Unambiguous demonstration of the Purcell effect in an optical nano-resonator
Fast (record-high Purcell factor) and bright (high extraction efficiency) spontaneous emission is unambiguously observed from an ensemble of Er3+ ions embedded in a very small metallic resonator. The metallic nano-cavity provides an acceptable resonant platform with extraction efficiency of over 50% even at optical frequencies. The Joule losses of metallic electrons are overcome by liberating the stored electromagnetic energy in just one or two optical cycles before it is dissipated as heat.
Ever since Purcell has predicted in 1946 that the spontaneous emission rate of an atom inside an electromagnetic resonator can be drastically enhanced, controlling spontaneous emission at optical frequencies has been the subject of intense research in the photonics community. A strong enhancement, or equivalently, a large Purcell factor, would not only facilitate the development of many novel devices that would benefit from fast and bright light emission, but would also provide a valuable tool in the fundamental studies of light-matter interactions. On many occasions, the Purcell factor was given to be proportional to Q/V, where Q is the quality-factor of the cavity, and V is the mode volume; much effort was directed to increasing the Q/V ratio, oftentimes using ultra-high Q cavities. However, the ratio is valid only for an emitter that is perfectly matched to the cavity in every way – spectrally, spatially, and polarization-wise.
For high-Q cavities, such a perfect match to a realistic emitter is difficult, especially at room temperature. Consequently, despite the “theoretical predictions” of Purcell factors in excess of 10,000, the actual values experimentally obtained have been much lower, typically in the range of 3-30. A Purcell factor of 75 had been reported for a “quantum well” in a photonic crystal cavity, but only at cryogenic temperatures.
Another possible approach is the use of metallic nano-cavities. Although the Q-factors of metallic nano-cavities are quite modest, the mode volume can be made very small, therefore achieving a high Q/V ratio. The reported values of Purcell factors, however, still remained quite low, in the range of 10-30 only. Furthermore, the presence of metal can introduce Joule losses, which result in an increase in the non-radiative decay rate and a reduction in the far-field radiant flux from the cavity. This not only makes quantitative analysis of the decay rate difficult, but also reduces the usefulness of such a cavity in practical applications.
In this work, researchers report on the enhancement of 1.54 μm emission from an ensemble of Er3+ ions placed in a very small metallic nano-cavity. As the intra-4f transition of Er3+ ions is a parity-forbidden transition of core electrons, its luminescence lifetime can be longer than 10 ms. Such a long luminescence lifetime allows for a direct measurement of a Purcell factor well over 1,000 since the temporal response of a typical avalanche photodetector is in the range of nanoseconds. In addition, since this is a core-level transition of dopant atoms immobilized in a host material such as SiO2, surface recombination and carrier diffusion do not arise here, in contrast to semiconductor-based emitters such as quantum dots that bring about complicated data analysis. A trench-type gold nano-cavity (Fig. a) was chosen for its small mode volume, and ease of fabrication. The cavity structure was systematically designed, not only to increase the Q/V ratio, but also to provide a high degree of matching between Er3+ ions and the cavity mode, both spectrally and spatially (Fig. b). In addition, care was taken to enhance the extraction of light from the cavity as well.
Based on a systematic investigation of many photonic properties together with comparison with full three-dimensional numerical simulations, researchers obtained strong experimental evidence that the spontaneous emission rate (Fig. c), as well as the far-field radiant flux (Fig. d) of Er3+ ions are enhanced as a result of spectral and spatial mode matching between the Er3+ ions and the resonant mode in the metallic nano-cavity. Optimally, the Purcell factor is as high as 170 at room temperature, in excellent agreement with the predicted value of 220. More than 90 times increase of the far-field radiant flux indicates extraction efficiency as high as 55%. This is thanks to the low Q-factor that enables an extremely fast radiation of electromagnetic energy into the free space within just one or two optical cycles before experiencing Joule losses.
These experimental results, matching with theoretical values, demonstrate unambiguously a hitherto largest ever achieved overall Purcell factor. A high extraction efficiency of 55% is achieved at the same time due to the low-Q nature of the metallic resonators. The metallic nano-cavity is expected to be a competitive platform that enables fast and bright spontaneous emission for applications such as fast and efficient LEDs and efficient single photon sources.
This study was published in the Nature Communications (May 5th, 2015)
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