Abstract

Nondegenerate four-wave mixing in a single-mode ridge waveguide has been demonstrated as a technique for simultaneous measurement of the imaginary component and the absolute magnitude of the third-order nonlinear susceptibility χ(3). In the same experimenal apparatus, Im χ(3)(ω2 = ω1 + ω2ω1) was obtained by measuring the pump-induced probe power loss and |χ(3)(ω3 = ω1 + ω1ω2)| was derived from Stokes wave generation efficiency. The ratio of these quantities was obtained without significant system uncertainties. The technique has been applied to AlGaAs/GaAs quantum-well waveguides with picosecond laser pulses. For ħω1ħω2 ≈ 1.43 eV, it was found that Im χ(3) = (6.1 ± 0.5) × 10−11 esu, |χ(3)| = (7.6 ± 1.7) × 10−11 esu with a system uncertainty of 25%, and Im χ(3)/|χ(3)| = 0.8 ± 31%, indicating the dominance of two-photon absorption.

© 1990 Optical Society of America

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References

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  1. For a general treatment of nonlinear guided-wave phenomena, see, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  2. G. M. Carter, Y. J. Chen, S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
    [Crossref]
  3. A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
    [Crossref]
  4. M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
    [Crossref]
  5. C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
    [Crossref]
  6. P. W. Smith, Bell Syst. Tech. J. 61, 1975 (1982).
  7. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, M. J. Andrejco, Opt. Lett. 14, 1140 (1989).
    [Crossref] [PubMed]
  8. H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
    [Crossref]
  9. H. Q. Le, H. K. Choi, C. A. Wang, Appl. Phys. Lett. 57, 212 (1990).
    [Crossref]
  10. R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron QE-18, 1062 (1982).
    [Crossref]

1990 (3)

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
[Crossref]

H. Q. Le, H. K. Choi, C. A. Wang, Appl. Phys. Lett. 57, 212 (1990).
[Crossref]

1989 (1)

1985 (1)

C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
[Crossref]

1983 (2)

G. M. Carter, Y. J. Chen, S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[Crossref]

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
[Crossref]

1982 (2)

P. W. Smith, Bell Syst. Tech. J. 61, 1975 (1982).

R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron QE-18, 1062 (1982).
[Crossref]

Agrawal, G. P.

For a general treatment of nonlinear guided-wave phenomena, see, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Anderson, K. K.

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

Andrejco, M. J.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron QE-18, 1062 (1982).
[Crossref]

Bossi, D. E.

H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
[Crossref]

Carter, G. M.

G. M. Carter, Y. J. Chen, S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[Crossref]

Chen, Y. J.

G. M. Carter, Y. J. Chen, S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[Crossref]

Choi, H. K.

H. Q. Le, H. K. Choi, C. A. Wang, Appl. Phys. Lett. 57, 212 (1990).
[Crossref]

DeLong, K. W.

Fujimoto, J.

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

Goodhue, W. D.

H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
[Crossref]

Haus, H. A.

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
[Crossref]

Ippen, E. P.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
[Crossref]

Karaguleff, C.

C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
[Crossref]

Lagasse, M. J.

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

Lattes, A.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
[Crossref]

Le, H. Q.

H. Q. Le, H. K. Choi, C. A. Wang, Appl. Phys. Lett. 57, 212 (1990).
[Crossref]

H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
[Crossref]

Leonberger, F. J.

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
[Crossref]

Mizrahi, V.

Nichols, K. B.

H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
[Crossref]

Saifi, M. A.

Seaton, C. T.

C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
[Crossref]

Smith, P. W.

P. W. Smith, Bell Syst. Tech. J. 61, 1975 (1982).

Stegeman, G. I.

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, M. J. Andrejco, Opt. Lett. 14, 1140 (1989).
[Crossref] [PubMed]

C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
[Crossref]

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron QE-18, 1062 (1982).
[Crossref]

Tripathy, S. K.

G. M. Carter, Y. J. Chen, S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[Crossref]

Wang, C. A.

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

H. Q. Le, H. K. Choi, C. A. Wang, Appl. Phys. Lett. 57, 212 (1990).
[Crossref]

Zanoni, R.

