Abstract

We present measured losses in waveguide sections that are caused by connecting two parallel noncollinear straight waveguides and compare the results with theory. Two different offset transitions are considered, one composed of a straight section with sharp corner bends and the other exhibiting a smooth S-shaped transition. These two types of transitions are compared with each other to determine when each has the lowest loss. In general, sharp corner bends are preferred for small offsets, whereas larger offsets exhibit lower loss with the S-bend design. The experimental results were measured for 3-μm-wide Ti-diffused LiNbO3 single-mode waveguides.

© 1980 Optical Society of America

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References

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  1. H. F. Taylor, “Power loss at directional change in dielectric waveguides,” Appl. Opt. 13, 642–647 (1974).
    [CrossRef] [PubMed]
  2. H. F. Taylor, “Losses at corner bends in dielectric waveguides,” Appl. Opt. 16, 711–716 (1977).
    [CrossRef] [PubMed]
  3. M. J. Taylor, H. F. Taylor, “Coherent mode coupling at waveguide bends,” presented at Topical Meeting on Integrated and Guided Wave Optics, Salt Lake City, Utah, 1978, paper WD4.
  4. E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
  5. L. Lewin, “Radiation from curved dielectric slabs and fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
    [CrossRef]
  6. E. F. Kuester, D. C. Chang, “Surface-wave radiation from curved dielectric slabs and fibers,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).
    [CrossRef]
  7. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216–220 (1976).
    [CrossRef]
  8. M. Miyagi, S. Nishida, “Bending losses of dielectric rectangular waveguides for integrated optics,” J. Opt. Soc. Am. 68, 316–319 (1978).
    [CrossRef]
  9. D. Marcuse, “Radiation losses of parabolic-index slabs and fibers with bent axis,” Appl. Opt. 17, 755–762 (1978).
    [CrossRef] [PubMed]
  10. I. A. White, “Radiation from bends in optical waveguides: the volume current method,” Microwave Opt. Acoust. 3, 186–188 (1979).
    [CrossRef]
  11. D. Marcuse, “Length optimization of an S-shaped transition between offset optical waveguides,” Appl. Opt. 17, 763–768 (1978).
    [CrossRef] [PubMed]
  12. I. A. White, L. D. Hutcheson, J. J. Burke, “Radiation loss due to directional changes of the axis of indiffused dielectric channel waveguides. Part I: Curvature-induced loss; Part II: Scattering loss at waveguide junctions,” J. Opt. Soc. Am. (submitted for publication).
  13. I. A. White, L. D. Hutcheson, J. J. Burke, “End-fire coupling between optical fibers and diffused channel waveguides: comment,” Appl. Opt. 18, 2362 (1979).
    [CrossRef]
  14. W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
    [CrossRef]
  15. G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
    [CrossRef]
  16. G. B. Hocker, W. K. Burns, “Mode dispersion in diffused channel waveguides by the effective index method,” Appl. Opt. 16, 113–118 (1977).
    [CrossRef] [PubMed]
  17. W. K. Burns, G. B. Hocker, “End fire coupling between optical fibers and diffused channel waveguides,” Appl. Opt. 16, 2048–2050 (1977).
    [CrossRef] [PubMed]
  18. L. D. Hutcheson, I. A. White, J. J. Burke, “Experimental measurements of loss due to bends,” Part III, J. Opt. Soc. Am. (submitted for publication).

1979 (3)

I. A. White, “Radiation from bends in optical waveguides: the volume current method,” Microwave Opt. Acoust. 3, 186–188 (1979).
[CrossRef]

I. A. White, L. D. Hutcheson, J. J. Burke, “End-fire coupling between optical fibers and diffused channel waveguides: comment,” Appl. Opt. 18, 2362 (1979).
[CrossRef]

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
[CrossRef]

1978 (3)

1977 (3)

1976 (1)

1975 (2)

E. F. Kuester, D. C. Chang, “Surface-wave radiation from curved dielectric slabs and fibers,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).
[CrossRef]

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

1974 (2)

H. F. Taylor, “Power loss at directional change in dielectric waveguides,” Appl. Opt. 13, 642–647 (1974).
[CrossRef] [PubMed]

L. Lewin, “Radiation from curved dielectric slabs and fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
[CrossRef]

1969 (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

Burke, J. J.

