I think you have slightly misreported your problem. Anyways have a look at the attached file. Hope it helps!

Dear Mohamed Saih,

I agree with Yuriy Pilgun and Vikash Pandey when they say  "it is not clear what you mean by "plane wave of multiple direction". Yuriy Pilgun also clears some important aspects of the plan waves. 

However, it is significant to add the following two points:

1)  it should be clarified if the Questioner meant nonuniform plan wave, which propagates in a given direction and attenuates in another direction (in these cases, the propagation vector of the wave is complex);

2) the plan waves are also important because in far zone, the field irradiated by an antenna can be locally treated as a plan wave (far field in Fraunhofer zone). In other words, the spherical wavefront can be locally approximated to a plan wave.

Best Regards

Angelo Gifuni

Both conceptions: "plane wave" and "plane-wave expansion" (that imply plane waves of multiple directions) can be found in Sommerfeld integral representation for the wedge diffraction problem.

Dear Mohamed Saih,

                                         I guess you could also consider a moment generating function of multiple dimensions which if exponential can have Fourier Transform features as suggested by Prof.Pilgun and then you will have the statistical properties of the position of the particle with various particle with various probabilities along various dimensiona which you can test experimentally. SKM PhD QC FEPS(D)