Abstract

The effect of light absorption by sample in the analysis of Maker fringe data for estimating a second-order nonlinear coefficient has been studied experimentally. Two theories, one by Jerphagnon and Kurtz that neglects the absorption effect and one by Herman and Hayden that takes into account the absorption effect, were compared with the experimental results. It was found that Jerphagnon and Kurtz’s formula was unable to predict correctly not only the magnitude but also the incident angle dependence or the sample thickness dependence of the second harmonic signal generated by the sample with strong absorption, whereas the theory by Herman and Hayden was able to make those predictions fairly well. It was also found that the error in the estimated nonlinear coefficient when one uses Jerphagnon and Kurtz’s formula could be as large as 2–4 times the true value, depending on sample thickness.

© 1998 Optical Society of America

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References

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  1. P. D. Maker, R. W. Terhune, M. Nisenhoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
    [CrossRef]
  2. J. Jerphagnon, S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
    [CrossRef]
  3. N. Okamoto, Y. Hirano, O. Sugihara, “Precise estimation of nonlinear-optical coefficients for anisotropic nonlinear films with C∞ν symmetry,” J. Opt. Soc. Am. B 9, 2083–2087 (1992).
    [CrossRef]
  4. G. A. Lindsay, K. D. Singer, eds., Polymers for Second-Order Nonlinear Optics, ACS Symposium Series 601 (American Chemical Society, Washington, D.C., 1995).
    [CrossRef]
  5. W. N. Herman, L. Michael Hayden, “Maker fringes revisited: second harmonic generation from birefringent or obsorbing materials,” J. Opt. Soc. Am. B 12, 416–427 (1995).
    [CrossRef]
  6. C. H. Wang, H. W. Guan, “Second harmonic generation and optical anisotropy of a spin-coated polymer film,” J. Polym. Sci. Part B 31, 1983–1988 (1993).
    [CrossRef]
  7. B. Tatian, “Fitting refractive-index data with the Sellmeier dispersion formula,” Appl. Opt. 23, 4477–4485 (1984).
    [CrossRef] [PubMed]
  8. T. K. Lim, M. Y. Jeong, S. Cha, “Cerenkov-type second harmonic generation with a nonlinear organic polymer waveguide,” J. Korean Phys. Soc. 30, 544–549 (1997).
  9. A. Dhinojwala, J. C. Hooker, J. M. Torkelson, “Quantitative, rational predictions of the long-term temporal decay properties of second-order nonlinear optical polymers form the analysis of relaxation dynamics,” in Ref. 4, Chap. 23, pp. 318–332.
  10. T. Todorov, L. Nikoroba, N. Tomova, “Polarization holography. 1: A new high-efficiency organic material with reversible photoinduced birefringence,” Appl. Opt. 23, 4309–4312 (1984).
    [CrossRef] [PubMed]

1997 (1)

T. K. Lim, M. Y. Jeong, S. Cha, “Cerenkov-type second harmonic generation with a nonlinear organic polymer waveguide,” J. Korean Phys. Soc. 30, 544–549 (1997).

1995 (1)

1993 (1)

C. H. Wang, H. W. Guan, “Second harmonic generation and optical anisotropy of a spin-coated polymer film,” J. Polym. Sci. Part B 31, 1983–1988 (1993).
[CrossRef]

1992 (1)

1984 (2)

1970 (1)

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

1962 (1)

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

Cha, S.

T. K. Lim, M. Y. Jeong, S. Cha, “Cerenkov-type second harmonic generation with a nonlinear organic polymer waveguide,” J. Korean Phys. Soc. 30, 544–549 (1997).

Guan, H. W.

C. H. Wang, H. W. Guan, “Second harmonic generation and optical anisotropy of a spin-coated polymer film,” J. Polym. Sci. Part B 31, 1983–1988 (1993).
[CrossRef]

Hayden, L. Michael

Herman, W. N.

Hirano, Y.

Jeong, M. Y.

T. K. Lim, M. Y. Jeong, S. Cha, “Cerenkov-type second harmonic generation with a nonlinear organic polymer waveguide,” J. Korean Phys. Soc. 30, 544–549 (1997).

Jerphagnon, J.

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

Kurtz, S. K.

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

Lim, T. K.

T. K. Lim, M. Y. Jeong, S. Cha, “Cerenkov-type second harmonic generation with a nonlinear organic polymer waveguide,” J. Korean Phys. Soc. 30, 544–549 (1997).

Maker, P. D.

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

Nikoroba, L.

Nisenhoff, M.

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

Okamoto, N.

Savage, C. M.

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

Sugihara, O.

Tatian, B.

Terhune, R. W.

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

Todorov, T.

Tomova, N.

Wang, C. H.

C. H. Wang, H. W. Guan, “Second harmonic generation and optical anisotropy of a spin-coated polymer film,” J. Polym. Sci. Part B 31, 1983–1988 (1993).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (1)

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

J. Korean Phys. Soc. (1)

T. K. Lim, M. Y. Jeong, S. Cha, “Cerenkov-type second harmonic generation with a nonlinear organic polymer waveguide,” J. Korean Phys. Soc. 30, 544–549 (1997).

