Abstract

The efficiency of optooptical light deflection by nondegenerate four-wave mixing can be increased significantly by placing the grating in a resonant cavity. Theory and experiment are presented for linear and ring cavities. Efficiency improvement by an order of magnitude is predicted, and improvements by a factor of 5.6 have been demonstrated.

© 1988 Optical Society of America

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References

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  1. A. Marrackhi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy in Two-Wave Mixing Experiments with Bi12SiO20 Crystals,” Appl. Phys. 24, 131 (1981).
    [CrossRef]
  2. E. Voit, C. Zaldo, P. N. Gunter, “Optically Induced Variable Light Deflection by Anisotropic Bragg Diffraction in Photorefractive KNbO3,” Opt. Lett. 11, 309 (1986).
    [CrossRef] [PubMed]
  3. J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).
  4. S. A. Collins, “Optical Interconnects Using Resonated Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper ME5.
  5. A. Yariv, P. Yeh, Optical Waves In Crystals (Wiley, New York, 1984), Chap. 6.
  6. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 10.
  7. P. D. Henshaw, “Laser Beam Steering Using the Photorefractive Effect,” Appl. Opt. 21, 2323 (1981).
    [CrossRef]
  8. G. T. Sincerbox, G. Roosen, “Opto-Optical Light Deflection,” Appl. Opt. 22, 690 (1983).
    [CrossRef] [PubMed]
  9. G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
    [CrossRef]
  10. G. Roosen, M. T. Plantegenest, “Prediction and Experimental Demonstration of High Angular Deviations Through Opto-Optical Light Deflection Technique,” Opt. Commun. 47, 358 (1983).
    [CrossRef]

1986

E. Voit, C. Zaldo, P. N. Gunter, “Optically Induced Variable Light Deflection by Anisotropic Bragg Diffraction in Photorefractive KNbO3,” Opt. Lett. 11, 309 (1986).
[CrossRef] [PubMed]

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

1983

G. Roosen, M. T. Plantegenest, “Prediction and Experimental Demonstration of High Angular Deviations Through Opto-Optical Light Deflection Technique,” Opt. Commun. 47, 358 (1983).
[CrossRef]

G. T. Sincerbox, G. Roosen, “Opto-Optical Light Deflection,” Appl. Opt. 22, 690 (1983).
[CrossRef] [PubMed]

1981

A. Marrackhi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy in Two-Wave Mixing Experiments with Bi12SiO20 Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

P. D. Henshaw, “Laser Beam Steering Using the Photorefractive Effect,” Appl. Opt. 21, 2323 (1981).
[CrossRef]

Bassat, J. M.

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

Collins, S. A.

S. A. Collins, “Optical Interconnects Using Resonated Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper ME5.

Delboulbe, A.

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

Gunter, P.

A. Marrackhi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy in Two-Wave Mixing Experiments with Bi12SiO20 Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

Gunter, P. N.

Henshaw, P. D.

Herriau, J. P.

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

Huignard, J. P.

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

A. Marrackhi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy in Two-Wave Mixing Experiments with Bi12SiO20 Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

Launay, J. C.

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

Marrackhi, A.

A. Marrackhi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy in Two-Wave Mixing Experiments with Bi12SiO20 Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

Pauliat, G.

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

Plantegenest, M. T.

G. Roosen, M. T. Plantegenest, “Prediction and Experimental Demonstration of High Angular Deviations Through Opto-Optical Light Deflection Technique,” Opt. Commun. 47, 358 (1983).
[CrossRef]

Rojas, D.

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

Roosen, G.

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

G. Roosen, M. T. Plantegenest, “Prediction and Experimental Demonstration of High Angular Deviations Through Opto-Optical Light Deflection Technique,” Opt. Commun. 47, 358 (1983).
[CrossRef]

G. T. Sincerbox, G. Roosen, “Opto-Optical Light Deflection,” Appl. Opt. 22, 690 (1983).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 10.

Sincerbox, G. T.

Voit, E.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves In Crystals (Wiley, New York, 1984), Chap. 6.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves In Crystals (Wiley, New York, 1984), Chap. 6.

Zaldo, C.

Appl. Opt.

Appl. Phys.

