Abstract

We have used resonant reflection mode Fabry–Perot microcavities (RFPM’s) to determine linear optical and electro-optical properties of poled nonlinear optical polymers (NLP’s). Measured reflectances from angular scans of RFPM’s have been analyzed with an electromagnetic plane-wave multilayer analysis that took into account the anisotropic nature of the NLP layer. We have numerically investigated the mutual dependence of refractive indices and layer thickness and the accuracy of the results obtained. As an illustration of this characterization technique, the refractive indices of a 10 mol. % Disperse Red 1/poly(methyl methacrylate) side-chain NLP have been determined to within ±0.005, the NLP layer thicknesses to within 1%, and electro-optic coefficients to within 5%. We optimized RFPM structures for measurements at the wavelength λ=430 nm by changing the electrode metal from gold to aluminum. Using a guest–host NLP, 5 wt. % diphenyl-tricyanovinyl-aniline in poly(methyl methacrylate), we show that the method is capable of measuring electrorefraction and electroabsorption as well as a converse piezoelectric contribution. We show that a NLP decal deposition technique is particularly well suited to fabrication of these RFPM’s.

© 1998 Optical Society of America

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  1. J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer film,” Appl. Opt. 29, 2839 (1990).
    [CrossRef] [PubMed]
  2. C. C. Teng and T. H. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734 (1990).
    [CrossRef]
  3. K. Clays and J. S. Schildkraut, “Dispersion of the complex electro-optic coefficient and electrochromic effects in poled polymer films,” J. Opt. Soc. Am. B 9, 2274 (1992).
    [CrossRef]
  4. F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78, 9 (1995).
    [CrossRef]
  5. K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
    [CrossRef]
  6. F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
    [CrossRef]
  7. L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
    [CrossRef]
  8. Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).
  9. P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
    [CrossRef]
  10. S. H. Han and J. W. Wu, “Single-beam polarization interferometry measurement of the linear electro-optic effect in poled polymer films with a reflection configuration,” J. Opt. Soc. Am. B 14, 1131 (1997).
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  12. J. D. Swalen and J. I. Thackara, “Electro-optic measurements of poled polymeric films,” Nonlinear Opt. 10, 371 (1995).
  13. C. A. Eldering, S. T. Kowel, and A. Knoesen, “Electrically induced transmissivity modulation in polymeric thin film Fabry–Perot etalons,” Appl. Opt. 28, 4442 (1989).
    [CrossRef] [PubMed]
  14. H. Uchiki and T. Kobayashi, “New determination method of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymers,” J. Appl. Phys. 64, 2625 (1988).
    [CrossRef]
  15. R. Meyrueix, J. P. Lecomte, and G. Tapolsky, “A Fabry– Perot interferometric technique for the electro-optical characterization of nonlinear optical polymers,” Nonlinear Opt. 1, 201 (1991).
  16. C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Perot devices for the characterization of polymeric electro-optic films,” J. Appl. Phys. 69, 3676 (1991).
    [CrossRef]
  17. D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
    [CrossRef]
  18. N. F. O’Brien, V. Dominic, and S. Caracci, “Electro-refraction and electro-absorption in poled polymer Fabry–Perot étalons,” J. Appl. Phys. 79, 7493 (1996).
    [CrossRef]
  19. K. D. Singer, J. E. Sohn, and S. L. Lalama, “Second-harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248 (1986).
    [CrossRef]
  20. M. A. Mortazavi, A. Knoesen, S. T. Kowel, B. G. Higgins, and A. Dienes, “Second-harmonic generation and absorption studies of polymer-dye films oriented by corona-onset poling at elevated temperatures,” J. Opt. Soc. Am. B 6, 733 (1989).
    [CrossRef]
  21. R. A. Hill, A. Knoesen, and M. A. Mortazavi, “Corona poling of nonlinear polymer thin films for electro-optic modulators,” Appl. Phys. Lett. 65, 1733 (1994).
    [CrossRef]
  22. G. Khanarian, M. A. Mortazavi, and A. J. East, “Phase-matched second-harmonic generation from free-standing periodically stacked polymer films,” Appl. Phys. Lett. 63, 1462 (1993).
    [CrossRef]
  23. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).
  24. See, e.g., R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987); P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1991).
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    [CrossRef]
  27. A. Knoesen, “Simple approach to reflectance analysis of birefringent stratified films,” Appl. Opt. 30, 4017 (1991).
    [CrossRef] [PubMed]
  28. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
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  32. In the error analysis, fitted parameters from the actual experiment (Fig. 8) are used as surrogates for the true parameters. Computer-generated random numbers within the specified error of the data, σmin, are used to simulate many (in our case 200) synthetic data sets. For each of these sets, best-fit parameters are evaluated to yield their distribution around the surrogate true parameters (algorithm available on PROFIT software from Quantum Soft, Zurich).
  33. D. Morichere, P.-A. Chollet, W. Fleming, M. Jurich, B. A. Smith, and J. D. Swalen, “Electro-optic effects in two tolane side-chain nonlinear-optical polymers: comparison between measured coefficients and second-harmonic generation,” J. Opt. Soc. Am. B 10, 1894 (1993).
    [CrossRef]
  34. R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 74, 1869 (1994).
    [CrossRef]
  35. C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
    [CrossRef]
  36. A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
    [CrossRef]
  37. S. A. Hamilton, D. R. Yankelevich, A. Knoesen, R. T. Weverka, R. A. Hill, and G. C. Bjorklund, “Polymer in-line fiber modulators for broadband radio-frequency optical links,” J. Opt. Soc. Am. B (to be published).