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

J. Polym. Sci. Part B (1)

C. H. Wang, H. W. Guan, “Second harmonic generation and optical anisotropy of a spin-coated polymer film,” J. Polym. Sci. Part B 31, 1983–1988 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (2)

A. Dhinojwala, J. C. Hooker, J. M. Torkelson, “Quantitative, rational predictions of the long-term temporal decay properties of second-order nonlinear optical polymers form the analysis of relaxation dynamics,” in Ref. 4, Chap. 23, pp. 318–332.

G. A. Lindsay, K. D. Singer, eds., Polymers for Second-Order Nonlinear Optics, ACS Symposium Series 601 (American Chemical Society, Washington, D.C., 1995).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Sample cell including nonlinear material with C ν symmetry and beam geometry; pol., polarization.

Fig. 2
Fig. 2

In the poled film, Maker fringe patterns for a representative thickness by the JK formula and the HH formula with absorption of 2.8/μm.

Fig. 3
Fig. 3

Computer simulation result of the intensity of the second harmonic signal as a function of the thickness at an incident angle of 50° by the JK and the HH formulas with absorption of 2.8/μm.

Fig. 4
Fig. 4

Absorption coefficient spectrum of Poly(DR1-MMA).

Fig. 5
Fig. 5

Contact poling setup.

Fig. 6
Fig. 6

Experimental configuration for Maker fringes: IR-M, 1064-nm mirror; M, 630-nm mirror; H-M, hot mirror; PD, photodiode; 1064-IF, 1064-nm interference filter; 532-IF, 532-nm interference filter; S, sample; PC, personal computer; Step-M, step motor and controller; IV-C & AMP, current-to-voltage converter and amplifier; A/D-C, analog-to-digital converter.

Fig. 7
Fig. 7

Maker fringe pattern; angular distribution of the second harmonic intensity of organic film at a thickness of 3.65 μm. The open circles are experimentally measured second harmonic intensity data, the dashed curve is the least-squares fitted results where the HH theory with film absorbance of 2.8/μm at 532 nm is used, and the solid curve is the least-squares fitted result where the JK theory is used.

Fig. 8
Fig. 8

Intensity of the second harmonic wave for various film thicknesses at an incident angle of 50° normalized by the intensity of the second harmonic wave of the quartz.

Fig. 9
Fig. 9

(a) Schematic diagram of the experimental setup for the measurement of birefringence. (b) The intensity of the second harmonic wave for birefringence of the sample at a thickness of 2.8/μm. The second harmonic intensity increases linearly as the birefringence of the sample increases.

Fig. 10
Fig. 10

Second-order nonlinear coefficient d 31 of the JK and the HH formula with the absorption coefficient of 2.8/μm.

Fig. 11
Fig. 11

Ratio of the nonlinear coefficient as obtained by the JK and the HH methods.

Equations (4)

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P 2 ω γ p = 128 π 3 cA | t af 1 γ | 4 | t fs 2 p | 2 | t sa 2 p | 2 n 2 2 c 2 2   P ω 2 2 π L λ 2 d eff 2 × exp - 2 δ 1 + δ 2 sin 2 ψ + sinh 2   χ ψ 2 + χ 2 , ψ = 2 π L / λ n 1 c 1 - n 2 c 2 , δ 1 = 2 π L / κ n 1 χ 1 / c 1 ,     δ 2 = 2 π L / κ n 2 χ 2 / c 2 , χ = δ 1 - δ 2 = 2 π L / λ n 1 κ 1 / c 1 - n 2 κ 2 / c 2 , t af 1 γ = 2   cos θ c 1 + n 1 cos θ ,   γ = p , 2   cos θ cos θ + n 1 c 1 ,   γ = s , t fs 2 p = 2 n 2 c 2 n 2 s c 2 + n 2 c 2 s ,     t sa 2 p = 2 n 2 s c 2 s n 2 s cos θ + c 2 s ,
d eff = 2 d 31 c 1 s 1 c 2 + d 31 c 1 2 s 2 + d 33 s 1 2 s 2 ,     γ = p d 31 s 2 ,     γ = s .
P 2 ω = 512 π 3 c ω 2   d 2 t ω γ 4 T 2 ω γ p 2 θ P ω 2 1 / n 1 2 - n 2 2 2 sin 2   ψ , ψ = 2 π L / λ n 1 c 1 - n 2 c 2 , t ω γ = 2   cos   θ n 1 c 1 + cos   θ ,   γ = s 2   cos   θ n 1 cos   θ + c 1 ,   γ = p , p θ = p 1 p 2 projection factor , T 2 ω γ = 2 n 2 c 2 cos θ + n 1 c 1 n 1 c 1 + n 2 c 2 n 2 c 2 + cos   θ 3 ,   γ = s 2 n 2 c 2 n 1 cos   θ + c 1 n 2 c 1 + n 1 c 2 c 2 + n 2 cos   θ 3 ,   γ = p .
Δ n = λ D eff π sin - 1 T ,     D eff = nD n 2 - sin 2   θ 1 / 2 ,

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