Abstract

Recent advances in the field of nonlinear optical phenomena are reviewed with particular emphasis placed on such topics as parametric oscillation, self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a material are then formulated in terms of Maxwell’s equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introduced which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental observations are described and interpreted in terms of this formalism.

© 1966 Optical Society of America

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1966 (24)

N. I. Adams, J. J. Barrett, “Electric field control of 90° phase matching in KDP,” IEEE J. of Quantum Electronics, vol. QE-2, p. xxxi, April1966.

C. K. N. Patel, “Optical harmonic generation in the infrared using a CO2laser,” Phys. Rev. Lett., vol. 16, pp. 613–616, April1966.
[CrossRef]

G. E. Francois, “CW Measurement of the optical nonlinearity of ADP,” Phys. Rev., vol. 143, pp. 597–600, March1966.
[CrossRef]

J. F. Ward, “Absolute measurement of an optical rectification coefficient in ADP,” Phys. Rev., vol. 143, pp. 569–574, March1966.
[CrossRef]

M. D. Martin, E. L. Thomas, “The generation of molecular vibrational frequencies by optical mixing,” Phys. Lett., vol. 19, pp. 651–652, January1966.
[CrossRef]

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev., vol. 146, pp. 187–198, June1966.
[CrossRef]

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

J. E. Bjorkholm, “Optical SHG using a focused laser beam,” Phys. Rev., vol. 142, pp. 126–136, February1966.
[CrossRef]

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second harmonic generation of light by focused laser beams,” Phvs. Rev., vol. 145, pp. 338–379, May1966.
[CrossRef]

R. K. Chang, N. Bloembergen, “Experimental verification of the laws for the reflected intensity of second harmonic light,” Phys. Rev., vol. 144, pp. 775–780, April1966.
[CrossRef]

F. Brown, R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett., vol. 16, pp. 507–509, March1966.
[CrossRef]

N. Bloembergen, R. K. Chang, C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett., vol. 16, pp. 986–989, May1966.
[CrossRef]

P. M. Rentzepis, J. A. Giordmaine, K. W. Wecht, “Coherent optical mixing in optically active liquids,” Phys. Rev. Lett., vol. 16, pp. 792–794, May1966.
[CrossRef]

D. Fröhlich, H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett., vol. 16, pp. 895–897, May1966.
[CrossRef]

G. G. Bret, M. M. Denariez, “Stimulated Raman effect in acetone and acetone-carbon disulfide mixtures,” Appl. Phys. Lett., vol. 8, pp. 151–154, March1966.
[CrossRef]

K. Shimoda, “Angular distribution of stimulated Raman radiation,” J. Appl. Phys. (Japan), vol. 5, pp. 86–92, January1966.
[CrossRef]

N. Bloembergen, P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett., vol. 16, pp. 81–84, January1966.
[CrossRef]

E. E. Hagenlocker, R. W. Minck, “Simultaneous stimulated Brillouin and Raman scattering in gases,’ IEEE J. of Quantum Electronics, vol. QE-2, p. liv, April1966.

R. W. Minck, E. E. Hagenlocker, W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett., pp. 229–231, August1966.
[CrossRef]

C. C. Wang, “Length-dependent threshold for stimulated Raman effect and self-focusing of laser beams in liquids,” Phys. Rev. Lett., vol. 16, pp. 344–346, February1966.
[CrossRef]

E. Garmire, R. Y. Chiao, C. H. Townes, “Dynamics and characteristics of the self-trapping of intense light beams,” Phys. Rev. Lett., vol. 16, pp. 347–349, February1966.
[CrossRef]

C. C. Wang, G. W. Racette, “Effect of linear absorption on self-focusing of laser beam in CS2,” Appl. Phys. Lett., vol. 8, pp. 256–257, May1966.
[CrossRef]

R. Y. Chiao, E. Garmire, “Self-trapping of optical beams,” IEEE J. of Quantum Electronics, vol. QE-2, pp. xxxviii–xxxix, April1966.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

1965 (29)

R. W. Terhune, P. D. Maker, C. M. Savage, “Measurement of nonlinear light scattering,” Phys. Rev. Lett., vol. 14, pp. 681–684, April1965.
[CrossRef]

A. Gold, H. B. Bebb, “Theory of multiphoton ionization,” Phys. Rev. Letters, vol. 14, pp. 60–63, January1965.
[CrossRef]

Y. R. Shen, Y. J. Shaham, “Beam deterioration and stimulated Raman effect,” Phys. Rev. Lett., vol. 15, pp. 1008–1010, December1965.
[CrossRef]

H. Hsu, W. Kavage, “Stimulated Brillouin scatterings in anisotropic media and observation of phonons,” Phys. Letters, vol. 15, pp. 207–209, April1965.
[CrossRef]

G. Hauchecorne, G. Mayer, “Effects de l’anisotropie moéculaire sur la propagation d’une lumiere intense,” Comptes Rendus, vol. 261, pp. 4014–4017, November1965.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett., vol. 15, pp. 1005–1008, December1965.
[CrossRef]

N. M. Kroll, “Excitation of hypersonic vibrations by means of photo-elastic coupling of high intensity light waves to elastic waves,” J. Appl. Phys., vol. 36, pp. 34–43, January1965.
[CrossRef]

E. E. Hagenlocker, W. G. Rado, “Stimulated Brillouin and Raman scattering in gases,” Appl. Phys. Lett., vol. 7, pp. 236–238, November1965.
[CrossRef]

D. P. Bortfeld, W. R. Sooy, “Gain in a diffusely pumped Raman amplifier,” Appl. Phys. Lett., vol. 7, pp. 283–285, November1965.
[CrossRef]

R. G. Brewer, “Growth of optical plane waves in stimulated Brillouin scattering,” Phys. Rev., vol. 140, pp. A800–A805, November1965.
[CrossRef]

Y. R. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev., vol. 137, pp. A1787–A1805, March1965.
[CrossRef]

D. I. Mash, V. V. Morozov, V. S. Starunov, I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” JETP Lett., vol. 2, pp. 25–27, July1965.

T. C. Damen, R. C. C. Leite, S. P. S. Porto, “Angular depednence of the Raman scattering from benzene excited by the He-Ne CW laser,” Phys. Rev. Lett., vol. 14, pp. 9–11, January1965.
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J. L. Hall, E. J. Robinson, L. M. Branscomb, “Laser double-quantum photodetachment of I−,” Phys Rev. Lett., vol. 14, pp. 1013–1016, June1965.
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S. Yatsiv, W. G. Wagner, G. S. Picus, F. J. McClung, “Saturation of a resonant optical double-quantum transition,” Phys. Rev. Lett., vol. 15, pp. 614–618, October1965.
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P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev., vol. 137, pp. A801–A818, February1965.
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J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev., vol. 138A, pp. A1599–A1606, June1965.
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S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev., vol. 140, pp. A2020–A2030, December1965.
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S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

F. Zernike, P. R. Berman, “Generation of far-infrared as a difference frequency,” Phys. Rev. Lett., vol. 15999–1001, December1965.
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D. H. McMahon, A. R. Franklin, “Detection of nonlinear optical sum spectra in ADP using incoherent light,” J. Appl. Phys., vol. 36, pp. 2807–2810, September1965.
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C. C. Wang, G. W. Racette, “Measurement of parametric gain accompanying optical difference frequency generation,” Appl. Phys. Lett., vol. 6, pp. 169–171, April1965.
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G. D. Boyd, A. Ashkin, J. M. Dziedzic, D. A. Kleinman, “SHG of light with double refraction,” Phvs. Rev., vol. 137, pp. A1305–A1320, February1965.
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R. K. Chang, J. Ducuing, N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett., vol. 15, pp. 6–8, July1965.
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C. C. Wang, G. W. Racette, “Saturation effects in second harmonic generation of light using unfocused laser beams,” J. Appl. Phys., vol. 36, pp. 3281–3284, October1965.
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R. C. Miller, G. D. Boyd, A. Savage, “Nonlinear optical interactions in LiNbO3without double refraction,” Appl. Phys. Lett., vol. 6, pp. 77–79, February1965.
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S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, R. V. Khokhlov, “Generation of uv radiation by using cascade frequency conversion,” JETP Lett., vol. 2, pp. 141–143, September1965.

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillations in LiNbO3at optical frequencies,” Phys. Rev. Lett., vol. 14, pp. 973–976, June1965.
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L. N. Ovander, “Nonlinear optical effects in crystals,” Soviet Phys. Uspekhi, vol. 8, pp. 337–359, November-December 1965.
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1964 (16)

W. J. Caspers, “Dispersion relations for nonlinear response,” Phys. Rev., vol. 133, pp. A1249–A1251, March1964.
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R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett., vol. 5, pp. 17–19, July1964.
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
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G. B. Benedek, J. B. Lastovka, K. Fritsch, T. Greytak, “Brillouin scattering in liquids and solids using low-power lasers,” J. Opt. Soc. Am., vol 54, pp. 1284–1285, October1964.
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R. Y. Chiao, B. P. Stoicheff, “Brillouin scattering in liquids excited by the He-Ne laser,” J. Opt. Soc. Am., vol. 54, pp. 1286–1287, October1964.
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G. Mayer, F. Gires, “Action of an intense light beam on the refractive index of liquids,” Comptes Rendus, vol. 258, pp. 2039–2042, February1964.

R. Y. Chiao, E. Garmire, C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, pp. 479–482, October1964.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett., vol. 12, pp. 507–509, May1964.
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W. J. Jones, B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett., vol. 13 pp. 657–659, November1964.
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H. Takuma, D. A. Jennings, “Coherent Raman effect in the off-axis Raman laser resonator,” Appl. Phys. Lett., vol. 4, pp. 185–186, June1964.
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P. M. Platzman, N. Tzoar, “Nonlinear Interaction of light in a plasma,” Phys. Rev., vol. 136, pp. A11–A16, October1964.
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E. Garmire, C. H. Townes, “Stimulated Brillouin scattering in liquids,” Appl. Phys. Lett., vol. 5, pp. 84–86, August1964.
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R. Y. Chiao, C. H. Townes, B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett., vol. 12, pp. 592–595, May1964.
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M. Hercher, “Laser induced damage in transparent media,” J. Opt. Soc. Am., vol. 54, p. 563A, April1964.

