Abstract

Two techniques are described for measurement of the indices of refraction of novel optical crystals. First a modification is presented of the traditional measurement of the angle of minimum deviation of a refracted beam and applied to lead tetraborate (PTB). The second method applies polarized Michelson interferometry to the principal refractive indices of RbNbB2O6 (RNB). Both PTB and RNB are nonlinear optical crystals that have been recently synthesized and grown for the first time.

© 1997 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1994).
  2. Y. R. Shen, Principles of Nonlinear Optics (McGraw-Hill, New York), 1984).
  3. A. Baucher, M. Gasperin, “On a new family of multiple oxides based on Boron: MIMIVB2O6(MI = Tl, Rb, MIV = Nb, Ta),” Mater. Res. Bull. 10, 469–470 (1975).
    [CrossRef]
  4. J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
    [CrossRef]
  5. J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).
  6. J. F. H. Nicholls, B Henderson, B. H. T. Chai, Linear and nonlinear optical properties of lead tetra-borate,” Opt. Mater. 8, 185–191 (1997).
  7. J. F. H. Nicholls, “Growth and characterisation of inorganic crystals with application in lasers and nonlinear optical devices,” Ph.D. dissertation (University of Strathclyde, Glasgow, Scotland, May1994).
  8. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).
  9. J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, England, 1985).
  10. D. J. McKee, J. F. H. Nicholls, I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. J. Phys. 16, 127–131 (1995).
    [CrossRef]
  11. D. L. Corker, Department of Physics, Clarendon Laboratory, University of Oxford (personal communication, 1995).

1997 (2)

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

J. F. H. Nicholls, B Henderson, B. H. T. Chai, Linear and nonlinear optical properties of lead tetra-borate,” Opt. Mater. 8, 185–191 (1997).

1995 (1)

D. J. McKee, J. F. H. Nicholls, I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. J. Phys. 16, 127–131 (1995).
[CrossRef]

1975 (1)

A. Baucher, M. Gasperin, “On a new family of multiple oxides based on Boron: MIMIVB2O6(MI = Tl, Rb, MIV = Nb, Ta),” Mater. Res. Bull. 10, 469–470 (1975).
[CrossRef]

Baucher, A.

A. Baucher, M. Gasperin, “On a new family of multiple oxides based on Boron: MIMIVB2O6(MI = Tl, Rb, MIV = Nb, Ta),” Mater. Res. Bull. 10, 469–470 (1975).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1994).

Chai, B. H. T.

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

J. F. H. Nicholls, B Henderson, B. H. T. Chai, Linear and nonlinear optical properties of lead tetra-borate,” Opt. Mater. 8, 185–191 (1997).

J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).

Corker, D. L.

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

D. L. Corker, Department of Physics, Clarendon Laboratory, University of Oxford (personal communication, 1995).

Gallagher, H. G.

J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).

Gasperin, M.

A. Baucher, M. Gasperin, “On a new family of multiple oxides based on Boron: MIMIVB2O6(MI = Tl, Rb, MIV = Nb, Ta),” Mater. Res. Bull. 10, 469–470 (1975).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

Henderson, B

J. F. H. Nicholls, B Henderson, B. H. T. Chai, Linear and nonlinear optical properties of lead tetra-borate,” Opt. Mater. 8, 185–191 (1997).

J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).

Henderson, B.

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

McKee, D. J.

D. J. McKee, J. F. H. Nicholls, I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. J. Phys. 16, 127–131 (1995).
[CrossRef]

Nicholls, J. F. H.

J. F. H. Nicholls, B Henderson, B. H. T. Chai, Linear and nonlinear optical properties of lead tetra-borate,” Opt. Mater. 8, 185–191 (1997).

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

D. J. McKee, J. F. H. Nicholls, I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. J. Phys. 16, 127–131 (1995).
[CrossRef]

J. F. H. Nicholls, “Growth and characterisation of inorganic crystals with application in lasers and nonlinear optical devices,” Ph.D. dissertation (University of Strathclyde, Glasgow, Scotland, May1994).

J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).

Nye, J. F.

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

Ruddock, I. S.

D. J. McKee, J. F. H. Nicholls, I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. J. Phys. 16, 127–131 (1995).
[CrossRef]

Russell, D. J.

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (McGraw-Hill, New York), 1984).

Wang, G

J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1994).

Eur. J. Phys. (1)

D. J. McKee, J. F. H. Nicholls, I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. J. Phys. 16, 127–131 (1995).
[CrossRef]

Mater. Res. Bull. (1)

A. Baucher, M. Gasperin, “On a new family of multiple oxides based on Boron: MIMIVB2O6(MI = Tl, Rb, MIV = Nb, Ta),” Mater. Res. Bull. 10, 469–470 (1975).
[CrossRef]

Opt. Mater. (2)

J. F. H. Nicholls, B. H. T. Chai, D. J. Russell, D. L. Corker, B. Henderson, “Structure and optical properties of the RbNbB2O6 family of mixed borates,” Opt. Mater. 8, 215–216 (1997).
[CrossRef]

J. F. H. Nicholls, B Henderson, B. H. T. Chai, Linear and nonlinear optical properties of lead tetra-borate,” Opt. Mater. 8, 185–191 (1997).

