## Closed-form Maker fringe formulas for poled polymer thin films in multilayer structures |

Optics Express, Vol. 20, Issue 1, pp. 173-185 (2012)

http://dx.doi.org/10.1364/OE.20.000173

Acrobat PDF (1216 KB)

### Abstract

We report new closed-form expressions for Maker fringes of anisotropic and absorbing poled polymer thin films in multilayer structures that include back reflections of both fundamental and second-harmonic waves. The expressions, based on boundary conditions at each interface, can be applied to multilayer structures containing a buffer and a transparent conducting oxide layer, which might enhance multiple reflections of fundamental and second-harmonic waves inside a nonlinear thin film layer. This formulation facilitates Maker fringe analysis for a sample containing additional multilayer structures on either side of a poled polymer thin film. Experimental data and numerical simulations are given to indicate the importance of inclusion of such a reflective layer in analyses for reliable characterization of second-harmonic tensor elements.

© 2011 OSA

## 1. Introduction

3. D. M. Burland, R. D. Miller, and C. A. Walsh, “Second-order nonlinearity in poled-polymer systems,” Chem. Rev. **94**(1), 31–75 (1994). [CrossRef]

4. 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]

6. 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]

7. P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. **8**(1), 21–22 (1962). [CrossRef]

17. V. Rodriguez and C. Sourisseau, “General Maker-fringe ellipsometric analyses in multilayer nonlinear and linear anisotropic optical media,” J. Opt. Soc. Am. B **19**(11), 2650–2664 (2002). [CrossRef]

7. P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. **8**(1), 21–22 (1962). [CrossRef]

*μ*= 1-3,

*j*= 1-6) associated with SHG. This technique, as further described in detail by Jerphagnon and Kurtz [8

8. J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. **41**(4), 1667–1681 (1970). [CrossRef]

*et al*. [9

9. N. Okamoto, Y. Hirano, and O. Sugihara, “Precise estimation of nonlinear-optical coefficients for anisotropic nonlinear films with C_{∞v} symmetry,” J. Opt. Soc. Am. B **9**(11), 2083–2087 (1970). [CrossRef]

10. 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]

11. T. K. Lim, M.-Y. Jeong, C. Song, and D. C. Kim, “Absorption effect in the calculation of a second-order nonlinear coefficient from the data of a maker fringe experiment,” Appl. Opt. **37**(13), 2723–2728 (1998). [CrossRef] [PubMed]

12. H. Hellwig and L. Bohaty, “Multiple reflections and Fabry-Perot interference corrections in Maker fringe experiments,” Opt. Commun. **161**(1-3), 51–56 (1999). [CrossRef]

14. M. Abe, I. Shoji, J. Suda, and T. Kondo, “Comprehensive analysis of multiple-reflection effects on rotational Maker-fringe experiments,” J. Opt. Soc. Am. B **25**(10), 1616–1624 (2008). [CrossRef]

15. M. Braun, F. Bauer, Th. Vogtmann, and M. Schwoerer, “Precise second-harmonic generation Maker fringe measurements in single crystals of the diacetylene NP/4-MPU and evaluation by a second-harmonic generation theory in 4×4 matrix formulation and ray tracing,” J. Opt. Soc. Am. B **14**(7), 1699–1706 (1997). [CrossRef]

16. M. Braun, F. Bauer, Th. Vogtmann, and M. Schwoerer, “Detailed analysis of second-harmonic-generation Maker fringes in biaxially birefringent materials by a 4×4 matrix formulation,” J. Opt. Soc. Am. B **15**(12), 2877–2884 (1998). [CrossRef]

17. V. Rodriguez and C. Sourisseau, “General Maker-fringe ellipsometric analyses in multilayer nonlinear and linear anisotropic optical media,” J. Opt. Soc. Am. B **19**(11), 2650–2664 (2002). [CrossRef]

