It is not a plane wave because it has a width and diverges or converges.

http://www.nhn.ou.edu/~abe/research/lgbeams/

While plane waves are the most immediate solutions of the wave equation, they do have one major problem, that is, they require infinite energy as they extend transversally without any attenuation. Plane waves can be understood as the limiting case of the fundamental Gaussian mode (l=0,p=1) for diverging beam radius (w_0->\infinity). Mathematically, plane waves and Gaussian beams are both valid solutions of the wave equation. From a physics point of view, however, plane waves do not really exist, even though we are teaching this in class to undergraduate students.