We experimentally demonstrate spatial light modulation based on graded-index plasma channels induced by femtosecond pulses. The spatial profile of the probe beam can be conveniently controlled by adjusting the intensity distribution of the pump beam or by changing the relative position between pump beam and probe beam. We also show that the modulation depth of the probe beam can be controlled by adjusting the power of the pump beam.
It is well known that hot images of small-scale scatterers can be formed. For phase-typed scatterers, hot image and second-order hot-image can be formed. However, when the number of scatterer is larger than one, the interaction between the scatterered waves will lead to new nonlinear propagation results. In this paper, the propagation of flat-topped intense laser beam through Kerr medium slab is investigated, with the incident beam modulated by two parallel wirelike phase-typed scatterers. We demonstrate that an intense fringe together with hot image and second-order hot image can be formed when the distance of the two scatterers is several millimeters. It is found that the on-axis position of the plane of this intense fringe is in the middle part between the exit surface of the Kerr medium slab and the secondorder hot image plane. This intense fringe shows the following basic properties: Firstly, its intensity is apparently higher than that of corresponding second-order hot image and can be comparable with that of corresponding hot image; Secondly, the distances between it and the in-beam positions of the scatterers are identical. The intensity profile shows that this intense fringe is the only prominent bright fringe in the corresponding plane, and thus it is not a nonlinear image of any scatterer. Besides, the influences of the properties of scatterer on the intensity of the fringe are discussed.
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 phase-typed wirelike scatterers through computer simulation. It is
found that, under certain conditions, there is no intense second-order hot image fringe in the predicated plane
half-distance from the medium to the scatterer, but there are other two intense fringes whose in-beam positions are
some distance deviated from those of the scatterers. These intense fringes are called second-order-hot-image-like
fringes in this paper. When compared with the corresponding single scatterer case, the intensity level of the fringes
is close to that of second-order hot image fringe. Besides, there are also hot images, but their intensities are much
lower. The influence of the phase modulation depth of the scatterers on the propagation for both double and single
scatterer cases is also investigated. First, as the phase modulation depth increases, the fringe intensity changes same
as second-order hot image fringe does and their intensities keep very close to each other. Second, the fringe
intensity increases at first and then decreases in a certain value range of phase modulation depth, but the hot image
intensity changes inversely. Third, in the Kerr medium, the maximum intensity of the beam in the double scatterer
case is higher than that in the single scatterer case except for the phase modulation value section around three rad.
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.
Based on the angular spectrum theory of light propagation and the mean-field approximation, an expression for intensity
of hot image of the intense laser beam through a thick Kerr medium with gain and loss is obtained, beyond the
thin-medium approximation. Thereby the dependence of intensity of hot image on the thickness and gain/loss of medium
and the property of obscuration are identified analytically and numerically. It is shown that, for a given obscuration, the
intensity of hot image decreases as the medium thickness increases for definite B integral and increases monotonously
with the medium thickness for definite input power of laser beam. For definite output power of laser beam and gain/loss
of medium, the intensity of hot image firstly increases and subsequently decreases as the medium thickness increases.
Furthermore, it is shown that hot image from obscuration of phase modulation is more intense than that from obscuration
of pure amplitude modulation, even in the presence of medium gain and loss. As the size of obscuration increases, the
intensity of hot image first increases gradually, after reaching a maximum value, it decreases rapidly to a minimum
value.
The phenomenon of hot image in high power lasers is closely related to the spatial uniformity of laser beams and the
running safety of laser systems. Here we study the formation of the second-order hot image of phase defect in the
high-power broadband laser system, special attention is payed to the role of bandwidth of incident beam in the formation
of the second-order hot image. It is shown that, as the laser bandwidth increases by either increasing the positive
temporal chirp or reducing the pulse duration the intensity of the second-order hot image decreases. However, as the
amount of negative chirp increases, the intensity of the second-order hot image increases first but decreases after
reaching a maximum value. The distance between the second-order hot image and the nonlinear medium is found to be
about half that between the phase defect and the nonlinear medium. The influence of phase shift caused by the phase
defect and nonlinear effect on the formation of the second-order hot image is also numerically studied.
Propagation of optical beam in optical lattices is studied. The conditions for spatial solitons formation are obtained by
using variational approach. A proposal for loss compensation for maintaining the spatial soliton propagation in loss
medium by varying the longitudinal depth of the optical lattice is demonstrated both analytically and numerically.
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