When plane waves interfere, is the resulting wave also a type of plane wave? An object reflects light from a beam, U_1 (a plane wave). I would like to, as simply as possible, describe the light reflected by the object. Can I describe the reflected light, U_2, as a plane wave?
i.e.
$$U_1=A_1e^{i(kz-\omega t)}$$
$$U_2=A_2e^{i(kz-\omega t)}$$
If so, why is this the case?
 A: A plane wave can be written as an infinite sum over Bessel functions. Each of these terms is a Fourier term in the expansion of the wave. If you have an interference between two plane waves then some of these terms are enhanced and other suppressed. similarly as the question refers to an interaction or reflection with an object. This forms a linear filter that again selects some of those Fourier terms over others. In general the result is not a plane wave, but rather something more complex.
A: The question you're asking seems to be about reflection, not interference. The reflection is not necessarily a plane wave.
If the reflecting object has a curved surface, the wavefronts will be distorted (think of the distorted image you see in a curved mirror). Furthermore, note that the plane-wave expression you wrote down (necessarily) has infinite extent in $x$ and $y$: any finite-sized object would "clip" the incident plane wave, so that the reflection would not be a plane wave.
A: If the object is a flat, polished mirror; and if the illuminating light is a collimated monochromatic beam, then the reflected beam will be a plane wave.  But in reality, every point on a typical object scatters light independently. The reflected light from a typical object can be represented as the coherent superposition of a lot of spherical waves (each centered on a different point on the object's surface), or as the coherent superposition of a lot of plane waves.  And there are lots of other mathematical ways to represent the reflected light.  But for a typical object, none of the representations will amount to a single plane wave.
The second equation you wrote is not useful except for a single plane wave.  Instead, it should represent U2 as the sum of a large number of plane waves, each with their own k and each with their own A.
