Abstract

Based on the tensorial nature of second-order nonlinear susceptibilities, we show how two orthogonal field components at frequency ω can interact by means of the generated second harmonic, with a resulting coherent control of one onto the other. All-optical transistor operation and polarization switching are among the signal functions that can be implemented in properly oriented crystals.

© 1994 Optical Society of America

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  1. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17,28 (1992).
    [CrossRef] [PubMed]
  2. G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
    [CrossRef] [PubMed]
  3. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993).
    [CrossRef]
  4. M. I. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18,1397 (1993).
    [CrossRef] [PubMed]
  5. R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).
    [CrossRef]
  6. G. I. Stegeman, E. M. Wright, J. Opt. Quantum Electron. 22, 95 (1990); G. Assanto, in Guided Wave Nonlinear Optics, D. B. Ostrowsky, R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 257–284.
    [CrossRef]
  7. S. Trillo, S. Wabnitz, R. Chisari, G. Cappellini, Opt. Lett. 17, 637 (1992).
    [CrossRef] [PubMed]
  8. P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
    [CrossRef]
  9. D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, Opt. Lett. 19, 1305 (1994).
    [CrossRef] [PubMed]
  10. S. Trillo, G. Assanto, “Polarization spatial chaos in second harmonic generation,” Opt. Lett. (to be published).
  11. T. Suhara, H. Nishihara, IEEE J. Quantum Electron. 26, 1265 (1990).
    [CrossRef]
  12. D. H. Jundt, M. Fejer, R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).Li-rich lithium niobate allows for higher temperatures in noncritical phase matching.
    [CrossRef]
  13. G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
    [CrossRef]
  14. C. G. Krautschik, G. I. Stegeman, R. H. Stolen, Appl. Phys. Lett. 61, 1751 (1992); P. Ferro, S. Trillo, S. Wabnitz, Opt. Lett. 19, 263 (1994).
    [CrossRef] [PubMed]

1994

1993

1992

1990

T. Suhara, H. Nishihara, IEEE J. Quantum Electron. 26, 1265 (1990).
[CrossRef]

D. H. Jundt, M. Fejer, R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).Li-rich lithium niobate allows for higher temperatures in noncritical phase matching.
[CrossRef]

G. I. Stegeman, E. M. Wright, J. Opt. Quantum Electron. 22, 95 (1990); G. Assanto, in Guided Wave Nonlinear Optics, D. B. Ostrowsky, R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 257–284.
[CrossRef]

Assanto, G.

G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
[CrossRef]

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

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

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

S. Trillo, G. Assanto, “Polarization spatial chaos in second harmonic generation,” Opt. Lett. (to be published).

Bierlein, J. D.

Bosshard, Ch.

Byer, R. L.

D. H. Jundt, M. Fejer, R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).Li-rich lithium niobate allows for higher temperatures in noncritical phase matching.
[CrossRef]

Cappellini, G.

Chisari, R.

DeSalvo, R.

Fejer, M.

D. H. Jundt, M. Fejer, R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).Li-rich lithium niobate allows for higher temperatures in noncritical phase matching.
[CrossRef]

Hagan, D. J.

Jundt, D. H.

D. H. Jundt, M. Fejer, R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).Li-rich lithium niobate allows for higher temperatures in noncritical phase matching.
[CrossRef]

Krautschik, C. G.

C. G. Krautschik, G. I. Stegeman, R. H. Stolen, Appl. Phys. Lett. 61, 1751 (1992); P. Ferro, S. Trillo, S. Wabnitz, Opt. Lett. 19, 263 (1994).
[CrossRef] [PubMed]

Nishihara, H.

T. Suhara, H. Nishihara, IEEE J. Quantum Electron. 26, 1265 (1990).
[CrossRef]

Russell, P. St. J.

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

Schiek, R.

Sheik-Bahae, M.

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

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

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

C. G. Krautschik, G. I. Stegeman, R. H. Stolen, Appl. Phys. Lett. 61, 1751 (1992); P. Ferro, S. Trillo, S. Wabnitz, Opt. Lett. 19, 263 (1994).
[CrossRef] [PubMed]

G. I. Stegeman, E. M. Wright, J. Opt. Quantum Electron. 22, 95 (1990); G. Assanto, in Guided Wave Nonlinear Optics, D. B. Ostrowsky, R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 257–284.
[CrossRef]

Stolen, R. H.

