Abstract

A monolithically integrated asymmetric graded index (GRIN) or step-index (GRIN) mode converters for microphotonic waveguides are proposed and described. The design parameters and tolerances are calculated for amorphous silicon (a-Si) couplers integrated with silicon-on-insulator waveguides. The GRIN and step-index couplers operate over a wide wavelength range with low polarization dependence, and the lithographic resolution needed is only ±1 μm. Finally, experimental results are presented for a single layer 3 μm thick step-index a-Si coupler integrated on a 0.8 μm thick SOI waveguide. The measured variation of coupling efficiency with coupler length is in agreement with theory, with an optimal coupling length of 15 μm for this device.

© 2006 Optical Society of America

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References

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  1. V.R. Almeida, R.R. Panepucci, and M. Lipson, "Nanotaper for compact mode conversion," Opt. Lett. 28, 1302-1304 (2003).
    [CrossRef] [PubMed]
  2. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, "Low loss mode size converter from 0.3 µm square Si wire waveguides to singlemode fibres," Electron. Lett. 38, 1669-1670 (2002).
    [CrossRef]
  3. K.K. Lee, D.R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L.C Kimmerling, K.P. Yap and M.T. Doan, "Mode transformer for miniaturized optical circuits," Opt. Lett. 30, 498-500 (2005).
    [CrossRef] [PubMed]
  4. G.Z. Masanovic, V.M.N. Passaro, and G.T. Reed, "Dual grating-assisted directional coupling between fibers and thin semiconductor waveguides," IEEE Photonics Technol. Lett. 15, 1395-1397 (2003).
    [CrossRef]
  5. A. Sure, T. Dillon, J. Murakowski, C. Lin, D. Pustai, and D. Prather, "Fabrication and characterization of three-dimensional silicon tapers," Optics Express 11, 3555-3561 (2003).
    [CrossRef] [PubMed]
  6. C. Manolatou and H.A. Haus, Passive components for Dense Optical Integration (Kluwer Academic Publishers, Boston, 2002), Chapter 6.
    [CrossRef]
  7. K. Shiraishi, C.S. Tsai, H. Yoda, and K. Minagawa, "A micro-GRIN slab tip for integrating coupling between superfine-core waveguides and single mode fibers," in Proceedings of CLEO/Pacific RIM 2003, CD-ROM (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 2003).
  8. K. Iizuka, Engineering Optics, 2nd Edition (Springer-Verlag, Berlin 1987), Chapter 5.
  9. H. Kogelnik, "Theory of Optical Waveguides," in Guided-wave Optoelectronics, T. Tamir, ed., 7-87 (Springer Verlag, Berlin 1990)
  10. A. Delâge, S. Janz, D.-X. Xu, D. Dalacu, B. Lamontagne, and A. Bogdanov, in Photonics North 2004: Optical Components and Devices, J.C. Armitage, S. Fafard, R.A. Lessard, and G.A Lamprpoulos, eds. "Graded-index coupler for microphotonic waveguides," Proc. SPIE Vol. 5577, 204-212 (2004).
    [CrossRef]
  11. L.B. Soldano and E.C.M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
    [CrossRef]
  12. R. Gordon, "Harmonic oscillation in a spatially finite array waveguide," Opt. Lett. 29, 2752-2755 (2004).
    [CrossRef] [PubMed]
  13. R.U. Ahmad, F. Pizzuto, G.S. Camarda, R.L. Espinola, H. Rao, and R.M. Osgood, "Ultracompact corner-mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
    [CrossRef]
  14. V. Nguyen, T. Montalbo, C. Manolatou, A. Agarwal, Yasaitis, L.C. Kimmerling, and J. Michel, "Compact 3dB single mode fibre-to-waveguide coupler," in Proceedings of the 2nd International Conference on Group IV Photonics, 195-197 (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 2005).

2nd International Conference on Group IV (1)

V. Nguyen, T. Montalbo, C. Manolatou, A. Agarwal, Yasaitis, L.C. Kimmerling, and J. Michel, "Compact 3dB single mode fibre-to-waveguide coupler," in Proceedings of the 2nd International Conference on Group IV Photonics, 195-197 (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 2005).

CLEO/Pacific RIM 2003 (1)

K. Shiraishi, C.S. Tsai, H. Yoda, and K. Minagawa, "A micro-GRIN slab tip for integrating coupling between superfine-core waveguides and single mode fibers," in Proceedings of CLEO/Pacific RIM 2003, CD-ROM (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 2003).

