Abstract

We present the experimental and theoretical considerations needed to determine the mechanisms of quadratic electro-optic modulation in dye-doped polymer systems. The modulation is observed in thin dye-doped polymer films and the quadratic Kerr coefficient is determined by using a modified Mach–Zehnder interferometric technique. The theory of several nonlinear mechanisms is developed and applied to representative systems to determine the various contributions. The fast, virtual electronic mechanism is shown to be the largest contribution, as inferred from the measured frequency dispersion of the quadratic electro-optic effect. This quick interferometric method is also shown to be useful for determining nonlinear-optical structure–property relationships.

© 1990 Optical Society of America

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), for example.
  2. D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988), for example.
    [CrossRef]
  3. B. I. Greene, R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779 (1982).
    [CrossRef]
  4. F. Kajzar, J. Messier, “Cubic nonlinear optical effects in conjugated polymers,” Polym. J. 19, 275 (1987).
    [CrossRef]
  5. P. Horan, W. Blau, “Dispersion of the third-order optical nonlinearity in semiconductor-doped glasses,” Semicond. Sci. Technol. 2, 382 (1987).
    [CrossRef]
  6. G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
    [CrossRef] [PubMed]
  7. M. G. Kuzyk, R. A. Norwood, J. W. Wu, A. F. Garito, “Frequency dependence of the optical Kerr effect and third-order electronic nonlinear-optical processes of organic liquids,” J. Opt. Soc. Am. B 6, 154 (1989).
    [CrossRef]
  8. A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds., Nonlinear Optical Properties of Polymers (Materials Research Society, Pittsburgh, Pa., 1988), for example.
  9. S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
    [CrossRef]
  10. M. J. Goodwin, C. Edge, C. Trundle, I. Bennion, “Intensity-dependent birefringence in nonlinear organic polymer waveguides,” J. Opt. Soc. Am. B 5, 419 (1988).
    [CrossRef]
  11. E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
    [CrossRef]
  12. R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016 (1979).
    [CrossRef]
  13. W. T. Coffey, S. G. McGoldrick, “Inertial effects in the theory of dielectric and Kerr effect relaxation of an assembly of non-interacting polar molecules in strong alternating fields,” Chem. Phys. 120, 1 (1988).
    [CrossRef]
  14. W. T. Coffey, S. G. McGoldrick, P. J. Cregg, “Inertial effects in the theory of dielectric and Kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields,” Chem. Phys. 125, 119 (1988).
    [CrossRef]
  15. I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).
  16. T. S. Dod, Yu. E. Perlin, B. S. Tsukerblat, “Electrooptic absorption of anisotropic Jahn–Tellet centers in cubic crystals,” Sov. Phys. Solid State 19, 916 (1977).
  17. W. Jamroz, J. Karniewicz, “The electro-optic Kerr effect in noncentrosymmetric KH2PO4 and KD2PO4 monocrystals,” Opt. Quantum Electron. 11, 23 (1979).
    [CrossRef]
  18. A. A. Arabidze, B. Ya. Chikvaidze, “Dispersion of the electrooptic effect in barium titanate crystals,” Sov. Phys. Solid State 21, 722 (1979).
  19. R. Enderlein, P. Renner, M. Scheele, “Electro-optic effects due to the Stark splitting of energy bands,” Phys. Status Solidi B 93, 539 (1979).
    [CrossRef]
  20. K. Srinivasan, G. Balakrishnan, “Kerr effect in KCl:Pb2+and KCl:Cu+,” J. Phys. C 13, 441 (1980).
    [CrossRef]
  21. N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).
  22. G. Balakrishnan, K. Srinivasan, “Dispersion of the Kerr constants of doped KC1 crystals,” J. Phys. C 15, 2965 (1982).
    [CrossRef]
  23. N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).
  24. V. G. Martynov, A. T. Anistratov, “Optical and electrooptic properties of NH4HSeO4 in the vicinity of a ferroelectric phase transition,” Sov. Phys. Solid State 24, 1149 (1982).
  25. N. N. Krainik, L. S. Kamzina, G. A. Smolenskii, “The influence of thermally activated orientation of the polarization on the electro-optic and elasto-optic effects near a diffuse phase transition,” Sov. Phys. Solid State 25, 202 (1983).
  26. G. Burns, F. H. Dacol, W. Taylor, “Optical properties of ferroelectric (Pb1 −x Bax)5Ge3O11 for x= 0 and 0.02,” Phys. Rev. B 28, 2531 (1983).
    [CrossRef]
  27. W. Kucharczyk, “On the nature of the quadratic electro-optic effect in LiF,” Phys. Status Solidi B 131, K107 (1985).
    [CrossRef]
  28. W. Kucharczyk, “A bond-charge calculation of the quadratic electro-optic effect in LiF,” J. Phys. C 20, 1875 (1987).
    [CrossRef]
  29. P. Gorski, W. Kucharczyk, “The quadratic electrooptical effect in KDP and ADP crystals,” Phys. Status Solidi A 103, K65 (1987).
    [CrossRef]
  30. J. Kobayashi, T. Asahi, S. Takahashi, “simultaneous measurements of electrogyration and electrooptic effects α-quartz,” Ferroelectrics 75, 139 (1987).
    [CrossRef]
  31. K. Saito, T. Kawabe, J. Kobayashi, “Anomalous electrooptic and electrogyration effects in an incommensurate phase of [N(CH3)4]2ZnCl4,” Ferroelectrics 75, 153 (1987).
    [CrossRef]
  32. V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).
  33. L. Lam, Z. C. Ou-Yang, M. Lax, “Ab initio theory of linear and nonlinear optics of liquid crystals,” Phys. Rev. A 37, 3469 (1988).
    [CrossRef] [PubMed]
  34. K. Brudzewski, “Ellipsometric investigation of quadratic electro-optic and electrostrictive effects in anodic tungsten oxide films,” Thin Solid Films 70, 197 (1980).
    [CrossRef]
  35. H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
    [CrossRef]
  36. H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
    [CrossRef]
  37. M. Yokosuka, “tudy of hot-pressed Ba(Ca1/3Nb2/3)O3–PbZrO3–;PbTiO3ceramics. I. Electrical and optical properties at room temperature,” J. Appl. Phys. 25, 993 (1986).
  38. Yu. Shaldin, D. A. Belogurov, “Determination of nonlinear (quadratic) optical susceptibility of GaAs and GaP from electro-optic measurements,” Sov. J. Quantum Electron. 6, 897 (1976).
    [CrossRef]
  39. A. M. Mamedov, “Nonlinear optical properties of SbSi,” Sov. Phys. Solid State 19, 488 (1977).
  40. B. A. Volkov, V. P. Kushnir, “Behavior of IV–VI semiconductors in a static electric field,” Sov. Phys. Solid State 25, 1038 (1983).
  41. H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
    [CrossRef]
  42. S. Adachi, K. Oe, “Quadratic electro-optic (Kerr) effects in zincblende-type semiconductors: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 56, 1499 (1984).
    [CrossRef]
  43. D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020 (1980).
    [CrossRef]
  44. M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
    [CrossRef]
  45. J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
    [CrossRef]
  46. T. H. Wood, R. W. Tkach, A. R. Chraplyvy, “Observation of large quadratic electro-optic effect in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett. 50, 798 (1987).
    [CrossRef]
  47. G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
    [CrossRef]
  48. J. C. Luong, N. F. Borelli, A. R. Olszewski, “Quadratic electrooptical characterization of molecular nonlinear optical materials,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 251.
  49. H. Uchiki, T. Kobayashi, “New method for the measurement of electro-optic constant of polycarbonate films doped with 4-dimethylamino-4′-nitrostilbene molecules,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 373.
  50. H. Uchiki, T. Kobayashi, “New determination of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymer,” J. Appl. Phys. 64, 2625 (1988).
    [CrossRef]
  51. V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
    [CrossRef]
  52. K. D. Singer, M. G. Kuzyk, J. E. Sohn, “second-order nonlinear optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
    [CrossRef]
  53. J. D. LeGrange, M. G. Kuzyk, K. D. Singer, “Effects of order on nonlinear optical processes in organic molecular materials,” Mol. Cryst. Liq. Cryst. 150b, 567 (1987).
  54. M. G. Kuzyk, K. D. Singer, H. E. Zahn, L. A. King, “second-order nonlinear-optical tensor properties of poled polymer films under stress,” J. Opt. Soc. Am. B 6, 742 (1989).
    [CrossRef]
  55. M. G. Kuzyk, R. C. Moore, L. A. King, “second-harmonic-generation measurements of the elastic constant of a molecule in a polymer matrix,” J. Opt. Soc. Am. B 7, 64 (1990).
    [CrossRef]
  56. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 89.
  57. B. Gross, Electrets, Vol. 33 of Topics in Applied Physics, G. M. Sessler, ed. (Springer-Verlag, New York, 1980), and references therein.
  58. K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
    [CrossRef]
  59. D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
    [CrossRef]
  60. M. G. Kuzyk, “Third-order nonlinear optical processes in organic systems,” Ph.D. dissertation(University of Pennsylvania, Philadelphia, Pa., 1985).
  61. M. G. Kuzyk, M. P. Andrews, “Nonlinear optical properties of polymer/silver-microsphere composites,” to be submitted to Phys. Rev. B.
  62. M. G. Kuzyk, C. W. Dirk, “A quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628 (1989).
    [CrossRef]
  63. The uncertainty from the two orientational effects subtract, because they are both derived from the uncertaintyin kθ [Eqs. (4.5) and (4.6)]. This results in an uncertainty of just less than 0.2 × 10−13esu. The experimental uncertainty in the electrooptic measurement of 0.1 × 10−13esu is added to the uncertainty from the orientational effects to get a total uncertainty of 0.3 × 10−13esu.
  64. B. J. Orr, J. R. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
    [CrossRef]
  65. M. L. Schilling, H. E. Katz, D. I. Cox, “Synthesis and reactions of cyanovinyl-substituted benzenediazonium salts for nonlinear optics,” J. Org. Chem. 53, 5538 (1988).
    [CrossRef]
  66. C. W. Dirk, M. G. Kuzyk, “Damping corrections and the calculations of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
    [CrossRef]
  67. C. W. Dirk, M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219 (1989).
    [CrossRef] [PubMed]
  68. C. W. Dirk, M. G. Kuzyk, “The quadratic electro-optic effect and the two-level model,” submitted toJ. Chem. Phys.
  69. J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
    [CrossRef]
  70. C. Maloney, W. Blau, “Third order nonlinearity of chlorophenols,” Physica 147C, 332 (1987).
  71. J. Brandrup, E. H. Immergut, eds. Polymer Handbook (Wiley, New York, 1975), p. V-55.

