Abstract

We observe two-photon absorption (2PA) of picosecond, 0.6-μm, 0.3-nJ pulses in a 0.4-μm film of ZnSe. We use high-frequency-modulation phase-sensitive detection to be near the shot-noise limit combined with a low-frequency pulse-delay modulation to discriminate against large thermal nohlinearities. This dual-modulation technique, combined with the field enhancement produced by placing the film in a resonant cavity, permits observation of 2PA and other fast nonlinearities by using pulses having peak powers of the order of 1 W.

© 1988 Optical Society of America

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  1. F. V. Karpushko, G. V. Sinitsyn, J. Appl. Spectrosk. (USSR) 29, 1323 (1978);see also S. D. Smith, J. G. H. Mathew, M. R. Taghizadeh, A. C. Walker, B. S. Wherrett, A. Hendry, Opt. Commun. 51, 357 (1984).
    [CrossRef]
  2. B. F. Levine, C. G. Bethea, Appl Phys. Lett. 36, 245 (1980).
    [CrossRef]
  3. B. F. Levine, C. V. Shank, J. P. Heritage, IEEE J. Quantum Electron. QE-15, 1418 (1979).
    [CrossRef]
  4. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).
  5. J.-C. Diels, E. W. Van Stryland, G. Benedict, Opt. Commun. 25, 93 (1979);J.-C. Diels, E. W. Van Stryland, D. Gold, in Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978), pp. 117–128.
    [CrossRef]

1985 (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

1980 (1)

B. F. Levine, C. G. Bethea, Appl Phys. Lett. 36, 245 (1980).
[CrossRef]

1979 (2)

B. F. Levine, C. V. Shank, J. P. Heritage, IEEE J. Quantum Electron. QE-15, 1418 (1979).
[CrossRef]

J.-C. Diels, E. W. Van Stryland, G. Benedict, Opt. Commun. 25, 93 (1979);J.-C. Diels, E. W. Van Stryland, D. Gold, in Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978), pp. 117–128.
[CrossRef]

1978 (1)

F. V. Karpushko, G. V. Sinitsyn, J. Appl. Spectrosk. (USSR) 29, 1323 (1978);see also S. D. Smith, J. G. H. Mathew, M. R. Taghizadeh, A. C. Walker, B. S. Wherrett, A. Hendry, Opt. Commun. 51, 357 (1984).
[CrossRef]

Benedict, G.

J.-C. Diels, E. W. Van Stryland, G. Benedict, Opt. Commun. 25, 93 (1979);J.-C. Diels, E. W. Van Stryland, D. Gold, in Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978), pp. 117–128.
[CrossRef]

Bethea, C. G.

B. F. Levine, C. G. Bethea, Appl Phys. Lett. 36, 245 (1980).
[CrossRef]

Boggess, T. F.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Diels, J.-C.

J.-C. Diels, E. W. Van Stryland, G. Benedict, Opt. Commun. 25, 93 (1979);J.-C. Diels, E. W. Van Stryland, D. Gold, in Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978), pp. 117–128.
[CrossRef]

Guha, S.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Heritage, J. P.

B. F. Levine, C. V. Shank, J. P. Heritage, IEEE J. Quantum Electron. QE-15, 1418 (1979).
[CrossRef]

Karpushko, F. V.

F. V. Karpushko, G. V. Sinitsyn, J. Appl. Spectrosk. (USSR) 29, 1323 (1978);see also S. D. Smith, J. G. H. Mathew, M. R. Taghizadeh, A. C. Walker, B. S. Wherrett, A. Hendry, Opt. Commun. 51, 357 (1984).
[CrossRef]

Levine, B. F.

B. F. Levine, C. G. Bethea, Appl Phys. Lett. 36, 245 (1980).
[CrossRef]

B. F. Levine, C. V. Shank, J. P. Heritage, IEEE J. Quantum Electron. QE-15, 1418 (1979).
[CrossRef]

Shank, C. V.

B. F. Levine, C. V. Shank, J. P. Heritage, IEEE J. Quantum Electron. QE-15, 1418 (1979).
[CrossRef]

Sinitsyn, G. V.

F. V. Karpushko, G. V. Sinitsyn, J. Appl. Spectrosk. (USSR) 29, 1323 (1978);see also S. D. Smith, J. G. H. Mathew, M. R. Taghizadeh, A. C. Walker, B. S. Wherrett, A. Hendry, Opt. Commun. 51, 357 (1984).
[CrossRef]

Smirl, A. L.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Soileau, M. J.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Van Stryland, E. W.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

J.-C. Diels, E. W. Van Stryland, G. Benedict, Opt. Commun. 25, 93 (1979);J.-C. Diels, E. W. Van Stryland, D. Gold, in Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978), pp. 117–128.
[CrossRef]

Vanherzeele, H.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Appl Phys. Lett. (1)

B. F. Levine, C. G. Bethea, Appl Phys. Lett. 36, 245 (1980).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. F. Levine, C. V. Shank, J. P. Heritage, IEEE J. Quantum Electron. QE-15, 1418 (1979).
[CrossRef]

