Direct Imaging of the Energy-Transfer Enhancement between Two Dipoles in a Photonic Cavity

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Direct Imaging of the Energy-Transfer Enhancement between Two Dipoles in a Photonic Cavity

Kaizad Rustomji, Marc Dubois, Boris Kuhlmey, C. Martijn de Sterke, Stefan Enoch, Redha Abdeddaim, and Jérôme Wenger

Phys. Rev. X 9, 011041 – Published 1 March 2019

Abstract

Photonic cavities are gathering a large amount of interest to enhance the energy transfer between two dipoles, with far-reaching consequences for applications in photovoltaics, lighting sources, and molecular biosensing. However, experimental difficulties in controlling the dipoles’ positions, orientations, and spectra have limited the earlier work in the visible part of the spectrum, and have led to inconsistent results. Here, we directly map the energy transfer of microwaves between two dipoles inside a resonant half-wavelength cavity with ultrahigh control in space and frequency. Our approach extends Förster resonance energy-transfer (FRET) theory to microwave frequencies and bridges the gap between the descriptions of FRET using quantum electrodynamics and microwave engineering. Beyond the conceptual interest, we show how this approach can be used to optimize the design of photonic cavities to enhance dipole-dipole interactions and FRET.

Received 24 October 2018
Revised 7 January 2019

DOI:https://doi.org/10.1103/PhysRevX.9.011041

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atoms, ions, & molecules in cavities Electromagnetism Nanophotonics Quantum description of light-matter interaction

Optical microcavities

Atomic, Molecular & OpticalGeneral PhysicsInterdisciplinary Physics

Authors & Affiliations

Kaizad Rustomji^1,2, Marc Dubois¹, Boris Kuhlmey², C. Martijn de Sterke², Stefan Enoch¹, Redha Abdeddaim¹, and Jérôme Wenger¹

¹Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France
²Institute for Photonics and Optical Sciences (IPOS), School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia

Popular Summary

Light can be trapped inside a cavity made by two mirrors, thus concentrating the light intensity and enhancing interactions between light and matter. Among the different applications of these photonic cavities, much attention is now focused on their ability to control the energy exchange between quantum emitters such as atoms, molecules, and quantum dots. Attempts to improve this exchange have been hampered by experimental difficulties in controlling the positions, orientations, and spectra of the emitter’s dipoles. Here, we thoroughly characterize dipole-dipole energy transfer inside a photonic cavity and provide design rules for cavity-enhanced applications.

At the nanoscale, the energy transfer between two light-sensitive elements is primarily governed by a dipole-dipole interaction described by a mathematical formalism known as Förster resonance energy transfer (FRET). We develop a general methodology to analyze FRET at microwave frequencies. While previous research has focused on optical frequencies, microwave experiments allow us to measure energy transfer with a high degree of control over dipole orientation and position. We then test our framework by investigating the energy transfer between two microwave antennas inside a photonic cavity and derive the conditions that enhance the transfer.

Our methodology bridges the gap between quantum electrodynamics and microwave engineering descriptions of dipole-dipole interactions. Beyond the conceptual interest, this approach provides a practical tool to quantitatively characterize photonic devices with an enhanced dipole-dipole interaction and can be readily applied to map energy transfer inside complex photonic systems at ultrahigh resolutions.

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Issue

Vol. 9, Iss. 1 — January - March 2019

Subject Areas

Photonics

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Images

Figure 1
(a) Quantum-mechanical description and (b) microwave engineering descriptions using a two-port network, of dipole-dipole energy transfer. (c) Photograph of the two dipoles set in parallel orientation. The dipole length is 30 mm and corresponds to $λ / 20$ . (d) Calibration of the power transferred versus the dipole-dipole separation $R$ in free space. Markers are experimental data for parallel dipoles (red) and aligned dipoles (blue) and dashed lines are theoretical predictions from Green’s function theory [25].
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Figure 2
Dipole-dipole energy transfer in a cavity. (a) Measured energy-transfer enhancement factor [Eq. (9)] between two dipoles versus cavity length, for different frequencies. The two dipoles are oriented parallel to each other and parallel to the mirror plates forming the cavity. From top to bottom, the different frequencies correspond to $k R$ values of 0.87, 0.84, 0.82, 0.80, and 0.77, respectively. The white disks indicate the cavity length that maximizes the energy transfer. It shifts to lower values with increasing frequency. (b) Simulations using Eq. (9) of the experimental results in (a). Because of the finite-size effects, the sharp peaks obtained at resonance (black disks) are smoothed in the experimental data in (a), but the main features (peak position and relative amplitude) are preserved as the frequency is tuned. (c) LDOS enhancement (Purcell factor) versus cavity length at 515 MHz, for a single dipole at 11.2 cm from the nearest mirror with orientation parallel to the mirrors. The blue line is the prediction from Green’s function theory while the red squares are experimental data. (d),(e) Energy-transfer enhancement versus cavity length and frequency. The experimental data (d) and the simulations (e) share the same color scale. The white dashed line represents the expected trend $L = λ / 2$ for the resonance condition. (f) Simulated evolution of the energy-transfer enhancement around the resonance for increasing dipole-dipole separations $R$ as function of the normalized cavity length $L / λ$ . For clarity, the curves are vertically shifted by $+ 1$ .
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Figure 3
Spatial maps of the energy-transfer enhancement inside the cavity. (a) Sketch of the experiment. The donor dipole (black) is fixed at 11.2 cm from the nearest mirror, while the acceptor dipole (red) is scanned to record the energy transfer at a fixed frequency. All data are then normalized to the same experiment performed without the cavity. (b) Simulation of the energy-transfer enhancement versus cavity lengths, with the lengths used in the experiments indicated by colored dots. For this simulation, a dipole-dipole distance of 7.6 cm (corresponding to $k R = 0.8$ ) was used. (c) Simulated maps of the energy-transfer enhancement inside the cavity for two dipoles oriented along $X$ and for different cavity lengths below, at, and above resonance. The white dot indicates the donor dipole position. Maps computed for a larger spatial domain up to $k R = 2$ are shown in the Supplemental Material, Fig. S2 [66]. (d) Measured maps of the energy-transfer enhancement for cavity lengths below, at, and above the resonance condition. The central dip (purple spot) corresponds to the donor dipole position.
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Figure 4
Two-dimensional maps summarizing the dipole-dipole energy-transfer enhancement $F_{E T}$ as functions of the normalized cavity length $L / λ$ and dipole-dipole separation $k R$ . (a) Simulated map and (b) experimental map for the dipoles in parallel orientation [as in Fig. 3]. The donor dipole is fixed at 11.2 cm from the nearest mirror. In (a) and (b) the black lines show the contour where the energy-transfer enhancement equals unity. The yellow dashed lines show the boundary between LDOS enhancement and quenching at $L / λ = 0.5$ . The theoretical and experimental maps share the same color scale. (c) Energy-transfer enhancement factor obtained for $k R = 0.9$ as a function of the normalized cavity length $L / λ$ . The solid dashed line represents the numerical prediction while the dots are experimental data. The gray dashed line indicates the level where $F_{ET} = 1$ . (d) Same as (c) for $k R = 0.1$ . The inset is a close-up view of the region enclosed in the dashed rectangle. (e) Energy-transfer enhancement factor at the cavity resonant length $L = λ / 2$ for increasing dipole-dipole separation $k R$ . In (c) and (e) the experimental error bars are estimated by summing a 5% experimental measurement error plus a 0.2 fixed contribution to represent the error in estimating the reference level in free space.
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