Abstract

Fiber waveguide arrays can be applied as a very useful tool for the investigation of effects in discrete optics. The observation of coherent propagation in such discrete waveguide arrays requires, however, high structural precision and great material homogeneity. The fabrication of such a fiber array with close tolerances compared to conventional fiber technology is discussed. Linear propagation effects are modeled for an ideal fiber waveguide array and are compared with experimental results. The good agreement of these results with each other indicates the applicability of such fiber waveguide arrays in studying linear and non-linear properties in discrete optics.

© 2007 Optical Society of America

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  1. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-1780.
    [CrossRef] [PubMed]
  2. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
    [CrossRef]
  3. A. Szameit, D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Express 13, 10552-10557 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10552.
    [CrossRef] [PubMed]
  4. D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
    [CrossRef]
  5. J. Proctor and J. N. Kutz, "Nonlinear mode-coupling for passive mode-locking: application of waveguide arrays, dual-core fibers, and/or fiber arrays," Opt. Express 13, 8933-8950 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-22-8933.
    [CrossRef] [PubMed]
  6. Y. Huo and P. K. Cheo, "Analysis of transverse mode competition and selection in multicore fiber lasers," J. Opt. Soc. Am. B 22, 2345-2349 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=josab-22-11-2345.
    [CrossRef]
  7. L. Michaille, C. R. Bennett, D. M. Taylor, T. J. Shepherd, J. Broeng, H. R. Simonsen, and A. Petersson, "Phase locking and supermode selection in multicore photonic crystal fiber lasers with a large doped area," Opt. Lett. 30, 1668-1670 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-13-1668.
    [CrossRef] [PubMed]
  8. L. Li, A. Schülzgen, S. Chen, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, "Phase locking and in-phase supermode selection in monolithic multicore fiber lasers," Opt. Lett. 31, 2577-2579 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-17-2577.
    [CrossRef] [PubMed]
  9. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
    [CrossRef] [PubMed]
  10. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
    [CrossRef]
  11. A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
    [CrossRef]
  12. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6055.
    [CrossRef] [PubMed]
  13. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
    [CrossRef] [PubMed]
  14. T. Pertsch, A. Chipouline, S. Nolte, F. Lederer, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, U. Peschel, and A. Tünnermann, "From diffusive to coherent light propagation in disordered nonlinear fiber arrays," in Photonic Metamaterials: From Random to Periodic, Technical Digest (CD) (Optical Society of America, 2006), paper WA7, http://www.opticsinfobase.org/abstract.cfm?URI=META-2006-WA7
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  17. K.P. Hansen, J. Broeng, " High -Power Photonic Crystal Fiber Lasers", Photonics Spectra, 82-89 (2006)

2006 (4)

2005 (5)

2004 (1)

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

2003 (2)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

2001 (1)

D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

Bartal, G.

Bartelt, H.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Bennett, C. R.

Bloemer, D.

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

Blömer, D.

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

Broeng, J.

Buljan, H.

Burghoff, J.

Chen, S.

Cheo, P. K.

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

Cohen, O.

Efremidis, N. K.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-1780.
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Eugenieva, E. D.

D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-1780.
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Freedman, B.

Hansen, K.P.

K.P. Hansen, J. Broeng, " High -Power Photonic Crystal Fiber Lasers", Photonics Spectra, 82-89 (2006)

Huo, Y.

Kobelke, J.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Kutz, J. N.

Lederer, F.

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6055.
[CrossRef] [PubMed]

A. Szameit, D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Express 13, 10552-10557 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10552.
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

Li, L.

Manela, O.

Michaille, L.

Moloney, J. V.

Nolte, S.

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6055.
[CrossRef] [PubMed]

A. Szameit, D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Express 13, 10552-10557 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10552.
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Pertsch, T.

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica," Opt. Express 14, 6055-6062 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6055.
[CrossRef] [PubMed]

A. Szameit, D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, "Discrete Nonlinear Localization in Femtosecond Laser Written Waveguides in Fused Silica," Opt. Express 13, 10552-10557 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-26-10552.
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

Peschel, U.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

Petersson, A.

Peyghambarian, N.

Proctor, J.

Schreiber, T.

Schülzgen, A.

Schuster, K.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Schwartz, T.

Segev, M.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-6-1780.
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Shepherd, T. J.

Simonsen, H. R.

Szameit, A.

Taylor, D. M.

Temyanko, V. L.

Tuennermann, A.

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Tünnermann, A.

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

Appl. Phys. A. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A. 77, 109-111 (2003).
[CrossRef]

Appl. Phys. B. (1)

A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, F. Lederer, and A. Tuennermann, "Hexagonal waveguide arrays written with fs-laser pulses," Appl. Phys. B. 82, 507-512 (2006).
[CrossRef]

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

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Photonics Spectra (1)

K.P. Hansen, J. Broeng, " High -Power Photonic Crystal Fiber Lasers", Photonics Spectra, 82-89 (2006)

Phys. Rev. Lett. (3)

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tuennermann, and F. Lederer, "Nonlinearity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 2339011-4 (2001).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 0939011-4 (2002).
[CrossRef]

Other (3)

T. Pertsch, A. Chipouline, S. Nolte, F. Lederer, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, U. Peschel, and A. Tünnermann, "From diffusive to coherent light propagation in disordered nonlinear fiber arrays," in Photonic Metamaterials: From Random to Periodic, Technical Digest (CD) (Optical Society of America, 2006), paper WA7, http://www.opticsinfobase.org/abstract.cfm?URI=META-2006-WA7

A. W. Snyder, J. D. Love, "Optical waveguide theory", (Chapman & Hall, 1983).

G. P. Agrawal, "Nonlinear fiber optics", 2nd ed., (Academic Press, 1995)

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Figures (3)

Fig. 1.
Fig. 1.

Cross-sections of a high-precision waveguide array: white light transmission microscopy (left), reflected-light/differential interference contrast microscopy image of an etched cleaved facet (right).

Fig. 2.
Fig. 2.

Eigenvalues of the supermodes of a 61-core array (left), and field distribution of the supermodes with the highest symmetry (right). The colors (yellow and blue) indicate the sign of the real-valued amplitudes ui .

Fig. 3.
Fig. 3.

Output distribution of light launched at specific cores: array center (upper row), boundary corner (middle row) and middle of a boundary line (lower row); columns (a) and (c) show experimental results for sample lengths zA = 26.5 mm and 55 mm, respectively; columns (b) and (d) show computer simulations of an ideal array with ζ = 0.42 and 0.85, respectively.

Equations (5)

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

L C = λ 0 4 Δ n 0 A E 0 2 dA AR E 0 ( x + Λ , y ) E 0 ( x , y ) dA .
i λ 0 2 π du dz + ( M D + λ 0 4 L C M C ) u = n 2 1 W A eff diag ( u i 2 ) u + ,
M D = Δ n 0 diag ( δn i Δ n 0 A E 0 2 dA + 2 πRδ R i E 0 ( R ) 2 + Γ i AR E 0 ( x + Λ , y ) 2 dA ) A E 0 2 dA .
i λ 0 2 π du dz + ( λ 0 4 L C M C ) u = 0 .
u ( z ) = exp ( i π z 2 L C M C ) u ( 0 ) .

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