Abstract

We describe more clearly our interpretation of the inverse rule, show the connection between our approach and Li’s, and describe at least one situation where our technique could be more useful.

© 2002 Optical Society of America

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References

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  1. P. P. Banerjee, J. M. Jarem, “Convergence of electromagnetic field components across discontinuous permittivity profiles,” J. Opt. Soc. Am. A 17, 491–492 (2000).
    [CrossRef]
  2. L. Li, “Convergence of electromagnetic field components across discontinuous permittivity profiles: comment,” J. Opt. Soc. Am. A 19, 1443–1444 (2002).
    [CrossRef]
  3. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]

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Equations (16)

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hA(x)=1fREC(x) n=-NNgnexp(jnx),
fREC(x)=n=-NN(1/f )nexp(jnx),
hA1(x)=n=-NNfnexp(jnx) n=-NNgnexp(jnx)
fREC(x)hA(x)=nn(1/f )n-nhAnexp(jnx).
n(1/f )n-nhAn=gn.
fREC̲̲hA̲=g̲.
hA̲=(fREC̲̲)-1g̲.
f˜M(x)m=-MM(1/fREC)mexp(jmx).
m=-MM(1/fREC)mexp(jmx) m=-MMgmexp(jmx)
hB(x)m=-MM(1/fREC)mexp(jmx)×m=-MMgmexp(jmx)=m=-2M2MhBmexp(jmx).
hBm=m=-MM(1/fREC)m-mgm.
hB̲=(1/fREC)̲̲g_.
hn=12π-ππ1fREC(x) n=-NNgnexp(jnx)×exp(-jnx)dx
h(x)=f(x)g(x),
h(x)=1[1/f(x)] g(x),
Dx=εxxEx+εxyEy=11/εxx Ex+εxyEy,

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