Abstract

Methods of reducing the insertion loss between single-mode fibers and graded-index channel waveguides, and backdiffusion, are analyzed theoretically and compared. Mode mismatch and namely, annealing misalignment losses are calculated to determine the best method and the optimal conditions for their use. The main result of this paper is that, in the single-mode regime, there is no apparent advantage in using backdiffusion instead of the simpler annealing process, in contrast with the multimode case. In the coupling a numerical simulation of waveguide formation by potassium–sodium ion exchange in glass is loss calculation, used for illustration.

© 1988 Optical Society of America

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References

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  1. J. J. Veselka, G. A. Bogert, “Low-Insertion-Loss Channel Waveguides in LiNbO3 Fabricated by Proton Exchange,” Electron. Lett. 23, 265 (1987).
    [CrossRef]
  2. K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
    [CrossRef]
  3. P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable-Index Transition for Efficient Ti:LiNbO3 Waveguide–Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246 (1987).
    [CrossRef]
  4. J. Albert, G. L. Yip, “Wide Single-Mode Channels and Directional Coupler by Two-Step Ion-Exchange in Glass,” IEEE/OSA J. Lightwave Technol. LT-6, 552 (1988).
    [CrossRef]
  5. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).
  6. L. McCaughan, E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3 Waveguide Insertion Loss at λ = 1.3 μm,” IEEE J. Quantum Electron. QE-19, 131 (1983).
    [CrossRef]
  7. A. Mahapatra, J. M. Connors, “Thermal Tapering of Ion-Exchanged Channel Guides in Glass,” Opt. Lett. 13, 169 (1988).
    [CrossRef] [PubMed]

1988 (2)

J. Albert, G. L. Yip, “Wide Single-Mode Channels and Directional Coupler by Two-Step Ion-Exchange in Glass,” IEEE/OSA J. Lightwave Technol. LT-6, 552 (1988).
[CrossRef]

A. Mahapatra, J. M. Connors, “Thermal Tapering of Ion-Exchanged Channel Guides in Glass,” Opt. Lett. 13, 169 (1988).
[CrossRef] [PubMed]

1987 (3)

J. J. Veselka, G. A. Bogert, “Low-Insertion-Loss Channel Waveguides in LiNbO3 Fabricated by Proton Exchange,” Electron. Lett. 23, 265 (1987).
[CrossRef]

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
[CrossRef]

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable-Index Transition for Efficient Ti:LiNbO3 Waveguide–Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246 (1987).
[CrossRef]

1983 (1)

L. McCaughan, E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3 Waveguide Insertion Loss at λ = 1.3 μm,” IEEE J. Quantum Electron. QE-19, 131 (1983).
[CrossRef]

Albert, J.

J. Albert, G. L. Yip, “Wide Single-Mode Channels and Directional Coupler by Two-Step Ion-Exchange in Glass,” IEEE/OSA J. Lightwave Technol. LT-6, 552 (1988).
[CrossRef]

Bogert, G. A.

J. J. Veselka, G. A. Bogert, “Low-Insertion-Loss Channel Waveguides in LiNbO3 Fabricated by Proton Exchange,” Electron. Lett. 23, 265 (1987).
[CrossRef]

Connors, J. M.

Komatsu, K.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
[CrossRef]

Kondo, M.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
[CrossRef]

Mahapatra, A.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).

McCaughan, L.

L. McCaughan, E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3 Waveguide Insertion Loss at λ = 1.3 μm,” IEEE J. Quantum Electron. QE-19, 131 (1983).
[CrossRef]

Murphy, E. J.

L. McCaughan, E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3 Waveguide Insertion Loss at λ = 1.3 μm,” IEEE J. Quantum Electron. QE-19, 131 (1983).
[CrossRef]

Ohta, Y.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
[CrossRef]

Ramaswamy, R. V.

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable-Index Transition for Efficient Ti:LiNbO3 Waveguide–Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246 (1987).
[CrossRef]

Suchoski, P. G.

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable-Index Transition for Efficient Ti:LiNbO3 Waveguide–Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246 (1987).
[CrossRef]

Veselka, J. J.

J. J. Veselka, G. A. Bogert, “Low-Insertion-Loss Channel Waveguides in LiNbO3 Fabricated by Proton Exchange,” Electron. Lett. 23, 265 (1987).
[CrossRef]

Yamazaki, S.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
[CrossRef]

Yip, G. L.