1997 (1)

1996 (1)

N. F. O’Brien, V. Dominic, and S. Caracci, “Electro-refraction and electro-absorption in poled polymer Fabry–Perot étalons,” J. Appl. Phys. 79, 7493 (1996).
[CrossRef]

1995 (3)

J. D. Swalen and J. I. Thackara, “Electro-optic measurements of poled polymeric films,” Nonlinear Opt. 10, 371 (1995).

F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78, 9 (1995).
[CrossRef]

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
[CrossRef]

1994 (5)

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
[CrossRef]

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 74, 1869 (1994).
[CrossRef]

R. A. Hill, A. Knoesen, and M. A. Mortazavi, “Corona poling of nonlinear polymer thin films for electro-optic modulators,” Appl. Phys. Lett. 65, 1733 (1994).
[CrossRef]

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

1993 (3)

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

G. Khanarian, M. A. Mortazavi, and A. J. East, “Phase-matched second-harmonic generation from free-standing periodically stacked polymer films,” Appl. Phys. Lett. 63, 1462 (1993).
[CrossRef]

D. Morichere, P.-A. Chollet, W. Fleming, M. Jurich, B. A. Smith, and J. D. Swalen, “Electro-optic effects in two tolane side-chain nonlinear-optical polymers: comparison between measured coefficients and second-harmonic generation,” J. Opt. Soc. Am. B 10, 1894 (1993).
[CrossRef]

1992 (2)

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

K. Clays and J. S. Schildkraut, “Dispersion of the complex electro-optic coefficient and electrochromic effects in poled polymer films,” J. Opt. Soc. Am. B 9, 2274 (1992).
[CrossRef]

1991 (4)

S. Herminghaus, B. A. Smith, and J. D. Swalen, “Electro-optic coefficients in electric-field-poled polymer waveguides,” J. Opt. Soc. Am. B 8, 2311 (1991).
[CrossRef]

A. Knoesen, “Simple approach to reflectance analysis of birefringent stratified films,” Appl. Opt. 30, 4017 (1991).
[CrossRef] [PubMed]

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, “A Fabry– Perot interferometric technique for the electro-optical characterization of nonlinear optical polymers,” Nonlinear Opt. 1, 201 (1991).

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Perot devices for the characterization of polymeric electro-optic films,” J. Appl. Phys. 69, 3676 (1991).
[CrossRef]

1990 (3)

C. C. Teng and T. H. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734 (1990).
[CrossRef]

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer film,” Appl. Opt. 29, 2839 (1990).
[CrossRef] [PubMed]

1989 (2)

1988 (2)

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

H. Uchiki and T. Kobayashi, “New determination method of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymers,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

1986 (1)

K. D. Singer, J. E. Sohn, and S. L. Lalama, “Second-harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248 (1986).
[CrossRef]

1972 (1)

1937 (1)

P. Rouard, “Études des propriétés optiques des lames métalliques très minces,” Ann. Phys. (Paris) 7, 291 (1937).

Berreman, D. W.

