In this work, we analyze and optimize invisibility cloaks stratified in concentric spherical homogeneous and isotropic layers, in which both the total scattering cross section and the number of layers have been minimized. In order to increase the range of frequencies in which there is invisibility, dispersive effects are taken into account. In microwaves, We obtained discretized invisibility cloaks (obtained from anisotropic cloaks) with significant reductions (greater than 20 dB) of the total scattering cross section, for only 20 layers (which is achieved in the literature with at least 80 layers). We obtained a reduction of 32 dB in the total scattering cross section for a cloak stratified in only 13 layers. This result was obtained in microwaves. In microwaves, we optimized dispersive invisibility cloaks which present a bandwidth 5.4 times larger than would be obtained by a optimized cloak without dispersive effects. Cloaks are designed to operate in optical frequencies, for a wide range of frequencies.
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