Abstract

We show that it is possible to determine the magnitude of the three principal refractive indices of a biaxial crystal from the measurement of the double-refraction effect at the exit of the crystal cut as a millimetric sphere and illuminated with a laser beam. By this way, we determined the indices of a monoclinic crystal, Ca4YO(BO3)3, at λ=0.6328μm with an accuracy of 6×103. The sphere method, which we implemented several years ago, is now self-sufficient for a complete characterization of the linear and nonlinear optical properties of any new biaxial crystal.

© 2006 Optical Society of America

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References

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  1. V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, 1999).
  2. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
    [CrossRef]
  3. F. Mougel, "Les oxoborates de calcium et de terres rares (TR)Ca4TRO(BO3)3. Une nouvelle famille de matériaux à fonctions multiples pour l'optique: croissance cristalline, propriétés non linéaires et laser," Ph.D. dissertation (Pierre et Marie Curie University, Paris, 1999).
  4. S. P. Velsko, "Direct measurements of phase matching properties in small single crystals of new nonlinear materials," Opt. Eng. 28, 76-84 (1989).
  5. G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and nonlinear crystalline optical studies," Opt. Commun. 72, 139-143 (1989).
    [CrossRef]
  6. See, for example, J. P. Fève, B. Boulanger, O. Pacaud, I. Rousseau, B. Ménaert, G. Marnier, P. Villeval, C. Bonnin, and G. M. Loiacono, "Phase-matching measurements and Sellmeier equations over the complete transparency range of KTiOAsO4, RbTiOAsO4, and CsTiOAsO4," J. Opt. Soc. Am. B 17, 775-780 (2000).
    [CrossRef]
  7. Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
    [CrossRef]
  8. P. Segonds, B. Boulanger, J. P. Fève, B. Ménaert, J. Zaccaro, G. Aka, and D. Pelenc, "Linear and nonlinear optical properties of the monoclinic Ca4YO(BO3)3 crystal," J. Opt. Soc. Am. B 21, 765-769 (2004).
    [CrossRef]
  9. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1983).
  10. B. Boulanger, J. P. Fève, G. Marnier, and B. Menaert, "Methodology for nonlinear optical studies: application to the isomorph family KTiOPO4, KTiOAsO4, RbTiOAsO4 and CsTiOAsO4," Pure Appl. Opt. 7, 239-256 (1998).
    [CrossRef]
  11. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, 1985).
  12. B. Boulanger, J. P. Fève, G. Marnier, C. Bonnin, P. Villeval, and J. J. Zondy, "Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic generation in a single KTP crystal cut as a sphere," J. Opt. Soc. Am. B 14, 1380-1386 (1997).
    [CrossRef]

2004 (1)

2003 (1)

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

2000 (1)

1998 (1)

B. Boulanger, J. P. Fève, G. Marnier, and B. Menaert, "Methodology for nonlinear optical studies: application to the isomorph family KTiOPO4, KTiOAsO4, RbTiOAsO4 and CsTiOAsO4," Pure Appl. Opt. 7, 239-256 (1998).
[CrossRef]

1997 (1)

1990 (1)

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
[CrossRef]

1989 (2)

S. P. Velsko, "Direct measurements of phase matching properties in small single crystals of new nonlinear materials," Opt. Eng. 28, 76-84 (1989).

G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and nonlinear crystalline optical studies," Opt. Commun. 72, 139-143 (1989).
[CrossRef]

Aka, G.

Bonnin, C.

Boulanger, B.

