Abstract

We have measured the nonlinear refractive-index coefficient γ interferometrically at 355 nm in fused silica and in BK-10, a borosilicate crown glass. These measurements are the first reported direct ultraviolet measurements of the nonlinear index of refraction in any transparent glass. Our results are γ = (2.5 ± 1.2) × 10−16 cm2/W and γ = (1.7 ± 0.8) × 10−16 cm2/W, respectively, for fused silica and BK-10.

© 1984 Optical Society of America

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  1. W. W. Simmons, J. T. Hunt, W. E. Warren, “Light propagation through large laser systems,” IEEE J. Quantum Electron. QE-17, 1727 (1981).
    [Crossref]
  2. M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive Index of glasses and crystals,” Opt. Eng. 17, 463 (1978).
  3. T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220 (1981).
  4. E. S. Bliss, D. R. Speck, W. W. Simmons, “Direct interferometric measurements of the nonlinear refractive index coefficient n2 in laser materials,” Appl. Phys. Lett. 25, 728 (1974).
    [Crossref]
  5. J. H. Nuckolls, “The feasibility of inertial-confinement fusion,” Phys. Today 35(9), 25 (1982).
    [Crossref]
  6. R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 56 (1977).
  7. N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1977).
  8. P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
    [Crossref]
  9. W. L. Smith, “Absoslute two-photon absorption coefficient at 355 nm in UV glasses,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), Postdeadline paper ThB21.
  10. N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978).
    [Crossref]
  11. C. C. Wang, “Empirical relation between the linear and the third-order nonlinear susceptibilities,” Phys. Rev. B 2, 2045 (1970).
    [Crossref]
  12. J. T. Fournier, E. Snitzer, “The nonlinear refractive index of glass,” IEEE J. Quantum Electron. QE-10, 473 (1974).
    [Crossref]
  13. Gan Fu-Xi, Lin Fen-Ying, “Nonlinear refractive index for glass and methods for its calculation,” Laser J. (Jiguang) 6, 12 (1979) (in Chinese).
  14. S. A. Jha, N. Bloembergen, “Nonlinear optical susceptibilities in group IV and III–V semiconductors,” Phys. Rev. 171, 891 (1968).
    [Crossref]
  15. A. J. Glass, KMS Fusion, Inc., P.O. Box 1567, Ann Arbor, Michigan 48106 (personal communication).
  16. J. Duthler, M. Sparks, “Theoretical studies of high-power ultraviolet and infrared materials,” Fifth Tech. Rep. (Xonics, Inc., 1333 Ocean Avenue, Santa Monica, California 90401, 1975).
  17. D. A. B. Miller, “Nonlinear optical effects in InSb with a cw CO laser,” Ph.D. Thesis (Heriot-Watt University, Edinburgh, U.K., 1979).
  18. A. P. Veduta, B. P. Kirsanov, “Variation of the refractive index of liquids and glasses in a high intensity field of a ruby laser,” Sov. Phys. JETP 27, 736 (1968).

1982 (1)

J. H. Nuckolls, “The feasibility of inertial-confinement fusion,” Phys. Today 35(9), 25 (1982).
[Crossref]

1981 (2)

W. W. Simmons, J. T. Hunt, W. E. Warren, “Light propagation through large laser systems,” IEEE J. Quantum Electron. QE-17, 1727 (1981).
[Crossref]

T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220 (1981).

1979 (1)

Gan Fu-Xi, Lin Fen-Ying, “Nonlinear refractive index for glass and methods for its calculation,” Laser J. (Jiguang) 6, 12 (1979) (in Chinese).

1978 (3)

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive Index of glasses and crystals,” Opt. Eng. 17, 463 (1978).

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978).
[Crossref]

1977 (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 56 (1977).

1974 (2)

E. S. Bliss, D. R. Speck, W. W. Simmons, “Direct interferometric measurements of the nonlinear refractive index coefficient n2 in laser materials,” Appl. Phys. Lett. 25, 728 (1974).
[Crossref]

J. T. Fournier, E. Snitzer, “The nonlinear refractive index of glass,” IEEE J. Quantum Electron. QE-10, 473 (1974).
[Crossref]

1970 (1)

C. C. Wang, “Empirical relation between the linear and the third-order nonlinear susceptibilities,” Phys. Rev. B 2, 2045 (1970).
[Crossref]

1968 (2)

S. A. Jha, N. Bloembergen, “Nonlinear optical susceptibilities in group IV and III–V semiconductors,” Phys. Rev. 171, 891 (1968).
[Crossref]

A. P. Veduta, B. P. Kirsanov, “Variation of the refractive index of liquids and glasses in a high intensity field of a ruby laser,” Sov. Phys. JETP 27, 736 (1968).

