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.
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