A plane wave ( y = A * sin (omega * t-k * x) is an idealization because the mathematical description is particularly simple, simplifying many calculations. But it is unphysical, because a plane wave transports infinite energy.

I think I got the answer!

http://www.rodenburg.org/theory/y500.html

 @ Suhash

This will clarify your doubts. See attached pictures.

Plane waves: When planes of constant phase and constant amplitude are parallel to each other. That would then correspond to a lossless energy propagation.

See, in Fig 1: Plot of sin(x), a plane wave. Let blue donate points of constant magnitude (picked maximum in this case). Pink denotes points of constant phase (picked minimum in this case). Join the points to form a line.

The line in 2D (or, planes in 3D representation) AB and CD are then parallel to each other.

Fig 2: Plot of exp(-0.1*x) * sin(x), an attenuating wave. In this case AB is NOT parallel to CD. Not a plane wave.

The rigorous and simplest definition of a plane wave is the following: It is a wave that depends on a single Cartesian spatial coordinate only, in addition to time dependence. The word "Cartesian" is important because it means using a rectangular (Cartesian) system of coordinates in the above definition. If this single spatial coordinate is, for example, a distance "r" in a spherical system of coordinates, this will be not a plane wave, but a symmetrical spherical wave. 

One good definition: “A plane wave is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector”

Agree with Prof. Victor V. Krylov answer, F(x,t) = F(x.n - ct) = F(x - ct) with n = (i,j,k) is a plane wave, but F(r,t) = 1 /r . F(r.n - ct) is not since in the latter case the source is needed. In addition, plane waves are infinite parallel planes normal to the phase velocity vector.