Antenna model of the Purcell effect

TL;DR

This paper introduces a classical antenna model to analyze the Purcell effect, enabling calculation and measurement of emission rate modifications for antennas and quantum emitters across various frequencies.

Contribution

It presents a universal, classical approach to quantify the Purcell effect using antenna radiation resistance, applicable to both electric and magnetic Purcell factors.

Findings

Provides a general equivalent scheme for the Purcell factor

Applicable to both radio antennas and quantum emitters

Versatile method for different frequency ranges

Abstract

The Purcell effect - the modification of the spontaneous emission rate in presence of resonant cavities or other resonant objects - is a fundamental effect of quantum electrodynamics. However, a change of the emission rate caused by environment different from free space has a classical counterpart. Not only quantum emitters, but any small antenna tuned to the resonance is an oscillator with radiative losses, and the influence of the environment on its radiation can be understood and measured in terms of the antenna radiation resistance. We present a general approach which is applicable to measurements of the Purcell factor for radio antennas and to calculations of these factors for quantum emitters. Our methodology is suitable for calculation and measurement of both electric and magnetic Purcell factors, it is versatile and applies to various frequency ranges. The approach is illustrated by a general equivalent scheme and allows the Purcell factor to be expressed through the continious radiation of a small antenna in presence of the environment.