Abstract

A two-beam second-harmonic generation technique is developed to calibrate the magnitude of the second-order nonlinear optical susceptibility components of surface and bulk (multipolar origin) of isotropic materials. The values obtained for fused silica calibrated against χXXX of crystalline quartz are χ ‖‖⊥=7.9(4), χ ⊥‖‖+γ=3.8(4), χ ⊥⊥⊥+γ=59(4), and δ′=7.8(4) in units of 10-22 m2/V. Similar values are obtained for BK7 glass. An alternative way of calibration against χXYZ of quartz is demonstrated. The technique could also be extended to characterize the susceptibility tensor of crystals as a convenient alternative to the Maker-fringe technique.

© 2008 Optical Society of America

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References

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  1. T. F. Heinz, "Second-order nonlinear optical effects at surfaces and interfaces," in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath, and G. I. Stegeman, eds., (Elsevier, Amsterdam, 1991).
  2. G. Lupke, "Characterization of semiconductor interfaces by second-harmonic generation," Surf. Sci. Rep. 35, 77-161 (1999).
    [CrossRef]
  3. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, "General-considerations on optical 2nd-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
    [CrossRef]
  4. J. E. Sipe, V. Mizrahi, and G. I. Stegeman, "Fundamental difficulty in the use of 2nd-harmonic generation as a strictly surface probe," Phys. Rev. B 35, 9091-9094 (1987).
    [CrossRef]
  5. Y. An, R. Carriles, and M. Downer, "Absolute phase and amplitude of second-order nonlinear optical susceptibility components at Si(001) interfaces," Phys. Rev. B 75, 241307(R) (2007).
    [CrossRef]
  6. X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
    [CrossRef]
  7. F. J. Rodriguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, "Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass," Opt. Express 15, 8695-8701 (2007).
    [CrossRef] [PubMed]
  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 (1970).
    [CrossRef]
  9. W. Herman and L. Hayden, "Maker fringes revisited - 2nd-harmonic generation from birefringent or absorbing materials," J. Opt. Soc. Am. B 12, 416-427 (1995).
    [CrossRef]
  10. I. Shoji, T. Kondo, and R. Ito, "Second-order nonlinear susceptibilities of various dielectric and semiconductor materials," Opt. Quantum Electron. 34, 797-833 (2002).
    [CrossRef]
  11. R. Gehr, and A. Smith, "Separated-beam nonphase-matched second-harmonic method of characterizing nonlinear optical crystals," J. Opt. Soc. Am.Bs 15, 2298-2307 (1998).
    [CrossRef]
  12. D. Armstrong, M. Pack, and A. Smith, "Instrument and method for measuring second-order nonlinear optical tensors," Rev. Sci. Instrum. 74, 3250-3257 (2003).
    [CrossRef]
  13. S. Cattaneo, M. Siltanen, F. Wang, and M. Kauranen, "Suppression of nonlinear optical signals in finite interaction volumes of bulk materials," Opt. Express 13, 9714-9720 (2005).
    [CrossRef] [PubMed]
  14. P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical 2nd-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
    [CrossRef]
  15. P. Guyot-Sionnest and Y. R. Shen, "Bulk contribution in surface 2nd-harmonic generation," Phys. Rev. B 38, 7985-7989 (1988).
    [CrossRef]
  16. M. Kauranen and S. Cattaneo, "Polarization techniques for surface nonlinear optics," in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 2008).
  17. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 2003).
  18. V. Rodriguez, "Quantitative determination of linear and second-harmonic generation optical effective responses of achiral or chiral materials in planar structures: Theory and materials," J. Chem. Phys. 128, 064707 (2008).
    [CrossRef] [PubMed]

2008 (1)

V. Rodriguez, "Quantitative determination of linear and second-harmonic generation optical effective responses of achiral or chiral materials in planar structures: Theory and materials," J. Chem. Phys. 128, 064707 (2008).
[CrossRef] [PubMed]

2007 (1)

2005 (1)

2003 (1)

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

2002 (1)

I. Shoji, T. Kondo, and R. Ito, "Second-order nonlinear susceptibilities of various dielectric and semiconductor materials," Opt. Quantum Electron. 34, 797-833 (2002).
[CrossRef]

2000 (1)

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

1999 (1)

G. Lupke, "Characterization of semiconductor interfaces by second-harmonic generation," Surf. Sci. Rep. 35, 77-161 (1999).
[CrossRef]

