, “Nonlinear optical properties of glasses in the system Ge/Ga-Sb-S/Se,” Opt. Lett. 31, 1495–1497(2006).
[CrossRef] [PubMed]

Chartier, T.

Chaudhari, C.

Chen, H.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

Cheng, L. K.

Cheong, S. W.

Cherukulappurath, S.

Churbanov, M. E.

De Angelis, C.

F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Di Domenico, M.

S. H. Wemple and M. Di Domenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Dianov, E. M.

Faber, A. J.

Fujiura, K.

Y. Ohishi, A. Mori, T. Kanamori, K. Fujiura, and S. Sudo, “Fabrication of praseodymium-doped arsenic sulfide chalcogenide fiber for 1.3μm fiber amplifiers,” Appl. Phys. Lett. 65, 13–15(1994).
[CrossRef]

Garito, A. E.

Gaylord, S.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

Gielesen, W. L. M.

Grishin, I. A.

Heflin, J. R.

Houizot, P.

Hu, J.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

Humeau, A.

Hwang, H. Y.

Itoh, H.

M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77, 5518–5523 (1995).
[CrossRef]

Iwamura, H.

Y. Kawamura and H. Iwamura, “InP/InAlAs resonant tunneling diodes grown by gas source molecular beam epitaxy,” Jpn. J. Appl. Phys. 31, L1733–L1735 (1992).
[CrossRef]

H. Kobayashi, H. Iwamura, and K. Kubodera, “Third‐harmonic generation in an AlGaAs/AlAs superlattice,” J. Appl. Phys. 65, 5202–5204 (1989).
[CrossRef]

Kaino, T.

M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77, 5518–5523 (1995).
[CrossRef]

Kajzar, F.

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[CrossRef] [PubMed]

Kamiya, K.

H. Nasu, K. Kubodera, H. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794–1796 (1990).
[CrossRef]

Kanamori, T.

M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77, 5518–5523 (1995).
[CrossRef]

Y. Ohishi, A. Mori, T. Kanamori, K. Fujiura, and S. Sudo, “Fabrication of praseodymium-doped arsenic sulfide chalcogenide fiber for 1.3μm fiber amplifiers,” Appl. Phys. Lett. 65, 13–15(1994).
[CrossRef]

Kanbara, H.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993).
[CrossRef]

Katsufuji, T.

Kawamura, Y.

Y. Kawamura and H. Iwamura, “InP/InAlAs resonant tunneling diodes grown by gas source molecular beam epitaxy,” Jpn. J. Appl. Phys. 31, L1733–L1735 (1992).
[CrossRef]

Kimerling, L.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

Kitao, M.

Kito, C.

Kobayashi, H.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993).
[CrossRef]

H. Kobayashi and K. Kubodera, “Analysis of asymmetric fringe patterns of third‐harmonic generation in a molecular crystal,” J. Appl. Phys. 69, 3807–3810 (1991).
[CrossRef]

H. Nasu, K. Kubodera, H. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794–1796 (1990).
[CrossRef]

H. Kobayashi, H. Iwamura, and K. Kubodera, “Third‐harmonic generation in an AlGaAs/AlAs superlattice,” J. Appl. Phys. 65, 5202–5204 (1989).
[CrossRef]

Koga, M.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993).
[CrossRef]

Kolobov, A. V.

A. V. Kolobov, Photo-Induced Metastability in Amorphous Semiconductors (Wiley-VCH, 2003).
[CrossRef]

Koltachev, V. V.

Kubodera, K.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993).
[CrossRef]

H. Kobayashi and K. Kubodera, “Analysis of asymmetric fringe patterns of third‐harmonic generation in a molecular crystal,” J. Appl. Phys. 69, 3807–3810 (1991).
[CrossRef]

H. Nasu, K. Kubodera, H. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794–1796 (1990).
[CrossRef]

H. Kobayashi, H. Iwamura, and K. Kubodera, “Third‐harmonic generation in an AlGaAs/AlAs superlattice,” J. Appl. Phys. 65, 5202–5204 (1989).
[CrossRef]

Kung, F.

