Abstract

A numerical model is presented for the evaluation of the dielectric permittivity tensor changes as induced by guided modes during the formation of holographic gratings in arbitrary photorefractive graded-index planar waveguides. Comparisons among lithium niobate waveguides with different cuts and technology are shown.

© 2002 Optical Society of America

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References

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  1. V. E. Wood, P. J. Cressman, R. L. Holman and C. M. Verber, �??Photorefractive effects in waveguides�?? in Photorefractive Materials and their Applications II,�?? 62, 45-100, Springer-Verlag, Berlin (1988).
  2. T. W. Mossberg, �??Planar holographic optical processing devices,�?? Opt. Lett. 26, 414-416 (2001).
    [CrossRef]
  3. K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, T. Toma, �??Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,�?? Opt. Express 2, 503-508 (1998), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-12-503">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-12-503</a>
    [CrossRef] [PubMed]
  4. O. Matoba, K. Ikewaza, K. Itoh and Y. Ichioka, �??Modification of photorefractive waveguides in lithium niobate by guided beam for optical interconnections,�?? Opt. Review 2, 438-443 (1995).
    [CrossRef]
  5. G. Glazov, I. Itkin, V. Shandarov, E. Shandarov and S. Shandarov, �??Planar hologram gratings in photorefractive waveguides in LiNbO3,�?? J. Opt. Soc. Am. B 7, 2279-2288 (1990).
    [CrossRef]
  6. J. G. P. dos Reis, H. J. A. da Silva, �??Modelling and simulation of passive optical devices,�?? <a href="http://www.it.uc.pt/oc/ocpub/jr99cp01.pdf">www.it.uc.pt/oc/ocpub/jr99cp01.pdf</a>.
  7. A. M. Prokhorov , Y. S. Kuz'minov, Physics and chemistry of cristalline lithium niobate, Adam Hilger Series on Optics and Optoelectronics, 275-327 (1990).
  8. I. Savatinova, S. Tonchev, R. Todorov, M. N. Armenise, V. M. N. Passaro and C. C. Ziling, �??Electrooptic Effect in Proton Exchanged LiNbO3 and LiTaO3 Waveguides,�?? J. Lightwave Technol. 14, 403-409 (1996).
    [CrossRef]

J. Lightwave Technol. (1)

I. Savatinova, S. Tonchev, R. Todorov, M. N. Armenise, V. M. N. Passaro and C. C. Ziling, �??Electrooptic Effect in Proton Exchanged LiNbO3 and LiTaO3 Waveguides,�?? J. Lightwave Technol. 14, 403-409 (1996).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Opt. Review (1)

O. Matoba, K. Ikewaza, K. Itoh and Y. Ichioka, �??Modification of photorefractive waveguides in lithium niobate by guided beam for optical interconnections,�?? Opt. Review 2, 438-443 (1995).
[CrossRef]

Other (3)

V. E. Wood, P. J. Cressman, R. L. Holman and C. M. Verber, �??Photorefractive effects in waveguides�?? in Photorefractive Materials and their Applications II,�?? 62, 45-100, Springer-Verlag, Berlin (1988).

J. G. P. dos Reis, H. J. A. da Silva, �??Modelling and simulation of passive optical devices,�?? <a href="http://www.it.uc.pt/oc/ocpub/jr99cp01.pdf">www.it.uc.pt/oc/ocpub/jr99cp01.pdf</a>.

A. M. Prokhorov , Y. S. Kuz'minov, Physics and chemistry of cristalline lithium niobate, Adam Hilger Series on Optics and Optoelectronics, 275-327 (1990).

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Figures (4)

Fig. 1.
Fig. 1.

Δε 11 dielectric perturbation in a Y-cut LiNbO3 graded-index waveguide, x-propagating without overlay at T = 300 K, induced by the collinear TE0-TM0 mode interaction at λ = 632.8 nm.

Fig. 2.
Fig. 2.

Δε 13 dielectric perturbation in the same waveguide.

Fig. 3.
Fig. 3.

Δε 22 dielectric tensor perturbation in the same waveguide.

Fig. 4.
Fig. 4.

Δε 23 dielectric tensor perturbation in the same waveguide.

Tables (2)

Tables Icon

Table I. Comparison among LiNbO3 cuts in Gaussian profile waveguides.

Tables Icon

Table II. Comparison among different X-cut LiNbO3 technologies.

Equations (7)

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d 2 φ d cut 2 K g 2 ε ρ S ε cut S φ = f ( t ) t 0 ε cut S ( i K g δ ρ ph + δ cut ph cut )
φ = φ ( cut , ρ , t ) = φ 0 ( cut , t 0 ) f ( t ) exp ( j K g ρ )
δ ph = β E A E B * exp ( j K g ρ )
d 2 φ 0 d cut 2 K g 2 ε ρ S ε cut S φ 0 = t 0 ε cut S ( j K g [ β E A E B ] ρ + cut [ β E A E B ] cut )
Δ b p = k = 1 3 r pk ξ k p = 1 , , 6
ξ = ( ξ 1 , ξ 2 , ξ 3 ) = { ( φ x , 0 , j K g φ ) [ X-cut ] ( j K g φ , φ y , 0 ) [ Y-cut ] ( j K g φ , 0 , φ z ) [ Z-cut ]
{ Δ ε 11 = ( b 2 S + Δ b 2 ) ( b 3 S + Δ b 3 ) Δ b 4 2 det ( b ) ε 11 S Δ ε 12 = Δ ε 21 = ( b 3 S + Δ b 3 ) Δ b 6 Δ b 4 Δ b 5 det ( b ) Δ ε 13 = Δ ε 31 = Δ b 4 Δ b 6 ( b 2 S + Δ b 2 ) Δ b 5 det ( b ) Δ ε 22 = ( b 1 S + Δ b 1 ) ( b 3 S + Δ b 3 ) Δ b 5 2 det ( b ) ε 22 S Δ ε 23 = Δ ε 32 = ( b 1 S + Δ b 1 ) Δ b 4 Δ b 5 Δ b 6 det ( b ) Δ ε 33 = ( b 1 S + Δ b 1 ) ( b 2 S + Δ b 2 ) Δ b 6 2 det ( b ) ε 33 S

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