J. Appl. Spectrosk. (USSR) (1)

F. V. Karpushko, G. V. Sinitsyn, J. Appl. Spectrosk. (USSR) 29, 1323 (1978);see also S. D. Smith, J. G. H. Mathew, M. R. Taghizadeh, A. C. Walker, B. S. Wherrett, A. Hendry, Opt. Commun. 51, 357 (1984).
[CrossRef]

Opt. Commun. (1)

J.-C. Diels, E. W. Van Stryland, G. Benedict, Opt. Commun. 25, 93 (1979);J.-C. Diels, E. W. Van Stryland, D. Gold, in Picosecond Phenomena, C. V. Shank, E. P. Ippen, S. L. Shapiro, eds. (Springer-Verlag, Berlin, 1978), pp. 117–128.
[CrossRef]

Opt. Eng. (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

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Figures (6)

Fig. 1
Fig. 1

Dual-modulation experimental setup. A corner cube (CC) is mounted on an audio speaker used for obtaining pulse-delay modulation (PDM); s denotes the sample. The 10-MHz amplitude modulation is provided by an electro-optic modulator placed between polarizers.

Fig. 2
Fig. 2

The pulse-delay modulation signal (in arbitrary units) as a function of the power in the excitation beam.

Fig. 3
Fig. 3

Transmitted signal for the interference filter as a function of external angle of incidence (α in Fig. 4), for the nonlinear line shape (solid line) and for the cube of the linear line shape (dotted line).

Fig. 4
Fig. 4

Geometrical arrangement for measuring the angular dependence of the signal as in Fig. 3. The angle θ for Fig. 3 was fixed at ∼6°, and α was varied. The detectors labeled L and NL indicate that the linear and nonlinear transmitted signals can be monitored simultaneously.

Fig. 5
Fig. 5

Pulse-delay modulation signal as a function of time delay between pulses for the bulk ZnSe sample (solid line) and the ZnSe interference filter (dotted line).

Fig. 6
Fig. 6

(a) Fabry–Perot spacer layer, showing the probe and excitation beams along with their reflections, (b) Fields and propagation directions used for calculating Eqs. (A5).

Equations (14)

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Δ T = 2 β I e L 1 e α L α L e α L × ( 1 R 1 ) 2 ( 1 R 2 ) ( 1 + R 2 e α L ) ( 1 + R α ) ( 1 R α ) 5 τ p 2 τ e ,
Δ T IF Δ T B = I IF L IF I B L B .
P nl = K p ( p 2 + 2 e 2 + 2 p r 2 + 2 e r 2 ) ,
1 p p z = α 2 K [ p 2 + 2 e 2 + 2 p r 2 + 2 e r 2 ] ,
1 p r p r z = α 2 + K [ p r 2 + 2 e r 2 + 2 p 2 + 2 e 2 ] ,
E p ( z ) = p ( 0 ) exp [ ( i k p α 2 β 1 2 ) z ] , E p r ( z ) = p r ( 0 ) exp [ ( i k p + α 2 + β 2 2 ) z ] ,
β 1 = K ( 1 e α L ) α L { p 2 ( 0 ) + 2 e 2 ( 0 ) + 2 [ p r 2 ( 0 ) + e r 2 ( 0 ) ] e α L } ,
β 2 = K ( 1 e α L ) α L { [ p r 2 ( 0 ) + 2 e r 2 ( 0 ) ] e α L + 2 p 2 ( 0 ) + 2 e 2 ( 0 ) } .
E 1 E 1 = 1 D ( 1 R 1 n ) 1 / 2 , E 1 E 1 = X X r D [ R 2 ( 1 R 1 ) n ] 1 / 2 , E 2 E 1 = X D [ ( 1 R 1 ) ( 1 R 2 ) n 2 ] 1 / 2 , E 2 E 1 = X D ( 1 R 1 n ) 1 / 2 , E 2 E 1 = X D [ R 2 ( 1 R 1 ) n ] 1 / 2 , E 1 E 1 = 1 D [ X X r ( R 2 ) 1 / 2 ( R 1 ) 1 / 2 ] ,
I T = I p n 2 | E 2 E 1 | 2 = I p ( 1 R 1 ) ( 1 R 2 ) | X D | 2 .
I T = I p [ ( 1 R 1 ) ( 1 R 2 ) e α L ( 1 R α ) 2 ( 1 + F α sin 2 k p L ) ] × { 1 β 1 L ( β 1 + β 2 ) L R α [ 1 R α 2 sin 2 k p L ] ( 1 R α ) 2 ( 1 F α sin 2 k p L ) } ,
β 1 = β ( 1 R 1 ) ( 1 R α ) 2 1 e α L α L × [ I p ( 1 + 2 R 2 e α L ) τ p + 2 I e ( 1 + R 2 e α L ) τ e ] ,
β 2 = β ( 1 R 1 ) ( 1 R α ) 2 1 e α L α L × [ I p ( 2 + R 2 e α L ) τ p + 2 I e ( 1 + R 2 e α L ) τ e ] ,
Δ I p = I p 2 β I e L 1 e α L α L e α L × ( 1 R 1 ) 2 ( 1 R 2 ) ( 1 + R 2 e α L ) ( 1 + R α ) ( 1 R α ) 5 τ p 2 τ e .

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