Abstract

Bend loss effects can be a significant concern in the design and performance of diffused, buried waveguide devices. Since diffused, buried waveguides typically do not have analytical mode solutions, the bend mode must be expressed as an expansion of straight waveguide modes. For the case of buried ion-exchanged waveguides, the bend loss is affected by bend radius, the duration of the ion exchange and burial processes, as well as the size of the mask opening used to create the waveguides and applied field during burial. The bend loss effects for each of these variables are explored under typical fabrication conditions.

© 2005 Optical Society of America

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  1. J.-S. Gu, P.-A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
    [CrossRef]
  2. T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
    [CrossRef]
  3. S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
    [CrossRef]
  4. W.-k. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
    [CrossRef]
  5. P. D. Sewell, T. M. Benson, “Efficient curvature analysis of buried waveguides,” J. Lightwave Technol. 18, 1321–1329 (2000).
    [CrossRef]
  6. W. J. Song, G. H. Song, B. H. Ahn, M. Kang, “Scalar BPM analyses of TE and TM polarized fields in bent waveguides,” IEEE Trans. Antenna Propagat. 51, 1185–1198 (2003).
    [CrossRef]
  7. D. Dai, S. He, “Analysis of characteristics of bent rib waveguides,” J. Opt. Soc. Am. A 21, 113–121 (2004).
    [CrossRef]
  8. A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
    [CrossRef]
  9. A. Melloni, P. Monguzzi, R. Costa, M. Martinelli, “Design of curved waveguides: the matched bend,” J. Opt. Soc. Am. A 20, 130–137 (2003).
    [CrossRef]
  10. R. K. Lagu, R. Ramaswamy, “Process and waveguide parameter relationships for the design of planar silver ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 176–181 (1986).
    [CrossRef]
  11. R. V. Ramaswamy, S. I. Najafi, “Planar, buried, ion-exchanged glass waveguides: diffusion characteristics,” IEEE J. Quantum Electron. 22, 883–891 (1986).
    [CrossRef]
  12. R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
    [CrossRef]
  13. J. Albert, J. W. Y. Lit, “Full modeling of field-assisted ion exchange for graded index buried channel optical waveguides,” Appl. Opt. 29, 2798–2804 (1990).
    [CrossRef] [PubMed]
  14. A. Tervonen, “Theoretical analysis of ion-exchanged glass waveguides,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech House, Norwood, Mass., 1992), pp. 73–105.
  15. R. G. Walker, C. D. W. Wilkinson, J. A. H. Wilkinson, “Integrated optical waveguiding structures made by silver ion-exchange in glass. 1: The propagation characteristics of stripe ion-exchanged waveguides; a theoretical and experimental investigation,” Appl. Opt. 22, 1923–1928 (1983).
    [CrossRef] [PubMed]
  16. H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
    [CrossRef]
  17. D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
    [CrossRef]
  18. J. Hazart, V. Minier, “Concentration profile calculation for buried ion-exchanged channel waveguides in glass using explicit space-charge analysis,” IEEE J. Quantum Electron. 37, 606–612 (2001).
    [CrossRef]
  19. P. Madasamy, B. R. West, M. M. Morrell, D. F. Geraghty, S. Honkanen, N. Peyghambarian, “Buried ion-exchanged glass waveguides: burial-depth dependence on waveguide width,” Opt. Lett. 28, 1132–1134 (2003).
    [CrossRef] [PubMed]

2004 (1)

2003 (3)

2001 (2)

J. Hazart, V. Minier, “Concentration profile calculation for buried ion-exchanged channel waveguides in glass using explicit space-charge analysis,” IEEE J. Quantum Electron. 37, 606–612 (2001).
[CrossRef]

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

2000 (1)

1997 (2)

W.-k. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
[CrossRef]

1996 (1)

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

1993 (1)

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

1991 (1)

J.-S. Gu, P.-A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

1990 (1)

1988 (1)

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

1986 (2)

R. K. Lagu, R. Ramaswamy, “Process and waveguide parameter relationships for the design of planar silver ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 176–181 (1986).
[CrossRef]

R. V. Ramaswamy, S. I. Najafi, “Planar, buried, ion-exchanged glass waveguides: diffusion characteristics,” IEEE J. Quantum Electron. 22, 883–891 (1986).
[CrossRef]

1983 (1)

1982 (1)

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
[CrossRef]

Ahn, B. H.

