Two-dimensional plane wave visualisation

Monochromatic plane waves have a fixed energy, wavelength, and their wavevector has a fixed length. Yet these solutions to the Helmholtz equation are an absurdity, as they are infinite in extent.
Confining a wavefield to finite region of space requires a range of spatial frequencies. Consider, for example, when a plane wave travelling in the y-direction passes through a slit that lets the wave through only within a range of x-values. Such a truncated wavefield can only be constructed from multiple spatial frequencies along x, but how are we to obtain the various undulations of the wave along x if it has a fixed wavelength?
By changing the direction of the monochromatic plane wave, we can generate a variable spatial frequency along the x-direction. Thus, any wavefield confined in the transverse dimension is composed of plane waves travelling in different directions.

[@chandman492]

I thought the plane wave solution for EM transmission in linear isotropic homogeneous media was a plane wave of constant phase and one of constant amplitude, if this is true why is amplitude varying across the plane wave here? I'm confused