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,” Optics Letters 26, 414–416 (2001).
    [Crossref]
  3. K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
    [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 and H. J. A. da Silva, “Modelling and simulation of passive optical devices,” www.it.uc.pt/oc/ocpub/jr99cp01.pdf.
  7. A. M. Prokhorov and 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]

2001 (1)

T. W. Mossberg, “Planar holographic optical processing devices,” Optics Letters 26, 414–416 (2001).
[Crossref]

1998 (1)

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

1996 (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]

1995 (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]

1990 (1)

1988 (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).

Armenise, M. N.

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]

Cressman, P. J.

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).

da Silva, H. J. A.

J. G. P. dos Reis and H. J. A. da Silva, “Modelling and simulation of passive optical devices,” www.it.uc.pt/oc/ocpub/jr99cp01.pdf.

dos Reis, J. G. P.

J. G. P. dos Reis and H. J. A. da Silva, “Modelling and simulation of passive optical devices,” www.it.uc.pt/oc/ocpub/jr99cp01.pdf.

Furuya, Y.

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

Glazov, G.

Holman, R. L.

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).

Ichioka, Y.

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]

Ikewaza, K.

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

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]

Itkin, I.

Itoh, K.

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

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]

Kuz’minov, Y. S.

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

Masuda, Y.

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

Matoba, O.

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]

Mossberg, T. W.

T. W. Mossberg, “Planar holographic optical processing devices,” Optics Letters 26, 414–416 (2001).
[Crossref]

Passaro, V. M. N.

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]

Prokhorov, A. M.

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

Savatinova, I.

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]

Shandarov, E.

Shandarov, S.

Shandarov, V.

Todorov, R.

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]

Toma, T.

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

Tonchev, S.

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]

Verber, C. M.

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).

Watanabe, W.

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

Wood, V. E.

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).

Ziling, C. C.

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. 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]

Optics Express (1)

K. Itoh, K. Ikewaza, W. Watanabe, Y. Furuya, Y. Masuda, and T. Toma, “Fabricating micro-Bragg reflectors in 3-D photorefractive waveguides,” Optics Express 2, 503–508 (1998).
[Crossref] [PubMed]

Optics Letters (1)

T. W. Mossberg, “Planar holographic optical processing devices,” Optics Letters 26, 414–416 (2001).
[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 and H. J. A. da Silva, “Modelling and simulation of passive optical devices,” www.it.uc.pt/oc/ocpub/jr99cp01.pdf.

A. M. Prokhorov and 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)

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

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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