Two-Dimensional Self-Similar Rotating Azimuthons in Strongly Nonlocal Nonlinear Media

We derive analytical 2D self-similar rotating azimuthons of a strongly nonlocal nonlinear media with a space-dependent diffraction coefficient, a gain (attenuation) coefficient based on the similarity transformation, and a variational approach. Remarkably, these self-similar azimuthons have the azimuthal angle modulated by the distributed diffraction coefficient, apart from the beam width and intensity changing self-similarly.