To achieve this a phase matching condition is required between the propagation constant of the mth mode in the waveguide \ beta _ m and the incident light at an angle \ theta _ m normal from the waveguide surface.
12.
The wavelengths of the signal and the idler are determined by the phase matching condition, which is changed e . g . by temperature or, in bulk optics, by the angle between the incident pump laser ray and the optical axes of the crystal.
13.
Periodic poling uses the largest value of lithium niobate's nonlinear tensor, d 33 = 27 pm / V . Quasi-phase matching gives maximum efficiencies that are 2 / ? ( 64 % ) of the full d 33, about 17 pm / V.
14.
These crystals have the necessary properties of being strongly birefringent ( necessary to obtain phase matching, see below ), having a specific crystal symmetry, being transparent for both the impinging laser light and the frequency-doubled wavelength, and having high damage thresholds, which makes them resistant against the high-intensity laser light.
15.
The spectral intensity can be found via a quadratic equation using the intensity of the dc and ac terms ( filtered independently via a similar method above ) or more commonly from an independent measurement ( typically the intensity of the dc term from the calibration trace ), since this provides the best signal to noise and no distortion from the upconversion process ( e . g . spectral filtering from the phase matching function of a'thick'crystal ).
