Induced Focusing of Optical Wave From Cross-Phase Modulation in Nonlinear Metamaterials

Abstract

In this paper, we investigate the novel behavior of induced focusing in nonlinear metamaterials (MMs) through designing probe-pump configuration, where the coupled waves may simultaneously experience negative refractive index or positive refractive index, or one experiences positive refractive index and another experiences negative refractive index both analytically and numerically. It is shown that cross-phase modulation (XPM) in MM not only brings some new features to the behavior of induced focusing, but also makes it possible in the ordinary positive-index materials (OMs), where it is otherwise impossible. First, we reveal that weak probe beam can be focused by strong pump beam even when their centers are completely overlapping each other. Moreover, it is found that the separated distance between coupled waves has an optimal value, which results in the strongest focusing of probe beam. Finally, another most notable property is that a spatial induced focusing is found to occur for different combinations of the signs of refractive index decided by the probe and pump beams, respectively, implying that a spatial XPM in MMs can be used as a more powerful tool for controlling the inducing focusing, when compared with the corresponding case in OMs. Our findings demonstrate that MMs can provide us unique opportunities unattainable in OMs to manipulate the all-optical control of optical focusing behavior through the new physical mechanism of XPM.

Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials

“…Therefore, in our pioneer work, we have reported that transverse-XPM MI can develop for different combinations of the signs of refractive index decided by the two waves, respectively, which makes the temporal MI in optical fibers find the corresponding transverse case in MMs [31]. Meanwhile, we also disclose the new temporal MI properties induced by XPM in MM and identify the influence of group-velocity mismatch(GVM) on MI [32].Very recently, we further investigate the novel behavior of induced focusing in nonlinear MMs through designing probe-pump configuration both analytically and numerically [30]. In addition, Chen et al report that there exists single-and multi-peak soliton pairs from XPM in two-component models of MMs and photonic crystals [33].…”

“…Very recently, advances in the fabrication of MMs, ranging from microwave to optical frequency and from linear to nonlinear effect, have further stimulated a great deal of research including the revaluation and characterization of the classical nonlinear optical processes [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Accordingly, the wide study of self-focusing phenomena in Kerr nonlinear NIM has recently become a new and exciting field of research that has been the subject of intense investigations [25][26][27][28][29][30][31]. Several intriguing and counterintuitive nonlinear phenomena associated with optical collapse, optical solitons as well as modulation instability (MI) have been substantially disclosed [24][25][26][27][28][29][30][31][32][33][34][35] due to the anomalous electromagnetic properties of such materials.…”

“…Accordingly, the wide study of self-focusing phenomena in Kerr nonlinear NIM has recently become a new and exciting field of research that has been the subject of intense investigations [25][26][27][28][29][30][31]. Several intriguing and counterintuitive nonlinear phenomena associated with optical collapse, optical solitons as well as modulation instability (MI) have been substantially disclosed [24][25][26][27][28][29][30][31][32][33][34][35] due to the anomalous electromagnetic properties of such materials. In particular, for MMs described by the Drude dispersive model, diffraction may be positive or negative, depending on the sign of refractive index seen by the propagating pulse in MMs [26][27][28][29][30].…”

“…Several intriguing and counterintuitive nonlinear phenomena associated with optical collapse, optical solitons as well as modulation instability (MI) have been substantially disclosed [24][25][26][27][28][29][30][31][32][33][34][35] due to the anomalous electromagnetic properties of such materials. In particular, for MMs described by the Drude dispersive model, diffraction may be positive or negative, depending on the sign of refractive index seen by the propagating pulse in MMs [26][27][28][29][30]. When two optical waves of different central frequency copropagate in MMs, they may simultaneously experience negative refractive index or positive refractive index, or one experiences positive refractive index and another experiences negative refractive index, depending on the spectra of the waves and the property of MMs [26][27][28][29][30].…”

“…In particular, for MMs described by the Drude dispersive model, diffraction may be positive or negative, depending on the sign of refractive index seen by the propagating pulse in MMs [26][27][28][29][30]. When two optical waves of different central frequency copropagate in MMs, they may simultaneously experience negative refractive index or positive refractive index, or one experiences positive refractive index and another experiences negative refractive index, depending on the spectra of the waves and the property of MMs [26][27][28][29][30]. This provides us more chances for the combinations of the signs of diffraction and nonlinearity, thus greatly enriching the dynamical behaviors of coupled wave propagation.…”