P. Segonds, B. Boulanger, J. P. Fève, B. Ménaert, J. Zaccaro, G. Aka, and D. Pelenc, "Linear and nonlinear optical properties of the monoclinic Ca4YO(BO3)3 crystal," J. Opt. Soc. Am. B 21, 765-769 (2004).
[CrossRef]

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

See, for example, J. P. Fève, B. Boulanger, O. Pacaud, I. Rousseau, B. Ménaert, G. Marnier, P. Villeval, C. Bonnin, and G. M. Loiacono, "Phase-matching measurements and Sellmeier equations over the complete transparency range of KTiOAsO4, RbTiOAsO4, and CsTiOAsO4," J. Opt. Soc. Am. B 17, 775-780 (2000).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, and B. Menaert, "Methodology for nonlinear optical studies: application to the isomorph family KTiOPO4, KTiOAsO4, RbTiOAsO4 and CsTiOAsO4," Pure Appl. Opt. 7, 239-256 (1998).
[CrossRef]

B. Boulanger, J. P. Fève, G. Marnier, C. Bonnin, P. Villeval, and J. J. Zondy, "Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic generation in a single KTP crystal cut as a sphere," J. Opt. Soc. Am. B 14, 1380-1386 (1997).
[CrossRef]

G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and nonlinear crystalline optical studies," Opt. Commun. 72, 139-143 (1989).
[CrossRef]

Byer, R. L.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
[CrossRef]

Dmitriev, V. D.

V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, 1999).

Douady, J.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

Eckardt, R. C.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
[CrossRef]

Fan, Y. X.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
[CrossRef]

Fève, J. P.

Guillien, Y.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

Gurzadyan, G. G.

V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, 1999).

Loiacono, G. M.

Marnier, G.

Masuda, H.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
[CrossRef]

Menaert, B.

B. Boulanger, J. P. Fève, G. Marnier, and B. Menaert, "Methodology for nonlinear optical studies: application to the isomorph family KTiOPO4, KTiOAsO4, RbTiOAsO4 and CsTiOAsO4," Pure Appl. Opt. 7, 239-256 (1998).
[CrossRef]

Ménaert, B.

Mougel, F.

F. Mougel, "Les oxoborates de calcium et de terres rares (TR)Ca4TRO(BO3)3. Une nouvelle famille de matériaux à fonctions multiples pour l'optique: croissance cristalline, propriétés non linéaires et laser," Ph.D. dissertation (Pierre et Marie Curie University, Paris, 1999).

Nikogosyan, D. N.

V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, 1999).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, 1985).

Pacaud, O.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

See, for example, J. P. Fève, B. Boulanger, O. Pacaud, I. Rousseau, B. Ménaert, G. Marnier, P. Villeval, C. Bonnin, and G. M. Loiacono, "Phase-matching measurements and Sellmeier equations over the complete transparency range of KTiOAsO4, RbTiOAsO4, and CsTiOAsO4," J. Opt. Soc. Am. B 17, 775-780 (2000).
[CrossRef]

Pelenc, D.

Rousseau, I.

Segonds, P.

P. Segonds, B. Boulanger, J. P. Fève, B. Ménaert, J. Zaccaro, G. Aka, and D. Pelenc, "Linear and nonlinear optical properties of the monoclinic Ca4YO(BO3)3 crystal," J. Opt. Soc. Am. B 21, 765-769 (2004).
[CrossRef]

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

Velsko, S. P.

S. P. Velsko, "Direct measurements of phase matching properties in small single crystals of new nonlinear materials," Opt. Eng. 28, 76-84 (1989).

Villeval, P.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1983).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1983).

Zaccaro, J.

Zondy, J. J.

IEEE J. Quantum Electron. (1)

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, "Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation," IEEE J. Quantum Electron. 26, 922-933 (1990).
[CrossRef]

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

Opt. Commun. (1)

G. Marnier and B. Boulanger, "The sphere method: a new technique in linear and nonlinear crystalline optical studies," Opt. Commun. 72, 139-143 (1989).
[CrossRef]

Opt. Eng. (1)

S. P. Velsko, "Direct measurements of phase matching properties in small single crystals of new nonlinear materials," Opt. Eng. 28, 76-84 (1989).

