Abstract

The process of type II second-harmonic generation has been investigated theoretically. It is found that, unlike in the process of type I second-harmonic generation, phase matching is not necessary for a significant shift of the pump wave phase to be produced. The simple inequality of the intensities of interacting waves suffices for this effect to occur.

© 1994 Optical Society of America

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References

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  1. L. A. Ostrovsky, Pis’ma Zh. Eksp. Teor. Fiz. 5, 331 (1967).
  2. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
    [CrossRef]
  3. P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
    [CrossRef]
  4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, H. Vanherzeele, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  5. G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).
  6. F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), Chap. 2, p. 65.

1993 (2)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
[CrossRef]

P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

1992 (1)

1988 (1)

G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).

1967 (1)

L. A. Ostrovsky, Pis’ma Zh. Eksp. Teor. Fiz. 5, 331 (1967).

Assanto, G.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
[CrossRef]

Chuzakov, Yu. L.

G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).

DeSalvo, R.

Hagan, D. J.

Maslov, V. A.

G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).

Midwinter, J. E.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), Chap. 2, p. 65.

Ostrovsky, L. A.

L. A. Ostrovsky, Pis’ma Zh. Eksp. Teor. Fiz. 5, 331 (1967).

Polivanov, Yu. N.

G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).

Russell, P. St. J.

P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

Sheik-Bahae, M.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, H. Vanherzeele, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Stegeman, G. I.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, H. Vanherzeele, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Van Stryland, E. W.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, H. Vanherzeele, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

Vanherzeele, H.

Vshivcova, G. D.

G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).

Zernike, F.

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), Chap. 2, p. 65.

Appl. Phys. Lett. (1)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
[CrossRef]

Electron. Lett. (1)

P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

Fiz. Tverd. Tela (1)

G. D. Vshivcova, V. A. Maslov, Yu. N. Polivanov, Yu. L. Chuzakov, Fiz. Tverd. Tela 30, 3550 (1988).

Opt. Lett. (1)

Pis’ma Zh. Eksp. Teor. Fiz. (1)

L. A. Ostrovsky, Pis’ma Zh. Eksp. Teor. Fiz. 5, 331 (1967).

Other (1)

F. Zernike, J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), Chap. 2, p. 65.

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Figures (3)

Fig. 1
Fig. 1

Evolution of (a) the intensities and (b) the phases of two pump waves (dashed curves, wave 1; solid curve, wave 2) and the second-harmonic wave (dotted curves) for exact phase matching. The input intensities of the pump waves are unequal (P1 = 0.07 GW/cm2, P2 = 0.1 GW/cm2).

Fig. 2
Fig. 2

Evolution of (a) the intensities and (b) the phases of two pump waves (dashed curves, wave 1; solid curve, wave 2) and the second-harmonic wave (dotted curves) for exact phase matching. The input intensities of the pump waves are unequal (P1 = 0.05 GW/cm2, P2 = 0.1 GW/cm2).

Fig. 3
Fig. 3

Evolution of (a) the intensities and (b) the phases of two pump waves (dashed curves, wave 1; solid curves, wave 2) and the second-harmonic wave (dotted curves) for the case of nonzero wave-vector mismatch, Δk = 3 cm−1. The input intensities of the pump waves are unequal (P1 = 0.05 GW/cm2, P2 = 0.1 GW/cm2).

Equations (6)

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k 1 ( ω ) + k 2 ( ω ) = k 3 ( 2 ω ) , k 1 ( ω ) k 2 ( ω ) 1 2 k 3 ( 2 ω ) .
E 1 z = i ω 2 n 1 c χ ( 2 ) ( ω ; 2 ω , ω ) E 2 * E 3 exp ( i Δ kz ) , E 2 z = i ω 2 n 2 c χ ( 2 ) ( ω ; 2 ω , ω ) E 1 * E 3 exp ( i Δ kz ) , E 3 z = i 2 ω 2 n 3 c χ ( 2 ) ( 2 ω ; ω , ω ) E 1 E 2 exp ( i Δ kz ) ,
A i = E i ( n i 2 I 0 ε 0 μ 0 ) 1 / 2 ,
A 1 z = i Γ A 2 * A 3 exp ( i Δ kz ) , A 2 z = i Γ A 1 * A 3 exp ( i Δ kz ) , A 3 z = i 2 Γ A 1 A 2 exp ( i Δ kz ) ,
Γ = ω c d eff n 1 n 2 n 3 ( 2 I 0 μ 0 ε 0 ) 1 / 2 .
Δ | A 1 | 2 = Δ | A 2 | 2 = 1 2 Δ | A 3 | 2 ,

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