1990 (2)

M. G. Kuzyk, R. C. Moore, L. A. King, “second-harmonic-generation measurements of the elastic constant of a molecule in a polymer matrix,” J. Opt. Soc. Am. B 7, 64 (1990).
[CrossRef]

C. W. Dirk, M. G. Kuzyk, “Damping corrections and the calculations of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

1989 (5)

C. W. Dirk, M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219 (1989).
[CrossRef] [PubMed]

M. G. Kuzyk, C. W. Dirk, “A quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

M. G. Kuzyk, K. D. Singer, H. E. Zahn, L. A. King, “second-order nonlinear-optical tensor properties of poled polymer films under stress,” J. Opt. Soc. Am. B 6, 742 (1989).
[CrossRef]

M. G. Kuzyk, R. A. Norwood, J. W. Wu, A. F. Garito, “Frequency dependence of the optical Kerr effect and third-order electronic nonlinear-optical processes of organic liquids,” J. Opt. Soc. Am. B 6, 154 (1989).
[CrossRef]

1988 (9)

M. J. Goodwin, C. Edge, C. Trundle, I. Bennion, “Intensity-dependent birefringence in nonlinear organic polymer waveguides,” J. Opt. Soc. Am. B 5, 419 (1988).
[CrossRef]

D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988), for example.
[CrossRef]

W. T. Coffey, S. G. McGoldrick, “Inertial effects in the theory of dielectric and Kerr effect relaxation of an assembly of non-interacting polar molecules in strong alternating fields,” Chem. Phys. 120, 1 (1988).
[CrossRef]

W. T. Coffey, S. G. McGoldrick, P. J. Cregg, “Inertial effects in the theory of dielectric and Kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields,” Chem. Phys. 125, 119 (1988).
[CrossRef]

L. Lam, Z. C. Ou-Yang, M. Lax, “Ab initio theory of linear and nonlinear optics of liquid crystals,” Phys. Rev. A 37, 3469 (1988).
[CrossRef] [PubMed]

M. L. Schilling, H. E. Katz, D. I. Cox, “Synthesis and reactions of cyanovinyl-substituted benzenediazonium salts for nonlinear optics,” J. Org. Chem. 53, 5538 (1988).
[CrossRef]

H. Uchiki, T. Kobayashi, “New determination of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymer,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
[CrossRef]

1987 (13)

C. Maloney, W. Blau, “Third order nonlinearity of chlorophenols,” Physica 147C, 332 (1987).

D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

K. D. Singer, M. G. Kuzyk, J. E. Sohn, “second-order nonlinear optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

J. D. LeGrange, M. G. Kuzyk, K. D. Singer, “Effects of order on nonlinear optical processes in organic molecular materials,” Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
[CrossRef]

T. H. Wood, R. W. Tkach, A. R. Chraplyvy, “Observation of large quadratic electro-optic effect in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett. 50, 798 (1987).
[CrossRef]

W. Kucharczyk, “A bond-charge calculation of the quadratic electro-optic effect in LiF,” J. Phys. C 20, 1875 (1987).
[CrossRef]

P. Gorski, W. Kucharczyk, “The quadratic electrooptical effect in KDP and ADP crystals,” Phys. Status Solidi A 103, K65 (1987).
[CrossRef]

J. Kobayashi, T. Asahi, S. Takahashi, “simultaneous measurements of electrogyration and electrooptic effects α-quartz,” Ferroelectrics 75, 139 (1987).
[CrossRef]

K. Saito, T. Kawabe, J. Kobayashi, “Anomalous electrooptic and electrogyration effects in an incommensurate phase of [N(CH3)4]2ZnCl4,” Ferroelectrics 75, 153 (1987).
[CrossRef]

F. Kajzar, J. Messier, “Cubic nonlinear optical effects in conjugated polymers,” Polym. J. 19, 275 (1987).
[CrossRef]

P. Horan, W. Blau, “Dispersion of the third-order optical nonlinearity in semiconductor-doped glasses,” Semicond. Sci. Technol. 2, 382 (1987).
[CrossRef]

S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
[CrossRef]

1986 (3)

H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
[CrossRef]

M. Yokosuka, “tudy of hot-pressed Ba(Ca1/3Nb2/3)O3–PbZrO3–;PbTiO3ceramics. I. Electrical and optical properties at room temperature,” J. Appl. Phys. 25, 993 (1986).

M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
[CrossRef]

1985 (2)

W. Kucharczyk, “On the nature of the quadratic electro-optic effect in LiF,” Phys. Status Solidi B 131, K107 (1985).
[CrossRef]

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

1984 (1)

S. Adachi, K. Oe, “Quadratic electro-optic (Kerr) effects in zincblende-type semiconductors: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 56, 1499 (1984).
[CrossRef]

1983 (5)

N. N. Krainik, L. S. Kamzina, G. A. Smolenskii, “The influence of thermally activated orientation of the polarization on the electro-optic and elasto-optic effects near a diffuse phase transition,” Sov. Phys. Solid State 25, 202 (1983).

G. Burns, F. H. Dacol, W. Taylor, “Optical properties of ferroelectric (Pb1 −x Bax)5Ge3O11 for x= 0 and 0.02,” Phys. Rev. B 28, 2531 (1983).
[CrossRef]

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

B. A. Volkov, V. P. Kushnir, “Behavior of IV–VI semiconductors in a static electric field,” Sov. Phys. Solid State 25, 1038 (1983).

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

1982 (5)

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

B. I. Greene, R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779 (1982).
[CrossRef]

G. Balakrishnan, K. Srinivasan, “Dispersion of the Kerr constants of doped KC1 crystals,” J. Phys. C 15, 2965 (1982).
[CrossRef]

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

V. G. Martynov, A. T. Anistratov, “Optical and electrooptic properties of NH4HSeO4 in the vicinity of a ferroelectric phase transition,” Sov. Phys. Solid State 24, 1149 (1982).

