## Analysis of reflective Mach-Zehnder interferometry for electro-optic characterization of poled polymer films in multilayer structures |

Optics Express, Vol. 20, Issue 16, pp. 18254-18267 (2012)

http://dx.doi.org/10.1364/OE.20.018254

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### 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

© 2012 OSA

## 1. Introduction

3. 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]

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. Express **14**(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,” Polymers **3**(3), 1310–1324 (2011). [CrossRef]

10. D. Morichère, 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**(10), 1894–1900 (1993). [CrossRef]

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]

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]

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]

3. 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]

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

*et al*. [14

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]

*et al*. [18

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]

*et al*. [19

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]

*et al*. [16

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]

*et al*. [17

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]

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. Express **14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

## 2. Theory

### 2.1 Rigorous Expressions for the rigorous MZIR model

**79**(23), 3749–3751 (2001). [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]

*, created by the rotating glass plate. The dc intensity is expressed aswhere the subscript*

_{m}*m*represents

*s-*or

*p-*polarization and

*r*. Similar to the dc intensity curve, the modulated intensity is collected from the lock-in amplifier under the application of AC voltage to the sample as a function of the phase Ω

_{m}*created by the glass plate. To first order in*

_{m}*V*, the modulated intensity

*A*,

*B*,

*δA*,

*δB*, and

*δ*Ψ for

*s-*and

*p-*polarized light. We note that Eqs. (2) and (4) are quite similar to those in the rigorous Teng-Man method [7

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. Express **14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

*s*- and

*p*- reflection coefficients for multilayered structures as shown in Fig. 2(a) have the form

*s*and

*p*subscripts and the reflection coefficient at the single interface is given bywith the

*s*- and

*p*- wave impedances (normalized to free space impedance) of each layer given bywhere

*s*- and

*p*- polarizations, respectively. The propagation constants are

*j*= 1 or 3 (

**14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

*s*- and

*p*- polarization and is given by [21]Note that Ref. 19

**97**(4), 041109 (2010). [CrossRef]

**14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

*m*(

*s*or

*p*) in reflection coefficients and propagation constants.

**97**(4), 041109 (2010). [CrossRef]

*d*

_{33}is determined by a separate measurement with the sample flipped and the back electrode acting as a mirror while the modulating voltage is applied. In this case, there is only modulation of the phase of the reflected beam given bywhere

*θ*is the angle of incidence. Measurement of this phase change then determines

*d*

_{33}to be used in all subsequent calculations. The details are given in Appendix A.

*d*

_{33}from Eq. (16) can be written in the matrix formsfor

*s*-polarization, and

*p*-polarization. The left hand sides are obtained from the experimental data by fitting Eqs. (2) and (4) and using

*d*

_{33}from Eq. (16). The

*H*functions in general depend on the refractive index and thickness of the layers in the sample structure. First, Eq. (17) is solved for

*r*

_{13}and

*s*

_{13}. Then these values are used in Eq. (18) to determine

*r*

_{33}and

*s*

_{33}.

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]

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]

**14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

### 2.2 Simple MZIR Model

*d*is the NLO film thickness.

*h*,

*b*for the simple model instead of

*H*,

*s*

_{j}_{3}and phase modulation only on

*r*

_{j}_{3}. In general, this is not true when all layers of the sample structure are taken into account.

*δψ*and

_{s}*δψ*are obtained from the experimental data, then Eq. (22) is first solved for

_{p}*r*

_{13}using the separately determined value of

*d*

_{33}as described above, and then the result used in Eq. (23) to obtain

*r*

_{33}.

*d*

_{33}. We note that Eq. (24) (with

*d*

_{33}= 0) and Eq. (25) agree with those in Refs. 4

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

**14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

### 2.3 Comparison to previous MZIR simple model equations

*s*

_{j}_{3}= 0, we derive the expressions in Eqs. (22) and (23) for the voltage induced phase change by differentiation of

*et al*. [14

**79**(23), 3749–3751 (2001). [CrossRef]

**97**(4), 041109 (2010). [CrossRef]

**83**(4), 1848–1853 (1998). [CrossRef]

**83**(4), 1848–1853 (1998). [CrossRef]

22. 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**(5), 1131–1137 (1997). [CrossRef]

*s*in Ref. 18

**83**(4), 1848–1853 (1998). [CrossRef]

*s*in Ref. 19

_{EO}**97**(4), 041109 (2010). [CrossRef]

*optical*path length

22. 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**(5), 1131–1137 (1997). [CrossRef]

*s*-

*p*phase difference is correct. The details of Eq. (26) from the point of view of diagrammatic phase delays in the thin film are given in Appendix A.

