Abstract

A modified Mach–Zehnder interferometer has been built for measurement of nonlinear-optical susceptibilities in bulk materials. Both slow- and fast-intensity-dependent refractive-index changes can be measured in absolute value, with femtosecond time resolution, high sensitivity, and precision, by means of a new fringe-locking technique. Results on fast nonlinearities of CS2 liquid and glasses are presented.

© 1994 Optical Society of America

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References

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  1. S. R. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
    [CrossRef]
  2. J. M. Halbout and C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
    [CrossRef]
  3. M. J. Lagasse, D. Liu-Wong, J. G. Fujimoto, and H. A. Haus, Opt. Lett. 14, 317 (1989).
    [CrossRef]
  4. N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 6, 675 (1989).
    [CrossRef]
  5. K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 16, 1683 (1991).
    [CrossRef] [PubMed]
  6. J. L. Oudar, IEEE J. Quantum Electron. QE-19, 4 (1983).
  7. L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, “Nuclear dynamics via coherent effects in pump–probe experiments,” submitted to Opt. Commun.
  8. E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).
  9. L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
    [CrossRef]
  10. M. E. Lines, Phys. Rev. B. 41, 3372 (1990).
    [CrossRef]
  11. M. E. Lines, Phys. Rev. B 41, 3383 (1990).
    [CrossRef]
  12. M. E. Lines, Phys. Rev. B 43, 11478 (1991).
    [CrossRef]
  13. C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
    [CrossRef]

1994 (1)

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

1992 (1)

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

1991 (3)

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 16, 1683 (1991).
[CrossRef] [PubMed]

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

M. E. Lines, Phys. Rev. B 43, 11478 (1991).
[CrossRef]

1990 (2)

M. E. Lines, Phys. Rev. B. 41, 3372 (1990).
[CrossRef]

M. E. Lines, Phys. Rev. B 41, 3383 (1990).
[CrossRef]

1989 (2)

1987 (1)

S. R. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

1983 (1)

J. L. Oudar, IEEE J. Quantum Electron. QE-19, 4 (1983).

1982 (1)

J. M. Halbout and C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

Banyai, W. C.

Canioni, L.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, “Nuclear dynamics via coherent effects in pump–probe experiments,” submitted to Opt. Commun.

Ducasse, A.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, “Nuclear dynamics via coherent effects in pump–probe experiments,” submitted to Opt. Commun.

Duchesne, C.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

Fargin, E.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

Finlayson, N.

Friberg, S. R.

S. R. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

Fujimoto, J. G.

Halbout, J. M.

J. M. Halbout and C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

Haus, H. A.

Kobayashi, T.

Krol, D. M.

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Lagasse, M. J.

Le Flem, G.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

Lines, M. E.

M. E. Lines, Phys. Rev. B 43, 11478 (1991).
[CrossRef]

M. E. Lines, Phys. Rev. B. 41, 3372 (1990).
[CrossRef]

M. E. Lines, Phys. Rev. B 41, 3383 (1990).
[CrossRef]

Liu-Wong, D.

Minoshima, K.

Olazcuaga, R.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

Oudar, J. L.

J. L. Oudar, IEEE J. Quantum Electron. QE-19, 4 (1983).

Sarger, L.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, “Nuclear dynamics via coherent effects in pump–probe experiments,” submitted to Opt. Commun.

Seaton, C. T.

Segonds, P.

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, “Nuclear dynamics via coherent effects in pump–probe experiments,” submitted to Opt. Commun.

Smith, P. W.

S. R. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

Stegeman, G. I.

Taiji, M.

Tang, C. L.

J. M. Halbout and C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

Vogel, E. M.

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Weber, M. J.

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Appl. Phys. Lett. (1)

J. M. Halbout and C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. L. Oudar, IEEE J. Quantum Electron. QE-19, 4 (1983).

