An important early step in nonlinear optics was the discovery of second-harmonic generation (SHG) using a ruby laser and crystalline quartz as the nonlinear medium. SHG, ωSH=ωF+ωF, is a special case of sum-frequency generation, ω3=ω1+ω2, and one can think of it as the annihilation of two photons at the fundamental frequency ωF to create a photon at ωSH. Today, SHG is used routinely in many laboratories, and also in mass-market products such as green laser pointers. The efficiency of the conversion process is determined by the degree of phase matching between the fundamental and the second-harmonic waves. For example, in a nonlinear birefringent uniaxial crystal this phase matching can be achieved by carefully adjusting the propagation direction of the input field (ordinary polarization) to a suitable angle relative to the optic axis of the crystal, with the second harmonic being generated in the extraordinary polarization. Another phase-matching method is to change the birefringence by tuning the temperature of the crystal.
The quadratic nonlinearity required for SHG is an inherent property of many crystals but is absent in centrosymmetric materials such as fused silica, from which standard optical fibers are made. This is unfortunate, since SHG in optical fibers could lead to less expensive, more efficient, and more compact devices. A quadratic nonlinearity can be artificially induced, however, by poling the silica optical fiber, meaning that a DC-field is applied and “frozen” into the fiber. SHG then occurs through the cubic nonlinearity as four-wave mixing of the fundamental and the second-harmonic fields with the frozen-in DC electric field from the poling process. Quasi-phase-matching is achieved by periodically changing the sign of the poling field. Unfortunately, the poling is unstable over time, thereby gradually decreasing the nonlinearity of the poled fiber.
The work presented here by Daengngam and colleagues overcomes this problem by taking a different approach. Instead of achieving quadratic nonlinearity in a silica fiber through poling, they apply a coating of nonlinear molecules to the outer surface of a silica fiber. The fiber is beforehand tapered down to have a radius of just a few micrometers. This increases the overlap between the light inside the fiber and the nonlinear molecules on the outer surface for increased efficiency. The coating is highly stable over time, resistant to increases in temperature (cycles to 150 °C have been tested), and mechanically stable, and it can be immersed in water and most organic solvents. This work therefore represents a significant practical step forward toward optical fibers for SHG.
The nonlinear conversion efficiency is limited so far, because the fibers are not phase matched for efficient SHG. But, similar to the case of poling, the authors suggest the use of periodic coating to achieve quasi-phase-matching to increase the efficiency. In periodically poled fibers, one can fine-tune the phase matching by compressing the fiber, but a potential disadvantage of the approach suggested here is that the tapered fiber could be too fragile for such fine-tuning. One could speculate whether the coated taper could entirely be avoided by instead doping a silica or polymer preform with the same (or similar) nonlinear molecules, before drawing it to a fiber. It would still be possible to achieve a small core size for high intensity by making the fiber microstructured with air holes (a so-called photonic crystal fiber). This would also have the advantage of allowing greater control of the dispersion properties of the fiber, so that it could be designed for phase matching between the pump and the second-harmonic wave.
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