Abstract

We consider the Mach-Zehnder interferometer (MZI) method that specifically uses a poled organic thin film as one of the reflective mirrors in order to characterize the two independent electro-optic tensor elements r13 and r33. We discuss both a simple analysis based on a three-layer structure and a rigorous method including multiple reflection effects in a multilayer structure. In doing so, we find that the simple analysis of the reflective MZI method yields identical results to the reflection ellipsometric method (simple Teng-Man method), first introduced by Teng and Man as well as Shildkraut in 1990, when the ratio of r13 to r33 obtained from the MZI method is used in the analysis of the simple Teng-Man method. Error introduced by ignoring the multilayer nature of the sample structures in the MZI method is discussed and corrections are given for previous expressions in the literature for the simple analysis.

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    [CrossRef]
  6. F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
    [CrossRef]
  7. D. H. Park, C. H. Lee, and W. N. Herman, “Analysis of multiple reflection effects in reflective measurements of electro-optic coefficients of poled polymers in multilayer structures,” Opt. Express14(19), 8866–8884 (2006).
    [CrossRef] [PubMed]
  8. C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Pérot devices for the characterization of polymeric electro‐optic films,” J. Appl. Phys.69(6), 3676–3686 (1991).
    [CrossRef]
  9. D. H. Park, J. Luo, A. K. Y. Jen, and W. N. Herman, “Simplified reflection Fabry-Perot method for determination of electro-optic coefficients of poled polymer thin films,” Polymers3(3), 1310–1324 (2011).
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  13. H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
    [CrossRef]
  14. W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
    [CrossRef]
  15. 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.75(4), 1869–1874 (1994).
    [CrossRef]
  16. 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(19), 1800–1802 (1988).
    [CrossRef]
  17. F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
    [CrossRef]
  18. M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
    [CrossRef]
  19. C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
    [CrossRef]
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    [CrossRef]
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  25. For discussion of the relationship between EO coefficients and nonlinear polarization, see, e.gK. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B4(6), 968–976 (1987).
  26. W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B12(3), 416–427 (1995).
    [CrossRef]

2011

D. H. Park, J. Luo, A. K. Y. Jen, and W. N. Herman, “Simplified reflection Fabry-Perot method for determination of electro-optic coefficients of poled polymer thin films,” Polymers3(3), 1310–1324 (2011).
[CrossRef]

2010

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

2006

2001

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[CrossRef]

1999

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
[CrossRef]

1998

M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
[CrossRef]

1997

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. B14(5), 1131–1137 (1997).
[CrossRef]

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

1995

Y. Shuto and M. Amano, “Reflection measurement technique of electro‐optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys.77(9), 4632–4638 (1995).
[CrossRef]

W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B12(3), 416–427 (1995).
[CrossRef]

1994

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.75(4), 1869–1874 (1994).
[CrossRef]

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[CrossRef]

1993

1991

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Pérot devices for the characterization of polymeric electro‐optic films,” J. Appl. Phys.69(6), 3676–3686 (1991).
[CrossRef]

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
[CrossRef]

1990

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro‐optic coefficient of poled polymers,” Appl. Phys. Lett.56(18), 1734–1736 (1990).
[CrossRef]

J. S. Schildkraut, “Determination of the electro optic coefficient of a poled polymer film,” Appl. Opt.29(19), 2839–2841 (1990).
[CrossRef] [PubMed]

1988

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(19), 1800–1802 (1988).
[CrossRef]

1987

Amano, M.

Y. Shuto and M. Amano, “Reflection measurement technique of electro‐optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys.77(9), 4632–4638 (1995).
[CrossRef]

Bertolotti, M.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
[CrossRef]

Chen, A.

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

Cheng, X.

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[CrossRef]

Cho, H. R.

M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
[CrossRef]

Chollet, P.-A.

Chuyanov, V.

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

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(19), 1800–1802 (1988).
[CrossRef]

Dalton, L. R.

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

Ding, Y. J.

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[CrossRef]

Eldering, C. A.

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Pérot devices for the characterization of polymeric electro‐optic films,” J. Appl. Phys.69(6), 3676–3686 (1991).
[CrossRef]

Fallahi, M.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Fang, C.