J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, L. E. Busse, P. Thielen, V. Nguyen, P. Pureza, S. Bayya, and F. Kung, “Applications of chalcogenide glass optical fibers at NRL,” J. Optoelectron. Adv. Mater. 3, 627–640 (2001).

Leneindre, L.

F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Lenz, G.

Li, H.

Liao, M.

Lines, M. E.

Lucas, J.

P. Houizot, C. Boussard-Plédel, A. J. Faber, L. K. Cheng, B. Bureau, P. A. Van Nijnatten, W. L. M. Gielesen, J. Pereira do Carmo, and J. Lucas, “Infrared single mode chalcogenide glass fiber for space,” Opt. Express 15, 12529–12538 (2007).
[CrossRef] [PubMed]

F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
[CrossRef]

Massera, J.

L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
[CrossRef]

Matsumoto, M.

Messier, J.

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[CrossRef] [PubMed]

Misumi, T.

Monteville, A.

Mori, A.

Y. Ohishi, A. Mori, T. Kanamori, K. Fujiura, and S. Sudo, “Fabrication of praseodymium-doped arsenic sulfide chalcogenide fiber for 1.3μm fiber amplifiers,” Appl. Phys. Lett. 65, 13–15(1994).
[CrossRef]

Naganuma, K.

M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77, 5518–5523 (1995).
[CrossRef]

Nakamura, M.

H. Nasu, K. Kubodera, H. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794–1796 (1990).
[CrossRef]

Nasu, H.

H. Nasu, K. Kubodera, H. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794–1796 (1990).
[CrossRef]

Nguyen, T.

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F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids 239, 139–142 (1998).
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L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
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[CrossRef] [PubMed]

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J. S. Sanghera, I. D. Aggarwal, L. B. Shaw, L. E. Busse, P. Thielen, V. Nguyen, P. Pureza, S. Bayya, and F. Kung, “Applications of chalcogenide glass optical fibers at NRL,” J. Optoelectron. Adv. Mater. 3, 627–640 (2001).

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Appl. Phys. Lett. (1)

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[CrossRef]

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E. R. Skordeva, “The dispersion energies Wemple–DiDomenico in chalcogenide films based on Ge-As(Sb)-S(Se),” J. Optoelectron. Adv. Mater. 1, 43–47 (1999).

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A. Zakery, “Low loss waveguides in pulsed laser deposited arsenic sulfide chalcogenide films,” J. Phys. D 35, 2909–2913(2002).
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L. Petit, N. Carlie, H. Chen, S. Gaylord, J. Massera, G. Boudebs, J. Hu, A. Agarwal, L. Kimerling, and K. Richardson, “Compositional dependence of the nonlinear refractive index of new germanium-based chalcogenide glasses,” J. Solid State Chem. 182, 2756–2761 (2009).
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Opt. Express (5)

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S. H. Wemple and M. Di Domenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Solar En. Mater. (1)

M. Zavetova, B. Velicky, and V. Vorlicek, “Index of refraction of the glassy As/x/Te/100-x/system,” Solar En. Mater. 8, 33–39 (1982).
[CrossRef]

Thin Solid Films (1)

K. Tanaka, “Optical properties and photoinduced changes in amorphous As-S films,” Thin Solid Films 66, 271–279(1980).
[CrossRef]

Other (5)

R.W. Boyd, “The Intensity-Dependent Refractive Index” in Nonlinear Optics (Academic, 1992), Chapter 4, p. 210.

M. A. Popescu, Non-Crystalline Chalcogenides (Kluwer Academic, 2000).

A. V. Kolobov, Photo-Induced Metastability in Amorphous Semiconductors (Wiley-VCH, 2003).
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G. P. Agrawal, Applications of Nonlinear Fiber Optics(Academic, 2001).

