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  1. H. P. Hsu, A F. Milton, Electron. Lett. 12, 404 (1976).
    [CrossRef]
  2. G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
    [CrossRef] [PubMed]
  3. L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).
  4. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  5. We approximate here by replacing E1(x,y) by E1(0,y), its value at the center of the channel. This makes E(x,y) a product of two field amplitudes, uncoupled in x and y, which can be fit to a rectangular Gaussian mode. The resulting error should not be too large for the first-order mode, whose power is maximum at x = 0.
  6. G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975).
    [CrossRef]
  7. W. E. Milne, Numerical Solution of Differential Equations (Wiley, New York, 1953), p. 88–89.
  8. H. Kogelnik, in Proceedings of the Symposium on Quasi-Optics, J. Fox, Ed. (Polytechnic Press, New York, 1964), p. 333.
  9. P. J. B. Clarricoats, K. B. Chan, Proc. IEE 120, 1371 (1973).
  10. D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).
  11. C. Vassallo, IEEE J. of Quantum Electron. QE-13, 165 (1977).
    [CrossRef]

1977 (2)

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[CrossRef] [PubMed]

C. Vassallo, IEEE J. of Quantum Electron. QE-13, 165 (1977).
[CrossRef]

1976 (1)

H. P. Hsu, A F. Milton, Electron. Lett. 12, 404 (1976).
[CrossRef]

1975 (1)

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975).
[CrossRef]

1973 (1)

P. J. B. Clarricoats, K. B. Chan, Proc. IEE 120, 1371 (1973).

1972 (1)

L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).

1970 (1)

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

1969 (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Burns, W. K.

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[CrossRef] [PubMed]

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975).
[CrossRef]

Chan, K. B.

P. J. B. Clarricoats, K. B. Chan, Proc. IEE 120, 1371 (1973).

Clarricoats, P. J. B.

P. J. B. Clarricoats, K. B. Chan, Proc. IEE 120, 1371 (1973).

Cohen, L. G.

L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).

Hocker, G. B.

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[CrossRef] [PubMed]

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975).
[CrossRef]

Hsu, H. P.

H. P. Hsu, A F. Milton, Electron. Lett. 12, 404 (1976).
[CrossRef]

Kogelnik, H.

H. Kogelnik, in Proceedings of the Symposium on Quasi-Optics, J. Fox, Ed. (Polytechnic Press, New York, 1964), p. 333.

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

Milne, W. E.

W. E. Milne, Numerical Solution of Differential Equations (Wiley, New York, 1953), p. 88–89.

Milton, A F.

H. P. Hsu, A F. Milton, Electron. Lett. 12, 404 (1976).
[CrossRef]

Vassallo, C.

C. Vassallo, IEEE J. of Quantum Electron. QE-13, 165 (1977).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (3)

L. G. Cohen, Bell Syst. Tech. J. 51, 573 (1972).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

Electron. Lett. (1)

H. P. Hsu, A F. Milton, Electron. Lett. 12, 404 (1976).
[CrossRef]

IEEE J. of Quantum Electron. (1)

C. Vassallo, IEEE J. of Quantum Electron. QE-13, 165 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975).
[CrossRef]

Proc. IEE (1)

P. J. B. Clarricoats, K. B. Chan, Proc. IEE 120, 1371 (1973).

Other (3)

W. E. Milne, Numerical Solution of Differential Equations (Wiley, New York, 1953), p. 88–89.

H. Kogelnik, in Proceedings of the Symposium on Quasi-Optics, J. Fox, Ed. (Polytechnic Press, New York, 1964), p. 333.

We approximate here by replacing E1(x,y) by E1(0,y), its value at the center of the channel. This makes E(x,y) a product of two field amplitudes, uncoupled in x and y, which can be fit to a rectangular Gaussian mode. The resulting error should not be too large for the first-order mode, whose power is maximum at x = 0.

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Figures (3)

Fig. 1
Fig. 1

The geometric aspect ratio of an isotropically diffused channel waveguide plotted vs the ratio of the undiffused channel width W to the diffusion length D.

Fig. 2
Fig. 2

The field amplitude in depth for a planar diffused waveguide with V = 3.55 is shown as a function of the normalized depth y/D for a computer calculation (solid curve) and a Gaussian fit (dashed curve). The insert shows the normalized mode width for other values of the normalized diffusion depth V.

Fig. 3
Fig. 3

Plotted in (a) is the ratio of the modal aspect ratio to the geometric aspect ratio for the first-order mode in several diffused channel waveguides. In (b) is the power coupling coefficient for end fire coupling between a circular fiber with mode radius a and a diffused channel waveguide with mode half-widths wx and wy. Both quantities are plotted vs the geometric aspect ratio of the diffused channel waveguide.

Tables (1)

Tables Icon

Table I Gaussian Fit Parameters to the First-Order Mode in Several Diffused Channel Waveguides

Equations (10)

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n 2 ( x , y ) = n b 2 + ( n s 2 - n b 2 ) f ( y / D ) g ( 2 x / W ) ,
f ( y / D ) = exp ( - y 2 / D 2 )
g ( 2 x / W ) = 1 2 { erf [ W 2 D ( 1 + 2 x W ) ] + erf [ W 2 D ( 1 - 2 x W ) ] } .
g ( 2 x 1 / 2 W ) = 1 2 g ( 0 ) .
E ( x , y ) E 1 ( 0 , y ) E 2 ( x ) .
2 E 1 ( u ) u 2 = V 2 ( 0 ) [ b ( 0 ) - f ( u ) E 1 ( u ) ,
V = V o b o 1 / 2 W / D ,
I α = - E c E G d α ( - E c 2 d α - E G 2 d α ) 1 / 2             α = x , y
κ = 4 ( w x a + a w x ) ( w y a + a w y ) ,
κ = ( T I x 2 I y 2 I a 4 ) κ ,

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