We discuss the prospects for low-contrast all-dielectric cloaking and offer a simple picture illustrating the basic obstacle for perfect cloaking without materials with an effective double-negative response. However, the same simple picture also gives directions for less perfect designs allowing for planar transmitted fields, but at the prize of phase-slips which can only be eliminated at well-defined frequencies where the phase-slip amounts to a multiple of 2pi. As a particular example, we consider assemblies of all-dielectric Luneburg lenses forming a porous structure allowing for hiding objects inside the pores, independently on the polarization of the incident field. Cloaking must in general be realized with metamaterials realized through sub-wavelength structures, i.e. Lambda lambda with Lambda being the period and lambda the free-space wavelength. Interestingly, cloaking-like operations with Luneburg-lens arrays perform in the opposite limit with Lambda lambda.
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Mortensen et al. (2009) studied this question.