Study On The Propagation Property Of Vortex Light Beams In Left-handed Materials

The left-handed material(LHM) is a novel material and its most impressive property is their negative permittivity and negative permeability. The most difference between NIM and ordinary optical material is the sign of their index. For electromagnetic waves propagating in such materials, the electric field E, magnetic field H and wave vector K form a left-handed triplet of vectors and so such materials are called left-handed materials(LHMs). Nowadays, it is considered that the LHM to be a revolutionary influence on the field of physics, electronics and communication when NIM in the near IR and optical range have also been experimentally demonstrated. In this thesis, we combine the standard theory for laser optics in conventional optical material with the unique properties of LHMs to study the propagation properties of rotating beams in LHMs. The investigation of propagation characteristics of rotating beams in LHMs not only have great scientific value, but also brings the new technologies of optical controlling. The main research results are listed below:Firstly, starting from the representation of plane-wave angular spectrum, we obtain the analytical description for a Laguerre-Gaussian beam propagating in LHMs. Then, we show that the negative refractive index of LHMs gives rise to a negative Gouy-phase shift and ultimately leads to a reversed screw of wavefront. In addition, we will explore how the negative index gives rise to the reversed transverse energy flow.Secondly, we investigate the rotation property of multimode Laguerre–Gauss beam in LHMs which is represent as a superposition of Laguerre-Gaussian beams with same frequency, same magnitude, paraxial propagation. We theoretically study that the negative refractive index of LHMs gives rise to the negative Rayleigh length and negative Gouy-phase shift of multimode Laguerre–Gauss beam. The latter one causes a reversed rotation of transverse intensity pattern. Furthermore, we demonstrate that the negative magnetic permeability of LHMs leads to an inverse spiral of transverse energy flow. In addition, we find that the damping part of LHMs plays an important role in the direction of angular momentum density. The angular momentum density in a lossy LHM can be parallel or antiparallel to the transverse energy flow. However, the angular momentum density of multimode Laguerre–Gauss beam in a lossless LHM is always opposite to the transverse energy flow.Finally, we theoretically study the role of dispersion in propagation of rotating Hermite-Gaussian(RHG) beams in left-handed materials (LHMs). By modeling the rotating beam as a superposition of two rotating Laguerre-Gaussian beams with opposite chirality, same magnitude and different frequencies, we demonstrate that the rotation property of the RHG beam in LHM is significantly dependent on the sign and strength of dispersion: In the normal dispersion region, the direction of transverse energy flow is reversed compared to the vacuum, due to the negative refractive index of LHM, while in the anomalous dispersion region it may be parallel or antiparallel to that in the case of vacuum, depending on the strength of dispersion. In addition, we find that the angular momentum density can be parallel or antiparallel to the transverse energy flow in LHM, while the angular momentum flow is always opposite to the transverse energy flow.