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[CrossRef]

Fleming, W.

Garner, S.

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

Greenlee, C.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Guilmo, A.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Han, S. H.

M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
[CrossRef]

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. B14(5), 1131–1137 (1997).
[CrossRef]

Hayden, L. M.

He, X. H.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
[CrossRef]

Herman, W. N.

Himmelhuber, R.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[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(19), 1800–1802 (1988).
[CrossRef]

Huang, S.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Jen, A. K. Y.

D. H. Park, J. Luo, A. K. Y. Jen, and W. N. Herman, “Simplified reflection Fabry-Perot method for determination of electro-optic coefficients of poled polymer thin films,” Polymers3(3), 1310–1324 (2011).
[CrossRef]

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Jurich, M.

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(19), 1800–1802 (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.75(4), 1869–1874 (1994).
[CrossRef]

Knoesen, A.

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Pérot devices for the characterization of polymeric electro‐optic films,” J. Appl. Phys.69(6), 3676–3686 (1991).
[CrossRef]

Kobayashi, T.

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[CrossRef]

Kowel, S. T.

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Pérot devices for the characterization of polymeric electro‐optic films,” J. Appl. Phys.69(6), 3676–3686 (1991).
[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.75(4), 1869–1874 (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(19), 1800–1802 (1988).
[CrossRef]

For discussion of the relationship between EO coefficients and nonlinear polarization, see, e.gK. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B4(6), 968–976 (1987).

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(19), 1800–1802 (1988).
[CrossRef]

Lee, C. H.

Luo, J.

D. H. Park, J. Luo, A. K. Y. Jen, and W. N. Herman, “Simplified reflection Fabry-Perot method for determination of electro-optic coefficients of poled polymer thin films,” Polymers3(3), 1310–1324 (2011).
[CrossRef]

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Man, H. T.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro‐optic coefficient of poled polymers,” Appl. Phys. Lett.56(18), 1734–1736 (1990).
[CrossRef]

Michelotti, F.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
[CrossRef]

Misawa, K.

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[CrossRef]

Morichère, D.

Mu, X.

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[CrossRef]

Nicolao, G.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
[CrossRef]

Norwood, R. A.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[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.75(4), 1869–1874 (1994).
[CrossRef]

Opadeyi, A.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Park, D. H.

D. H. Park, J. Luo, A. K. Y. Jen, and W. N. Herman, “Simplified reflection Fabry-Perot method for determination of electro-optic coefficients of poled polymer thin films,” Polymers3(3), 1310–1324 (2011).
[CrossRef]

D. H. Park, C. H. Lee, and W. N. Herman, “Analysis of multiple reflection effects in reflective measurements of electro-optic coefficients of poled polymers in multilayer structures,” Opt. Express14(19), 8866–8884 (2006).
[CrossRef] [PubMed]

Peyghambarian, N.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Qiu, F.

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[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(19), 1800–1802 (1988).
[CrossRef]

Shi, W.

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[CrossRef]

Shih, Y. H.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
[CrossRef]

Shin, M. J.

M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
[CrossRef]

Shuto, Y.

Y. Shuto and M. Amano, “Reflection measurement technique of electro‐optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys.77(9), 4632–4638 (1995).
[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(19), 1800–1802 (1988).
[CrossRef]

For discussion of the relationship between EO coefficients and nonlinear polarization, see, e.gK. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B4(6), 968–976 (1987).

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(19), 1800–1802 (1988).
[CrossRef]

For discussion of the relationship between EO coefficients and nonlinear polarization, see, e.gK. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B4(6), 968–976 (1987).

Steier, W. H.

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

Swalen, J. D.

Tang, S. H.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
[CrossRef]

Teng, C. C.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro‐optic coefficient of poled polymers,” Appl. Phys. Lett.56(18), 1734–1736 (1990).
[CrossRef]

Tesi, F.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
[CrossRef]

Ueki, A.

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[CrossRef]

Wu, J. W.

M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
[CrossRef]

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. B14(5), 1131–1137 (1997).
[CrossRef]

Yin, X.

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[CrossRef]

Zhang, H. Y.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
[CrossRef]

Zhou, X.-H.

