Abstract

The evanescently coupled multicore waveguide lattice composed of 37 linear type I cores hexagonally arranged has been theoretically studied and fabricated by low-repetition-rate femtosecond laser inscription of bulk fused silica. The effects of the single core’s numerical apertures (NAs) and spacing on the mode characteristics of the 37-core waveguide were calculated by the finite-element method. It was found that the mode field areas of the fundamental mode LP01 with 5 μm spacing of different NAs were all larger than 577μm2, which was confirmed by the experiments. The measured near-field mode profiles for different writing conditions and different spacing also showed that the waveguide supported both a single mode (LP01) and two modes (LP01 and LP11). The multicore waveguide, according to our study, is particularly interesting for mode converters.

© 2013 Optical Society of America

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2013 (4)

2012 (5)

2011 (1)

2010 (2)

2009 (3)

2008 (2)

2006 (1)

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

2005 (3)

2004 (5)

2003 (2)

R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. D. Silvestri, and G. Cerullo, “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20, 1559–1567 (2003).
[CrossRef]

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

1999 (1)

1997 (1)

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

1996 (2)

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[CrossRef]

Abdou-Ahmed, M.

Alberich, M.

Ams, M.

An, Q.

R. He, Q. An, J. R. Vázquez de Aldana, Q. Lu, and F. Chen, “Femtosecond-laser micromachined optical waveguides in Bi4Ge3O12 crystals,” Appl. Opt. 52, 3173–3178 (2013).
[CrossRef]

Arezki, B.

Arriola, A.

Audouard, E.

Bai, J.

Berenger, J. P.

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

Blömer, D.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

Borrelli, N. F.

Boukenter, A.

Boukos, N.

Brocas, A.

Burakov, I. M.

Burghoff, J.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[CrossRef]

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

Calmano, T.

Canioni, L.

Cerullo, G.

Charles, N.

Chen, F.

R. He, Q. An, J. R. Vázquez de Aldana, Q. Lu, and F. Chen, “Femtosecond-laser micromachined optical waveguides in Bi4Ge3O12 crystals,” Appl. Opt. 52, 3173–3178 (2013).
[CrossRef]

Chen, G.

Cheng, G.

Chiodo, N.

Clark, J.

D’Amico, C.

Davis, K. M.

Ebendorff-Heidepriem, H.

Fotakis, C.

Fuerbach, A.

Fujimoto, J. G.

Gaeta, A. L.

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[CrossRef]

Ghosh, S.

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

Giridhar, M. S.

Graf, T.

Gross, S.

He, R.

R. He, Q. An, J. R. Vázquez de Aldana, Q. Lu, and F. Chen, “Femtosecond-laser micromachined optical waveguides in Bi4Ge3O12 crystals,” Appl. Opt. 52, 3173–3178 (2013).
[CrossRef]

Hibino, Y.

Hirao, K.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[CrossRef]

Homoelle, D.

Huber, G.

Hui, R.

Huo, G.

Inouye, H.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

Ippen, E. P.

Ireland, M.

Jha, A.

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE, 2002).

Jose, G.

Jovanovic, N.

Kar, A.

Kar, A. K.

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

Kern, P.

Khulbe, P.

Killi, A.

Kohtoku, M.

Kopf, D.

Kowalevicz, A. M.

Kuan, K.

Labadie, L.

Lancaster, D. G.

Lanzani, G.

Laporta, P.

Lawrence, J. S.

Lederer, F.

Lederer, M.

Liu, X.

Long, X.

Lopez, C.

Lu, Q.

R. He, Q. An, J. R. Vázquez de Aldana, Q. Lu, and F. Chen, “Femtosecond-laser micromachined optical waveguides in Bi4Ge3O12 crystals,” Appl. Opt. 52, 3173–3178 (2013).
[CrossRef]

Mansuripur, M.

Marangoni, M.

Martin, G.

Mauclair, C.

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[CrossRef]

Mermillod-Blondin, A.

Miese, C.

Minoshima, K.

Mishchik, K.

Mitsuyu, T.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

Miura, K.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[CrossRef]

Monro, T. M.

Morgner, U.

Nasu, Y.

Nolte, S.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[CrossRef]

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

Olaizola, S. M.

Osellame, R.

Ouerdane, Y.

Pal, B. P.

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

Parriaus, O.

Pertsch, T.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[CrossRef]

Peschel, U.

Petermann, K.

Peyghambarian, N.

Polli, D.

Psaila, N.

Psaila, N. D.

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

Qiu, J.

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

Ramponi, R.

Richardson, K.

Richardson, M.

Ródenas, A.

Rosenfeld, A.

Sarger, L.

Schulzgen, A.

Seong, K.

Sharma, V.

Siebenmorgen, J.

Silvestri, S. D.

Smith, C.

Spaleniak, I.

Stoian, R.

Sugimoto, N.

Svelto, O.

Szameit, A.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

Taccheo, S.

Thomson, R.

Thomson, R. R.

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

Tuennermann, A.

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

Tünnermann, A.

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[CrossRef]

Tuthill, P. G.

Valle, G. D.

Varshney, R. K.