**97**(4), 041109 (2010). [CrossRef]

**97**(4), 041109 (2010). [CrossRef]

**79**(23), 3749–3751 (2001). [CrossRef]

*p*-polarization case, however, expressions for

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]

**79**(23), 3749–3751 (2001). [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]

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]

**79**(23), 3749–3751 (2001). [CrossRef]

**65**(13), 1605–1607 (1994). [CrossRef]

**79**(23), 3749–3751 (2001). [CrossRef]

*n*and

_{o}*n*, we obtain an expression for the effective EO coefficient in the formassuming the operating wavelength is outside the absorption band. As a consequence of Eq. (27) and the previous results, the ratio of

_{e}**79**(23), 3749–3751 (2001). [CrossRef]

## 3. Results: numerical estimation of errors from use of the simple analysis

*r*

_{13}to

*r*

_{33}is used. This implies that results from the simple MZIR method might be erroneous when multiple reflection effects are ignored. In this section, we simulate the relative error of

*r*

_{13}and

*r*

_{33}resulting from use of the simple analysis of the MZIR method. As in Ref. 7

**14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

*n*,

_{o}*n*) = (1.73, 1.79) at the wavelength of 1320 nm and a 150 nm thick Abrisa

_{e}^{®}ITO/glass substrate (the ITO refractive index is about 1 + 0.2

*i*at 1320 nm). The EO coefficients are assumed to be 100 pm/V and 300 pm/V for

*r*

_{13}and

*r*

_{33}, respectively. First, modulated phases of

*s-*and

*p-*waves,

*r*

_{33}by the simple model analysis of MZIR will be exactly same as that by the simple Teng-Man method when the ratio of

*r*

_{13}to

*r*

_{33}obtained from the MZIR method is used in the simple Teng-Man analysis. Figure 3(b) shows errors when a 45 nm thick ITO (Thin Film Devices, Inc., with refractive index about 1.2 + 0.15

*i*at 1320 nm) was used to compare with a thicker Abrisa ITO. It shows much smaller error in

*r*

_{33}compared with the Abrisa ITO because of much lower reflectivity from the ITO layer that reduces overall multiple reflection effects.

*r*

_{33}to

*r*

_{13}as a function of thickness of the nonlinear polymer for the case of thick ITO (Abrisa) and thin ITO (TFD). When the thickness is less than ~0.2 μm, the ratios for both cases are larger than 10, which is much higher than the correct value of 3 that was assumed in the simulation. For the thickness larger than ~0.2 μm, the simulated ratio for the case of Abrisa ITO shows a large cyclic variation from approximately 0 to 8, as expected in the

*r*

_{33}and

*r*

_{13}from Fig. 3(a), whereas the ratio for the TFD ITO is much smaller than that for the Abrisa ITO because of lower absorption of the TFD ITO at the operating wavelength of 1320 nm. Nevertheless, even with the less reflective TFD ITO, values of the ratio

*r*-coefficient ratios if the multilayer nature of the sample is neglected.

## 4. Conclusions

*r*

_{13}to

*r*

_{33}obtained from the simple MZIR analysis is used in the simple Teng-Man measurement, indicating that the simple MZIR method can be erroneous because of the multiple reflection effects. This means that, although the MZIR method has the advantage of separate determination of

*r*

_{13}and

*r*

_{33}, the simple MZIR method cannot be viewed as an independent measurement to check simple Teng-Man measurements.

