Abstract

We use the separated-beams, second-harmonic method to measure the full second-order nonlinear optical tensor of KNbO3 relative to dzxy of KDP for a fundamental wavelength of 1064 nm. Assuming dzxy(KDP)= 0.39 pm/V, we find for KNbO3 that dxxx=21.9 pm/V, dxyy=8.9 pm/V, dxzz=12.4 pm/V, dyxy= 9.2 pm/V, and dzxz=13.0 pm/V with estimated uncertainties of ±2–5%.

© 2003 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics (Academic, New York, 1999).
  2. B. Zysset, I. Biaggio, and P. Gunter, “Refractive indices of orthorhombic KNbO3. I. Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992). Our x-ray diffraction measurements confirm that the z-axis lattice spacing is 0.370 nm and that the x- and y-axis lattice spacings are both approximately 0.57 nm, but our resolution was not sufficient to differentiate between the x- and y-axis lattice spacings.
    [CrossRef]
  3. I. Biaggio, P. Kerkoc, L.-S. Wu, P. Guenter, and B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phase-matching configurations for nonlinear optical interactions,” J. Opt. Soc. Am. B 9, 507–517 (1992).
    [CrossRef]
  4. J.-C. Baumert, “Nichtlineare optische Eigenschaften und Anwendungen von KNbO3 Kristallen,” Ph.D. dissertation ETH 7802 (Swiss Federal Institute of Technology, Zurich, Switzerland, 1985).
  5. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
    [CrossRef]
  6. Y. Uematsu, “Nonlinear optical properties of KNbO3 single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
    [CrossRef]
  7. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
    [CrossRef]
  8. J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
    [CrossRef]
  9. W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B 12, 416–427 (1995).
    [CrossRef]
  10. J.-C. Baumert, J. Hoffnagle, and P. Guenter, “Nonlinear optical effects in KNbO3 crystals at AlxGa1−xAs, dye, ruby, and Nd:YAG laser wavelengths,” 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger and H. A. Ferwerda, eds., Proc. SPIE 492, 374–385 (1984).
    [CrossRef]
  11. W. J. Alford and A. V. Smith, “Wavelength variation of the second-order nonlinear coefficients of KNbO3, KTiOPO4, KTiOAsO4, LiNbO3, LiIO3, β-BaB2O4, KH2PO4, and LiB3O5 crystals: a test of Miller wavelength scaling,” J. Opt. Soc. Am. B 18, 524–533 (2001).
    [CrossRef]
  12. W. R. Bosenberg and R. H. Jarman, “Type-II phase-matched KNbO3 optical-parametric oscillator,” Opt. Lett. 18, 1323–1325 (1993).
    [CrossRef]
  13. J.-P. Meyn, M. E. Klein, D. Woll, R. Wallenstein, and D. Rytz, “Periodically poled potassium niobate for second-harmonic generation at 463 nm,” Opt. Lett. 24, 1154–1156 (1999).
    [CrossRef]
  14. J. H. Kim and C. S. Yoon, “Domain switching characteristics and fabrication of periodically poled potassium niobate for second-harmonic generation,” Appl. Phys. Lett. 81, 3332–3334 (2002).
    [CrossRef]
  15. R. J. Gehr and A. V. Smith, “Separated-beam, nonphase-matched, second-harmonic method of characterizing nonlinear optical crystals,” J. Opt. Soc. Am. B 15, 2298–2307 (1998).
    [CrossRef]
  16. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [CrossRef]
  17. D. J. Armstrong, M. V. Pack, and A. V. Smith, “Instrument and method for measuring second-order nonlinear optical tensors,” Rev. Sci. Instrum. 74, 3250–3257 (2003).
    [CrossRef]
  18. G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. QE-18, 143–145 (1982).
    [CrossRef]
  19. N. Umemura, K. Yoshida, and K. Kato, “Phase-matching properties of KNbO3 in the mid-infrared,” Appl. Opt. 38, 991–994 (1999).
    [CrossRef]

