Abstract

A new organic crystal, N-(4-aminobenzenesulfonyl)acetamide, was identified as a promising candidate for frequency doubling to the blue region. Large square-bipyramidal single crystals up to 8 mm × 8 mm × 18 mm in size have been successfully grown by the slow-cooling technique. Optical transmission of the crystal ranges from 400 to 1100 nm. The dispersions of refractive indices were measured by the minimum-deviation method. The nonlinear-optical d coefficients at 1064 nm were evaluated to be d33 = 6.2 pm/V, d31 = 3.3 pm/ V, and d15 = 2.8 pm/V by the Maker-fringe technique. Type II phase matching was theoretically and experimentally demonstrated when the crystal was pumped at fundamental wavelengths between 762 and 1064 nm. Detailed characteristics of phase-matched second-harmonic generation were evaluated, along with crystal processing techniques such as cutting, polishing, and antireflection coating.

© 1996 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
    [CrossRef]
  4. W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  25. H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
    [CrossRef]
  26. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
    [CrossRef]
  27. 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]
  28. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [CrossRef]
  29. G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
    [CrossRef]
  30. T. Sasaki and Y. Namba, “Growth and surface polishing of organic nonlinear optical crystals,” Jpn. J. Opt. 21, 284–285 (1992).

1994 (3)

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

T. Kinoshita, S. Horinouchi, K. Sasaki, H. Okamoto, N. Tanaka, T. Fukaya, and M. Goto, “Nonlinear-optical properties of a novel organic crystal: 2-furyl methacrylic anhydride,” J. Opt. Soc. Am. B 11, 986–994 (1994).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
[CrossRef]

1993 (4)

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Intracavity second-harmonic generation using a deuterated organic ionic crystal,” Appl. Phys. Lett. 63, 3565–3567 (1993).
[CrossRef]

G. Puccetti, A. Perigaud, J. Badan, I. Ledoux, and J. Zyss, “5-Nitrouracil: a transparent and efficient nonlinear organic crystal,” J. Opt. Soc. Am. B 10, 733–744 (1993).
[CrossRef]

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

1992 (5)

H. Nakatani, H. Hayashi, and T. Hidaka, “Linear and nonlinear optical properties of 2-cyano-3-(2-methoxyphenyl)-2-propenoic acid methyl ester,” Jpn. J. Appl. Phys. 31, 1802–1806 (1992).
[CrossRef]

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

T. Sasaki and Y. Namba, “Growth and surface polishing of organic nonlinear optical crystals,” Jpn. J. Opt. 21, 284–285 (1992).

1991 (2)

Y. Kitaoka, T. Sasaki, S. Nakai, and Y. Goto, “New nonlinear optical crystal thienylchalcone and its harmonic generation properties,” Appl. Phys. Lett. 59, 19–21 (1991).
[CrossRef]

Y. Goto, A. Hayashi, Y. Kimura, and M. Nakayama, “Second harmonic generation and crystal growth of substituted thienyl chalcone,” J. Cryst. Growth 108, 688–698 (1991).
[CrossRef]

1990 (2)

S. N. Oliver, P. Pantelis, and P. L. Dunn, “Polymorphism and crystal-crystal transformations of the highly optically nonlinear organic compound α[(4′-methoxyphenyl)methylene]-4-nitro-benzeneacetonitrile,” Appl. Phys. Lett. 56, 307–309 (1990).
[CrossRef]

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

1987 (2)

1982 (1)

J. Zyss and J. L. Oudar, “Relations between microscopic and macroscopic lowest-order optical nonlinearities of molecular crystals with one- or two-dimensional units,” Phys. Rev. A 26, 2028–2048 (1982).
[CrossRef]

1978 (1)

K. Moriya and T. Ogawa, “Observation of growth defects in synthetic quartz crystals by light-scattering tomography,” J. Cryst. Growth 44, 53–60 (1978).
[CrossRef]

1970 (1)

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]

1968 (2)

R. Brooks, A. T. Horton, and J. L. Torgesen, “Occlusion of mother liquor in solution-grown crystals,” J. Cryst. Growth 2, 279–283 (1968).
[CrossRef]

S. K. Kurtz and T. T. Perry, “A powder technique for the evaluation of nonlinear optical materials,” J. Appl. Phys. 39, 3798–3813 (1968).
[CrossRef]

1965 (2)

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[CrossRef]

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Akita, S.

