Abstract

Complex absorption spectra obtained from thin films at normal incidence can be difficult to interpret owing to the appearance of Fabry–Perot interference fringes in the data. We describe a technique for modeling such spectra so that true absorption features can be identified and evaluated separately from the overlying fringes. The technique is used to interpret data obtained from photosensitive germanosilicate solgel films on fused-silica substrates but may be easily extended to analysis in other material systems.

© 1996 Optical Society of America

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  1. W. H. Brattain and H. B. Briggs, "The optical constants of germanium in the infra-red," Phys. Rev. 75, 1705 (1949).
    [CrossRef]
  2. J. F. Hall and W. F. C. Ferguson, "Optical properties of cadmium sulfide and zinc sulfide from 0.6 micron to 14 microns," J. Opt. Soc. Am. 45, 714 (1955).
    [CrossRef]
  3. S. P. Lyshenko and V. K. Miloslavskii, "A simple method for the determination of the thickness and optical constants of semiconducting and dielectric layers," Opt. Spectrosc. (USSR) 16, 80 (1964).
  4. J. C. Manifacier and J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E. 9, 1002 (1976).
    [CrossRef]
  5. J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
    [CrossRef]
  6. R. Swanepoel, "Determination of the thickness of optical constants of amorphous silicon," J. Phys. E. 16, 1214 (1983).
    [CrossRef]
  7. R. Swanepoel, "Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films," J. Phys. E. 17, 897 (1984).
    [CrossRef]
  8. M. Kubinyi, R. Allott, A. Grofcsik, and W. J. Jones, "Elimination of interference effects from photoinduced-transmission decay curves of thin silicon films," Appl. Opt. 34, 2949 (1995).
    [CrossRef] [PubMed]
  9. K. D. Simmons, G. I. Stegeman, B. G. Potter, Jr., and J. H. Simmons, "Photosensitivity of solgel-derived germanosilicate planar waveguides," Opt. Lett. 18, 25 (1993).
    [CrossRef] [PubMed]
  10. I. H. Malitson, "Interspecimen comparison of the refractive index of fused silica," J. Opt. Soc. Am. 55, 1205 (1965).
    [CrossRef]
  11. J. W. Fleming, "Dispersion in GeO2–SiO2 glasses," Appl. Opt. 23, 4486 (1984).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  13. K. Ohta and H. Ishida, "Comparison among several numerical integration methods for Kramers–Kronig transformation," Appl. Spectrosc. 42, 952 (1988).
    [CrossRef]
  14. V. Garino-Canina, "La bande d'absorption à 2420 Å de la silice vitreuse: impureté germanium et perte d'oxyg`ne," Comp. Rend. 242, 1982 (1956).
  15. A. J. Cohen, "Neutron specific color center in fused silica and an impurity band of identical wavelength," Phys. Rev. 105, 1151 (1957).
    [CrossRef]
  16. E. J. Friebele and D. L. Griscom, "Color centers in glass optical fiber waveguides," Mater. Res. Soc. Symp. Proc. 61, 319 (1986).
    [CrossRef]
  17. M. J. Yuen, "Ultraviolet absorption studies of germanium silicate glasses," Appl. Opt. 21, 136 (1982).
    [CrossRef] [PubMed]
  18. A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
    [CrossRef]
  19. V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
    [CrossRef]
  20. E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

1995

1993

1991

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

1989

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

1988

K. Ohta and H. Ishida, "Comparison among several numerical integration methods for Kramers–Kronig transformation," Appl. Spectrosc. 42, 952 (1988).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

1986

E. J. Friebele and D. L. Griscom, "Color centers in glass optical fiber waveguides," Mater. Res. Soc. Symp. Proc. 61, 319 (1986).
[CrossRef]

1984

R. Swanepoel, "Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films," J. Phys. E. 17, 897 (1984).
[CrossRef]

J. W. Fleming, "Dispersion in GeO2–SiO2 glasses," Appl. Opt. 23, 4486 (1984).
[CrossRef]

1983

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

R. Swanepoel, "Determination of the thickness of optical constants of amorphous silicon," J. Phys. E. 16, 1214 (1983).
[CrossRef]

1982

1976

J. C. Manifacier and J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E. 9, 1002 (1976).
[CrossRef]

1965

1964

S. P. Lyshenko and V. K. Miloslavskii, "A simple method for the determination of the thickness and optical constants of semiconducting and dielectric layers," Opt. Spectrosc. (USSR) 16, 80 (1964).