Adhav, R. S.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

Bechtel, J. H.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

Bliss, E. S.

E. S. Bliss, D. R. Speck, W. W. Simmons, “Direct interferometric measurements of the nonlinear refractive index coefficient n2 in laser materials,” Appl. Phys. Lett. 25, 728 (1974).
[Crossref]

Bloembergen, N.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

S. A. Jha, N. Bloembergen, “Nonlinear optical susceptibilities in group IV and III–V semiconductors,” Phys. Rev. 171, 891 (1968).
[Crossref]

N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1977).

Boling, N. L.

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978).
[Crossref]

Chang, T. Y.

T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220 (1981).

Duthler, J.

J. Duthler, M. Sparks, “Theoretical studies of high-power ultraviolet and infrared materials,” Fifth Tech. Rep. (Xonics, Inc., 1333 Ocean Avenue, Santa Monica, California 90401, 1975).

Fen-Ying, Lin

Gan Fu-Xi, Lin Fen-Ying, “Nonlinear refractive index for glass and methods for its calculation,” Laser J. (Jiguang) 6, 12 (1979) (in Chinese).

Fournier, J. T.

J. T. Fournier, E. Snitzer, “The nonlinear refractive index of glass,” IEEE J. Quantum Electron. QE-10, 473 (1974).
[Crossref]

Fu-Xi, Gan

Gan Fu-Xi, Lin Fen-Ying, “Nonlinear refractive index for glass and methods for its calculation,” Laser J. (Jiguang) 6, 12 (1979) (in Chinese).

Glass, A. J.

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978).
[Crossref]

A. J. Glass, KMS Fusion, Inc., P.O. Box 1567, Ann Arbor, Michigan 48106 (personal communication).

Hellwarth, R. W.

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 56 (1977).

Hunt, J. T.

W. W. Simmons, J. T. Hunt, W. E. Warren, “Light propagation through large laser systems,” IEEE J. Quantum Electron. QE-17, 1727 (1981).
[Crossref]

Jha, S. A.

S. A. Jha, N. Bloembergen, “Nonlinear optical susceptibilities in group IV and III–V semiconductors,” Phys. Rev. 171, 891 (1968).
[Crossref]

Kirsanov, B. P.

A. P. Veduta, B. P. Kirsanov, “Variation of the refractive index of liquids and glasses in a high intensity field of a ruby laser,” Sov. Phys. JETP 27, 736 (1968).

Liu, P.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

Lotem, H.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

Milam, D.

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive Index of glasses and crystals,” Opt. Eng. 17, 463 (1978).

Miller, D. A. B.

D. A. B. Miller, “Nonlinear optical effects in InSb with a cw CO laser,” Ph.D. Thesis (Heriot-Watt University, Edinburgh, U.K., 1979).

Nuckolls, J. H.

J. H. Nuckolls, “The feasibility of inertial-confinement fusion,” Phys. Today 35(9), 25 (1982).
[Crossref]

Owyoung, A.

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978).
[Crossref]

Simmons, W. W.

W. W. Simmons, J. T. Hunt, W. E. Warren, “Light propagation through large laser systems,” IEEE J. Quantum Electron. QE-17, 1727 (1981).
[Crossref]

E. S. Bliss, D. R. Speck, W. W. Simmons, “Direct interferometric measurements of the nonlinear refractive index coefficient n2 in laser materials,” Appl. Phys. Lett. 25, 728 (1974).
[Crossref]

Smith, W. L.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive Index of glasses and crystals,” Opt. Eng. 17, 463 (1978).

W. L. Smith, “Absoslute two-photon absorption coefficient at 355 nm in UV glasses,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), Postdeadline paper ThB21.

Snitzer, E.

J. T. Fournier, E. Snitzer, “The nonlinear refractive index of glass,” IEEE J. Quantum Electron. QE-10, 473 (1974).
[Crossref]

Sparks, M.

J. Duthler, M. Sparks, “Theoretical studies of high-power ultraviolet and infrared materials,” Fifth Tech. Rep. (Xonics, Inc., 1333 Ocean Avenue, Santa Monica, California 90401, 1975).

Speck, D. R.

E. S. Bliss, D. R. Speck, W. W. Simmons, “Direct interferometric measurements of the nonlinear refractive index coefficient n2 in laser materials,” Appl. Phys. Lett. 25, 728 (1974).
[Crossref]

Veduta, A. P.