S. Akita, M. Ihara, K. Tojo, and T. Yoshida, “Blue light generation by SHG using BBO,” in Digest of Technical Papers, 14th Annual Meeting of the Laser Society of Japan (Laser Society of Japan, Osaka, 1994), p. 56.

Andou, T.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Ashkin, A.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[CrossRef]

Badan, J.

Barzoukas, M.

Black, S. N.

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

Bona, G. L.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Bond, W. L.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Boyd, G. D.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[CrossRef]

Brooks, R.

R. Brooks, A. T. Horton, and J. L. Torgesen, “Occlusion of mother liquor in solution-grown crystals,” J. Cryst. Growth 2, 279–283 (1968).
[CrossRef]

Davey, R. J.

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

Dewey, A. G.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Dunn, P. L.

S. N. Oliver, P. Pantelis, and P. L. Dunn, “Polymorphism and crystal-crystal transformations of the highly optically nonlinear organic compound α[(4′-methoxyphenyl)methylene]-4-nitro-benzeneacetonitrile,” Appl. Phys. Lett. 56, 307–309 (1990).
[CrossRef]

Dziedzic, J. M.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[CrossRef]

Fremaux, P.

Fukaya, T.

Funato, S.

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Goto, M.

Goto, Y.

Y. Goto, A. Hayashi, Y. Kimura, and M. Nakayama, “Second harmonic generation and crystal growth of substituted thienyl chalcone,” J. Cryst. Growth 108, 688–698 (1991).
[CrossRef]

Y. Kitaoka, T. Sasaki, S. Nakai, and Y. Goto, “New nonlinear optical crystal thienylchalcone and its harmonic generation properties,” Appl. Phys. Lett. 59, 19–21 (1991).
[CrossRef]

Halfpenny, P.

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

Hayashi, A.

Y. Goto, A. Hayashi, Y. Kimura, and M. Nakayama, “Second harmonic generation and crystal growth of substituted thienyl chalcone,” J. Cryst. Growth 108, 688–698 (1991).
[CrossRef]

Hayashi, H.

H. Nakatani, H. Hayashi, and T. Hidaka, “Linear and nonlinear optical properties of 2-cyano-3-(2-methoxyphenyl)-2-propenoic acid methyl ester,” Jpn. J. Appl. Phys. 31, 1802–1806 (1992).
[CrossRef]

Hidaka, T.

H. Nakatani, H. Hayashi, and T. Hidaka, “Linear and nonlinear optical properties of 2-cyano-3-(2-methoxyphenyl)-2-propenoic acid methyl ester,” Jpn. J. Appl. Phys. 31, 1802–1806 (1992).
[CrossRef]

Horinouchi, S.

Horton, A. T.

R. Brooks, A. T. Horton, and J. L. Torgesen, “Occlusion of mother liquor in solution-grown crystals,” J. Cryst. Growth 2, 279–283 (1968).
[CrossRef]

Hosomi, T.

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

Hurst, J. E.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Ihara, M.

S. Akita, M. Ihara, K. Tojo, and T. Yoshida, “Blue light generation by SHG using BBO,” in Digest of Technical Papers, 14th Annual Meeting of the Laser Society of Japan (Laser Society of Japan, Osaka, 1994), p. 56.

Ishii, K.

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

Jerphagnon, J.

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]

Johnson, R. E.

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Josse, D.

Juliana, A.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Kagawa, K.

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

Kaji, K.

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

Kakuta, A.

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

Kato, M.

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

Katogi, S.

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

Kimura, Y.

Y. Goto, A. Hayashi, Y. Kimura, and M. Nakayama, “Second harmonic generation and crystal growth of substituted thienyl chalcone,” J. Cryst. Growth 108, 688–698 (1991).
[CrossRef]

Kinoshita, T.

Kitaoka, Y.

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

Y. Kitaoka, T. Sasaki, S. Nakai, and Y. Goto, “New nonlinear optical crystal thienylchalcone and its harmonic generation properties,” Appl. Phys. Lett. 59, 19–21 (1991).
[CrossRef]

Kleinman, D. A.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[CrossRef]

Kozlovsky, W. J.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Kurtz, S. K.

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]

S. K. Kurtz and T. T. Perry, “A powder technique for the evaluation of nonlinear optical materials,” J. Appl. Phys. 39, 3798–3813 (1968).
[CrossRef]

Latta, E. E.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Latta, M. R.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Ledoux, I.

