Abstract

We examine the waveguide dimension and refractive-index difference space for the optimization of single-mode channel waveguide pigtails and optical fiber splices, and we explain these results using modal analysis. We present closed-form equations for the evaluation of the optimal index difference and the allowable variation in its value in any material. We provide a novel way of viewing common waveguide physical parameters and translating them into information that determines the efficacy of a fiber connection.

© 1998 Optical Society of America

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References

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  1. H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
    [CrossRef]
  2. L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
    [CrossRef]
  3. L. Robitaille, C. L. Callender, J. P. Noad, “Polymer waveguide devices for WDM applications,” in Polymer Photonic Devices, B. Kippelen, D. D. C. Bradley, eds., Proc. SPIE3281, 14–24 (1998).
    [CrossRef]
  4. C. Kane, R. R. Krchnavek, “Benzocyclobutene optical waveguides,” Photon. Technol. Lett. 7, 535–537 (1995).
    [CrossRef]
  5. C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
    [CrossRef]
  6. T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
    [CrossRef]
  7. N. Takato, M. Yasu, M. Kawachi, “Low loss high-silica single-mode channel waveguides,” Electron. Lett. 22, 321–322 (1986).
    [CrossRef]
  8. C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” Photon. Technol. Lett. 3, 896–899 (1991).
    [CrossRef]
  9. W. C. Young, D. R. Frey, “Fiber connectors,” in Optical Fiber Telecommunications II, S. E. Miller, I. P. Kaminow, eds. (Academic, New York, 1988), pp. 301–326.

1996 (2)

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

1995 (1)

C. Kane, R. R. Krchnavek, “Benzocyclobutene optical waveguides,” Photon. Technol. Lett. 7, 535–537 (1995).
[CrossRef]

1992 (1)

H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
[CrossRef]

1991 (1)

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

1986 (1)

N. Takato, M. Yasu, M. Kawachi, “Low loss high-silica single-mode channel waveguides,” Electron. Lett. 22, 321–322 (1986).
[CrossRef]

Andrews, M. P.

T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
[CrossRef]

Callender, C. L.

L. Robitaille, C. L. Callender, J. P. Noad, “Polymer waveguide devices for WDM applications,” in Polymer Photonic Devices, B. Kippelen, D. D. C. Bradley, eds., Proc. SPIE3281, 14–24 (1998).
[CrossRef]

Dragone, C.

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Du, X. M.

T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
[CrossRef]

Edwards, C. A.

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Eldada, L.

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

Fardad, M. A.

T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
[CrossRef]

Frey, D. R.

W. C. Young, D. R. Frey, “Fiber connectors,” in Optical Fiber Telecommunications II, S. E. Miller, I. P. Kaminow, eds. (Academic, New York, 1988), pp. 301–326.

Kane, C.

C. Kane, R. R. Krchnavek, “Benzocyclobutene optical waveguides,” Photon. Technol. Lett. 7, 535–537 (1995).
[CrossRef]

Kawachi, M.

N. Takato, M. Yasu, M. Kawachi, “Low loss high-silica single-mode channel waveguides,” Electron. Lett. 22, 321–322 (1986).
[CrossRef]

Kistler, R. C.

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Krchnavek, R. R.

C. Kane, R. R. Krchnavek, “Benzocyclobutene optical waveguides,” Photon. Technol. Lett. 7, 535–537 (1995).
[CrossRef]

Najafi, S. I.

T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
[CrossRef]

Nakamura, S.

H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
[CrossRef]

Noad, J. P.

L. Robitaille, C. L. Callender, J. P. Noad, “Polymer waveguide devices for WDM applications,” in Polymer Photonic Devices, B. Kippelen, D. D. C. Bradley, eds., Proc. SPIE3281, 14–24 (1998).
[CrossRef]

Norwood, R. A.

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

Ohyama, I.

H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
[CrossRef]

Robitaille, L.

L. Robitaille, C. L. Callender, J. P. Noad, “Polymer waveguide devices for WDM applications,” in Polymer Photonic Devices, B. Kippelen, D. D. C. Bradley, eds., Proc. SPIE3281, 14–24 (1998).
[CrossRef]

Shacklette, L. W.

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

Shimizu, T.

H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
[CrossRef]

Stengel, K. M. T.

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

Takato, N.

N. Takato, M. Yasu, M. Kawachi, “Low loss high-silica single-mode channel waveguides,” Electron. Lett. 22, 321–322 (1986).
[CrossRef]

Touam, T.

T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
[CrossRef]

Wu, C.

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

Xu, C.

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

Yanagawa, H.

H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
[CrossRef]

Yardley, J. T.

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

Yasu, M.