2003

D. J. Armstrong, M. V. Pack, and A. V. Smith, “Instrument and method for measuring second-order nonlinear optical tensors,” Rev. Sci. Instrum. 74, 3250–3257 (2003).
[CrossRef]

2002

J. H. Kim and C. S. Yoon, “Domain switching characteristics and fabrication of periodically poled potassium niobate for second-harmonic generation,” Appl. Phys. Lett. 81, 3332–3334 (2002).
[CrossRef]

2001

1999

1998

1997

1995

1993

1992

1984

J.-C. Baumert, J. Hoffnagle, and P. Guenter, “Nonlinear optical effects in KNbO3 crystals at AlxGa1−xAs, dye, ruby, and Nd:YAG laser wavelengths,” 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger and H. A. Ferwerda, eds., Proc. SPIE 492, 374–385 (1984).
[CrossRef]

1982

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. QE-18, 143–145 (1982).
[CrossRef]

1974

Y. Uematsu, “Nonlinear optical properties of KNbO3 single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
[CrossRef]

1970

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

1962

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

Alford, W. J.

Armstrong, D. J.

D. J. Armstrong, M. V. Pack, and A. V. Smith, “Instrument and method for measuring second-order nonlinear optical tensors,” Rev. Sci. Instrum. 74, 3250–3257 (2003).
[CrossRef]

Baumert, J.-C.

J.-C. Baumert, J. Hoffnagle, and P. Guenter, “Nonlinear optical effects in KNbO3 crystals at AlxGa1−xAs, dye, ruby, and Nd:YAG laser wavelengths,” 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger and H. A. Ferwerda, eds., Proc. SPIE 492, 374–385 (1984).
[CrossRef]

Bhar, G. C.

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. QE-18, 143–145 (1982).
[CrossRef]

Biaggio, I.

Bosenberg, W. R.

Gehr, R. J.

Ghosh, G. C.

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. QE-18, 143–145 (1982).
[CrossRef]

Guenter, P.

I. Biaggio, P. Kerkoc, L.-S. Wu, P. Guenter, and B. Zysset, “Refractive indices of orthorhombic KNbO3. II. Phase-matching configurations for nonlinear optical interactions,” J. Opt. Soc. Am. B 9, 507–517 (1992).
[CrossRef]

J.-C. Baumert, J. Hoffnagle, and P. Guenter, “Nonlinear optical effects in KNbO3 crystals at AlxGa1−xAs, dye, ruby, and Nd:YAG laser wavelengths,” 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger and H. A. Ferwerda, eds., Proc. SPIE 492, 374–385 (1984).
[CrossRef]

Gunter, P.

Hayden, L. M.

Herman, W. N.

Hoffnagle, J.

J.-C. Baumert, J. Hoffnagle, and P. Guenter, “Nonlinear optical effects in KNbO3 crystals at AlxGa1−xAs, dye, ruby, and Nd:YAG laser wavelengths,” 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger and H. A. Ferwerda, eds., Proc. SPIE 492, 374–385 (1984).
[CrossRef]

Ito, R.

Jarman, R. H.

Jerphagnon, J.

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

Kato, K.

Kerkoc, P.

Kim, J. H.

J. H. Kim and C. S. Yoon, “Domain switching characteristics and fabrication of periodically poled potassium niobate for second-harmonic generation,” Appl. Phys. Lett. 81, 3332–3334 (2002).
[CrossRef]

Kitamoto, A.

Klein, M. E.

Kondo, T.

Kurtz, S. K.

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

Maker, P. D.

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

Meyn, J.-P.

Nisenoff, M.

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

Pack, M. V.

D. J. Armstrong, M. V. Pack, and A. V. Smith, “Instrument and method for measuring second-order nonlinear optical tensors,” Rev. Sci. Instrum. 74, 3250–3257 (2003).
[CrossRef]

Roberts, D. A.

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

Rytz, D.