Lenth, W.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Lupo, D.

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Minemoto, H.

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Intracavity second-harmonic generation using a deuterated organic ionic crystal,” Appl. Phys. Lett. 63, 3565–3567 (1993).
[CrossRef]

Miyai, T.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Miyata, S.

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

Moriya, K.

K. Moriya and T. Ogawa, “Observation of growth defects in synthetic quartz crystals by light-scattering tomography,” J. Cryst. Growth 44, 53–60 (1978).
[CrossRef]

Morley, J. O.

Morley, P. R.

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

Moser, A.

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Muraoka, K.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Nakai, S.

Y. Kitaoka, T. Sasaki, S. Nakai, and Y. Goto, “New nonlinear optical crystal thienylchalcone and its harmonic generation properties,” Appl. Phys. Lett. 59, 19–21 (1991).
[CrossRef]

Nakamura, J.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Nakatani, H.

H. Nakatani, H. Hayashi, and T. Hidaka, “Linear and nonlinear optical properties of 2-cyano-3-(2-methoxyphenyl)-2-propenoic acid methyl ester,” Jpn. J. Appl. Phys. 31, 1802–1806 (1992).
[CrossRef]

Nakayama, H.

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

Nakayama, M.

Y. Goto, A. Hayashi, Y. Kimura, and M. Nakayama, “Second harmonic generation and crystal growth of substituted thienyl chalcone,” J. Cryst. Growth 108, 688–698 (1991).
[CrossRef]

Namba, Y.

T. Sasaki and Y. Namba, “Growth and surface polishing of organic nonlinear optical crystals,” Jpn. J. Opt. 21, 284–285 (1992).

Nicoud, J. F.

Norwood, R. A.

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Ogawa, T.

K. Moriya and T. Ogawa, “Observation of growth defects in synthetic quartz crystals by light-scattering tomography,” J. Cryst. Growth 44, 53–60 (1978).
[CrossRef]

Ohmori, S.

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

Okamoto, H.

Okaniwa, K.

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Oliver, S. N.

S. N. Oliver, P. Pantelis, and P. L. Dunn, “Polymorphism and crystal-crystal transformations of the highly optically nonlinear organic compound α[(4′-methoxyphenyl)methylene]-4-nitro-benzeneacetonitrile,” Appl. Phys. Lett. 56, 307–309 (1990).
[CrossRef]

Oudar, J. L.

J. Zyss and J. L. Oudar, “Relations between microscopic and macroscopic lowest-order optical nonlinearities of molecular crystals with one- or two-dimensional units,” Phys. Rev. A 26, 2028–2048 (1982).
[CrossRef]

Ozaki, Y.

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Intracavity second-harmonic generation using a deuterated organic ionic crystal,” Appl. Phys. Lett. 63, 3565–3567 (1993).
[CrossRef]

Page, D. A.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Pantelis, P.

S. N. Oliver, P. Pantelis, and P. L. Dunn, “Polymorphism and crystal-crystal transformations of the highly optically nonlinear organic compound α[(4′-methoxyphenyl)methylene]-4-nitro-benzeneacetonitrile,” Appl. Phys. Lett. 56, 307–309 (1990).
[CrossRef]

Payne, R. N.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Perigaud, A.

Perry, T. T.

S. K. Kurtz and T. T. Perry, “A powder technique for the evaluation of nonlinear optical materials,” J. Appl. Phys. 39, 3798–3813 (1968).
[CrossRef]

Puccetti, G.

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Sagawa, M.

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

Sasaki, K.

Sasaki, T.

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Intracavity second-harmonic generation using a deuterated organic ionic crystal,” Appl. Phys. Lett. 63, 3565–3567 (1993).
[CrossRef]

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

T. Sasaki and Y. Namba, “Growth and surface polishing of organic nonlinear optical crystals,” Jpn. J. Opt. 21, 284–285 (1992).

Y. Kitaoka, T. Sasaki, S. Nakai, and Y. Goto, “New nonlinear optical crystal thienylchalcone and its harmonic generation properties,” Appl. Phys. Lett. 59, 19–21 (1991).
[CrossRef]

Sato, H.

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, C. T. Seaton, and R. Zanoni, “Organic films in nonlinear integrated optics structures,” Thin Solid Films 152, 231–263 (1987).
[CrossRef]

Shepherd, E. E. A.

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

Sherwood, J. N.

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

Sonoda, N.