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro‐optic coefficient of poled polymers,” Appl. Phys. Lett.56(18), 1734–1736 (1990).
[CrossRef]

W. Shi, Y. J. Ding, X. Mu, X. Yin, and C. Fang, “Electro-optic and electromechanical properties of poled polymer thin films,” Appl. Phys. Lett.79(23), 3749–3751 (2001).
[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(19), 1800–1802 (1988).
[CrossRef]

F. Qiu, K. Misawa, X. 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(13), 1605–1607 (1994).
[CrossRef]

C. Greenlee, A. Guilmo, A. Opadeyi, R. Himmelhuber, R. A. Norwood, M. Fallahi, J. Luo, S. Huang, X.-H. Zhou, A. K. Y. Jen, and N. Peyghambarian, “Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films,” Appl. Phys. Lett.97(4), 041109 (2010).
[CrossRef]

Chem. Phys.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys.245(1-3), 311–326 (1999).
[CrossRef]

J. Appl. Phys.

C. A. Eldering, A. Knoesen, and S. T. Kowel, “Use of Fabry–Pérot devices for the characterization of polymeric electro‐optic films,” J. Appl. Phys.69(6), 3676–3686 (1991).
[CrossRef]

Y. Shuto and M. Amano, “Reflection measurement technique of electro‐optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys.77(9), 4632–4638 (1995).
[CrossRef]

M. J. Shin, H. R. Cho, S. H. Han, and J. W. Wu, “Analysis of a Mach-Zehnder interferometry measurement of the Pockels coefficients in a poled polymer film with a reflection configuration,” J. Appl. Phys.83(4), 1848–1853 (1998).
[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.75(4), 1869–1874 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun.86(6), 509–512 (1991).
[CrossRef]

Opt. Express

Polymers

D. H. Park, J. Luo, A. K. Y. Jen, and W. N. Herman, “Simplified reflection Fabry-Perot method for determination of electro-optic coefficients of poled polymer thin films,” Polymers3(3), 1310–1324 (2011).
[CrossRef]

Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series

A. Chen, V. Chuyanov, S. Garner, W. H. Steier, and L. R. Dalton, “Modified attenuated total reflection for the fast and routine electro-optic measurement of nonlinear optical polymer thin films,” Technical Digest of the Organic Thin Films for Photonics Applications, OSA Technical Digest Series14, 158–160 (1997).

Other

D. H. Park, “Characterization of linear electro-optic effect of poled organic thin films”, Ph. D. Dissertation, University of Maryland, College Park, (2008).

W. N. Herman, S. R. Flom, and S. H. Foulger, eds., Organic Thin Films for Photonic Applications (ACS, Symposium Series 2010) Vol. 1039.

G. A. Lindsay and K. D. Singer, eds., Polymers for Second-Order Nonlinear Optics (ACS, Symposium Series 1995) Vol. 601.

I. P. Kaminow, An Introduction to Electrooptic Devices (Academic Press Inc., 1974).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (John Wiley & Sons, 2003).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).

J. F. Nye, Physical Properties of Crystals (Oxford University Press, 1957).

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Figures (5)

Fig. 1
Fig. 1

Schematic of a MZIR experimental setup. PD is a photo-detector. Laser is continuous-wave operating at a communication wavelength of 1.3 or 1.55 μm.

Fig. 2
Fig. 2

Multilayered structures in (a) the rigorous model and (b) the simple model.

Fig. 3
Fig. 3

Plot of the error in r13 (black) and r33 (red) by the simple MZIR method for the case of thick ITO. Error in r33 (blue dot) by the simple Teng-Man method is plotted for comparison. Anisotropic index of refraction (1.73, 1.79) was used for the NLO thin film. For a TCO layer, (a) a 150 nm thick Abrisa ITO substrate and (b) a 45 nm thick TFD ITO substrate were used for this simulation.

Fig. 4
Fig. 4

Ratio of r33 to r13 for the case of 150 nm thick Abrisa ITO and 45 nm thick TFD ITO at the wavelength of 1320 nm resulting from simple analysis of MZIR when the correct value is 3.

