A comparative study of the Rayleigh hypothesis and analytic continuation methods as applied to sinusoidal gratings

Two methods are investigated for solving the problem of plane-wave diffraction by gratings with sinusoidal profiles. The first is based on an extension of the Rayleigh hypothesis, and the second employs an analytic continuation technique for computing the field in regions in which the Rayleigh hypothesis breaks down. Some numerical results are presented to compare the two methods.     

Some important geometrical features of conic-section-generated offset refelector antennas

Geometrical characteristics of conic-section-generated offset reflectors are studied in a unified fashion. Some unique geometrical features of the reflector rim constructed from the intersection of the reflector surface and a cone or cylinder are explored in detail. It is found that the intersection curve (rim) of the rotationally generated conic-section reflector surface and a circular cone with its tip at the focal point is always a planar curve and has a circular projection on the focal plane only for the offset parabolic reflector. Furthermore, in this case, the line going through the center of the circle, parallel to the focal axis, and the central axis of the cone do not intersect the reflector surface at the same point. Numerical results are presented to demonstrate some unique features of offset parabolic reflectors.