Brombacher, L.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
[CrossRef]

Caracci, S.

N. F. O’Brien, V. Dominic, and S. Caracci, “Electro-refraction and electro-absorption in poled polymer Fabry–Perot étalons,” J. Appl. Phys. 79, 7493 (1996).
[CrossRef]

Chastaing, E.

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Cheng, X. M.

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

Chollet, P.-A.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
[CrossRef]

D. Morichere, P.-A. Chollet, W. Fleming, M. Jurich, B. A. Smith, and J. D. Swalen, “Electro-optic effects in two tolane side-chain nonlinear-optical polymers: comparison between measured coefficients and second-harmonic generation,” J. Opt. Soc. Am. B 10, 1894 (1993).
[CrossRef]

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Clays, K.

Comizzoli, R. B.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Dienes, A.

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

M. A. Mortazavi, A. Knoesen, S. T. Kowel, B. G. Higgins, and A. Dienes, “Second-harmonic generation and absorption studies of polymer-dye films oriented by corona-onset poling at elevated temperatures,” J. Opt. Soc. Am. B 6, 733 (1989).
[CrossRef]

Dominic, V.

N. F. O’Brien, V. Dominic, and S. Caracci, “Electro-refraction and electro-absorption in poled polymer Fabry–Perot étalons,” J. Appl. Phys. 79, 7493 (1996).
[CrossRef]

Dumont, M.

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

East, A. J.

G. Khanarian, M. A. Mortazavi, and A. J. East, “Phase-matched second-harmonic generation from free-standing periodically stacked polymer films,” Appl. Phys. Lett. 63, 1462 (1993).
[CrossRef]

Eldering, C. A.

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Perot devices for the characterization of polymeric electro-optic films,” J. Appl. Phys. 69, 3676 (1991).
[CrossRef]

C. A. Eldering, S. T. Kowel, and A. Knoesen, “Electrically induced transmissivity modulation in polymeric thin film Fabry–Perot etalons,” Appl. Opt. 28, 4442 (1989).
[CrossRef] [PubMed]

Fleming, W.

Furman, E.

F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78, 9 (1995).
[CrossRef]

Gadret, G.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
[CrossRef]

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Graf, M.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
[CrossRef]

Haertling, G. H.

F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78, 9 (1995).
[CrossRef]

Han, S. H.

Hayden, L. M.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Heldmann, C.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
[CrossRef]

Henry, R. A.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Herminghaus, S.

Higgins, B. G.

Hill, R. A.

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

R. A. Hill, A. Knoesen, and M. A. Mortazavi, “Corona poling of nonlinear polymer thin films for electro-optic modulators,” Appl. Phys. Lett. 65, 1733 (1994).
[CrossRef]

Holland, W. R.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Hoover, J. M.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Jurich, M.

Kajzar, F.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
[CrossRef]

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Katz, H. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Keosian, R. A.

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 74, 1869 (1994).
[CrossRef]

Khanarian, G.

G. Khanarian, M. A. Mortazavi, and A. J. East, “Phase-matched second-harmonic generation from free-standing periodically stacked polymer films,” Appl. Phys. Lett. 63, 1462 (1993).
[CrossRef]

Knoesen, A.

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

R. A. Hill, A. Knoesen, and M. A. Mortazavi, “Corona poling of nonlinear polymer thin films for electro-optic modulators,” Appl. Phys. Lett. 65, 1733 (1994).
[CrossRef]

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

A. Knoesen, “Simple approach to reflectance analysis of birefringent stratified films,” Appl. Opt. 30, 4017 (1991).
[CrossRef] [PubMed]

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Perot devices for the characterization of polymeric electro-optic films,” J. Appl. Phys. 69, 3676 (1991).
[CrossRef]

C. A. Eldering, S. T. Kowel, and A. Knoesen, “Electrically induced transmissivity modulation in polymeric thin film Fabry–Perot etalons,” Appl. Opt. 28, 4442 (1989).
[CrossRef] [PubMed]

M. A. Mortazavi, A. Knoesen, S. T. Kowel, B. G. Higgins, and A. Dienes, “Second-harmonic generation and absorption studies of polymer-dye films oriented by corona-onset poling at elevated temperatures,” J. Opt. Soc. Am. B 6, 733 (1989).
[CrossRef]

Kobayashi, T.

