Abstract

The UV-induced refractive-index increase in photosensitive planar waveguides is modeled by an exponential profile. Closed-form field solutions are given and dispersion curves are calculated for TE and TM modes. Modes in air-covered waveguides can be less sensitive to the UV-written profile than modes in buried waveguides.

© 1998 Optical Society of America

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References

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  1. G. D. Maxwell and B. J. Ainslie, Electron. Lett. 31, 95 (1995). M. Svalgard, C. V. Poulsen, A. Bjarklev, and O. Poulsen, Electron. Lett. 30, 1401 (1994); D. Moss, M. Ibsen, F. Oullette, P. Leech, M. Faith, P. Kemeny, O. Leistiko, and C. V. Poulsen, “Photo-induced planar germanosilicate waveguides,” presented at the Australian Conference on Optical Fiber Technology, Melbourne, Australia, December 1994; V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, Appl. Phys. Lett. 13, 1727 (1993); D. Johlen, P. Klose, and E. Brinkmeyer, in Optical Fiber Communication Conference, Vol.??6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper ThI5, pp. 279–280.
    [CrossRef]
  2. B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
    [CrossRef]
  3. D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
    [CrossRef]
  4. D. P. Hand and P. St. J. Russell, Opt. Lett. 15, 102 (1990); J. Albert, B. Malo, F. Bilodeau, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Kawachi, Opt. Lett. 19, 387 (1994)
    [CrossRef] [PubMed]
  5. P. J. Lemaire, A. M. Vengsarkar, W. A. Reed, and D. J. Giovanni, in Optical Fiber Communication Conference, Vol.??8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper WN1, pp. 158–159.
  6. T. Erdogan, A. Partovi, V. Mizrahi, P. J. Lemaire, W. L. Wilson, T. A. Strasser, and A. M. Glass, Appl. Opt. 34, 6738 (1995).
    [CrossRef] [PubMed]
  7. D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).
  8. M. Janos, J. Canning, and M. G. Sceats, Opt. Lett. 21, 1827 (1996).
    [CrossRef] [PubMed]
  9. E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
    [CrossRef]
  10. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).
  11. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  12. H. Kirchhoff, AEU Arch. Elektron. Uebertraguagstech. Electron. Commun. 26, 537 (1972).

1996 (2)

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

M. Janos, J. Canning, and M. G. Sceats, Opt. Lett. 21, 1827 (1996).
[CrossRef] [PubMed]

1995 (2)

T. Erdogan, A. Partovi, V. Mizrahi, P. J. Lemaire, W. L. Wilson, T. A. Strasser, and A. M. Glass, Appl. Opt. 34, 6738 (1995).
[CrossRef] [PubMed]

G. D. Maxwell and B. J. Ainslie, Electron. Lett. 31, 95 (1995). M. Svalgard, C. V. Poulsen, A. Bjarklev, and O. Poulsen, Electron. Lett. 30, 1401 (1994); D. Moss, M. Ibsen, F. Oullette, P. Leech, M. Faith, P. Kemeny, O. Leistiko, and C. V. Poulsen, “Photo-induced planar germanosilicate waveguides,” presented at the Australian Conference on Optical Fiber Technology, Melbourne, Australia, December 1994; V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, Appl. Phys. Lett. 13, 1727 (1993); D. Johlen, P. Klose, and E. Brinkmeyer, in Optical Fiber Communication Conference, Vol.??6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper ThI5, pp. 279–280.
[CrossRef]

1993 (2)

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

1990 (1)

1973 (1)

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

1972 (1)

H. Kirchhoff, AEU Arch. Elektron. Uebertraguagstech. Electron. Commun. 26, 537 (1972).

Abe, M.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

Ainslie, B. J.