_{3}or a thin NLOP film on a thick substrate prepared by corona poling or other poling methods where electrodes are not necessary. However, NLOP films prepared by electrode contact poling require two additional electrode layers for application of voltage, and the transparent conducting oxide (TCO) electrode between the NLO film layer and a substrate were neglected in previous analyses [18

18. S. Lee, B. Park, S.-D. Lee, G. Park, and Y. D. Kim, “Second-harmonic generation in poled films of nonlinear optical polymer composites,” Opt. Quantum Electron. **27**(5), 411–420 (1995). [CrossRef]

## 2. Theory

10. 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]

*mm*point-group symmetry (space group C

_{∞}

*) and has complex ordinary and extraordinary indices of refraction,*

_{v}*n*

_{o}and

*n*

_{e}, respectively [19]. The SH

*d*-coefficient tensor contains three independent complex elements and is given by [10

10. 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]

4. 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]

6. 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]

20. J. P. Drummond, S. J. Clarson, J. S. Zetts, F. K. Hopkins, and S. J. Caracci, “Enhanced electro-optic poling in guest–host systems using conductive polymer-based cladding layers,” Appl. Phys. Lett. **74**(3), 368–370 (1999). [CrossRef]

*p*-polarized plane wave of angular frequency

*ω*(fundamental wave) is incident from the left at an angle of incidence

*θ*. Derivation of the incident

*s*-polarized case is similar and straightforward. The SH electric (

**E**) and magnetic (

**H**) fields in each region are given as

*p*-wave reflection and transmission coefficients, respectively (

*p*→

*p*: fundamental

*p*-wave input to SH

*p*-wave output,

*s*→

*p*: fundamental

*s*-wave input to SH

*p*-wave output) and

*A*,

*B*,

*C*,

*D*,

*E*, and

*F*are constants. In case of isotropic layers,

**H**. In the anisotropic layers, the unit vectors along the SH electric field directions are

*γ*at the fundamental (

_{il}*i*= 1) and SH (

*i*= 2) wavelengths are included because of birefringence of the anisotropic layers [10

**12**(3), 416–427 (1995). [CrossRef]

*l*at the fundamental and SH wavelengths, respectively. For birefringent NLO films, we have for

*p*-polarizationwhere

*n*and

_{io}*n*, to prevent the notation from becoming unduly cumbersome, but Eq. (3) also can be applied to other anisotropic layers. The bound waves [8

_{ie}8. J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. **41**(4), 1667–1681 (1970). [CrossRef]

9. N. Okamoto, Y. Hirano, and O. Sugihara, “Precise estimation of nonlinear-optical coefficients for anisotropic nonlinear films with C_{∞v} symmetry,” J. Opt. Soc. Am. B **9**(11), 2083–2087 (1970). [CrossRef]

**E**and

**H**components at each interface gives the boundary conditions. The matrix method employing multiple interface boundary conditions [22] is used to calculate and , which are the

*p*-wave SH transmission and reflection coefficients, respectively for the case of a fundamental

*p*-wave input. From Eq. (B3), we find that the SH transmission coefficient from the multilayer structure containing an absorptive and birefringent NLO film is given as

**12**(3), 416–427 (1995). [CrossRef]

*p*-polarized transmission coefficient of the SH wave at the substrate/air interface and

*A*is the cross-sectional area of the fundamental wave.

_{cross}23. D. Guo, R. Lin, and W. Wang, “Gaussian-optics-based optical modeling and characterization of a Fabry-Perot microcavity for sensing applications,” J. Opt. Soc. Am. A **22**(8), 1577–1588 (2005). [CrossRef] [PubMed]

*η*-polarization Fresnel reflection coefficient from

*j*layer to

*k*layer as described in Eqs. (B5)-(B8).