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Intracavity second-harmonic generation using a deuterated organic ionic crystal,” Appl. Phys. Lett. 63, 3565–3567 (1993).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, C. T. Seaton, and R. Zanoni, “Organic films in nonlinear integrated optics structures,” Thin Solid Films 152, 231–263 (1987).
[CrossRef]

Sugiyama, H.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Takahashi, M.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Tanaka, N.

Tatsuno, K.

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Tojo, K.

S. Akita, M. Ihara, K. Tojo, and T. Yoshida, “Blue light generation by SHG using BBO,” in Digest of Technical Papers, 14th Annual Meeting of the Laser Society of Japan (Laser Society of Japan, Osaka, 1994), p. 56.

Torgesen, J. L.

R. Brooks, A. T. Horton, and J. L. Torgesen, “Occlusion of mother liquor in solution-grown crystals,” J. Cryst. Growth 2, 279–283 (1968).
[CrossRef]

Watanabe, T.

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

Werlich, H.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

Yamamoto, H.

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Yamamoto, K.

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

Yoshida, T.

S. Akita, M. Ihara, K. Tojo, and T. Yoshida, “Blue light generation by SHG using BBO,” in Digest of Technical Papers, 14th Annual Meeting of the Laser Society of Japan (Laser Society of Japan, Osaka, 1994), p. 56.

Yu, N.

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

Zanoni, R.

G. I. Stegeman, C. T. Seaton, and R. Zanoni, “Organic films in nonlinear integrated optics structures,” Thin Solid Films 152, 231–263 (1987).
[CrossRef]

Zyss, J.

Appl. Phys. Lett. (6)

Y. Kitaoka, S. Ohmori, K. Yamamoto, M. Kato, and T. Sasaki, “Stable and efficient green light generation by intracavity frequency doubling of Nd:YVO4 lasers,” Appl. Phys. Lett. 63, 299–301 (1993).
[CrossRef]

W. J. Kozlovsky, W. Lenth, E. E. Latta, A. Moser, and G. L. Bona, “Generation of 41 mW of blue radiation by frequency doubling of a GaAlAs diode laser,” Appl. Phys. Lett. 56, 2291–2292 (1990).
[CrossRef]

Y. Kitaoka, T. Sasaki, S. Nakai, and Y. Goto, “New nonlinear optical crystal thienylchalcone and its harmonic generation properties,” Appl. Phys. Lett. 59, 19–21 (1991).
[CrossRef]

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Intracavity second-harmonic generation using a deuterated organic ionic crystal,” Appl. Phys. Lett. 63, 3565–3567 (1993).
[CrossRef]

H. Yamamoto, S. Katogi, T. Watanabe, H. Sato, S. Miyata, and T. Hosomi, “New molecular design approach for noncentrosymmetric crystal structures: Lambda (Λ)-shaped molecules for frequency doubling,” Appl. Phys. Lett. 60, 935–937 (1992).
[CrossRef]

S. N. Oliver, P. Pantelis, and P. L. Dunn, “Polymorphism and crystal-crystal transformations of the highly optically nonlinear organic compound α[(4′-methoxyphenyl)methylene]-4-nitro-benzeneacetonitrile,” Appl. Phys. Lett. 56, 307–309 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

J. Appl. Phys. (4)

H. Minemoto, Y. Ozaki, N. Sonoda, and T. Sasaki, “Crystal growth and the nonlinear optical properties of 4-nitrophenol sodium salt dihydrate and its deuterated material,” J. Appl. Phys. 76, 3975–3980 (1994).
[CrossRef]

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

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

S. K. Kurtz and T. T. Perry, “A powder technique for the evaluation of nonlinear optical materials,” J. Appl. Phys. 39, 3798–3813 (1968).
[CrossRef]

J. Cryst. Growth (4)

Y. Goto, A. Hayashi, Y. Kimura, and M. Nakayama, “Second harmonic generation and crystal growth of substituted thienyl chalcone,” J. Cryst. Growth 108, 688–698 (1991).
[CrossRef]

K. Kagawa, M. Sagawa, A. Kakuta, K. Kaji, H. Nakayama, and K. Ishii, “Single crystal growth and characterization of a new organic nonlinear optical material: 8-(4′-acetylphenyl)-1, 4-dioxa-8-azaspiro[4,5]decane (APDA),” J. Cryst. Growth 139, 309–318 (1994).
[CrossRef]