S. Singh, L. T. Bradley, “Three photon absorption in naphthalene crystals by laser excitation,” Phys. Rev. Lett., vol. 12, pp. 612–614, June1964.
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W. E. Lambe, “Theory of an optical maser,” Phys. Rev., vol. 134, pp. A1429–A1450, June1964.
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1963 (13)

R. Loudon, “Theory of stimulated Raman scattering from lattice vibrations,” Proc. Phys. Soc. (London), vol. 82, pp. 393–400, September1963.
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G. Eckhardt, D. P. Bortfeld, M. Geller, “Stimulated emission of Stokes and anti-Stokes Raman lines from diamond, calcite and α-sulfur single crystals,” Appl. Phys. Lett., vol. 3, pp. 137–138, October1963.
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R. W. Minck, R. W. Terhune, W. G. Rado, “Stimulated Raman effect and resonant four photon interactions in gases,” Appl. Phys. Lett., vol. 3, pp. 181–184, November1963.
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J. J. Hopfield, J. M. Worlock, K. Park, “Two quantum absorption spectrum of KI,” Phys. Rev. Lett., vol. 11, pp. 414–417, November1963.
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J. A. Giordmaine, J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev Lett., vol. 11, pp. 207–209, September1963.
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R. J. Elliott, R. Loudon, “The possible observation of electronic Raman transitions in crystals,” Phys. Lett., vol. 3, pp. 189–191, January1963.
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J. T. Hougen, S. Singh, “Electronic Raman effect in Pr3+ions in single crystals of PrCl3,” Phys. Rev. Lett., vol. 10, pp. 406–407, May1963
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J. Ducuing, N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett., vol. 10, pp. 474–476, June1963.
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P. J. Price, “Theory of quadratic response functions,” Phys. Rev., vol. 130, pp. 1792–1797, June1963.
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A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Observation of continuous optical harmonic generation with gas masers,” Phys. Rev. Lett., vol. 11, pp. 14–17, July1963.
[CrossRef]

P. A. Franken, J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys., vol. 35, pp. 23–29, January1963.
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P. S. Pershan, “Nonlinear optical properties of solids: Energy considerations,” Phys. Rev., vol. 130, pp. 919–928, May1963.
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R. C. Miller, D. A. Kleinman, A. Savage, “Quantitative studies of optical harmonic generation in CdS, BaTiO3, and KH2PO4type crystals,” Phys. Rev. Lett., vol. 11, pp. 146–149, August1963.
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1962 (11)

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett., vol. 8, pp. 21–22, January1962.
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J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett., vol. 8, pp. 19–20, January1962.
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D. A. Kleinman, “Theory of second harmonic generation of light,” Phys. Rev., vol. 128, pp. 1761–1775, November1962.
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D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol. 126, pp. 1977–1979, June1962.
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J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev., vol. 127, pp. 1918–1939, September1962.
[CrossRef]

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev., vol. 128, pp. 606–622, October1962.
[CrossRef]

R. W. Terhune, P. D. Maker, C. M. Savage, “Optical harmonic generation in Calcite,” Phys. Rev. Lett., vol. 8, pp. 404–406, May1962.
[CrossRef]

M. Bass, P. A. Franken, J. F. Ward, G. Weinreich, “Optical rectification,” Phys. Rev. Lett., vol. 9, pp. 446–448, December1962.
[CrossRef]

R. R. Briss, “Property tensors in magnetic crystal classes,” Proc. Phys. Soc. (London), vol. 79, pp. 946–953, May1962.
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E. J. Woodbury, W. K. Ng, “Ruby laser operation in the near IR,” Proc. IRE (Correspondence), vol. 50, p. 2367, November1962.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

1961 (2)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118–119, August1961.
[CrossRef]

W. Kaiser, C. G. B. Garrett, “Two-photon excitation in CaF2:Eu2+.” Phys. Rev. Lett., vol. 7, pp. 229–231, September1961.
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Adams, N. I.

N. I. Adams, J. J. Barrett, “Electric field control of 90° phase matching in KDP,” IEEE J. of Quantum Electronics, vol. QE-2, p. xxxi, April1966.

Akhmanov, S. A.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, R. V. Khokhlov, “Generation of uv radiation by using cascade frequency conversion,” JETP Lett., vol. 2, pp. 141–143, September1965.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev., vol. 127, pp. 1918–1939, September1962.
[CrossRef]

Ashkin, A.

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second harmonic generation of light by focused laser beams,” Phvs. Rev., vol. 145, pp. 338–379, May1966.
[CrossRef]

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev., vol. 146, pp. 187–198, June1966.
[CrossRef]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, D. A. Kleinman, “SHG of light with double refraction,” Phvs. Rev., vol. 137, pp. A1305–A1320, February1965.
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Observation of continuous optical harmonic generation with gas masers,” Phys. Rev. Lett., vol. 11, pp. 14–17, July1963.
[CrossRef]

Barrett, J. J.

N. I. Adams, J. J. Barrett, “Electric field control of 90° phase matching in KDP,” IEEE J. of Quantum Electronics, vol. QE-2, p. xxxi, April1966.

Bass, M.

M. Bass, P. A. Franken, J. F. Ward, G. Weinreich, “Optical rectification,” Phys. Rev. Lett., vol. 9, pp. 446–448, December1962.
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Bebb, H. B.

A. Gold, H. B. Bebb, “Theory of multiphoton ionization,” Phys. Rev. Letters, vol. 14, pp. 60–63, January1965.
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Benedek, G. B.

Berman, P. R.

F. Zernike, P. R. Berman, “Generation of far-infrared as a difference frequency,” Phys. Rev. Lett., vol. 15999–1001, December1965.
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Bjorkholm, J. E.

J. E. Bjorkholm, “Optical SHG using a focused laser beam,” Phys. Rev., vol. 142, pp. 126–136, February1966.
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Bloembergen, N.

N. Bloembergen, R. K. Chang, C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett., vol. 16, pp. 986–989, May1966.
[CrossRef]

R. K. Chang, N. Bloembergen, “Experimental verification of the laws for the reflected intensity of second harmonic light,” Phys. Rev., vol. 144, pp. 775–780, April1966.
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N. Bloembergen, P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett., vol. 16, pp. 81–84, January1966.
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Y. R. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev., vol. 137, pp. A1787–A1805, March1965.
[CrossRef]

R. K. Chang, J. Ducuing, N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett., vol. 15, pp. 6–8, July1965.
[CrossRef]

J. Ducuing, N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett., vol. 10, pp. 474–476, June1963.
[CrossRef]

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev., vol. 128, pp. 606–622, October1962.
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev., vol. 127, pp. 1918–1939, September1962.
[CrossRef]

N. Bloembergen, Nonlinear Optics. New York: Benjamin, 1965.

Bond, W. L.

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
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Born, M.

M. Born, E. Wolf, Principles of Optics. New York: Pergamon, 1959, pp. 434–448.

Bortfeld, D. P.

D. P. Bortfeld, W. R. Sooy, “Gain in a diffusely pumped Raman amplifier,” Appl. Phys. Lett., vol. 7, pp. 283–285, November1965.
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G. Eckhardt, D. P. Bortfeld, M. Geller, “Stimulated emission of Stokes and anti-Stokes Raman lines from diamond, calcite and α-sulfur single crystals,” Appl. Phys. Lett., vol. 3, pp. 137–138, October1963.
[CrossRef]

Boyd, G. D.

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev., vol. 146, pp. 187–198, June1966.
[CrossRef]

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second harmonic generation of light by focused laser beams,” Phvs. Rev., vol. 145, pp. 338–379, May1966.
[CrossRef]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, D. A. Kleinman, “SHG of light with double refraction,” Phvs. Rev., vol. 137, pp. A1305–A1320, February1965.
[CrossRef]

R. C. Miller, G. D. Boyd, A. Savage, “Nonlinear optical interactions in LiNbO3without double refraction,” Appl. Phys. Lett., vol. 6, pp. 77–79, February1965.
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Observation of continuous optical harmonic generation with gas masers,” Phys. Rev. Lett., vol. 11, pp. 14–17, July1963.
[CrossRef]

Bradley, L. T.

S. Singh, L. T. Bradley, “Three photon absorption in naphthalene crystals by laser excitation,” Phys. Rev. Lett., vol. 12, pp. 612–614, June1964.
[CrossRef]

Branscomb, L. M.

J. L. Hall, E. J. Robinson, L. M. Branscomb, “Laser double-quantum photodetachment of I−,” Phys Rev. Lett., vol. 14, pp. 1013–1016, June1965.
[CrossRef]

Bret, G. G.

G. G. Bret, M. M. Denariez, “Stimulated Raman effect in acetone and acetone-carbon disulfide mixtures,” Appl. Phys. Lett., vol. 8, pp. 151–154, March1966.
[CrossRef]

Brewer, R. G.

R. G. Brewer, “Growth of optical plane waves in stimulated Brillouin scattering,” Phys. Rev., vol. 140, pp. A800–A805, November1965.
[CrossRef]

Briss, R. R.

R. R. Briss, “Property tensors in magnetic crystal classes,” Proc. Phys. Soc. (London), vol. 79, pp. 946–953, May1962.
[CrossRef]

Brown, F.

F. Brown, R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett., vol. 16, pp. 507–509, March1966.
[CrossRef]

Cady, W. G.

W. G. Cady, Piezoelectricity. New York: McGraw-Hill, 1946, pp. 177–199.

Caspers, W. J.

W. J. Caspers, “Dispersion relations for nonlinear response,” Phys. Rev., vol. 133, pp. A1249–A1251, March1964.
[CrossRef]

Cederquist, A. L.

A. L. Cederquist, T. Kushida, L. Rimai, “High resolution Brillouin and Rayleigh spectra with single mode He-Ne laser and detection by photon counting,” Phys. Lett., to be published.

Chang, R. K.

N. Bloembergen, R. K. Chang, C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett., vol. 16, pp. 986–989, May1966.
[CrossRef]

R. K. Chang, N. Bloembergen, “Experimental verification of the laws for the reflected intensity of second harmonic light,” Phys. Rev., vol. 144, pp. 775–780, April1966.
[CrossRef]

R. K. Chang, J. Ducuing, N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett., vol. 15, pp. 6–8, July1965.
[CrossRef]

Chiao, R. Y.

E. Garmire, R. Y. Chiao, C. H. Townes, “Dynamics and characteristics of the self-trapping of intense light beams,” Phys. Rev. Lett., vol. 16, pp. 347–349, February1966.
[CrossRef]

R. Y. Chiao, E. Garmire, “Self-trapping of optical beams,” IEEE J. of Quantum Electronics, vol. QE-2, pp. xxxviii–xxxix, April1966.