## 3. Results

*p*→

*p*) for X-cut quartz (rotation is about

*z*-axis), which is commonly used for reference. The focused incident laser spot size used in the experiment is a few tens of microns, which is much smaller than the thickness of the X-cut quartz (533 μm). Therefore, multiply reflected beams at the quartz/air interface are spatially localized, so they don’t interfere. On the other hand, Eq. (4) is derived based on the plane wave analysis. One can simply make reflections

*μ*m thick film. Then 100 nm thick gold was deposited on the film using a thermal evaporator. After contact poling at the glass transition temperature of 135 °C using a poling voltage of ~100 V/μm, the gold poling electrode was etched off using a gold etchant KI + I

_{2}+ H

_{2}O (4:1:40) for a transmission type Maker fringe experiment. The optical properties of ITO and the NLOP film were measured using a spectroscopic ellipsometer (VASE

^{®}, J. A. Woollam Co., Inc.) as shown in Figs. 3(a) and (b) . Note that the large linear absorption of ITO in the infrared region can lead to considerable back reflections of fundamental waves.

*p*→

*p*and

*s*→

*p*cases. Noteworthy is that one can see a slight dip around 50° angle of incidence caused by back reflections in both the experimental and simulation data. However, this dip is not accounted for properly when back reflections of fundamental waves are ignored (green dash and black curve), which demonstrates that back reflections of fundamental waves should be taken into account in the analysis of SH transmission. In fact, the fundamental wave is more reflective than the SH at the ITO layer because of free carrier absorption of ITO in the infrared region as shown in Fig. 3(a). Depending on the thickness and optical properties of the NLOP film and the ITO layers, the shape and the dip position may change drastically. The linear absorption of the NLO film and the ITO is taken into account in the analysis based on the complex index of refraction in Figs. 3(a) and (b), but the nonparametric nonlinear absorption of the NLO film (imaginary part of

*d*-tensor component) is ignored for this specific nonlinear polymer because it is expected to be small compared with the real part of the

*d*-tensor component. The effect of a nonlinear absorption up to 20%

*d*-tensor component in the analysis is negligible in the fitting results, whereas the linear absorption of ITO and NLO film does affect the fitting. We also see that the analysis by the three layer model (blue curves in Figs. 3(c) and (d)), ignoring back reflection terms, is not suitable for the analysis of Maker fringe data from the multilayered structures involving reflective layers. Therefore, inclusion of the back reflection of fundamental waves and multilayer structures in the analysis is crucial in order to reliably estimate SH

*d*-tensor components for the poled polymer thin films.

*d*

_{33}of 360 ± 5 pm/V with the ratio of

*r*

_{33}is estimated to be 140 ± 30 pm/V and 100 ± 20 pm/V at 1300 nm and 1550 nm respectively, where the large error bound results from imprecise knowledge of local field effects. We were unable to directly measure EO coefficients of this sample, because the 1.2 μm thick film can support only one guided mode, which doesn’t allow use of the Attenuated Total Reflection (ATR) method for an accurate characterization. Direct measurement of EO coefficients of a thicker AJL49/APC sample with the higher weight percentage of 45 wt.% and lower poling field of 70 V/μm gave an EO coefficient

*r*

_{33}of 110 pm/V and 80 pm/V at 1300 nm and 1550 nm, respectively, which are comparable to our estimation from the measured SH

*d*

_{33}.

## 4. Conclusions

*d*-coefficients from Maker fringe SHG experiments on poled polymer thin films embedded in a multilayer structure with reflective layers, which can be dielectric or non-dielectric. The multilayer analysis including back reflections is necessary for second-order NLOP thin films prepared by electrode contact poling. We have shown that a TCO layer as a poling electrode has to be included in the analysis because it can enhance multiple reflections. We expect the proposed formulation to be useful to characterize Maker fringes of a multilayered poled polymer thin film or thick organic material [25

25. R. C. Hoffman, A. G. Mott, M. J. Ferry, T. M. Pritchett, W. Shensky, J. A. Orlicki, G. R. Martin, J. Dougherty, J. L. Leadore, A. M. Rawlett, and D. H. Park, “Poling of visible chromophores in millimeter-thick PMMA host,” Opt. Mater. Express **1**(1), 67–77 (2011). [CrossRef]