Opt. Mater. (1)

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, "Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4," Opt. Mater. 22, 155-162 (2003).
[CrossRef]

Pure Appl. Opt. (1)

B. Boulanger, J. P. Fève, G. Marnier, and B. Menaert, "Methodology for nonlinear optical studies: application to the isomorph family KTiOPO4, KTiOAsO4, RbTiOAsO4 and CsTiOAsO4," Pure Appl. Opt. 7, 239-256 (1998).
[CrossRef]

Other (4)

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, 1985).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1983).

V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, 1999).

F. Mougel, "Les oxoborates de calcium et de terres rares (TR)Ca4TRO(BO3)3. Une nouvelle famille de matériaux à fonctions multiples pour l'optique: croissance cristalline, propriétés non linéaires et laser," Ph.D. dissertation (Pierre et Marie Curie University, Paris, 1999).

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Figures (5)

Fig. 1
Fig. 1

Orientation of the wave vectors k, k 1 , and k 2 (dashed arrows) and Poynting vectors P, P 1 , and P 2 (continuous lines) of the incident beam and of the two double-refraction beams inside and outside the sphere. ( u , v , w ) is the optical frame; R is the sphere radius; α is the propagation angle of the two wave vectors in the u v principal plane; ρ u v and ρ u v ext are the walk-off angles inside and outside the sphere, respectively; A u v is the distance between the exit surface of the sphere and the intersection point of the two emergent beams; d u v is the distance between the two beam axes; L is the distance between the exit surface of the sphere and the observation plane.

Fig. 2
Fig. 2

Example of a recording of the transverse profiles of the two emergent beams by using a 3 cm long CCD camera composed of 2048   pixels with 14 μ m dimensions each and located at 31 cm behind the YCOB sphere. The propagation is at θ = 30 deg with the x axis in the x z principal plane. The Gaussian fit gives the distance d u v = d z x between the two maxima, which is equal to 7684 μ m .

Fig. 3
Fig. 3

Double refraction in the x y principal plane of YCOB: d x y is the distance between the two double-refraction beams at L = 32.75 cm behind the sphere; φ is the angle between the wave vectors and the x axis; the dots and the solid curve correspond to the experiment and the fit, respectively.

Fig. 4
Fig. 4

Double refraction in the x z principal plane of YCOB: d x z is the distance between the two double-refraction beams at L = 31.00 cm behind the sphere; θ is the angle between the wave vectors and the z axis; the dots and the solid curve correspond to the experiment and the fit, respectively.

Fig. 5
Fig. 5

Double refraction in the y z principal plane of YCOB: d y z is the distance between the two double-refraction beams at L = 31.00 cm behind the sphere; θ is the angle between the wave vectors and the z axis; the dots and the solid curve correspond to the experiment and the fit, respectively.

Tables (1)

Tables Icon

Table 1 Magnitudes of the Principal Refractive Indices of YCOB Obtained from the Sphere and Prism Methods at Room Temperature at λ = 0.6328 μ m

Equations (6)

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ρ u v ( α ) = arccos { [ sin 2 α + ( n u n v ) 2 cos 2 α ] [ sin 2 α + ( n u n v ) 4 cos 2 α ] 1 2 } ,
ρ u v ext ( α ) = arcsin { n u v ( α ) sin [ 2 ρ u v ( α ) ] } 2 ρ u v ( α ) ,
n u v ( α ) = ( n v 2 cos 2 α + n u 2 sin 2 α ) 1 2 .
d u v ( α ) = [ L A u v ( α ) ] tan [ ρ u v ext ( α ) ] .
A u v ( α ) = R { n u v ( α ) sin [ 2 ρ u v ( α ) ] sin [ ρ u v ext ( α ) ] 1 } ,
Δ d eff ( λ G ) d eff ( λ G ) 1 2 [ Δ η ( α pm ) η ( α pm ) + Δ η ( λ a ) n ( λ a ) + Δ n ( λ b ) n ( λ b ) + Δ n ( λ G ) n ( λ G ) ] .

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