## The Plane Wave Spectrum Representation of Electromagnetic Fields |

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Page 46

With this in view the method of

procedure in some respects akin to that of stationary phase, but leading more

readily to a rigorous analysis. 3.2.2. Rigorous Approach:

...

With this in view the method of

**steepest descents**is next introduced, being aprocedure in some respects akin to that of stationary phase, but leading more

readily to a rigorous analysis. 3.2.2. Rigorous Approach:

**Steepest Descents**The...

Page 48

The merit of the

part of the path in the vicinity of the saddle- point contributes significantly to the

integral. In this respect its importance is akin to that of the stationary phase path.

The merit of the

**steepest descents**path is basically that, when k0r ^> 1, only thatpart of the path in the vicinity of the saddle- point contributes significantly to the

integral. In this respect its importance is akin to that of the stationary phase path.

Page 56

... give uniform asymptotic approximations to more general plane wave

representations that are characterized by spectra containing simple poles is now

described. 3.3.3.

once again ...

... give uniform asymptotic approximations to more general plane wave

representations that are characterized by spectra containing simple poles is now

described. 3.3.3.

**Steepest Descents**with Saddle-point Near a Pole Consideronce again ...

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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