ABSTRACT
Exploring the interaction of light with materials periodically structured in space and time is intellectually rewarding and, simultaneously, a computational challenge. Appropriate computational tools are urgently needed to explore how such upcoming photonic materials can control light on demand. Here, we introduce a semi-analytical approach based on the transition matrix (also known as T-matrix) to analyze the optical response of a spatiotemporal metasurface. The metasurface consists of a periodic arrangement of time-varying scattering particles. In our approach, we depart from an individual scatterer's T-matrix to construct the effective T-matrix of the metasurface. From that effective T-matrix, all observable properties can reliably be predicted. We verify our semi-analytical approach with full-wave numerical simulations. We demonstrate a speed-up with our approach by a factor of more than 500 compared to a finite-element simulation. Finally, we exemplify our approach by studying the effect of time modulation on a Huygens' metasurface and discuss some emerging observable features.
ABSTRACT
Hierarchical plasmonic-photonic microspheres (PPMs) with high controllability in their structures and optical properties have been explored toward surface-enhanced Raman spectroscopy. The PPMs consist of gold nanocrystal (AuNC) arrays (3rd-tier) anchored on a hexagonal nanopattern (2nd-tier) assembled from silica nanoparticles (SiO2NPs) where the uniform microsphere backbone is termed the 1st-tier. The PPMs sustain both photonic stop band (PSB) properties, resulting from periodic SiO2NP arrangements of the 2nd-tier, and a surface plasmon resonance (SPR), resulting from AuNC arrays of the 3rd-tier. Thanks to the synergistic effects of the photonic crystal (PC) structure and the AuNC array, the electromagnetic (EM) field in such a multiscale composite structure can tremendously be enhanced at certain wavelengths. These effects are demonstrated by experimentally evaluating the Raman enhancement of benzenethiol (BT) as a probe molecule and are confirmed via numerical simulations. We achieve a maximum SERS enhancement factor of up to â¼108 when the resonances are tailored to coincide with the excitation wavelength by suitable structural modifications.
