Handbook of the Eurolaser Academy pp 51-84 | Cite as

# 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.

## Keywords

Electric Field Strength Gaussian Beam Beam Waist Plane Mirror Beam Radius## Preview

Unable to display preview. Download preview PDF.

## References

- Kogelnik, H. (1965)
*Imaging of Optical Modes–Resonators with Internal Lenses*, Bell Syst. Tech.,**Vol. 44**, No. 3, pp. 455–494Google Scholar - Hodgson, N. and Weber, H. (1992)
*Optische Resonatoren*,Springer.Google Scholar