Photorefractive Beam Fanning Optical Limiter
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Mat. Res. Soc. Symp. Proc. Vol. 479 01997 Materials Research Society
necessarily mimic that of the intensity distribution) and only its time for formation is dependent on beam intensity. For short pulsed lasers the important parameter to limit is the optical fluence, F = Energy/Area, since that is what determines damage to detectors and the eye. These differences in how the nonlinear effect performs allows for a distinct advantage by using the photorefractive limiter. Limiters based on this effect should be able to selectively deplete an intense coherent optical beam and yet allow the weak white light images associated with the scene to pass through. This feature has motivated much of the research toward implementing these type of devices.
PHOTOREFRACTIVE EFFECT The term "photorefractive effect" is used to describe a special kind of optically induced refractive index change which can occur in ferroelectric crystals and other electro-optic materials. The microscopic details of the photorefractive mechanism are normally described using a band
transport model, which assumes the existence of a pool of charges residing in low-lying traps. When two coherent beams are interfered in the medium, photo-excitation of the low-lying trapped charges (either electrons or holes) occurs at the maxima of the spatially varying intensity pattern. The photo-excited charges migrate by diffusion out of the illuminated regions and are eventually retrapped in the dark regions of the crystal This results in a periodic charge distribution which is balanced by a strong space-charge field according to Poisson's equation. This strong electrostatic field (-10' V/cm) then produces a change in the refractive indices (An = 0.001) through the electro-optic effect. As mentioned earlier, the unique thing about this index grating is that it is phase-shifted (i.e., non-local) with respect to the incident intensity pattern. The phase shift between the incident intensity pattern and the index grating causes the two interfering or "writing" beams to couple and transfer energy from one beam into the other as they propagate through the crystal. The direction of the steady-state energy transfer relative to the crystalline c-axis is determined by the signs of the electro-optic coefficients and charge carriers. The energy transfer is maximized for a ir/2 phase shift between the index grating and the light fringes. Under these conditions, exponential gains of 50 cm' are typically achieved in many photorefractive crystals. As a result, substantial weak beam amplification (thousands fold) has been realized. For example, Feinberg et al. demonstrated that one beam can deplete nearly all of the power of the other beam after propagating through only a few millimeters of a barium titanate (BaTiO3) crystal. This feature has been used to demonstrate effective optical limiting.' BEAM FANNING Beam fanning occurs when the incident laser beam passes through the photorefractive crystal and light is scattered by crystal imperfections in all directions. The scattered l
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