Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers

Abstract

The low efficiency of Raman spectroscopy can be overcome by placing the active molecules in the vicinity of scatterers, typically rough surfaces or nanostructures with various shapes. This surface-enhanced Raman scattering (SERS) leads to substantial enhancement that depends on the scatterer that is used. In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. According to our metric, silver is optimal in visible wavelengths while aluminum is better in the near-UV region. Our general analytical bound scales as the volume of the scatterer and the inverse sixth power of the distance to the active molecule. Numerical computations show that simple geometries fall short of the bounds, suggesting further design opportunities for future improvement. For periodic scatterers, we use two formulations to discover different bounds, and the tighter of the two always must apply. Comparing these bounds suggests an optimal period depending on the volume of the scatterer. arXiv:1909.00202v1 [physics.optics]

Inverse design of nanoparticles for enhanced Raman scattering

“…III E). We find that the huge enhancements observed from TO structures compared to simple geometries are in qualitative agreement with recently discovered theoretical upper bounds to Raman scattering [21]. Quantitatively, for a material with susceptibility χ, the key figure of merit for light-matter interactions is F = |χ| 2 /Im(χ) [22][23][24] and the Raman bounds scale as a factor of F 3 V where V is the volume of the scatterer: a factor of F 2 maximum focusing enhancement and a factor of F maximum emission enhancement.…”

“…Figure 5 shows the Raman enhancement relative to a molecule in free space versus the area of Ω D with the three designs and their performance plotted in black, red and blue and a trend line of slope 1 included to guide the eye. The data shows an approximately linear scaling of the emission enhancement with volume (area) in agreement with the upper bounds derived in [21], demonstrating that the proposed approach finds the expected volume scaling.…”

“…It was recently shown that an upper bound for enhancing the Raman scattering process using metallic nanostructures scales linearly with the volume (area in 2d) of the design region [21]. To investigate if this scaling is found using the proposed design approach, we perform a study considering three different outer radii of Ω D .…”

“…The upper bound for enhancing the Raman scattering process, derived in [21], scales cubically with the material-related quantity F = |χ| 2 /Im(χ). Here a factor of F 2 stems from energy-focusing enhancement while the remaining factor of F stems from dipole-emission enhancement.…”

“…While many different materials and antenna geometries have been used for SERS substrates [27][28][29], so far the optimization of these geometries has been limited to one or two degrees of freedom in designs such as bowtie antennas [10,[30][31][32][33]. Comparison with the recently derived upper bound to Raman enhancement showed these geometries to be greatly suboptimal, with performance several orders of magnitude below the bounds [21]. Although it is possible that the bounds can be tightened (e.g.…”