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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 11 — Nov. 1, 2002
  • pp: 2650–2664

General Maker-fringe ellipsometric analyses in multilayer nonlinear and linear anisotropic optical media

Vincent Rodriguez and Claude Sourisseau  »View Author Affiliations

JOSA B, Vol. 19, Issue 11, pp. 2650-2664 (2002)

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A general new 4(n+1)×4(n+1) matrix formulation of Maker fringes applicable to any anisotropic material containing n layers, convenient and straightforward for experimental data analyses, is proposed. The treatment of the transmitted and reflected harmonic waves includes the contribution of anisotropic one-photon absorption for the fundamental and harmonic waves under the assumption of no pump depletion and leads to a complete analysis of any linearly or elliptically polarized harmonic signal recorded under various incident polarization configurations. In the framework of the proposed model, we report detailed results of Maker fringes in various samples, for instance, in one and two z-cut quartz plates separated by a controlled air gap.

© 2002 Optical Society of America

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(160.4890) Materials : Organic materials
(160.5470) Materials : Polymers
(160.6030) Materials : Silica
(190.0190) Nonlinear optics : Nonlinear optics
(190.4160) Nonlinear optics : Multiharmonic generation

Vincent Rodriguez and Claude Sourisseau, "General Maker-fringe ellipsometric analyses in multilayer nonlinear and linear anisotropic optical media," J. Opt. Soc. Am. B 19, 2650-2664 (2002)

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  1. J. Zyss, in Molecular Nonlinear Optics. Materials, Physics and Devices (Academic, Boston, Mass., 1994).
  2. M. G. Kuzyk and C. W. Dirk, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials (Marcel Dekker, New York, 1998).
  3. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997). [CrossRef]
  4. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962). [CrossRef]
  5. M. S. Wong, F. Pan, M. Bösch, R. Spreiter, C. Bosshard, P. Günter, and V. Gramlich, “Novel electro-optic molecular cocrystals with ideal chromophoric orientation and large second-order optical nonlinearities,” J. Opt. Soc. Am. B 15, 426–431 (1998). [CrossRef]
  6. C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688–10701 (2000). [CrossRef]
  7. W. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B 12, 416–427 (1995). [CrossRef]
  8. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962). [CrossRef]
  9. J. Jerphagnon and 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]
  10. M. G. Kuzyk, K. D. Singer, H. E. Zahn, and L. A. King, “Second-order nonlinear-optical tensor properties of poled films under stress,” J. Opt. Soc. Am. B 6, 742–752 (1989). [CrossRef]
  11. D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques,” J. Opt. Soc. Am. B 6, 910–916 (1989). [CrossRef]
  12. D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: extension of optical transfer matrix approach to include anisotropic materials,” J. Opt. Soc. Am. B 8, 367–373 (1991). [CrossRef]
  13. M. Braun, F. Bauer, T. 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, 1699–1706 (1997). [CrossRef]
  14. M. Braun, F. Bauer, T. Vogtmann, and M. Schwoerer, “Detailed analysis of second-harmonic-generation Maker fringes in biaxially birefringent materials by 4×4 matrix formulation,” J. Opt. Soc. Am. B 15, 2877–2884 (1998). [CrossRef]
  15. D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972). [CrossRef]
  16. R. M. A. Azzam and N. M. Bashara, in Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 340–355.
  17. F. Abéles, in Optical Properties of Solids (Academic, New York, 1972).
  18. D. Pureur, A. C. Liu, M. J. F. Digonnet, and G. S. Kino, “Absolute prism-assisted Maker fringe measurements of the nonlinear profile in thermally poled silica,” in Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1977), pp. 299–301.
  19. D. Pureur, A. C. Liu, J. F. Digonnet, and G. S. Kino, “Absolute measurement of the second-order nonlinearity profile in poled silica,” Opt. Lett. 23, 588–590 (1998). [CrossRef]
  20. Y. Quiquempois, G. Martinelli, P. Duthérage, P. Bernage, P. Niay, and M. Douay, “Localization of the induced second-order nonlinearity within Infrasil and Suprasil thermally poled glasses,” Opt. Commun. 176, 479–487 (2000). [CrossRef]
  21. D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977–1979 (1962). [CrossRef]
  22. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, in Handbook of Nonlinear Optical Crystal. Optical Sciences 2nd ed. (Springer, Berlin, 1997), pp. 67–288.
  23. V. Rodriguez and C. Sourisseau, “SHG at near resonance and chromophore orientational distribution function in p(DR1M) thin films oriented by corona poling,” Nonlinear Opt. 25, 259–264 (2000).
  24. V. Rodriguez and F. Adamietz, “Time evolution and polar orientation of the orientational distribution function of DR1/PMMA polymer films wire poled under high field conditions,” presented at ICONO’6, Tucson, Ariz., December 16–20, 2001.
  25. G. A. Lindsay and K. D. Singer, in “Polymer for second-order nonlinear optics,” ACS Symp. Ser. 601, 130–238 (1995).
  26. U. Meier, M. Bösch, C. Bosshard, and P. Günter, “DAST a high optical nonlinearity organic crystal,” Synth. Met. 109, 19–22 (2000). [CrossRef]
  27. A. Yokoo, I. Yokohama, H. Kobayashi, and T. Kaino, “Linear and nonlinear optical properties of the organic nonlinear optical crystal 2-adamantylamino-5-nitropyridine,” J. Opt. Soc. Am. B 15, 432–437 (1998). [CrossRef]
  28. B. Ferreira, “Etude de la génération de seconde harmonique dans des verres polarisés thermiquement,” Ph.D. dissertation (University Bordeaux I, Bordeaux, France, 2002).

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