1981 (1)

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).

1980 (3)

K. Brudzewski, “Ellipsometric investigation of quadratic electro-optic and electrostrictive effects in anodic tungsten oxide films,” Thin Solid Films 70, 197 (1980).
[CrossRef]

K. Srinivasan, G. Balakrishnan, “Kerr effect in KCl:Pb2+and KCl:Cu+,” J. Phys. C 13, 441 (1980).
[CrossRef]

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020 (1980).
[CrossRef]

1979 (4)

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016 (1979).
[CrossRef]

W. Jamroz, J. Karniewicz, “The electro-optic Kerr effect in noncentrosymmetric KH2PO4 and KD2PO4 monocrystals,” Opt. Quantum Electron. 11, 23 (1979).
[CrossRef]

A. A. Arabidze, B. Ya. Chikvaidze, “Dispersion of the electrooptic effect in barium titanate crystals,” Sov. Phys. Solid State 21, 722 (1979).

R. Enderlein, P. Renner, M. Scheele, “Electro-optic effects due to the Stark splitting of energy bands,” Phys. Status Solidi B 93, 539 (1979).
[CrossRef]

1977 (2)

T. S. Dod, Yu. E. Perlin, B. S. Tsukerblat, “Electrooptic absorption of anisotropic Jahn–Tellet centers in cubic crystals,” Sov. Phys. Solid State 19, 916 (1977).

A. M. Mamedov, “Nonlinear optical properties of SbSi,” Sov. Phys. Solid State 19, 488 (1977).

1976 (1)

Yu. Shaldin, D. A. Belogurov, “Determination of nonlinear (quadratic) optical susceptibility of GaAs and GaP from electro-optic measurements,” Sov. J. Quantum Electron. 6, 897 (1976).
[CrossRef]

1974 (1)

E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
[CrossRef]

1971 (1)

B. J. Orr, J. R. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Adachi, H.

H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
[CrossRef]

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

Adachi, S.

S. Adachi, K. Oe, “Quadratic electro-optic (Kerr) effects in zincblende-type semiconductors: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 56, 1499 (1984).
[CrossRef]

Andrews, M. P.

M. G. Kuzyk, M. P. Andrews, “Nonlinear optical properties of polymer/silver-microsphere composites,” to be submitted to Phys. Rev. B.

Anistratov, A. T.

V. G. Martynov, A. T. Anistratov, “Optical and electrooptic properties of NH4HSeO4 in the vicinity of a ferroelectric phase transition,” Sov. Phys. Solid State 24, 1149 (1982).

Arabidze, A. A.

A. A. Arabidze, B. Ya. Chikvaidze, “Dispersion of the electrooptic effect in barium titanate crystals,” Sov. Phys. Solid State 21, 722 (1979).

Artigliere, A.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

Asahi, T.

J. Kobayashi, T. Asahi, S. Takahashi, “simultaneous measurements of electrogyration and electrooptic effects α-quartz,” Ferroelectrics 75, 139 (1987).
[CrossRef]

Bach, H. G.

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

Balakrishnan, G.

G. Balakrishnan, K. Srinivasan, “Dispersion of the Kerr constants of doped KC1 crystals,” J. Phys. C 15, 2965 (1982).
[CrossRef]

K. Srinivasan, G. Balakrishnan, “Kerr effect in KCl:Pb2+and KCl:Cu+,” J. Phys. C 13, 441 (1980).
[CrossRef]

Belogurov, D. A.

Yu. Shaldin, D. A. Belogurov, “Determination of nonlinear (quadratic) optical susceptibility of GaAs and GaP from electro-optic measurements,” Sov. J. Quantum Electron. 6, 897 (1976).
[CrossRef]

Bennion, I.

Blau, W.

P. Horan, W. Blau, “Dispersion of the third-order optical nonlinearity in semiconductor-doped glasses,” Semicond. Sci. Technol. 2, 382 (1987).
[CrossRef]

C. Maloney, W. Blau, “Third order nonlinearity of chlorophenols,” Physica 147C, 332 (1987).

Borelli, N. F.

J. C. Luong, N. F. Borelli, A. R. Olszewski, “Quadratic electrooptical characterization of molecular nonlinear optical materials,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 251.

Broussoux, D.

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020 (1980).
[CrossRef]

Brudzewski, K.

K. Brudzewski, “Ellipsometric investigation of quadratic electro-optic and electrostrictive effects in anodic tungsten oxide films,” Thin Solid Films 70, 197 (1980).
[CrossRef]

Burns, G.

G. Burns, F. H. Dacol, W. Taylor, “Optical properties of ferroelectric (Pb1 −x Bax)5Ge3O11 for x= 0 and 0.02,” Phys. Rev. B 28, 2531 (1983).
[CrossRef]

Cassidy, E. C.

E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
[CrossRef]

Chasting, E.

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

Chikvaidze, B. Ya.

A. A. Arabidze, B. Ya. Chikvaidze, “Dispersion of the electrooptic effect in barium titanate crystals,” Sov. Phys. Solid State 21, 722 (1979).

Choe, E. W.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

Chraplyvy, A. R.

T. H. Wood, R. W. Tkach, A. R. Chraplyvy, “Observation of large quadratic electro-optic effect in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett. 50, 798 (1987).
[CrossRef]

Coffey, W. T.

W. T. Coffey, S. G. McGoldrick, “Inertial effects in the theory of dielectric and Kerr effect relaxation of an assembly of non-interacting polar molecules in strong alternating fields,” Chem. Phys. 120, 1 (1988).
[CrossRef]

W. T. Coffey, S. G. McGoldrick, P. J. Cregg, “Inertial effects in the theory of dielectric and Kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields,” Chem. Phys. 125, 119 (1988).
[CrossRef]

Comizzoli, R. B.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Cox, D. I.

M. L. Schilling, H. E. Katz, D. I. Cox, “Synthesis and reactions of cyanovinyl-substituted benzenediazonium salts for nonlinear optics,” J. Org. Chem. 53, 5538 (1988).
[CrossRef]

Cregg, P. J.

W. T. Coffey, S. G. McGoldrick, P. J. Cregg, “Inertial effects in the theory of dielectric and Kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields,” Chem. Phys. 125, 119 (1988).
[CrossRef]

Dacol, F. H.

G. Burns, F. H. Dacol, W. Taylor, “Optical properties of ferroelectric (Pb1 −x Bax)5Ge3O11 for x= 0 and 0.02,” Phys. Rev. B 28, 2531 (1983).
[CrossRef]

DeMar-tino, R.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

Dentan, V.

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

Dirk, C. W.

C. W. Dirk, M. G. Kuzyk, “Damping corrections and the calculations of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk, C. W. Dirk, “A quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

C. W. Dirk, M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219 (1989).
[CrossRef] [PubMed]

C. W. Dirk, M. G. Kuzyk, “The quadratic electro-optic effect and the two-level model,” submitted toJ. Chem. Phys.

Dod, T. S.

T. S. Dod, Yu. E. Perlin, B. S. Tsukerblat, “Electrooptic absorption of anisotropic Jahn–Tellet centers in cubic crystals,” Sov. Phys. Solid State 19, 916 (1977).

Dumont, M.

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

Edge, C.

Enderlein, R.

R. Enderlein, P. Renner, M. Scheele, “Electro-optic effects due to the Stark splitting of energy bands,” Phys. Status Solidi B 93, 539 (1979).
[CrossRef]

Faist, J.

J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
[CrossRef]

Farrow, R. C.

B. I. Greene, R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779 (1982).
[CrossRef]

Garito, A. F.

M. G. Kuzyk, R. A. Norwood, J. W. Wu, A. F. Garito, “Frequency dependence of the optical Kerr effect and third-order electronic nonlinear-optical processes of organic liquids,” J. Opt. Soc. Am. B 6, 154 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
[CrossRef]

Glick, M.

M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
[CrossRef]

Goodwin, M. J.

Gorski, P.

P. Gorski, W. Kucharczyk, “The quadratic electrooptical effect in KDP and ADP crystals,” Phys. Status Solidi A 103, K65 (1987).
[CrossRef]

Greene, B. I.

B. I. Greene, R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779 (1982).
[CrossRef]

Grigor’ev, V. A.

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

Gross, B.

