Abstract

We demonstrate and characterize symmetric [3×3] three-dimensional directional couplers fabricated in glass using a high-pulse energy femtosecond laser oscillator. The characteristics of the [3×3] directional couplers closely agree with the theoretical prediction, except for small errors caused by the fabrication process. We show that deviations from symmetry are dominated by vertical position errors of the coupling waveguide.

© 2006 Optical Society of America

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  1. S. K. Sheem, "Optical fiber interferometers with [3x3] directional couplers: Analysis," J. Appl. Phys. 52, 3865-3872 (1981).
    [CrossRef]
  2. K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994).
    [CrossRef]
  3. M. A. Choma, C. Yang, and J. A. Izatt, "Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers," Opt. Lett. 28, 2162-2164 (2003).
    [CrossRef] [PubMed]
  4. 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] [PubMed]
  5. 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]
  6. Y. Nasu, M. Kohtoku, Y. Hibino, and Y. Inoue, "Three-dimensional waveguide interconnection formed with femtosecond laser in planar lightwave circuits," in Proceedings of Optical Fiber Communication Conference, 2005. Technical Digest. OFC/NFOEC, 4, (Anaheim, Calif., 2005), pp. 503-505.
  7. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Opt. Lett. 28, 2491-2493 (2003).
    [CrossRef] [PubMed]
  8. M. Kowalevicz, V. Sharma, E. P. Ippen and J. G. Fujimoto, "3D photonic devices fabricated in glass using a femtosecond laser oscillator," Opt. Lett. 21, 1060-1062 (2005).
    [CrossRef]
  9. M. Kowalevicz, Jr., A. Tucay Zare, F. X. Kärtner, and J. G. Fujimoto, "Generation of 150-nJ pulses from a multiple-pass cavity Kerr-lens mode-locked Ti:Al2O3 oscillator," Opt. Lett. 28, 1597-1599 (2003).
    [CrossRef] [PubMed]
  10. Kenya Suzuki NTT Photonics Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan, Yusuke Nasu, Vikas Sharma, Takahiro Ikeda, James G. Fujimoto, Erich P. Ippen, and Michael S. Feld are preparing a manuscript to be called "Characteristics of waveguide in soda-lime glass caused by irradiation of femtosecond laser pulses."
  11. R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Optical property of waveguides written by a 26 MHz stretched cavity Ti:sapphire Femtosecond oscillator," Opt. Express 13, 612-620 (2005).
    [CrossRef] [PubMed]
  12. K. Okamoto, Fundamentals of optical waveguides, (Academic Press, 2000).
  13. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Opt. Express 10, 645-652 (2002).
    [PubMed]

2005 (2)

2003 (4)

2002 (1)

1996 (1)

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] [PubMed]

1994 (1)

K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994).
[CrossRef]

1981 (1)

S. K. Sheem, "Optical fiber interferometers with [3x3] directional couplers: Analysis," J. Appl. Phys. 52, 3865-3872 (1981).
[CrossRef]

Aiello, L.

Asano, T.

Burghoff, J.

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]

Cerullo, G.

Chiodo, N.

Choma, M. A.

Davis, K. M.

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] [PubMed]

De Nicola, S.

Ferraro, P.

Finizio, A.

Fujimoto, J. G.

Hirao, K.

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] [PubMed]

Horiguchi, M.

K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994).
[CrossRef]

Ippen, E. P.

M. Kowalevicz, V. Sharma, E. P. Ippen and J. G. Fujimoto, "3D photonic devices fabricated in glass using a femtosecond laser oscillator," Opt. Lett. 21, 1060-1062 (2005).
[CrossRef]

K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Opt. Express 10, 645-652 (2002).
[PubMed]

Itoh, K.

Izatt, J. A.

Kärtner, F. X.

Kowalevicz, A. M.

Kowalevicz, M.

