1.2 PLANE ELECTROMAGNETIC WAVES

Notice that in all the examples so far, we have only considered waves in the form of planes, that is, the field components of the wave are assumed to be traveling in the z direction and to have no x and y dependence. If one tries to visualize such a wave, it would look like a uniform plane of electric and magnetic fields on the x-y plane moving in the z direction, and hence such waves are called uniform plane waves. It could be easily inferred that the source of a plane wave is supposed to be uniform over an infinite plane in order to generate uniform fields over a plane parallel to the source plane. As a result, there is no actual uniform plane wave in nature. However, if one observes an incoming wave far away from a finite extent source, the constant phase surface of the fields (wavefront) becomes almost spherical. Hence, the wave looks like a uniform plane wave over a small area of a gigantic sphere of wavefront, where the observer is actually located. Perhaps it is more important for advanced studies of electromagnetic (EM) waves that an arbitrary field or wave can always be expressed in terms of plane waves, known as the plane wave spectrum representation of electromagnetic waves. Therefore, they are the building blocks of more complex waves. As a result, since plane waves play very important roles in the fields of microwaves, antenna,...