Noncritical vectorial phase matchings in nonlinear optics of crystals and infrared up-conversion

The exact analytic expressions for the vectorial group phase matching (PM) conditions have been obtained for sum and difference frequency generation processes ω₃ = ω₁ ± ω₂ (ω₃= ω₂ − ω₁) in nonlinear anisotropy crystals, which ensure a wide-band conversion of signals (ω₂) and images. The tangential PM conditions for all possible interaction types in the negative and positive uniaxial crystals have been studied. Scanning of the frequency of vectorial group PM has been studied by examples of LiNbO₃, LiIO, and HgGa₂S₄ crystals when changing the pump direction or pump frequency ω₁. The possibility of tuning the wide-band operation all over the transparency region of the LiIO₃, crystal has been shown. The double noncriticality conditions of PM in frequency cd; and acceptance angle have been studied and the possibility of their realization in a near and middle infrared region (IR) has been shown. A generalization of consideration to the other types of noncritical PMs (including multiples ones), has been made, including at an angle 90° between the propagation directions of waves with frequencies ω₁ (1) and ω₂ (2). The method of definition of the spectral bandwidths and acceptance angles of critical and noncritical PM taking into account the concordant change in the propagation angles of waves 1 and 2 has been proposed.