R. Y. Chiao, E. Garmire, C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, pp. 479–482, October1964.
[CrossRef]

R. Y. Chiao, B. P. Stoicheff, “Brillouin scattering in liquids excited by the He-Ne laser,” J. Opt. Soc. Am., vol. 54, pp. 1286–1287, October1964.
[CrossRef]

R. Y. Chiao, C. H. Townes, B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett., vol. 12, pp. 592–595, May1964.
[CrossRef]

Close, D. L.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

Damen, T. C.

T. C. Damen, R. C. C. Leite, S. P. S. Porto, “Angular depednence of the Raman scattering from benzene excited by the He-Ne CW laser,” Phys. Rev. Lett., vol. 14, pp. 9–11, January1965.
[CrossRef]

Denariez, M. M.

G. G. Bret, M. M. Denariez, “Stimulated Raman effect in acetone and acetone-carbon disulfide mixtures,” Appl. Phys. Lett., vol. 8, pp. 151–154, March1966.
[CrossRef]

Ducuing, J.

R. K. Chang, J. Ducuing, N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett., vol. 15, pp. 6–8, July1965.
[CrossRef]

J. Ducuing, N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett., vol. 10, pp. 474–476, June1963.
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev., vol. 127, pp. 1918–1939, September1962.
[CrossRef]

Dziedzic, J. M.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, D. A. Kleinman, “SHG of light with double refraction,” Phvs. Rev., vol. 137, pp. A1305–A1320, February1965.
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Observation of continuous optical harmonic generation with gas masers,” Phys. Rev. Lett., vol. 11, pp. 14–17, July1963.
[CrossRef]

Eckhardt, G.

G. Eckhardt, D. P. Bortfeld, M. Geller, “Stimulated emission of Stokes and anti-Stokes Raman lines from diamond, calcite and α-sulfur single crystals,” Appl. Phys. Lett., vol. 3, pp. 137–138, October1963.
[CrossRef]

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

Elliott, R. J.

R. J. Elliott, R. Loudon, “The possible observation of electronic Raman transitions in crystals,” Phys. Lett., vol. 3, pp. 189–191, January1963.
[CrossRef]

Fabelinskii, I. L.

D. I. Mash, V. V. Morozov, V. S. Starunov, I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” JETP Lett., vol. 2, pp. 25–27, July1965.

Fadeev, V. V.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

Francois, G. E.

G. E. Francois, “CW Measurement of the optical nonlinearity of ADP,” Phys. Rev., vol. 143, pp. 597–600, March1966.
[CrossRef]

Franken, P. A.

P. A. Franken, J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys., vol. 35, pp. 23–29, January1963.
[CrossRef]

M. Bass, P. A. Franken, J. F. Ward, G. Weinreich, “Optical rectification,” Phys. Rev. Lett., vol. 9, pp. 446–448, December1962.
[CrossRef]

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118–119, August1961.
[CrossRef]

Franklin, A. R.

D. H. McMahon, A. R. Franklin, “Detection of nonlinear optical sum spectra in ADP using incoherent light,” J. Appl. Phys., vol. 36, pp. 2807–2810, September1965.
[CrossRef]

Fritsch, K.

Fröhlich, D.

D. Fröhlich, H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett., vol. 16, pp. 895–897, May1966.
[CrossRef]

Garmire, E.

E. Garmire, R. Y. Chiao, C. H. Townes, “Dynamics and characteristics of the self-trapping of intense light beams,” Phys. Rev. Lett., vol. 16, pp. 347–349, February1966.
[CrossRef]

R. Y. Chiao, E. Garmire, “Self-trapping of optical beams,” IEEE J. of Quantum Electronics, vol. QE-2, pp. xxxviii–xxxix, April1966.

R. Y. Chiao, E. Garmire, C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, pp. 479–482, October1964.
[CrossRef]

E. Garmire, C. H. Townes, “Stimulated Brillouin scattering in liquids,” Appl. Phys. Lett., vol. 5, pp. 84–86, August1964.
[CrossRef]

Garrett, C. G. B.

W. Kaiser, C. G. B. Garrett, “Two-photon excitation in CaF2:Eu2+.” Phys. Rev. Lett., vol. 7, pp. 229–231, September1961.
[CrossRef]

Geller, M.

G. Eckhardt, D. P. Bortfeld, M. Geller, “Stimulated emission of Stokes and anti-Stokes Raman lines from diamond, calcite and α-sulfur single crystals,” Appl. Phys. Lett., vol. 3, pp. 137–138, October1963.
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Giordmaine, J. A.

P. M. Rentzepis, J. A. Giordmaine, K. W. Wecht, “Coherent optical mixing in optically active liquids,” Phys. Rev. Lett., vol. 16, pp. 792–794, May1966.
[CrossRef]

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillations in LiNbO3at optical frequencies,” Phys. Rev. Lett., vol. 14, pp. 973–976, June1965.
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J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev., vol. 138A, pp. A1599–A1606, June1965.
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J. A. Giordmaine, J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev Lett., vol. 11, pp. 207–209, September1963.
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J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett., vol. 8, pp. 19–20, January1962.
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Gires, F.

G. Mayer, F. Gires, “Action of an intense light beam on the refractive index of liquids,” Comptes Rendus, vol. 258, pp. 2039–2042, February1964.

Giuliano, C. R.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

Gold, A.

A. Gold, H. B. Bebb, “Theory of multiphoton ionization,” Phys. Rev. Letters, vol. 14, pp. 60–63, January1965.
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Greytak, T.

Hagenlocker, E. E.

R. W. Minck, E. E. Hagenlocker, W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett., pp. 229–231, August1966.
[CrossRef]

E. E. Hagenlocker, R. W. Minck, “Simultaneous stimulated Brillouin and Raman scattering in gases,’ IEEE J. of Quantum Electronics, vol. QE-2, p. liv, April1966.

E. E. Hagenlocker, W. G. Rado, “Stimulated Brillouin and Raman scattering in gases,” Appl. Phys. Lett., vol. 7, pp. 236–238, November1965.
[CrossRef]

E. E. Hagenlocker, R. W. Minck, W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering,” to be published.

Hall, J. L.

J. L. Hall, E. J. Robinson, L. M. Branscomb, “Laser double-quantum photodetachment of I−,” Phys Rev. Lett., vol. 14, pp. 1013–1016, June1965.
[CrossRef]

Hauchecorne, G.

G. Hauchecorne, G. Mayer, “Effects de l’anisotropie moéculaire sur la propagation d’une lumiere intense,” Comptes Rendus, vol. 261, pp. 4014–4017, November1965.

Hellwarth, R. W.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

Hercher, M.

M. Hercher, “Laser induced damage in transparent media,” J. Opt. Soc. Am., vol. 54, p. 563A, April1964.

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118–119, August1961.
[CrossRef]

Hopfield, J. J.

J. J. Hopfield, J. M. Worlock, K. Park, “Two quantum absorption spectrum of KI,” Phys. Rev. Lett., vol. 11, pp. 414–417, November1963.
[CrossRef]

Hougen, J. T.

J. T. Hougen, S. Singh, “Electronic Raman effect in Pr3+ions in single crystals of PrCl3,” Phys. Rev. Lett., vol. 10, pp. 406–407, May1963
[CrossRef]

Howe, J. A.

J. A. Giordmaine, J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev Lett., vol. 11, pp. 207–209, September1963.
[CrossRef]

Hsu, H.

H. Hsu, W. Kavage, “Stimulated Brillouin scatterings in anisotropic media and observation of phonons,” Phys. Letters, vol. 15, pp. 207–209, April1965.
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Jennings, D. A.

H. Takuma, D. A. Jennings, “Coherent Raman effect in the off-axis Raman laser resonator,” Appl. Phys. Lett., vol. 4, pp. 185–186, June1964.
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Jha, S. S.

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev., vol. 140, pp. A2020–A2030, December1965.
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Jones, W. J.

W. J. Jones, B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett., vol. 13 pp. 657–659, November1964.
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Kaiser, W.

W. Kaiser, C. G. B. Garrett, “Two-photon excitation in CaF2:Eu2+.” Phys. Rev. Lett., vol. 7, pp. 229–231, September1961.
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Kavage, W.

H. Hsu, W. Kavage, “Stimulated Brillouin scatterings in anisotropic media and observation of phonons,” Phys. Letters, vol. 15, pp. 207–209, April1965.
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Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett., vol. 15, pp. 1005–1008, December1965.
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Khokhlov, R. V.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, R. V. Khokhlov, “Generation of uv radiation by using cascade frequency conversion,” JETP Lett., vol. 2, pp. 141–143, September1965.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

Kleinman, D. A.

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second harmonic generation of light by focused laser beams,” Phvs. Rev., vol. 145, pp. 338–379, May1966.
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G. D. Boyd, A. Ashkin, J. M. Dziedzic, D. A. Kleinman, “SHG of light with double refraction,” Phvs. Rev., vol. 137, pp. A1305–A1320, February1965.
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R. C. Miller, D. A. Kleinman, A. Savage, “Quantitative studies of optical harmonic generation in CdS, BaTiO3, and KH2PO4type crystals,” Phys. Rev. Lett., vol. 11, pp. 146–149, August1963.
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D. A. Kleinman, “Theory of second harmonic generation of light,” Phys. Rev., vol. 128, pp. 1761–1775, November1962.
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D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol. 126, pp. 1977–1979, June1962.
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Kolosov, V. A.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

Kovrigin, A. I.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, R. V. Khokhlov, “Generation of uv radiation by using cascade frequency conversion,” JETP Lett., vol. 2, pp. 141–143, September1965.

Kroll, N. M.

N. M. Kroll, “Excitation of hypersonic vibrations by means of photo-elastic coupling of high intensity light waves to elastic waves,” J. Appl. Phys., vol. 36, pp. 34–43, January1965.
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Kushida, T.

A. L. Cederquist, T. Kushida, L. Rimai, “High resolution Brillouin and Rayleigh spectra with single mode He-Ne laser and detection by photon counting,” Phys. Lett., to be published.

Lallemand, P.

N. Bloembergen, P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett., vol. 16, pp. 81–84, January1966.
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Lambe, W. E.

W. E. Lambe, “Theory of an optical maser,” Phys. Rev., vol. 134, pp. A1429–A1450, June1964.
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Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media. New York: Pergamon, 1960, pp. 377–397.

Lastovka, J. B.

Lee, C. H.

N. Bloembergen, R. K. Chang, C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett., vol. 16, pp. 986–989, May1966.
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Leite, R. C. C.

