The theoretical model of electromagnetic transmission through solitary sub-wavelength nanoapertures is considered. The model is based on a rigorous solution of the plane wave diffraction problem by a slot in the perfectly conducting screen of a finite thickness. The local energy of the electric field inside the plane dielectrics arranged behind the screen is used for calculations. The results demonstrate the principal features of the phenomenon that confirms that the diffraction theory can be applied successfully without the concept of surface plasmons.