G. D. Maxwell and B. J. Ainslie, Electron. Lett. 31, 95 (1995). M. Svalgard, C. V. Poulsen, A. Bjarklev, and O. Poulsen, Electron. Lett. 30, 1401 (1994); D. Moss, M. Ibsen, F. Oullette, P. Leech, M. Faith, P. Kemeny, O. Leistiko, and C. V. Poulsen, “Photo-induced planar germanosilicate waveguides,” presented at the Australian Conference on Optical Fiber Technology, Melbourne, Australia, December 1994; V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, Appl. Phys. Lett. 13, 1727 (1993); D. Johlen, P. Klose, and E. Brinkmeyer, in Optical Fiber Communication Conference, Vol.??6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper ThI5, pp. 279–280.
[CrossRef]

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Albert, J.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Armitage, J. R.

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Bilodeau, F.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Campbell, R. J.

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Canning, J.

Conwell, E. M.

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

Erdogan, T.

Giovanni, D. J.

P. J. Lemaire, A. M. Vengsarkar, W. A. Reed, and D. J. Giovanni, in Optical Fiber Communication Conference, Vol.??8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper WN1, pp. 158–159.

Glass, A. M.

Hand, D. P.

Hibino, Y.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Hill, K. O.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Inniss, D.

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

Janos, M.

Johnson, D. C.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Kashyap, R.

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Kirchhoff, H.

H. Kirchhoff, AEU Arch. Elektron. Uebertraguagstech. Electron. Commun. 26, 537 (1972).

Kosinski, S. G.

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

Lemaire, P. J.

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

T. Erdogan, A. Partovi, V. Mizrahi, P. J. Lemaire, W. L. Wilson, T. A. Strasser, and A. M. Glass, Appl. Opt. 34, 6738 (1995).
[CrossRef] [PubMed]

P. J. Lemaire, A. M. Vengsarkar, W. A. Reed, and D. J. Giovanni, in Optical Fiber Communication Conference, Vol.??8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper WN1, pp. 158–159.

Malo, B.

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

Maxwell, G. D.

G. D. Maxwell and B. J. Ainslie, Electron. Lett. 31, 95 (1995). M. Svalgard, C. V. Poulsen, A. Bjarklev, and O. Poulsen, Electron. Lett. 30, 1401 (1994); D. Moss, M. Ibsen, F. Oullette, P. Leech, M. Faith, P. Kemeny, O. Leistiko, and C. V. Poulsen, “Photo-induced planar germanosilicate waveguides,” presented at the Australian Conference on Optical Fiber Technology, Melbourne, Australia, December 1994; V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, Appl. Phys. Lett. 13, 1727 (1993); D. Johlen, P. Klose, and E. Brinkmeyer, in Optical Fiber Communication Conference, Vol.??6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper ThI5, pp. 279–280.
[CrossRef]

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Mizrahi, V.

Partovi, A.

Reed, W. A.

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

P. J. Lemaire, A. M. Vengsarkar, W. A. Reed, and D. J. Giovanni, in Optical Fiber Communication Conference, Vol.??8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper WN1, pp. 158–159.

Russell, P. St. J.

Sceats, M. G.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Strasser, T. A.

Vengsarkar, A. M.

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

P. J. Lemaire, A. M. Vengsarkar, W. A. Reed, and D. J. Giovanni, in Optical Fiber Communication Conference, Vol.??8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper WN1, pp. 158–159.

Williams, D. L.

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Wilson, W. L.

Wyatt, R. R.

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Zhong, Q.

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

AEU Arch. Elektron. Uebertraguagstech. Electron. Commun. (1)

H. Kirchhoff, AEU Arch. Elektron. Uebertraguagstech. Electron. Commun. 26, 537 (1972).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

D. Inniss, Q. Zhong, A. M. Vengsarkar, W. A. Reed, S. G. Kosinski, and P. J. Lemaire, Appl. Phys. Lett. 21, 1827 (1996).

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

Electron. Lett. (1)

