FRACTAL MEMBRANES Wen, Zhou, et al.

Applied Physics Letters Volume 82, No. 7, 17 February 2003 Abstract: Reflectivity of Planar Metallic Fractal Patterns Lei Zhou, Weijia Wen, C. T. Chan, and Ping Sheng Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China (Received 17 October 2002; accepted 20 December 2002) We studied the reflective properties of a small dielectric plate covered with a fractal-like metallic pattern generated by a particular type of space-filling curves. We found, both experimentally and theoretically, that the plate can reflect electromagnetic waves in a multitude of frequencies, generated from a near-field monopole antenna. Some of the reflected waves have wavelengths mush larger than the lateral dimension of the plate. In comparison, a metal plate of the same size failed to reflect when its lateral size was smaller than half of the corresponding wavelength. © 2003 American Institute of Physics. [DOI: / ]

Schematic Figure 1:

Fractal-Membrane-Reflector Component of Li-Baker High-Frequency Gravitational Wave Detector. Fabricated in Hong Kong, displayed by Bonnie Baker, May 2008 (Also constructed from solid copper, aluminum and stainless steel)

Summary In short, we have demonstrated through both theory and experiment that a specific kind of metallic fractal patter can serve as a multi-band, sub-wavelength reflector. We emphasize here that the effect is not tied to the selected geometry but is an intrinsic property of the fractal pattern. Similar effects will be observed for other geometries (say without the ground plane) However, the resonance frequency may shift if other objects are placed in the near field. For example, the resonance frequency will downshift if we apply a dielectric coating on the fractal surface. Such effects are common to all frequency selective reflectors operating on the principle of resonance.

PHYSICAL REVIEW LETTERS, Vol. 89, No. 22, 25 November 2002 Subwavelength Photonic Band Gaps from Planar Fractals Weijia Wen, Lei Zhou, Jensen Li, Weikun Ge, C.T. Chan, and Ping Sheng Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China (Received 26 March 2002; published 12 November 2002) We show by both experiment and theory that a specific class of planar conducting fractals possesses a series of self-similar resonances, leading to multiple gaps and pass bands for electromagnetic waves over an ultra-wide frequency range. A double stack of these fractal patterns exhibits polarization-independent absolute gaps over a wide range of incidence angles. These characteristics are retained even when the fractal patterns are significantly sub-wavelength in all dimensions. In addition, the transmittance can be modulated by an external current source. DOJ: /PhysRevLett n1PACS numbers: Qs, 47

Figure 1

Conclusions In short, we found that a particular fractal pattern (space-filling curves) has a self-similar series of resonances, leading to a log- periodic sequence of gaps. In addition, the lower frequency stop bands correspond to wavelengths that are significantly longer than the lateral dimension of the fractal plate, making the fractal plates sub-wavelength reflectors. The connected topological structure makes it possible to modulate the transmission property via a second source. This work was supported by RGC Hong Kong through Grants No. N_HKUST025/00 and No. HKUST6145/99P.