C. G. Krautschik, G. I. Stegeman, R. H. Stolen, Appl. Phys. Lett. 61, 1751 (1992); P. Ferro, S. Trillo, S. Wabnitz, Opt. Lett. 19, 263 (1994).
[CrossRef] [PubMed]

Suhara, T.

T. Suhara, H. Nishihara, IEEE J. Quantum Electron. 26, 1265 (1990).
[CrossRef]

Sundheimer, M. I.

Torelli, I.

G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
[CrossRef]

Trillo, S.

G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
[CrossRef]

S. Trillo, S. Wabnitz, R. Chisari, G. Cappellini, Opt. Lett. 17, 637 (1992).
[CrossRef] [PubMed]

S. Trillo, G. Assanto, “Polarization spatial chaos in second harmonic generation,” Opt. Lett. (to be published).

Van Stryland, E.

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

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

Van Stryland, E. W.

Wabnitz, S.

Wang, Z.

Wright, E. M.

G. I. Stegeman, E. M. Wright, J. Opt. Quantum Electron. 22, 95 (1990); G. Assanto, in Guided Wave Nonlinear Optics, D. B. Ostrowsky, R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 257–284.
[CrossRef]

Appl. Phys. Lett.

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

C. G. Krautschik, G. I. Stegeman, R. H. Stolen, Appl. Phys. Lett. 61, 1751 (1992); P. Ferro, S. Trillo, S. Wabnitz, Opt. Lett. 19, 263 (1994).
[CrossRef] [PubMed]

Electron. Lett.

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

G. Assanto, I. Torelli, S. Trillo, Electron. Lett. 30, 733 (1994).
[CrossRef]

IEEE J. Quantum Electron.

T. Suhara, H. Nishihara, IEEE J. Quantum Electron. 26, 1265 (1990).
[CrossRef]

D. H. Jundt, M. Fejer, R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990).Li-rich lithium niobate allows for higher temperatures in noncritical phase matching.
[CrossRef]

J. Opt. Quantum Electron.

G. I. Stegeman, E. M. Wright, J. Opt. Quantum Electron. 22, 95 (1990); G. Assanto, in Guided Wave Nonlinear Optics, D. B. Ostrowsky, R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 257–284.
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Other

S. Trillo, G. Assanto, “Polarization spatial chaos in second harmonic generation,” Opt. Lett. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram elucidating all-optical transistor operation with two orthogonal coherent input waves of identical frequency. In general, amplitude or phase modulation of the weak beam translates into amplitude and phase modulation of both beams at the output, with energy interchange.

Fig. 2
Fig. 2

(a) Pump throughput versus fraction of input signal power and relative phase at the input; (b) pump [|A1(L)|2/|A1(0)|2; solid curve] and signal [|A2(L)|2/|A1(0)|2; dashed curve] throughputs and gain γ versus signal input for ϕ21 = 2π/5. Here k1= −1.40 = −k2 and ξ2 (L) = 5.0. [The input axis in (a) starts at 0.002 because a large pump transmission in |A2(0)|= 0 would hide the remaining part of the picture.]

Fig. 3
Fig. 3

(a) Signal throughput versus signal squared modulus and relative phase at the input; (b) signal [|A2(L)|2/|A1(0)|2; solid curve] and pump [|A1(L)|2/|A1(0)|2; dashed curve] throughputs and gain γ versus signal input for ϕ21 = 2π/5. Here k1 = 0.36, k2 = 1.81, and ξ2(L) = 3.0.

Fig. 4
Fig. 4

Polarization switching: graph of normalized ω throughputs |Ai(L)|2/[|A1(0)|2 + =|A2(0)|2, i =1,2 in pump (solid curve) and signal (dashed curve) polarizations versus relative phase changes about a bias of ϕ21 = 0.87π. Parameters are as in Fig. 2, with |A2(0)|2/|A1(0)|2 = 0.05.

Equations (1)

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- i d A j d ξ = χ j A j * B - k j 2 A j , - i d B d ξ = χ 1 A 1 2 + χ 2 A 2 2 ,             j = 1 , 2 ,

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