26. J. Zhang, G. Wang, Z. Liu, L. Wang, G. Zhang, X. Zhang, Y. Wu, P. Fu, and Y. Wu, “Growth and optical properties of a new nonlinear Na_{3}La_{9}O_{3}(BO_{3})_{8} crystal,” Opt. Express **18**(1), 237–243 (2010). [CrossRef] [PubMed]

27. C. Chen, Z. Shao, J. Jiang, J. Wei, J. Lin, J. Wang, N. Ye, J. Lv, B. Wu, M. Jiang, M. Yoshimura, Y. Mori, and T. Sasaki, “Determination of the nonlinear optical coefficients of YCa_{4}O(BO_{3})_{3} crystal,” J. Opt. Soc. Am. B **17**(4), 566–571 (2000). [CrossRef]

*d*coefficients depending on the spatial symmetry and crystal cut.

## Appendix A: Bound waves

*cgs*unit convention iswhere the nonlinear polarization is given by

**12**(3), 416–427 (1995). [CrossRef]

*x*- and

*y*-components of the forward bound electric and magnetic field, respectively, and the superscript

*r*denotes the reflected bound field. The phase terms are

*d*-coefficients for forward and backward waves arewith

*s*→

*p*case, we have

*e.g*.

*α*→

*s*(

*α*-polarized fundamental input to

*s*-polarized SH), should be considered in order to determine

*d*

_{15}separately. In this case, the fundamental electric field inside nonlinear medium can be expressed as

*s*-polarized SH transmission coefficient for

*α*-polarized fundamental input is given in Appendix C.

## Appendix B: Boundary conditions

**E**and

**H**components at each interface provides boundary conditions, which can be expressed in the matrix form

**are given as**ℙ

*s*- and

*p*- propagation constants are given by

*j*to

*k*are given by

*s*- and

*p*- wave impedances of each anisotropic and/or absorbing layer given by [28]where

*θ*is the external angle of incidence from air, and

*i =*1 or 2 represents fundamental and SH wavelengths, respectively. These can be applied to other layers with corresponding refractive indices and angle of incidence from air.

## Appendix C: *α*-polarized fundamental to *s*-polarized SHG

*α*(

*e.g*. 0° and 90° mean

*s*- and

*p*-polarizations, respectively). Similar to the

*p*→

*p*calculations in Appendix B, we can solve boundary conditions such that

*E*

_{y}and

*H*

_{x}are continuous at each interface and obtain the

*s*-polarized SH transmission coefficient in the form

*s*-polarized light inside the film. Substituting

**E**

_{2 }for the bound wave

*s*and

*p*electric fields,

*α*-polarized input fundamental wave is

*s*-polarized SH transmission coefficient in a similar form to Eq. (7):

## Acknowledgments

## References and links

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

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

3. | D. M. Burland, R. D. Miller, and C. A. Walsh, “Second-order nonlinearity in poled-polymer systems,” Chem. Rev. |

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

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

6. | 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 |

7. | P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. |

8. | J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. |

9. | N. Okamoto, Y. Hirano, and O. Sugihara, “Precise estimation of nonlinear-optical coefficients for anisotropic nonlinear films with C |

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

11. | T. K. Lim, M.-Y. Jeong, C. Song, and D. C. Kim, “Absorption effect in the calculation of a second-order nonlinear coefficient from the data of a maker fringe experiment,” Appl. Opt. |

12. | H. Hellwig and L. Bohaty, “Multiple reflections and Fabry-Perot interference corrections in Maker fringe experiments,” Opt. Commun. |

13. | N. A. Sanford and J. A. Aust, “Nonlinear optical characterization of LiNbO |

14. | M. Abe, I. Shoji, J. Suda, and T. Kondo, “Comprehensive analysis of multiple-reflection effects on rotational Maker-fringe experiments,” J. Opt. Soc. Am. B |

15. | M. Braun, F. Bauer, Th. Vogtmann, and M. Schwoerer, “Precise second-harmonic generation Maker fringe measurements in single crystals of the diacetylene NP/4-MPU and evaluation by a second-harmonic generation theory in 4×4 matrix formulation and ray tracing,” J. Opt. Soc. Am. B |

