Non-linear Optics

  • J. N. Hodgson


We have assumed in previous chapters that the electric current density and polarization in a medium are linear functions of the electric field of an electromagnetic wave. The linear optical properties are defined in terms of these functions. The justification for the linear theory is that the applied field is much less than the atomic fields which act on an electron in a solid. An electromagnetic wave can therefore be treated as a small perturbation for which linear theory is an accurate approximation. We can estimate the order of magnitude of the atomic field acting on a valence electron in a solid as (e/a 2) e.s.u. where a is a typical interatomic distance. Assuming a = 3 Å, this gives a field of about 108 volt cm-1. The field produced by an incoherent light source is such a small fraction of this atomic field that any non-linear response by the medium is un- observably small. With the advent of the laser, however, the experimental possibilities have been transformed. It is possible to have fields of about 106 volt cm-1 in the focussed beam of a high-power laser. This is still only a small fraction of an atomic field, so the non-linearities are unlikely to be large. However, a small nonlinear response by a single atom or lattice cell can lead to large effects when many atoms or cells act coherently.


Harmonic Generation Lithium Niobate Gallium Arsenide Harmonic Wave Pump Wave 
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  1. N. Bloembergen, ‘Nonlinear Optics’ (Benjamin, New York, 1965 ).Google Scholar
  2. R. W. Minck, R. W. Terhune, and C. C. Wang, Nonlinear optics, Proc. IEEE, 54, 1357–74 (1966).CrossRefGoogle Scholar
  3. A. F. Gibson, Nonlinear optics, Science Progress, 56, 479–97 (1968).Google Scholar

Copyright information

© J. N. Hodgson 1970

Authors and Affiliations

  • J. N. Hodgson
    • 1
  1. 1.University of KeeleUK

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