A. P. Veduta, B. P. Kirsanov, “Variation of the refractive index of liquids and glasses in a high intensity field of a ruby laser,” Sov. Phys. JETP 27, 736 (1968).

Wang, C. C.

C. C. Wang, “Empirical relation between the linear and the third-order nonlinear susceptibilities,” Phys. Rev. B 2, 2045 (1970).
[Crossref]

Warren, W. E.

W. W. Simmons, J. T. Hunt, W. E. Warren, “Light propagation through large laser systems,” IEEE J. Quantum Electron. QE-17, 1727 (1981).
[Crossref]

Weber, M. J.

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive Index of glasses and crystals,” Opt. Eng. 17, 463 (1978).

Appl. Phys. Lett. (1)

E. S. Bliss, D. R. Speck, W. W. Simmons, “Direct interferometric measurements of the nonlinear refractive index coefficient n2 in laser materials,” Appl. Phys. Lett. 25, 728 (1974).
[Crossref]

IEEE J. Quantum Electron. (3)

W. W. Simmons, J. T. Hunt, W. E. Warren, “Light propagation through large laser systems,” IEEE J. Quantum Electron. QE-17, 1727 (1981).
[Crossref]

J. T. Fournier, E. Snitzer, “The nonlinear refractive index of glass,” IEEE J. Quantum Electron. QE-10, 473 (1974).
[Crossref]

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978).
[Crossref]

Laser J. (Jiguang) (1)

Gan Fu-Xi, Lin Fen-Ying, “Nonlinear refractive index for glass and methods for its calculation,” Laser J. (Jiguang) 6, 12 (1979) (in Chinese).

Opt. Eng. (2)

M. J. Weber, D. Milam, W. L. Smith, “Nonlinear refractive Index of glasses and crystals,” Opt. Eng. 17, 463 (1978).

T. Y. Chang, “Fast self-induced refractive index changes in optical media: a survey,” Opt. Eng. 20, 220 (1981).

Phys. Rev. (1)

S. A. Jha, N. Bloembergen, “Nonlinear optical susceptibilities in group IV and III–V semiconductors,” Phys. Rev. 171, 891 (1968).
[Crossref]

Phys. Rev. B (1)

C. C. Wang, “Empirical relation between the linear and the third-order nonlinear susceptibilities,” Phys. Rev. B 2, 2045 (1970).
[Crossref]

Phys. Rev. B. (1)

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B. 17, 4620 (1978).
[Crossref]

Phys. Today (1)

J. H. Nuckolls, “The feasibility of inertial-confinement fusion,” Phys. Today 35(9), 25 (1982).
[Crossref]

Prog. Quantum Electron. (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 56 (1977).

Sov. Phys. JETP (1)

A. P. Veduta, B. P. Kirsanov, “Variation of the refractive index of liquids and glasses in a high intensity field of a ruby laser,” Sov. Phys. JETP 27, 736 (1968).

Other (5)

A. J. Glass, KMS Fusion, Inc., P.O. Box 1567, Ann Arbor, Michigan 48106 (personal communication).

J. Duthler, M. Sparks, “Theoretical studies of high-power ultraviolet and infrared materials,” Fifth Tech. Rep. (Xonics, Inc., 1333 Ocean Avenue, Santa Monica, California 90401, 1975).

D. A. B. Miller, “Nonlinear optical effects in InSb with a cw CO laser,” Ph.D. Thesis (Heriot-Watt University, Edinburgh, U.K., 1979).

N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1977).

W. L. Smith, “Absoslute two-photon absorption coefficient at 355 nm in UV glasses,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), Postdeadline paper ThB21.

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Figures (1)

Fig. 1
Fig. 1

Experimental layout for interferometrically measuring the nonlinear refractive index. BS1 and BS2, bare silicssa beam splitters; BS3, 50–50 beam splitter; M1, kinematically mounted, removable mirror; L1 and L2, imaging lenses; ND, optical density filters.

Tables (1)

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Table 1 Nonlinear Refractive-Index Coefficienta

Equations (5)

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Δ ϕ = 2 π ( γ I / λ 0 ) Δ z ,
γ = Δ m λ 0 / [ 0 L I 1 ( z ) d z + 0 L I 2 ( z ) d z ] ,
γ = Δ m λ 0 β ln { 1 + T I 0 [ 1 exp ( α L ) ] [ 1 + T 2 exp ( α L ) ] β / α } .
γ = Δ m λ 0 / T ( 1 + T 2 ) I 0 L .
I 0 = 2 ( ln 2 / π ) 1 / 2 ( Γ 0 / τ ) .

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