M. Kowalevicz, V. Sharma, E. P. Ippen and J. G. Fujimoto, "3D photonic devices fabricated in glass using a femtosecond laser oscillator," Opt. Lett. 21, 1060-1062 (2005).
[CrossRef]

M. Kowalevicz, Jr., A. Tucay Zare, F. X. Kärtner, and J. G. Fujimoto, "Generation of 150-nJ pulses from a multiple-pass cavity Kerr-lens mode-locked Ti:Al2O3 oscillator," Opt. Lett. 28, 1597-1599 (2003).
[CrossRef] [PubMed]

Laporta, P.

Maselli, V.

Minoshima, K.

Miura, K.

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] [PubMed]

Nishii, J.

Nolte, S.

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]

Osellame, R.

Pierattini, G.

Sharma, V.

M. Kowalevicz, V. Sharma, E. P. Ippen and J. G. Fujimoto, "3D photonic devices fabricated in glass using a femtosecond laser oscillator," Opt. Lett. 21, 1060-1062 (2005).
[CrossRef]

Sheem, S. K.

S. K. Sheem, "Optical fiber interferometers with [3x3] directional couplers: Analysis," J. Appl. Phys. 52, 3865-3872 (1981).
[CrossRef]

Sugimoto, N.

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] [PubMed]

Takada, K.

K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994).
[CrossRef]

Tucay Zare, A.

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]

Watanabe, W.

Will, M.

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]

Yamada, H.

K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994).
[CrossRef]

Yamada, K.

Yang, C.

Yin, A.

Zavelani-Rossi, M.

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]

IEEE Photonics Technol. Lett. (1)

K. Takada, H. Yamada, and M. Horiguchi, "Optical low coherence reflectometer using [3x3] fiber coupler," IEEE Photonics Technol. Lett. 6, 1014-1016 (1994).
[CrossRef]

J. Appl. Phys. (1)

S. K. Sheem, "Optical fiber interferometers with [3x3] directional couplers: Analysis," J. Appl. Phys. 52, 3865-3872 (1981).
[CrossRef]

Opt Lett. (1)

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] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Other (3)

Kenya Suzuki NTT Photonics Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan, Yusuke Nasu, Vikas Sharma, Takahiro Ikeda, James G. Fujimoto, Erich P. Ippen, and Michael S. Feld are preparing a manuscript to be called "Characteristics of waveguide in soda-lime glass caused by irradiation of femtosecond laser pulses."

K. Okamoto, Fundamentals of optical waveguides, (Academic Press, 2000).

Y. Nasu, M. Kohtoku, Y. Hibino, and Y. Inoue, "Three-dimensional waveguide interconnection formed with femtosecond laser in planar lightwave circuits," in Proceedings of Optical Fiber Communication Conference, 2005. Technical Digest. OFC/NFOEC, 4, (Anaheim, Calif., 2005), pp. 503-505.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic configuration of a [3×3] directional coupler, and (b) characteristics of an optical, symmetric [3×3] directional coupler.

Fig. 2.
Fig. 2.

Coupling characteristics of a fabricat ed [3×3] directional coupler with an optical signal from input port 1. The separations between the coupling waveguides S are designed to be (a) 25 μm, (b) 20 μm, and (c) 15 μm. The solid lines and dotted lines correspond to TM and TE polarization modes, respectively.

Fig. 3.
Fig. 3.

Calculated coupling characteristics of [3×3] directional couplers, when (a) the position of waveguide 1 is not aligned correctly, and when (b) the propagation constant of the waveguide is different from the others.

Fig. 4.
Fig. 4.

Cross-sectional diagram of the optical coupling region of a general [3×3] directional coupler.