Electron. Lett. (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, "Low loss mode size converter from 0.3 µm square Si wire waveguides to singlemode fibres," Electron. Lett. 38, 1669-1670 (2002).
[CrossRef]

Guided-wave Optoelectronics (1)

H. Kogelnik, "Theory of Optical Waveguides," in Guided-wave Optoelectronics, T. Tamir, ed., 7-87 (Springer Verlag, Berlin 1990)

IEEE Photon. Technol. Lett. (1)

R.U. Ahmad, F. Pizzuto, G.S. Camarda, R.L. Espinola, H. Rao, and R.M. Osgood, "Ultracompact corner-mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

G.Z. Masanovic, V.M.N. Passaro, and G.T. Reed, "Dual grating-assisted directional coupling between fibers and thin semiconductor waveguides," IEEE Photonics Technol. Lett. 15, 1395-1397 (2003).
[CrossRef]

J. Lightwave Technol. (1)

L.B. Soldano and E.C.M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Opt. Lett. (3)

Optics Express (1)

A. Sure, T. Dillon, J. Murakowski, C. Lin, D. Pustai, and D. Prather, "Fabrication and characterization of three-dimensional silicon tapers," Optics Express 11, 3555-3561 (2003).
[CrossRef] [PubMed]

Photonics North 2004: Optical Components (1)

A. Delâge, S. Janz, D.-X. Xu, D. Dalacu, B. Lamontagne, and A. Bogdanov, in Photonics North 2004: Optical Components and Devices, J.C. Armitage, S. Fafard, R.A. Lessard, and G.A Lamprpoulos, eds. "Graded-index coupler for microphotonic waveguides," Proc. SPIE Vol. 5577, 204-212 (2004).
[CrossRef]

Other (2)

K. Iizuka, Engineering Optics, 2nd Edition (Springer-Verlag, Berlin 1987), Chapter 5.

C. Manolatou and H.A. Haus, Passive components for Dense Optical Integration (Kluwer Academic Publishers, Boston, 2002), Chapter 6.
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

(a) The calculated TE polarized intensity distribution in a waveguide consisting of a 0.5 μm Si waveguide core (n = 3.47) with an optimized 3.5 μm thick GRIN layer with a quadratic index profile (see Fig. 3(c)), and (b) a schematic of a monolithic GRIN waveguide coupler based on this layer structure.

Fig. 2.
Fig. 2.

(a) The field distribution in a full quadratic index waveguide (n0 = 3.405, x0 = 8.23 μm), for mode expansion coefficients that alternate in phase by π (solid curve) and 2π. (b) The corresponding field distribution in a semi-infinite quadratic index waveguide, for modes that alternate in phase by 2π (solid curve) and π (dashed curve).

Fig. 3.
Fig. 3.

The index profiles (shaded regions) and the lowest order electric field TE mode profiles for (a) a full quadratic index waveguide, (b) a truncated quadratic index waveguide, (c) an optimized asymmetric-GRIN coupler on a 0.5 μm Si waveguide, and (d) a single layer step-index coupler on a 0.5 μm Si waveguide.

Fig. 4.
Fig. 4.

The modal wave vectors βv for TE polarized light in the full quadratic index waveguide, the truncated quadratic index waveguide, and the optimized asymmetric-GRIN coupler on a 0.5 μm Si waveguide shown in Fig. 3. The dashed curved represents a linear extrapolation of the wave vector dependence on mode number.

Fig. 5.
Fig. 5.

The variation of coupling efficiency on coupler length for an optimized asymmetric-GRIN coupler on a 0.5 μm Si waveguide (solid curve), and a single layer step-index coupler on a 0.5 μm Si waveguide (dashed curve). The calculations are for TE polarized light.

Fig. 6.
Fig. 6.

The variation of coupling efficiency on (a) input beam offset position (b) angular alignment and (c) wavelength, and (d) the polarization dependent loss (PTE -PTM), for an optimized quadratic GRIN coupler on a 0.5 μm Si waveguide (solid curves), and a single layer step-index coupler on a 0.5 μm Si waveguide (dashed curves). TE polarized light is assumed in all calculations except for (d).

Fig. 7.
Fig. 7.

(a) Cross-section of the fabricated asymmetric-GRIN single layer coupler structure, and (b) a scanning electron microscope (SEM) view of the etched waveguide facets showing the 3 μm deposited a-Si layer on the 0.8 μm high Si ridge waveguides, and the outline of the SiO2 window that defines the coupler length.

Fig. 8.
Fig. 8.

The variation of the measured output power with coupler length for a 3 μm thick single layer a-Si coupler integrated with a 0.8 μm SOI waveguide as described in the text. The solid curve is the calculated coupling efficiency assuming TE polarized light and an a-Si refractive index of n=3.365.

Tables (2)

Tables Icon

Table 1. Mode expansion coefficients and coupling efficiencies a for the truncated quadratic index and GRIN coupler structures in Fig. 3(b) and 3(c). The calculated coefficients are for TE polarized light.

Tables Icon

Table 2. Coefficients c v and g v for the 1-layer coupler structure of Fig. 3(d). TE polarized light is assumed.

Equations (8)

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n 2 ( x ) = n 0 2 ( 1 x 2 x 0 2 ) ,
M v ( x ) = H v ( x k 0 n 0 x 0 ) exp ( x 2 2 k 0 n 0 x 0 ) , v = 0,1 ,
β v = k 0 n 0 1 2 v + 1 k 0 x 0 n 0 , v = 0,1 ,
E x z = v c v M v ( x ) exp ( i β v z )
c k = M k ( x ) S ( x ) dx = v c v M k ( x ) M v ( x ) dx .
η in = v c v 2 .
η c = E x L G ( x ) dx 2 = v c v exp ( v L ) M v ( x ) G ( x ) dx 2
= v c v g v exp ( v L ) 2

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