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Figures (5)

Fig. 1
Fig. 1

DSC curves of the studied chalcogenide glasses.

Fig. 2
Fig. 2

Absorbance spectra of the studied chalcogenide glasses and silica.

Fig. 3
Fig. 3

Optical transmission spectra of the studied chalcogenide glasses.

Fig. 4
Fig. 4

Schematic of the TH light measurement setup.

Fig. 5
Fig. 5

Maker fringe patterns and relative TH light intensities of (a) Ge 17 Ga 4 Sb 10 S 69 , (b) As 2 S 3 , (c) Ge 20 Ga 5 Sb 10 S 65 , and (d) Ge 20 Ga 5 Sb 6 S 69 glasses recorded at λ = 633 nm in comparison to the fused silica standards.

Tables (3)

Tables Icon

Table 1 Refractive Indices and the Optical Transmission of As 2 S 3 and Ge-Ga-Sb-S Glasses

Tables Icon

Table 2 Sellmeier Coefficients of As 2 S 3 and Ge-Ga-Sb-S Glasses

Tables Icon

Table 3 Nonlinear Optical Susceptibility χ ( 3 ) and Nonlinear Index n 2 As 2 S 3 and Ge-Ga-Sb-S Glasses

Equations (14)

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

I ω in = ( P ω S ) T ω ( cos θ ex cos θ in ) ,
I 3 ω in = ( 4 π ) 4 ω 3 ω 2 c 4 n 3 ω n ω 3 { χ eff 3 } 2 ( I ω in ) 3 F ( d ) .
P 3 ω = ( 4 π ) 4 ω 3 ω 2 c 4 n 3 ω n ω 3 { χ eff 3 } 2 P 3 ω 1 T 3 ω T ω 3 cos 2 θ ex S 2 cos 2 θ in F ( d ) ,
F ( d ) = 4 l c π 2 sin ( π d 2 l c cos θ in ) ,
χ ( 3 ) = χ S ( 3 ) l c , S l c { P 3 ω ( 0 ) n 3 ω n ω 3 T 3 ω , S T ω , S 3 P 3 ω , S ( 0 ) n 3 ω , S n ω , S 3 T 3 ω T ω 3 } 1 / 2 ,
χ ( 3 ) = χ S ( 3 ) l c , S l c { P 3 ω ( 0 ) P 3 ω , S ( 0 ) } 1 / 2 ( n ω + 1 n ω , S + 1 ) 4 .
χ ( 3 ) = χ S ( 3 ) l c , S { P 3 ω ( 0 ) P 3 ω , S ( 0 ) } 1 / 2 ( n ω + 1 n ω , S + 1 ) 4 2 π { ( π / l c ) 2 + ( 2 / α 0 ) 2 } 1 / 2 1 + e α 0 l / 2 ,
l c = d Δ m { 1 1 ( sin θ j / n 3 ω ) 2 1 1 ( sin θ i / n 3 ω ) 2 } ,
χ ( 3 ) ( m 2 / V 2 ) = 4 π c 2 × 10 8 4 χ ( 3 ) ( esu ) = 5.59 × 10 8 χ ( 3 ) ( esu ) .
n 2 ( m 2 / W ) = 3 4 c ε 0 n 2 χ ( 3 ) ( m 2 / V 2 ) = 282.5 n 2 χ ( 3 ) ( m 2 / V 2 ) .
n 2 ( m 2 / W ) = 80 π c n n 2 ( esu ) = 8.38 × 10 7 n n 2 ( esu ) ,
n = n 0 + n 2 I = n 0 + n 2 c ε 0 n 0 2 | E w 1 | 2 .
I m = 2 m 1 ω 2 I 1 m ( n c ) m + 1 ε 0 m 1 ( χ ( m ) ) 2 l 2 T 1 m T m × sin 2 ( Δ k l / 2 ) / ( Δ k l / 2 ) 2 ,
Δ k π / l c = 2 m π ( n m n 1 ) / λ p ,

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