_{3}can be analyzed using the simple MZIR method because the thickness is large enough to avoid multiple reflections. However, it is not generally possible to avoid multiple reflection effects in a thin NLO film, because reflections from interfaces in multilayer structures overlap. We have also discussed the relative error caused by ignoring multiple reflection effects. Depending on the optical properties of NLO and TCO such as refractive index and thickness, the error in using the simple model can be large (>100%) in both

*r*

_{13}and

*r*

_{33}and oscillates from positive and negative, as can be seen in the simple Teng-Man method as discussed in Ref. 7

**14**(19), 8866–8884 (2006). [CrossRef] [PubMed]

## Appendix A: calculation of the modulated phase term for reflection from a thin slab

**83**(4), 1848–1853 (1998). [CrossRef]

**97**(4), 041109 (2010). [CrossRef]

**83**(4), 1848–1853 (1998). [CrossRef]

*b*

_{1}and

*b*

_{2}are the reflections at the air-gold interfaces with and without a voltage-induced thickness change, respectively. Then, since the optical paths are always in air, the path length difference is simply

*b*

_{1}is the reflection at the glass-film interface, beam

*b*

_{2}is the single pass trace through the film reflected off the gold, and beam

*b*

_{2}and the voltage-deviated beam

## Appendix B: Effective EO coefficient for *p*-polarization

*p*-polarized light propagating at non-normal incidence through a poled polymer film. Electro-optic coefficients are typically defined in connection with the electric impermeability tensor

*E*, electro-optically induced changes in the refractive index are represented by

_{k}*k, p, q =*1, 2, 3) [23]. The linear electro-optic coefficients

*z*-direction only.

*s*-and

*p*- polarizations are desired in the formrecalling that

*m = s*or

*p*. Because

*s*-polarization is straightforward and

*p*-polarization, we recall the well-known expression [24] resulting from Maxwell’s equations for a plane electric wave

**D**

_{ω}is the electric displacement vector and

*n*is the refractive index appropriate to the propagation direction and polarization. In the absence of nonlinear effects,

**D**

_{ω}, and then take the dot product of Eq. (34) with

*p*-polarization, we have

*α*is constant, we haveThus,This is the expression used in Refs. 8

_{p}**69**(6), 3676–3686 (1991). [CrossRef]

**65**(13), 1605–1607 (1994). [CrossRef]

*α*and thus

_{p}**97**(4), 041109 (2010). [CrossRef]

**79**(23), 3749–3751 (2001). [CrossRef]

*j=*1,3) for

*p*-polarization [25

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. B **4**(6), 968–976 (1987).

*γ*is the walk-off angle [26

26. W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B **12**(3), 416–427 (1995). [CrossRef]

**D**

_{ω}and

**E**

_{ω}, i.e.,

*α*is constant in this derivation. If one ignores the walk-off angle, as done in Ref. 14

_{p}**79**(23), 3749–3751 (2001). [CrossRef]

**79**(23), 3749–3751 (2001). [CrossRef]

26. W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B **12**(3), 416–427 (1995). [CrossRef]

*α*. The appropriate

_{p}## Acknowledgments

## References and links

1. | W. N. Herman, S. R. Flom, and S. H. Foulger, eds., |

2. | G. A. Lindsay and K. D. Singer, eds., |

3. | C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro‐optic coefficient of poled polymers,” Appl. Phys. Lett. |

4. | J. S. Schildkraut, “Determination of the electro optic coefficient of a poled polymer film,” Appl. Opt. |

5. | Y. Shuto and M. Amano, “Reflection measurement technique of electro‐optic coefficients in lithium niobate crystals and poled polymer films,” J. Appl. Phys. |

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. |

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. Express |

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. |

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,” Polymers |

10. | D. Morichère, 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 |

11. | 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 Series |

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

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. |

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. |

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. |

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. |

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. |

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. |

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. |

20. | M. Born and E. Wolf, |

21. | J. F. Nye, |

22. | 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 |

23. | I. P. Kaminow, |

24. | A. Yariv and P. Yeh, |

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. B |

26. | W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(190.4710) Nonlinear optics : Optical nonlinearities in organic materials

(310.6860) Thin films : Thin films, optical properties

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: May 14, 2012

Revised Manuscript: July 19, 2012

Manuscript Accepted: July 20, 2012

Published: July 25, 2012

**Citation**

Dong Hun Park and Warren N. Herman, "Analysis of reflective Mach-Zehnder interferometry for electro-optic characterization of poled polymer films in multilayer structures," Opt. Express **20**, 18254-18267 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18254

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### References

- 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.
- 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]
- 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]
- 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]
- 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]
- 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]
- 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. Morichère, 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. B10(10), 1894–1900 (1993). [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).
- D. H. Park, “Characterization of linear electro-optic effect of poled organic thin films”, Ph. D. Dissertation, University of Maryland, College Park, (2008).
- 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]
- 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]
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