[Paper Review] Giant Spin Hall Effect in Single Photon Plasmonics

G. S. Agarwal, Svend‐Age Biehs|arXiv (Cornell University)|Dec 24, 2012

Plasmonic and Surface Plasmon Research20 references3 citations

TL;DR

This paper proposes a giant spin Hall effect of light (SHEL) in single-photon plasmonics via Förster energy transfer (FRET) between two atoms mediated by resonant surface plasmons on graphene and metal films. The effect arises from spin-orbit coupling in non-paraxial dipole fields, leading to conversion of σ⁺ photons into σ⁻ photons with two units of orbital angular momentum, resulting in a four-order-of-magnitude enhancement in SHEL probability due to plasmonic field enhancement and local field effects.

ABSTRACT

We show the existence of a very large spin Hall effect of light (SHEL) in single photon plasmonics based on spontaneous emission and the dipole-dipole interaction initiated energy transfer (FRET) on plasmonic platforms. The spin orbit coupling inherent in Maxwell equations is seen in the conversion of sigma + photon to sigma - photon. The FRET is mediated by the resonant surface plasmons and hence we find very large SHEL. We present explicit results for SHEL on both graphene and metal films. We also study how the splitting of the surface plasmon on a metal film affects the SHEL. In contrast to most other works which deal with SHEL as correction to the paraxial results, we consider SHEL in the near field of dipoles which are far from paraxial.

Motivation & Objective

• To demonstrate a giant spin Hall effect of light in single-photon plasmonic systems beyond the paraxial approximation.
• To explore how resonant surface plasmons on graphene and metal films enhance the spin Hall effect via Förster energy transfer (FRET).
• To investigate the role of non-paraxial fields and evanescent waves in enabling large spin-orbit coupling effects in plasmonic platforms.
• To show that the SHEL can be experimentally monitored through population transfer to orthogonally polarized excited atomic states.

Proposed method

• Model the interaction between two three-level atoms using the interaction picture Hamiltonian involving dipole operators and the electromagnetic field operator.
• Use the dipole-dipole interaction and vacuum field coupling to describe spontaneous emission and absorption in the presence of plasmonic environments.
• Apply the rotating wave approximation and derive the transition probability for FRET from a σ⁺-polarized excited state to a σ⁻-polarized state.
• Calculate the plasmonic enhancement factor E using the Fresnel reflection coefficient r_p and the Drude model for silver, incorporating propagation length and wavevector dependence.
• Analyze the SHEL via the probability D_sh of exciting the orthogonally polarized state, including contributions from poles and non-pole terms in the reflection coefficient.
• Study the effect of surface plasmon splitting on dielectric substrates (e.g., 15 nm Ag on silica) and its impact on SHEL enhancement through 3D plots of Im[r_p] and wavelength dependence.

Experimental results

Research questions

• RQ1 Can a giant spin Hall effect of light be realized in single-photon plasmonics via Förster energy transfer on plasmonic platforms?
• RQ2 How does the non-paraxial nature of dipole fields contribute to large spin-orbit coupling and polarization conversion in FRET?
• RQ3 What is the role of resonant surface plasmons in enhancing the SHEL probability beyond vacuum values?
• RQ4 How does the splitting of surface plasmon modes on thin metallic films affect the SHEL enhancement?
• RQ5 Can the SHEL be experimentally detected by monitoring the population of orthogonally polarized excited atomic states?

Key findings

• The SHEL probability D_sh is enhanced by four orders of magnitude on silver films at the surface plasmon resonance wavelength λ_sp = 291.7 nm due to resonant plasmonic enhancement.
• On suspended graphene with E_F = 1 eV, the SHEL enhancement factor E reaches large values across a broad wavelength range, with significant dependence on distance normalized to the surface plasmon propagation length.
• The Fano-like line shapes in the SHEL spectrum arise from interference between pole and non-pole contributions in the reflection coefficient r_p.
• For a 15 nm silver film on silica, surface plasmon splitting leads to two distinct surface mode branches, with long-range plasmons (λ < 300 nm) producing significantly larger SHEL enhancement than short-range plasmons (λ > 320 nm).
• The plasmonic enhancement factor E decays exponentially for interatomic distances d ≫ l, where l is the surface plasmon propagation length, confirming the role of evanescent fields in the effect.
• The conversion of σ⁺ to σ⁻ photons is accompanied by the generation of two units of orbital angular momentum, confirming the spin-orbit coupling mechanism in the near field.