S. R. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

J. Non-Cryst. Solids (1)

C. Duchesne, E. Fargin, R. Olazcuaga, G. Le Flem, L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, J. Non-Cryst. Solids 168, 132 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Chem. Glasses (1)

E. M. Vogel, M. J. Weber, and D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Phys. Rev. B (2)

M. E. Lines, Phys. Rev. B 41, 3383 (1990).
[CrossRef]

M. E. Lines, Phys. Rev. B 43, 11478 (1991).
[CrossRef]

Phys. Rev. B. (1)

M. E. Lines, Phys. Rev. B. 41, 3372 (1990).
[CrossRef]

Solid State Commun. (1)

L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne, E. Fargin, R. Olazcuaga, and G. Le Flem, Solid State Commun. 84, 1065 (1992).
[CrossRef]

Other (1)

L. Canioni, L. Sarger, P. Segonds, and A. Ducasse, “Nuclear dynamics via coherent effects in pump–probe experiments,” submitted to Opt. Commun.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. D-I, D-II: Optical delays; GL1, GL2: Glan prisms; PZT1, PZT2: piezoelectric translators; EOM: electro-optic modulator; FTIR1, FTIR2: frustrated total internal reflectors; L1, L2: convergent lenses; CH1, CH2: signal and reference channels, respectively.

Fig. 2
Fig. 2

Time-resolved nonlinear phase shift in CS2 liquid. Nonlinear average response. Inset: absolute value with details of the dynamic curve displaying coherent nonlinear fringes.

Fig. 3
Fig. 3

Typical interferometric nonlinear response of a TiO2 glass. a, Average response; b, full signal, including coherent effects.

Tables (1)

Tables Icon

Table 1 Experimental Nonlinear Refractive Indices for Metal Oxide Glasses (TiO2)a

Equations (13)

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F = Δ n fast Δ n slow ,
E I = E 2 + E 1 exp ( i ϕ 12 ) exp ( i π ) + ( η E p ) exp ( i ϕ p 2 ) exp ( i π ) , E II = E 2 + E 1 exp ( i ϕ 12 ) + ( η E p ) exp ( i ϕ p 2 ) ,
I I = I 0 2 ( 1 + δ ϕ p 1 ) + η 2 I p + 1 2 n 0 ɛ 0 c ( η E p ) E 0 [ cos δ ϕ p + sin δ ϕ p ( 1 + δ ϕ p 1 ) ] , I II = I 0 2 ( 1 - δ ϕ p 1 ) + η 2 I p - 1 2 n 0 ɛ 0 c ( η E p ) E 0 [ cos δ ϕ p - sin δ ϕ p ( 1 - δ ϕ p 1 ) ] ,
Δ I = I 0 δ ϕ p 1 + n 0 ɛ 0 c ( η E p ) E 0 ( cos δ ϕ p ) ,
n - n 0 = Δ n ( t + τ ) = n 2 e I p ( t + τ ) + i n 2 ( i ) τ ( i ) - t + τ I p ( t ) exp [ - ( t + τ - t ) τ i ] d t .
d ( Δ I ) = 2 π λ [ - + Δ n ( r , z , t + τ ) I 0 ( r , z , t ) d t ] d s d z .
d ( Δ I ) = 2 π λ K ( τ ) I 0 ( r , z ) I p ( r , z ) d s d z .
I j ( r , z , t ) = { 2 P j c π exp [ - 2 r 2 w 2 ( z ) ] w 2 ( z ) } [ exp ( - t 2 τ j 2 ) ] ,
K ( τ ) π n 2 ( 1 ) τ ( 1 ) τ p τ s exp - τ τ ( 1 ) .
K ( τ ) = n 2 e ( τ p 2 + τ s 2 ) 1 / 2 τ s τ p π exp ( - τ 2 τ p 2 + τ s 2 ) .
V d = σ 2 K ( τ = 0 ) λ P p c P 0 c 0 - 1 / 2 + 1 / 2 l w 4 ( z ) × { exp [ - 4 r 2 w 2 ( z ) ] } 8 r d r d z ,
V d = σ K ( τ = 0 ) λ 2 P p c P 0 c 4 π arctan ( λ 1 2 π w 0 2 ) .
n 2 e = ( δ ϕ 1 p 1 ) λ 2 ( 1 + τ p 2 / τ s 2 ) 1 / 2 P p c 4 π arctan ( l λ 2 π w 0 2 ) .

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