Multiple narrowband whispering-gallery model and transparent display applications of spherical hyperbolic dispersive metamaterial cavity

Abstract

A novel spherical hyperbolic metamaterial (HMM) cavity for enhancing color-transparent display is designed in this work. This HMM cavity consists of a silver core wrapped alternatively by several dielectric layers and silver layers. According to the effective medium theory and Mie scattering theory, we demonstrate that such an HMM cavity supports multiple whispering-gallery modes with deep subwavelength characteristics. The number of whispering-gallery modes with the same angular momentum is equal to the number of silver layers within the HMM cavity. Furthermore, we demonstrate that these excited whispering-gallery modes are capable of strongly confining the electric fields within the different dielectric shell layers, thus reducing Ohmic losses and narrowing resonance linewidths. In addition, we systematically investigate how the structure parameters affect whispering-gallery modes for an HMM cavity with 5 alternative dielectric layers and silver layers. Interestingly, by increasing the thickness of outermost dielectric layer and silver layer, the resonance wavelength of TM<sub>1,2</sub> mode and TM<sub>1,3</sub> mode remain nearly unchanged. However, the TM<sub>1,1</sub> mode experiences a significant blueshift, and the intensity of the TM<sub>1,1</sub>, TM<sub>1,2</sub> and TM<sub>1,3</sub> mode can be substantially tuned. Consequently, through structural optimization, the HMM cavity can support triple narrowband resonances in the red, green, and blue spectral regions. Finally, we show that the HMM cavity exhibits dipole radiation characteristics at the three resonance wavelengths, effectively confining light within an angular range from –45° to +45° relative to the incident light direction, and confirming the scattered light viewed from a wide angle. These features make the HMM cavity suitable for achieving high transparency, brightness, and wide viewing angles in full-color transparent displays.