## The Plane Wave Spectrum Representation of Electromagnetic Fields |

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Page 10

1 for -a <f <a (1.35) [O for | > a has

singularity at ij = 0, and the r\ path of integration runs undisturbed along the real

axis. Finally it is remarked that free use will be made of the concept of the delta ...

1 for -a <f <a (1.35) [O for | > a has

**spectrum function**Here, of course, F(rf) has nosingularity at ij = 0, and the r\ path of integration runs undisturbed along the real

axis. Finally it is remarked that free use will be made of the concept of the delta ...

Page 45

For plane aperture distributions that are spatially bounded, in the sense that they

can be completely enclosed by some circle of finite radius, the associated

...

For plane aperture distributions that are spatially bounded, in the sense that they

can be completely enclosed by some circle of finite radius, the associated

**spectrum functions**, being integrals such as (2.111) over finite ranges, are free of...

Page 51

For example, in the asymptotic expansion of the Hankel function just mentioned

the power series in r is that of (1 — \ir2)-*, ... It turns out that in a number of

problems the

particular ...

For example, in the asymptotic expansion of the Hankel function just mentioned

the power series in r is that of (1 — \ir2)-*, ... It turns out that in a number of

problems the

**spectrum function**P(cos «) contains a simple pole, and that thisparticular ...

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### Contents

PRELIMINARIES | 3 |

PLANE WAVE REPRESENTATION | 11 |

SUPPLEMENTARY THEORY | 39 |

Copyright | |

7 other sections not shown

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The Plane Wave Spectrum Representation of Electromagnetic Fields ... P. C. Clemmow Limited preview - 2013 |

### Common terms and phrases

angle angular frequency angular spectrum approximation asymptotic expansion Babinet's principle Bessel function boundary conditions branch-points Cerenkov radiation complex considered corresponding cos2 cosh current distribution dielectric tensor diffraction dipole direction of phase evaluated exponential expressed in terms factor finite formula Fourier Fresnel integral given gives half-plane half-space Hankel function homogeneous plane wave incident field integrand line-source magnetostatic field Maxwell's equations obtained P(cos path of integration perfectly conducting permittivity phase propagation plane wave spectrum point charge point of observation polarized field pole power radiated problem pure imaginary radiation field real axis reflection coefficient refractive index replaced respectively result scattered field screen simple sin2 sinh solution specified spectrum function steepest descents superposition surface current density surface wave theory time-averaged power flux time-harmonic tion total field transmitted two-dimensional uniaxial medium unity upper/lower sign vacuum field wave spectrum representation wavelength written z-axis zero