T. C. Damen, R. C. C. Leite, S. P. S. Porto, “Angular depednence of the Raman scattering from benzene excited by the He-Ne CW laser,” Phys. Rev. Lett., vol. 14, pp. 9–11, January1965.
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Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media. New York: Pergamon, 1960, pp. 377–397.

Loudon, R.

R. J. Elliott, R. Loudon, “The possible observation of electronic Raman transitions in crystals,” Phys. Lett., vol. 3, pp. 189–191, January1963.
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R. Loudon, “Theory of stimulated Raman scattering from lattice vibrations,” Proc. Phys. Soc. (London), vol. 82, pp. 393–400, September1963.
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Louisell, W. H.

W. H. Louisell, Coupled-Mode and Parametric Electronics. New York: Wiley, 1960.

Mahr, H.

D. Fröhlich, H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett., vol. 16, pp. 895–897, May1966.
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Maker, P. D.

R. W. Terhune, P. D. Maker, C. M. Savage, “Measurement of nonlinear light scattering,” Phys. Rev. Lett., vol. 14, pp. 681–684, April1965.
[CrossRef]

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev., vol. 137, pp. A801–A818, February1965.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett., vol. 12, pp. 507–509, May1964.
[CrossRef]

R. W. Terhune, P. D. Maker, C. M. Savage, “Optical harmonic generation in Calcite,” Phys. Rev. Lett., vol. 8, pp. 404–406, May1962.
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett., vol. 8, pp. 21–22, January1962.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Quantum Electronics III. New York: Columbia University Press, 1964, p. 1559.

R. W. Terhune, P. D. Maker, Advances in Lasers, II, A. K. Levine, Ed. New York: Marcel Dekker, to be published.

Martin, M. D.

M. D. Martin, E. L. Thomas, “The generation of molecular vibrational frequencies by optical mixing,” Phys. Lett., vol. 19, pp. 651–652, January1966.
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Mash, D. I.

D. I. Mash, V. V. Morozov, V. S. Starunov, I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” JETP Lett., vol. 2, pp. 25–27, July1965.

Mayer, G.

G. Hauchecorne, G. Mayer, “Effects de l’anisotropie moéculaire sur la propagation d’une lumiere intense,” Comptes Rendus, vol. 261, pp. 4014–4017, November1965.

G. Mayer, F. Gires, “Action of an intense light beam on the refractive index of liquids,” Comptes Rendus, vol. 258, pp. 2039–2042, February1964.

McClung, F. J.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

S. Yatsiv, W. G. Wagner, G. S. Picus, F. J. McClung, “Saturation of a resonant optical double-quantum transition,” Phys. Rev. Lett., vol. 15, pp. 614–618, October1965.
[CrossRef]

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

McMahon, D. H.

D. H. McMahon, A. R. Franklin, “Detection of nonlinear optical sum spectra in ADP using incoherent light,” J. Appl. Phys., vol. 36, pp. 2807–2810, September1965.
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Miller, R. C.

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillations in LiNbO3at optical frequencies,” Phys. Rev. Lett., vol. 14, pp. 973–976, June1965.
[CrossRef]

R. C. Miller, G. D. Boyd, A. Savage, “Nonlinear optical interactions in LiNbO3without double refraction,” Appl. Phys. Lett., vol. 6, pp. 77–79, February1965.
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
[CrossRef]

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett., vol. 5, pp. 17–19, July1964.
[CrossRef]

R. C. Miller, D. A. Kleinman, A. Savage, “Quantitative studies of optical harmonic generation in CdS, BaTiO3, and KH2PO4type crystals,” Phys. Rev. Lett., vol. 11, pp. 146–149, August1963.
[CrossRef]

Minck, R. W.

E. E. Hagenlocker, R. W. Minck, “Simultaneous stimulated Brillouin and Raman scattering in gases,’ IEEE J. of Quantum Electronics, vol. QE-2, p. liv, April1966.

R. W. Minck, E. E. Hagenlocker, W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett., pp. 229–231, August1966.
[CrossRef]

R. W. Minck, R. W. Terhune, W. G. Rado, “Stimulated Raman effect and resonant four photon interactions in gases,” Appl. Phys. Lett., vol. 3, pp. 181–184, November1963.
[CrossRef]

E. E. Hagenlocker, R. W. Minck, W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering,” to be published.

Morozov, V. V.

D. I. Mash, V. V. Morozov, V. S. Starunov, I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” JETP Lett., vol. 2, pp. 25–27, July1965.

Nassau, K.

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
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Ng, W. K.

E. J. Woodbury, W. K. Ng, “Ruby laser operation in the near IR,” Proc. IRE (Correspondence), vol. 50, p. 2367, November1962.

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett., vol. 8, pp. 21–22, January1962.
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Ovander, L. N.

L. N. Ovander, “Nonlinear optical effects in crystals,” Soviet Phys. Uspekhi, vol. 8, pp. 337–359, November-December 1965.
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Park, K.

J. J. Hopfield, J. M. Worlock, K. Park, “Two quantum absorption spectrum of KI,” Phys. Rev. Lett., vol. 11, pp. 414–417, November1963.
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Parks, R. E.

F. Brown, R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett., vol. 16, pp. 507–509, March1966.
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Patel, C. K. N.

C. K. N. Patel, “Optical harmonic generation in the infrared using a CO2laser,” Phys. Rev. Lett., vol. 16, pp. 613–616, April1966.
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Pershan, P. S.

P. S. Pershan, “Nonlinear optical properties of solids: Energy considerations,” Phys. Rev., vol. 130, pp. 919–928, May1963.
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J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev., vol. 127, pp. 1918–1939, September1962.
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N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev., vol. 128, pp. 606–622, October1962.
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P. S. Pershan, “Nonlinear Optics,” in Progress in Optics, vol. 5. New York: Interscience, Amsterdam: North-Holland, 1966, in progress.

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118–119, August1961.
[CrossRef]

Picus, G. S.

S. Yatsiv, W. G. Wagner, G. S. Picus, F. J. McClung, “Saturation of a resonant optical double-quantum transition,” Phys. Rev. Lett., vol. 15, pp. 614–618, October1965.
[CrossRef]

Piskarskas, A. S.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, R. V. Khokhlov, “Generation of uv radiation by using cascade frequency conversion,” JETP Lett., vol. 2, pp. 141–143, September1965.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

Platzman, P. M.

P. M. Platzman, N. Tzoar, “Nonlinear Interaction of light in a plasma,” Phys. Rev., vol. 136, pp. A11–A16, October1964.
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Porto, S. P. S.

T. C. Damen, R. C. C. Leite, S. P. S. Porto, “Angular depednence of the Raman scattering from benzene excited by the He-Ne CW laser,” Phys. Rev. Lett., vol. 14, pp. 9–11, January1965.
[CrossRef]

Price, P. J.

P. J. Price, “Theory of quadratic response functions,” Phys. Rev., vol. 130, pp. 1792–1797, June1963.
[CrossRef]

Racette, G. W.

C. C. Wang, G. W. Racette, “Effect of linear absorption on self-focusing of laser beam in CS2,” Appl. Phys. Lett., vol. 8, pp. 256–257, May1966.
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C. C. Wang, G. W. Racette, “Measurement of parametric gain accompanying optical difference frequency generation,” Appl. Phys. Lett., vol. 6, pp. 169–171, April1965.
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C. C. Wang, G. W. Racette, “Saturation effects in second harmonic generation of light using unfocused laser beams,” J. Appl. Phys., vol. 36, pp. 3281–3284, October1965.
[CrossRef]

Rado, W. G.

R. W. Minck, E. E. Hagenlocker, W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett., pp. 229–231, August1966.
[CrossRef]

E. E. Hagenlocker, W. G. Rado, “Stimulated Brillouin and Raman scattering in gases,” Appl. Phys. Lett., vol. 7, pp. 236–238, November1965.
[CrossRef]

R. W. Minck, R. W. Terhune, W. G. Rado, “Stimulated Raman effect and resonant four photon interactions in gases,” Appl. Phys. Lett., vol. 3, pp. 181–184, November1963.
[CrossRef]

E. E. Hagenlocker, R. W. Minck, W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering,” to be published.

Rentzepis, P. M.

P. M. Rentzepis, J. A. Giordmaine, K. W. Wecht, “Coherent optical mixing in optically active liquids,” Phys. Rev. Lett., vol. 16, pp. 792–794, May1966.
[CrossRef]

Rimai, L.

A. L. Cederquist, T. Kushida, L. Rimai, “High resolution Brillouin and Rayleigh spectra with single mode He-Ne laser and detection by photon counting,” Phys. Lett., to be published.

Robinson, E. J.

J. L. Hall, E. J. Robinson, L. M. Branscomb, “Laser double-quantum photodetachment of I−,” Phys Rev. Lett., vol. 14, pp. 1013–1016, June1965.
[CrossRef]

Savage, A.

R. C. Miller, G. D. Boyd, A. Savage, “Nonlinear optical interactions in LiNbO3without double refraction,” Appl. Phys. Lett., vol. 6, pp. 77–79, February1965.
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
[CrossRef]

R. C. Miller, D. A. Kleinman, A. Savage, “Quantitative studies of optical harmonic generation in CdS, BaTiO3, and KH2PO4type crystals,” Phys. Rev. Lett., vol. 11, pp. 146–149, August1963.
[CrossRef]

Savage, C. M.

R. W. Terhune, P. D. Maker, C. M. Savage, “Measurement of nonlinear light scattering,” Phys. Rev. Lett., vol. 14, pp. 681–684, April1965.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett., vol. 12, pp. 507–509, May1964.
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett., vol. 8, pp. 21–22, January1962.
[CrossRef]

R. W. Terhune, P. D. Maker, C. M. Savage, “Optical harmonic generation in Calcite,” Phys. Rev. Lett., vol. 8, pp. 404–406, May1962.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Quantum Electronics III. New York: Columbia University Press, 1964, p. 1559.

Schwarz, S. E.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

Shaham, Y. J.

Y. R. Shen, Y. J. Shaham, “Beam deterioration and stimulated Raman effect,” Phys. Rev. Lett., vol. 15, pp. 1008–1010, December1965.
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Shen, Y. R.

Y. R. Shen, Y. J. Shaham, “Beam deterioration and stimulated Raman effect,” Phys. Rev. Lett., vol. 15, pp. 1008–1010, December1965.
[CrossRef]

Y. R. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev., vol. 137, pp. A1787–A1805, March1965.
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Shimoda, K.

