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The Fisher transformation acts on cubic graphs by replacing each vertex by a triangle. We explore the action of the Fisher transformation on the set of self-avoiding walks of a cubic graph. Iteration of the transformation yields a sequence of graphs with common critical exponents, and with connective constants converging geometrically to the golden mean. We… (More)

Nanostructured metals have received a significant amount of attention in recent years due to their exciting plasmonic and photonic properties enabling strong field localization, light concentration, and strong absorption and scattering at their resonance frequencies. Resonant plasmonic and metamaterial absorbers are of particular interest for applications… (More)

- Zhongyang Li, Yingfang Ma, Ran Huang, Ranjan Singh, Jianqiang Gu, Zhen Tian +2 others
- Optics express
- 2011

Coupling between superradiant and subradiant mode resonators in a metamaterial unit cell plays an important role in observing the sharp transparency peak due to destructive interference between the resonators. This effect is enhanced as the resonators are brought closer to each other in a conventional planar arrangement. We present a novel coupling scheme… (More)

We show that a triple-layer metal-insulator-metal (MIM) structure has spectrally selective IR absorption, while an ultra-thin metal film has non-selective absorption in the near infrared wavelengths. Both sub-wavelength scale structures were implemented with an ultra-thin 6 nm Cr top layer. MIM structure was demonstrated to have near perfect absorption at λ… (More)

Ultrathin metasurfaces have recently emerged as promising materials that have huge potential to enable novel, flat optical components, and surface-confined, miniature photonic devices. Metasurfaces offer new degrees of freedom in molding the optical wavefronts by introducing abrupt and drastic changes in the amplitude, phase, and/or polarization of… (More)

Nanostructured photonic materials enable control and manipulation of light at subwavelength scales and exhibit unique optical functionalities. In particular, plasmonic materials and metamaterials have been widely utilized to achieve spectral transmission, reflection, and absorption filters based on localized or delocalized resonances arising from the… (More)

Resonant absorbers based on nanostructured materials are promising for variety of applications including optical filters, thermophotovoltaics, thermal emitters, and hot-electron collection. One of the significant challenges for such micro/nanoscale featured medium or surface, however, is costly lithographic processes for structural patterning which… (More)

The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. Strict inequalities are proved for connective constants of vertex-transitive graphs. First, the connective constant decreases strictly when the graph is replaced by a nontrivial quotient graph. Second, the connective constant… (More)

The control of light−material interactions at the nanoscale requires optical elements with sizes much smaller than the wavelength of light. Plasmonic nanostructures and optical metamaterials enable drastic control and manipulation of light at such small scales. However it is quite challenging to further reduce the size of resonant elements using… (More)

The objective-first inverse-design algorithm is used to design an ultra-compact optical diode. Based on silicon and air only, this optical diode relies on asymmetric spatial mode conversion between the left and right ports. The first even mode incident from the left port is transmitted to the right port after being converted into an odd mode. On the other… (More)