Abstract

We monitor the induced phase change produced by a cascaded χ(2):χ(2) process in KTP near the phase-matching angle on a picosecond 1.06-μm-wavelength beam using the Z-scan technique. This nonlinear refraction is observed to change sign as the crystal is rotated through the phase-match angle in accordance with theory. This theory predicts the maximum small-signal effective nonlinear refractive index of n2eff±2×1014 cm2/W (±1 × 10−11 esu) for an angle detuning of ±5° from phase match for this 1-mm-thick crystal with a measured deff of 3.1 pm/V For a fixed phase mismatch, this n2eff scales linearly with length and as deff2; however, for the maximum n2eff the nonlinear phase distortion becomes sublinear with irradiance for phase shifts near π/4.

© 1992 Optical Society of America

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References

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  1. H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
    [CrossRef] [PubMed]
  2. P. C. M. Planken, H. J. Bakker, L. Kuipers, A. Lagendijk, J. Opt. Soc. Am. B 7, 2150 (1990).
    [CrossRef]
  3. R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
    [CrossRef]
  4. G. B. Altshuler, M. V. Inochkin, in Digest of Conference on Quantum Electronics (Optical Society of America, Washington, D.C., 1990), paper QWB6.
  5. N. R. Belashenkov, S. V Gagarskii, M. V. Inochkin, Opt. Spectrosc. 66, 806 (1989).
  6. J. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, E. W Van Stryland, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper MTT7.
  7. M. Sheik-Bahae, A. A. Said, E. W Van Stryland, Opt. Lett. 14, 955 (1989).
    [CrossRef] [PubMed]
  8. J. D. Bierlien, H. Vanherzeele, J. Opt. Soc. Am. B 6, 622 (1989).
    [CrossRef]
  9. R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
    [CrossRef]
  10. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  11. T. F. Carruthers, I. L. Duling, Opt. Lett. 15, 804 (1990).
    [CrossRef] [PubMed]

1991 (1)

1990 (5)

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

P. C. M. Planken, H. J. Bakker, L. Kuipers, A. Lagendijk, J. Opt. Soc. Am. B 7, 2150 (1990).
[CrossRef]

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

T. F. Carruthers, I. L. Duling, Opt. Lett. 15, 804 (1990).
[CrossRef] [PubMed]

1989 (3)

Altshuler, G. B.

G. B. Altshuler, M. V. Inochkin, in Digest of Conference on Quantum Electronics (Optical Society of America, Washington, D.C., 1990), paper QWB6.

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

P. C. M. Planken, H. J. Bakker, L. Kuipers, A. Lagendijk, J. Opt. Soc. Am. B 7, 2150 (1990).
[CrossRef]

Belashenkov, N. R.

N. R. Belashenkov, S. V Gagarskii, M. V. Inochkin, Opt. Spectrosc. 66, 806 (1989).

Bierlien, J. D.

Byer, R. L.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

Carruthers, T. F.

Desalvo, J. R.

J. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, E. W Van Stryland, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper MTT7.

Duling, I. L.

Eckardt, R. C.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

Fan, Y. X.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

Gagarskii, S. V

N. R. Belashenkov, S. V Gagarskii, M. V. Inochkin, Opt. Spectrosc. 66, 806 (1989).

Graener, H.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, E. W Van Stryland, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper MTT7.

Inochkin, M. V.

N. R. Belashenkov, S. V Gagarskii, M. V. Inochkin, Opt. Spectrosc. 66, 806 (1989).

G. B. Altshuler, M. V. Inochkin, in Digest of Conference on Quantum Electronics (Optical Society of America, Washington, D.C., 1990), paper QWB6.

Kuipers, L.

P. C. M. Planken, H. J. Bakker, L. Kuipers, A. Lagendijk, J. Opt. Soc. Am. B 7, 2150 (1990).
[CrossRef]

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Laenen, R.

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

P. C. M. Planken, H. J. Bakker, L. Kuipers, A. Lagendijk, J. Opt. Soc. Am. B 7, 2150 (1990).
[CrossRef]

Laubereau, A.

Masuda, H.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

Planken, P. C. M.

P. C. M. Planken, H. J. Bakker, L. Kuipers, A. Lagendijk, J. Opt. Soc. Am. B 7, 2150 (1990).
[CrossRef]

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, E. W Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, E. W Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

J. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, E. W Van Stryland, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper MTT7.

Van Stryland, E. W

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, E. W Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

J. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, E. W Van Stryland, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper MTT7.

Vanherzeele, H.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, IEEE J. Quantum Electron. 26, 922 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (2)

Opt. Spectrosc. (1)

N. R. Belashenkov, S. V Gagarskii, M. V. Inochkin, Opt. Spectrosc. 66, 806 (1989).

Phys. Rev. A (1)

H. J. Bakker, P. C. M. Planken, L. Kuipers, A. Lagendijk, Phys. Rev. A 42, 4085 (1990).
[CrossRef] [PubMed]

Other (2)

J. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, E. W Van Stryland, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1990), paper MTT7.

G. B. Altshuler, M. V. Inochkin, in Digest of Conference on Quantum Electronics (Optical Society of America, Washington, D.C., 1990), paper QWB6.

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Figures (3)

Fig. 1
Fig. 1

Induced nonlinear phase shift versus Γ2L2 for several values of phase mismatch as calculated by the numerical solution of Eq. (4).

Fig. 2
Fig. 2

(a) Calculation of the depletion of the fundamental wave as a function of phase mismatch ΔkL. (b) Experimental measurement of the depletion of the fundamental beam versus ΔkL. (c) Calculation of nonlinear phase shift (ΔΦNL) as a function of ΔkL;. the dashed curve is the small conversion efficiency limit, and the solid curve is the exact solution of Eq. (4). (d) Experimental measurement of ΔTpυ as a function of ΔkL. as the crystal is rotated through its phase-matching angle.

Fig. 3
Fig. 3

Z scans showing positive ΔΦNL (circles) performed at ΔkL = −6 and negative ΔΦNL (triangles) performed at ΔkL = +6. The positive ΔΦNL is significantly larger owing to the positive contribution of n2 (Kerr).

Equations (7)

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d E 2 d z = i ω 2 c n 2 ω χ ( 2 ) ( 2 ω ; ω , ω ) E 1 E 1 exp ( i Δ k z ) ,
d E 1 d z = i ω 4 c n ω χ ( 2 ) ( ω ; 2 ω , ω ) E 2 E 1 * exp ( i Δ k z ) ,
Γ = ω d eff | E 0 | c n 2 ω n ω ,
d 2 E 1 d z 2 + i Δ k d E 1 d z Γ 2 ( 1 2 | E 1 / E 0 | 2 ) E 1 = 0 .
Δ Φ NL Δ k L 2 { 1 [ 1 + ( 2 Γ / Δ k ) 2 ] 1 / 2 } .
Δ Φ NL Γ 2 L 2 Δ k L ,
n 2 eff = 4 π c ε 0 L λ d eff 2 n 2 ω n ω 2 1 Δ k L .

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