Complex variable function Gaussian beam in strongly nonlocal nonlinear media

We introduce a novel class of spatial complex variable function Gaussian (CVF-Gaussian) beam, which is the product of an arbitrary analytic complex variable function and a Gaussian function, in strongly nonlocal nonlinear media (SNNM). The CVF-Gaussian beam rotates generally during propagation. By choosing the input power of the beam, we can obtain the CVF-Gaussian breather or the CVF-Gaussian soliton. We reveal that stable CVF-Gaussian beam can exist in SNNM with different forms, including rotating dipole, and rotating elliptic donut. A distribution factor which is the parameter for the description of the transverse distribution of the CVF-Gaussian beam is discussed.