[Paper Review] Depolarization induced by subwavelength metal hole arrays

Cyriaque Genet, E. Altewischer+2 more|ArXiv.org|Nov 28, 2003

Optical Coatings and Gratings2 references3 citations

TL;DR

This paper presents a symmetry-based theoretical framework explaining depolarization in subwavelength metal hole arrays due to surface plasmon (SP) excitations under finite-diameter beam illumination. It shows that angularly integrated transmission from SPs with spatial dispersion leads to intrinsic depolarization, with square and hexagonal arrays acting as purely depolarizing elements characterized by diagonal Mueller matrices, confirming that depolarization arises from spatially variant polarization states induced by SP propagation and beam angular spread.

ABSTRACT

We present a symmetry-based theory of the depolarization induced by subwavelength metal hole arrays. We derive the Mueller matrices of hole arrays with various symmetries (in particular square and hexagonal) when illuminated by a finite-diameter (e.g. gaussian) beam. The depolarization is due to a combination of two factors: (i) propagation of surface plasmons along the surface of the array, (ii) a spread of wave vectors in the incident beam.

Motivation & Objective

• To develop a theoretical framework explaining the experimentally observed depolarization in subwavelength metal hole arrays when illuminated by finite-diameter beams.
• To clarify why depolarization occurs despite symmetry arguments suggesting pure input polarization should yield pure output polarization.
• To identify the role of surface plasmon (SP) excitations and spatial dispersion in inducing polarization state variations across the far-field pattern.
• To establish that depolarization arises from angular integration of SP transmission amplitudes dependent on far-field angles, not from polarization mixing.

Proposed method

• Formal analysis of the transmission matrix $\mathbf{t}(\lambda;\theta)$ relating input and output electric fields in the paraxial approximation.
• Use of Mueller algebra and Stokes parameters to describe polarization states, with the Mueller matrix $\mathbf{M}$ derived from angularly averaged transmission amplitudes.
• Application of tensorial symmetry analysis to show that $\mathbf{M}$ is diagonal for square and hexagonal arrays due to $C_{nv}$ point group symmetry.
• Derivation of the Mueller matrix elements $M_0, M_1, M_2, M_3$ as angular averages of $|t_{ij}|^2$ and $\Re[t_{ij}t_{kl}^*]$ terms, revealing no Stokes parameter mixing.
• Identification of two key physical mechanisms: (i) multi-plane wave illumination (angular spread in incident beam), and (ii) spatial dispersion from SPs with direction-dependent transmission.
• Demonstration that depolarization is intrinsic and arises from the interplay of symmetry, SP propagation, and finite beam angular spread, not from material imperfections.

Experimental results

Research questions

• RQ1 Why does a fully polarized input beam become depolarized upon transmission through a subwavelength metal hole array, despite symmetry arguments suggesting otherwise?
• RQ2 How do surface plasmon excitations and their angular dependence contribute to spatially variant polarization in the output beam?
• RQ3 What is the role of finite-diameter (e.g. Gaussian) beam illumination in enabling depolarization, compared to plane wave illumination?
• RQ4 Why are the Mueller matrices of square and hexagonal arrays diagonal, and what does this imply about polarization mixing?
• RQ5 How does the symmetry of the array (e.g. $C_{4v}$, $C_{6v}$) determine the structure of the Mueller matrix and the degree of depolarization?

Key findings

• The Mueller matrix for square and hexagonal hole arrays is diagonal, indicating no mixing of Stokes parameters and confirming that the arrays act as purely depolarizing elements.
• Depolarization arises from angular integration of transmission amplitudes that depend on far-field angles due to spatial dispersion from surface plasmons.
• For an input beam with degree of polarization $\Pi^{\rm in} = 1$, the output degree of polarization is reduced to $\Pi^{\rm out} = M_i / M_0 < 1$, with the value depending on the beam's opening angle.
• In the limit of zero hole size or highly dissipative metal (e.g. Cr), the Mueller matrix becomes proportional to the identity, confirming no depolarization.
• For hexagonal arrays, $M_1 = M_2$, meaning inputs with $S_1 = \pm 1$ and $S_2 = \pm 1$ suffer identical depolarization, enabling direct measurement via crossed-polarization analysis.
• The theory explains that depolarization is fundamentally due to the combination of multi-plane wave illumination and SP-induced spatial dispersion, not from symmetry-breaking defects.