Power Transmittance of a Laterally Shifted Gaussian Beam through a   Circular Aperture
  Gaussian beams are often used in optical systems. The fundamental Gaussian TEM00 mode is the most common of the Gaussian modes present in various optical devices, systems and equipment. Within an optical system, it is common that this Gaussian TEM00 beam passes through a circular aperture of a finite diameter. Such circular apertures include irises, spatial filters, circular Photo-Detectors (PDs) and optical mounts with circular rims. The magnitude of optical power passing through a finite-sized circular aperture is well-documented for cases where the Gaussian beam passes through the center of the clear circular aperture, and is chopped off symmetrically in all radial directions on a given plane. More often than not, a non-axial incident Gaussian Beam is not blocked in a radially uniform manner by a circular aperture. Such situations arise due to a lateral displacement of the beam from tilted glass blocks, manufacturing errors and imperfect surface flatness or parallelness of surfaces. The fraction of optical power of a laterally-shifted Gaussian Beam passing through a circular aperture is calculated in this paper through conventional integration techniques. 
Tariq Shamim Khwaja and Syed Azer Reza
physics.gen-ph