  We show that a metallic plate with fractal-shaped slits can be homogenitized
as a plasmonic metamaterial with plasmon frequency dictated by the fractal
geometry. Owing to the all-dimensional subwavelength nature of the fractal
pattern, our system supports both transverse-electric and transverse-magnetic
surface plasmons. As a result, this structure can be employed to focus light
sources with all-dimensional subwavelength resolutions and enhanced field
strengths. Microwave experiments reveal that the best achievable resolution is
only, and simulations demonstrate that similar effects can be realized at
infrared frequencies with appropriate designs.
