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, ?SH=?F+?F, is a special case of sum-frequency generation, ?3=?1+?2, and one can think of it as the annihilation of two photons at the fundamental frequency ?F to create a photon at ?SH. 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 one can achieve this phase matching 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. A quadratic nonlinearity can be artificially induced, however, by poling the silica optical fiber; SHG then occurs through the cubic nonlinearity as four-wave mixing of the fundamental and second-harmonic fields with a frozen-in DC electric field from the poling process. Quasi-phase-matching is achieved by periodically changing the sign of the poling field, and previously it has been possible only to tune the phase-matching condition in poled optical fibers by compressing the fiber.
Now, the work presented by E. Y. Zhu and colleagues demonstrates that the phase matching in periodically poled birefringent optical fibers can also be tuned by simply twisting the fiber. Twisting the fiber leads to coupling between the x and the y polarizations and twisting-dependent polarization eigenmodes. This also leads to a change in the phase matching between the polarization modes. By adjusting the twist of the fiber, one can therefore tune the phase-matching wavelengths and also obtain types of phase-matchings between the polarization modes not possible in an untwisted fiber.
The work demonstrates, both theoretically and experimentally, how twist-tuning can be used to control the efficiencies of the different SHG signals. It is demonstrated experimentally that, for one of the signals (X+X?X), the wavelength of maximum conversion efficiency for the fundamental wave can be shifted by about 0.8 nm by twisting the fiber a little more than one turn. One type of signal (Y+X?X) not obtainable in an untwisted fiber is clearly shown to arise when the fiber is twisted a little more than one turn.
The work of Zhu et al. is interesting because it clearly demonstrates the possibility of tuning SHG in optical fibers though a simple mechanical twisting of the fiber. Further research could explore the possibility of obtaining analogous results for the third-order nonlinearity in birefringent photonic crystal fibers, as well as for generating polarization-entangled photons through the reverse process of SHG, spontaneous parametric down conversion.
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