Abstract

We experimentally investigate the formation of reconfigurable three-dimensional (3D) nonlinear photonic lattices in an externally biased cerium doped strontium barium niobate photorefractive crystal by a spatial light modulator-assisted versatile simplified single step optical induction approach. The analysis of the generated 3D nonlinear photonic lattices by plane wave guiding, momentum space spectroscopy, and far field diffraction pattern imaging is presented, which points to the embedded potential of these 3D structures as reconfigurable platform to investigate advanced nonlinear light-matter interaction in periodic structures.

© 2009 Optical Society of America

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  1. K. Busch, S. Loelkes, R. B. Wehrspohn, and H. Foell, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
    [Crossref]
  2. C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
    [Crossref]
  3. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, Opt. Express 13, 1780 (2005).
    [Crossref] [PubMed]
  4. D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, J. Nonlinear Opt. Phys. Mater. 16, 1 (2007).
    [Crossref]
  5. A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, Opt. Lett. 30, 869 (2005).
    [Crossref] [PubMed]
  6. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
    [Crossref]
  7. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [Crossref] [PubMed]
  8. B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
    [Crossref]
  9. L. Z. Cai, X. L. Yang, and Y. R. Wang, Opt. Lett. 27, 900 (2002).
    [Crossref]
  10. A. Dwivedi, J. Xavier, J. Joseph, and K. Singh, Appl. Opt. 47, 1973 (2008).
    [Crossref] [PubMed]
  11. D. Xu, K. P. Chen, K. Ohlinger, and Y. Lin, Appl. Phys. Lett. 93, 031101 (2008).
    [Crossref]
  12. X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
    [Crossref]
  13. N. J. Jenness, K. D. Wulff, M. S. Johannes, M. J. Padgett, D. G. Cole, and R. L. Clark, Opt. Express 16, 15942 (2008).
    [Crossref] [PubMed]
  14. P. Rose, B. Terhalle, J. Imbrock, and C. Denz, J. Phys. D 41, 224004 (2008).
    [Crossref]
  15. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
    [Crossref] [PubMed]
  16. M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
    [Crossref]
  17. J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

2008 (4)

2007 (3)

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, J. Nonlinear Opt. Phys. Mater. 16, 1 (2007).
[Crossref]

2005 (3)

2003 (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

2002 (3)

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

L. Z. Cai, X. L. Yang, and Y. R. Wang, Opt. Lett. 27, 900 (2002).
[Crossref]

1987 (1)

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[Crossref]

Ahles, M.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

Bartal, G.

Bersch, C.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

Buljan, H.

Busch, K.

K. Busch, S. Loelkes, R. B. Wehrspohn, and H. Foell, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
[Crossref]

Cai, L. Z.

Chen, K. P.

D. Xu, K. P. Chen, K. Ohlinger, and Y. Lin, Appl. Phys. Lett. 93, 031101 (2008).
[Crossref]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Clark, R. L.

Cohen, O.

Cole, D. G.

Cory, W. K.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[Crossref]

Denz, C.

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, J. Phys. D 41, 224004 (2008).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, Opt. Lett. 30, 869 (2005).
[Crossref] [PubMed]

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

Desyatnikov, A. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, Opt. Lett. 30, 869 (2005).
[Crossref] [PubMed]

Dwivedi, A.

Efremidis, N. K.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, Opt. Express 13, 1780 (2005).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Ewbank, M. D.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[Crossref]

Feinberg, J.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[Crossref]

Fleischer, J. W.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, Opt. Express 13, 1780 (2005).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Foell, H.

K. Busch, S. Loelkes, R. B. Wehrspohn, and H. Foell, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
[Crossref]

Freedman, B.

Imbrock, J.

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, J. Phys. D 41, 224004 (2008).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

Jägers, J.

Jenness, N. J.

Johannes, M. S.

Joseph, J.

A. Dwivedi, J. Xavier, J. Joseph, and K. Singh, Appl. Opt. 47, 1973 (2008).
[Crossref] [PubMed]

J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

Kartashov, Y. V.

Kivshar, Y. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, J. Nonlinear Opt. Phys. Mater. 16, 1 (2007).
[Crossref]

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, Opt. Lett. 30, 869 (2005).
[Crossref] [PubMed]

Krolikowski, W.

D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, J. Nonlinear Opt. Phys. Mater. 16, 1 (2007).
[Crossref]

Lin, Y.

D. Xu, K. P. Chen, K. Ohlinger, and Y. Lin, Appl. Phys. Lett. 93, 031101 (2008).
[Crossref]

Loelkes, S.

K. Busch, S. Loelkes, R. B. Wehrspohn, and H. Foell, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
[Crossref]

Manela, O.

Neshev, D. N.

Neurgaonkar, R. R.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[Crossref]

Ohlinger, K.

D. Xu, K. P. Chen, K. Ohlinger, and Y. Lin, Appl. Phys. Lett. 93, 031101 (2008).
[Crossref]

Padgett, M. J.

Petter, J.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

Rose, P.

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, J. Phys. D 41, 224004 (2008).
[Crossref]

J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

Sagemerten, N.

