Abstract

The thermal expansion and temperature dependence of the refractive index in gradient-index glass have been investigated. In an earlier paper [ P. O. McLaughlin and D. T. Moore, “ Models for the Thermal Expansion Coefficient and Temperature Coefficient of the Refractive Index in Gradient Index Glass,” Appl. Opt. 24, this issue ( 15 Dec. 1985)] these two thermal properties were modeled as functions of the local glass composition within the gradient-index region. In this paper measurements of αL and dn/dT are described. A modified multiple Fabry-Perot interferometer was designed and built into an environmental temperature chamber to measure these thermal properties in gradient-index glass in the 0–100°C range. The interferometer operated under computer control to measure optically the differential thermal expansion and change in refractive-index profile in several samples of gradient-index glass.

© 1985 Optical Society of America

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References

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  1. R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
    [CrossRef]
  2. J. H. Wray, J. T. Neu, “Refractive Index as Function of Wavelength,” J. Opt. Soc. Am. 59, 774 (1969).
    [CrossRef]
  3. Fred A. Molby, “Index of Refraction and Coefficients of Expansion of Optical Glasses at Low Temperatures,” J. Opt. Soc. Am. 39, 600 (1949).
    [CrossRef]
  4. Perkin-Elmer Thermo-Mechanical Analyzer model TMS-1.
  5. L. W. Tilton, “Standard Conditions for Precise Prism Refractometry,” J. Res. Nat. Bur. Stand. 14, 393 (1935).
    [CrossRef]
  6. P. O. McLaughlin, D. T. Moore, “Models for the Thermal Expansion Coefficient and Temperature Coefficient of the Refractive Index in Gradient Index Glass,” Appl. Opt.24, this issue (15Dec.1985).
    [PubMed]
  7. D. T. Moore, “Gradient Index Optics: Aspects of Design, Testing, Tolerancing, and Fabrication,” Ph.D. Thesis, U. Rochester, New York (1974).
  8. J. M. Eastman, “Surface Scattering in Optical Interference Coatings,” Ph.D. Thesis, U. Rochester, New York (1974).
  9. P. O. McLaughlin, “Thermal Expansion and Temperature Dependence of the Refractive Index in Gradient Refractive Index Glass,” Ph.D. Thesis, U. Rochester, New York (1982).
  10. D. T. Moore, “Gradient-Index Optical Glass Lenses,” National Science Foundation Research Contract ENG. 74-11993-AO1, Annual Report (1976).
  11. S. D. Fantone, “Design, Engineering, and Manufacturing Aspects of Gradient Index Optical Components,” Ph.D. Thesis, U. Rochester, New York (1979).
  12. J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication, and Testing,” Ph.D. Thesis, U. Rochester, New York (1982).
  13. Y. Koike, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 15: GRIN Rod Prepared by Photocopolymerization of a Ternary Monomer System.” Appl. Opt. 22, 418 (1983).
    [CrossRef] [PubMed]

1983 (1)

1971 (1)

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

1969 (1)

1949 (1)

1935 (1)

L. W. Tilton, “Standard Conditions for Precise Prism Refractometry,” J. Res. Nat. Bur. Stand. 14, 393 (1935).
[CrossRef]

Cleek, G. W.

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

Dodge, M. J.

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

Eastman, J. M.

J. M. Eastman, “Surface Scattering in Optical Interference Coatings,” Ph.D. Thesis, U. Rochester, New York (1974).

Fantone, S. D.

S. D. Fantone, “Design, Engineering, and Manufacturing Aspects of Gradient Index Optical Components,” Ph.D. Thesis, U. Rochester, New York (1979).

Hahn, T. A.

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

Koike, Y.

Malitson, I. H.

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

McLaughlin, P. O.

P. O. McLaughlin, “Thermal Expansion and Temperature Dependence of the Refractive Index in Gradient Refractive Index Glass,” Ph.D. Thesis, U. Rochester, New York (1982).

P. O. McLaughlin, D. T. Moore, “Models for the Thermal Expansion Coefficient and Temperature Coefficient of the Refractive Index in Gradient Index Glass,” Appl. Opt.24, this issue (15Dec.1985).
[PubMed]

Miceli, J. J.

J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication, and Testing,” Ph.D. Thesis, U. Rochester, New York (1982).

Molby, Fred A.

Moore, D. T.

P. O. McLaughlin, D. T. Moore, “Models for the Thermal Expansion Coefficient and Temperature Coefficient of the Refractive Index in Gradient Index Glass,” Appl. Opt.24, this issue (15Dec.1985).
[PubMed]

D. T. Moore, “Gradient Index Optics: Aspects of Design, Testing, Tolerancing, and Fabrication,” Ph.D. Thesis, U. Rochester, New York (1974).

D. T. Moore, “Gradient-Index Optical Glass Lenses,” National Science Foundation Research Contract ENG. 74-11993-AO1, Annual Report (1976).

Neu, J. T.

Ohtsuka, Y.

Tilton, L. W.

L. W. Tilton, “Standard Conditions for Precise Prism Refractometry,” J. Res. Nat. Bur. Stand. 14, 393 (1935).
[CrossRef]

Waxler, R. M.

