Abstract

We show numerically and experimentally that second-harmonic generation in spatially nonsymmetrical structures can show a direction-dependent or nonreciprocal behavior under a variety of conditions.

© 1996 Optical Society of America

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  1. P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
    [CrossRef]
  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
  3. R. De Salvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 1 (1992).
    [CrossRef]
  4. M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
    [CrossRef] [PubMed]
  5. Y. Baek, R. Schiek, G. I. Stegeman, Opt. Lett. 20, 21 (1995).
    [CrossRef]
  6. D. J. Hagan, M. Sheik-Bahae, Z. Wang, G. I. Stegeman, E. W. Van Stryland, Opt. Lett. 19, 1305 (1994).
    [CrossRef] [PubMed]
  7. C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
    [CrossRef]
  8. R. Schiek, J. Opt. Soc. Am. B 10, 10 (1993).
    [CrossRef]
  9. P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
    [CrossRef]

1995 (3)

Y. Baek, R. Schiek, G. I. Stegeman, Opt. Lett. 20, 21 (1995).
[CrossRef]

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

1994 (1)

1993 (2)

1992 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).

Ashieri, P.

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

Baek, Y.

Y. Baek, R. Schiek, G. I. Stegeman, Opt. Lett. 20, 21 (1995).
[CrossRef]

Baldi, P.

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

Bierlein, J. D.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).

Bosshard, Ch.

De Micheli, M.

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

De Micheli, M. P.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

De Salvo, R.

Delacourt, D.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Hagan, D. J.

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Nouh, S.

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

Ostrowsky, D. B.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

Papuchon, M.

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Schiek, R.

Y. Baek, R. Schiek, G. I. Stegeman, Opt. Lett. 20, 21 (1995).
[CrossRef]

R. Schiek, J. Opt. Soc. Am. B 10, 10 (1993).
[CrossRef]

Sheik-Bahae, M.

Stegeman, G.

Stegeman, G. I.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

Y. Baek, R. Schiek, G. I. Stegeman, Opt. Lett. 20, 21 (1995).
[CrossRef]

D. J. Hagan, M. Sheik-Bahae, Z. Wang, G. I. Stegeman, E. W. Van Stryland, Opt. Lett. 19, 1305 (1994).
[CrossRef] [PubMed]

M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
[CrossRef] [PubMed]

Sundheimer, M. L.

Trevino-Palacios, C. G.

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

Van Stryland, E. W.

Wang, Z.

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Appl. Phys. Lett. (1)

C. G. Trevino-Palacios, G. I. Stegeman, M. P. De Micheli, P. Baldi, S. Nouh, D. B. Ostrowsky, D. Delacourt, M. Papuchon, Appl. Phys. Lett. 67, 2 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Baldi, P. Ashieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

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

R. Schiek, J. Opt. Soc. Am. B 10, 10 (1993).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. A 127, 1918 (1962).

Phys. Rev. Lett. (1)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Numerically calculated SHG detuning curves, showing the difference between forward (solid curves) and backward (dashed curves) propagation. Calculations were done in a structure with a discontinuity along the propagation direction at position L1 (inset), (a) 0.0 (uniform case), (b) 0.25L, (c) 0.50L, (d) 0.75L, and (e) L (uniform case). The vertical dashed lines show the position for phase matching on each region.

Fig. 2
Fig. 2

Wavelength scan of SHG in the LiNbO3 quasi-phase-matching waveguide, showing a nonreciprocal behavior in the high-depletion regime (ηmax = 39%) without (dashed curve) and with a layer of photoresist on half of the waveguide for forward (open circles) and backward (filled circles) propagation. Solid arrows show phase matching in the region without photoresist. Dashed arrows show the phase-matching peak induced by the photoresist layer.

Fig. 3
Fig. 3

SHG wavelength scan of the same waveguide in a low-depletion regime (ηmax = 0.8%). This figure shows the same characteristics as in Fig. 2, with some minor differences arising from power-dependent effects.

Fig. 4
Fig. 4

Theoretical curves (solid curves) fitted to the experimental high-power detuning curve (filled circles) from Fig. 2 for the case of (a) backward and (b) forward propagation. Complementary calculations [forward for (a) and backward for (b)] are shown as dashed curves for comparison. Parameters used are A0 = 1, L = 1, and ΔK = 5.65, with a change in nonlinear strength κ from 1 to 0.8 at L1 = 0.4L.

Equations (1)

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d A ω d z + i δ k ω ( z ) A ω = i κ ( z ) A 2 ω ( A ω ) * exp ( i Δ k 0 z ) , d A 2 ω d z + i δ k 2 ω ( z ) A 2 ω = i κ ( z ) ( A ω ) 2 exp ( + i Δ k 0 z ) .

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