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

H. Uchiki and T. Kobayashi, “New determination method of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymers,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

Kowel, S. T.

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Perot devices for the characterization of polymeric electro-optic films,” J. Appl. Phys. 69, 3676 (1991).
[CrossRef]

C. A. Eldering, S. T. Kowel, and A. Knoesen, “Electrically induced transmissivity modulation in polymeric thin film Fabry–Perot etalons,” Appl. Opt. 28, 4442 (1989).
[CrossRef] [PubMed]

M. A. Mortazavi, A. Knoesen, S. T. Kowel, B. G. Higgins, and A. Dienes, “Second-harmonic generation and absorption studies of polymer-dye films oriented by corona-onset poling at elevated temperatures,” J. Opt. Soc. Am. B 6, 733 (1989).
[CrossRef]

Kuzyk, M. G.

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 74, 1869 (1994).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Lalama, S. J.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Lalama, S. L.

K. D. Singer, J. E. Sohn, and S. L. Lalama, “Second-harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248 (1986).
[CrossRef]

Lecomte, J. P.

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, “A Fabry– Perot interferometric technique for the electro-optical characterization of nonlinear optical polymers,” Nonlinear Opt. 1, 201 (1991).

Lévy, Y.

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Lindsay, G. A.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Man, T. H.

C. C. Teng and T. H. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734 (1990).
[CrossRef]

Meyrueix, R.

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, “A Fabry– Perot interferometric technique for the electro-optical characterization of nonlinear optical polymers,” Nonlinear Opt. 1, 201 (1991).

Misawa, K.

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

Molau, N. E.

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

Morichere, D.

Mortazavi, M. A.

R. A. Hill, A. Knoesen, and M. A. Mortazavi, “Corona poling of nonlinear polymer thin films for electro-optic modulators,” Appl. Phys. Lett. 65, 1733 (1994).
[CrossRef]

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

G. Khanarian, M. A. Mortazavi, and A. J. East, “Phase-matched second-harmonic generation from free-standing periodically stacked polymer films,” Appl. Phys. Lett. 63, 1462 (1993).
[CrossRef]

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

M. A. Mortazavi, A. Knoesen, S. T. Kowel, B. G. Higgins, and A. Dienes, “Second-harmonic generation and absorption studies of polymer-dye films oriented by corona-onset poling at elevated temperatures,” J. Opt. Soc. Am. B 6, 733 (1989).
[CrossRef]

Neher, D.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
[CrossRef]

Norwood, R. A.

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 74, 1869 (1994).
[CrossRef]

O’Brien, N. F.

N. F. O’Brien, V. Dominic, and S. Caracci, “Electro-refraction and electro-absorption in poled polymer Fabry–Perot étalons,” J. Appl. Phys. 79, 7493 (1996).
[CrossRef]

Ore, F. R.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Pasillas, P. L.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Qiu, F. S.

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

Raimond, P.

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
[CrossRef]

Robin, P.

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Rouard, P.

P. Rouard, “Études des propriétés optiques des lames métalliques très minces,” Ann. Phys. (Paris) 7, 291 (1937).

Sauter, G. F.

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

Schildkraut, J. S.

Schilling, M. L.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Singer, K. D.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

K. D. Singer, J. E. Sohn, and S. L. Lalama, “Second-harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248 (1986).
[CrossRef]

Smith, B. A.

Sohn, J. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

K. D. Singer, J. E. Sohn, and S. L. Lalama, “Second-harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248 (1986).
[CrossRef]

Swalen, J. D.

Tapolsky, G.

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, “A Fabry– Perot interferometric technique for the electro-optical characterization of nonlinear optical polymers,” Nonlinear Opt. 1, 201 (1991).

Teng, C. C.

C. C. Teng and T. H. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734 (1990).
[CrossRef]

Thackara, J. I.

J. D. Swalen and J. I. Thackara, “Electro-optic measurements of poled polymeric films,” Nonlinear Opt. 10, 371 (1995).

Uchiki, H.

H. Uchiki and T. Kobayashi, “New determination method of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymers,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

Ueki, A.

