Optics, resonators and beams

Abstract

If a certain area A of arbitrary curvature and shape is illuminated with linearly polarised light with electric field strength E, all points emit spherical waves according to Huygen’s law. The electric field strength generated at a point P distant from the illuminated area results from the superposition of all these spherical waves. If an infinitely small area dA is considered, and the electric field strength in this area is approximately constant and equal to E, the contribution to the field at P is proportional to E.dA, since the electric field strength determines the light emitted per unit area. This contribution reduces with increasing distance ρ from the emitting surface element dA, due to conservation of energy, as the wave energy distributed across the spherical wave front remains constant, while the radius increases during propagation. The field strength at point P is reduced by a factor 1/ρ since the light intensity is given by the square of the electric field strength. There is also a phase difference between the waves arriving at P, and those at the origin dA, given by ikρ, due to the propagation time between dA and P according to equation (2.1). Finally, the electric field strength generated at P due to the emission of the area element dA also depends on the angle φ between the beam from dA to P, and the area element dA. The maximum contribution is obtained when the beam is perpendicular to the area element. An angle φ greater than zero between the vector normal to dA and the direction between dA and P, reduces the area which is seen from the point P.