Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial

Abstract

Kerr-type left-handed metamaterial (LHM) slab is proved to have an effect of focusing paraxial Gaussian beams and changing their waist radius, as conventional lens can do. The expressions for the focusing distance and the spot radius at the focal point are derived by the variational approach. We show that the incident Gaussian beams can be compressed or expanded by a single Kerr LHM slab, according to the sign of the Kerr nonlinearity and the divergence of the incident beam. Especially, it is demonstrated the focusing properties are significantly tuned by the slab thickness, the beam power and the divergence of the incident Gaussian beam.

Control of nonlinear self-action of high-power Gaussian beams: using a nonlinear left-handed material slab

“…Note that the output beam of the nonlinear LHM slab is at first convergent and then divergent behind its waist in R3 [28] and the spot size at the incident surface of the CKM is related to both L 2 and L 3 . For the above case (i), L 3 is small, therefore, firstly, when L 2 is also small, the beam waist in R3 locates not far before Z 0,4 , and thus the increase of L 2 leads to smaller w 3 (Z 0,4 ) and the effect of the nonlinear interplay is enhanced in the nonlinear LHM slab; secondly, as L 2 increases further, the waist in R3 locates far behind Z 0,4 and thus w 3 (Z 0,4 ) increases with L 2 .…”

“…As L 2 increases, the beam waist in R3 becomes smaller and moves toward Z 0,4 , and thus L sf decreases. From another aspect, however, if the beam power is much higher than P c,4 , the change of L 2 can lead to the fluctuation of w 0,3 and thus indirectly lead to fluctuations of w 3 (Z 0,4 ) and L sf [28]. So there is a hump in the curve L sf (L 2 ).…”

“…For nonlinear LHMs which have the third-order nonlinear electric response, the anomalous interplay between diffraction and nonlinear effects [24] leads to the requirement of an effective negative third-order nonlinearity for the formation of transverse solitary waves in LHMs [25], the unique modulation instability [26,27] and the anomalous effect of the focusing property of the incident Gaussian beam on its self-focusing in nonlinear LHMs [12]. Nonlinear LHM slabs especially, have a special ability in modifying the spatial properties of high-power light beams [28]. However, it should be pointed out that nonlinear optics in LHMs remain so far a less developed branch.…”

Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs

“…In 2001, by using composite materials, the material with the negative permittivity and the negative permeability in microwave was first successfully produced by Smith [23,24] . Recently, the research about LHMs has received much attention [25][26][27] . On the other hand, in the optical fiber communication field, a chirp can be defined as a phenomenon where the signal frequency changes over time, and the frequency spectrum is widened before and after the pulse due to modulation.…”

Transverse power flow reversing of guided waves in extreme nonlinear metamaterials

“…In the nonlinear realm, the nonlinear properties of lefthanded metamaterials have been investigated [8] together with various soliton manifestations [9,10,11]. Propagation in metamaterials exhibiting cubic nonlinear response has also been considered [12,13] and, for ultra-short pulse nonlinear dynamics, it has been suggested that metamaterial linear property tailoring allows the observation of different nonlinear regimes [14].In this Letter we show that a metamaterial with a very small linear dielectric constant and exhibiting a nonlinear cubic response is able to support nonlinear guided waves whose Poynting vector has the very peculiar property of being parallel and anti-parallel to the propagation direction in different transverse portion of the field. This novel phenomenology is a consequence of the fact that, since the metamaterial linear dielectric permittivity can be arbitrary small, the nonlinear contribution to the dielectric response can easily (i.e.…”