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This allows quasi-phase-matching to exist at different domain widths . From this equation it is apparent, however, that as the quasi-phase match order increases, the efficiency decreases by . For example, for 3rd order quasi-phase matching only a third of the crystal is effectively used for the generation of signal frequency, as a consequence ...
The structure is designed to achieve quasi-phase-matching (QPM) in the material. Periodically poled crystals are frequently used as nonlinear optical materials. They are more efficient at second-harmonic generation than crystals of the same material without periodic structure.
Nonlinear photonic crystals are usually used as quasi-phase-matching materials. They can be one-dimensional, [1] two-dimensional [2] or three-dimensional. [3]
Quasi-phase-matching can be expanded to chirped gratings to get more bandwidth and to shape an SHG pulse like it is done in a dazzler. SHG of a pump and self-phase modulation (emulated by second-order processes) of the signal and an optical parametric amplifier can be integrated monolithically.
This makes it possible to artificially create an electric-field grating with arbitrary period, [7] which satisfies the condition necessary for quasi-phase-matching. Periodic poling is used for efficient frequency-doubling in optical fibers. [8]
The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
Diagram of second-harmonic generation with perfect phase matching =. Diagram of second-harmonic generation with an imperfect phase matching . In this case energy flows forth and back from the pump to the frequency doubled signal, and having a thick crystal can lead to a smaller amount of SHG produced.
The phase fronts (wave vector) do not point in the same direction as the energy flow (Poynting vector) because of walk-off. The phase matching angle makes possible any gain at all (0th order). In a collinear setup, the freedom to choose the center wavelength allows a constant gain up to first order in wavelength.