I am talking about frequency of 1 GHz and up. I found in one reference (John D. Kraus, Electromagnetics) a material named "Ferrite-titanate" has relative permittivity and relative permeability equal to 60(2-j).

Dear Dr. Yahya,

You may find the contents of this patent

http://www.google.com/patents/US6063719

and the references therein to be relevant for your question.

It looks like they attempt to get the real parts of epsilon and mu to be big and, at the same time, to be able to match them (epsilon=mu) while making the imaginary parts small in order to avoid losses. For your purposes of reducing backscattering, you need epsilon = mu if the surrounding medium is air. I think that whether the imaginary parts are big or not does not actually play a role.

For zero backscattering, you also need some geometrical conditions of your scatterer, which you may be aware of. Just in case, here they are: You need the scatterer to have rotational symmetry of degree higher than three, that is, the symmetry of a triangle, or a square, or a pentagon ... etc .... which in the limit becomes the symmetry of a cylinder. Degree 2, that is, the symmetry of a rod, does not work. Here is a reference about this:

https://www.researchgate.net/publication/258884025_Forward_and_backward_helicity_scattering_coefficients_for_systems_with_discrete_rotational_symmetry

Actually, when epsilon=mu, your scatterer has another symmetry, this time non-geometrical, called electromagnetic duality symmetry, which helps understanding the origin of zero backscattering.

Article Forward and backward helicity scattering coefficients for sy...