16. | M. Braun, F. Bauer, Th. Vogtmann, and M. Schwoerer, “Detailed analysis of second-harmonic-generation Maker fringes in biaxially birefringent materials by a 4×4 matrix formulation,” J. Opt. Soc. Am. B |

17. | V. Rodriguez and C. Sourisseau, “General Maker-fringe ellipsometric analyses in multilayer nonlinear and linear anisotropic optical media,” J. Opt. Soc. Am. B |

18. | S. Lee, B. Park, S.-D. Lee, G. Park, and Y. D. Kim, “Second-harmonic generation in poled films of nonlinear optical polymer composites,” Opt. Quantum Electron. |

19. | I. P. Kaminow, |

20. | J. P. Drummond, S. J. Clarson, J. S. Zetts, F. K. Hopkins, and S. J. Caracci, “Enhanced electro-optic poling in guest–host systems using conductive polymer-based cladding layers,” Appl. Phys. Lett. |

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

22. | P. Yeh, |

23. | D. Guo, R. Lin, and W. Wang, “Gaussian-optics-based optical modeling and characterization of a Fabry-Perot microcavity for sensing applications,” J. Opt. Soc. Am. A |

24. | K. D. Singer, M. D. 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 |

25. | R. C. Hoffman, A. G. Mott, M. J. Ferry, T. M. Pritchett, W. Shensky, J. A. Orlicki, G. R. Martin, J. Dougherty, J. L. Leadore, A. M. Rawlett, and D. H. Park, “Poling of visible chromophores in millimeter-thick PMMA host,” Opt. Mater. Express |

26. | J. Zhang, G. Wang, Z. Liu, L. Wang, G. Zhang, X. Zhang, Y. Wu, P. Fu, and Y. Wu, “Growth and optical properties of a new nonlinear Na |

27. | C. Chen, Z. Shao, J. Jiang, J. Wei, J. Lin, J. Wang, N. Ye, J. Lv, B. Wu, M. Jiang, M. Yoshimura, Y. Mori, and T. Sasaki, “Determination of the nonlinear optical coefficients of YCa |

28. | S. Ramo, J. R. Whinnery, and T. V. Duzer, |

**OCIS Codes**

(160.5470) Materials : Polymers

(190.4710) Nonlinear optics : Optical nonlinearities in organic materials

(310.6860) Thin films : Thin films, optical properties

**ToC Category:**

Thin Films

**History**

Original Manuscript: November 7, 2011

Revised Manuscript: December 9, 2011

Manuscript Accepted: December 12, 2011

Published: December 19, 2011

**Citation**

Dong Hun Park and Warren N. Herman, "Closed-form Maker fringe formulas for poled polymer thin films in multilayer structures," Opt. Express **20**, 173-185 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-173