Schroeder, J.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

Schwartz, T.

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Segev, M.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, Opt. Express 13, 1780 (2005).
[Crossref] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Singh, K.

A. Dwivedi, J. Xavier, J. Joseph, and K. Singh, Appl. Opt. 47, 1973 (2008).
[Crossref] [PubMed]

J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

Sukhorukov, A. A.

D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, J. Nonlinear Opt. Phys. Mater. 16, 1 (2007).
[Crossref]

Sun, X. H.

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

Szeto, Y. -S.

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

Tang, L.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

Tao, X. M.

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

Terhalle, B.

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, J. Phys. D 41, 224004 (2008).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

Träger, D.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, Opt. Lett. 30, 869 (2005).
[Crossref] [PubMed]

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

Wang, Y. R.

Wehrspohn, R. B.

K. Busch, S. Loelkes, R. B. Wehrspohn, and H. Foell, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
[Crossref]

Weilnau, C.

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

Wulff, K. D.

Xavier, J.

A. Dwivedi, J. Xavier, J. Joseph, and K. Singh, Appl. Opt. 47, 1973 (2008).
[Crossref] [PubMed]

J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

Xu, D.

D. Xu, K. P. Chen, K. Ohlinger, and Y. Lin, Appl. Phys. Lett. 93, 031101 (2008).
[Crossref]

Xue, P.

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

Yang, X. L.

Ye, T. J.

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

Ann. Phys. (Leipzig) (1)

C. Weilnau, M. Ahles, J. Petter, D. Träger, J. Schroeder, and C. Denz, Ann. Phys. (Leipzig) 11, 573 (2002).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (2)

X. H. Sun, X. M. Tao, T. J. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 65 (2007).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, Appl. Phys. B 86, 399 (2007).
[Crossref]

Appl. Phys. Lett. (1)

D. Xu, K. P. Chen, K. Ohlinger, and Y. Lin, Appl. Phys. Lett. 93, 031101 (2008).
[Crossref]

J. Appl. Phys. (1)

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, J. Nonlinear Opt. Phys. Mater. 16, 1 (2007).
[Crossref]

J. Phys. D (1)

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, J. Phys. D 41, 224004 (2008).
[Crossref]

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Phys. Rev. Lett. (1)

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902 (2005).
[Crossref] [PubMed]

Other (2)

J. Xavier, P. Rose, J. Joseph, K. Singh, and C. Denz, in Proceedings of Topical Meeting on Photorefractive Materials, Effects, and Devices, K.Buse and C.Denz, eds. (2009), pp. 68-69. The manuscript was submitted in January 2009. We later became aware that Zhang et al. submitted in May 2009 the results on 3D photonic lattices composed of superimposing two 2D lattices from orthogonal directions, to an upcoming OSA Annual Meeting (Frontiers in Optics 2009).

K. Busch, S. Loelkes, R. B. Wehrspohn, and H. Foell, Photonic Crystals: Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

(a)–(c) Computer simulation of the light intensity distribution by the interference of lattice-forming beams. (a) 3D interference pattern formed by seven-beam configuration. (b), (c) Light intensity distribution, respectively, in the x - y and x - z planes. (d) Computed phase engineered pattern to generate seven lattice-forming beams.

Fig. 2
Fig. 2

Schematic representation of experimental scheme for the generation and analysis of 3D nonlinear photonic lattices in an externally biased SBN:Ce. PBS, polarizing beam splitter; S, shutter; MO, microscope objective; PH, pin-hole; L, lens; BS, beam splitter; FF, Fourier filter; M, mirror; RD, rotating diffuser; ID, iris diaphragm. Beam-launching scheme is given in inset.

Fig. 3
Fig. 3

3D nonlinear photonic lattices in self-focusing photorefractive media. (a) x - y plane of the photonic lattice formed by o-polarized lattice wave. (b), (c) Image of photonic lattice formed by e-polarized lattice wave respectively in the same direction as in (a) and perpendicular to it. (d) x - y plane of the photonic lattice using lattice wave generated by rotating the phase pattern by an angle 45° about z axis in comparison to (b). (e) Far-field diffraction pattern of photonic lattice in (a) imaged using CCD camera. (f) Momentum space spectroscopic image of 3D photonic lattice generated by o-polarized lattice wave rotated by 90° about z axis with respect to the crystal c axis, as compared to photonic lattice image of (a).

Fig. 4
Fig. 4

Far-field diffraction patterns of generated photonic lattices (respective lattices in inset). (a), (b) x - y plane of photonic lattices formed by o-polarized lattice wave and e-polarized lattice wave, respectively. (c) x - z plane of photonic lattice formed by e-polarized lattice wave. (d) x - y plane of the photonic lattice using lattice wave generated by rotating the phase pattern by an angle 45° about z axis in comparison to (b).

Equations (2)

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I ( r ) = j = 1 7 | E j | 2 + i j 7 E i E j   exp [ i ( k i k j ) r + i ψ i j ] ,
k m = k [ cos ( q m π ) sin θ i , sin ( q m π ) sin θ i , cos θ i ] ,

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