Abstract

We propose and demonstrate an all-optical deflection switch with photorefractive duplex two-wave mixing (TWM) in which common grating is shared by the TWM of the two control beams and that of signal beams in a photorefractive crystal. TWM occurs both with the signal beams and with the control beams. By calculating the output intensities of the signal beams, we show that the output intensities of the signal beams are controllable by use of the phase difference of the control beams. We analyze the practical ratio of the intensities of the control beams to those of the signal beams for effective switching. A comparison of the numerical analysis with a basic experiment is given. Qualitative agreement is exhibited.

© 2001 Optical Society of America

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References

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  1. I.-C. Khoo, Y. Liang, and H. Li, “Coherent-beam amplification and polarization switching in a birefringent medium photorefractive crystal,” IEEE J. Quantum Electron. 28, 1816–1824 (1992).
    [CrossRef]
  2. M. Aguilar, M. Carrascosa, and F. Agulló-Lópex, “Optimization of selective erasure in photorefractive memories,” J. Opt. Soc. Am. B 14, 110–115 (1997).
    [CrossRef]
  3. G. C. Petrisor, A. A. Goldstein, B. Jenkins, E. J. Herbulock, and A. R. Tanguay, Jr., “Convergence of backward-error-propagation learning in photorefractive crystals,” Appl. Opt. 35, 1328–1342 (1996).
    [CrossRef] [PubMed]
  4. R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μm by two-wave mixing in InP:Fe,” Electron. Lett. 24, 360–362 (1988).
    [CrossRef]
  5. G. C. Valley, “Two-wave mixing with an applied field and a moving grating,” J. Opt. Soc. Am. B 1, 868–873 (1984).
    [CrossRef]
  6. C. Ozkul, G. Picoli, P. Gravey, and N. Wolffer, “High gain coherent amplification in thermally stabilized InP:Fe crystals under dc fields,” Appl. Opt. 29, 2711–2717 (1990).
    [CrossRef] [PubMed]
  7. G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
    [CrossRef]
  8. G. Picoli, P. Gravey, and C. Ozkul, “Model for resonant intensity dependence of photorefractive two-wave mixing in InP:Fe,” Opt. Lett. 14, 1362–1364 (1989).
    [CrossRef] [PubMed]
  9. M. Saito, A. Okamoto, Y. Takayama, and M. Takamura, “Phase matching property of cross polarized four wave mixing in BaTiO3 crystal and optical bus application,” in Proceedings of 1997 Topical Meeting on Photorefractive Materials, Effects and Devices (PR'97), D. Z. Anderson, M. Cronin-Golomb, and M. J. Damzem, eds. (Optical Society of America, Washington, D.C., 1997), pp. 204–207, paper WP28.
  10. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  11. S. Honma, A. Okamoto, and Y. Takayama, “All-optical photorefractive switch with phase difference between control beams,” in Advances in Photorefractive Materials, Effects, and Devices, P. E. Andersen, P. M. Johansen, H. C. Pedersen, P. M. Petersen, and M. Saffman, eds., Vol. 27 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 575–580.

1997 (1)

1996 (1)

1992 (1)

I.-C. Khoo, Y. Liang, and H. Li, “Coherent-beam amplification and polarization switching in a birefringent medium photorefractive crystal,” IEEE J. Quantum Electron. 28, 1816–1824 (1992).
[CrossRef]

1990 (1)

1989 (2)

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

G. Picoli, P. Gravey, and C. Ozkul, “Model for resonant intensity dependence of photorefractive two-wave mixing in InP:Fe,” Opt. Lett. 14, 1362–1364 (1989).
[CrossRef] [PubMed]

1988 (1)

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μm by two-wave mixing in InP:Fe,” Electron. Lett. 24, 360–362 (1988).
[CrossRef]

1984 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Aguilar, M.

Agulló-Lópex, F.

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μm by two-wave mixing in InP:Fe,” Electron. Lett. 24, 360–362 (1988).
[CrossRef]

Carrascosa, M.

Glass, A. M.

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μm by two-wave mixing in InP:Fe,” Electron. Lett. 24, 360–362 (1988).
[CrossRef]

Goldstein, A. A.

Gravey, P.

Herbulock, E. J.

Jenkins, B.

Khoo, I.-C.

I.-C. Khoo, Y. Liang, and H. Li, “Coherent-beam amplification and polarization switching in a birefringent medium photorefractive crystal,” IEEE J. Quantum Electron. 28, 1816–1824 (1992).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Li, H.

I.-C. Khoo, Y. Liang, and H. Li, “Coherent-beam amplification and polarization switching in a birefringent medium photorefractive crystal,” IEEE J. Quantum Electron. 28, 1816–1824 (1992).
[CrossRef]

Liang, Y.

I.-C. Khoo, Y. Liang, and H. Li, “Coherent-beam amplification and polarization switching in a birefringent medium photorefractive crystal,” IEEE J. Quantum Electron. 28, 1816–1824 (1992).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Olson, D. H.

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μm by two-wave mixing in InP:Fe,” Electron. Lett. 24, 360–362 (1988).
[CrossRef]

Ozkul, C.

Petrisor, G. C.

Picoli, G.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Tanguay Jr., A. R.

Valley, G. C.

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Wolffer, N.