B. Gross, Electrets, Vol. 33 of Topics in Applied Physics, G. M. Sessler, ed. (Springer-Verlag, New York, 1980), and references therein.

Hebner, R. E.

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016 (1979).
[CrossRef]

E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
[CrossRef]

Heflin, J. R.

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
[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, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Horan, P.

P. Horan, W. Blau, “Dispersion of the third-order optical nonlinearity in semiconductor-doped glasses,” Semicond. Sci. Technol. 2, 382 (1987).
[CrossRef]

Hurst, W. S.

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 89.

Jamroz, W.

W. Jamroz, J. Karniewicz, “The electro-optic Kerr effect in noncentrosymmetric KH2PO4 and KD2PO4 monocrystals,” Opt. Quantum Electron. 11, 23 (1979).
[CrossRef]

Kaino, T.

S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
[CrossRef]

Kajzar, F.

F. Kajzar, J. Messier, “Cubic nonlinear optical effects in conjugated polymers,” Polym. J. 19, 275 (1987).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).

Kamzina, L. S.

N. N. Krainik, L. S. Kamzina, G. A. Smolenskii, “The influence of thermally activated orientation of the polarization on the electro-optic and elasto-optic effects near a diffuse phase transition,” Sov. Phys. Solid State 25, 202 (1983).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).

Karniewicz, J.

W. Jamroz, J. Karniewicz, “The electro-optic Kerr effect in noncentrosymmetric KH2PO4 and KD2PO4 monocrystals,” Opt. Quantum Electron. 11, 23 (1979).
[CrossRef]

Katz, H. E.

M. L. Schilling, H. E. Katz, D. I. Cox, “Synthesis and reactions of cyanovinyl-substituted benzenediazonium salts for nonlinear optics,” J. Org. Chem. 53, 5538 (1988).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Kawabe, T.

K. Saito, T. Kawabe, J. Kobayashi, “Anomalous electrooptic and electrogyration effects in an incommensurate phase of [N(CH3)4]2ZnCl4,” Ferroelectrics 75, 153 (1987).
[CrossRef]

Kawaguchi, T.

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

Kaznacheev, A. V.

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

Kenney-Wallace, G. A.

D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988), for example.
[CrossRef]

Keosian, R.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

Khanarian, G.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

King, L. A.

Kobayashi, J.

K. Saito, T. Kawabe, J. Kobayashi, “Anomalous electrooptic and electrogyration effects in an incommensurate phase of [N(CH3)4]2ZnCl4,” Ferroelectrics 75, 153 (1987).
[CrossRef]

J. Kobayashi, T. Asahi, S. Takahashi, “simultaneous measurements of electrogyration and electrooptic effects α-quartz,” Ferroelectrics 75, 139 (1987).
[CrossRef]

Kobayashi, T.

H. Uchiki, T. Kobayashi, “New determination of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymer,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

H. Uchiki, T. Kobayashi, “New method for the measurement of electro-optic constant of polycarbonate films doped with 4-dimethylamino-4′-nitrostilbene molecules,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 373.

Krainik, N. N.

N. N. Krainik, L. S. Kamzina, G. A. Smolenskii, “The influence of thermally activated orientation of the polarization on the electro-optic and elasto-optic effects near a diffuse phase transition,” Sov. Phys. Solid State 25, 202 (1983).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).

Krauser, J.

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

Kubodera, K.

S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
[CrossRef]

Kucharczyk, W.

W. Kucharczyk, “A bond-charge calculation of the quadratic electro-optic effect in LiF,” J. Phys. C 20, 1875 (1987).
[CrossRef]

P. Gorski, W. Kucharczyk, “The quadratic electrooptical effect in KDP and ADP crystals,” Phys. Status Solidi A 103, K65 (1987).
[CrossRef]

W. Kucharczyk, “On the nature of the quadratic electro-optic effect in LiF,” Phys. Status Solidi B 131, K107 (1985).
[CrossRef]

Kukh-tevich, V. I.

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

Kurihara, T.

S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
[CrossRef]

Kushnir, V. P.

B. A. Volkov, V. P. Kushnir, “Behavior of IV–VI semiconductors in a static electric field,” Sov. Phys. Solid State 25, 1038 (1983).

Kuzyk, M. G.

M. G. Kuzyk, R. C. Moore, L. A. King, “second-harmonic-generation measurements of the elastic constant of a molecule in a polymer matrix,” J. Opt. Soc. Am. B 7, 64 (1990).
[CrossRef]

C. W. Dirk, M. G. Kuzyk, “Damping corrections and the calculations of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk, C. W. Dirk, “A quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

M. G. Kuzyk, K. D. Singer, H. E. Zahn, L. A. King, “second-order nonlinear-optical tensor properties of poled polymer films under stress,” J. Opt. Soc. Am. B 6, 742 (1989).
[CrossRef]

C. W. Dirk, M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219 (1989).
[CrossRef] [PubMed]

M. G. Kuzyk, R. A. Norwood, J. W. Wu, A. F. Garito, “Frequency dependence of the optical Kerr effect and third-order electronic nonlinear-optical processes of organic liquids,” J. Opt. Soc. Am. B 6, 154 (1989).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

K. D. Singer, M. G. Kuzyk, J. E. Sohn, “second-order nonlinear optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

J. D. LeGrange, M. G. Kuzyk, K. D. Singer, “Effects of order on nonlinear optical processes in organic molecular materials,” Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

M. G. Kuzyk, “Third-order nonlinear optical processes in organic systems,” Ph.D. dissertation(University of Pennsylvania, Philadelphia, Pa., 1985).

M. G. Kuzyk, M. P. Andrews, “Nonlinear optical properties of polymer/silver-microsphere composites,” to be submitted to Phys. Rev. B.

C. W. Dirk, M. G. Kuzyk, “The quadratic electro-optic effect and the two-level model,” submitted toJ. Chem. Phys.

Lalama, S. J.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Lam, L.

L. Lam, Z. C. Ou-Yang, M. Lax, “Ab initio theory of linear and nonlinear optics of liquid crystals,” Phys. Rev. A 37, 3469 (1988).
[CrossRef] [PubMed]

Lax, M.

L. Lam, Z. C. Ou-Yang, M. Lax, “Ab initio theory of linear and nonlinear optics of liquid crystals,” Phys. Rev. A 37, 3469 (1988).
[CrossRef] [PubMed]

LeGrange, J. D.

J. D. LeGrange, M. G. Kuzyk, K. D. Singer, “Effects of order on nonlinear optical processes in organic molecular materials,” Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

Lei, D.

D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Levy, Y.

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

Logan, R. A.

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

Lotshaw, W. T.

D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988), for example.
[CrossRef]

Luong, J. C.

J. C. Luong, N. F. Borelli, A. R. Olszewski, “Quadratic electrooptical characterization of molecular nonlinear optical materials,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 251.

Maloney, C.

C. Maloney, W. Blau, “Third order nonlinearity of chlorophenols,” Physica 147C, 332 (1987).

Mamedov, A. M.

A. M. Mamedov, “Nonlinear optical properties of SbSi,” Sov. Phys. Solid State 19, 488 (1977).

Martin, D.

J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
[CrossRef]

Martynov, V. G.

V. G. Martynov, A. T. Anistratov, “Optical and electrooptic properties of NH4HSeO4 in the vicinity of a ferroelectric phase transition,” Sov. Phys. Solid State 24, 1149 (1982).

Matsumoto, S.

S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
[CrossRef]

McGoldrick, S. G.

W. T. Coffey, S. G. McGoldrick, P. J. Cregg, “Inertial effects in the theory of dielectric and Kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields,” Chem. Phys. 125, 119 (1988).
[CrossRef]

W. T. Coffey, S. G. McGoldrick, “Inertial effects in the theory of dielectric and Kerr effect relaxation of an assembly of non-interacting polar molecules in strong alternating fields,” Chem. Phys. 120, 1 (1988).
[CrossRef]

McMorrow, D.

D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988), for example.
[CrossRef]

Messier, J.

F. Kajzar, J. Messier, “Cubic nonlinear optical effects in conjugated polymers,” Polym. J. 19, 275 (1987).
[CrossRef]

Micheron, F.

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020 (1980).
[CrossRef]

Misakian, M.

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016 (1979).
[CrossRef]

Mitsuyu, T.