Fig. 5
Fig. 5

Reflection with a voltage bias across the film. (a) Back-side reflection from metal (gold) surface. Horizontal dashed line represents a voltage-induced thickness change. (b) Front-side reflection from a glass-film-gold with only an EO effect. (c) Front-side reflection with only a converse piezoelectric effect.

Equations (42)

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I dc (m) = | E 0 | 2 | r m r 1m t 2m t gm t 1m r 2m | 2 ,
I dc (m) = | r 1m t 1m E 0 | 2 | r m t gm | 2 = I 0 4 | r m t gm | 2 = A m + B m sin 2 ( Ψ m Ω m 2 ),
A m = I 0 4 ( | r m || t gm | ) 2 , B m = I 0 | r m || t gm |, I 0 =4 | r 1m t 1m E 0 | 2 , r m =| r m | e i Ψ m , t gm =| t gm | e i Ω m .
I M (m) =δ A m +δ B m sin 2 ( Ψ m Ω m 2 )+ B m 2 sin( Ψ m Ω m )δ Ψ m .
δ B m B m +iδ Ψ m = δ r m r m .
r= r 23 + r ^ 34 e 2i β 3 d 3 1+ r 23 r ^ 34 e 2i β 3 d 3 r ^ 34 = r 34 + r ^ 45 e 2i β 4 d 4 1+ r 34 r ^ 45 e 2i β 4 d 4 r ^ 45 = r 45 + r 56 e 2i β 5 d 5 1+ r 45 r 56 e 2i β 5 d 5 ,
r jk = Z k Z j Z k + Z j ,
Z s = 1 n ˜ o 2 N 2 , Z p = 1 n ˜ o 1 ( N n ˜ e ) 2 ,
1 n ˜ p 2 = cos 2 α ˜ p n ˜ o 2 + sin 2 α ˜ p n ˜ e 2 .
δ r s r s = 1 r s r s n ˜ o δ n ˜ o + 1 r s r s d δd, δ r p r p = 1 r p r p n ˜ o δ n ˜ o + 1 r p r p n ˜ e δ n ˜ e + 1 r p r p d δd.
δ n ˜ j = 1 2 n ˜ j 3 ( r j3 +i s j3 ) E 3 ,
δd d = d 33 E 3 .
δ r s r s = H 1 (s) ( r 13 +i s 13 )+ H d (s) d 33 , δ r p r p = H 1 (p) ( r 13 +i s 13 )+ H 3 (p) ( r 33 +i s 33 )+ H d (p) d 33 ,
H j (m) n ˜ j 3 V 2d 1 r m r m n ˜ j , H d (m) =V 1 r m r m d .
H d (m) =V 1 r r d = 2iV β 4 r ^ 45 e 2i β 4 d e 2i β 3 d 3 ( 1+ r 23 r ^ 34 e 2i β 3 d 3 )( 1+ r 34 r ^ 45 e 2i β 4 d ) [ 1 r r 23 ][ 1 r ^ 34 r 34 ],
δψ=2 k 0 cosθδd=2 k 0 V d 33 cosθ,
( δ Ψ s Im[ H d (s) ] d 33 δ B s B s Re[ H d (s) ] d 33 )=( Im[ H 1 (s) ] Re[ H 1 (s) ] Re[ H 1 (s) ] Im[ H 1 (s) ] )( r 13 s 13 ),
( δ Ψ p Im[ H d (p) ] d 33 δ B p B p Re[ H d (p) ] d 33 )=( Im[ H 1 (p) ] Re[ H 1 (p) ] Re[ H 1 (p) ] Im[ H 1 (p) ] )( r 13 s 13 )+( Im[ H 3 (p) ] Re[ H 3 (p) ] Re[ H 3 (p) ] Im[ H 3 (p) ] )( r 33 s 33 ).
r s = e i2 β s d , r p = e i2 β p d ,
h 1 (s) =i k 0 V n ˜ o 4 n ˜ o 2 N 2 , h 1 (p) =i k 0 V n ˜ o 3 1 ( N n ˜ e ) 2 , h 3 (p) =i k 0 V n ˜ o n ˜ e N 2 n ˜ e 2 N 2