1998 (1)

R. Gehr, and A. Smith, "Separated-beam nonphase-matched second-harmonic method of characterizing nonlinear optical crystals," J. Opt. Soc. Am.Bs 15, 2298-2307 (1998).
[CrossRef]

1988 (1)

P. Guyot-Sionnest and Y. R. Shen, "Bulk contribution in surface 2nd-harmonic generation," Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

1987 (2)

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, "Fundamental difficulty in the use of 2nd-harmonic generation as a strictly surface probe," Phys. Rev. B 35, 9091-9094 (1987).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical 2nd-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

1986 (1)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, "General-considerations on optical 2nd-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

1970 (1)

J. Jerphagnon and S. K. Kurtz, "Maker Fringes: A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals," J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Armstrong, D.

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

Canfield, B. K.

Cattaneo, S.

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, "General-considerations on optical 2nd-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

Gehr, R.

R. Gehr, and A. Smith, "Separated-beam nonphase-matched second-harmonic method of characterizing nonlinear optical crystals," J. Opt. Soc. Am.Bs 15, 2298-2307 (1998).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, "Bulk contribution in surface 2nd-harmonic generation," Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical 2nd-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, "General-considerations on optical 2nd-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

Held, H.

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

Hong, S. C.

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

Ito, R.

I. Shoji, T. Kondo, and R. Ito, "Second-order nonlinear susceptibilities of various dielectric and semiconductor materials," Opt. Quantum Electron. 34, 797-833 (2002).
[CrossRef]

Jerphagnon, J.

J. Jerphagnon and S. K. Kurtz, "Maker Fringes: A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals," J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Kauranen, M.

Kondo, T.

I. Shoji, T. Kondo, and R. Ito, "Second-order nonlinear susceptibilities of various dielectric and semiconductor materials," Opt. Quantum Electron. 34, 797-833 (2002).
[CrossRef]

Kurtz, S. K.

J. Jerphagnon and S. K. Kurtz, "Maker Fringes: A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals," J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Lupke, G.

G. Lupke, "Characterization of semiconductor interfaces by second-harmonic generation," Surf. Sci. Rep. 35, 77-161 (1999).
[CrossRef]

Lvovsky, A. I.

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

Mizrahi, V.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, "Fundamental difficulty in the use of 2nd-harmonic generation as a strictly surface probe," Phys. Rev. B 35, 9091-9094 (1987).
[CrossRef]

Pack, M.

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

Rodriguez, F. J.

Rodriguez, V.

V. Rodriguez, "Quantitative determination of linear and second-harmonic generation optical effective responses of achiral or chiral materials in planar structures: Theory and materials," J. Chem. Phys. 128, 064707 (2008).
[CrossRef] [PubMed]

Shen, Y. R.

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Bulk contribution in surface 2nd-harmonic generation," Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical 2nd-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, "General-considerations on optical 2nd-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

Shoji, I.

I. Shoji, T. Kondo, and R. Ito, "Second-order nonlinear susceptibilities of various dielectric and semiconductor materials," Opt. Quantum Electron. 34, 797-833 (2002).
[CrossRef]

Siltanen, M.

Sipe, J. E.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, "Fundamental difficulty in the use of 2nd-harmonic generation as a strictly surface probe," Phys. Rev. B 35, 9091-9094 (1987).
[CrossRef]

Smith, A.

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

R. Gehr, and A. Smith, "Separated-beam nonphase-matched second-harmonic method of characterizing nonlinear optical crystals," J. Opt. Soc. Am.Bs 15, 2298-2307 (1998).
[CrossRef]

Stegeman, G. I.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, "Fundamental difficulty in the use of 2nd-harmonic generation as a strictly surface probe," Phys. Rev. B 35, 9091-9094 (1987).
[CrossRef]

Wang, F.

Wang, F. X.

Wei, X.