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

Wang, F.

F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78, 9 (1995).
[CrossRef]

Wu, J. W.

Yankelevich, D. R.

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

Yoon, H. N.

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

Ann. Phys. (Paris) (1)

P. Rouard, “Études des propriétés optiques des lames métalliques très minces,” Ann. Phys. (Paris) 7, 291 (1937).

Appl. Opt. (3)

Appl. Phys. Lett. (6)

K. D. Singer, J. E. Sohn, and S. L. Lalama, “Second-harmonic generation in poled polymer films,” Appl. Phys. Lett. 49, 248 (1986).
[CrossRef]

C. C. Teng and T. H. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734 (1990).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

F. S. Qiu, K. Misawa, X. M. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605 (1994).
[CrossRef]

R. A. Hill, A. Knoesen, and M. A. Mortazavi, “Corona poling of nonlinear polymer thin films for electro-optic modulators,” Appl. Phys. Lett. 65, 1733 (1994).
[CrossRef]

G. Khanarian, M. A. Mortazavi, and A. J. East, “Phase-matched second-harmonic generation from free-standing periodically stacked polymer films,” Appl. Phys. Lett. 63, 1462 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

D. R. Yankelevich, R. A. Hill, A. Knoesen, M. A. Mortazavi, H. N. Yoon, and S. T. Kowel, “Polymeric modulator for high frequency optical interconnects,” IEEE Photonics Technol. Lett. 6, 386 (1994).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

A. Knoesen, N. E. Molau, D. R. Yankelevich, M. A. Mortazavi, and A. Dienes, “Corona-poled nonlinear polymeric films: in situ electric field measurement, characterization and ultrashort-pulse applications,” Int. J. Nonlinear Opt. Phys. 1, 73 (1992).
[CrossRef]

J. Appl. Phys. (6)

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 74, 1869 (1994).
[CrossRef]

N. F. O’Brien, V. Dominic, and S. Caracci, “Electro-refraction and electro-absorption in poled polymer Fabry–Perot étalons,” J. Appl. Phys. 79, 7493 (1996).
[CrossRef]

H. Uchiki and T. Kobayashi, “New determination method of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymers,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78, 9 (1995).
[CrossRef]

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Perot devices for the characterization of polymeric electro-optic films,” J. Appl. Phys. 69, 3676 (1991).
[CrossRef]

L. M. Hayden, G. F. Sauter, F. R. Ore, P. L. Pasillas, J. M. Hoover, G. A. Lindsay, and R. A. Henry, “Second-order nonlinear optical measurements in guest-host and side-chain polymers,” J. Appl. Phys. 68, 456 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (5)

Nonlinear Opt. (3)

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, “A Fabry– Perot interferometric technique for the electro-optical characterization of nonlinear optical polymers,” Nonlinear Opt. 1, 201 (1991).

J. D. Swalen and J. I. Thackara, “Electro-optic measurements of poled polymeric films,” Nonlinear Opt. 10, 371 (1995).

Y. Lévy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Nonlinear Opt. 4, 1 (1993).

Thin Solid Films (2)

P.-A. Chollet, G. Gadret, F. Kajzar, and P. Raimond, “Electro-optic coefficient determination in stratified organized molecular thin films: application to poled polymers,” Thin Solid Films 242, 132 (1994).
[CrossRef]

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241 (1995).
[CrossRef]

Other (8)

S. A. Hamilton, D. R. Yankelevich, A. Knoesen, R. T. Weverka, R. A. Hill, and G. C. Bjorklund, “Polymer in-line fiber modulators for broadband radio-frequency optical links,” J. Opt. Soc. Am. B (to be published).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

See, e.g., R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987); P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1991).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

F. Wooten, Optical Properties of Solids (Academic, San Diego, Calif., 1972).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes–The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

In the error analysis, fitted parameters from the actual experiment (Fig. 8) are used as surrogates for the true parameters. Computer-generated random numbers within the specified error of the data, σmin, are used to simulate many (in our case 200) synthetic data sets. For each of these sets, best-fit parameters are evaluated to yield their distribution around the surrogate true parameters (algorithm available on PROFIT software from Quantum Soft, Zurich).