Appl. Opt. (2)

Electron. Lett. (1)

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μm by two-wave mixing in InP:Fe,” Electron. Lett. 24, 360–362 (1988).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

I.-C. Khoo, Y. Liang, and H. Li, “Coherent-beam amplification and polarization switching in a birefringent medium photorefractive crystal,” IEEE J. Quantum Electron. 28, 1816–1824 (1992).
[CrossRef]

J. Appl. Phys. (1)

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Other (2)

M. Saito, A. Okamoto, Y. Takayama, and M. Takamura, “Phase matching property of cross polarized four wave mixing in BaTiO3 crystal and optical bus application,” in Proceedings of 1997 Topical Meeting on Photorefractive Materials, Effects and Devices (PR'97), D. Z. Anderson, M. Cronin-Golomb, and M. J. Damzem, eds. (Optical Society of America, Washington, D.C., 1997), pp. 204–207, paper WP28.

S. Honma, A. Okamoto, and Y. Takayama, “All-optical photorefractive switch with phase difference between control beams,” in Advances in Photorefractive Materials, Effects, and Devices, P. E. Andersen, P. M. Johansen, H. C. Pedersen, P. M. Petersen, and M. Saffman, eds., Vol. 27 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 575–580.

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Figures (11)

Fig. 1
Fig. 1

Optical geometry of two-wave mixing. Aj(j=12) denotes the complex field amplitude. The c axis is the crystal axis.

Fig. 2
Fig. 2

(a) Interaction of the beams in TWM when the special phase shift between the interference pattern and the refractive-index variation is π/2. A1*, which is the sum of transmitted beam A1 and diffracted beam A2, becomes small. A2*, which is the sum of transmitted beam A2 and diffracted beam A1, becomes large. Then the energy of A1 is transferred to A2*. (b) The spatial phase shift between the interference pattern and the refractive index variation.

Fig. 3
Fig. 3

(a) Interaction of the beams in TWM when the special phase shift between the interference pattern and the refractive-index variation is 3π/2. A1* becomes large. A2*, which is the sum of transmitted beam A2 and diffracted beam A1, becomes small. Then the energy of A2 is transferred to A1*. (b) Spatial phase shift between the interference pattern and the refractive-index variation.

Fig. 4
Fig. 4

Optical geometry of PR CPD TWM. The z axis is the interaction direction. A1 and A2 are ordinary rays. A3 and A4 are extraordinary rays. The TWM of the ordinary rays and the TWM of the extraordinary rays overlap to share common a photorefractive index grating.

Fig. 5
Fig. 5

Interference patterns Iog and Ieg of the ordinary rays and the extraordinary rays, respectively, total intensity pattern Itotal=Iog+Ieg, and refractive-index variation Δn, as indicated by continuous curves for ϕ1-2=ϕ3-4. The dashed curves indicate the situation when ϕ1-2 deviates from ϕ3-4.

Fig. 6
Fig. 6

Optical setup for the all-optical deflection switch. The abbreviations are defined in text.

Fig. 7
Fig. 7

Output intensity of the signal beams typical incident intensities of the control beams: (a) m=0.1;Is1(L) and Is2(L) are almost independent of ΔϕC(0). (b) m=1; each grating written by the control beams and by the signal beams cancels the other out when ΔϕC(0)=π.(c)m=10; the ratio of IS1(L) to IS2(L) can be well controlled by ΔϕC(0).

Fig. 8
Fig. 8

Output intensity of the signal beams for the phase difference of the control beams in case of γSL=3.5 with m=10.

Fig. 9
Fig. 9

Experimental setup for the all-optical defection switch.

Fig. 10
Fig. 10

Theoretical results for output intensities of the signal beams: (a) m=0.1, (b) m=1, (c) m=10.

Fig. 11
Fig. 11

Experimental results for output intensities of the signal beams: (a) m=0.1, (b) m=1, (c) m=10.

Tables (1)

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Table 1 Values of Parameters of the Experiment

Equations (19)

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kS1=ωcnS1[(sin θS1)xˆ+(cos θS1)zˆ],
kS2=ωcnS2[(-sin θS2)xˆ+(cos θS2)zˆ],
kC1=ωcnC1[(sin θC1)xˆ+(cos θC1)zˆ],
kC2=ωcnC2[(-sin θC2)xˆ+(cos θC2)zˆ],
nS1=cos(α-θS1)no2+sin(α-θS1)ne2-1/2,
nS2=cos(α+θS2)no2+sin(α+θS2)ne2-1/2,
nC1=nC2=no,
Δk=(kC1-kC2)-(kS1-kS2).
Δkx=ωc[nC1 sin θC1+nC2 sin θC2-nS1 sin θS1-nS2 sin θS2],
Δkz=ωc[nC1 cos θC1-nC2 cos θC2-nS1 cos θS1+nS2 cos θS2],
zIS1=2γSI0[IS1IS2+(IS1IS2IC1IC2)1/2 cos Φ],
zIS2=-2γSI0[IS1IS2+(IS1IS2IC1IC2)1/2 cos Φ],
zIC1=2γCI0[IC1IC2+(IS1IS2IC1IC2)1/2 cos Φ],
zIC2=2γCI0[IC1IC2+(IS1IS2IC1IC2)1/2 cos Φ],
zΔϕS=γSI0IC1IC2[(IS2/IS1)1/2-(IS1/IS2)1/2]sin Φ,
zΔϕC=γCI0IS1IS2[(IC2/IC1)1/2-(IC1/IC2)1/2]sin Φ,
ΔϕS=ϕS1-ϕS2,
ΔϕC=ϕC1-ϕC2,
Φ=ΔϕC-ΔϕS.

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