Optical implementation of propagation-invariant pulsed free ... - Tartu

along the planesk z = γk − 2βγ (3.19)(3.5) ork z (k) =γk − ξ (γ ± 1) (3.20)(3.8). It can be seen that the possible supports of the angular spectrums of plane wavescan be divided into four explicit special cases (see Fig. 3.2) that can be taken as the naturalclassification of the FWM’s:1. β =0(ξ =0), γ ≤ 1, the support is a cone in k-space, typical examples are Bessel-Xpulse and X-pulse (the case γ =1corresponds to plane wave pulse);2. β 6= 0(ξ 6= 0), γ =1, the support is a paraboloid in k-space, typical example isFWM’s, propagating at velocity of light;3. β 6= 0(ξ 6= 0), γ>1, the support is an ellipsoid in k-space, the group velocity of theFWM’s satisfies v g