This work was supported by the National Natural Science Foundation of China (Grant Nos. It is demonstrated that under certain conditions, the beam at the object Acknowledgement The field distributions in every region in the cascaded system are obtained. Using the developed ABCD law, the propagation properties of paraxial Gaussian beam through cascaded isotropic LHM slab systems are investigated. The transfer matrices for several elementary optical structures about LHM are derived. Now an interesting question naturally arises: How to describe the field distributions with ABCD law in every these LHM slab system? ConclusionsĪ simple ABCD matrix formalism is applied to investigate beams propagation in left-handed material slab systems. n R is the index of RHM, g is the spacing between two LHM slabs, a is the distance from the object plane to the first LHM slab. 2), Here, n L and d are the index and thickness of the LHM slab, respectively. In this section, we apply the ABCD law to investigate the propagation properties in different LHM slab systems (Fig. For light beam traveling in the z direction, the field distribution can be written as E = u ( x, y, z ) exp ( - ikz ), Propagation of Gaussian beams through cascaded LHM slab systems Gaussian beams are similar in many respects to plane waves, however, their intensity distributions are not uniform, but are concentrated near the propagation axis and their phase fronts are slightly curved. In this section, we first derive several transfer matrices for LHM slabs, and using these matrices to investigate the propagation properties of Gaussian beams through single LHM slab. We hope that the obtained ABCD law will be helpful to the investigation on such LHM slab systems. LHM slab systems can also be used as a near-field optical storage system, a high image quality system, a waveguide with contra-propagation of guided mode. Second, we investigate propagation of Gaussian beams through various cascaded LHM slab systems by using the ABCD law. Based on the obtained ABCD law, the propagation properties of Gaussian beams in the single LHM slab will be analyzed. First, the transfer matrices for several elementary optical structures of LHM are derived. In this paper, we will apply a simple ABCD matrix formalism to investigate beam propagation in LHM slab systems. In addition, we know that the transmission and reflection of a ray through a stratified medium are calculated by the characteristic matrix,.
We note that previous treatments on the propagation of light beam in LHMs involve the complicated integral operation, while the well-known ABCD matrix formalism for light beam propagation in ordinary optical systems can avoid the complex situation, and every matrix element has an explicit physical meaning, and is thus a very simple but efficient tool for dealing with the propagation problems. In addition, rotational Doppler effect can induce a transfer of angular momentum of the LHM to orbital angular momentum of the light beam. When light beams propagate through LHMs, there will appear some intriguing or even counterintuitive phenomena, such as the large negative lateral shifts, , negative refraction of electromagnetic energy, beam focusing and phase compensation. The most prominent application of LHM is the concept of perfect lens, which can lead to subwavelength imaging beyond the diffraction limit. In addition to left-handed characteristic and anomalous refraction, LHMs have many other dramatically different phenomena compared with ordinary materials, such as reverse Doppler effect, inverse Cerenkov radiation, and negative radiation pressure. LHMs at optical frequencies are also proven to be possible, ,, ,, ,.
The material with negative index of refraction, also known as left-handed material (LHM), after the first experimental observation of negative refraction at microwave frequency, , has recently received intense attention,.
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