“…In equations (11) and (12) we use the following designations: 11 , 22 , 33 , 12 , 13 , 21 , 23 , 13 and 32 are the overlap integrals between the corresponding waves ( iv for each pair of i th and v th modes), while we assume that = 0,1 , where 0,i , are determined for the corresponding frequencies ωi and unperturbed values n0,i at these frequencies. The factor exp( ) j in (11) is determined by the difference of the topological charges (an integer) ℓi of the vortex beams for each of the waves and represents the projection of the orbital angular momentum (OAM) on the direction of propagation [1][2][3][4]; it is determined by the dependence of the electromagnetic field of the vortex beam on the azimuthal angle φ. If the waves have no OAM, then the specified multiplier is not taken into account, i.e.…”