The speed with which electromagnetic energy can be wirelessly transferred from a source to the user is a crucial indicator for the performance of a large number of electronic and photonic devices. We expect that energy transfer can be enhanced using special materials. In this paper, we determine the constituent parameters of a medium which can support theoretically infinite energy concentration close to its boundary; such a material combines properties of Perfectly Matched Layers (PML) and Double-Negative (DNG) media. It realizes conjugate matching with free space for every possible mode including, most importantly, all evanescent modes; we call this medium Conjugate Matched Layer (CML). Sources located outside such layer deliver power to the conjugate-matched body exceptionally effectively, impressively overcoming the black-body absorption limit which takes into account only propagating waves. We also expand this near-field concept related to the infinitely fast absorption of energy along the air-medium interface to enhance the far-field radiation. This becomes possible with the use of small particles randomly placed along the boundary; the induced currents due to the extremely high-amplitude resonating fields can play the role of emission ‘‘vessels’’, by sending part of the theoretically unlimited near-field energy far away from the CML structure.