Abstract

Improper eigenmodes of the planar waveguide dispersion relation, or leaky modes, are often used to represent the nonbound optical field in planar waveguides. Here we show that the improper leaky solutions give an inadequate description of the nonbound field for the important case of a waveguide just below cutoff.

© 1995 Optical Society of America

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References

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  1. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991), Chap. 1.
  2. R. E. Smith, S. N. Houde-Walter, J. Opt. Soc. Am. A 12, 715 (1995).
    [CrossRef]
  3. A. K. Ghatak, Opt. Quantum. Electron. 17, 311 (1985).
    [CrossRef]
  4. R. E. Smith, S. N. Houde-Walter, J. Lightwave Technol. 11, 1760 (1993).
    [CrossRef]

1995

1993

R. E. Smith, S. N. Houde-Walter, J. Lightwave Technol. 11, 1760 (1993).
[CrossRef]

1985

A. K. Ghatak, Opt. Quantum. Electron. 17, 311 (1985).
[CrossRef]

Ghatak, A. K.

A. K. Ghatak, Opt. Quantum. Electron. 17, 311 (1985).
[CrossRef]

Houde-Walter, S. N.

R. E. Smith, S. N. Houde-Walter, J. Opt. Soc. Am. A 12, 715 (1995).
[CrossRef]

R. E. Smith, S. N. Houde-Walter, J. Lightwave Technol. 11, 1760 (1993).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991), Chap. 1.

Smith, R. E.

R. E. Smith, S. N. Houde-Walter, J. Opt. Soc. Am. A 12, 715 (1995).
[CrossRef]

R. E. Smith, S. N. Houde-Walter, J. Lightwave Technol. 11, 1760 (1993).
[CrossRef]

J. Lightwave Technol.

R. E. Smith, S. N. Houde-Walter, J. Lightwave Technol. 11, 1760 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Quantum. Electron.

A. K. Ghatak, Opt. Quantum. Electron. 17, 311 (1985).
[CrossRef]

Other

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, Calif., 1991), Chap. 1.

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Figures (3)

Fig. 1
Fig. 1

Waveguide comprising three sections: an input guide that supports two TE modes (left), an identical output guide (right), and a middle guide whose guiding layer has a variable width 1.

Fig. 2
Fig. 2

Excitation of the TE1 mode and the radiation continuum for the structure in Fig. 1. In each case the percentage of power in the radiation continuum and in the TE1 mode are given. The power in the TE0 mode contains the remaining power.

Fig. 3
Fig. 3

Ratio of transmitted to incident field amplitudes, |t1/i1|, as a function of the central section length, , for the structure in Fig. 1.

Tables (1)

Tables Icon

Table 1 Propagation Constants for TE1 Mode as It Migrates Toward and Beyond Cutoff with Decreasing Waveguide Thickness

Equations (11)

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TE :             E ¯ ( x , z ) = E 0 y ^ m ( x ) exp [ i ( β z - ω t ) ] ,
TM :             H ¯ ( x , z ) = H 0 y ^ m ( x ) exp [ i ( β z - ω t ) ] .
2 m ( x ) x 2 + ( k j 2 - β 2 ) m ( x ) = 0.
m ( x ) = A j ( x ) exp { α j ( x ) [ x - d j ( x ) ] } + B j ( x ) exp { - α j ( x ) [ x - d j ( x ) ] } .
( A j B j ) = M j ( A j - 1 B j - 1 ) ,
M j = 1 2 ρ j × [ ( ρ j + α j - 1 α j ) exp ( δ j ) ( ρ j - α j - 1 α j ) exp ( δ j ) ( ρ j - α j - 1 α j ) exp ( - δ j ) ( ρ j + α j - 1 α j ) exp ( - δ j ) ] .
( A N B N ) = [ T 11 T 12 T 21 T 22 ] ( A 0 B 0 ) ,
T = M N M N - 1 M 1 .
t l i j = k bound O j k O k l O j j O k k exp ( i β ˜ k D ˜ ) + C 1 Θ j l ( β ˜ ) exp ( i β ˜ k D ˜ ) d β ˜ ,
O a b = m a ( x ) m b ( x ) d x ,
Θ j l ( β ˜ ) = O j β ˜ O β ˜ l O j j O β ˜ β ˜ [ w ˜ N ˜ π β ˜ k ˜ N ˜ 2 - β ˜ 2 ] .

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