Limits for superfocusing with finite evanescent wave amplification

Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provides extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This Letter provides a relation between the achievable focus spot size, the amplification available, and the focal length. This may be considered as a revised version of Abbe's diffraction limit for focusing systems that have evanescent wave amplification. It is useful in comparing the amplification achieved in various subwavelength focusing implementations as well as determining when it is better to use existing near-field techniques, such as simple diffraction from an aperture or slit, than to attempt complicated superfocusing.