Analysis of noncollinear-phase-matching effects in uniaxial crystals*

Exact Solutions for Vector Phase-Matching Conditions in Nonlinear Uniaxial Crystals

“…Indeed, according to (15), the refractive index n i (ω i ; δ i ) is a very elaborated function of θ i , so (18) is strongly transcendental. This fact could motivate more the study of numerical approaches than the search for analytical solutions [11,19,20]. However, we are going to show that the complexity of solving (18) is reduced by transforming it into a fourth-order polynomial equation.…”

“…As the refractive index of extraordinarily polarized light is an elaborated function of the unknowns, and the latter are encapsulated by trigonometric functions, determining the parameters requires solving strongly transcendental equations, a fact that has motivated the study of numerical approximations than the search for analytical solutions [11,19,20].…”

Surface roughness dependence of noncollinear phase matching

“…where 3 is the angle between the crystallographic axis and the k 3 vector, and the geometrical relationships with the position α 3 , ϕ 3 on the screen and the momentum mismatch, are: …”

“…SNCPM is a phenomenon which has been known for a long time, it was observed for the first time by Giordmaine in 1961 [1] and basically described by Bates [2,3] a few years later. At that time, research was intended to explain the geometrical shape of the second harmonic wave; nearly circular hollow cones were observed and described theoretically.…”

“…Normally it is achieved impinging in the crystal with two external light beams inclined on one another to produce a third beam of frequency 2ω. Under particular conditions, if one intense incident beam interacts in the crystal with its own elastic scattered light, that acts as a second wave, the result is a hollow cone of second harmonic light which has been named the spontaneous noncollinear phase matching (SNCPM) effect [1][2][3][4].…”