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We propose and investigate the quasi-phase matched (QPM) nonlinear optical frequency conversion of optical vortices in periodically poled Lithium Niobate (PPLN). Laguerre-Gaussian (LG) modes are used to represent the orbital angular momentum (OAM) states, characterized with the azimuthal and radial indices. Typical three-wave nonlinear interactions among the involved OAM modes are studied with the help of coupling wave equations. Being different from normal QPM process where the energy and quasi-momentum conservations are satisfied, both of the azimuthal and radial indices of the OAM states keep constant in most of the cases. However, abnormal change of the radial index is observed when there is asynchronous nonlinear conversion in different parts of the beams. The QPM nonlinear evolution of fractional OAM states is also discussed showing some interesting properties. In comparison with the traditional birefringent phase matching (BPM), the QPM technique avoids the undesired walk-off effect to reserve high-quality LG modes. We believe the QPM is an efficient way to convert, amplify and switch OAM states in various optical vortex related applications.

We propose a scheme to realize arbitrarily polarized light optical parametric amplification in a periodically poled Lithium Niobate using quasi-phase matching. The domain structure should be well-designed with suitable electric field applied on selected sections.

A tunable dual-wavelength filter is experimentally demonstrated in domain-engineered lithium niobate. Application of an electric field on the y-surfaces of the sample results in the optical axes rotating clockwise and anticlockwise, which makes selective polarization rotation. The quasi phase-matching wavelengths could be adjusted through suitable domain design. A unique dual valley spectrum is obtained in a periodically poled lithium niobate structure with a central defect if the sample is placed between two parallel polarizers. The expected bandwidth could be varied from ∼1 nm to ∼40 nm. Moreover, both the spectral response and group delay dispersion could be engineered.

Optical parametric amplification (OPA) of arbitrarily polarized light is proposed in a multi-section periodically poled Lithium Niobate (PPLN). External electric field is applied on selected sections to induce the polarization rotation of involved lights, thus the quasi-phase matched optical parametric processes exhibit polarization insensitivity under suitable voltage. In addition to the amplified signal wave, an idler wave with the same polarization is generated simultaneously. As an example, a ~10 times OPA showing polarization independency is simulated. Applications of this technology are also discussed.