A. Marrackhi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy in Two-Wave Mixing Experiments with Bi12SiO20 Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

Ferroelectrics

J. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, J. C. Launay, “Highly Efficient Diffraction in Photorefractive BSO–BGO Crystals at Large Applied Fields,” Ferroelectrics 66, 1 (1986).

J. Opt. Soc. Am B

G. Pauliat, J. P. Herriau, A. Delboulbe, G. Roosen, J. P. Huignard, “Dynamic Beam Deflection Using Photorefractive Gratings in Bi12SiO20 Crystals,” J. Opt. Soc. Am B 3, 306 (1986).
[CrossRef]

Opt. Commun.

G. Roosen, M. T. Plantegenest, “Prediction and Experimental Demonstration of High Angular Deviations Through Opto-Optical Light Deflection Technique,” Opt. Commun. 47, 358 (1983).
[CrossRef]

Opt. Lett.

Other

S. A. Collins, “Optical Interconnects Using Resonated Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper ME5.

A. Yariv, P. Yeh, Optical Waves In Crystals (Wiley, New York, 1984), Chap. 6.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 10.

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Figures (8)

Fig. 1
Fig. 1

Enhanced optooptical light deflection using a linear cavity. The dashed lines are the signal beam; the solid lines are control beams.

Fig. 2
Fig. 2

Linear cavity showing the location of the various E fields used in the analysis.

Fig. 3
Fig. 3

Experimental layout.

Fig. 4
Fig. 4

Oscilloscope traces showing the experimental results for the linear cavity: upper trace, cavity output showing two cavity longitudinal modes; lower trace, sawtooth voltage applied to the piezoelectric mirror mount.

Fig. 5
Fig. 5

Ring cavity resonator. The dashed lines are the signal beam paths; the solid lines are the control beam paths.

Fig. 6
Fig. 6

Ring cavity showing the location of the various E fields used in the analysis.

Fig. 7
Fig. 7

Oscilloscope traces showing the experimental results for the ring cavity: upper trace, cavity output showing two cavity longitudinal modes; lower trace, sawtooth voltage applied to the piezoelectric mirror mount.

Fig. 8
Fig. 8

Confocal resonator for enhanced efficiency beam steering. The mirror radii and mirror spacing are equal. The dashed lines are the beam path of the signal beam. The fixed gratings maintain the Bragg condition as λc is varied as per Ref. 10.

Equations (25)

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E out = T E 1 ,
E 2 = R E 1 ,
E 3 = E 2 exp ( i k s l 1 )
E 4 = 1 ν E 3 i ν E i ,
E 5 = 1 Δ E 4 exp ( 2 i k s l 2 ) ,
E 6 = 1 ν E 5 ,
E 1 = E 6 exp ( i k s l 1 ) ,
E t = 1 ν E i i ν E 3 ,
E r = i ν E 5 .
E i = i ν ( l ν ) ( l Δ ) E i exp [ i k s ( 2 l 2 + l 1 ) ] 1 ( 1 ν ) R ( 1 Δ ) exp [ 2 i k s ( l 1 + l 2 ) ] .
I 0 I i = T ν ( 1 ν ) ( 1 Δ ) [ 1 ( 1 ν ) ( 1 Δ ) R ] 2 .
R ( optimum ) = ( 1 Δ ) ( 1 ν ) 2 .
I t I i = ( 1 ν ) [ 1 R ( 1 Δ ) ] 2 [ 1 ( 1 ν ) R ( 1 Δ ) ] 2 .
I r I i = ν 2 [ 1 ( 1 ν ) R ( 1 Δ ) ] 2 .
F = 2 Π δ , δ = fractional round-trip loss = Δ + 2 ν + T .
E out = T E 1 ,
E 2 = R E 1 ,
E 3 = E 2 exp ( i k s l 1 ) ,
E 4 = 1 ν E 3 i ν E i ,
E 5 = 1 Δ E 4 exp ( i k s l 2 ) ,
E 1 = E 5 exp ( i k s l 3 ) ,
E t = i ν E 3 + 1 ν E i .
I O I i = T ν ( 1 Δ ) [ 1 ( 1 ν ) ( 1 Δ ) R ] 2 .
I t I i = [ 1 ν ( 1 Δ ) R ] 2 [ 1 ( 1 ν ) ( 1 Δ ) R ] 2 .
F = 2 Π δ , δ = Δ + ν + T .

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