Abstract

We present a comparison of two recently developed methods of analyzing optical waveguides. One of them is numerical, and the other is an approximate analytical method.

© 1990 Optical Society of America

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References

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  1. C. H. Henry, B. H. Verbeek, “Solution of the Scalar Wave Equation for Arbitrarily Shaped Dielectric Waveguides by Two-Dimensional Fourier Analysis,” IEEE/IOSA J. Lightwave Technol. LT-7, 308–313 (1989).
    [CrossRef]
  2. J. C. Bradley, A. L. Kellner, “Modal Analysis of Dielectric Channel Waveguides Using a Tensor Product Method,” J. Opt. Soc. Am. A 6, 1529–1537 (1989); see also J. C. Bradley, “Multimode Structure of Diffused Slab/Channel Waveguides in Uniaxial Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 80–89 (1983).
    [CrossRef]
  3. I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “Approximate Solution to the Scalar Wave Equation for Planar Optical Waveguides,” submitted to Appl. Opt.
  4. A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical Analysis of Planar Optical Waveguides Using Matrix Approach,” IEEE/IOSA J. Lightwave Technol. LT-5, 660–667 (1987).
    [CrossRef]
  5. E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328–330 (1973).
    [CrossRef]
  6. A. Gedeon, “Comparison Between Rigorous Theory and WKB Analysis of Modes in Graded Index Waveguides,” Opt. Commun. 12, 329–332 (1974).
    [CrossRef]

1989 (2)

1987 (1)

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical Analysis of Planar Optical Waveguides Using Matrix Approach,” IEEE/IOSA J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

1974 (1)

A. Gedeon, “Comparison Between Rigorous Theory and WKB Analysis of Modes in Graded Index Waveguides,” Opt. Commun. 12, 329–332 (1974).
[CrossRef]

1973 (1)

E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328–330 (1973).
[CrossRef]

Bradley, J. C.

Conwell, E. M.

E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328–330 (1973).
[CrossRef]

Gallawa, R. L.

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “Approximate Solution to the Scalar Wave Equation for Planar Optical Waveguides,” submitted to Appl. Opt.

Gedeon, A.

A. Gedeon, “Comparison Between Rigorous Theory and WKB Analysis of Modes in Graded Index Waveguides,” Opt. Commun. 12, 329–332 (1974).
[CrossRef]

Ghatak, A. K.

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical Analysis of Planar Optical Waveguides Using Matrix Approach,” IEEE/IOSA J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “Approximate Solution to the Scalar Wave Equation for Planar Optical Waveguides,” submitted to Appl. Opt.

Goyal, I. C.

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “Approximate Solution to the Scalar Wave Equation for Planar Optical Waveguides,” submitted to Appl. Opt.

Henry, C. H.

C. H. Henry, B. H. Verbeek, “Solution of the Scalar Wave Equation for Arbitrarily Shaped Dielectric Waveguides by Two-Dimensional Fourier Analysis,” IEEE/IOSA J. Lightwave Technol. LT-7, 308–313 (1989).
[CrossRef]

Kellner, A. L.

Shenoy, M. R.

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical Analysis of Planar Optical Waveguides Using Matrix Approach,” IEEE/IOSA J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

Thyagarajan, K.

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical Analysis of Planar Optical Waveguides Using Matrix Approach,” IEEE/IOSA J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

Verbeek, B. H.

C. H. Henry, B. H. Verbeek, “Solution of the Scalar Wave Equation for Arbitrarily Shaped Dielectric Waveguides by Two-Dimensional Fourier Analysis,” IEEE/IOSA J. Lightwave Technol. LT-7, 308–313 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

E. M. Conwell, “Modes in Optical Waveguides Formed by Diffusion,” Appl. Phys. Lett. 23, 328–330 (1973).
[CrossRef]

IEEE/IOSA J. Lightwave Technol. (2)

C. H. Henry, B. H. Verbeek, “Solution of the Scalar Wave Equation for Arbitrarily Shaped Dielectric Waveguides by Two-Dimensional Fourier Analysis,” IEEE/IOSA J. Lightwave Technol. LT-7, 308–313 (1989).
[CrossRef]

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, “Numerical Analysis of Planar Optical Waveguides Using Matrix Approach,” IEEE/IOSA J. Lightwave Technol. LT-5, 660–667 (1987).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

A. Gedeon, “Comparison Between Rigorous Theory and WKB Analysis of Modes in Graded Index Waveguides,” Opt. Commun. 12, 329–332 (1974).
[CrossRef]

Other (1)

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “Approximate Solution to the Scalar Wave Equation for Planar Optical Waveguides,” submitted to Appl. Opt.

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Figures (4)

Fig. 1
Fig. 1

Electromagnetic field for Profile 1 (as shown) for V = 4, n1 = 2.2195, n2 = 2.177, nc = 1.

Fig. 2
Fig. 2

Error in the electromagnetic field for Profile 1 (as shown) for V = 4, n1 = 2.2195, n2 = 2.177, nc = 1.

Fig. 3
Fig. 3

Error in the normalized propagation constant b for Profile 1 for n1 = 2.2195, n2 = 2.177, nc = 1.

Fig. 4
Fig. 4

Error in the normalized propagation constant b for Profile 2 for n1 = 2.2195, n2 = 2.177, nc = 1.

Equations (14)

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d 2 ψ ( x ) d x 2 + ψ ( x ) κ 2 ( x ) = 0 ,
κ 2 ( x ) = k 2 n 2 ( x ) - β 2 ,
d 2 ψ d x 2 + p ( x ) d ψ d x + q ( x ) ψ ( x ) = 0
ψ ( x ) = j = 1 N a j ϕ j ,
ϕ j = 2 L x sin j π x L x .
j ( A i j - k 2 n e 2 δ i j ) a j = 0 ,
A i j = K j 2 δ i j + k 2 ϕ i ( x ) n 2 ( x ) ϕ j ( x ) ,
ψ ( x ) = c 1 F ( x ) A i [ ξ ( x ) ] + c 2 G ( x ) B i [ ξ ( x ) ] .
ξ ( x ) = [ x 0 x 3 2 - κ 2 ( x ) d x ] 2 / 3 ,
F ( x ) , G ( x ) = 1 ξ ( x ) .
n ( x ) = [ n 2 2 + ( n 1 2 - n 2 2 ) exp ( - x / d ) ] 1 / 2
n ( x ) = [ n 1 2 - ( n 1 2 - n 2 2 ) ( x / a ) 2 ] 1 / 2
b = ( β / k ) 2 - n 2 2 n 1 2 - n 2 2 ,
V = 2 π α λ n 1 2 - n 2 2 ,

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