Electromagnetic parameters of matter and conditions for physical realizability

Abstract

1) The conditions are examined which a complex function of real variable must satisfy in order that it may be considered as the frequency response of a linear system. The cases of the physical realizability and of the stability of the system are considered and use is made of the Hilbert transforms. 2) The relations existing between the real and the imaginary part of the e.m. parameters of matter are studied by means of the Hilbert transforms, also known as Kramers-Kronig equations. The case of imperfect dielectrics is particularly examined and a suitably modified form of K.-K. equations is presented. 3) The above considerations are extended to the anysotropic media; special reference is made to the susceptivity of magnetized ferrites. When losses are present, and the parameters of the tensor are consequently finite for any frequency, said parameters must comply with Kramers-Kronig equations. This is actually the case for the expressions which are generally used.