1957

A. J. Cohen, "Neutron specific color center in fused silica and an impurity band of identical wavelength," Phys. Rev. 105, 1151 (1957).
[CrossRef]

1956

V. Garino-Canina, "La bande d'absorption à 2420 Å de la silice vitreuse: impureté germanium et perte d'oxyg`ne," Comp. Rend. 242, 1982 (1956).

1955

1949

W. H. Brattain and H. B. Briggs, "The optical constants of germanium in the infra-red," Phys. Rev. 75, 1705 (1949).
[CrossRef]

Allott, R.

Anoikin, E. V.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

Arguello, Z. P.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Bilac, S.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Brattain, W. H.

W. H. Brattain and H. B. Briggs, "The optical constants of germanium in the infra-red," Phys. Rev. 75, 1705 (1949).
[CrossRef]

Briggs, H. B.

W. H. Brattain and H. B. Briggs, "The optical constants of germanium in the infra-red," Phys. Rev. 75, 1705 (1949).
[CrossRef]

Cisneros, J. I.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Cohen, A. J.

A. J. Cohen, "Neutron specific color center in fused silica and an impurity band of identical wavelength," Phys. Rev. 105, 1151 (1957).
[CrossRef]

Dianov, E. M.

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Ferguson, W. F. C.

Fillard, J. P.

J. C. Manifacier and J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E. 9, 1002 (1976).
[CrossRef]

Fleming, J. W.

Friebele, E. J.

E. J. Friebele and D. L. Griscom, "Color centers in glass optical fiber waveguides," Mater. Res. Soc. Symp. Proc. 61, 319 (1986).
[CrossRef]

Garino-Canina, V.

V. Garino-Canina, "La bande d'absorption à 2420 Å de la silice vitreuse: impureté germanium et perte d'oxyg`ne," Comp. Rend. 242, 1982 (1956).

Goncalves, J. M.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Griscom, D. L.

E. J. Friebele and D. L. Griscom, "Color centers in glass optical fiber waveguides," Mater. Res. Soc. Symp. Proc. 61, 319 (1986).
[CrossRef]

Grofcsik, A.

Gur'yanov, A. N.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Gusovskii, D. D.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

Hall, J. F.

Ishida, H.

Jones, W. J.

Khopin, V. F.

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Kim, V. M.

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Kubinyi, M.

Lyshenko, S. P.

S. P. Lyshenko and V. K. Miloslavskii, "A simple method for the determination of the thickness and optical constants of semiconducting and dielectric layers," Opt. Spectrosc. (USSR) 16, 80 (1964).

Malitson, I. H.

Manifacier, J. C.

J. C. Manifacier and J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E. 9, 1002 (1976).
[CrossRef]

Mashinskii, V. M.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Miloslavskii, V. K.

S. P. Lyshenko and V. K. Miloslavskii, "A simple method for the determination of the thickness and optical constants of semiconducting and dielectric layers," Opt. Spectrosc. (USSR) 16, 80 (1964).

Miroshnichenko, S. I.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

Neustruev, V. B.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Ohta, K.

Potter, B. G.

Rego, G. B.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Rodriguez, A. E.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Romanov, M. V.

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

Simmons, J. H.

Simmons, K. D.

Stegeman, G. I.

Swanepoel, R.

R. Swanepoel, "Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films," J. Phys. E. 17, 897 (1984).
[CrossRef]

R. Swanepoel, "Determination of the thickness of optical constants of amorphous silicon," J. Phys. E. 16, 1214 (1983).
[CrossRef]

Tikhomirov, V. A.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Tomyiama, M.

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Yuen, M. J.

Appl. Opt.

Appl. Spectrosc.

Comp. Rend.

V. Garino-Canina, "La bande d'absorption à 2420 Å de la silice vitreuse: impureté germanium et perte d'oxyg`ne," Comp. Rend. 242, 1982 (1956).

Fibers Integ. Opt.

