Abstract

The method of parallel end-butt coupling has been used to couple GaAs laser diodes to Ta2O5 thin film waveguides. Theoretical caluclations predict that a coupling efficiency into the lowest order waveguide mode of 90% is achievable if the thicknesses of the waveguide (tg) and the laser light emitting layer (tL) are equal. Experimentally, efficiencies as high as 45.1% have been measured for laser and waveguide combinations with tg/tL = 0.34. The tolerance to misalignment of the laser and waveguide has been theoretically and experimentally evaluated.

© 1977 Optical Society of America

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References

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  1. R. G. Hunsperger, A. Lee, in Digest of Technical Papers, OSA Topical Meeting on Integrated Optics, Salt Lake City, Utah, 12–14 January1976.
  2. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]

1973

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Hunsperger, R. G.

R. G. Hunsperger, A. Lee, in Digest of Technical Papers, OSA Topical Meeting on Integrated Optics, Salt Lake City, Utah, 12–14 January1976.

Lee, A.

R. G. Hunsperger, A. Lee, in Digest of Technical Papers, OSA Topical Meeting on Integrated Optics, Salt Lake City, Utah, 12–14 January1976.

Yariv, A.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Other

R. G. Hunsperger, A. Lee, in Digest of Technical Papers, OSA Topical Meeting on Integrated Optics, Salt Lake City, Utah, 12–14 January1976.

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Figures (5)

Fig. 1
Fig. 1

Butt coupled laser colinear with waveguide.

Fig. 2
Fig. 2

Butt coupled laser angled with waveguide.

Fig. 3
Fig. 3

Comparison of theoretical and experimental coupling coefficient data for t L = 5.8 μm.

Fig. 4
Fig. 4

Tolerance to transverse displacement.

Fig. 5
Fig. 5

Tolerance to laser/waveguide spacing.

Tables (2)

Tables Icon

Table I Measured Coupling Efficiencies Based on Transmitted Power Uncorrected for Waveguide Losses

Tables Icon

Table II Coupling Efficiencies Corrected for Waveguide Attenuation and Output Reflection Loss

Equations (28)

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E g ( x ) = 2 ( ω μ 0 β g t g ) 1 / 2 cos π x t g , E L ( x ) = 2 ( ω μ 0 β L t L ) 1 / 2 cos π x t L ,
E g S ( x ) = 2 ( ω μ 0 β g S t g ) 1 / 2 cos π x S t g , S = 1 , 3 , 5 , E g S ( x ) = 2 ( ω μ 0 β g S t g ) 1 / 2 sin π x S t g , S = 2 , 4 .
- 1 2 - E y H x * d x = 1
E y and H x = - i ω μ 0 δ E y δ z
- 1 2 - E y H x * d x
E ¯ y ( x ) = E ¯ o ( x ) exp ( - i β ¯ o z ) + r o E ¯ o ( x ) exp ( - i β ¯ o z ) + k 0 r k E ¯ k ( x ) exp ( - β ¯ k z ) .
H ¯ y ( x ) = - i ω μ o δ δ z E ¯ y ( x ) = - β ¯ o ω μ o E ¯ o ( x ) exp ( - i β ¯ o z ) + 1 ω μ o k 0 r k β ¯ k E ¯ k ( x ) × exp ( i β ¯ k z ) + r o β ¯ o ω μ o E ¯ o ( x ) exp ( i β ¯ o z ) .
E y ( x ) = m A m E m ( x ) exp ( - i β m z ) , H y ( x ) = m - β m A m ω μ o E m ( x ) exp ( - i β m z ) .
k 0 r k E ¯ k ( x ) + ( r o + 1 ) E ¯ o ( x ) = m A m E m ( x ) ,
k 0 β ¯ k r k E ¯ k ( x ) + β ¯ o ( r o - 1 ) E ¯ o ( x ) = m - β m A m E m ( x ) .
m / S - E m ( x ) E S ( x ) = 2 ω μ 0 β S δ S , m .
k 0 r k k ¯ S + ( r o + 1 ) 0 ¯ S = 2 ω μ o β S A S ,
k 0 r k β ¯ k k ¯ S + β ¯ o ( r o - 1 ) 0 ¯ S = - 2 ω μ o A s ,
k ¯ S - E ¯ k ( x ) E S ( x ) d x .
k 0 r k k ¯ S + ( r o - 1 )     0 ¯ S = - 2 ω μ o A S β ¯ o .
0 ¯ S = ω μ o A S ( 1 β S + 1 β ¯ o ) .
A S = 1 ω μ o ( β ¯ o β S β ¯ o + β S ) - E ¯ o ( x ) E S ( x ) d x .
A S = 4 β ¯ o 1 / 2 β S 1 / 2 ( β ¯ o + β S ) ( t g t L ) 1 / 2 - t g / 2 t g / 2 cos π x S t g cos π x t L d x ,
A S 4 ( n L n S ) 1 / 2 ( n L + n S ) ( t g t L ) 1 / 2 - t g / 2 t g / 2 cos π x S t g cos π x t L d x             S = 1 , 3 , 5 A S 0             S = 2 , 4
A S = 8 ( n L n S ) 1 / 2 π S ( n L + n S ) cos ( π t g 2 t L ) ( t g t L ) 1 / 2 1 1 - ( t g / S t L ) 2 .
A S 2 = ( 8 π S ) 2 n L n S ( n L + n S ) 2 cos 2 ( π t g 2 t L ) × 1 [ 1 - ( t g / S t L ) 2 ] 2 ( t g t L )             S = 1 , 3 , 5 A S 2 0             S = 2 , 4 .
A S 2 = 64 S 2 π 2 · n L n g ( n L + n g ) 2 · cos 2 ( π t g 2 t L ) · 1 [ 1 - ( t g / S t L ) 2 ] 2 · t g t L sin 2 ( S π 2 ) .
z = z cos ϕ - x sin ϕ , x = z sin ϕ + x cos ϕ ,
- t g / 2 t g / 2 E ¯ o x cos ϕ E S ( x ) exp ( i β S x tan ϕ ) d x .
( tan ϕ ) max ( λ o ) / ( n g t g ) ,
( tan ϕ ) max ¼ , ϕ max ~ 14° .
S = 1 1.6 dB / cm ; S = 3 1.6 dB / cm ; S = 5 1.8 dB / cm .
R = ( n 2 - n 1 n 2 + n 1 ) 2 = ( 2.0 - 1 2.0 + 1 ) 2 = 0.11.

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