h d (s) =2i k 0 V n ˜ o 2 N 2 , h d (p) =2i k 0 V n ˜ o 1 ( N n ˜ e ) 2
δ ψ s 2 k 0 V n o 2 N 2 d 33 = k 0 V n o 4 n o 2 N 2 r 13 , δ b s b s = k 0 V n o 4 n o 2 N 2 s 13 ,
δ ψ p 2 k 0 V n o 1 ( N n e ) 2 d 33 = k 0 V n o 3 1 ( N n e ) 2 r 13 k 0 V n o n e N 2 n e 2 N 2 r 33 , δ b p b p = k 0 V n o 3 1 ( N n e ) 2 s 13 + k 0 V n o n e N 2 n e 2 N 2 s 33 .
δ ψ sp 2 k 0 V n o ( 1 ( N n o ) 2 1 ( N n e ) 2 ) d 33 = k 0 V[ ( n o 4 n o 2 N 2 n o 3 n e n e 2 N 2 ) r 13 n o n e N 2 n e 2 N 2 r 33 ].
δ ψ sp = n 2 N 2 n 2 N 2 ( r 33 r 13 ) k 0 V,
δ ψ m =δ( 2 β m d )=2 k 0 [ d cos α m δ n m + n m cos α m δd ],
r eff (p) = n o 2 n p 2 ( r 13 cos 2 α p + r 33 sin 2 α p ),
r 33 r 13 = ( n p 2 n o 2 r eff (p) r 13 cos 2 α p ) / sin 2 α p ,
δψ= k 0 n air ( 2 AB ¯ AD ¯ )=2 k 0 cosθδd,
δ ψ m = k 0 [ n m ( A B ¯ + B C ¯ ) n m ( AB ¯ + BC ¯ ) n g D D ¯ ] = k 0 { [ n m ( A B ¯ + B C ¯ ) n g A D ¯ ][ n m ( AB ¯ + BC ¯ ) n g AD ¯ ] } =2 k 0 d( n m cos α m n m cos α m )=2 k 0 dδ( n m cos α m ),
δ ψ m = ψ m ( b 2 ) ψ m ( b 2 ) = k 0 [ n m ( A B ¯ + B C ¯ ) n m ( AB ¯ + BC ¯ ) n g D D ¯ ] = k 0 [ n m ( A B ¯ + B C ¯ ) n m ( AB ¯ + BC ¯ ) n g ( A D ¯ AD ¯ ) ] = k 0 [ n m ( 2 d cos α m ) n m ( 2d cos α m ) n g ( 2 d tan α m sin θ 1 2dtan α m sin θ 1 ) ] =2 k 0 n m cos α m δd,
B =diag[ 1 n o 2 1 n o 2 1 n e 2 ].
δ( 1 n m 2 )= r eff (m) E 3 ,
n 2 [ E ω k ^ ( E ω k ^ ) ] 1 ε 0 D ω =0,
u ^ B u ^ = 1 n 2 ,
δ( 1 n p 2 )= u ^ p δ B u ^ p = cos 2 α p δ B 11 + sin 2 α p δ B 33 ( α p fixed).
[ r eff (p) ] α p =constant = r 13 cos 2 α p + r 33 sin 2 α p .
δ( 1 n p 2 )=δ u ^ p B u ^ p + u ^ p δ B u ^ p + u ^ p B δ u ^ p = n o 2 n p 2 [ r 13 cos 2 α p + r 33 sin 2 α p ] E 3 ,
n p 2 [ e ^ p E ω e ^ p k ^ ( E ω k ^ ) ] 1 ε 0 e ^ p ε E ω = 1 ε 0 e ^ p P ω NL ,
δ( n p 2 )= 1 ε 0 e ^ p P ω NL E ω cos 2 γ =[ n o 4 r 13 cos 2 ( α p γ ) cos 2 γ + n e 4 r 33 sin 2 ( α p γ ) cos 2 γ ] E 3 ,
[ r eff (p) ] α p =constant = 1 n p 4 [ n o 4 r 13 cos 2 ( α p γ ) cos 2 γ + n e 4 r 33 sin 2 ( α p γ ) cos 2 γ ],
cos( α p γ )= [ n p n o ] 2 cosγcos α p and sin( α p γ )= [ n p n e ] 2 cosγsin α p ,

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