Abstract

Two-modulator generalized ellipsometry is applied to determination of the optical functions of uniaxial rutile. For a nondepolarizing sample the two-modulator generalized ellipsometer determines all the elements of the normalized Jones matrix with one measurement and thereby totally characterizes light reflecting from the sample. If a uniaxial crystal is appropriately aligned, then determining its optical functions requires only a single measurement. We have used this new instrument to obtain optical functions of rutile that are the most accurate available for optical energies above the band edge.

© 1997 Optical Society of America

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References

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  1. E. D. Palik, ed., Handbook of Optical Constants of Solids I (Academic, New York, 1985).
  2. E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic, New York, 1991).
  3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  4. G. E. Jellison, Opt. Mater. 1, 41 (1992).
    [CrossRef]
  5. M. Cardona and G. Harbeke, Phys. Rev. A 137, 1467 (1965).
    [CrossRef]
  6. K. Vos and H. J. Krusemeyer, Physica C 10, 3893 (1977).
  7. M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, and C. M. Herzinger, J. Opt. Soc. Am. A 13, 875 (1996).
    [CrossRef]
  8. V. V. Filippov, A. Yu. Tronin, and A. F. Konstantinova, Crystallogr. Rep. 39, 313 (1994).
  9. D. J. De Smet, J. Appl. Phys. 76, 2571 (1994).
    [CrossRef]
  10. G. E. Jellison and F. A. Modine, Appl. Opt. 36, 8184 (1997).
    [CrossRef]
  11. G. E. Jellison and F. A. Modine, Appl. Opt. 36, 8190 (1997).
    [CrossRef]
  12. G. E. Jellison, Thin Solid Films 290-291, 40 (1996).
    [CrossRef]
  13. D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
    [CrossRef]
  14. D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972).
    [CrossRef]
  15. P. J. Lin-Chung and S. Teitler, J. Opt. Soc. Am. A 1, 703 (1984).
    [CrossRef]
  16. J. R. Devore, J. Opt. Soc. Am. 41, 416 (1951).
    [CrossRef]

1997 (2)

1996 (2)

1994 (2)

V. V. Filippov, A. Yu. Tronin, and A. F. Konstantinova, Crystallogr. Rep. 39, 313 (1994).

D. J. De Smet, J. Appl. Phys. 76, 2571 (1994).
[CrossRef]

1992 (1)

G. E. Jellison, Opt. Mater. 1, 41 (1992).
[CrossRef]

1984 (1)

1977 (1)

K. Vos and H. J. Krusemeyer, Physica C 10, 3893 (1977).

1972 (1)

1965 (1)

M. Cardona and G. Harbeke, Phys. Rev. A 137, 1467 (1965).
[CrossRef]

1951 (1)

1935 (1)

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Berreman, D. W.

Bruggeman, D. A. G.

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Cardona, M.

M. Cardona and G. Harbeke, Phys. Rev. A 137, 1467 (1965).
[CrossRef]

De Smet, D. J.

D. J. De Smet, J. Appl. Phys. 76, 2571 (1994).
[CrossRef]

Devore, J. R.

Filippov, V. V.

V. V. Filippov, A. Yu. Tronin, and A. F. Konstantinova, Crystallogr. Rep. 39, 313 (1994).

Harbeke, G.

M. Cardona and G. Harbeke, Phys. Rev. A 137, 1467 (1965).
[CrossRef]

Herzinger, C. M.

Jellison, G. E.

Johs, B.

Konstantinova, A. F.

V. V. Filippov, A. Yu. Tronin, and A. F. Konstantinova, Crystallogr. Rep. 39, 313 (1994).

Krusemeyer, H. J.

K. Vos and H. J. Krusemeyer, Physica C 10, 3893 (1977).

Lin-Chung, P. J.

Modine, F. A.

Rheinländer, B.

Schubert, M.

Teitler, S.

Tronin, A. Yu.

V. V. Filippov, A. Yu. Tronin, and A. F. Konstantinova, Crystallogr. Rep. 39, 313 (1994).

Vos, K.

K. Vos and H. J. Krusemeyer, Physica C 10, 3893 (1977).

Woollam, J. A.

Ann. Phys. (Leipzig) (1)

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Appl. Opt. (2)

Crystallogr. Rep. (1)

V. V. Filippov, A. Yu. Tronin, and A. F. Konstantinova, Crystallogr. Rep. 39, 313 (1994).

J. Appl. Phys. (1)

D. J. De Smet, J. Appl. Phys. 76, 2571 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Mater. (1)

G. E. Jellison, Opt. Mater. 1, 41 (1992).
[CrossRef]

Phys. Rev. A (1)

M. Cardona and G. Harbeke, Phys. Rev. A 137, 1467 (1965).
[CrossRef]

Physica C (1)

K. Vos and H. J. Krusemeyer, Physica C 10, 3893 (1977).

Thin Solid Films (1)

G. E. Jellison, Thin Solid Films 290-291, 40 (1996).
[CrossRef]

Other (3)

E. D. Palik, ed., Handbook of Optical Constants of Solids I (Academic, New York, 1985).

E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic, New York, 1991).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

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Figures (2)

Fig. 1
Fig. 1

ρ data for sample Para1 of rutile with the c axis oriented near the plane of the sample at 45° off normal toward the PSG from the 2-MGE. The solid curves indicate fits to the data with drough=5.0 nm, frutile=0.34, θ=86°, ϕ=44°, and no, ne, k0, and ke shown in Fig.  2. The resulting χ2=1.23.

Fig. 2
Fig. 2

Optical functions of rutile obtained from the 2-MGE. Top, real and imaginary parts of the complex refractive index for the ordinary and the extraordinary directions; bottom, absorption coefficients for the ordinary and the extraordinary directions.

Tables (1)

Tables Icon

Table 1 Comparison of Data for the Optical Functions of Rutile Determined from This Study and from Selected Values in the Literature

Equations (4)

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

J=[rpprpsrsprss]=rss[ρppρpsρsp1],
It=Idc+IX0X0+IY0Y0+IX1X1+IY1Y1+IX0X1×X0X1+IX0Y1X0Y1+IY0X1Y0X1+IY0Y1Y0Y1, 
Xi=sinAi sinωit,
Yi=cosAi sinωit, i=0, 1.

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