Based on the optical path model for nonlinear imaging, we systematically investigated the propagation of flat-topped
Gaussian beam which is modulated by two parallel gain-typed wirelike scatterers through computer simulation. It is
found that hot image for each scatterer can be formed, with the hot image plane several centimeters behind the predicted conjugated plane obtained by the approximate theory for attenuation-typed scatterers. It is found that the object distance, i.e. the distance from the scatterer plane to the incident surface of the Kerr medium slab, has an important influence on the propagation properties and results in a new phenomenon. Under certain object distances, the evolution of the maximum intensity of the beam has one prominent peak before that for hot image, where the on-axis location is dozens of centimeters ahead of the hot image plane. As the size of the scatterers increases, the value of this peak increases at first and then decreases. As the object distance increases, the value of this peak decreases. The intensity distribution corresponding to this peak shows that, there is an intense fringe, which is the most intense fringe in the plane, at the middle point of the line connecting the two scatterers, indicating that it is a unique result of the interaction of the two scatterers. Besides, the influences of the object distance and the scatterer size on hot image intensity are discussed.
The nonlinear imaging effect for small-scale defects with gain defect, which may be caused by the uneven gain in gain
media, is investigated through numerically solving the propagation model with the standard split-step fast-Fouriertransform
algorithm. Two cases, i.e. defects only causing gain and defects causing both gain and phase modulation, are
considered. It is proved that nonlinear images can also be formed. However, when compared to the nonlinear imaging
effect for defects causing attenuation, it is found that: firstly, the intensity at the point corresponding to the center of the
scatterer experiences an obvious decreasing just before the nonlinear image is formed, contrary to the case the defect
causing attenuation; secondly, this decreasing is enhanced as the gain caused by the defect increases; thirdly, there is a
distance several centimeters, even more than ten centimeters, between the nonlinear images for gain defects and those for
attenuation defects. For defects which cause both gain and phase modulation, above differences are ignorable, but the
nonlinear imaging effect has some new properties: firstly, the beam peak intensity on the exit surface of the nonlinear
medium is higher than that in the case the defect only causing phase modulation; secondly, the second-order nonlinear
image is increased obviously, but the effect of the defect's gain on the image's peak intensity is limited. Besides, the
effect of the distance between the defect and the nonlinear medium and that of the power of incident beam are discussed.
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