Optical Limiting with Lithium Niobate
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candidates for cw visible lasers. They have already demonstrated the potential to provide a high degree of optical limiting for a variety of lasers3 . The photorefractive effect As the name suggests, photorefractives are materials that change their refractive index when exposed to light. More accurately, they respond to gradients in light intensities, such as occur when two overlapping laser beams interfere. The photorefractive effect is usually described by a band transport model which assumes that the material has a pool of charges that are located in shallow traps. Light falling onto the material excites these charges into the conduction band, where they are free to diffuse away from the light source. In a uniformly illuminated area, the charges would randomly re-distribute themselves, but would be unable to settle back into traps because of the constant re-excitation by the light. However, if charges diffuse into dark areas of the crystal, they can settle back into vacant trap sites. When two laser beams interfere, charges excited from the bright fringes diffuse into the dark fringes. This produces a periodic charge distribution throughout the illuminated region, which in turn produces a periodic electric space-charge field. This field locally changes the refractive index of the material through the linear Pockel's effect. The resulting refractive index grating is phase shifted (ideally by 90 degrees) with respect to the light interference pattern, and it is this phase shift which allows light from one beam to be coupled into another'. When two laser beams couple together in this way, one beam increases in power while the other is attenuated. This is the key for using photorefractives as optical limiters. In most photorefractive materials, the magnitude of the nonlinear effect is independent of the laser intensity. This is an unusual characteristic, not normally encountered in nonlinear optics. The 263 Mat. Res. Soc. Symp. Proc. Vol. 597 ©2000 Materials Research Society
explanation is linked to the charge excitation process. The number of charges available for excitation within the material volume is limited. Once all of the charges have been excited out of their trap sites, no further build-up of the space charge field is possible. This places a limit on the maximum obtainable refractive index change, and therefore on the degree of beam coupling for a given grating spacing and crystal path length. Increasing the laser intensity usually affects only the speed of the coupling process. GRATING SPACING The generated grating spacing depends on both the laser wavelength and on the intersection angle between the two beams. The grating spacing is usually 6 chosen to maximise the photorefractive response. The magnitude of the diffusion field, ED, is given by E
=2(1) eA
where kb is Boltzmann's constant, T is the absolute temperature, e is the electron charge and A is the grating spacing. It would therefore seem logical to use the finest possible grating spacing, i.e. counterpropagating beams, since this would maximi
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