In this paper, I present a comprehensive theoretical framework for understanding surface-enhanced Raman scattering (SERS) measurements in both solution and thin film setups, focusing on electromagnetic enhancement principles. Two prevalent types of SERS substrates found in the literature are investigated: plasmonic colloidal particles, including spherical and spheroid nanoparticles, nanoparticle diameters, and thin-film-based SERS substrates like ultra-thin substrates, bundled nanorods, plasmonic, and porous thin films. The investigation explores the impact of analyte adsorption, orientation, and the polarization of the excitation laser on effective SERS enhancement factors. Notably, it considers the impact of analyte size on the SERS spectrum, by examining scenarios where the analyte is significantly smaller or larger than the hot-spot dimensions. The analysis also incorporates optical attenuations arising from the optical properties of the analyte and the SERS substrates. The findings provide possible explanations for many observations made in SERS measurements, such as variations in relative peak intensities during SERS assessments, reductions in SERS intensity at high analyte concentrations, and the occurrence of significant baseline fluctuations. The study offers valuable guidance for optimizing SERS substrate design, enhancing SERS measurements, and improving the quantification of SERS detection.

A comprehensive theory is developed for the chiral optical response of two configurations of the N-oscillator Born-Kuhn model (NOBK): the helically stacked and the corner stacked models. In the helical NOBK model, there is always a chiral response regardless of the value of N, whereas in the corner NOBK, only configurations with even N demonstrate a chiral response. Generally, the magnitudes of optical rotatory dispersion (ORD) and circular dichroism (CD) increase with N when the parameters of each oscillator are fixed. In cases of weak coupling, the spectral shapes of ORD and CD remain invariant, while strong coupling significantly alters the spectral shapes. For large damping, the spectral amplitude becomes smaller, and the spectral features become broader. In the presence of small damping, strong coupling introduces degeneracy in the coupled oscillator system, leading to multiple spectral features in both ORD and CD across the entire spectral region. This simple model not only can help in the design of tunable chiral metamaterials but also enhance our understanding of chiro-optical responses in structures with different configurations.

A systematic investigation of the dynamic clustering behavior of active particles under confinement, including the effects of both particle density and active driving force is presented based on a hybrid coarse-grained molecular dynamics simulation. First, a series of scaling laws were derived with power relationships for the dynamic clustering time as a function of both particle density and active driving force. Notably, the average number of clusters N ̅ assembled from active particles in the simulation system exhibits a scaling relationship with clustering time t described by N ̅∝t^(-m). Simultaneously, the scaling behavior of the average cluster size S ̅ is characterized by S ̅∝t^m. Our findings reveals the presence of up to four distinct dynamic regions concerning clustering over time, with transitions contingent upon the particle density within the system. Furthermore, as the active driving force increases, the aggregation behavior also accelerates, while an increase in density of active particles induce alterations in the dynamic procession of the system.