Sort: Year | Journal | Reset

### References

- G. A. Lindsay and K. D. Singer, eds., Polymers for Second-Order Nonlinear Optics, Vol 601 of ACS Symposium Series (ACS, 1995).
- W. N. Herman, S. R. Flom, and S. H. Foulger, eds., Organic Thin Films for Photonic Applications, Vol. 1039 of ACS Symposium Series (ACS, 2010).
- D. M. Burland, R. D. Miller, and C. A. Walsh, “Second-order nonlinearity in poled-polymer systems,” Chem. Rev.94(1), 31–75 (1994). [CrossRef]
- 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]
- 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]
- P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.8(1), 21–22 (1962). [CrossRef]
- J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys.41(4), 1667–1681 (1970). [CrossRef]
- N. Okamoto, Y. Hirano, and O. Sugihara, “Precise estimation of nonlinear-optical coefficients for anisotropic nonlinear films with C∞v symmetry,” J. Opt. Soc. Am. B9(11), 2083–2087 (1970). [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]
- T. K. Lim, M.-Y. Jeong, C. Song, and D. C. Kim, “Absorption effect in the calculation of a second-order nonlinear coefficient from the data of a maker fringe experiment,” Appl. Opt.37(13), 2723–2728 (1998). [CrossRef] [PubMed]
- H. Hellwig and L. Bohaty, “Multiple reflections and Fabry-Perot interference corrections in Maker fringe experiments,” Opt. Commun.161(1-3), 51–56 (1999). [CrossRef]
- N. A. Sanford and J. A. Aust, “Nonlinear optical characterization of LiNbO3. I. Theoretical analysis of Maker fringe patterns for x-cut wafers,” J. Opt. Soc. Am. B15(12), 2885–2908 (1998). [CrossRef]
- M. Abe, I. Shoji, J. Suda, and T. Kondo, “Comprehensive analysis of multiple-reflection effects on rotational Maker-fringe experiments,” J. Opt. Soc. Am. B25(10), 1616–1624 (2008). [CrossRef]
- M. Braun, F. Bauer, Th. Vogtmann, and M. Schwoerer, “Precise second-harmonic generation Maker fringe measurements in single crystals of the diacetylene NP/4-MPU and evaluation by a second-harmonic generation theory in 4×4 matrix formulation and ray tracing,” J. Opt. Soc. Am. B14(7), 1699–1706 (1997). [CrossRef]
- M. Braun, F. Bauer, Th. Vogtmann, and M. Schwoerer, “Detailed analysis of second-harmonic-generation Maker fringes in biaxially birefringent materials by a 4×4 matrix formulation,” J. Opt. Soc. Am. B15(12), 2877–2884 (1998). [CrossRef]
- V. Rodriguez and C. Sourisseau, “General Maker-fringe ellipsometric analyses in multilayer nonlinear and linear anisotropic optical media,” J. Opt. Soc. Am. B19(11), 2650–2664 (2002). [CrossRef]
- S. Lee, B. Park, S.-D. Lee, G. Park, and Y. D. Kim, “Second-harmonic generation in poled films of nonlinear optical polymer composites,” Opt. Quantum Electron.27(5), 411–420 (1995). [CrossRef]
- I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, 1974).
- J. P. Drummond, S. J. Clarson, J. S. Zetts, F. K. Hopkins, and S. J. Caracci, “Enhanced electro-optic poling in guest–host systems using conductive polymer-based cladding layers,” Appl. Phys. Lett.74(3), 368–370 (1999). [CrossRef]
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
- P. Yeh, Optical Waves in Layered Media (Wiley, 1988)
- D. Guo, R. Lin, and W. Wang, “Gaussian-optics-based optical modeling and characterization of a Fabry-Perot microcavity for sensing applications,” J. Opt. Soc. Am. A22(8), 1577–1588 (2005). [CrossRef] [PubMed]
- K. D. Singer, M. D. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B17, 566–571 (2000).
- R. C. Hoffman, A. G. Mott, M. J. Ferry, T. M. Pritchett, W. Shensky, J. A. Orlicki, G. R. Martin, J. Dougherty, J. L. Leadore, A. M. Rawlett, and D. H. Park, “Poling of visible chromophores in millimeter-thick PMMA host,” Opt. Mater. Express1(1), 67–77 (2011). [CrossRef]
- J. Zhang, G. Wang, Z. Liu, L. Wang, G. Zhang, X. Zhang, Y. Wu, P. Fu, and Y. Wu, “Growth and optical properties of a new nonlinear Na3La9O3(BO3)8 crystal,” Opt. Express18(1), 237–243 (2010). [CrossRef] [PubMed]
- C. Chen, Z. Shao, J. Jiang, J. Wei, J. Lin, J. Wang, N. Ye, J. Lv, B. Wu, M. Jiang, M. Yoshimura, Y. Mori, and T. Sasaki, “Determination of the nonlinear optical coefficients of YCa4O(BO3)3 crystal,” J. Opt. Soc. Am. B17(4), 566–571 (2000). [CrossRef]
- S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965), Chap. 6.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.