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

Wray, J. H.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Res. Nat. Bur. Stand. (1)

L. W. Tilton, “Standard Conditions for Precise Prism Refractometry,” J. Res. Nat. Bur. Stand. 14, 393 (1935).
[CrossRef]

J. Res., Res. Nat. Bur. Stand. Sect. A (1)

R. M. Waxler, G. W. Cleek, I. H. Malitson, M. J. Dodge, T. A. Hahn, “Optical and Mechanical Properties of Some Neodymium-Doped Laser Glasses,” J. Res., Res. Nat. Bur. Stand. Sect. A 75, 163 (1971).
[CrossRef]

Other (8)

Perkin-Elmer Thermo-Mechanical Analyzer model TMS-1.

P. O. McLaughlin, D. T. Moore, “Models for the Thermal Expansion Coefficient and Temperature Coefficient of the Refractive Index in Gradient Index Glass,” Appl. Opt.24, this issue (15Dec.1985).
[PubMed]

D. T. Moore, “Gradient Index Optics: Aspects of Design, Testing, Tolerancing, and Fabrication,” Ph.D. Thesis, U. Rochester, New York (1974).

J. M. Eastman, “Surface Scattering in Optical Interference Coatings,” Ph.D. Thesis, U. Rochester, New York (1974).

P. O. McLaughlin, “Thermal Expansion and Temperature Dependence of the Refractive Index in Gradient Refractive Index Glass,” Ph.D. Thesis, U. Rochester, New York (1982).

D. T. Moore, “Gradient-Index Optical Glass Lenses,” National Science Foundation Research Contract ENG. 74-11993-AO1, Annual Report (1976).

S. D. Fantone, “Design, Engineering, and Manufacturing Aspects of Gradient Index Optical Components,” Ph.D. Thesis, U. Rochester, New York (1979).

J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication, and Testing,” Ph.D. Thesis, U. Rochester, New York (1982).

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Figures (10)

Fig. 1
Fig. 1

Gradient-index sample preparation.

Fig. 2
Fig. 2

Multiple Fabry-Perot interferometer.

Fig. 3
Fig. 3

Multiple Fabry-Perot interferometer system.

Fig. 4
Fig. 4

Phase modulation.

Fig. 5
Fig. 5

Computer interfacing.

Fig. 6
Fig. 6

Optical system.

Fig. 7
Fig. 7

Change in surface profile for sample BL:Li1.

Fig. 8
Fig. 8

Change in surface profile for sample BL:K1.

Fig. 9
Fig. 9

Change in surface profile for sample BL:LiK1.

Fig. 10
Fig. 10

Gradient-index profile for sample BL:LiK2.

Tables (7)

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Table I Physical Properties Homogeneous Base Glass

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Table II Gradient-Index Glass Samples

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Table III Differential Thermal Expansion in Sample BL:Li1

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Table IV Differential Thermal Expansion in Sample BL:K1

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Table V Differential Thermal Expansion in Sample BL:LiK1

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Table VI Gradient-Index Measurement

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Table VII Temperature Dependence of Refractive Index in Gradient-Index Glass

Equations (9)

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OPD = 2 n Z ,
OPD = ( x , y , T ) = 2 n RFP ( T ) [ z ( T ) l ( x , y , T ) ] + 2 n ( x , y , T ) l ( x , y , T ) ,
OPD ( x , y , T 1 ) OPD ( x , y , T 2 ) = 2 [ n RFP ( T 1 ) z ( T 1 ) n RFP ( T 2 ) z ( T 2 ) ] 2 [ n RFP ( T 1 ) l ( x , y , T 1 ) n RFP ( T 2 ) l ( x , y , T 2 ) ] + 2 [ n ( x , y , T 1 ) l ( x , y , T 1 ) n ( x , y , T 2 ) l ( x , y , T 2 ) ]
p ex = p ex ( 1 u υ ) , p b = p ex u , p c = p ex υ , 0 u 1 0 υ 1 0 u + υ 1 , }
| δ α L | < 0.6 × 10 6 / ° C .
δ α L = ( α Ag α Na ) P Na u ,
OPD ( x , y , T 1 ) OPD ( x , y , T 2 ) = 2 [ n RFP ( T 1 ) z ( T 1 ) n RFP ( T 2 ) z ( T 2 ) ] 2 { n RFP ( T 1 ) l ( x , y , T 1 ) [ n RFP ( T 1 ) + d n RFP d T Δ T ] l ( x , y , T 1 ) ( 1 + α L ( x , y ) Δ T ) } + 2 { n ( x , y , T 1 ) l ( x , y , T 1 ) [ n ( x , y , T 1 ) + d n d T ( x , y ) Δ T ] l ( x , y , T 1 ) ( 1 + α L ( x , y ) Δ T ) } .
d n ( x , y ) d T = 1 2 l 1 Δ T [ OPD ( x , y , T 1 ) OPD ( x , y , T 2 ) ] [ n ( x , y ) n RFP ] α L ( x , y ) .
d n ( x , y ) d T = [ n RFP n ( x , y ) ] α L ( x , y ) ± 1 2 l 1 Δ T ( λ / 5 ) ,

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