H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
[CrossRef]

Moore, R. C.

Myl’nikova, I. E.

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).

Newnham, R. E.

D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Nolting, H. P.

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

Norwood, R. A.

Oe, K.

S. Adachi, K. Oe, “Quadratic electro-optic (Kerr) effects in zincblende-type semiconductors: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 56, 1499 (1984).
[CrossRef]

Ohji, K.

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

Olszewski, A. R.

J. C. Luong, N. F. Borelli, A. R. Olszewski, “Quadratic electrooptical characterization of molecular nonlinear optical materials,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 251.

Orr, B. J.

B. J. Orr, J. R. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Ou-Yang, Z. C.

L. Lam, Z. C. Ou-Yang, M. Lax, “Ab initio theory of linear and nonlinear optics of liquid crystals,” Phys. Rev. A 37, 3469 (1988).
[CrossRef] [PubMed]

Perlin, Yu. E.

T. S. Dod, Yu. E. Perlin, B. S. Tsukerblat, “Electrooptic absorption of anisotropic Jahn–Tellet centers in cubic crystals,” Sov. Phys. Solid State 19, 916 (1977).

Reinhart, F. K.

J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
[CrossRef]

M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
[CrossRef]

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

Renner, P.

R. Enderlein, P. Renner, M. Scheele, “Electro-optic effects due to the Stark splitting of energy bands,” Phys. Status Solidi B 93, 539 (1979).
[CrossRef]

Robin, P.

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

Rosasco, G. J.

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

Runt, J.

D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Saito, K.

K. Saito, T. Kawabe, J. Kobayashi, “Anomalous electrooptic and electrogyration effects in an incommensurate phase of [N(CH3)4]2ZnCl4,” Ferroelectrics 75, 153 (1987).
[CrossRef]

Salaev, F. M.

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).

Sarari, A.

D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Scheele, M.

R. Enderlein, P. Renner, M. Scheele, “Electro-optic effects due to the Stark splitting of energy bands,” Phys. Status Solidi B 93, 539 (1979).
[CrossRef]

Schilling, M. L.

M. L. Schilling, H. E. Katz, D. I. Cox, “Synthesis and reactions of cyanovinyl-substituted benzenediazonium salts for nonlinear optics,” J. Org. Chem. 53, 5538 (1988).
[CrossRef]

Schlapp, W.

M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
[CrossRef]

Setsune, K.

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

Shaldin, Yu.

Yu. Shaldin, D. A. Belogurov, “Determination of nonlinear (quadratic) optical susceptibility of GaAs and GaP from electro-optic measurements,” Sov. J. Quantum Electron. 6, 897 (1976).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), for example.

Sher, E. S.

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

Shilling, M. L.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Singer, K. D.

M. G. Kuzyk, K. D. Singer, H. E. Zahn, L. A. King, “second-order nonlinear-optical tensor properties of poled polymer films under stress,” J. Opt. Soc. Am. B 6, 742 (1989).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

J. D. LeGrange, M. G. Kuzyk, K. D. Singer, “Effects of order on nonlinear optical processes in organic molecular materials,” Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

K. D. Singer, M. G. Kuzyk, J. E. Sohn, “second-order nonlinear optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

Smolenskii, G. A.

N. N. Krainik, L. S. Kamzina, G. A. Smolenskii, “The influence of thermally activated orientation of the polarization on the electro-optic and elasto-optic effects near a diffuse phase transition,” Sov. Phys. Solid State 25, 202 (1983).

Sohn, J. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

K. D. Singer, M. G. Kuzyk, J. E. Sohn, “second-order nonlinear optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

Sojka, R. J.

E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
[CrossRef]

Sonin, A. S.

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

Srinivasan, K.

G. Balakrishnan, K. Srinivasan, “Dispersion of the Kerr constants of doped KC1 crystals,” J. Phys. C 15, 2965 (1982).
[CrossRef]

K. Srinivasan, G. Balakrishnan, “Kerr effect in KCl:Pb2+and KCl:Cu+,” J. Phys. C 13, 441 (1980).
[CrossRef]

Stuetz, D.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

Takahashi, S.

J. Kobayashi, T. Asahi, S. Takahashi, “simultaneous measurements of electrogyration and electrooptic effects α-quartz,” Ferroelectrics 75, 139 (1987).
[CrossRef]

Taylor, W.

G. Burns, F. H. Dacol, W. Taylor, “Optical properties of ferroelectric (Pb1 −x Bax)5Ge3O11 for x= 0 and 0.02,” Phys. Rev. B 28, 2531 (1983).
[CrossRef]

Teng, C. C.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

Tkach, R. W.

T. H. Wood, R. W. Tkach, A. R. Chraplyvy, “Observation of large quadratic electro-optic effect in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett. 50, 798 (1987).
[CrossRef]

Trundle, C.

Tsukerblat, B. S.

T. S. Dod, Yu. E. Perlin, B. S. Tsukerblat, “Electrooptic absorption of anisotropic Jahn–Tellet centers in cubic crystals,” Sov. Phys. Solid State 19, 916 (1977).

Tuncel, E.

J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
[CrossRef]

Uchiki, H.

H. Uchiki, T. Kobayashi, “New determination of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymer,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

H. Uchiki, T. Kobayashi, “New method for the measurement of electro-optic constant of polycarbonate films doped with 4-dimethylamino-4′-nitrostilbene molecules,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 373.

Volkov, B. A.

B. A. Volkov, V. P. Kushnir, “Behavior of IV–VI semiconductors in a static electric field,” Sov. Phys. Solid State 25, 1038 (1983).

Ward, J. R.

B. J. Orr, J. R. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Wasa, K.

H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
[CrossRef]

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

Weimann, G.

M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
[CrossRef]

Wong, K. Y.

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
[CrossRef]

Wood, T. H.

T. H. Wood, R. W. Tkach, A. R. Chraplyvy, “Observation of large quadratic electro-optic effect in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett. 50, 798 (1987).
[CrossRef]

Wu, J. W.

Yamazaki, O.

H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
[CrossRef]

Yokosuka, M.

M. Yokosuka, “tudy of hot-pressed Ba(Ca1/3Nb2/3)O3–PbZrO3–;PbTiO3ceramics. I. Electrical and optical properties at room temperature,” J. Appl. Phys. 25, 993 (1986).

Zahn, H. E.

Zahn, M.

E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
[CrossRef]

Zamani-Khamiri, O.

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
[CrossRef]

Zhelkobaev, Zh.

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

Appl. Phys. Lett. (8)

S. Matsumoto, K. Kubodera, T. Kurihara, T. Kaino, “Nonlinear optical properties of an azo dye attached polymer,” Appl. Phys. Lett. 51, 1 (1987).
[CrossRef]

H. Adachi, T. Kawaguchi, K. Setsune, K. Ohji, K. Wasa, “Electro-optic effects of (Pb,La)(Zr,Ti)O3thin films prepared by rf-planar magnetron sputtering,” Appl. Phys. Lett. 42, 867 (1983).
[CrossRef]

M. Glick, F. K. Reinhart, G. Weimann, W. Schlapp, “Quadratic electro-optic light modulation in a GaAs/AlGaAs multi-quantum well heterostructure near the excitonic gap,” Appl. Phys. Lett. 48, 989 (1986).
[CrossRef]

J. Faist, F. K. Reinhart, D. Martin, E. Tuncel, “Orientation dependence of the phase modulation in a p–n junction GaAs/ Alx Ga1 −x As waveguide,”Appl. Phys. Lett. 50, 68 (1987).
[CrossRef]

T. H. Wood, R. W. Tkach, A. R. Chraplyvy, “Observation of large quadratic electro-optic effect in GaAs/AlGaAs multiple quantum wells,” Appl. Phys. Lett. 50, 798 (1987).
[CrossRef]

H. G. Bach, J. Krauser, H. P. Nolting, R. A. Logan, F. K. Reinhart, “Electro-optic light modulation in InGaAsP/InP double heterostructure diodes,” Appl. Phys. Lett. 42, 692 (1983).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, M. L. Shilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

M. G. Kuzyk, C. W. Dirk, “A quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

Chem. Phys. (2)

W. T. Coffey, S. G. McGoldrick, “Inertial effects in the theory of dielectric and Kerr effect relaxation of an assembly of non-interacting polar molecules in strong alternating fields,” Chem. Phys. 120, 1 (1988).
[CrossRef]

