## 1. Introduction

[2] In satellite communications a CP wave is often employed to combat the Faraday rotation introduced by the ionosphere [*Richharia*, 1999]. An example is the right-hand circularly polarized (RHCP) used in the GPS reception. Because of this, how to obtain a CP wave for a given incident polarization finds some applications. An anisotropic medium can change the polarization state of the wave. Usually a perfect CP transformation can be achieved only at a particular frequency using a suitable anisotropic slab with a particular slab thickness. However, the same slab may not be able to achieve a perfect CP at all frequencies in a given band. Similarly, a perfect CP cannot be obtained using an inaccurate slab thickness. We study the transformation bandwidth and the thickness sensitivity of the anisotropic slab for LP to CP polarizers.

[3] The polarization locus of an electromagnetic wave is in general an ellipse, which can be characterized by the axial ratio, tilt angle and sense of rotation [*Kelso*, 1964; *Institute of Electrical and Electronics Engineers* (*IEEE*), 1983; *Mott*, 1992]. The axial ratio of a perfect CP wave is equal to one. In general, the polarization state of the wave transmitted through an anisotropic slab depends on the frequency and the slab thickness. When an exact CP cannot be obtained, an approximation may be acceptable if its axial ratio is below a specified value, e.g., 3 dB. For this reason, a transformation bandwidth and the thickness sensitivity of the anisotropic-slab LP to CP polarizer based on the axial ratio can be defined. A given axial ratio will thus correspond to the transformation bandwidth or the thickness sensitivity.

[4] On the complex polarization ratio (**R**) plane, the contours of constant axial ratio are circles [e.g., *Booker et al.*, 1951; *Kelso*, 1964], and the loci of the polarization as the wave propagates in the lossless anisotropic media follow a circle, too [*Yeh et al.*, 1999a]. On the complex **R** plane, the transformation bandwidth and the thickness sensitivity can be determined from the relations between these two sets of circles. The formulation is described in section 2. As examples, in section 3, we study the case of a linearly polarized wave incident normally to a slab corresponding to one of three different media: biaxial, chiral, and magnetoionic. The results are used to explain how to obtain the transformation bandwidth or the thickness sensitivity. Properties of the bandwidth or the thickness sensitivity and design issues to obtain the maximum bandwidth or thickness sensitivity are investigated. Discussion on some advantages of this approach over analytical methods is given in section 4.