Silica microfibers are ordinary optical fibers which have been tapered down to micron or even sub-micron outer diameters over a length of a few millimeters or centimeters. Incoupling and outcoupling into these devices is straightforward, as the fiber is of standard diameter in both ends. In the tapered section, the fundamental guided mode adiabatically evolves into the fundamental mode of a micron-sized silica strand in air, implying an enhancement of the nonlinear coefficient with up to two orders of magnitude. However, parametric processes like the THG enabled by the third-order nonlinearity of amorphous silica, are not only limited by intensity, but also by phase-matching requirements. When three pump photons are converted into one signal photon, both momentum and energy must be conserved, which translates into a requirement that the effective index of propagation for the guided mode should be the same at the pump and signal wavelengths. The monotonous increase of the silica refractive index with frequency usually precludes such phase-matching between fundamental modes in a given fiber. However, in microfibers phase-matching to higher-order modes at the signal wavelength is straightforwardly achieved. Earlier theoretical results suggest that a 50% conversion efficiency can be achieved in a 1 cm-piece of microfiber, and more than 90% can be obtained over 5 cm, using a pump power of 1 kW. These calculations, however, assume an ideal microfiber with a uniform diameter. Since the phase-matching is critically dependent on the fiber diameter being just right, inevitable diameter fluctuations has made it impossible to achieve such conversion rates in fabricated microfibers.
One solution could be to increase the pump power, since microfiber damage typically does not set in before reaching the 10 kW level. This will allow using shorter fiber lengths, alleviating the problem of diameter fluctuations. Instead of just increasing the output of the pump laser, Lee and co-workers suggest a more clever approach. By twisting the microfiber into a loop, whose in- and outgoing fiber ends are in close proximity, a resonant cavity for the pump light can be formed within the loop. In this way, the pump intensity in the loop cavity can be enhanced by almost an order of magnitude. Conversion efficiencies on the percent level are then obtained already at a pump power level of 100 W in a loop having a length of only 3 mm. At 600 W, the conversion efficiency is more than 50%. The reduced length of the microfiber means that longitudinal homogeneity is more likely to be maintained. The authors also show that it may be possible to further enhance the THG efficiency by making the loop resonant for light at the signal frequency as well as at the pump frequency.
While the present paper is purely numerical, microfiber loop resonators are well established in the laboratory, and the work therefore points out a direction of research which can immediately be taken up by experimenters. It will indeed be interesting to see if present-day state-of-the-art microfibers will allow efficient THG by utilizing the loop resonator concept.
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