Abstract

An inverse scattering method is used to design single-mode planar optical waveguides. Waveguides with wider cores compared with those designed by direct scattering methods are obtained, and a numerical example is given.

© 1989 Optical Society of America

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References

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  1. M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).
  2. S. P. Yukon, B. Bendow, J. Opt. Soc. Am. 70, 172 (1980).
    [CrossRef]
  3. A clear exposition of the Gel’fand, Levitan, and Marchenko (GLM) theory is given by I. Kay, The Inverse Scattering Problem, report no. EM-74 (New York University, 1955); Commun. Pure Appl. Math. 13, 371 (1960). See also I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Science, Brookline, Mass., 1982).
  4. A. K. Jordan, S. Ahn, Proc. Inst. Electr. Eng. 126, 945 (1979).
    [CrossRef]
  5. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

1980

1979

A. K. Jordan, S. Ahn, Proc. Inst. Electr. Eng. 126, 945 (1979).
[CrossRef]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

Ahn, S.

A. K. Jordan, S. Ahn, Proc. Inst. Electr. Eng. 126, 945 (1979).
[CrossRef]

Bendow, B.

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).

Jordan, A. K.

A. K. Jordan, S. Ahn, Proc. Inst. Electr. Eng. 126, 945 (1979).
[CrossRef]

Kay, I.

A clear exposition of the Gel’fand, Levitan, and Marchenko (GLM) theory is given by I. Kay, The Inverse Scattering Problem, report no. EM-74 (New York University, 1955); Commun. Pure Appl. Math. 13, 371 (1960). See also I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Science, Brookline, Mass., 1982).

Sodha, M. S.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).

Yukon, S. P.

J. Opt. Soc. Am.

Proc. Inst. Electr. Eng.

A. K. Jordan, S. Ahn, Proc. Inst. Electr. Eng. 126, 945 (1979).
[CrossRef]

Other

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977).

A clear exposition of the Gel’fand, Levitan, and Marchenko (GLM) theory is given by I. Kay, The Inverse Scattering Problem, report no. EM-74 (New York University, 1955); Commun. Pure Appl. Math. 13, 371 (1960). See also I. Kay, H. E. Moses, Inverse Scattering Papers: 1955–1963 (Math Science, Brookline, Mass., 1982).

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Figures (2)

Fig. 1
Fig. 1

Physical model of an inhomogeneous planar optical waveguide for the inverse scattering application.

Fig. 2
Fig. 2

Reconstructed normalized refractive-index profile.

Tables (1)

Tables Icon

Table 1 Comparison of V Values Obtained by Direct and Inverse Methods

Equations (25)

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d 2 E y ¯ ( x ¯ , k 0 ) d x ¯ 2 + [ k 0 2 n 2 ( x ¯ ) - β 2 ] E y ¯ ( x ¯ , k 0 ) = 0 ,
x = x ¯ / L
ψ ( x , k 0 ) = E y ¯ ( x ¯ , k 0 ) E y ¯ 0 ,
V 2 = k 0 2 L 2 ( n 1 2 - n 2 2 ) ,
n 2 ( x ) = { n 1 2 [ 1 - g ( x ) ] 0 x 1 n 2 2 x 0 , x 1 ,
d 2 ψ ( x , k ) d x 2 + [ k 2 - q ( x ) ] ψ ( x , k ) = 0 ,
k 2 = L 2 ( - β 2 + k 0 2 n 2 2 )
q ( x ) = V 2 n 1 2 ( n 1 2 - n 2 2 ) g ( x ) - V 2 .
d d x K ( x , x ) = 1 2 q ( x ) ,
R ( x + t ) + K ( x , t ) + - t x K ( x , ξ ) R ( ξ + t ) d ξ = 0 ,             t < x .
Ψ ( x , t ) = Ψ 0 ( x , t ) + - K ( x , ξ ) Ψ 0 ( ξ , t ) d ξ ,
Ψ 0 ( x , t ) = δ ( x - t ) + R ( x + t ) .
R ( x + t ) = 1 2 π - r ( k ) exp [ - i k ( x + t ) ] d k - i n = 1 N r n exp [ - i k n ( x + t ) ] ,
r ( k ) = - i k 3 + i ,
R ( x + t ) = - 1 + i 3 6 exp [ - ( x + t ) 2 ( 1 + i 3 ) ] - 1 - i 3 6 exp [ - ( x + t ) 2 ( 1 - i 3 ) ] + 1 3 exp ( x + t ) .
f ( p ) = ( p + i k 1 ) ( p + i k 2 ) ( p + i k 3 ) = p 3 - 1.
f ( p ) K ( x , t ) + K ( x , - t ) = 0 ,
f ( - p ) K ( x , - t ) + K ( x , t ) = 0.
K ( x , t ) t = - x = 0 ,
K ( x , t ) t = - x = - R ( x ) x = 0 = 0 ,
K ( x , t ) t = - x = - R ( x ) x = 0 = - 1 ,
K ( x , t ) = - x 8 x 3 + 12 ( t 4 + 12 t ) + x 3 - 3 4 x 3 + 6 t 2 - x 5 + 6 x 2 2 ( 4 x 3 + 6 ) ,
q ( x ) = 24 x ( x 3 - 3 ) ( 2 x 3 + 3 ) 2 ,             x 0.
n 2 ( x ) = { n 2 2 - ( n 1 2 - n 2 2 ) V 2 [ 24 x ( x 3 - 3 ) ( 2 x 3 + 3 ) 2 ] 0 x 1 n 2 2 x 0 , x 1 .
Δ ( x ) = n 2 ( x ) - n 2 2 n 1 2 - n 2 2 ,

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