W. T. Coffey, S. G. McGoldrick, P. J. Cregg, “Inertial effects in the theory of dielectric and Kerr effect relaxation. III. Assemblies of nondipolar anisotropically polarizable molecules in alternating and pulsed fields,” Chem. Phys. 125, 119 (1988).
[CrossRef]

Ferroelectrics (2)

J. Kobayashi, T. Asahi, S. Takahashi, “simultaneous measurements of electrogyration and electrooptic effects α-quartz,” Ferroelectrics 75, 139 (1987).
[CrossRef]

K. Saito, T. Kawabe, J. Kobayashi, “Anomalous electrooptic and electrogyration effects in an incommensurate phase of [N(CH3)4]2ZnCl4,” Ferroelectrics 75, 153 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988), for example.
[CrossRef]

IEEE Trans. Electr. Insul. (1)

E. C. Cassidy, R. E. Hebner, M. Zahn, R. J. Sojka, “Kerr-effect studies of an insulating liquid under varied high-voltage conditions,” IEEE Trans. Electr. Insul. EI-9, 43 (1974).
[CrossRef]

J. Appl. Phys. (6)

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016 (1979).
[CrossRef]

S. Adachi, K. Oe, “Quadratic electro-optic (Kerr) effects in zincblende-type semiconductors: key properties of InGaAsP relevant to device design,” J. Appl. Phys. 56, 1499 (1984).
[CrossRef]

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020 (1980).
[CrossRef]

H. Uchiki, T. Kobayashi, “New determination of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymer,” J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

H. Adachi, T. Mitsuyu, O. Yamazaki, K. Wasa, “Ferroelectric (Pb,La)(Zr,Ti)O3 epitaxial thin films on sapphire grown by rf-planar magnetron sputtering,” J. Appl. Phys. 60, 736 (1986).
[CrossRef]

M. Yokosuka, “tudy of hot-pressed Ba(Ca1/3Nb2/3)O3–PbZrO3–;PbTiO3ceramics. I. Electrical and optical properties at room temperature,” J. Appl. Phys. 25, 993 (1986).

J. Chem. Phys. (1)

B. I. Greene, R. C. Farrow, “Direct measurement of a subpicosecond birefringent response in CS2,” J. Chem. Phys. 77, 4779 (1982).
[CrossRef]

J. Opt. Soc. Am. B (5)

J. Org. Chem. (1)

M. L. Schilling, H. E. Katz, D. I. Cox, “Synthesis and reactions of cyanovinyl-substituted benzenediazonium salts for nonlinear optics,” J. Org. Chem. 53, 5538 (1988).
[CrossRef]

J. Phys. C (3)

W. Kucharczyk, “A bond-charge calculation of the quadratic electro-optic effect in LiF,” J. Phys. C 20, 1875 (1987).
[CrossRef]

K. Srinivasan, G. Balakrishnan, “Kerr effect in KCl:Pb2+and KCl:Cu+,” J. Phys. C 13, 441 (1980).
[CrossRef]

G. Balakrishnan, K. Srinivasan, “Dispersion of the Kerr constants of doped KC1 crystals,” J. Phys. C 15, 2965 (1982).
[CrossRef]

Macromolecules (1)

D. Lei, J. Runt, A. Sarari, R. E. Newnham, “Dielectric properties of azo dye-poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

J. D. LeGrange, M. G. Kuzyk, K. D. Singer, “Effects of order on nonlinear optical processes in organic molecular materials,” Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

Mol. Phys. (1)

B. J. Orr, J. R. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Opt. Commun. (1)

V. Dentan, Y. Levy, M. Dumont, P. Robin, E. Chasting, “Electrooptic properties of a ferroelectric polymer studied by attenuated total reflection,” Opt. Commun. 69, 379 (1989).
[CrossRef]

Opt. Quantum Electron. (1)

W. Jamroz, J. Karniewicz, “The electro-optic Kerr effect in noncentrosymmetric KH2PO4 and KD2PO4 monocrystals,” Opt. Quantum Electron. 11, 23 (1979).
[CrossRef]

Phys. Rev. A (3)

G. J. Rosasco, W. S. Hurst, “Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy,” Phys. Rev. A 32, 281 (1985).
[CrossRef] [PubMed]

L. Lam, Z. C. Ou-Yang, M. Lax, “Ab initio theory of linear and nonlinear optics of liquid crystals,” Phys. Rev. A 37, 3469 (1988).
[CrossRef] [PubMed]

C. W. Dirk, M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219 (1989).
[CrossRef] [PubMed]

Phys. Rev. B (3)

C. W. Dirk, M. G. Kuzyk, “Damping corrections and the calculations of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573 (1988).
[CrossRef]

G. Burns, F. H. Dacol, W. Taylor, “Optical properties of ferroelectric (Pb1 −x Bax)5Ge3O11 for x= 0 and 0.02,” Phys. Rev. B 28, 2531 (1983).
[CrossRef]

Phys. Status Solidi A (1)

P. Gorski, W. Kucharczyk, “The quadratic electrooptical effect in KDP and ADP crystals,” Phys. Status Solidi A 103, K65 (1987).
[CrossRef]

Phys. Status Solidi B (2)

W. Kucharczyk, “On the nature of the quadratic electro-optic effect in LiF,” Phys. Status Solidi B 131, K107 (1985).
[CrossRef]

R. Enderlein, P. Renner, M. Scheele, “Electro-optic effects due to the Stark splitting of energy bands,” Phys. Status Solidi B 93, 539 (1979).
[CrossRef]

Physica (1)

C. Maloney, W. Blau, “Third order nonlinearity of chlorophenols,” Physica 147C, 332 (1987).

Polym. J. (1)

F. Kajzar, J. Messier, “Cubic nonlinear optical effects in conjugated polymers,” Polym. J. 19, 275 (1987).
[CrossRef]

Semicond. Sci. Technol. (1)

P. Horan, W. Blau, “Dispersion of the third-order optical nonlinearity in semiconductor-doped glasses,” Semicond. Sci. Technol. 2, 382 (1987).
[CrossRef]

Sov. J. Quantum Electron. (1)

Yu. Shaldin, D. A. Belogurov, “Determination of nonlinear (quadratic) optical susceptibility of GaAs and GaP from electro-optic measurements,” Sov. J. Quantum Electron. 6, 897 (1976).
[CrossRef]

Sov. Phys. Solid State (8)

A. M. Mamedov, “Nonlinear optical properties of SbSi,” Sov. Phys. Solid State 19, 488 (1977).

B. A. Volkov, V. P. Kushnir, “Behavior of IV–VI semiconductors in a static electric field,” Sov. Phys. Solid State 25, 1038 (1983).

A. A. Arabidze, B. Ya. Chikvaidze, “Dispersion of the electrooptic effect in barium titanate crystals,” Sov. Phys. Solid State 21, 722 (1979).

T. S. Dod, Yu. E. Perlin, B. S. Tsukerblat, “Electrooptic absorption of anisotropic Jahn–Tellet centers in cubic crystals,” Sov. Phys. Solid State 19, 916 (1977).

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, E. S. Sher, “Characteristics of dielectric and electrooptic properties of cadmium pyroniobate,” Sov. Phys. Solid State 24, 970 (1982).

V. G. Martynov, A. T. Anistratov, “Optical and electrooptic properties of NH4HSeO4 in the vicinity of a ferroelectric phase transition,” Sov. Phys. Solid State 24, 1149 (1982).

N. N. Krainik, L. S. Kamzina, G. A. Smolenskii, “The influence of thermally activated orientation of the polarization on the electro-optic and elasto-optic effects near a diffuse phase transition,” Sov. Phys. Solid State 25, 202 (1983).

V. A. Grigor’ev, Zh. Zhelkobaev, A. V. Kaznacheev, V. I. Kukh-tevich, A. S. Sonin, “Flexoelectric effect in MBBA in strong electric fields,” Sov. Phys. Solid State 24, 1801 (1982).

Sov. Tech. Phys. Lett. (1)

N. N. Krainik, L. S. Kamzina, F. M. Salaev, I. E. Myl’nikova, “Quadratic electrooptic effect in cadmium pyroniobate crystals,” Sov. Tech. Phys. Lett. 6, 18 (1981).