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

Vázquez de Aldana, J. R.

R. He, Q. An, J. R. Vázquez de Aldana, Q. Lu, and F. Chen, “Femtosecond-laser micromachined optical waveguides in Bi4Ge3O12 crystals,” Appl. Opt. 52, 3173–3178 (2013).
[CrossRef]

Virgili, T.

Vishnubhatla, K. C.

Vogel, M. M.

Voss, A.

Wang, Y.

Wielandy, S.

Will, M.

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[CrossRef]

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

Withford, M. J.

Zergioti, I.

Zhao, W.

Zorba, V.

Zoubir, A.

Appl. Opt. (4)

Appl. Phys. A (1)

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

Appl. Phys. B (1)

A. Szameit, D. Blömer, J. Burghoff, T. Pertsch, S. Nolte, and A. Tünnermann, “Hexagonal waveguide arrays written with fs-laser pulses,” Appl. Phys. B 82, 507–512 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

S. Ghosh, N. D. Psaila, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett. 100, 101102 (2012).
[CrossRef]

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71, 3329–3331 (1997).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[CrossRef]

Opt. Express (6)

Opt. Lett. (14)

G. Cheng, C. D’Amico, X. Liu, and R. Stoian, “Large mode area waveguides with polarization functions by volume ultrafast laser photoinscription of fused silica,” Opt. Lett. 38, 1924–1926 (2013).
[CrossRef]

Y. Nasu, M. Kohtoku, and Y. Hibino, “Low-loss waveguides written with a femtosecond laser for flexible interconnection in a planar light-wave circuit,” Opt. Lett. 30, 723–725 (2005).
[CrossRef]

S. Gross, M. Alberich, A. Arriola, M. J. Withford, and A. Fuerbach, “Fabrication of fully integrated antiresonant reflecting optical waveguides using the femtosecond laser direct-write technique,” Opt. Lett. 38, 1872–1874 (2013).
[CrossRef]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24, 1311–1313 (1999).
[CrossRef]

S. Taccheo, G. D. Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, and U. Morgner, “Er:Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29, 2626–2628 (2004).
[CrossRef]

A. Ródenas, G. Martin, B. Arezki, N. Psaila, G. Jose, A. Jha, L. Labadie, P. Kern, A. Kar, and R. Thomson, “Three-dimensional mid-infrared photonic circuits in chalcogenide glass,” Opt. Lett. 37, 392–394 (2012).
[CrossRef]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[CrossRef]

R. Osellame, N. Chiodo, G. D. Valle, S. Taccheo, R. Ramponi, G. Cerullo, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Optical waveguide writing with a diode-pumped femtosecond oscillator,” Opt. Lett. 29, 1900–1902 (2004).
[CrossRef]

M. M. Vogel, M. Abdou-Ahmed, A. Voss, and T. Graf, “Very-large-mode-area, single-mode multicore fiber,” Opt. Lett. 34, 2876–2878 (2009).
[CrossRef]

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Other (1)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Multicore hexagonal design. (b) Mode field distributions of the fundamental mode (LP01) with NA of 0.03, 0.05, 0.06, 0.08, and 0.1, respectively. (c) Mode field distributions of higher-order modes with NA of 0.06, 0.08, and 0.1, respectively.

Fig. 2.
Fig. 2.

Evolution of (a) effective index neff and (b) effective area Aeff of the fundamental mode LP01 as a function of NA.

Fig. 3.
Fig. 3.

Near-field modes of 37-core waveguides with NA of 0.05 and (a) Λ=3μm, (b) Λ=5μm, (c) Λ=7μm, and (d) Λ=10μm, respectively.

Fig. 4.
Fig. 4.

Experimental setup of the femtosecond laser waveguide writing arrangement indicating the irradiation geometry and sample orientation. CCD, charge-coupled device.

Fig. 5.
Fig. 5.

Illustration of multicore guiding (left, WL cross-sectional image; middle, PCM side picture; right, guided modes) with different scan velocities. (a) 600μm/s, (b) 300μm/s, and (c) 150μm/s. All the waveguides are written by 2.5 μJ, 1 kHz laser pulses in fused silica glass. The length of all waveguides is 4.5 mm. Near-field modes were obtained by injecting 980 nm light into the waveguide.

Fig. 6.
Fig. 6.

Phase contrast and near-field images of the 37-core waveguide in fused silica written with femtosecond laser pulse. The writing pulse energy was 5.0 μJ, and the scan velocity was 600μm/s. The length of the waveguide is 4.5 mm. (a) Top-view PCM image of the 37-core waveguide. The cell spacing is 5 μm. (b), (c) Near-field modes of the waveguide injected with 980 nm radiation in the central and lateral regions.

Fig. 7.
Fig. 7.

Optical micrographs of the end-face WL (left) and mode profile images (right) of the 37-core waveguides with core spacing of (a) 3 μm and (b) 7 μm. All the waveguides are produced by 5.0 μJ, 1 kHz laser pulses at a scan velocity of 600μm/s. The length of all the waveguides is 4.5 mm.

Equations (3)

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NA=2n2Δn+(Δn)2,
n1=n22+NA2.
Aeff=πω02,

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