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# Properties of Laser Beams

Chapter

## Abstract

In Chap. 1 it was stated that the most characteristic properties of laser beams are (1) monochromaticity, (2) coherence (spatial and temporal), (3) directionality, (4) brightness. The material presented in earlier chapters allows us to now examine these properties in more detail and compare them with the properties of conventional light sources (thermal sources).

In most cases of interest to us, the spectral bandwidth of the light source Δω is much smaller than the mean frequency < ω > of the spectrum (quasi-monochromatic wave). In this case, the electric field of the wave, at position r and time t, can be written as
$$\begin{array}{rcl} E(\mathbf{r},t) = A(\mathbf{r},t)\exp j\left [<\omega >t - \phi (\mathbf{r},t)\right ]& &\end{array}$$
(11.1.1)
where A(r, t) and ϕ(r, t) are both slowly varying over an optical period, i.e.,
$$\begin{array}{rcl} \left [\left \vert \frac{\partial \,A} {A\partial \,t}\right \vert ,\;\left \vert \frac{\partial \,\phi } {\partial \,t} \right \vert \right ]\, \ll \langle \omega \rangle & &\end{array}$$
(11.1.2)
We then define the intensity of the beam as
$$\begin{array}{rcl} I(\mathbf{r},t) = E(\mathbf{r},t){E}^{{_\ast}}(\mathbf{r},t) =\vert A{(\mathrm{\mathbf{r}},t)\vert }^{2}& &\end{array}$$
(11.1.3)

## Keywords

Gaussian Beam Spatial Coherence Beam Divergence Temporal Coherence Speckle Noise
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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## Copyright information

© Springer Science+Business Media, LLC 2010

## Authors and Affiliations

1. 1.Dipto. FisicaPolitecnico di MilanoMilanoItaly