While calculating the optical spectrum for nanowire (theoretically) I got three curves for all three different direction but as per my knowledge the spectrum contains two curve, one for z axis and one for xy plane if the growth direction of wire is z axis.
I am not sure about what you mean with 'optical spectrum', but from your question I assume that you refer to the dielectric constant of the composite material. I would consider the most general way to formulate a dielectric constant as a 3x3 tensor, linking the E-field to the D-field in the material. Often it makes sense to reduce this to a diagonal matrix with three elements Exx, Eyy and Ezz by an appropriate choice of your coordinate system, reducing the problem to finding the three eigenvalues of the 3x3 tensor.
For optically isotropic materials these three eigenvalues will be identical and you can forget about the tensor nature of the dielectric constant altogether and treat the dielectric constant as a scalar.
Structures that are anisotropic will show some kind of birefringence, i.e. either uniaxial or biaxial. I expect the rotationally symmetric rods to have 2 distinct values of epsilon, (i.e. Exx=Eyy in your notation) and corresponding to a uniaxial material. More complicated shapes for the particles will break this symmetry and give 3 different indices making the material biaxial.
Because you ask about a 2D structure, I suspect that you placed the particles in an array. In that case you need to consider the symmetry of the lattice together with the symmetry of the particle.
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