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Figures (18)

Fig. 1
Fig. 1

Five-step sample preparation procedure using the lift-off technique: 1, Spin polymer onto a release layer (e.g., water-soluble PAA) coated donor substrate. 2, Corona pole the polymer. 3, Deposit thin (30-nm) top metal electrode by e-beam evaporation and dice polymer into segments. 4, Dissolve release layer (in water) and lift off polymer. 5, Deposit polymer onto final substrate, which is covered with a thick (150-nm) metal ground electrode.

Fig. 2
Fig. 2

Chemical structures of the 10 mol. % DR1–PMMA side chain and the 5 wt.% PhTCV/PMMA guest–host NLP.

Fig. 3
Fig. 3

Experimental setup: P’s, polarizers; L1, collimating lens (f=200 mm); L2, collimating lens (f=19 mm); I, iris for beam alignment; I0, laser power monitor. Reflectance R is measured with an analog-to-digital converter; the change in reflectance ΔR, with lock-in amplification. Only half of the substrate is covered with the bottom electrode. The NLP film overlaps this boundary so the second-harmonic generation experiment can be performed on the transparent side of the same sample.

Fig. 4
Fig. 4

Refractive index n and extinction coefficient k of DR1–PMMA and PhTCV/PMMA as measured by variable-angle spectroscopic ellipsometry.

Fig. 5
Fig. 5

Refractive index n and extinction coefficient k of gold as measured by variable-angle spectroscopic ellipsometry for three sample-preparation methods: solid curves, 150 nm upon glass, 1-nm/s deposition rate; dashed curves, 10 nm upon silicon, 0.1-nm/s deposition rate; dotted–dashed curves, as in Ref. 23.

Fig. 6
Fig. 6

Refractive index n and extinction coefficient k of aluminum as measured by variable-angle spectroscopic ellipsometry for several sample-preparation methods: solid curves, 100 nm upon glass, 1-nm/s deposition rate; dotted–dashed curves, 100 nm upon glass, 0.1-nm/s deposition rate; dashed curves, 20 nm upon silicon, 0.1-nm/s deposition rate; dashed–multidotted curves, as in Ref. 23.

Fig. 7
Fig. 7

Oblique reflection and transmission of a plane wave. (a) Single interface. The xz plane is the plane of incidence. TE and TM refer to the electric fields perpendicular to and in the plane of incidence, respectively. kz is the effective wave-vector z component. Note that kx is common to all the layers because it corresponds to the tangential wave-vector component. (b) Multiple layers. The ambient (layer 0) and the substrate (layer 1) media are infinitely extended. The iterative reduction of the reflection coefficients of layers j, k, and l to a single interface reflection coefficient is sketched schematically.

Fig. 8
Fig. 8

Reflectance of a DR1–PMMA/gold RFPM for TM polarization as a function of angle of incidence at λ=633 nm. Solid curve, best fit; dashed curve, worst fit for 1.5kAu6.5; dashed–dotted curves fit for kAu as measured by ellipsometry. The error bar indicates σmin for an acceptable fit for kAu=3.1. Notice the increase in reflectance minima values with increasing angle of incidence for the worst fit with kAu=1.5; see text.

Fig. 9
Fig. 9

Change in reflectance of the DR1–PMMA/gold RFPM for TM polarization at λ=633 nm. Solid and dashed curves as in Fig. 10.

Fig. 10
Fig. 10

Calculated reflectance for different degrees of NLP surface roughness of the DR1–PMMA/gold RFPM for TE polarization as a function of angle of incidence at λ=633 nm.

Fig. 11
Fig. 11

Apparent extinction coefficient as a function of surface roughness for the NLP film of the DR1–PMMA/gold RFPM; TE polarization, λ=633 nm. The phenomenological quadratic dependence extrapolates to 2% surface roughness, assuming that the NLP virtually has no absorption at this wavelength.

Fig. 12
Fig. 12

Modeled reflectance of the PhTCV/PMMA RFPM with gold and aluminum electrodes for TM polarization at λ =430 nm. Model parameters are given in Table 3.

Fig. 13
Fig. 13

Modeled change in reflectance of the PhTCV/PMMA RFPM with gold and aluminum electrodes for TM polarization at λ=430 nm. Model parameters are given in Table 3. Notice the difference in modulation’s dynamic range for one and the same NLP.