Other (7)

J. F. H. Nicholls, “Growth and characterisation of inorganic crystals with application in lasers and nonlinear optical devices,” Ph.D. dissertation (University of Strathclyde, Glasgow, Scotland, May1994).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

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

J. F. H. Nicholls, G Wang, B Henderson, H. G. Gallagher, B. H. T. Chai, “Single crystal growth of the RbNbB2O6 family of compounds,” J. Cryst. Growth (to be published).

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1994).

Y. R. Shen, Principles of Nonlinear Optics (McGraw-Hill, New York), 1984).

D. L. Corker, Department of Physics, Clarendon Laboratory, University of Oxford (personal communication, 1995).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic illustration of the measurement of the refractive index when the angular deviation of a beam of light is measured by a prism of angle α. (b) Orientations of two prisms that are needed to allow measurements of the three principal indices nx, ny, and nz.

Fig. 2
Fig. 2

Optical indicatrix for a biaxial crystal.

Fig. 3
Fig. 3

Angle of deviation Δ of a beam of light incident on a PTB prism with apex angle α ≈ 45° at angle θ and wavelength λ = 600 nm.

Fig. 4
Fig. 4

Dispersion of refractive indices of (a) PTB measured with the angle of deviation technique and fitted to a single oscillator Sellmeier equation and (b) RNB measured by the polarized interferometer technique and fitted to a double-oscillator Sellmeier equation.

Fig. 5
Fig. 5

Michelson interferometric technique for measuring the indices of refraction of a biaxial crystal.

Fig. 6
Fig. 6

Various terms contributing to the change in path length as the crystal rotates in one arm of the Michelson interferometer.

Fig. 7
Fig. 7

Contribution to the error in the index of refraction Δn measured by polarized Michelson interferometry. (a) The error δnθ induced as the angle of rotation θ is increased and (b) the error δnt in n caused by uncertainty in the measurement of thickness t of the crystal.

Tables (4)

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Table 1 Sellmeier Parameters for PTB

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Table 2 Refractive Indices of Three RNB Crystals Measured at 632.8 nm with Polarized Michelson Interferometry

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Table 3 Sellmeier Parameters for RNB

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Table 4 Comparison of Refractive Indices of PTB, RNB, and Other Nonlinear Optical Borate Crystals

Equations (20)

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n i = sin [ 1 2 ( Δ m + α ) ] sin ( 1 2 α ) .
sin θ 1 sin ϕ 1 = n i = sin ϕ 2 sin θ 2 ,
Δ = θ 1 + arcsin { n i sin [ α - arcsin ( sin θ 1 n i ) ] } - α ,
n 2 ( λ ) = 1 + A + S d λ d 2 λ 2 ( λ 2 - λ d 2 ) ,
Δ n = ( δ n θ 2 + δ n Δ 2 + δ n α 2 ) 1 / 2 ,
δ n θ = δ θ 1 n θ θ 1 ,
s = [ Σ ( y - y ^ ) 2 N - ( k + 1 ) ] 1 / 2 ,
δ d = 2 ( - δ x 1 + n 0 δ t + δ x 2 ) ,
δ d = N λ .
n 0 = 1 + ( n λ / 2 ) 2 + N λ t cos θ 2 t 2 ( 1 - cos θ ) - N λ t .
n x 2 ( ϕ ) = [ ( N λ / 2 t ) + cos ( ϕ ) + n y - 1 ] 2 + sin 2 ( θ ) ,
1 n x 2 ( ϕ ) = cos 2 ( ϕ ) n y 2 + sin 2 ( ϕ ) n x 2 .
n x 2 = n y 2 sin 2 ( θ ) n y 2 - n x 2 ( ϕ ) + sin 2 ( θ ) ,
n 2 ( λ ) = 1 + S 1 λ 1 2 λ 2 ( λ 2 - λ 1 2 ) + S 2 λ 2 2 λ 2 ( λ 2 - λ 2 2 ) ,
Δ n = ( δ n θ 2 + δ n t 2 ) 1 / 2 ,
δ n θ = δ θ n θ θ ,
δ n t = δ t n t t .
n θ = - N λ t sin θ 2 t 2 ( 1 - cos θ ) - N λ t - 2 t 2 sin θ [ ( N λ 2 ) 2 + N λ t cos θ ] [ 2 t 2 ( 1 - cos θ ) - N λ t ] 2 ,
n t = - N λ t cos θ 2 t 2 ( 1 - cos θ ) - N λ t - [ 4 t 2 ( 1 - cos θ ) - N λ ] [ ( N λ 2 ) 2 + N λ t cos θ ] [ 2 t 2 ( 1 - cos θ ) - N λ t ] 2 .
N = 2 t λ [ ( n 2 - sin 2 θ ) - cos θ - ( n - 1 ) ] .

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