Savage, C. M.

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

Shirane, M.

Shoji, I.

Smith, A. V.

Terhune, R. W.

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

Uematsu, Y.

Y. Uematsu, “Nonlinear optical properties of KNbO3 single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
[CrossRef]

Umemura, N.

Wallenstein, R.

Woll, D.

Wu, L.-S.

Yoon, C. S.

J. H. Kim and C. S. Yoon, “Domain switching characteristics and fabrication of periodically poled potassium niobate for second-harmonic generation,” Appl. Phys. Lett. 81, 3332–3334 (2002).
[CrossRef]

Yoshida, K.

Zysset, B.

Appl. Opt.

Appl. Phys. Lett.

J. H. Kim and C. S. Yoon, “Domain switching characteristics and fabrication of periodically poled potassium niobate for second-harmonic generation,” Appl. Phys. Lett. 81, 3332–3334 (2002).
[CrossRef]

IEEE J. Quantum Electron.

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

G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, and KD*P for nonlinear devices,” IEEE J. Quantum Electron. QE-18, 143–145 (1982).
[CrossRef]

J. Appl. Phys.

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

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

Y. Uematsu, “Nonlinear optical properties of KNbO3 single crystal in the orthorhombic phase,” Jpn. J. Appl. Phys. 13, 1362–1368 (1974).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

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

Proc. SPIE

J.-C. Baumert, J. Hoffnagle, and P. Guenter, “Nonlinear optical effects in KNbO3 crystals at AlxGa1−xAs, dye, ruby, and Nd:YAG laser wavelengths,” 1984 European Conference on Optics, Optical Systems, and Applications, B. Bolger and H. A. Ferwerda, eds., Proc. SPIE 492, 374–385 (1984).
[CrossRef]

Rev. Sci. Instrum.

D. J. Armstrong, M. V. Pack, and A. V. Smith, “Instrument and method for measuring second-order nonlinear optical tensors,” Rev. Sci. Instrum. 74, 3250–3257 (2003).
[CrossRef]

Other

R. W. Boyd, Nonlinear Optics (Academic, New York, 1999).

J.-C. Baumert, “Nichtlineare optische Eigenschaften und Anwendungen von KNbO3 Kristallen,” Ph.D. dissertation ETH 7802 (Swiss Federal Institute of Technology, Zurich, Switzerland, 1985).

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Figures (8)

Fig. 1
Fig. 1

Diagram of crystal geometry showing the fundamental wave incident normal to left-hand (input) crystal face and the five possible second-harmonic waves refracted at various angles at the right-hand or (exit) crystal face. The dashed line is normal to the output face, and α and β are the incident and refracted angles. The two eigenpolarizations are labeled a and b. The free waves Fb and Fa refract according to n sin α=sin β with refractive index n equal to nb(2ω) and na(2ω), respectively, while the driven waves Daa, Dab, and Dbb refract with refractive index n equal to na(ω), [nb(ω)+na(ω)]/2, and nb(ω), respectively. The a- and b-polarized fundamental waves refract in the same direction as Daa and Dbb, respectively.

Fig. 2
Fig. 2

Diagram of crystal geometry showing the labeling of the angles of the transmitted and reflected waves. The incident fundamental wave and the free and driven harmonic waves propagate along one of the principal axes. A p-polarized wave will reflect at angle σ, which is slightly different from the exit face angle α because of birefringence. For a p-polarized wave the reflected beam also experiences birefringent walk-off indicated by angle ρ. An s-polarized wave reflects at angle α with ρ=0. Angles β and δ are the beam exit angles measured relative to the exit face normal and relative to the original beam direction, respectively.

Fig. 3
Fig. 3

Diagram of the experimental apparatus. The fundamental pulse energy is adjusted by a half-wave retardation plate (WP1), and the fundamental polarization at the crystal is adjusted by another half-wave plate (WP3). The beam of interest is selected by setting the angle of the swivel arm that carries the 532-nm signal detector. We monitor the fundamental by measuring the 1064-nm energy and by measuring the second harmonic generated in a phase-matched KTP crystal.