C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
[Crossref]

Appl. Phys. Lett. (5)

M. J. Lagasse, K. K. Anderson, C. A. Wang, H. A. Haus, J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[Crossref]

C. Karaguleff, G. I. Stegeman, R. Zanoni, C. T. Seaton, Appl. Phys. Lett. 47, 621 (1985).
[Crossref]

G. M. Carter, Y. J. Chen, S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[Crossref]

H. Q. Le, D. E. Bossi, K. B. Nichols, W. D. Goodhue, Appl. Phys. Lett. 56, 1008 (1990).
[Crossref]

H. Q. Le, H. K. Choi, C. A. Wang, Appl. Phys. Lett. 57, 212 (1990).
[Crossref]

Bell Syst. Tech. J. (1)

P. W. Smith, Bell Syst. Tech. J. 61, 1975 (1982).

IEEE J. Quantum Electron (2)

R. H. Stolen, J. E. Bjorkholm, IEEE J. Quantum Electron QE-18, 1062 (1982).
[Crossref]

A. Lattes, H. A. Haus, F. J. Leonberger, E. P. Ippen, IEEE J. Quantum Electron, QE-19, 1718 (1983).
[Crossref]

Opt. Lett. (1)

Other (1)

For a general treatment of nonlinear guided-wave phenomena, see, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental configuration for four-wave mixing in a single-mode ridge waveguide. The Al0.2Ga0.8As core layer contains four 9-nm-thick GaAs quantum wells. (b), (c) Numerically calculated near-field profile and far-field profile, respectively, for the vertical mode. The measured value for full width at half-maximum is indicated in (c).

Fig. 2
Fig. 2

Typical time-resolved response for (a) Stokes wave generation and (b), (c) pump-induced probe power losses at low and high pump powers, respectively. The long-lived tail in (c) is due to carriers.

Fig. 3
Fig. 3

(a) Pump-induced probe power loss and (b) Stokes wave conversion efficiency as functions of input pump pulse energy. The straight line in (a) and the quadratic curve in (b) are theoretical fits, indirectly yielding Im χ̄(3) and |χ̄(3)|, respectively.

Equations (14)

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P j ( z , t ̅ j ) = c 8 π n ( ω j ) | A j ( z , t ̅ j ) | 2 d x d y | F j ( x , y ) | 2 ;
A 1 z + α 2 A 1 = i β 11 | A 1 | 2 A 1 ,
A 2 * z + α 2 A 2 * = i ( 2 β 21 * | A 1 | 2 A 2 * + β 23 * A 1 * 2 A 3 e i Δ k z ) ,
A 3 z + α 2 A 3 = i ( 2 β 31 | A 1 | 2 A 3 + β 32 A 1 2 A 2 * e i Δ k z ) .
β i j = 3 π 2 λ i n i D i 2 d ρ F i ( ρ ) χ ( 3 ) : F 1 ( ρ ) F 1 ( ρ ) F j ( ρ ) ,
A 1 ( z , t ̅ ) = A 1 ( 0 , t ̅ ) exp [ 1 2 α z γ 1 φ ( z , t ̅ ) ] × exp [ i δ 1 φ ( z , t ̅ ) ] ,
A 2 ( z , t ̅ ) = A 2 ( 0 , t ̅ ) exp [ 1 2 α z 2 γ 2 φ ( z , t ̅ ) ] × exp [ 2 i δ 2 φ ( z , t ̅ ) ] ,
φ ( z , t ̅ ) = 1 2 γ 1 ln [ 1 + 2 γ 1 | A 1 ( 0 , t ̅ ) | 2 z ( 1 e α z α z ) ] | A 1 ( 0 , t ̅ ) | 2 z .
R [ Q 2 ( 0 ) e α z Q 2 ( z , τ ) ] 1 / 2 1 + [ Im χ ̅ ( 3 ) 8 π c n 1 Q 1 ( 0 ) D 1 2 T 1 ] × ( D 21 2 D 2 2 ) ( 6 π 2 z λ 2 n 2 ) ( 1 e α z α z ) U 1 ( τ ) ,
A 3 ( z , t ̅ ) = i β 32 A 2 * ( z , t ̅ ) exp [ 2 i ( β 21 * + β 31 ) φ ( z , t ̅ ) ] × 0 z d z | A 1 ( z , t ̅ ) | 2 exp { i [ ξ φ ( z , t ̅ ) + Δ k z ] } ,
| A 3 ( z , t ̅ ) | 2 = z 2 | β 32 A 1 2 ( 0 , t ̅ ) | 2 | A 2 * ( z , t ̅ ) | 2 G ( z , t ̅ ) ,
G ( z , t ̅ ) = e α ̂ z sin 2 ( Δ k ̂ z / 2 ) + ( 1 e α ̂ z ) 2 / 4 ( α ̂ z / 2 ) 2 + ( Δ k ̂ z / 2 ) 2 .
| A 3 ( z , t ̅ ) | 2 = | β 32 φ ( z , t ̅ ) | 2 [ sin δ 1 φ ( z , t ̅ ) δ 1 φ ( z , t ̅ ) ] 2 | A 2 * ( z , t ̅ ) | 2 .
η Q 3 ( z ) Q 2 ( z ) = [ | χ ̅ ( 3 ) | 8 π c n 1 Q 1 ( 0 ) D 1 2 T 1 ] 2 ( D 23 4 D 2 2 D 3 2 ) × ( 3 π 2 z λ 3 ) 2 1 n 2 n 3 U 2 ( τ ) G ( z ) ,

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