K. Shimoda, “Angular distribution of stimulated Raman radiation,” J. Appl. Phys. (Japan), vol. 5, pp. 86–92, January1966.
[CrossRef]

Singh, S.

S. Singh, L. T. Bradley, “Three photon absorption in naphthalene crystals by laser excitation,” Phys. Rev. Lett., vol. 12, pp. 612–614, June1964.
[CrossRef]

J. T. Hougen, S. Singh, “Electronic Raman effect in Pr3+ions in single crystals of PrCl3,” Phys. Rev. Lett., vol. 10, pp. 406–407, May1963
[CrossRef]

Sooy, W. R.

D. P. Bortfeld, W. R. Sooy, “Gain in a diffusely pumped Raman amplifier,” Appl. Phys. Lett., vol. 7, pp. 283–285, November1965.
[CrossRef]

Starunov, V. S.

D. I. Mash, V. V. Morozov, V. S. Starunov, I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” JETP Lett., vol. 2, pp. 25–27, July1965.

Stoicheff, B. P.

W. J. Jones, B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett., vol. 13 pp. 657–659, November1964.
[CrossRef]

R. Y. Chiao, B. P. Stoicheff, “Brillouin scattering in liquids excited by the He-Ne laser,” J. Opt. Soc. Am., vol. 54, pp. 1286–1287, October1964.
[CrossRef]

R. Y. Chiao, C. H. Townes, B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett., vol. 12, pp. 592–595, May1964.
[CrossRef]

Takuma, H.

H. Takuma, D. A. Jennings, “Coherent Raman effect in the off-axis Raman laser resonator,” Appl. Phys. Lett., vol. 4, pp. 185–186, June1964.
[CrossRef]

Terhune, R. W.

R. W. Terhune, P. D. Maker, C. M. Savage, “Measurement of nonlinear light scattering,” Phys. Rev. Lett., vol. 14, pp. 681–684, April1965.
[CrossRef]

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev., vol. 137, pp. A801–A818, February1965.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett., vol. 12, pp. 507–509, May1964.
[CrossRef]

R. W. Minck, R. W. Terhune, W. G. Rado, “Stimulated Raman effect and resonant four photon interactions in gases,” Appl. Phys. Lett., vol. 3, pp. 181–184, November1963.
[CrossRef]

R. W. Terhune, P. D. Maker, C. M. Savage, “Optical harmonic generation in Calcite,” Phys. Rev. Lett., vol. 8, pp. 404–406, May1962.
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett., vol. 8, pp. 21–22, January1962.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Quantum Electronics III. New York: Columbia University Press, 1964, p. 1559.

R. W. Terhune, P. D. Maker, Advances in Lasers, II, A. K. Levine, Ed. New York: Marcel Dekker, to be published.

Thomas, E. L.

M. D. Martin, E. L. Thomas, “The generation of molecular vibrational frequencies by optical mixing,” Phys. Lett., vol. 19, pp. 651–652, January1966.
[CrossRef]

Townes, C. H.

E. Garmire, R. Y. Chiao, C. H. Townes, “Dynamics and characteristics of the self-trapping of intense light beams,” Phys. Rev. Lett., vol. 16, pp. 347–349, February1966.
[CrossRef]

R. Y. Chiao, E. Garmire, C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, pp. 479–482, October1964.
[CrossRef]

R. Y. Chiao, C. H. Townes, B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett., vol. 12, pp. 592–595, May1964.
[CrossRef]

E. Garmire, C. H. Townes, “Stimulated Brillouin scattering in liquids,” Appl. Phys. Lett., vol. 5, pp. 84–86, August1964.
[CrossRef]

Tzoar, N.

P. M. Platzman, N. Tzoar, “Nonlinear Interaction of light in a plasma,” Phys. Rev., vol. 136, pp. A11–A16, October1964.
[CrossRef]

Wagner, W. G.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

S. Yatsiv, W. G. Wagner, G. S. Picus, F. J. McClung, “Saturation of a resonant optical double-quantum transition,” Phys. Rev. Lett., vol. 15, pp. 614–618, October1965.
[CrossRef]

Wang, C. C.

C. C. Wang, G. W. Racette, “Effect of linear absorption on self-focusing of laser beam in CS2,” Appl. Phys. Lett., vol. 8, pp. 256–257, May1966.
[CrossRef]

C. C. Wang, “Length-dependent threshold for stimulated Raman effect and self-focusing of laser beams in liquids,” Phys. Rev. Lett., vol. 16, pp. 344–346, February1966.
[CrossRef]

C. C. Wang, G. W. Racette, “Measurement of parametric gain accompanying optical difference frequency generation,” Appl. Phys. Lett., vol. 6, pp. 169–171, April1965.
[CrossRef]

C. C. Wang, G. W. Racette, “Saturation effects in second harmonic generation of light using unfocused laser beams,” J. Appl. Phys., vol. 36, pp. 3281–3284, October1965.
[CrossRef]

C. C. Wang, “Nonlinear susceptibility constants and self-focusing of optical beams in liquids,” Phys. Rev., to be published.

Ward, J. F.

J. F. Ward, “Absolute measurement of an optical rectification coefficient in ADP,” Phys. Rev., vol. 143, pp. 569–574, March1966.
[CrossRef]

P. A. Franken, J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys., vol. 35, pp. 23–29, January1963.
[CrossRef]

M. Bass, P. A. Franken, J. F. Ward, G. Weinreich, “Optical rectification,” Phys. Rev. Lett., vol. 9, pp. 446–448, December1962.
[CrossRef]

Wecht, K. W.

P. M. Rentzepis, J. A. Giordmaine, K. W. Wecht, “Coherent optical mixing in optically active liquids,” Phys. Rev. Lett., vol. 16, pp. 792–794, May1966.
[CrossRef]

Weiner, D.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

Weinreich, G.

M. Bass, P. A. Franken, J. F. Ward, G. Weinreich, “Optical rectification,” Phys. Rev. Lett., vol. 9, pp. 446–448, December1962.
[CrossRef]

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118–119, August1961.
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics. New York: Pergamon, 1959, pp. 434–448.

Woodbury, E. J.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

E. J. Woodbury, W. K. Ng, “Ruby laser operation in the near IR,” Proc. IRE (Correspondence), vol. 50, p. 2367, November1962.

Worlock, J. M.

J. J. Hopfield, J. M. Worlock, K. Park, “Two quantum absorption spectrum of KI,” Phys. Rev. Lett., vol. 11, pp. 414–417, November1963.
[CrossRef]

Yatsiv, S.

S. Yatsiv, W. G. Wagner, G. S. Picus, F. J. McClung, “Saturation of a resonant optical double-quantum transition,” Phys. Rev. Lett., vol. 15, pp. 614–618, October1965.
[CrossRef]

Zernike, F.

F. Zernike, P. R. Berman, “Generation of far-infrared as a difference frequency,” Phys. Rev. Lett., vol. 15999–1001, December1965.
[CrossRef]

Appl. Phys. Lett. (12)

R. C. Miller, G. D. Boyd, A. Savage, “Nonlinear optical interactions in LiNbO3without double refraction,” Appl. Phys. Lett., vol. 6, pp. 77–79, February1965.
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G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, A. Savage, “LiNbO3: An efficient phase matchable nonlinear optical material,” Appl. Phys. Lett., vol. 5, pp. 234–236, December1964.
[CrossRef]

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett., vol. 5, pp. 17–19, July1964.
[CrossRef]

C. C. Wang, G. W. Racette, “Measurement of parametric gain accompanying optical difference frequency generation,” Appl. Phys. Lett., vol. 6, pp. 169–171, April1965.
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G. Eckhardt, D. P. Bortfeld, M. Geller, “Stimulated emission of Stokes and anti-Stokes Raman lines from diamond, calcite and α-sulfur single crystals,” Appl. Phys. Lett., vol. 3, pp. 137–138, October1963.
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R. W. Minck, R. W. Terhune, W. G. Rado, “Stimulated Raman effect and resonant four photon interactions in gases,” Appl. Phys. Lett., vol. 3, pp. 181–184, November1963.
[CrossRef]

G. G. Bret, M. M. Denariez, “Stimulated Raman effect in acetone and acetone-carbon disulfide mixtures,” Appl. Phys. Lett., vol. 8, pp. 151–154, March1966.
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H. Takuma, D. A. Jennings, “Coherent Raman effect in the off-axis Raman laser resonator,” Appl. Phys. Lett., vol. 4, pp. 185–186, June1964.
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D. P. Bortfeld, W. R. Sooy, “Gain in a diffusely pumped Raman amplifier,” Appl. Phys. Lett., vol. 7, pp. 283–285, November1965.
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E. E. Hagenlocker, W. G. Rado, “Stimulated Brillouin and Raman scattering in gases,” Appl. Phys. Lett., vol. 7, pp. 236–238, November1965.
[CrossRef]

E. Garmire, C. H. Townes, “Stimulated Brillouin scattering in liquids,” Appl. Phys. Lett., vol. 5, pp. 84–86, August1964.
[CrossRef]

C. C. Wang, G. W. Racette, “Effect of linear absorption on self-focusing of laser beam in CS2,” Appl. Phys. Lett., vol. 8, pp. 256–257, May1966.
[CrossRef]

Comptes Rendus (2)

G. Hauchecorne, G. Mayer, “Effects de l’anisotropie moéculaire sur la propagation d’une lumiere intense,” Comptes Rendus, vol. 261, pp. 4014–4017, November1965.

G. Mayer, F. Gires, “Action of an intense light beam on the refractive index of liquids,” Comptes Rendus, vol. 258, pp. 2039–2042, February1964.

IEEE J. of Quantum Electronics (4)

N. I. Adams, J. J. Barrett, “Electric field control of 90° phase matching in KDP,” IEEE J. of Quantum Electronics, vol. QE-2, p. xxxi, April1966.

R. Y. Chiao, E. Garmire, “Self-trapping of optical beams,” IEEE J. of Quantum Electronics, vol. QE-2, pp. xxxviii–xxxix, April1966.

D. L. Close, C. R. Giuliano, R. W. Hellwarth, F. J. McClung, W. G. Wagner, “Light trapping and anomalous stimulated Raman scattering,” IEEE J. of Quantum Electronics, vol. QE-2, p. liii, April1966.

E. E. Hagenlocker, R. W. Minck, “Simultaneous stimulated Brillouin and Raman scattering in gases,’ IEEE J. of Quantum Electronics, vol. QE-2, p. liv, April1966.

