RESONATOR BEAM ANGLE (degrees)
4.5 Dependence of the Output Power on the Input Beam Size and Shape
One consequence of the dependence of the output power of the SLPCM on the beam path through the crystal, is the sensitivity of the output power to factors that affect the beam path. As discussed previously, the beam path depends on beam angles and entry positions. However it also depends on the sizes (Feinberg 1982 [22]) and shapes of the beams that are used in the FWM interaction.
To investigate the dependence of the SLPCM output power on beam size a 150 mm focal length biconvex lens was mounted on a translation stage that allowed the lens to be moved parallel to the direction of propagation of the gaussian input beam. The radius of the beam (defined to be half the distance between the e '2 intensity points of the beam) that enters the crystal was then varied by changing the separation of the BaTiC>3 crystal and
the lens. All other param eters such as beam angles and entry positions were kept constant.
Figure 4.7 shows the observed SLPCM output as a function of the radius of the input beam for two different input angles. Both curves show that as the beam radius is reduced that the output power increases slightly, until a radius is reached where the SLPCM shuts down. This turn off occurs because of the start up of the cat mirror and the subsequent competitive effects that are introduced.
The trend of increasing output power as the beam radius is reduced is not predicted by the single interaction, one dimensional model discussed in section 3.3. In fact this model predicts the opposite, that is, the output power should increase as the beam radius increases because the interaction length and, therefore, coupling strength both become larger. It appears then that the observed behaviour is a result of three dimensional effects (Tikhonchuk et al 1991 [75]). The appearance of three dimensional effects is not entirely unexpected because of the obvious three dimensional nature of beam fanning and as a result of the assumptions of the one dimensional model not being satisfied by our system. Specifically the beams used in our system are smaller, in transverse extent, than the width of the photorefractive material and gaussian beams are used rather than beams of uniform intensity profile.
Three dimensional effects have been observed previously by other researchers where the behaviour of a mutually pumped phase conjugate mirror, which is a type of DPCM, was found to depend on the ratio of the sizes of the pump beams (Mameav et al 1991 [61]).
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BEAM RADIUS (mm)
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Figure 4.7. The observed normalized output power as a function o f input beam size.
The dots indicate the behaviour when the input beam angle was 72°, while the squares indicate the behaviour for an input angle of 75°.
The behaviour observed in that system was predicted by a three dimensional model that applies in the undepleted pump approximation [16, 61, 75]. This approximation assumes that the beams that supply the energy to be transferred in the two or four wave mixing interaction, lose a negligible fraction of their initial power through the interaction. Clearly the undepleted pump approximation does not apply in the case discussed in this thesis, because of the large fraction of input energy that is diffracted into the resonator. As a consequence the three dimensional model that is given in references [16, 61, 75] cannot be used to analyse the SLPCM. Furthermore in order to do so, this model must also incorporate a description of the complicated phenomena of beam fanning. At the time of writing no such three dimensional description was known to us. However such a description would probably not provide significant information about the physics of our
SLPCM, that is not already provided by the one dimensional model. This is because the one dimensional model has been successfully used to predict the wide range of dynamic and steady state behaviour that was observed for the SLPCM. Evidence of the good agreement between the observed and predicted behaviour is provided throughout this thesis. Therefore any three dimensional effects appear to act as small perturbations to the one dimensional model for the particular SLPCM application discussed in this thesis.
Since the size of the input beam used in the SLPCM caused three dimensional effects that vary the output power of the SLPCM, then it follows that the shape of the input beam will also affect the output power. In order to investigate the dependence of the SLPCM output power on input beam shape two 100mm focal length cylindrical lenses were mounted on translation stages so that the axes of the lenses were orthogonal to one another. Both translation stages were arranged so that the lenses were able to move parallel to the direction of propagation of the input beam. This then allowed the shape of the beam to be varied from circular to elliptical without changing beam angles and beam entry positions to the crystal.
Figure 4.8 shows the typically observed output power of the SLPCM as a function of the ratio of the horizontal waist size to the vertical waist size. The triangular data points show the effect of varying the vertical size of the beam while keeping the horizontal dimension fixed, while the circular data points show the effect of varying the horizontal size of the beam while keeping the vertical size fixed. These curves show that as the input beam is made more elliptical, with the horizontal axis the major axis of the ellipse, that the output power increases. Qualitatively this occurs because as the beam is made more elliptical a large beam overlap in the horizontal plane and, therefore, a large interaction length are maintained while the beam becomes more intense. In order to examine this behaviour quantitatively a three dimensional approach will be needed.
In summary, it is possible to increase the output power of the SLPCM by varying the size and shape of the input beam. The output power of the SLPCM increases as the beam size is reduced until a critical beam size is reached where any further reduction results in a dramatic reduction in output power. If the beam is made more elliptical, with the major axis of the ellipse horizontal, the output power increases. Qualitatively this occurs because of the larger coupling strengths that can be achieved with elliptical beams without a reduction in beam intensities. In order to explain the effect of size and shape of the input beam on the SLPCM output power quantitatively a three dimensional model of the interaction will be required.
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