K. Moriya and T. Ogawa, “Observation of growth defects in synthetic quartz crystals by light-scattering tomography,” J. Cryst. Growth 44, 53–60 (1978).
[CrossRef]

R. Brooks, A. T. Horton, and J. L. Torgesen, “Occlusion of mother liquor in solution-grown crystals,” J. Cryst. Growth 2, 279–283 (1968).
[CrossRef]

J. Mater. Chem. (1)

S. N. Black, R. J. Davey, P. R. Morley, P. Halfpenny, E. E. A. Shepherd, and J. N. Sherwood, “Crystal growth and characterization of the electro-optic material 3-(2,2-dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole,” J. Mater. Chem. 3, 129–132 (1993).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (2)

H. Nakatani, H. Hayashi, and T. Hidaka, “Linear and nonlinear optical properties of 2-cyano-3-(2-methoxyphenyl)-2-propenoic acid methyl ester,” Jpn. J. Appl. Phys. 31, 1802–1806 (1992).
[CrossRef]

K. Tatsuno, M. Takahashi, K. Muraoka, H. Sugiyama, J. Nakamura, T. Andou, and T. Miyai, “High storage density optical recording with a stable micro green laser consisting of Nd:YVO4 and KTP,” Jpn. J. Appl. Phys. 31, 601–604 (1992).
[CrossRef]

Jpn. J. Opt. (1)

T. Sasaki and Y. Namba, “Growth and surface polishing of organic nonlinear optical crystals,” Jpn. J. Opt. 21, 284–285 (1992).

Phys. Rev. (1)

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, A1305–A1320 (1965).
[CrossRef]

Phys. Rev. A (1)

J. Zyss and J. L. Oudar, “Relations between microscopic and macroscopic lowest-order optical nonlinearities of molecular crystals with one- or two-dimensional units,” Phys. Rev. A 26, 2028–2048 (1982).
[CrossRef]

Thin Solid Films (1)

G. I. Stegeman, C. T. Seaton, and R. Zanoni, “Organic films in nonlinear integrated optics structures,” Thin Solid Films 152, 231–263 (1987).
[CrossRef]

Other (5)

R. A. Norwood, R. E. Johnson, S. Funato, D. Lupo, K. Okaniwa, H. Yamamoto, and N. Yu, “Frequency doubling in organic crystals and NLO polymers,” presented at the International Conference on Nonlinear Optics I, Val Thorens, France, 1994.

W. J. Kozlovsky, A. G. Dewey, A. Juliana, J. E. Hurst, M. R. Latta, D. A. Page, R. N. Payne, and H. Werlich, “Optical recording in the blue using a frequency-doubled diode laser,” in Optical Data Storage, D. B. Carlin and D. B. Kay, eds., Proc. SPIE1663, 410–415 (1992).
[CrossRef]

S. Akita, M. Ihara, K. Tojo, and T. Yoshida, “Blue light generation by SHG using BBO,” in Digest of Technical Papers, 14th Annual Meeting of the Laser Society of Japan (Laser Society of Japan, Osaka, 1994), p. 56.

D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, Orlando, Fla., 1987), Vols. 1 and 2.

S. Miyata, ed., Proceedings of the Fifth Toyota Conference on Nonlinear Optical Materials (Elsevier, Amsterdam, 1992).

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Figures (15)

Fig. 1
Fig. 1

Molecular structure of ABSA.

Fig. 2
Fig. 2

Crystal structure of ABSA: (a), (b), projections along the c and a axes, respectively. Dashed lines indicate hydrogen bonds.

Fig. 3
Fig. 3

Solubility curves of ABSA solutions as a function of temperature.

Fig. 4
Fig. 4

(a) Microscope photograph of inclusions (negative crystals) inside an ABSA crystal. (b) As-grown ABSA single crystal.

Fig. 5
Fig. 5

Defects observed by light-scattering tomography (a) in a good-quality part and (b) in a low-quality part of a crystal.

Fig. 6
Fig. 6

Typical crystal habit of ABSA.

Fig. 7
Fig. 7

Optical transmission spectra of ABSA crystals: solid curve, a 11-mm-thick sample; dashed and dashed– dotted curves, 1-mm-thick samples.

Fig. 8
Fig. 8

Dispersion curves of refractive indices no for the ordinary ray (filled squares) and ne for the extraordinary ray (triangles).