W. J. Song, G. H. Song, B. H. Ahn, M. Kang, “Scalar BPM analyses of TE and TM polarized fields in bent waveguides,” IEEE Trans. Antenna Propagat. 51, 1185–1198 (2003).
[CrossRef]

Albert, J.

Benson, T. M.

Besse, P.-A.

J.-S. Gu, P.-A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

Carniel, F.

Cheng, D.

D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
[CrossRef]

Costa, R.

Dai, D.

Geraghty, D. F.

Gopinath, A.

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

Gu, J.-S.

J.-S. Gu, P.-A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

Hazart, J.

J. Hazart, V. Minier, “Concentration profile calculation for buried ion-exchanged channel waveguides in glass using explicit space-charge analysis,” IEEE J. Quantum Electron. 37, 606–612 (2001).
[CrossRef]

He, S.

Honkanen, S.

Kang, M.

W. J. Song, G. H. Song, B. H. Ahn, M. Kang, “Scalar BPM analyses of TE and TM polarized fields in bent waveguides,” IEEE Trans. Antenna Propagat. 51, 1185–1198 (2003).
[CrossRef]

Kim, S.

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

Koshiba, M.

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

Lagu, R. K.

R. K. Lagu, R. Ramaswamy, “Process and waveguide parameter relationships for the design of planar silver ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 176–181 (1986).
[CrossRef]

Lilienhof, H. J.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
[CrossRef]

Lit, J. W. Y.

Madasamy, P.

Martinelli, M.

Melchior, H.

J.-S. Gu, P.-A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

Melloni, A.

Minier, V.

J. Hazart, V. Minier, “Concentration profile calculation for buried ion-exchanged channel waveguides in glass using explicit space-charge analysis,” IEEE J. Quantum Electron. 37, 606–612 (2001).
[CrossRef]

Monguzzi, P.

Morrell, M. M.

Muehlner, D. J.

W.-k. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

Najafi, S. I.

R. V. Ramaswamy, S. I. Najafi, “Planar, buried, ion-exchanged glass waveguides: diffusion characteristics,” IEEE J. Quantum Electron. 22, 883–891 (1986).
[CrossRef]

Pantschew, B.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
[CrossRef]

Peyghambarian, N.

Ramaswamy, R.

R. K. Lagu, R. Ramaswamy, “Process and waveguide parameter relationships for the design of planar silver ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 176–181 (1986).
[CrossRef]

Ramaswamy, R. V.

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

R. V. Ramaswamy, S. I. Najafi, “Planar, buried, ion-exchanged glass waveguides: diffusion characteristics,” IEEE J. Quantum Electron. 22, 883–891 (1986).
[CrossRef]

Ritter, D.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
[CrossRef]

Saarikoski, H.

D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
[CrossRef]

Saarinen, J.

D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
[CrossRef]

Scotti, R.

W.-k. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

Sewell, P. D.

Song, G. H.

W. J. Song, G. H. Song, B. H. Ahn, M. Kang, “Scalar BPM analyses of TE and TM polarized fields in bent waveguides,” IEEE Trans. Antenna Propagat. 51, 1185–1198 (2003).
[CrossRef]

Song, W. J.

W. J. Song, G. H. Song, B. H. Ahn, M. Kang, “Scalar BPM analyses of TE and TM polarized fields in bent waveguides,” IEEE Trans. Antenna Propagat. 51, 1185–1198 (2003).
[CrossRef]

Srivastava, R.

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

Tervonen, A.

D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
[CrossRef]

A. Tervonen, “Theoretical analysis of ion-exchanged glass waveguides,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech House, Norwood, Mass., 1992), pp. 73–105.

Voges, E.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
[CrossRef]

Walker, R. G.

Wang, W.-k.

W.-k. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

West, B. R.

Wilkinson, C. D. W.

Wilkinson, J. A. H.

Yamamoto, T.