V. B. Neustruev, E. M. Dianov, V. M. Kim, V. M. Mashinskii, M. V. Romanov, A. N. Gur'yanov, V. F. Khopin, and V. A. Tikhomirov, "Ultraviolet radiation- and ϒ radiation-induced color centers in germanium-doped silica glass and fibers," Fibers Integ. Opt. 8, 143 (1989).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. E.

J. C. Manifacier and J. P. Fillard, "A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film," J. Phys. E. 9, 1002 (1976).
[CrossRef]

R. Swanepoel, "Determination of the thickness of optical constants of amorphous silicon," J. Phys. E. 16, 1214 (1983).
[CrossRef]

R. Swanepoel, "Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films," J. Phys. E. 17, 897 (1984).
[CrossRef]

Mater. Res. Soc. Symp. Proc.

E. J. Friebele and D. L. Griscom, "Color centers in glass optical fiber waveguides," Mater. Res. Soc. Symp. Proc. 61, 319 (1986).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

S. P. Lyshenko and V. K. Miloslavskii, "A simple method for the determination of the thickness and optical constants of semiconducting and dielectric layers," Opt. Spectrosc. (USSR) 16, 80 (1964).

Phys. Rev.

W. H. Brattain and H. B. Briggs, "The optical constants of germanium in the infra-red," Phys. Rev. 75, 1705 (1949).
[CrossRef]

A. J. Cohen, "Neutron specific color center in fused silica and an impurity band of identical wavelength," Phys. Rev. 105, 1151 (1957).
[CrossRef]

Phys. Status Solidi

A. N. Gur'yanov, E. M. Dianov, V. M. Kim, V. M. Mashinskii, V. B. Neustruev, V. A. Tikhomirov, and V. F. Khopin, "UV and ϒ-induced paramagnetic colour centers in germanium-doped silica glass," Phys. Status Solidi (a) 110, K107 (1988).
[CrossRef]

Sov. Lightwave Commun.

E. V. Anoikin, A. N. Gur'yanov, D. D. Gusovskii, V. M. Mashinskii, S. I. Miroshnichenko, V. B. Neustruev, and V. A. Tikhomirov, "Formation and bleaching of colour centers in germanium-doped silica glass by 3.68 eV photons," Sov. Lightwave Commun. 1, 29 (1991).

Thin Solid Films

J. I. Cisneros, G. B. Rego, M. Tomyiama, S. Bilac, J. M. Goncalves, A. E. Rodriguez, and Z. P. Arguello, "A method for the determination of the complex refractive index of non-metallic thin films using photometric measurements at normal incidence," Thin Solid Films 100, 155 (1983).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

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Figures (3)

Fig. 1
Fig. 1

Comparison of UV absorption data taken from a 45-mol. % GeO2 thin-film sample in (a) its reduced and (b) its oxidized states with (c) a theoretically generated FP fringe fit.

Fig. 2
Fig. 2

Series of curves (dashed) generated from the FP fringe analysis described in Section 2 plotted along with the optical loss spectrum from a reduced, 45-mol. % GeO2 sample (solid curve). The optical losses in the generated spectra have been modeled by constant kf values of 0.0001, 0.005, 0.015, and 0.03.

Fig. 3
Fig. 3

Triangles represent the experimental absorbance data from a reduced, 45-mol. % GeO2 sample. The solid curve is the theoretical fit to the data, and the dashed curves depict the five Gaussian bands used to model absorption in the sample. The bands are centered at 181.0, 202.5, 237.5, 264.8, and 300 nm.

Equations (5)

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

n 2 1 = i = 1 3 [ SA i + X ( GA i SA i ) ] λ 2 λ 2 [ SL i + X ( GL i SL i ) ] 2 .
A t A i = t 0 t 1 exp ( i δ / 2 ) 1 r 0 r 1 exp ( i δ ) .
T 1 = t 0 2 t 1 2 exp ( b ) 1 2 r 0 r 1 ( cos a ) exp ( b ) + r 0 2 r 1 2 exp ( 2 b ) .
T 2 = t 0 2 t 1 2 exp ( b ) 1 2 r 0 r 1 ( cos a ) exp ( b ) + r 0 2 r 1 2 exp ( 2 b ) T 1 .
ρ ( ν ) = A exp [ ( ν ν ) 2 2 Δ ν 2 ] .

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