Fig. 9
Fig. 9

Experimental setup for Maker-fringe measurement: PM, powermeter; A’s, apertures (ϕ = 1 mm); BS, beam splitter; ND, neutral-density filter; HW, half-wave plate; IRP, infrared-passing filter; GS, goniometer stage; CS, CuSO4 solution cell; IRC, infrared-cut filter; P, polarizer; SHP, SH-passing filter; PMT, photomultiplier; Boxcar, boxcar integrator; OSC, oscilloscope; PC, personal computer.

Fig. 10
Fig. 10

Maker fringes of ABSA for (a) d33, (b) d31, and (c) d15.

Fig. 11
Fig. 11

Calculated and experimental phase-matching angles as a function of the fundamental wavelength.

Fig. 12
Fig. 12

Calculated walk-off angle (thick curve) and effective d coefficient (thin curve) as a function of the fundamental wavelength.

Fig. 13
Fig. 13

SH power of KTP, BBO, and ABSA crystals at 1064 nm as a function of the fundamental power.

Fig. 14
Fig. 14

Results of angular phase matching of (a) KTP and (b) ABSA crystals at 1064 nm and 10-kW input power.

Fig. 15
Fig. 15

Transmission spectrum of antireflection-coated ABSA crystal.

Tables (4)

Tables Icon

Table 1 Crystal Data of ABSA

Tables Icon

Table 2 Sellmeier Coefficients of ABSA Crystal

Tables Icon

Table 3 Experimental and Fitted Values of Refractive Indices

Tables Icon

Table 4 Results of Maker-Fringe Analyses

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

β x x x 2 ω = 3 e 2 ћ 2 4 m 0 W e g [ W e g 2 ( 2 ћ ω ) 2 ] [ W e g 2 ( ћ ω ) 2 ] f Δ μ ,
β x x x 2 ω = F ( W , ω ) β ( 0 ) ,
F ( W , ω ) = W e g 4 [ W e g 2 ( 2 ћ ω ) 2 ] [ W e g 2 ( ћ ω ) 2 ]
β ( 0 ) = 3 e 2 ћ 2 4 m 0 W e g 3 .
n = sin [ ( θ + ϕ ) / 2 ] / sin ( ϕ / 2 ) ,
n 2 = A + B λ 2 / ( λ 2 C ) D λ 2 ,
P x 2 ω = 2 0 d 15 E x ω E z ω , P y 2 ω = 2 0 d 15 E y ω E z ω , P z 2 ω = 0 ( d 31 E x ω E x ω + d 31 E y ω E y ω + d 33 E z ω E z ω ) ,
d I J K = ( N / z ) f I 2 ω f J ω f K ω i j k s cos θ I i ( s ) cos θ J j ( s ) cos θ K k ( s ) × β i j k ( s ) × C ,
l c exp = l ( sin 2 θ m + 1 sin 2 θ m ) 4 n ω n 2 ω ,
( d i i / d i j ) cal = 2.4 , ( d i i / d i j ) exp = 2.0 ,
n o 2 ω = [ n o ω + n e ω ( θ PM ) ] / 2 ,
sin 2 θ PM = [ n o ω / ( 2 n o 2 ω n o ω ) ] 2 1 ( n o ω / n e ω ) 2 1 ,
n o ω sin ( θ PM o θ cut ) = sin ( θ ext θ cut )
n e ω ( θ PM e ) sin ( θ PM e θ cut ) = sin ( θ ext θ cut ) ,
n e ω ( θ PM e ) = n o ω n e ω [ ( n e ω ) 2 cos 2 θ PM e + ( n o ω ) 2 sin 2 θ PM e ] 1 / 2 ,
ρ = tan 1 { ½ [ n e ω ( θ PM ) ] 2 [ ( n o ω ) 2 ( n e ω ) 2 ] sin ( 2 θ PM ) } .
l e ff = w 0 π tan ρ ,
P 2 ω = 2 μ 0 3 / 2 0 1 / 2 ω 2 d e ff 2 l 2 ( P ω ) 2 π w 0 2 n PM 3 .
Δ k ( θ ) = 4 π λ Fun ( n o 2 ω ½ { ( n o ω ) 2 + [ n e ω ( θ in e ) ] 2 + 2 n o ω n e ω ( θ in e ) cos ( θ in o θ in e ) } 1 / 2 ) ,
Δ k ( λ ) = 4 π λ { n o ( λ / 2 ) ½ [ n o ( λ ) + n e ( θ PM , λ ) ] }

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