[Paper Review] Polarization effects in metallic films perforated with a bidimensional array of subwavelength rectangular holes

Michaël Sarrazin, J. P. Vigneron|CERN Bulletin|Nov 4, 2003

Optical Coatings and Gratings3 citations

TL;DR

This paper demonstrates that metallic films perforated with a 2D array of subwavelength rectangular holes exhibit polarization-dependent zeroth-order transmission, unlike circular holes, due to anisotropic coupling to surface plasmons. The effect arises from asymmetric hole geometry breaking rotational symmetry, enabling the structure to function as a broadband polarizer with enhanced transmission, offering a new platform for plasmonic polarizers with applications in integrated optics.

ABSTRACT

For several years, periodical arrays of subwavelength cylindrical holes in thin metallic layers have taken a crucial importance in the context of the results reported by Ebbesen et al, on particularly attractive optical transmission experiments. It had been underlined that the zeroth order transmission pattern does not depend on the polarization of the incident light at normal incidence. In the present paper, we show that it is not the case for rectangular holes, by contrast to the case of circular holes. In this context, we suggest a new kind of polarizer that present the advantages brought by the original Ebbesen devices. Assuming the recent technological interest for these kinds of metallic gratings, such a kind of polarizer could lead to new technological applications.

Motivation & Objective

• To investigate polarization-dependent optical transmission in metallic films with subwavelength rectangular hole arrays.
• To determine whether the zeroth-order transmission pattern depends on incident light polarization, contrasting with circular hole arrays.
• To explore the potential of such structures as efficient, broadband polarizers by leveraging surface plasmon resonance and anisotropic diffraction.
• To provide a theoretical foundation for designing plasmonic polarizers with enhanced transmission and polarization control.

Proposed method

• Numerical simulations using a coupled-mode method combined with the scattering matrix (S-matrix) formalism to solve Maxwell’s equations in periodic structures.
• Representation of the permittivity and electromagnetic fields via Fourier series expansions in the transverse (x,y) directions.
• Modeling the system as a stack of thin layers along the z-axis, with S-matrix propagation and combination to compute total transmission and reflection amplitudes.
• Calculation of transmission amplitudes for both s- and p-polarized light across different incident angles and wavelengths.
• Use of experimentally derived permittivity values for chromium and fused silica substrates in the 1000–1500 nm range.
• Validation of results against established methods (e.g., FDTD, KKR), with convergence achieved using only 25 reciprocal lattice vectors.

Experimental results

Research questions

• RQ1 Does the zeroth-order transmission through a 2D array of subwavelength rectangular holes depend on the polarization of incident light?
• RQ2 How does the anisotropic geometry of rectangular holes influence surface plasmon coupling and transmission characteristics compared to circular holes?
• RQ3 Can such a structure function as an efficient polarizer while retaining the high transmission features of Ebbesen-type devices?
• RQ4 What is the role of phase differences (dephasing) between x- and y-polarized transmission components in determining the polarization state of the transmitted beam?
• RQ5 How do the transmission amplitudes and polarization states vary with incident angle and wavelength?

Key findings

• The zeroth-order transmission through rectangular-hole arrays is polarization-dependent, unlike in circular-hole arrays where it is polarization-insensitive at normal incidence.
• Transmission is higher for polarization aligned with the long axis of the rectangular holes (e.g., θ = 60°) compared to the short axis (θ = 30°), with a 20% increase in transmission observed at 1300 nm.
• The transmitted field exhibits elliptical polarization for intermediate incident angles (e.g., θ = 45°), indicating a phase difference between x- and y-polarized components.
• The dephasing δ between transmitted x- and y-components varies with both wavelength and incident angle, peaking near surface plasmon resonance wavelengths, though the dependence is not explicitly captured by simple models.
• Numerical results show qualitative agreement with a simple analytical model based on asymmetric coupling, despite the underlying complexity of multi-scattering and surface plasmon contributions.
• The system supports high transmission with polarization filtering capability, suggesting potential for use in plasmonic polarizers with enhanced performance.