Properties of Laser Beams



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
$$\begin{array}{rcl} E(\mathbf{r},t) = A(\mathbf{r},t)\exp j\left [<\omega >t - \phi (\mathbf{r},t)\right ]& &\end{array}$$
where A(r, t) and ϕ(r, t) are both slowly varying over an optical period, i.e.,
$$\begin{array}{rcl} \left [\left \vert \frac{\partial \,A} {A\partial \,t}\right \vert ,\;\left \vert \frac{\partial \,\phi } {\partial \,t} \right \vert \right ]\, \ll \langle \omega \rangle & &\end{array}$$
We then define the intensity of the beam as
$$\begin{array}{rcl} I(\mathbf{r},t) = E(\mathbf{r},t){E}^{{_\ast}}(\mathbf{r},t) =\vert A{(\mathrm{\mathbf{r}},t)\vert }^{2}& &\end{array}$$


Gaussian Beam Spatial Coherence Beam Divergence Temporal Coherence Speckle Noise 
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  1. 1.
    M. Born and E. Wolf, Principles of Optics, 6th edn. (Pergamon Press, Oxford, 1980), pp. 491–544.CrossRefGoogle Scholar
  2. 2.
    W. H. Louisell, Radiation and Noise in Quantum Electronics (McGraw-Hill, New York, 1964), pp. 47–53.Google Scholar
  3. 3.
    A. Jeffrey, Handbook of Mathematical Formulas and Integrals (Academic, San Diego 1995) p. 244.Google Scholar
  4. 4.
    Reference [1], pp. 508–518.Google Scholar
  5. 5.
    J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).Google Scholar
  6. 6.
    Reference [1], pp. 395–398.Google Scholar
  7. 7.
    A. E. Siegman, Defining and Measuring Laser Beam Quality, in Solid-State Lasers-New Developments and Applications, ed. by M. Inguscio and R. Wallenstein (Plenum, New York, 1993) pp. 13–28.Google Scholar
  8. 8.
    Reference [4], Chapter 5.Google Scholar
  9. 9.
    Laser Speckle and Related Phenomena, ed. by J. C. Dainty (Springer-Verlag, Berlin 1975).Google Scholar
  10. 10.
    M. Françon, Laser Speckle and Applications in Optics (Academic, New York, 1979).Google Scholar
  11. 11.
    R. J. Glauber, Optical Coherence and Photon Statistics, in Quantum Optics and Electronics, ed. by C. De Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), pp. 71, 94–98, 103, 151–155.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipto. FisicaPolitecnico di MilanoMilanoItaly

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