G. D. Maxwell and B. J. Ainslie, Electron. Lett. 31, 95 (1995). M. Svalgard, C. V. Poulsen, A. Bjarklev, and O. Poulsen, Electron. Lett. 30, 1401 (1994); D. Moss, M. Ibsen, F. Oullette, P. Leech, M. Faith, P. Kemeny, O. Leistiko, and C. V. Poulsen, “Photo-induced planar germanosilicate waveguides,” presented at the Australian Conference on Optical Fiber Technology, Melbourne, Australia, December 1994; V. Mizrahi, P. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, and R. M. Atkins, Appl. Phys. Lett. 13, 1727 (1993); D. Johlen, P. Klose, and E. Brinkmeyer, in Optical Fiber Communication Conference, Vol.??6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper ThI5, pp. 279–280.
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

B. Malo, F. Bilodeau, J. Albert, D. C. Johnson, K. O. Hill, Y. Hibino, and M. Abe, Proc. SPIE 2044, 42 (1993).
[CrossRef]

D. L. Williams, B. J. Ainslie, R. Kashyap, G. D. Maxwell, J. R. Armitage, R. J. Campbell, and R. R. Wyatt, Proc. SPIE 2044, 55 (1993).
[CrossRef]

Other (3)

P. J. Lemaire, A. M. Vengsarkar, W. A. Reed, and D. J. Giovanni, in Optical Fiber Communication Conference, Vol.??8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper WN1, pp. 158–159.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

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Figures (4)

Fig. 1
Fig. 1

Normalized refractive-index profile of an UV-written waveguide. Solid and dashed curves show the unexposed and the UV-induced profiles, respectively.

Fig. 2
Fig. 2

Dispersion curves of (a) symmetric buried wave-guide  I and (b) asymmetric air-covered waveguide  II. Solid and dashed curves represent TE and TM modes, respectively.

Fig. 3
Fig. 3

Modal fields of symmetric (solid curves) and asymmetric (dashed curves) waveguides  I and II: (a) magnetic field of the fundamental TM mode at V=2.776, (b)–(d) electric TE mode fields at V=9.714. The vertical dotted lines mark the core region.

Fig. 4
Fig. 4

Increase of the normalized propagation constant δB=Bθ/Δ/H-B0 of the fundamental TE mode versus the UV-induced profile height θ/Δ for profile decay parameters A=1, 2, 3. Solid and dashed curves represent buried and air-covered waveguides  I and II, respectively.

Equations (17)

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n2x=nc2-<x<0ns2+ng22Δ+2θ exp-2αx0<x<tns2t<x<,
1-fX=-C-<X<0H+1-Hexp-2AX0<X<101<X<,
d2dX2+V21-fX-BΨX=0,
ΨX=a expSX, -<X0,
ΨX=b exp-WX, 1X<,
d2dX2+V2H+1-Hexp-2AX-BΨ=0.
ΨX=cJΨJX+cYΨYX,
ΨJX=JνQ exp-AX, ΨYX=YνQ exp-AX,
ν=νB=VB-H1/2/A, Q=V1-H1/2/A,
ΨJ0-SΨJ0ΨY1+WΨY1-ΨY0-SΨY0ΨJ1+WΨJ1=0,
ΨC0=CνQ0, ΨC1=CνQ1,
ΨC0=AQ02Cν+1Q0-Cν-1Q0, ΨC1=AQ12Cν+1Q1-Cν-1Q1,
d2dX2-1n2dn2dXddX+V21-fX-BΨ=0.
d2dX2+V2H+1-H+4A2θV2×exp-2AX-BΦ=0.
ΨCX=1+θ exp-2AXCνQ¯ exp-AX,
ΨJ0-η0SΨJ0ΨY1+η1WΨY1-ΨY0-η0SΨY0ΨJ1+η1WΨJ1=0,
ΨC0=1+θ0CνQ¯0, ΨC1=1+θ1CνQ¯1, ΨC0=AQ02Cν+1Q¯01+θ01+2/ν-Cν-1Q¯01+θ01-2/ν, ΨC1=AQ12Cν+1Q¯11+θ11+2/ν-Cν-1Q¯11+θ11-2/ν.

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