Dispersion of polarization coupling, localized and collective plasmon modes in a metallic photonic crystal mapped by Mueller Matrix Ellipsometry

Abstract

We report a spectroscopic Mueller matrix experimental study of a plasmonic photonic crystal consisting of gold hemispheroidal particles (lateral radius 54 nm, height 25 nm) arranged on a square lattice (lattice constant 210 nm) and supported by a glass substrate. Strong polarization coupling is observed for ultraviolet wavelengths and around the surface plasmon resonance for which the off-block-diagonal Mueller matrix elements show pronounced anisotropies. Due to the Rayleigh anomalies, the block-diagonal Mueller matrix elements produce a direct image of the Brillouin Zone (BZ) boundaries of the lattice and resonances are observed at the M-point in the first and at the X-point in the second BZ. These elements show also the dispersion of the localized surface plasmon resonance.

Critical dimension metrology of a plasmonic photonic crystal based on Mueller matrix ellipsometry and the reduced Rayleigh equation

“…Indeed, a fast retrieval method allows for extracting in real time the morphological parameters during growth and, hence, reveals the kinetics of the growth processes [3]. Recently, spectroscopic standard, generalized, and Mueller matrix ellipsometry have been suggested for the characterization of surfaces and composite systems of complex geometries, such as photonic crystals and metamaterials [2,[4][5][6][7][8][9][10].Spectroscopic ellipsometry has for several decades been used for the characterization of one-dimensional gratings, although limited to non-conical incidence [11,12]. The use of conical incidence was, for example, reported in [13], where the modeling of the Mueller matrix elements was based on the rigorous coupled wave analysis (RCWA), and used to fit the spectroscopic data.…”

“…The use of conical incidence was, for example, reported in [13], where the modeling of the Mueller matrix elements was based on the rigorous coupled wave analysis (RCWA), and used to fit the spectroscopic data. Critical dimension retrieval obtained by combining RCWA and Mueller matrix ellipsometry (or scatterometry) has also been investigated for two-dimensional gratings [14,15], and may be regarded as an established, but computationally expensive, technique.Spectroscopic Mueller matrix ellipsometry of arrays of gold particles supported by a glass substrate was recently shown to exhibit a rich optical response, including Rayleigh-Wood anomalies and significant polarization coupling around the localized surface plasmon resonance (LSPR) [6].In this Letter, the reduced Rayleigh equation (RRE) [16] is combined with angle-resolved spectroscopic Mueller matrix ellipsometry to produce a computationally efficient and reliable method for the reconstruction of the geometrical parameters of a two-dimensional photonic crystal. The method correctly reproduces the Rayleigh-Wood anomalies and polarization coupling, and is sufficiently fast to practically be used for online metrology.…”

“…The sample was produced by focused ion beam milling of a 40 nm thick Au film. The intention was to produce a square array of particles of a lattice parameter of 210 nm [6,17]. However, SEM and AFM characterization of the sample [ Fig.…”

“…However, SEM and AFM characterization of the sample [ Fig. 1(a)] revealed a rectangular array of lattice parameters a 1 208 2 nm and a 2 211 2 nm, where the particles had an in-plane radius of r k 58 4 nm and a height of r ⊥ 36 5 nm [6,17]. This characterization also established that an over-milling into the substrate had taken place during sample preparation which expressed itself as a "trench network" milled into the substrate in regions not covered by Au particles.…”

“…Indeed, a fast retrieval method allows for extracting in real time the morphological parameters during growth and, hence, reveals the kinetics of the growth processes [3]. Recently, spectroscopic standard, generalized, and Mueller matrix ellipsometry have been suggested for the characterization of surfaces and composite systems of complex geometries, such as photonic crystals and metamaterials [2,[4][5][6][7][8][9][10].…”