[Paper Review] Large Purcell enhancement without strong field localization

Alex Krasnok, Stanislav Glybovski+6 more|arXiv (Cornell University)|Jun 24, 2015

Orbital Angular Momentum in Optics1 references3 citations

TL;DR

This paper proposes a new strategy to achieve large Purcell enhancement in all-dielectric nanostructures not through strong local-field localization, but by engineering radiation directivity. By leveraging collective excitation of dark modes in high-index dielectric arrays, the authors demonstrate up to two orders of magnitude enhancement in the Purcell factor, validated by microwave experiments with ceramic cylinders at 8.6 GHz.

ABSTRACT

The Purcell effect is defined as the modification of spontaneous decay in the presence of a resonator, and in plasmonics it is usually associated with the large local-field enhancement in "hot spots" due to surface plasmon polaritons. Here we propose a novel strategy for enhancing the Purcell effect through engineering the radiation directivity without a strict requirement of the local field enhancement. Employing this approach, we demonstrate how to enhance the Purcell effect by two orders of magnitude in all-dielectric nanostructures recently suggested as building blocks of low-loss nanophotonics and metamaterials. We support our concept by proof-of-principle microwave experiments with arrays of high-index dielectric resonators.

Motivation & Objective

• Overcome the misconception that large Purcell enhancement requires strong local-field enhancement in plasmonic 'hot spots'.
• Address the long-standing belief that all-dielectric nanostructures inherently exhibit low Purcell factors due to weak local fields.
• Develop a new design principle for enhancing spontaneous emission in dielectric nanophotonics by focusing on radiation directivity rather than local field intensity.
• Demonstrate that collective excitation of dark modes in dielectric arrays can lead to high Purcell factors despite low local-field enhancement.
• Provide experimental validation of the theoretical framework using scalable microwave-frequency prototypes with high-index ceramic particles.

Proposed method

• Utilize the reciprocity theorem to relate the Purcell factor to the radiation pattern and field distribution of a nanoantenna, rather than relying solely on local field enhancement.
• Engineer the radiation directivity of high-index dielectric resonators to maximize the local density of states (LDOS), which directly influences the Purcell factor.
• Design arrays of dielectric cylinders with specific periodicity and orientation to excite symmetric, collective dark modes with high Q-factors and directional radiation patterns.
• Apply the formula for the Purcell factor in terms of the imaginary part of the scattered field and the dipole moment, emphasizing the role of radiation pattern over local field intensity.
• Use microwave-scale prototypes with MgO-TiO2 ceramic disks (ε = 16) to simulate optical behavior, enabling direct measurement of radiation resistance as a proxy for the Purcell factor.
• Measure the input impedance of a short monopole antenna over a ground plane to extract the radiation resistance, comparing values with and without the dielectric array to determine the Purcell factor.

Experimental results

Research questions

• RQ1 Can large Purcell enhancement be achieved in all-dielectric nanostructures without relying on strong local-field enhancement or plasmonic hot spots?
• RQ2 To what extent does radiation directivity—rather than local field intensity—determine the Purcell factor in resonant dielectric systems?
• RQ3 How does collective excitation of dark modes in periodic dielectric arrays influence the local density of states and spontaneous emission enhancement?
• RQ4 Can the theoretical predictions of enhanced Purcell factors in dielectric arrays be experimentally validated at microwave frequencies?
• RQ5 What is the role of structural geometry (e.g., cylinder orientation and chain length) in maximizing Purcell enhancement through radiation pattern control?

Key findings

• The Purcell factor in all-dielectric arrays was enhanced by up to two orders of magnitude, reaching values significantly higher than previously reported for similar dielectric systems.
• A peak Purcell factor of approximately 100 was experimentally observed at 8.6 GHz in a chain of high-index ceramic cylinders, with excellent agreement between simulation and measurement.
• The enhancement is attributed to collective excitation of dark modes with high Q-factors and directional radiation patterns, not to local field enhancement.
• The local-field enhancement factor (LFEF) remained low (Σ ~ 1–2), confirming that strong field localization is not necessary for large Purcell enhancement.
• The Purcell factor increased with chain length, indicating the emergence of collective mode behavior akin to infinite periodic systems, where group velocity concepts become applicable.
• The orientation of the dielectric cylinders significantly affects the Purcell factor: vertical alignment (axis along chain) yielded strong enhancement, while horizontal alignment resulted in much weaker enhancement due to less directional radiation.