J. Appl. Phys. (3)

N. M. Kroll, “Excitation of hypersonic vibrations by means of photo-elastic coupling of high intensity light waves to elastic waves,” J. Appl. Phys., vol. 36, pp. 34–43, January1965.
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D. H. McMahon, A. R. Franklin, “Detection of nonlinear optical sum spectra in ADP using incoherent light,” J. Appl. Phys., vol. 36, pp. 2807–2810, September1965.
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C. C. Wang, G. W. Racette, “Saturation effects in second harmonic generation of light using unfocused laser beams,” J. Appl. Phys., vol. 36, pp. 3281–3284, October1965.
[CrossRef]

J. Appl. Phys. (Japan) (1)

K. Shimoda, “Angular distribution of stimulated Raman radiation,” J. Appl. Phys. (Japan), vol. 5, pp. 86–92, January1966.
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J. Opt. Soc. Am. (3)

JETP Lett. (4)

D. I. Mash, V. V. Morozov, V. S. Starunov, I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” JETP Lett., vol. 2, pp. 25–27, July1965.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, R. V. Khokhlov, “Generation of uv radiation by using cascade frequency conversion,” JETP Lett., vol. 2, pp. 141–143, September1965.

S. A. Akhmanov, A. I. Kovrigin, V. A. Kolosov, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Tunable parametric light generator with KDP crystal,” JETP Lett., vol. 3, pp. 241–245, May1966.

S. A. Akhmanov, A. I. Kovrigin, A. S. Piskarskas, V. V. Fadeev, R. V. Khokhlov, “Observation of parametric amplification in the optical range,” JETP Lett., vol. 2, pp. 191–193, October1965.

Phvs. Rev. (2)

D. A. Kleinman, A. Ashkin, G. D. Boyd, “Second harmonic generation of light by focused laser beams,” Phvs. Rev., vol. 145, pp. 338–379, May1966.
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G. D. Boyd, A. Ashkin, J. M. Dziedzic, D. A. Kleinman, “SHG of light with double refraction,” Phvs. Rev., vol. 137, pp. A1305–A1320, February1965.
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Phys Rev. Lett. (1)

J. L. Hall, E. J. Robinson, L. M. Branscomb, “Laser double-quantum photodetachment of I−,” Phys Rev. Lett., vol. 14, pp. 1013–1016, June1965.
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Phys. Lett. (2)

R. J. Elliott, R. Loudon, “The possible observation of electronic Raman transitions in crystals,” Phys. Lett., vol. 3, pp. 189–191, January1963.
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M. D. Martin, E. L. Thomas, “The generation of molecular vibrational frequencies by optical mixing,” Phys. Lett., vol. 19, pp. 651–652, January1966.
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Phys. Letters (1)

H. Hsu, W. Kavage, “Stimulated Brillouin scatterings in anisotropic media and observation of phonons,” Phys. Letters, vol. 15, pp. 207–209, April1965.
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Phys. Rev Lett. (1)

J. A. Giordmaine, J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev Lett., vol. 11, pp. 207–209, September1963.
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Phys. Rev. (19)

Y. R. Shen, N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev., vol. 137, pp. A1787–A1805, March1965.
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R. G. Brewer, “Growth of optical plane waves in stimulated Brillouin scattering,” Phys. Rev., vol. 140, pp. A800–A805, November1965.
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W. E. Lambe, “Theory of an optical maser,” Phys. Rev., vol. 134, pp. A1429–A1450, June1964.
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G. E. Francois, “CW Measurement of the optical nonlinearity of ADP,” Phys. Rev., vol. 143, pp. 597–600, March1966.
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J. F. Ward, “Absolute measurement of an optical rectification coefficient in ADP,” Phys. Rev., vol. 143, pp. 569–574, March1966.
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J. E. Bjorkholm, “Optical SHG using a focused laser beam,” Phys. Rev., vol. 142, pp. 126–136, February1966.
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D. A. Kleinman, “Theory of second harmonic generation of light,” Phys. Rev., vol. 128, pp. 1761–1775, November1962.
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P. J. Price, “Theory of quadratic response functions,” Phys. Rev., vol. 130, pp. 1792–1797, June1963.
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W. J. Caspers, “Dispersion relations for nonlinear response,” Phys. Rev., vol. 133, pp. A1249–A1251, March1964.
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D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol. 126, pp. 1977–1979, June1962.
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P. S. Pershan, “Nonlinear optical properties of solids: Energy considerations,” Phys. Rev., vol. 130, pp. 919–928, May1963.
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J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev., vol. 127, pp. 1918–1939, September1962.
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P. M. Platzman, N. Tzoar, “Nonlinear Interaction of light in a plasma,” Phys. Rev., vol. 136, pp. A11–A16, October1964.
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P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev., vol. 137, pp. A801–A818, February1965.
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N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev., vol. 128, pp. 606–622, October1962.
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R. K. Chang, N. Bloembergen, “Experimental verification of the laws for the reflected intensity of second harmonic light,” Phys. Rev., vol. 144, pp. 775–780, April1966.
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S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev., vol. 140, pp. A2020–A2030, December1965.
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G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev., vol. 146, pp. 187–198, June1966.
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J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev., vol. 138A, pp. A1599–A1606, June1965.
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Phys. Rev. Lett. (34)

P. M. Rentzepis, J. A. Giordmaine, K. W. Wecht, “Coherent optical mixing in optically active liquids,” Phys. Rev. Lett., vol. 16, pp. 792–794, May1966.
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F. Brown, R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett., vol. 16, pp. 507–509, March1966.
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N. Bloembergen, R. K. Chang, C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett., vol. 16, pp. 986–989, May1966.
[CrossRef]

R. W. Terhune, P. D. Maker, C. M. Savage, “Optical harmonic generation in Calcite,” Phys. Rev. Lett., vol. 8, pp. 404–406, May1962.
[CrossRef]

J. Ducuing, N. Bloembergen, “Observation of reflected light harmonics at the boundary of piezoelectric crystals,” Phys. Rev. Lett., vol. 10, pp. 474–476, June1963.
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J. T. Hougen, S. Singh, “Electronic Raman effect in Pr3+ions in single crystals of PrCl3,” Phys. Rev. Lett., vol. 10, pp. 406–407, May1963
[CrossRef]

R. Y. Chiao, E. Garmire, C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, pp. 479–482, October1964.
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett., vol. 12, pp. 507–509, May1964.
[CrossRef]

T. C. Damen, R. C. C. Leite, S. P. S. Porto, “Angular depednence of the Raman scattering from benzene excited by the He-Ne CW laser,” Phys. Rev. Lett., vol. 14, pp. 9–11, January1965.
[CrossRef]

S. Yatsiv, W. G. Wagner, G. S. Picus, F. J. McClung, “Saturation of a resonant optical double-quantum transition,” Phys. Rev. Lett., vol. 15, pp. 614–618, October1965.
[CrossRef]

W. J. Jones, B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett., vol. 13 pp. 657–659, November1964.
[CrossRef]

J. J. Hopfield, J. M. Worlock, K. Park, “Two quantum absorption spectrum of KI,” Phys. Rev. Lett., vol. 11, pp. 414–417, November1963.
[CrossRef]

D. Fröhlich, H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett., vol. 16, pp. 895–897, May1966.
[CrossRef]

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118–119, August1961.
[CrossRef]

W. Kaiser, C. G. B. Garrett, “Two-photon excitation in CaF2:Eu2+.” Phys. Rev. Lett., vol. 7, pp. 229–231, September1961.
[CrossRef]

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillations in LiNbO3at optical frequencies,” Phys. Rev. Lett., vol. 14, pp. 973–976, June1965.
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett., vol. 8, pp. 21–22, January1962.
[CrossRef]

J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett., vol. 8, pp. 19–20, January1962.
[CrossRef]

C. K. N. Patel, “Optical harmonic generation in the infrared using a CO2laser,” Phys. Rev. Lett., vol. 16, pp. 613–616, April1966.
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A. Ashkin, G. D. Boyd, J. M. Dziedzic, “Observation of continuous optical harmonic generation with gas masers,” Phys. Rev. Lett., vol. 11, pp. 14–17, July1963.
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R. C. Miller, D. A. Kleinman, A. Savage, “Quantitative studies of optical harmonic generation in CdS, BaTiO3, and KH2PO4type crystals,” Phys. Rev. Lett., vol. 11, pp. 146–149, August1963.
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R. K. Chang, J. Ducuing, N. Bloembergen, “Relative phase measurement between fundamental and second-harmonic light,” Phys. Rev. Lett., vol. 15, pp. 6–8, July1965.
[CrossRef]

M. Bass, P. A. Franken, J. F. Ward, G. Weinreich, “Optical rectification,” Phys. Rev. Lett., vol. 9, pp. 446–448, December1962.
[CrossRef]

F. Zernike, P. R. Berman, “Generation of far-infrared as a difference frequency,” Phys. Rev. Lett., vol. 15999–1001, December1965.
[CrossRef]

S. Singh, L. T. Bradley, “Three photon absorption in naphthalene crystals by laser excitation,” Phys. Rev. Lett., vol. 12, pp. 612–614, June1964.
[CrossRef]

R. W. Terhune, P. D. Maker, C. M. Savage, “Measurement of nonlinear light scattering,” Phys. Rev. Lett., vol. 14, pp. 681–684, April1965.
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Y. R. Shen, Y. J. Shaham, “Beam deterioration and stimulated Raman effect,” Phys. Rev. Lett., vol. 15, pp. 1008–1010, December1965.
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P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett., vol. 15, pp. 1005–1008, December1965.
[CrossRef]

C. C. Wang, “Length-dependent threshold for stimulated Raman effect and self-focusing of laser beams in liquids,” Phys. Rev. Lett., vol. 16, pp. 344–346, February1966.
[CrossRef]

E. Garmire, R. Y. Chiao, C. H. Townes, “Dynamics and characteristics of the self-trapping of intense light beams,” Phys. Rev. Lett., vol. 16, pp. 347–349, February1966.
[CrossRef]

R. Y. Chiao, C. H. Townes, B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett., vol. 12, pp. 592–595, May1964.
[CrossRef]

N. Bloembergen, P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett., vol. 16, pp. 81–84, January1966.
[CrossRef]

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, “Stimulated Raman scattering from organic liquids,” Phys. Rev. Lett., vol. 9, pp. 455–457, December1962.
[CrossRef]

R. W. Minck, E. E. Hagenlocker, W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett., pp. 229–231, August1966.
[CrossRef]

Phys. Rev. Letters (1)

A. Gold, H. B. Bebb, “Theory of multiphoton ionization,” Phys. Rev. Letters, vol. 14, pp. 60–63, January1965.
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Proc. IRE (Correspondence) (1)

E. J. Woodbury, W. K. Ng, “Ruby laser operation in the near IR,” Proc. IRE (Correspondence), vol. 50, p. 2367, November1962.