N. Takato, M. Yasu, M. Kawachi, “Low loss high-silica single-mode channel waveguides,” Electron. Lett. 22, 321–322 (1986).
[CrossRef]

Young, W. C.

W. C. Young, D. R. Frey, “Fiber connectors,” in Optical Fiber Telecommunications II, S. E. Miller, I. P. Kaminow, eds. (Academic, New York, 1988), pp. 301–326.

Chem. Mater. (1)

C. Xu, L. Eldada, C. Wu, R. A. Norwood, L. W. Shacklette, J. T. Yardley, “Photoimageable, low shrinkage, organic-inorganic hybrid materials for practical multimode channel waveguides,” Chem. Mater. 8, 2701–2703 (1996).
[CrossRef]

Electron. Lett. (1)

N. Takato, M. Yasu, M. Kawachi, “Low loss high-silica single-mode channel waveguides,” Electron. Lett. 22, 321–322 (1986).
[CrossRef]

J. Lightwave Technol. (2)

H. Yanagawa, T. Shimizu, S. Nakamura, I. Ohyama, “Index-and-dimensional taper and its application to photonic devices,” J. Lightwave Technol. 10, 587–591 (1992).
[CrossRef]

L. Eldada, C. Xu, K. M. T. Stengel, L. W. Shacklette, J. T. Yardley, “Laser-fabricated low-loss single-mode raised-rib waveguiding devices in polymers,” J. Lightwave Technol. 14, 1704–1713 (1996).
[CrossRef]

Photon. Technol. Lett. (2)

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

C. Kane, R. R. Krchnavek, “Benzocyclobutene optical waveguides,” Photon. Technol. Lett. 7, 535–537 (1995).
[CrossRef]

Other (3)

W. C. Young, D. R. Frey, “Fiber connectors,” in Optical Fiber Telecommunications II, S. E. Miller, I. P. Kaminow, eds. (Academic, New York, 1988), pp. 301–326.

L. Robitaille, C. L. Callender, J. P. Noad, “Polymer waveguide devices for WDM applications,” in Polymer Photonic Devices, B. Kippelen, D. D. C. Bradley, eds., Proc. SPIE3281, 14–24 (1998).
[CrossRef]

T. Touam, X. M. Du, M. A. Fardad, S. I. Najafi, M. P. Andrews, “Theoretical and experimental study of ridge waveguides derived from hybrid sol-gel glasses,” in Photosensitive Optical Materials and Devices II, M. P. Andrews, ed., Proc. SPIE3282, 17–30 (1998).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Contour plot for the pigtail coupling loss as a function of waveguide size and refractive-index difference between the core and the cladding in a material of refractive index 1.5, as is typical in polymers, solgels, and glass. The single-mode/multimode boundary is also shown. The shaded area represents the region of operation where single-mode waveguides can be fiber pigtailed with less than 0.1-dB loss.

Fig. 2
Fig. 2

Contour plot for the FWHM mode size of a waveguide (n = 1.5) as a function of guide size and index difference.

Fig. 3
Fig. 3

Fundamental mode profiles in waveguides (n = 1.5) for (a) a weakly confining single-mode waveguide, (b) a tightly confining single-mode guide, and (c) a multimode guide.

Fig. 4
Fig. 4

Contour plot for the FWHM mode size of a waveguide (n = 1.5) minus the FWHM mode size of a glass fiber as a function of guide size and index difference.

Fig. 5
Fig. 5

Pigtail coupling loss as a function of the difference in the mode widths of a waveguide (n = 1.5) and a fiber for index difference values of 0.001 to 0.010 (each at core dimensions of 1–10 μm). A wide range of Δn values and guide dimensions results in efficient pigtails.

Fig. 6
Fig. 6

Contour plot for the pigtail coupling loss as a function of waveguide size and index difference in a waveguide with a refractive index of 3.5. The single-mode/multimode boundary is also shown. The shaded area represents the region of operation where single-mode waveguides can be fiber pigtailed with less than 0.1-dB loss.

Fig. 7
Fig. 7

Optimal low-loss single-mode index difference value (solid curve) and allowable variation in this value when pigtail losses below 0.1 dB are desired (dashed curve), as a function of the material index.

Equations (5)

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η = -   E 1 x ,   y E 2 x ,   y d x d y 2 -   | E 1 | 2 d x d y   -   | E 2 | 2 d x d y ,
L = - 0.00013   m 4 + 0.03   m 2 .
Δ n = 0.0115 / n .
V = kh 2 n Δ n - Δ n 2 1 / 2 kh 2 n Δ n 1 / 2 Δ n 2     2 n Δ n ,
δ Δ n = 0.0035 / n .

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