Abstract

The GaAlAs laser-diode-to-diffused-waveguide edge-coupling efficiency has been evaluated using a Gaussian model for both the waveguide mode and the laser-output mode. The results of the calculation are shown to be in good agreement with previously unpublished coupling data.

© 1979 Optical Society of America

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References

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  1. E. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328 (1973).
    [CrossRef]
  2. W. K. Burns, G. B. Hocker, “End fire coupling between optical fibers and diffused channel waveguides,” Appl. Opt. 16, 2048 (1977).
    [CrossRef] [PubMed]
  3. D. Botez, M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-hetero-junction lasers,” IEEE J. Quantum Electron. QE-14, 827 (1978).
    [CrossRef]
  4. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, and Winston, New York, 1976).
  5. W. K. Burns, “Laser-diode end-fire coupling into Ti:LiNbO3 waveguides,” to be published.

1978

D. Botez, M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-hetero-junction lasers,” IEEE J. Quantum Electron. QE-14, 827 (1978).
[CrossRef]

1977

1973

E. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

Botez, D.

D. Botez, M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-hetero-junction lasers,” IEEE J. Quantum Electron. QE-14, 827 (1978).
[CrossRef]

Burns, W. K.

Conwell, E.

E. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

Ettenberg, M.

D. Botez, M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-hetero-junction lasers,” IEEE J. Quantum Electron. QE-14, 827 (1978).
[CrossRef]

Hocker, G. B.

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, and Winston, New York, 1976).

Appl. Opt.

Appl. Phys. Lett.

E. Conwell, “Modes in optical waveguides formed by diffusion,” Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

IEEE J. Quantum Electron.

D. Botez, M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-hetero-junction lasers,” IEEE J. Quantum Electron. QE-14, 827 (1978).
[CrossRef]

Other

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, and Winston, New York, 1976).

W. K. Burns, “Laser-diode end-fire coupling into Ti:LiNbO3 waveguides,” to be published.

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Figures (3)

Fig. 1
Fig. 1

Comparison of measured (open circles) and calculated dependence of the coupling efficiency on longitudinal misalignment (z). Tabular inset shows the (z = 0) coupling efficiencies inferred from the calculation.

Fig. 2
Fig. 2

Effect of phase on calculated coupling efficiency. Upper curve neglects phase variation, whereas lower curve includes phase variation of ψ1(x,z).

Fig. 3
Fig. 3

Phase variation of ψ1(x,z) at z = 2.0 μm, the position of the peak of the upper curve in Fig. 2.

Equations (8)

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ψ 1 ( x , z ) = A ( z ) exp [ - ( x - Δ w 1 ) 2 ] × exp [ - i k ( x - Δ ) 2 2 R 1 ( z ) ] exp [ - i ( k z - ω t ) ] ,
w 1 2 ( z ) = w 10 2 [ 1 + ( λ z π w 10 2 ) 2 ] ,
R 1 ( z ) = z [ 1 + ( π w 10 2 λ z ) 2 ] .
ψ 2 ( x , z ) = B ( z ) exp [ - ( x w 20 ) 2 ] exp [ - i ( k z - ω t ) ] ,
η = | - ψ 1 ( x , z ) ψ 2 * ( x , z ) d x | 2 - ψ 1 ( x , z ) ψ 1 * ( x , z ) d x - ψ 2 ( x , z ) ψ 2 * ( x , z ) d x .
η = η 0 1 + γ exp { - [ ( w 20 / w 1 ) η 0 + 2 γ 1 + γ ] Δ 2 w 20 2 } ,
γ = [ k 2 R 1 ( z ) ] 2 ( w 1 w 20 η 0 2 ) 2 ,
η 0 = 2 w 1 w 20 w 1 2 + w 20 2

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