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4.4 Dependence of the Output Power on the Input Beam Entry Position
The angular distribution of the fanned radiation was observed to depend on the distance from the exit face that the input beam entered the crystal (see figure 4.1). Consequently the overall beam path through the crystal and the output power of the SLPCM will also depend on the input beam entry position. To investigate this dependence the crystal was mounted on a translation stage that allowed it to be moved perpendicularly to the direction of propagation of the input beam. This arrangem ent allowed the entry position of the beam to be varied without changing the input and resonator beam angles. An input beam angle of 76° and a resonator beam angle of 51° were used throughout this investigation. The input beam was an elliptical gaussian with dimensions 0.8mm x 0.4mm (horizontal diameter x vertical diameter defined at the e '2 intensity points of the beams), at the entry
point to the crystal. These experimental parameters ensured that the cat mirror was prohibited from operating over the entire range of input beam entry positions.
Figure 4.5 shows the observed angular distribution of the fanned radiation for various input beam entry positions. These curves show the shift of the fanned peak towards the c axis, which corresponds to a resonator beam angle of 0°, as the input entry position is moved away from the exit face of the crystal. This observation cannot be explained by the single interaction region model used to analyse the SLPCM in chapter 3. In that model the only interaction that exists is between the input beam and the scattered light. Therefore once the scattered light leaves the region of beam overlap with the input beam, no further amplification via TWM should occur. Consequently the angular distribution of the fanned radiation should remain the same regardless of the entry position of the input beam as long as the region of beam overlap is wholly contained within the crystal. However as shown in figure 4.5 this was not the case, as in all three examples the entire beam overlap region existed inside the crystal, yet each example displays a different angular distribution of fanned radiation. This suggests that the fanned radiation undergoes further TWM after leaving the interaction region formed by it and the input beam.
This dependence of the fanned radiation on the entry position and the curved nature of the beam path through the crystal (see figure 3.5) therefore both suggest that more than one interaction region exist in the crystal. It has been speculated that the beam path through the crystal is comprised of a series of interconnected interaction regions where the output of one region becomes the input for the following region (Wang et al 1989 [79], Eliseev et al 1991 [17], Eliseev et al 1992 [18]). This approach has been used to explain the curved beam path that appears in a form of the double phase conjugate mirror known as a bridge conjugator [18]. However this model can only explain the shape of the path and in its present form cannot be used to give quantitative estimates of the steady state behaviour of phase conjugate mirrors.
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Figure 4.5. The observed angular distribution of the fanned radiation as a function of
resonator beam angle for three different input entry positions; a) x = 4.5mm; b) x = 3.0mm; c) x= 1.5mm.
As previously discussed a change in input beam entry position will cause a variation in the overall path length through the crystal. This change in path length will in turn, produce a change in output power of the SLPCM due to the varying interaction length. Figure 4.6 shows the observed output power as a function of beam path length, for two different input beam angles. Due to the curved beam path through the crystal (figure 3.5) the path length was calculated assuming an elliptical beam path.
As figure 4.6 indicates there appears to be an optimum beam path length that produces the maximum output power. This peak exists because of the combined effect of depletion of the input beam energy and absorption. To understand the effects of these processes first
consider the simpler situation when no absorption exists in the photorefractive material. In this case, when the beam path length is small, the SLPCM output power will be low because the coupling strength, which is a product of coupling strength per unit length and interaction length, is also small. Increasing the path length will produce a corresponding increase in output power due to diffraction of a larger fraction of input beam power into the resonator. Eventually coupling strengths will be reached which are large enough to cause the diffraction of the majority of the input beam power into the resonator. Therefore any further increase in path length can only produce a small increase in the amount of power diffracted. Hence if the photorefractive material has no absorption the output power of the SLPCM will increase asymptotically towards a limiting value as a function of path length. An example of the expected behaviour of the SLPCM output power when there is no absorption is indicated by the dashed line in figure 4.6. However if the effects of the non zero absorption of BaTiC>3 are taken into account, then increasing the path length will increase the absorption losses. Therefore when path lengths are reached which cause depletion of the input beam, any subsequent increase in path length will reduce the output power because of the increased absorption losses.
The solid line in figure 4.6 indicates the theoretically predicted variation in the output power as a function of path length, assuming the whole path length to be the interaction length. This curve clearly shows the same features as those that were observed. Therefore, in order to obtain as large a SLPCM output power as possible, the position that the input beam enters the crystal is chosen as a compromise between the input beam depletion and the absorption loss.
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Figure 4.6. The dots and the triangles indicate the observed normalized output power as a function o f beam path length fo r input beam angles o f 72° (dots) and 75° (triangles). The asterisks indicate predicted behaviour when there is no absorption, while the continuous line indicates the predicted behaviour when absorption is taken into account.