J. Albert, G. L. Yip, “Wide Single-Mode Channels and Directional Coupler by Two-Step Ion-Exchange in Glass,” IEEE/OSA J. Lightwave Technol. LT-6, 552 (1988).
[CrossRef]

Electron. Lett. (1)

J. J. Veselka, G. A. Bogert, “Low-Insertion-Loss Channel Waveguides in LiNbO3 Fabricated by Proton Exchange,” Electron. Lett. 23, 265 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. McCaughan, E. J. Murphy, “Influence of Temperature and Initial Titanium Dimensions on Fiber-Ti:LiNbO3 Waveguide Insertion Loss at λ = 1.3 μm,” IEEE J. Quantum Electron. QE-19, 131 (1983).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (3)

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-Loss Broad-Band LiNbO3 Guided-Wave Phase Modulators Using Titanium/Magnesium Double Diffusion Method,” IEEE/OSA J. Lightwave Technol. LT-5, 1239 (1987).
[CrossRef]

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable-Index Transition for Efficient Ti:LiNbO3 Waveguide–Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246 (1987).
[CrossRef]

J. Albert, G. L. Yip, “Wide Single-Mode Channels and Directional Coupler by Two-Step Ion-Exchange in Glass,” IEEE/OSA J. Lightwave Technol. LT-6, 552 (1988).
[CrossRef]

Opt. Lett. (1)

Other (1)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1982).

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Figures (10)

Fig. 1
Fig. 1

(a) Refractive-index change contours normalized to the value found at the surface of the initial guide: Δn s = 0.09 (substrate index 1.513). Case 1, annealing of initial guide with D = 5 μm and t = 48 min. (b) Normalized amplitude contours of the fundamental TE mode of waveguides shown in (a) (amplitude maximum shown as +).

Fig. 2
Fig. 2

(A) Width (w||) and depth (w) mode size resulting from annealing of case 1. The mode size of the fiber (w f ) is shown for comparison. (B) Ellipticity (e) and asymmetry (a) resulting from annealing of case 1. (C) Coupling loss per facet due to mode mismatch between the waveguide of case 1 and a single-mode fiber (described in the text).

Fig. 3
Fig. 3

(a) Same as Fig. 1(a) for case 2: Annealing of initial guide with D = 2 μm and t = 120 min. (b) Same as Fig. 1(b) for case 2.

Fig. 4
Fig. 4

Same as Fig. 2 for case 2.

Fig. 5
Fig. 5

(a) Same as Fig. 1(a) for case 3: backdiffusion of initial guide with D = 5 μm and t = 48 min. (b) Same as Fig. 1(b) for case 3.

Fig. 6
Fig. 6

Same as Fig. 2 for case 3.

Fig. 7
Fig. 7

(a) Same as Fig. 1(a) for case 4: backdiffusion of initial guide with D = 2 μm and t 120 = min. (b) Same as Fig. 1(b) for case 4.

Fig. 8
Fig. 8

Same as Fig. 2 for case 4.

Fig. 9
Fig. 9

Maximum value of index change, normalized to the surface value of the initial guides (Δn s ), as a function of time for a, case 1; b, case 2; c, case 3; d, case 4.

Fig. 10
Fig. 10

Effect of misalignment between the fiber and channel waveguide on the coupling loss for case 1 and case 2: (a) offset in Y (lateral direction); (b) offset in X (depth direction).

Tables (1)

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Table I Definition of Size Parameters

Equations (5)

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I = ( - + d x d y ψ g ψ l ) 2 ( - + d x d y d ψ f 2 ) ( - + d x d y ψ g 2 ) .
E y ( x , y ) = G ( y ) F ( x ) , G ( y ) = exp [ - ( y 2 / w 2 ) ] , F ( x ) = exp [ - ( x 2 / 4 w u 2 ) ] ; x < 0 exp [ - ( x 2 / 4 w d 2 ) ] ; x > 0.
I = 4 [ ( 4 w f 2 + 1 w u 2 ) - 1 / 2 + ( 4 w f 2 + 1 w d 2 ) - 1 / 2 ] 2 ( 1 w f 2 + 2 w 2 ) w f 2 w w .
w i = w i ( 0 ) + m i t A .
I = 4 w w f exp [ - ( 2.8 y 0 2 w f 2 + w 2 ) ] w ( w f 2 + w 2 ) [ w d exp [ - ( 2.8 x 0 2 w f 2 + 4 w d 2 ) ] w f 2 + 4 w d 2 erfc ( - 2.4 x 0 w d w f w f 2 + 4 w d 2 ) + w u exp [ - ( 2.8 x 0 2 w f 2 + 4 w u 2 ) ] w f 2 + 4 w u 2 erfc ( - 2.4 x 0 w u w f w f 2 + 4 w u 2 ) ] 2 .

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