Proc. Phys. Soc. (London) (2)

R. R. Briss, “Property tensors in magnetic crystal classes,” Proc. Phys. Soc. (London), vol. 79, pp. 946–953, May1962.
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R. Loudon, “Theory of stimulated Raman scattering from lattice vibrations,” Proc. Phys. Soc. (London), vol. 82, pp. 393–400, September1963.
[CrossRef]

Rev. Mod. Phys. (1)

P. A. Franken, J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys., vol. 35, pp. 23–29, January1963.
[CrossRef]

Soviet Phys. Uspekhi (1)

L. N. Ovander, “Nonlinear optical effects in crystals,” Soviet Phys. Uspekhi, vol. 8, pp. 337–359, November-December 1965.
[CrossRef]

Other (11)

P. S. Pershan, “Nonlinear Optics,” in Progress in Optics, vol. 5. New York: Interscience, Amsterdam: North-Holland, 1966, in progress.

R. W. Terhune, P. D. Maker, Advances in Lasers, II, A. K. Levine, Ed. New York: Marcel Dekker, to be published.

W. G. Cady, Piezoelectricity. New York: McGraw-Hill, 1946, pp. 177–199.

N. Bloembergen, Nonlinear Optics. New York: Benjamin, 1965.

W. H. Louisell, Coupled-Mode and Parametric Electronics. New York: Wiley, 1960.

P. D. Maker, R. W. Terhune, C. M. Savage, Quantum Electronics III. New York: Columbia University Press, 1964, p. 1559.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media. New York: Pergamon, 1960, pp. 377–397.

M. Born, E. Wolf, Principles of Optics. New York: Pergamon, 1959, pp. 434–448.

A. L. Cederquist, T. Kushida, L. Rimai, “High resolution Brillouin and Rayleigh spectra with single mode He-Ne laser and detection by photon counting,” Phys. Lett., to be published.

E. E. Hagenlocker, R. W. Minck, W. G. Rado, “Effects of phonon lifetime on stimulated optical scattering,” to be published.

C. C. Wang, “Nonlinear susceptibility constants and self-focusing of optical beams in liquids,” Phys. Rev., to be published.

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Figures (20)

Fig. 1
Fig. 1

Observed dependence of second harmonic generation in a quartz platelet as a function of angle between the surface normal of the platelet and the direction of the laser beam. The effective thickness of the crystal changes with rotation. The data demonstrate the oscillatory behavior of harmonic generation due to an index mismatch such as described in (18) (from Maker, Terhune, Nisenoff, and Savage [14].)

Fig. 2
Fig. 2

The growth of the normalized second harmonic amplitude and decrease of the normalized fundamental amplitude for perfect phase matching, the second harmonic being initially zero. The interaction length l/lSHG = (k2/2k2)χ2|E(ω, 0)| is a measure of the length necessary for appreciable second harmonic generation (from Armstrong et.al [8]).

Fig. 3
Fig. 3

Variation of second harmonic power with σ, the angle between the fundamental beam in the lowest order mode and the phase matching direction as observed by Ashkin, Boyd, and Dziedzic [25] using a gas laser. The observed results in ADP agree well with the predicted dependence of (sin2ψ/ψ2), where ψ = β/σ with β proportional to the double refraction angle.

Fig. 4
Fig. 4

Experimental data showing the wavelengths at which parametric oscillations were observed as a function of crystal temperature in LiNbO3. The wavelengths at a given temperature are those for which Δk = 0 in a direction making an angle of 90° with the optic axis of the crystal; by scanning the crystal temperature, oscillation was scanned over the wavelength range indicated above. This parametric oscillator was pumped with the coherent radiation at 0.529 μ obtained by doubling the radiation from a Nd-doped CaWO4 laser. The solid curve is a theoretical fit using the known temperature-dependence of birefringence (from Giordmaine and Miller [3]).

Fig. 5
Fig. 5

Schematic of the experimental arrangement used to measure the phase difference between X 2 in GaAs and KDP. Data show the observed interference effect between the second harmonic beams produced in the KDP platelet and from the boundary of a GaAs mirror as a function of the air pressure in the space between them. The phases of the second harmonic beams generated in both the KDP and GaAs bear a fixed relationship to the phase of the laser beam where the second harmonic is generated. Since the index mismatch in air between the laser frequency and its second harmonic varies linearly with the air pressure, the relative phases of the two second harmonic beams is scanned by varying the air pressure (from Chang, Ducuing, and Bloem-bergen [22]).

Fig. 6
Fig. 6

Schematic illustrating (a) the optical Kerr effect and (b) the intensity-induced rotation of the vibrational ellipse. Both of these effects are due to the intensity-dependent changes in the refractive index. In (a), the light beam at ω2 induces birefringence at ω1 so that E(ω1) is changed from linear polarization to elliptical polarization. In (b), the self-induced index change with an elliptically polarized beam leads to rotation of its own vibrational ellipse; the amount of rotation is proportional to χ31221 (−ω, ω, ω, −ω), and to the distance propagated.

Fig. 7
Fig. 7

Schematic to indicate the additional two photon processes which one would observe in absorption spectra due to the presence of an intense laser beam at frequency ωL. The dashed lines indicate the additional features that one might observe: simultaneous absorption at ω1 and ωL; absorption at ω2 with simultaneous emission at ωL; and the inverse, absorption at ωL with emission at ω3. The latter process is referred to as Raman laser action.

Fig. 8
Fig. 8

Schematic to indicate the frequency dependence of δ X 1 (−ω, ω) due to the presence of the laser beam at ωL. X 1 (−ω, ω) is also shown.

Fig. 9
Fig. 9

High resolution spectrum of CS2 showing the Rayleigh line and the resolved Brillouin components. The scattering was observed at 90° to the direction, of the beam from a frequency-stabilized single mode He-Ne laser. The lower trace is a measurement of the scattering from large suspended particles and represents the resolution limit of the pressure scanning Fabry-Perot interferometer (from Cederquist et al. [61]).

Fig. 10
Fig. 10

Two-photon spectrum of anthracene single crystals. The relative change in transmission ΔI/I of light from a source of variable photon energy is plotted vs. the combined photon energy of both sources. For type-I spectrum, the Nd laser light and the light from the variable source were both polarized along the crystal b axis. For the type-II spectrum, the laser light was polarized along the crystal a axis and the light from the variable source was unpolarized in a plane perpendicular to the crystal b axis (from Frödhlich et.al [67]).

Fig. 11
Fig. 11

Schematic of the experimental arrangement employed by Woodbury et al. [68] in the first observations of stimulated Raman effect. The mirrors are reflecting for both the laser and Stokes frequencies. The onset of Raman laser action exhibited a sharp threshold dependence on laser intensity and resulted in a large fractional conversion of energy into the Stokes lines.

Fig. 12
Fig. 12

Observed Stokes intensity as a function of incident laser power in several different materials. One class of materials gives qualitative agreement with the anticipated variation Is ~ exp (gILl) while the other exhibits an abrupt increase in Stokes energy at low laser power (from Bret et.al [72]).

Fig. 13
Fig. 13

Results of focusing a pulsed laser beam into benzene. The ring pattern shown was produced by placing film behind the sample at right angles to the optical axis. Each of the visible lines are separated by 992 cm−1, the frequency of the strongest Raman line in benzene. The relative strengths of the lines are indicated.

Fig. 14
Fig. 14

Examples of transient phenomena associated with stimulated Raman scattering in hydrogen gas. The Stokes energy is observed both in the direction of the laser beam and in the reverse direction. When stimulated by a modulated laser beam, the reverse Stokes exhibits highly transient behavior, its width being instrument limited.

Fig. 15
Fig. 15

Schematic of the experimental arrangement used by Chiao et al. [85] to study stimulated Brillouin scattering. The Stokes energy is radiated in the backward direction allowing it to reenter the laser cavity, be amplified, and returned to the material where it can then cause repeated Stokes lines.

Fig. 16
Fig. 16

Damage characteristics observed in BK-7 glass at the focus of a 46 cm lens. The ruby laser pulse used was 60 mJ in energy and 50 ns in width. The damage appears as a combination of a gross fracture and a long filament made up of very small bubbles and extending along the lens axis. In general these filaments may be has long as several centimeters and at the same time have a diameter of only a few wavelengths. In the absence of the self-focusing action of the laser beam, it would be difficult to explain the preservation of such long thin filaments over a distance longer than the order of wavelengths. (Courtesy of J. G. Atwood, Perkin-Elmer Corp.).

Fig. 17
Fig. 17

Schematic illustrating the self-focusing effect and its equivalent convergent lens. The self-focusing action may be likened to a convergent lens, for which the difference in optical path length between the marginal and axial rays is compensated by the presence of lens material located on the lens axis so that both rays arrive at the focus in phase. The equivalent focal length is thus by analogy determined by the relation Δnl = n0{l[1 + (a/l)2]1/2l}, where a is the beam radius at half-intensity points. Equation (48) follows after a few manipulations.

Fig. 18
Fig. 18

Plot of the square root of the threshold laser power as a function of the inverse of the cell length for benzene, toluene, and nitrobenzene. The threshold for stimulated Raman emission was taken as the threshold for self-focusing. These plots show that the predicted dependence in (48) is well satisfied for self-focusing; the vertical intercepts of these straight lines give the values of critical power for self-trapping.

Fig. 19
Fig. 19

Random polarization of Stokes energy in the filaments resulting from Raman laser action and self-focusing in nitrobenzene when stimulated by a circularly polarized laser beam. The radiation was analyzed for orthogonal components of linear polarization (top and bottom) and dispersed by a grating to separate the laser (left) and Stokes (right) beams for the photograph. The circularly polarized laser beam produces an identical spatial pattern having (nearly) equal intensity for the two plane components. In contrast, the ratios of intensities in the two polarizations for each small Stokes filament are uncorrelated, indicating that each filament is plane polarized in an arbitrary direction (from McClung et.al [98]).

Fig. 20
Fig. 20

Observed unpolarized nonlinear scattering spectra and infrared absorption spectra for water. The scattering intensity is given in photoelectrons per laser pulse ( 1 2MW peak power) averaged over approximately 25 pulses. Standard errors are indicated. When no signal was observed, the 70 percent probability limits using Poisson statistics are shown. The spectrometer band pass was 80 cm−1 (from Terhune et al. [99]).

