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An Archiedean planar spiral antenna is numerically analyzed in the presence of a conducting plane reflector. The analysis shows that the spiral antenna backed by the plane reflector has two distinct regions in the current distribution, which explain the radiation of a circularly polarized wave for the outer circumference C ranging over shout 1.3 X < C < 1.5 A and C > 2.9 X, where A is a free-space wavelength. Further consideration is given to a truncated spiral antenna whose outer circumference is on the order of 1.4 A. The truncated spiral antenna maintains a decaying current distribution and radiates a circularly polarized wave over a k1.2 frequency bandwidth. It is also demonstrated that a power gain on the order of 8.5 dB is realized over the same frequency range.

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Abstract-A monofilar spiral antenna is analyzed in the presence of a conducting plane reflector, using the method of moments. The circumference of the spiral antenna is chosen to be 2.3 wavelengths. A tilted beam of circular polarization is realized by superposing the fields from two active regions. The gain of the tilted beam is approximately 8 dB. The frequency bandwidths for 1-dB gain drop and 3-dB axial ratio criterions are 12% and 23%, respectively. An array consisting of the four monofilar spiral antennas is also analyzed, where the array element spacing is chosen to be 0.8 wavelength at a design frequency f 0 . The input impedances of the four spirals are almost the same as the impedance of the single monofilar spiral antenna at f 0 . The array radiates a tilted fan beam with a gain increase of approximately 6 dB from the gain of the single spiral antenna at f0. The frequency bandwidth for a 3-dB axial ratio criterion is almost the same as that of the single spiral antenna.

Abstract-The modified finite-difference formula is presented for the second derivative of a semivectorial field in a step-index optical waveguide. The present formula achieves a truncation error of O(1x 2 ) provided the discontinuity coincides with a mesh point or lies midway between two mesh points. Furthermore, the formula allows a general position of the interface, when used with the beam-propagation method (BPM). To demonstrate the effectiveness of the formula, asymmetric step-index waveguides are analyzed using the imaginary-distance BPM.

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