Abstract

We analyze the operable angle range of the c axis and the incident angle of the input beam in the beam-fanning novelty filter (BFNF). With Fourier transforms we show the analysis method for the beam-fanning phenomenon. We investigate the beam-fanning phenomenon for not only the c axis but also the incident angle of the input beam in order to operate the BFNF sufficiently. Consequently, we clarify the angle range of the c axis and the incident angle, from which sufficient strong beam-fanning effect can be obtained to operate the BFNF. In addition, we verify the numerical results experimentally.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, ed., Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  2. D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
    [CrossRef]
  3. H. Rehn, R. Kowarschik, K. H. Ringhofer, “Beam-fanning novelty filter with enhanced dynamic phase resolution,” Appl. Opt. 34, 4907–4911 (1995).
    [CrossRef] [PubMed]
  4. J. E. Ford, Y. Fainman, S. H. Lee, “Time-integrating interferometry using photorefractive fanout,” Opt. Lett. 13, 856–858 (1988).
    [CrossRef] [PubMed]
  5. M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
    [CrossRef]
  6. A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
    [CrossRef]
  7. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
    [CrossRef]
  8. A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
    [CrossRef] [PubMed]
  9. Y.-H. Hong, P. Xie, J.-H. Dai, Y. Zhu, H.-G. Yang, H.-J. Zhang, “Fanning effects in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).
    [CrossRef] [PubMed]
  10. M. Segav, D. Engin, A. Yariv, G. C. Valley, “Temporal evolution of fanning in photorefractive materials,” Opt. Lett. 18, 956–958 (1993).
    [CrossRef]
  11. J. W. Goodman, ed., Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).
  12. Y. Takayama, A. Okamoto, M. Saito, K. Sato, “Cross-polarized photorefractive four-wave mixing with extraordinary writing beams and an ordinary reading beam,” Appl. Opt. 37, 2967–2973 (1998).
    [CrossRef]

1998 (1)

1995 (2)

H. Rehn, R. Kowarschik, K. H. Ringhofer, “Beam-fanning novelty filter with enhanced dynamic phase resolution,” Appl. Opt. 34, 4907–4911 (1995).
[CrossRef] [PubMed]

M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[CrossRef]

1994 (1)

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

1993 (3)

1989 (1)

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

1988 (1)

1982 (1)

Anderson, D. Z.

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Dai, J.-H.

Denz, C.

M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[CrossRef]

Engin, D.

Fainman, Y.

Feinberg, J.

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
[CrossRef]

Ford, J. E.

Hong, Y.-H.

Kowarschik, R.

Lee, S. H.

Okamoto, A.

Rauch, T.

M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[CrossRef]

Rehn, H.

Ringhofer, K. H.

Saffman, M.

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

Saito, M.

Sato, K.

Sedlatschek, M.

M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[CrossRef]

Segav, M.

Takayama, Y.

Tschdi, T.

M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[CrossRef]

Valley, G. C.

Xie, P.

Yang, H.-G.

Yariv, A.

Zhang, H.-J.

Zhu, Y.

Zozulya, A. A.

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Opt. Mater. (1)

M. Sedlatschek, T. Rauch, C. Denz, T. Tschdi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

Other (2)

J. W. Goodman, ed., Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

P. Yeh, ed., Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Optical configuration of the BFNF.

Fig. 2
Fig. 2

Effect of the beam-fanning phenomenon in the BFNF: (a) initial state, (b) steady state in the case of the strong beam-fanning effect, (c) initial state in the case the image varies, (d) steady state of (c), and (e) the case of the weak beam-fanning effect.

Fig. 3
Fig. 3

Geometry of the Fourier analysis.

Fig. 4
Fig. 4

Spectrum distribution of the beam and the threshold for the bright and dark states.

Fig. 5
Fig. 5

Optical configuration in which the input beam is perpendicularly turned on the crystal.

Fig. 6
Fig. 6

Property of the BFNF for the c axis: (a) 0° ≤ φ ≤ 45°, (b) 45° < φ ≤ 90°, (c) 90° < φ ≤ 135°, and (d) 135° < φ ≤ 180°. The solid transverse lines indicate threshold I TH.

Fig. 7
Fig. 7

Optical configuration with a 45°-cut BaTiO3 crystal.

Fig. 8
Fig. 8

Optical configuration with a 90°-cut BaTiO3 crystal.

Fig. 9
Fig. 9

Spectrum distributions of the beam in the steady state: (a) initial state, (b) φ = 45°: -60° ≤ Θ ≤ -10°, (c) φ = 45°: 0° ≤ Θ ≤ 60°, and (d) φ = 90°.

Fig. 10
Fig. 10

Experimental setup.

Fig. 11
Fig. 11

Comparison between the numerical and the experimental results: (a) numerical result and (b) experimental result.

Tables (2)

Tables Icon

Table 1 Parameters in Theoretical Analysis

Tables Icon

Table 2 Parameters in Experiment

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

Ay=- fqexpi2πqydq,
dfθdz=1I0-π/2π/2 γθ, θ|fθ|2dθfθ-i 2πq22ϕθ fθ,
γθ, θ=ωno3reffθ, θ2c cos θkgθ, θkBTe1+kg2θ, θkD2.
nθsinθ=sinΘ,
Ey, z=ω0ωzexp-ikz-ϕ-r21ω2z+ik2R,ω2z=ω021+λzπω022,R=z1+πω02λz,
ϕ=tan-1λzπω02,
Ey, 0, Θ=ω0ωy sin Θ exp-iky sin Θ-ϕ-y cos Θ21ω2y sin Θ+ik2R,ω2y sin Θ=ω021+λy sin Θπω02,R=y sin Θ1+πω02λy sin Θ,
ϕ=tan-1λy sin Θπω02.
2E-ωμ00˜s·R˜·Esc·˜sE=-iωμ0ρ-ω2μ00˜sE,
Ey, z=- fq, zeqexpi2πqy+iϕqzdq exp-iωt+c.c.
Escy, z=--Escq, qdqdq=-- Eaq, qexpikgq, q·rdqdq,
Iaq, q=fqf*qeq·eq,
Eaq, q=-i kg2q, qkBTe1+kg2q, qkD2Iaq, qI0.
2Ey, z=i2πq2+2iϕqz+iϕq2×- fqeqexpi2πqyexpiϕqzdq.
reffq, q=˜s·R˜·kgq, qkgq, q·˜no3,
γ0q, q=-ωno3reffq, qi kg2q, qkBTe1+kg2q, qkDeq·eq.
i2πq2+2iϕqz+iϕq2fqeqwxpiϕqz-1I0-- γ0q, qfqf*qexpiϕqzdqdq=-iωμ0ρ-ω2μ00˜sfqefexpiϕqz.
z fq=1I0-eTqγ0q, qeq2iϕq f*qfqdqfq-i 2πq22ϕq fq-ωμ0ρ2ϕq fq-12iϕq×ω2μ00˜s+iϕq2fq.
γq, q=eTqγ0q, qeq2iϕq
z fq=1I0- γq, qf*qfqdqfq-i 2πq22ϕq fq.

Metrics