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We present a semi-analytical method to extract transverse polarizability parameters of an arbitrary bi-anisotropic sub-wavelength scatterer both in homogeneous medium and placed at the boundary of two simple (homogeneous, isotropic, and linear) media. Using this technique, polarizability parameters of various dielectric and/or metallic scatterers are obtained, effectively. In this method, a scatterer is placed at the middle of a rectangular waveguide which in general is filled by two different simple media in either sides of the scatterer. The waveguide is designed so that the two TE10 and TE01 fundamental modes are propagating in a given frequency band. All 16 transverse polarizabilities are fast obtained having 16 different generalized scattering parameters (S-parameters). The S-parameters are associated with excitations at two different ports of the waveguide and the two different modes (TE10 and TE01). Comparing to existing polarizability extraction methods, the presented waveguide method is easy to run, fast and almost accurate. In order to validate the method, we present three examples including omega particle and magneto-dielectric sphere in free-space and an electric resonance particle, placed on top of a dielectric half-space.
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