Fig. 14
Fig. 14

Measured reflectance of the PhTCV/PMMA RFPM with gold and aluminum electrodes for TM polarization at λ =430 nm. The RFPM was fabricated based on the modeling results. Solid curves calculated with RFPM parameters given in Table 4.

Fig. 15
Fig. 15

Measured change in reflectance of the PhTCV/PMMA RFPM with gold and aluminum electrodes for TM polarization at λ=430 nm. Curves are data fits with RFPM parameters as given in Table 4. Notice that the ordinates for gold and aluminum electrode measurements have the same scale.

Fig. 16
Fig. 16

Measured change in reflectance of the PhTCV/PMMA RFPM with gold and aluminum electrodes for TE polarization at λ=430 nm. Curves are data fits with RFPM parameters as given in Table 4. The measured and calculated phases are also shown.

Fig. 17
Fig. 17

DR1–PMMA/gold RFPM; linear optical parameters as a function of the extinction coefficient of the gold layer kAu at λ =633 nm. Filled squares, TE; open square, TM measurements. (a) Left-hand scale, χ2 of measured data fits assuming normally distributed errors with equal standard deviation σi for all data points i; right-hand scale, standard deviation σmin in data errors required for an acceptable fit; see text. σmin is given with respect to normalized reflectances. Arrows, kAu as measured ellipsometrically (left arrow) and best-fit value kAu for TM polarization (right arrow). (b) Refractive index of the top gold layer. (c) Thickness of the top gold layer. (1 Å=0.1 nm.) Arrow, crossover between TE and TM data for kAu close to the value measured by ellipsometry for a 150-nm-thick gold layer; solid curves, power-law dependence. (d) NLP film thickness. (e) nO and nE of the NLP layer. Arrow, crossover point between TE and TM data at the isotropic index of the NLP as measured by ellipsometry; solid curves, power-law dependence. (f) kO and kE of the NLP layer. Values higher than measured by ellipsometry; see text.

Fig. 18
Fig. 18

DR1–PMMA/gold RFPM; EO parameters as a function of the extinction coefficient of the gold layer kAu at λ=633 nm. Filled squares, TE; open squares, TM measurements. (a) EO coefficients r13 and r33. (b) Left-hand scale, χ2 of measured data fits assuming normally distributed errors with equal standard deviation σi for all data points i; right-hand scale, standard deviation σmin,EO in data errors required for an acceptable fit; see text. σmin,EO are given in percent with respect to changes in reflectance.  

Tables (5)

Tables Icon

Table 1 Indices of Refraction and Extinction Coefficients of Gold and Aluminum Measured by Ellipsometry for Several Sample-Preparation Conditions

Tables Icon

Table 2 Accuracy of a RFPM for Linear Optical and Electro-Optical Measurements at λ=633 nm (10 mol. % DR1–PMMA Side-Chain NLP)

Tables Icon

Table 3 Modeling Parameters for Top Metal Layer and NLP for a RFPM Based on 5 wt. % PhTCV in PMMA

Tables Icon

Table 4 Measured Parameters with Intrinsic Errors for Top Metal Layer and NLP for a RFPM Based on 5 wt. % PhTCV in PMMA

Tables Icon

Table 5 NLP Parameter Sets for 10 mol. % DR1–PMMA with Similar Least-Squares Deviation to Measured Data for kAu=4.5 at λ=633 nm

Equations (13)

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

rij(TE, TM)=ki,z(εi,x)δ-kj,z(εj,x)δki,z(εi,x)δ+kj,z(εj,x)δ,
TE,δ=0;TM,δ=1
rijk=rij+rjk exp(2ikj,zdj)1+rijrjk exp(2ikj,zdj),
rijk=rij+rjkl exp(2ikj,zdj)1+rijrjkl exp(2ikj,zdj).
R=|r012|2.
ki,z=2πλ εOεE (εE-sin2 θ0)1/2,
ki,z=2πλ (εi-sin2 θ0)1/2,
Δ1εi=r˜i3E3,
Δεi=-εi2 r˜i3E3,
Δni=-ni32 ri3E3,
Δd=dd33E3,
ΔRR(E3)-R(0).
Reff12πΔd2 d0-4Δdd0+4ΔdR(d)exp-(d-d0)22Δd2dd,

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