Fig. 4
Fig. 4

Relative pulse energy of the z-polarized free harmonic wave from the KDP reference sample as the polarization angle of the linearly polarized fundamental wave is rotated through 180°. At 90° the fundamental is z polarized. The fitted curve has the form of Eq. (13).

Fig. 5
Fig. 5

Relative pulse energy of the x-polarized free harmonic wave from the y-cut KNbO3 sample as the polarization angle of the linearly polarized fundamental wave is rotated through 180°. At the left and right edges of the graph the fundamental is x polarized and at the center it is z polarized. The fitted curve has the form of Eq. (14).

Fig. 6
Fig. 6

Relative pulse energy of the z-polarized free harmonic wave from y-cut KNbO3 as the polarization angle of the linearly polarized fundamental wave is rotated through 90°. At the left the fundamental is x polarized, and at the right it is z polarized. The fitted curve has the form of Eq. (15).

Fig. 7
Fig. 7

Relative pulse energy of the x-polarized free harmonic wave from z-cut KNbO3 as the polarization angle of the linearly polarized fundamental wave is rotated through 180°. At the left and right edges of the graph the fundamental is x polarized, and at the center it is y polarized. The fitted curve has the form of Eq. (17).

Fig. 8
Fig. 8

Relative pulse energy of the y-polarized free harmonic wave from z-cut KNbO3 as the polarization angle of the linearly polarized fundamental wave is rotated through 90°. At the left edge of the graph the fundamental is x polarized, and at the right it is y polarized. The fitted curve has the form of Eq. (18).

Tables (5)

Tables Icon

Table 1 Comparison of Measured Values of dijk Coefficients (in pm/V) for Frequency Doubling 1064-nm Light in KNbO3

Tables Icon

Table 2 Multiplier Nijk and Factors Based on Sellmeier Refractive Indices for KDP with Exit Face Tilted by α=19.782° and the Face Normal Lying in the yx Plane

Tables Icon

Table 3 Measured Refraction Angles and Refractive Indices a for KNbO3

Tables Icon

Table 4 Multiplier Nijk and Factors, Calculated from the Measured Refractive Indices for KNbO3

Tables Icon

Table 5 Relative Free-Wave Energies and Derived Values of the d Coefficients of KNbO3 Assuming dzxy for KDP of 0.39 pm/V

Equations (18)

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χ(2)2=d=dxxxdxyydxzz00000000dyxy0000dzxz0.
Efree=2deff k0E1E1Δk(n2+n¯1)n¯1+1n2+1t1t1t2=deff E1E1N,
t1=21+n1,
t1=21+n1.
t2=2n2cos αn2cos α+cos β
t2=nrcos α cos ρ+n2cos(σ+ρ)nrcos β cos ρ+cos(σ+ρ)
n2sin α=nrsin σ,
N=N cos βcos α1/2.
Ufree=CU1U1deff2N2,
deff=deff (ref)EfreeE1E1NE1E1NEfreeref.
deff=deff (ref) NrefNFFref.
d=000dxyz000000dxyz000000dzxy.
Fz=CU12|dzxyNzxycos2 ψ|2=A2cos4(ψm+),
Fx=CU12|dxzzNxzzsin2 ψ+dxxxNxxxcos2 ψ|2=|B sin2(ψm+)+D cos2(ψm+)|2,
Fz=CU12|dzxzNzxzsin(2ψ)|2=G2sin2(2ψm+).
dxxx=drefNrefNxxxDA=0.39 (11.04)(1.597)(3.858)(0.4747)=21.9pm/V.
Fx=CU12|dxyyNxyysin2 ψ+dxxxNxxxcos2 ψ|2=|R sin2(ψm+)+S cos2(ψm+)|2.
Fy=CU12|dyxyNyxysin(2ψ)|2=T2sin2(2ψm+).

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