Equations (38)

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d A 1 dz + j κ 12 A 2 e j 2 δ 21 z + j κ 13 A 3 e + j 2 δ 13 z = 0
d A 2 dz + j κ 23 A 3 e j 2 δ 23 z + j κ 21 A 1 e + j 2 δ 21 z = 0
d A 3 dz + j κ 31 A 1 e j 2 δ 13 z + j κ 32 A 2 e + j 2 δ 23 z = 0
d z 1 d z 0 = tan θ 0 tan θ 1
θ 0 = arcsin ( NA / n 0 )
θ 1 = arcsin ( NA / n 1 )
× E p = μ 0 H p
× H p = ε 0 N p 2 E p
E = A 1 ( z ) E 1 + A 2 ( z ) E 2 + A 3 ( z ) E 3
H = A 1 ( z ) H 1 + A 2 ( z ) H 2 + A 3 ( z ) H 3
× E = μ 0 H
× H = ε 0 N 2 E
× ( AE ) = A xE + AxE
= A xE + dA dz u z xE
( u z x E ¯ 1 ) d A 1 dz + ( u z x E ¯ 2 ) d A 2 dz + ( u z x E ¯ 3 ) d A 3 dz = 0
[ ( u z x H ¯ 1 ) d A 1 dz ε 0 ( N 2 N 1 2 ) A 1 E ¯ ]
+ [ ( u z x H ¯ 2 ) d A 2 dz ε 0 ( N 2 N 2 2 ) A 2 E ¯ ]
+ [ ( u z x H ¯ 3 ) d A 3 dz ε 0 ( N 2 N 3 2 ) A 3 E ¯ ] = 0
[ E ¯ 1 * · ( A 5 ) H ¯ 1 * · ( A 6 ) ] dxdy = 0
[ E ¯ 2 * · ( A 5 ) H ¯ 2 * · ( A 6 ) ] dxdy = 0
[ E ¯ 3 * · ( A 5 ) H ¯ 3 * · ( A 6 ) ] dxdy = 0
E ¯ p = E p e j β p z
H ¯ p = H p e j β p z
d A 1 dz + c 12 d A 2 dz e j ( β 2 β 1 ) + c 13 d A 3 dz e j ( β 3 β 1 ) + j χ 1 A 1 + j κ 12 A 2 e j ( β 2 β 1 ) + j κ 13 A 3 e j ( β 3 β 1 )
d A 2 dz + c 23 d A 3 dz e j ( β 3 β 2 ) + c 21 d A 1 dz e j ( β 1 β 2 ) + j χ 2 A 2 + j κ 23 A 3 e j ( β 3 β 2 ) + j κ 21 A 1 e j ( β 1 β 2 )
d A 3 dz + c 31 d A 1 dz e j ( β 1 β 3 ) + c 32 d A 2 dz e j ( β 2 β 3 ) + j χ 3 A 3 + j κ 31 A 1 e j ( β 1 β 3 ) + j κ 32 A 2 e j ( β 2 β 3 )
κ pq = ω ε 0 ( N 2 N q 2 ) E P * · E q dxdy u z · ( E P * × H p + E p × H P * ) dxdy
c pq = u z · ( E P * × H q + E q × H P * ) dxdy u z · ( E P * × H p + E p × H P * ) dxdy
χ p = ω ε 0 ( N 2 N p 2 ) E P * · E p dxdy u z · ( E P * × H p + E p × H P * ) dxdy
κ 12 = κ 21 *
κ 23 = κ 32 *
κ 31 = κ 13 *
d A 1 dz + j κ 12 A 2 e j 2 δ 21 z + j κ 13 A 3 e + j 2 δ 13 z = 0
d A 2 dz + j κ 21 A 1 e + j 2 δ 21 z + j κ 23 A 3 e j 2 δ 23 z = 0
d A 3 dz + j κ 31 A 1 e j 2 δ 13 z + j κ 32 A 2 e + j 2 δ 23 z = 0
δ 21 = β 2 β 1 2 κ 12 = κ 21
δ 32 = β 3 β 2 2 κ 23 = κ 32
δ 13 = β 1 β 3 2 κ 31 = κ 13

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