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

Bs (1)

R. Gehr, and A. Smith, "Separated-beam nonphase-matched second-harmonic method of characterizing nonlinear optical crystals," J. Opt. Soc. Am.Bs 15, 2298-2307 (1998).
[CrossRef]

J. Appl. Phys. (1)

J. Jerphagnon and S. K. Kurtz, "Maker Fringes: A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals," J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

J. Chem. Phys. (1)

V. Rodriguez, "Quantitative determination of linear and second-harmonic generation optical effective responses of achiral or chiral materials in planar structures: Theory and materials," J. Chem. Phys. 128, 064707 (2008).
[CrossRef] [PubMed]

J. Phys. Chem. B (1)

X. Wei, S. C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, "Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries," J. Phys. Chem. B 104, 3349-3354 (2000).
[CrossRef]

Opt. Express (2)

Opt. Quantum Electron. (1)

I. Shoji, T. Kondo, and R. Ito, "Second-order nonlinear susceptibilities of various dielectric and semiconductor materials," Opt. Quantum Electron. 34, 797-833 (2002).
[CrossRef]

Phys. Rev. B (4)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, "General-considerations on optical 2nd-harmonic generation from surfaces and interfaces," Phys. Rev. B 33, 8254-8263 (1986).
[CrossRef]

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, "Fundamental difficulty in the use of 2nd-harmonic generation as a strictly surface probe," Phys. Rev. B 35, 9091-9094 (1987).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Local and nonlocal surface nonlinearities for surface optical 2nd-harmonic generation," Phys. Rev. B 35, 4420-4426 (1987).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, "Bulk contribution in surface 2nd-harmonic generation," Phys. Rev. B 38, 7985-7989 (1988).
[CrossRef]

Rev. Sci. Instrum. (1)

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

Surf. Sci. Rep. (1)

G. Lupke, "Characterization of semiconductor interfaces by second-harmonic generation," Surf. Sci. Rep. 35, 77-161 (1999).
[CrossRef]

Other (5)

T. F. Heinz, "Second-order nonlinear optical effects at surfaces and interfaces," in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath, and G. I. Stegeman, eds., (Elsevier, Amsterdam, 1991).

Y. An, R. Carriles, and M. Downer, "Absolute phase and amplitude of second-order nonlinear optical susceptibility components at Si(001) interfaces," Phys. Rev. B 75, 241307(R) (2007).
[CrossRef]

W. Herman and L. Hayden, "Maker fringes revisited - 2nd-harmonic generation from birefringent or absorbing materials," J. Opt. Soc. Am. B 12, 416-427 (1995).
[CrossRef]

M. Kauranen and S. Cattaneo, "Polarization techniques for surface nonlinear optics," in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 2008).

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 2003).

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Figures (2)

Fig. 1.
Fig. 1.

(a). Geometry of the fundamental (lower-case letters) and SH (upper-case letters) fields inside the nonlinear material (glass or quartz) and orientation of the crystallographic axes for the case of quartz. (b). SH intensity as a function of the relative position of the overlap of the two fundamental beams and the surface of the nonlinear material. The maximum of the peak corresponds to the overlap centered at one of the surfaces.

Fig. 2.
Fig. 2.

Measured intensity of SHG from fused silica as a function of the angle of the quarter-wave plate in one fundamental beam for the combinations of the polarization of the other fundamental beam/detected SHG: (circles) 45°/90°, (squares) 45°/0°, (up triangles) 0°/45°, and (down triangles) 90°/45°. The solid lines correspond to fits with the theoretical model.

Tables (1)

Tables Icon

Table I. SHG susceptibility tensor components for fused silica and BK7 glass in units of 10-22 m2/V

Equations (9)

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E s ± = i 8 π ω N c cos Θ ( ( χ ∥∥⊥ sin θ a + δ ω n 2 c Δ k ± sin ( θ a θ b ) ) a p b s
+ ( χ ∥∥⊥ sin θ b δ ω n 2 c Δ k ± sin ( θ a θ b ) ) a s b p )
E p ± = i 8 π ω Nc ( ( χ ∥∥⊥ sin ( θ a + θ b ) + ( χ ⊥∥∥ cos θ a cos θ b + χ ⊥⊥⊥ sin θ a sin θ b ) tan Θ
+ δ n 4 N cos Θ sin ( θ a θ b ) ( cos θ a cos θ b ) ) a p b p + χ ⊥∥∥ tan Θ a s b s )
E s ± = 0
E p ± = 8 π ω N o c cos Θ Δ k ± ( χ XXX ( cos ( θ a + θ b Θ ) a p b p
+ χ XYZ ( sin ( θ a ± Θ ) a p b s + sin ( θ b ± Θ ) a s b p ) )
E s ± = i 8 π ω 2 n N c 2 cos Θ Δ k ± δ sin θ b a p b s , E p ± = 0 .
E s ± = 0 , E p ± = ± 8 π ω N o c Δ k ± χ XYZ tan Θ a p b s .

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