Thin Solid Films (1)

K. Brudzewski, “Ellipsometric investigation of quadratic electro-optic and electrostrictive effects in anodic tungsten oxide films,” Thin Solid Films 70, 197 (1980).
[CrossRef]

Other (13)

I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), for example.

A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds., Nonlinear Optical Properties of Polymers (Materials Research Society, Pittsburgh, Pa., 1988), for example.

G. Khanarian, A. Artigliere, R. Keosian, E. W. Choe, R. DeMar-tino, D. Stuetz, C. C. Teng, “Electrooptic and third harmonic generation studies of polymer alloys and solutions,” in Molecular and Polymeric Optoelectronic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 153 (1986).
[CrossRef]

J. C. Luong, N. F. Borelli, A. R. Olszewski, “Quadratic electrooptical characterization of molecular nonlinear optical materials,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 251.

H. Uchiki, T. Kobayashi, “New method for the measurement of electro-optic constant of polycarbonate films doped with 4-dimethylamino-4′-nitrostilbene molecules,” in Nonlinear Optical Properties of Polymers, A. J. Heeger, J. O. Orenstein, D. R. Ulrich, eds. (Materials Research Society, Pittsburgh, Pa., 1988), p. 373.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 89.

B. Gross, Electrets, Vol. 33 of Topics in Applied Physics, G. M. Sessler, ed. (Springer-Verlag, New York, 1980), and references therein.

J. Brandrup, E. H. Immergut, eds. Polymer Handbook (Wiley, New York, 1975), p. V-55.

C. W. Dirk, M. G. Kuzyk, “The quadratic electro-optic effect and the two-level model,” submitted toJ. Chem. Phys.

The uncertainty from the two orientational effects subtract, because they are both derived from the uncertaintyin kθ [Eqs. (4.5) and (4.6)]. This results in an uncertainty of just less than 0.2 × 10−13esu. The experimental uncertainty in the electrooptic measurement of 0.1 × 10−13esu is added to the uncertainty from the orientational effects to get a total uncertainty of 0.3 × 10−13esu.

M. G. Kuzyk, “Third-order nonlinear optical processes in organic systems,” Ph.D. dissertation(University of Pennsylvania, Philadelphia, Pa., 1985).

M. G. Kuzyk, M. P. Andrews, “Nonlinear optical properties of polymer/silver-microsphere composites,” to be submitted to Phys. Rev. B.

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Figures (8)

Fig. 1
Fig. 1

Upper curve shows light intensity read by the photodiode detector (in units of detector voltage) as a function of the zero-voltage phase difference between the two arms of the interferometer. The middle curve shows the amplitude of the modulated light read by the lock-in amplifier at twice the modulating frequency. The bottom curve shows the light intensity read by the lock-in amplifier at the modulating voltage for a centrosymmetric film. Note that the scales on the three curves are different. Typically, the signal voltage at twice the modulating frequency is down by approximately a factor of 103–104 from the zero-frequency voltage.

Fig. 2
Fig. 2

Absorption spectra for films of four different concentrations of DR1 in PMMA, normalized to a film thickness of 1 μm.

Fig. 3
Fig. 3

Number density versus normalized absorption for films of DR1 in PMMA. The departure from linearity at higher concentrations shows the possibility of molecular aggregation such as pairing.

Fig. 4
Fig. 4

X-ray diffraction spectra of DR1 as a powder and as a film in PMMA with N = 1.18 × 1020 cm−3.

Fig. 5
Fig. 5

Concentration dependence of the third-order susceptibility of DR1 in PMMA as measured by quadratic electro-optic modulation.

Fig. 6
Fig. 6

Frequency dependence of the quadratic electro-optic coefficient of DCV dye in PMMA. The lower curve shows a 1(ωω0) dependence and the upper curve a 1(ωω0)2 dependence. Note that damping is not included here. ω0 was determined from linear absorption spectra.

Fig. 7
Fig. 7

Photon energy dependence of the quadratic electro-optic coefficient of ISQ in PMMA. The solid curve through the data points is a guide to the eye. The inset shows the theoretical energy dependence of quadratic electro-optic modulation for a two-level model with no damping. Damping will broaden the frequency dependence of the theoretical curve. Note that electronic-absorption studies show that the absorption peak shape is Lorentzian.

Fig. 8
Fig. 8

Molecular structures of dopants: DNTA, a diaminonitrothiophene aniline dye; NPCV, a nitrophenylcyanovinylazo dye; DNBA, a diaminonitrobenzaniline dye; NFAI, a nitrofuran-substituted dye.

Tables (7)

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Table 1 Some Physical Properties of PMMA at Room Temperaturea

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Table 2 Heating Contribution to the Third-Order Susceptibility in PMMAa

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Table 3 Molecular Values Used to Calculate Orientational Contributions in DRl/PMMAa

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Table 4 Orientational Contributions and Quadratic Electro-Optic Coefficienta

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Table 5 Third-Order Susceptibility Comparison between Electro-Optic Measurement and Third-Harmonic Measurementa

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Table 6 Third-Order Susceptibility of a Series of Molecules as Determined with Quadratic Electro-Optic Modulationa

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Table 7 Experimental and Theoretical Isotropic Averages of Molecular Nonlinear-Optical Susceptibilities of Small Moleculesa

Equations (98)