Tables (2)

Tables Icon

TABLE I Summary of Second Harmonic Generation Experiments*

Tables Icon

TABLE II Values of the Nonlinear Susceptibility Constants and the Critical Power for Self-Trapping in Several Liquids

Equations (51)

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× H ¯ = t ( ɛ ¯ ) + P ¯ N L t .
ɛ i ( r , t ) = E i ( 0 , r ) + 1 2 l = - N N E i ( w l , r ) · exp [ i ( k l r - ω l t ) ]
P i N L ( r , t ) = P i N L ( 0 , r ) + 1 2 l = - M M P i N L ( w l , r ) · exp ( - i ω l t )
d d r E i ( ω l , r ) = i k l 2 l P i N L ( ω l , r ) exp ( - i k l r ) .
E ( ω l , r ) = E ( ω l , 0 ) exp [ i ( k l / 2 k l ) δ χ 1 r ] .
P ¯ N L ( r , t ) = 2 0 X 2 : ɛ ¯ ( r , t ) ɛ ¯ ( r , t ) + ( similar terms involving time derivative operators ) ,
P i N L ( 2 ω l , r ) = 0 χ 2 i j k E j ( ω l , r ) E k ( ω l , r ) exp ( i 2 k l r )
P i N L ( 0 , r ) = 1 2 0 l = - N N χ 2 i j k E j ( ω l , r ) E k * ( ω l , r )
P i N L ( ω l , r ) = 2 0 χ 2 i j k E j ( ω m , r ) E k ( ω n , r ) · exp [ i ( k m + k m ) r ]
P i N L ( ω l , r ) = 2 ɛ 0 χ 2 i j k E j ( ω m , r ) E k * ( ω n , r ) · exp [ i ( k m - k n ) r [
P i N L ( ω l , r ) = [ 4 0 χ 2 i j k E j ( 0 , r ) ] E k ( ω l , r ) exp ( i k l r ) .
P x N L = 2 0 d 14 E y E z P y N L = 2 0 d 14 E z E x P z N L = 2 0 d 36 E x E y
χ 2 i j k ( - ω 1 , ω 2 , ω 3 ) = χ 2 i k j ( - ω 1 , ω 3 , ω 2 ) ,
χ 2 i j k ( - ω 1 , ω 2 , ω 3 ) = χ 2 * i j k ( ω 1 , - ω 2 , - ω 3 ) .
χ 2 i j k ( - ω 1 , ω 2 , ω 3 ) = χ 2 i j k ( ω 2 , - ω 1 , ω 3 ) .
d d r E i ( ω , r ) = i ( k 1 2 κ 1 ) 2 χ 2 i j k ( - ω , 2 ω , - ω ) E j ( 2 ω , r ) E k * ( ω , r ) · exp ( i Δ k r )
d d r E j ( 2 ω , r ) = i ( k 2 2 κ 2 ) χ 2 j i k ( - 2 ω , ω , ω ) E i ( ω , r ) E k ( ω , r ) · exp ( - i Δ k r )
χ 2 i j k ( - ω , 2 ω , - ω ) = χ 2 j i k ( - 2 ω , ω , ω ) .
E j ( 2 ω , r ) = i ( k 2 2 κ 2 ) χ 2 j i k ( - 2 ω , ω , ω ) E i ( ω , 0 ) E k ( ω , 0 ) · [ 1 - exp ( - i Δ k r ) i Δ k ]
P i N L ( 0 , r ) = 0 χ 2 i j k ( 0 , ω , - ω ) E j ( ω l , r ) E k * ( ω l , r ) .
d d r E i ( ω 1 , r ) = i ( k 1 2 κ 1 ) 2 χ 2 i j k ( - ω 1 , ω 2 , ω 3 ) E j ( ω 2 , r ) E k ( ω 3 , r ) · exp ( - i Δ k r )
d d r E j ( ω 2 , r ) = i ( k 2 2 κ 2 ) 2 χ 2 j i k ( - ω 2 , ω 1 , - ω 3 ) E i ( ω 1 , r ) E k * ( ω 3 , r ) · exp ( i Δ k r )
d d r E k ( ω 3 , r ) = i ( k 3 2 κ 3 ) 2 χ 2 k i j ( - ω 3 , ω 1 , - ω 2 ) E i ( ω 1 , r ) E j * ( ω 2 , r ) · exp ( i Δ k r )
E i ( ω 1 , r ) = E i ( ω 1 , 0 ) + i ( k 1 2 κ 1 ) 2 χ 2 i j k ( - ω 1 , ω 2 , ω 3 ) E j ( ω 2 , 0 ) E k ( ω 3 , 0 ) · [ 1 - exp ( - i Δ k r ) i Δ k ] .
E j ( ω s , r ) = E j ( ω s , 0 ) cosh ( g r )
E k ( ω I , r ) = i ( ω I / ω s ) 1 / 2 E j ( ω s , 0 ) sinh ( g r )
g = [ k I k s κ I κ s ] 1 / 2 χ 2 i j k ( - ω I , ω p , ω s ) E i ( ω p , 0 )
E ( ω s , r ) = 1 2 E ( ω s , 0 ) e g r
E ( ω I , r ) = i 2 ( ω I , ω s ) 1 / 2 E ( ω s , 0 ) e g r .
g g [ 1 - ( Δ k / 2 g ) 2 ] 1 / 2
g > Δ k / 2.
g l = ( 1 - R )
P ¯ N L ( r , t ) = 4 0 χ 3 ɛ ¯ ( r , t ) ɛ ¯ ( r , t ) ɛ ¯ ( r , t ) + ( similar terms involving time derivative operators )
P i N L ( 3 ω , r ) = 3 ɛ 0 χ 3 1122 ( - 3 ω , ω , ω , ω ) E i ( ω , r ) E j ( ω , r ) E j ( ω , r ) · exp ( i 3 k r )
P i N L ( 2 ω , r ) = 6 0 χ 3 i j k j l ( - 2 ω , 0 , ω , ω ) E j ( 0 , r ) E k ( ω , r ) E l ( ω , r ) · exp ( i 2 k r ) .
P i N L ( ω 1 , r ) = D 0 χ 3 i j k l ( - ω 1 , ω 2 , ω 3 , ω 4 ) E j ( ω 2 , r ) E k ( ω 3 , r ) E l ( ω 4 , r ) · exp [ i ( k 2 + k 3 + k 4 ) r ]
P i N L ( ω 1 , r ) = 6 0 χ 3 1122 ( - ω 1 , ω 1 , ω 2 , - ω 2 ) E i ( ω 1 , r ) · E j ( ω 2 , r ) E j * ( ω 2 , r ) exp ( i k 1 r ) + 6 0 χ 3 1212 ( - ω 1 , ω 1 , ω 2 , - ω 2 ) E j ( ω 1 , r ) · E i ( ω 2 , r ) E j * ( ω 2 , r ) exp ( i k 1 r ) + 6 0 χ 3 1221 ( - ω 1 , ω 1 , ω 2 , - ω 2 ) E j ( ω 1 , r ) · E j ( ω 2 , r ) E i * ( ω 2 , r ) exp ( i k 1 r )
Δ n = δ n - δ n = 2 π n 1 [ 6 χ 3 1212 ( - ω 1 , ω 1 , ω 2 , - ω 2 ) + 6 χ 3 1221 ( - ω 1 , ω 1 , ω 2 , - ω 2 ) ] E i ( ω 2 , r ) E i * ( ω 2 , r )
δ n + = ( 2 π / n ) 3 { ( χ 1122 [ ω ] + χ 3 1212 [ ω ] ) E + 2 + ( χ 3 1122 [ ω ] + χ 3 1212 [ ω ] + 2 χ 3 1221 [ ω ] ) E - 2 } δ n - = ( 2 π / n ) 3 { ( χ 3 1122 [ ω ] + χ 3 1212 [ ω ] ) E - 2 + ( χ 3 1122 [ ω ] + χ 3 1212 [ ω ] + 2 χ 3 1221 [ ω ] ) E + 2 } .
δ n = ( 2 π / n ) 3 { χ 3 1122 [ ω ] + χ 3 1212 [ ω ] + χ 3 1221 [ ω ] } E 2 .
δ χ 1 i j ( - ω , ω ) = 6 χ 3 i j k l ( - ω , ω , ω L , - ω L ) E k ( ω L , r ) E l * ( ω L , r )
6 χ 3 i j k l ( - ω , ω , ω L , - ω L ) = 6 χ 3 N R i j k l ( - ω , ω , ω L , - ω L ) + χ 3 t i l j k ( - ω , - ω L , ω , ω L ) [ Γ t ω t - ( ω + ω L ) - i Γ t ] + χ 3 r i k j l ( - ω , ω L , ω , - ω L ) [ Γ r ω r - ( ω - ω L ) - i Γ r + Γ r ω r - ( ω L - ω ) + i Γ r ] .
χ 3 s i j k l ( ω 1 , ω 2 , ω 3 , ω 4 ) = 0 N L 4 Γ s g α i j ( ω 1 , ω 2 ) s g α k l ( - ω 3 , - ω 4 ) s *
6 χ 3 i j k l [ - ( ω 1 - ω r ) , ω 1 , ( ω 2 - ω r ) , - ω 2 ) ] = 6 χ 3 N R i j k l [ - ( ω 1 - ω r ) , ω 1 , ( ω 2 - ω r ) , - ω 2 ] + χ 3 r i j k l [ - ( ω 1 - ω r ) , ω 1 , ( ω 2 - ω r ) , - ω 2 ] .
g = k s 2 κ s χ 3 r 1122 ( - ω s , ω L , ω s , - ω L ) E j ( ω L , r ) E j * ( ω L , r ) .
t E s ( r , t ) - ( c / n ) r E s ( r , t ) = C 1 S * ( r , t ) t S * ( r , t ) - ( 1 / 2 τ ) S * ( r , t ) + v a r S * ( r , t ) = C 2 E s ( r , t ) ,
E s ( l , t ) E s ( 0 , t ) = exp [ ( g I L l t τ ) 1 / 2 - t 2 τ ] ; t < g I L l τ .
ω a / ω L = 2 ( n v a / c ) sin ( θ / 2 )
P 1 / 2 = P c r 1 / 2 + A l
A = n 4 ( a 2 f ) ( c n 2 ) 1 / 2
P c r = 5.763 λ 2 c 16 π 3 n 2 ,

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