I. A. White, L. D. Hutcheson, J. J. Burke, “End-fire coupling between optical fibers and diffused channel waveguides: comment,” Appl. Opt. 18, 2362 (1979).
[CrossRef]

L. D. Hutcheson, I. A. White, J. J. Burke, “Experimental measurements of loss due to bends,” Part III, J. Opt. Soc. Am. (submitted for publication).

I. A. White, L. D. Hutcheson, J. J. Burke, “Radiation loss due to directional changes of the axis of indiffused dielectric channel waveguides. Part I: Curvature-induced loss; Part II: Scattering loss at waveguide junctions,” J. Opt. Soc. Am. (submitted for publication).

Burns, W. K.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
[CrossRef]

G. B. Hocker, W. K. Burns, “Mode dispersion in diffused channel waveguides by the effective index method,” Appl. Opt. 16, 113–118 (1977).
[CrossRef] [PubMed]

W. K. Burns, G. B. Hocker, “End fire coupling between optical fibers and diffused channel waveguides,” Appl. Opt. 16, 2048–2050 (1977).
[CrossRef] [PubMed]

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

Chang, D. C.

E. F. Kuester, D. C. Chang, “Surface-wave radiation from curved dielectric slabs and fibers,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).
[CrossRef]

Hocker, G. B.

Hutcheson, L. D.

I. A. White, L. D. Hutcheson, J. J. Burke, “End-fire coupling between optical fibers and diffused channel waveguides: comment,” Appl. Opt. 18, 2362 (1979).
[CrossRef]

L. D. Hutcheson, I. A. White, J. J. Burke, “Experimental measurements of loss due to bends,” Part III, J. Opt. Soc. Am. (submitted for publication).

I. A. White, L. D. Hutcheson, J. J. Burke, “Radiation loss due to directional changes of the axis of indiffused dielectric channel waveguides. Part I: Curvature-induced loss; Part II: Scattering loss at waveguide junctions,” J. Opt. Soc. Am. (submitted for publication).

Klein, P. H.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
[CrossRef]

Kuester, E. F.

E. F. Kuester, D. C. Chang, “Surface-wave radiation from curved dielectric slabs and fibers,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).
[CrossRef]

Lewin, L.

L. Lewin, “Radiation from curved dielectric slabs and fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

Marcuse, D.

Miyagi, M.

Nishida, S.

Plew, L. E.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
[CrossRef]

Taylor, H. F.

H. F. Taylor, “Losses at corner bends in dielectric waveguides,” Appl. Opt. 16, 711–716 (1977).
[CrossRef] [PubMed]

H. F. Taylor, “Power loss at directional change in dielectric waveguides,” Appl. Opt. 13, 642–647 (1974).
[CrossRef] [PubMed]

M. J. Taylor, H. F. Taylor, “Coherent mode coupling at waveguide bends,” presented at Topical Meeting on Integrated and Guided Wave Optics, Salt Lake City, Utah, 1978, paper WD4.

Taylor, M. J.

M. J. Taylor, H. F. Taylor, “Coherent mode coupling at waveguide bends,” presented at Topical Meeting on Integrated and Guided Wave Optics, Salt Lake City, Utah, 1978, paper WD4.

West, E. J.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
[CrossRef]

White, I. A.

I. A. White, “Radiation from bends in optical waveguides: the volume current method,” Microwave Opt. Acoust. 3, 186–188 (1979).
[CrossRef]

I. A. White, L. D. Hutcheson, J. J. Burke, “End-fire coupling between optical fibers and diffused channel waveguides: comment,” Appl. Opt. 18, 2362 (1979).
[CrossRef]

I. A. White, L. D. Hutcheson, J. J. Burke, “Radiation loss due to directional changes of the axis of indiffused dielectric channel waveguides. Part I: Curvature-induced loss; Part II: Scattering loss at waveguide junctions,” J. Opt. Soc. Am. (submitted for publication).

L. D. Hutcheson, I. A. White, J. J. Burke, “Experimental measurements of loss due to bends,” Part III, J. Opt. Soc. Am. (submitted for publication).

Appl. Opt. (7)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

IEEE J. Quantum Electron. (2)

E. F. Kuester, D. C. Chang, “Surface-wave radiation from curved dielectric slabs and fibers,” IEEE J. Quantum Electron. QE-11, 903–907 (1975).
[CrossRef]

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

L. Lewin, “Radiation from curved dielectric slabs and fibers,” IEEE Trans. Microwave Theory Tech. MTT-22, 718–727 (1974).
[CrossRef]

J. Appl. Phys. (1)

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, “Ti diffusion in Ti:LiNbO3 planar and channel optical waveguides,” J. Appl. Phys. 50, 6175–6182 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

Microwave Opt. Acoust. (1)

I. A. White, “Radiation from bends in optical waveguides: the volume current method,” Microwave Opt. Acoust. 3, 186–188 (1979).
[CrossRef]

Other (3)

M. J. Taylor, H. F. Taylor, “Coherent mode coupling at waveguide bends,” presented at Topical Meeting on Integrated and Guided Wave Optics, Salt Lake City, Utah, 1978, paper WD4.

