[Paper Review] Purcell factors and Forster resonance energy transfer in proximity to helical structures

Asaf Farhi, Aristide Dogariu|arXiv (Cornell University)|Jan 24, 2022

Metamaterials and Metasurfaces Applications42 references3 citations

TL;DR

This paper investigates how helical nanostructures, such as microtubules, enhance spontaneous emission and Förster resonance energy transfer (FRET) via synchronous vibrational modes. Using the eigenpermittivity formalism in the quasistatic regime, it demonstrates that these modes generate large Purcell factors and long-range, oscillatory FRET due to delocalized surface responses, offering a mechanism for long-range molecular interactions near biologically relevant helices.

ABSTRACT

Both spontaneous emission and resonant energy transfer can be enhanced significantly when the emitter is placed in the vicinity of metallic or crystal structures. This enhancement can be described using the electromagnetic Green tensor and is determined by the dominant surface modes of the structure. Here we use the eigenpermittivity formalism to derive the spontaneous emission and FRET rates in the quasistatic regime in a two-constituent medium with an anisotropic inclusion. We then apply our results to a helical structure supporting synchronous vibrations and evaluate the contribution of these modes, which are associated with a strong and delocalized response. We show that this contribution can result in large Purcell factors and long-range FRET, which oscillates with the helix pitch. These findings may have implications in understanding and controlling the interactions of molecules close to helical structures such as the microtubules.

Motivation & Objective

• To understand how helical structures such as microtubules enhance light-matter interactions.
• To analyze spontaneous emission and FRET rates near helical structures using electromagnetic theory.
• To identify the role of synchronous vibrational modes in enabling strong, long-range energy transfer.
• To quantify Purcell factors and FRET efficiency in proximity to helical inclusions with anisotropic permittivity.
• To explore the implications for molecular interactions in biological systems like DNA and tubulin-based cytoskeletal structures.

Proposed method

• Applies the eigenpermittivity formalism to model electromagnetic response in a two-constituent medium with anisotropic inclusion.
• Uses the quasistatic approximation to derive expressions for spontaneous emission and FRET rates.
• Models the helical structure as a periodic anisotropic medium with axial symmetry, introducing effective permittivity ϵ1z(k) for axial modes.
• Identifies synchronous-vibration modes satisfying k = mkz, where kz = 2π/a, leading to real and degenerate eigenpermittivities.
• Expands the electric field using eigenfunctions of the system to compute the Green's tensor and local density of states.
• Calculates the Purcell factor and FRET efficiency based on the imaginary part of the Green tensor and dipole-dipole coupling.

Experimental results

Research questions

• RQ1 How do helical structures support delocalized electromagnetic modes that enhance light-matter interactions?
• RQ2 What is the role of synchronous vibrational modes in enabling long-range FRET near helical inclusions?
• RQ3 To what extent can Purcell factors be enhanced in helical nanostructures due to resonant surface modes?
• RQ4 How does the FRET efficiency vary with helix pitch and emitter position?
• RQ5 Can the eigenpermittivity formalism accurately predict enhanced emission and energy transfer in biologically relevant helical systems?

Key findings

• Synchronous vibrational modes in helical structures produce real, degenerate eigenpermittivities, enabling strong and delocalized electromagnetic responses.
• The Purcell factor is significantly enhanced near helical structures due to resonant coupling with these modes, especially when physical frequency matches the mode frequency.
• Förster resonance energy transfer (FRET) exhibits long-range behavior, extending beyond typical dipole-dipole limits, due to delocalized modes.
• FRET efficiency oscillates with the helix pitch, indicating a periodic dependence on structural periodicity.
• The enhancement is most pronounced when the physical permittivity matches the eigenpermittivity of the system, indicating resonance conditions.
• The results suggest that microtubules and similar helical structures can mediate long-range, coherent energy transfer in biological environments.