The modified Watson transform is applied to the Mie series for the electromagnetic wave transmitted into the double negative cylinder due to high frequency plane wave incidence The Debye series expansion is adapted to the transmission coefficients to reveal the transmission mechanism at high frequency. The first term of the Debye series is examined. Two kinds of geometrical shadow regions and two kinds of geometrically lit regions are shown to exist. The field formation mechanisms in these regions are indicated. Several differences between a double positive cylinder and a double negative cylinder are determined. The field computations are performed in the geometrical shadow and the geometrically lit regions for the first term of the Debye series. The residue series and steepest descent computations are shown to be in good agreement with the Mie series computations.
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