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (4)

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-induced index profiles of multimode ion-exchanged strip waveguides,” IEEE J. Quantum Electron. QE-18, 1877–1883 (1982).
[CrossRef]

J. Hazart, V. Minier, “Concentration profile calculation for buried ion-exchanged channel waveguides in glass using explicit space-charge analysis,” IEEE J. Quantum Electron. 37, 606–612 (2001).
[CrossRef]

R. V. Ramaswamy, S. I. Najafi, “Planar, buried, ion-exchanged glass waveguides: diffusion characteristics,” IEEE J. Quantum Electron. 22, 883–891 (1986).
[CrossRef]

J.-S. Gu, P.-A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

IEEE Trans. Antenna Propagat. (1)

W. J. Song, G. H. Song, B. H. Ahn, M. Kang, “Scalar BPM analyses of TE and TM polarized fields in bent waveguides,” IEEE Trans. Antenna Propagat. 51, 1185–1198 (2003).
[CrossRef]

J. Lightwave Technol. (7)

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

W.-k. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

P. D. Sewell, T. M. Benson, “Efficient curvature analysis of buried waveguides,” J. Lightwave Technol. 18, 1321–1329 (2000).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

R. K. Lagu, R. Ramaswamy, “Process and waveguide parameter relationships for the design of planar silver ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 176–181 (1986).
[CrossRef]

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

Opt. Commun. (1)

D. Cheng, J. Saarinen, H. Saarikoski, A. Tervonen, “Simulation of filed-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity,” Opt. Commun. 137, 233–238 (1997).
[CrossRef]

Opt. Lett. (1)

Other (1)

A. Tervonen, “Theoretical analysis of ion-exchanged glass waveguides,” in Introduction to Glass Integrated Optics, S. I. Najafi, ed. (Artech House, Norwood, Mass., 1992), pp. 73–105.

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Figures (8)

Fig. 1
Fig. 1

Contour plots of the index distribution for waveguides produced with a 20-min ion exchange (a) before burial with contours representing an index change of 0.01 from 1.51 to 1.55 and (b) after 240-min burial at 600 V with contours representing an index change of 0.0015 from 1.5085 to 1.519.

Fig. 2
Fig. 2

Contour plots of the TE fundamental modes for the straight waveguides in Fig. 1. Contours represent a 15% increase in mode field irradiance for both plots.

Fig. 3
Fig. 3

Effect of ion exchange time on bend loss. Waveguides are created by a 10–25-min ion exchange with a 3.0-μm waveguide opening, followed by a 600-V burial. A 1.4-cm bend radius is used in each case.

Fig. 4
Fig. 4

Effect of waveguide opening width on bend loss. Waveguides are created by a 20-min ion exchange with a 2.0–3.5-μm waveguide opening, followed by a 600-V burial. A bend radius of 1.4 cm is used in each case.

Fig. 5
Fig. 5

Effect of bend radius on bend loss for waveguides created by a 20-min ion exchange with a 3.0-μm waveguide opening and a 240-min burial at 600 V.

Fig. 6
Fig. 6

Effect of applied field on bend loss for waveguides created by a 20-min ion exchange with a 3.0-μm waveguide opening and a 1.4-cm bend radius.

Fig. 7
Fig. 7

Bend loss of waveguides buried to a depth of approximately 8.0 μm by use of different applied fields and a bend radius of 1.4 cm. Each waveguide was created by a 20-min ion exchange with a 3.0-μm waveguide opening.

Fig. 8
Fig. 8

Effect of thermal annealing on bend loss. The waveguides are buried to a depth of approximately 8.0 μm after 135, 150, 180, 210, and 240 min (for a 1000–600-V burial voltages), then the applied field is removed. The waveguides are then annealed for a total time (burial plus anneal) of 240 min.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

d z ( x ) = r ( x ) d θ .
E B ( x , y ) θ = 0 = n = 1 N a n Ψ n ( x , y ) ,
E B ( x , y ) θ = d θ = n = 1 N a n Ψ n ( x , y ) exp ( - γ n d z ) ,
exp ( - ν d θ ) ( 1 - ν d θ ) ,
n = 1 N a n Ψ n ( 1 - γ n r d θ ) = ( 1 - v d θ ) n = 1 N a n Ψ n .
n = 1 N a n Ψ n γ n ( R + x ) = v n = 1 N a n Ψ n .
a m γ m R + n = 1 N a n γ n c m n = ν a m ,
c m n = x Ψ n Ψ m * d x d y .
( R I + C ) Ga = ν a ,
n eff = λ 2 π R Im ( ν ) .
loss = m n 0 θ c m n d θ .
C A t = D A 1 - α C A [ 2 C A + α ( C A ) 2 1 - α C A - e E ext C A k B T ] .

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