I. A. White, L. D. Hutcheson, J. J. Burke, “Radiation loss due to directional changes of the axis of indiffused dielectric channel waveguides. Part I: Curvature-induced loss; Part II: Scattering loss at waveguide junctions,” J. Opt. Soc. Am. (submitted for publication).

L. D. Hutcheson, I. A. White, J. J. Burke, “Experimental measurements of loss due to bends,” Part III, J. Opt. Soc. Am. (submitted for publication).

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Figures (2)

Fig. 1
Fig. 1

Two configurations showing transverse and axial offset. (a) Two-corner-bend approach, (b) S-bend approach.

Fig. 2
Fig. 2

Loss for the two configurations shown in Fig. 1 as a function of Xs/Zs. The S bend is plotted with the radius of curvature with R0 as a parameter.

Tables (1)

Tables Icon

Table 1 Waveguide Parameters for Z-Cut TE-Mode LiNbO3

Equations (22)

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P c = P i a 12 2 a 23 2 exp ( - γ 0 L 0 ) ,
a 12 2 = a 23 2 = exp ( - β 2 X 0 2 sin 2 θ T / 4 ) ,
P s = P i a 45 2 a 56 2 a 67 2 × exp ( - γ 0 L 1 - γ 2 L 2 - γ 3 L 3 ) ,
γ 23 = { [ ( π Q ) 3 R 0 ] - 1 / 2 ( V 2 Y 1 ) 2 I y 2 × exp [ ( Q X 0 ) 2 2 - 2 y 0 2 ( Y 0 2 + D 2 ) ] × [ ( 1 + d X 1 ) I x ( 1 ) + d I x ( 2 ) ] 2 exp ( - 2 Q 3 R 0 / 3 β 2 ) } / { 8 X 0 Y 0 [ 1 + ( d X 0 2 ) 2 ] S y } ,
V 2 = k 0 2 ( n s 2 - n b 2 ) ,
Q 2 = ( β 2 - n b 2 k 0 2 ) ,
Y 1 = Y 0 D / ( Y 0 2 + D 2 ) 1 / 2 ,
S y = Y 0 2 ( y 0 2 Y 0 2 + 0.25 ) [ 1 + erf ( 2 y 0 / Y 0 ) ] ,
I y = Y 1 { Y 1 y 0 Y 0 2 [ 1 + erf ( Y 1 y 0 Y 0 2 ) ] + exp [ - ( Y 1 y 0 Y 0 2 ) 2 ] / π } ,
I x ( 1 ) = X 0 [ erf ( ω + D / X 0 ) + erf ( ω - D / X 0 ) - erf ( ω + / P ) - erf ( ω - / P ) ] ,
I x ( 2 ) = π X 0 3 p D sinh ( W Q X 0 2 / 2 D 2 p 2 ) × exp ( - { ( W / 2 D ) 2 + [ ( X 1 / D ) 2 / p 2 ] } ) ,
P 2 = 1 + ( X 0 / D ) 2 ,
X 1 = Q X 0 2 / 2 ,
d = ( k 0 n b X 0 ) 2 / 2 R 0 ,
ω ± = W / 2 D ± ( X 1 / D ) .
E ( Y ) = Y exp [ - ( Y - y 0 ) 2 / Y 0 2 ] .
a 45 2 = a 67 2 = 1 / [ 1 + ( d X 0 / 2 ) 2 ] ,
a 56 2 = [ 1 - ( d X 0 / 2 ) 2 ] 2 / [ 1 + ( d X 0 / 2 ) 2 ] 2 .
θ T = tan - 1 ( X s / Z s ) ,
R 0 = ( Z s / 4 ) { [ 1 + ( X s / Z s ) 2 ] / ( X s / Z s ) } ,
ϕ = cos - 1 { [ 1 - ( X s / Z s ) 2 ] / [ 1 + ( X s / Z s ) 2 } .
L 0 - L 1 X s 2 / 2 Z s ,

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