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G ( Ω ) = exp [ ( 1 / k T ) U ( Ω ) ] d Ω exp [ ( 1 / k T ) U ( Ω ) ] ,
G ( cos θ ) = l = 0 2 l + 1 2 A l P l ( cos θ ) ,
α 11 * = ( 1 / 3 ) ( 1 A 2 ) α z z * ( 1 / 3 ) α z z * Δ A 2
α 33 * = ( 1 / 3 ) ( 1 + 2 A 2 ) α z z * + ( 2 / 3 ) α z z * Δ A 2 ,
χ i i ( 1 ) = χ iso + N α i i * .
n i i = n 0 [ 1 + 4 π N α i i * n 0 2 ] 1 / 2 ,
F θ = μ * E sin θ 2 α * E 2 sin θ cos θ ,
μ * E sin ( θ 0 + ) α * E 2 sin [ 2 ( θ 0 + ) ] k θ = 0 ,
= ( μ * E / k θ ) sin θ 0 ( α * E 2 / k θ ) sin 2 θ 0 1 + ( μ * E / k θ ) cos θ 0 + 2 ( α * E 2 / k θ ) cos 2 θ 0 .
μ * E k θ sin θ 0 α * E 2 k θ sin 2 θ 0 + 1 2 ( μ * E k θ ) 2 sin 2 θ 0 .
sin θ Δ G ( cos θ ) = sin ( θ + Δ θ ) G ( cos θ sin θ Δ θ ) i sin θ G ( cos θ ) 0 ,
sin θ [ Δ G ( cos θ ) ] Δ θ = [ ( sin θ + cos θ Δ θ ) G ( cos θ ) sin 2 θ Δ θ d G d ( cos θ ) ] × i sin θ G ( cos θ ) 0 .
o = ( θ o )
i = ( θ Δ θ + i ) ,
o = μ * E k θ sin θ + α * E 2 k θ sin 2 θ
i = o + [ μ * E k θ cos θ + 2 α * E 2 k θ cos 2 θ ] Δ θ .
Δ G = 2 α * E 2 k θ [ ( 3 cos 2 θ 1 ) G ( cos θ ) ( cos θ cos 3 θ ) d G ( cos θ ) d ( cos θ ) ] .
( cos 2 1 ) d P l d ( cos θ ) = l P 1 ( cos θ ) P l ( cos θ ) l P l 1 ( cos θ ) ,
Δ G 2 ( α * E 2 / k θ ) = l = 0 2 l + 1 2 A l [ ( l + 3 ) ( l + 2 ) ( l + 1 ) ( 2 l + 1 ) ( 2 l + 3 ) P l + 2 + l ( l + 1 ) ( 2 l 1 ) ( 2 l + 3 ) P l l ( l 1 ) ( l 2 ) ( 2 l + 1 ) ( 2 l 1 ) P l 2 ] .
Δ G = l = 0 2 l + 1 2 Δ A l P l ( cos θ ) ,
Δ A l = 1 + 1 d ( cos θ ) Δ G ( cos θ ) P l ( cos θ ) .
Δ A l = 2 α * E 2 k θ [ ( l 1 ) l ( l + 1 ) ( 2 l 1 ) ( 2 l + 1 ) A l 2 + l ( l + 1 ) ( 2 l + 3 ) ( 2 l 1 ) A l l ( l + 1 ) ( l + 2 ) ( 2 l + 1 ) ( 2 l + 3 ) A l + 2 ] .
Δ n 11 = 8 105 π N α * ( Ω ; Ω ) α * ( ω ; ω ) n 11 0 k θ × ( 7 + 5 A 2 12 A 4 ) ( E Ω ) 2
Δ n 33 = + 16 105 π N α * ( Ω ; Ω ) α * ( ω ; ω ) n 33 0 k θ × ( 7 + 5 A 2 12 A 4 ) ( E Ω ) 2 ,
F A = V 2 8 π d 2 ,
Δ d d = 1 K F A .
Δ d d = V 2 8 π K d 2 .
Δ ϕ ϕ = Δ n n + Δ d d .
χ i j k ( 2 ) = N ( ξ i j k ( 1 ) A 1 + ξ i j k ( 3 ) A 3 ) ,
χ 333 ( 2 ) = N β z z z * [ ( 3 / 5 ) A 1 + ( 2 / 5 ) A 3 ]
χ 113 ( 2 ) = N β z z z * [ ( 1 / 5 ) A 1 ( 1 / 5 ) A 3 ] ,
Δ A l = l ( l + 1 ) 2 l + 1 μ * E k θ ( A l 1 A l + 1 ) .
Δ A 1 = 2 μ * E 3 k θ ( 1 A 2 )
Δ A 3 = 12 μ * E 7 k θ ( A 2 A 4 ) .
χ 1133 ( 3 ) = N β z z z * μ * 105 k θ ( 14 50 A 2 + 36 A 4 )
χ 3333 ( 3 ) = 2 N β z z z * μ * 35 k θ ( 7 + 5 A 2 12 A 4 ) ,
P i ω + 2 Ω = j { χ i j ( 1 ) ( ω ; ω ) E j + 3 χ i i j j ( 3 ) ( ω 2 Ω ; ω , Ω , Ω ) ( E j Ω ) 2 E i ω } ,
P 1 = χ 11 ( 1 ) E 1 ω + 3 χ 1133 ( 3 ) ( E 3 Ω ) 2 E 1 ω ,
P 3 = χ 33 ( 1 ) E 3 ω + 3 χ 3333 ( 3 ) ( E 3 Ω ) 2 E 3 ω .
Δ n 11 = 6 π χ 1133 ( 3 ) ( E Ω ) 2 n 11 ( 0 )
Δ n 33 = 6 π χ 3333 ( 3 ) ( E Ω ) 2 n 33 ( 0 ) ,
Δ n 11 = 2 π N β z z z * μ * 35 k θ n 11 ( 0 ) ( 14 50 A 2 + 36 A 4 ) ( E Ω ) 2
Δ n 33 = 12 π N β z z z * μ * 35 k θ n 33 ( 0 ) ( 7 + 5 A 2 12 A 4 ) ( E Ω ) 2 .
U = 1 2 i j E i α i j * E j ,
F i = δ U δ x i = 1 2 k α j k * ( E k E j x i + E j E k x i ) .
F r = α 11 * E 1 2 2 d .
K r Δ r r = F r A ,
A = 2 π r d .
δ V = 2 π r δ r d ,
Δ r r = N δ r α z z * E z 2 2 K r d
Δ d d = 2 Δ r r = N α z z * V z 2 K r d 2 ,
χ i j k l ( 3 ) = N ( u i j k l ( 0 ) + u i j k l ( 2 ) A 2 + u i j k l ( 4 ) A 4 ) ,
χ 3333 ( 3 ) = N γ z z z z * 35 ( 7 + 20 A 2 + 8 A 4 )
χ 1133 ( 3 ) = N γ z z z z * 105 ( 7 + 5 A 2 12 A 4 ) .
Δ n 33 = 6 π N γ z z z z * 35 n 33 ( 0 ) ( 7 + 20 A 2 + 8 A 4 ) ( E Ω ) 2
Δ n 11 = 2 π N γ z z z z * 35 n 11 ( 0 ) ( 7 + 5 A 2 12 A 4 ) ( E Ω ) 2 .
P ( t ) = 2 V rms 2 R cos 2 ( Ω t ) ,
P 2 Ω ( t ) = V rms 2 R cos ( 2 Ω t ) ,
Δ H = | 0 π / 4 Ω P ( t ) d t | .
Δ H = V rms 2 Ω R .
Δ T = Δ H / ρ d A c ,
Δ n n = ( 1 n n T ) Δ T
Δ d d = ( 1 d d T ) Δ T .
Δ n n = ( 1 n n T ) V rms 2 Ω ρ A d c R [ 1 exp ( t τ ) ]
Δ d d = ( 1 d d T ) V rms 2 Ω ρ A d c R [ 1 exp ( t τ ) ] ,
I = E 01 2 + E 02 2 + 2 E 01 E 02 cos ( ϕ 2 ϕ 1 ) ,
Δ n = n 3 2 [ r E + s E 2 ] ,
E = 2 1 / 2 V rms d cos ( Ω t ) ,
ϕ 2 ϕ 1 = ϕ + A cos ( Ω t ) + B cos 2 ( Ω t ) ,
A = 2 1 / 2 π n 3 r V rms λ
B = 2 π n 3 s V rms 2 λ d
I Ω rms = 2 1 / 2 E 01 E 02 A | δ 1 + sin ϕ |
I 2 Ω rms = 2 E 01 E 02 2 1 / 2 | δ 2 + A 2 2 cos ϕ B sin ϕ | ,
ϕ I 2 Ω rms = 0 .
2 ϕ 2 I 2 Ω rms < 0 ,
2 ϕ 2 I 2 Ω rms > 0 ,
r 113 = λ π n 3 V rms I sig I max Ω + I min Ω ,
s 1133 = λ d 2 π n 3 V rms 2 [ ( I max 2 Ω + I min 2 Ω ) 2 I sig 2 / 8 ( I max Ω + I min Ω ) 4 4 I sig 4 ] 1 / 2 ,
J 1133 = n ( 1 n n T ) d Ω ρ A c R [ 1 exp ( t τ ) ] .
Δ n = n Δ d d ,
J 1133 = ( n 1 ) 4 π K ,
J 1133 = 2 N α z z * ( n 1 ) K .
J 1133 = 4 π N β z z z * μ * 35 k θ n 11 ( 14 50 A 2 + 36 A 4 ) .
J 1133 = 16 105 π N α * ( Ω ; Ω ) α * ( ω ; ω ) k θ n 11 ( 7 + 5 A 2 12 A 4 ) .
α z z = A / ( ω ω 0 ) ,
β z z z = A / ( ω ω 0 ) + B / ( ω ω 0 ) 2 ,
γ z z z z = A / ( ω ω 0 ) + B / ( ω ω 0 ) 2 + C / ( ω ω 0 ) 3 ,
χ ( 3 ) μ 01 2 [ μ 01 2 ( Δ μ ) 2 ] ,
γ = χ ( 3 ) L N .
Δ n = n 3 s 2 E 2 ,
Δ n = J 2 E 2 ,
J = 9 × 10 8 × n 3 × s .
P i = χ i j ( 1 ) E j + χ i j k l ( 3 ) E j E k E l ,
P 1 = χ 11 ( 1 ) E 1 + 3 χ 1133 ( 3 ) E 1 E 3 2 .
n = 1 / 2 = ( 1 + 4 π χ 11 ( 1 ) + 12 π χ 1133 ( 3 ) E 3 2 ) 1 / 2 n 0 + 6 π χ 1133 ( 3 ) n 0 E 3 2 ,
χ ( 3 ) = n 0 J 12 π .
χ i j k l = N 0 2 π d ϕ 0 π d ( cos θ ) × 0 2 π d ψ a i z a j z a k z a l z γ z z z z * G ( ϕ , θ , ψ ) ,
γ = μ 01 2 ( μ 01 2 D 1 ( ω 10 , ω ) ( Δ μ ) 2 D 2 ( ω 10 , ω ) ) + i = 2 N X i D i ( ω i 0 , ω ) ,

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