Epsilon-near-zero materials are ideal platforms for nonlinear optics. Extreme electric field enhancements are predicted when a transverse-magnetic polarized field impinges obliquely on a film of material whose real part of the dielectric permittivity approaches zero. Under these circumstances, the component of the electric field with polarization normal to the film surface is enhanced by a factor proportional to the inverse square root of the dielectric permittivity. Nonlinear processes benefit from such uniquely favorable field localization, whether the condition is achieved in natural or artificial materials. Nonlinear optical processes have also been shown to be affected by the interference mechanism that occurs when two counter-propagating beams/pulses interact. Counter-propagating pulse dynamics has been investigated for surface plasmons and guided beams, they have been used for direct characterization of ultra-short pulses, to control emission of high-harmonics and to indirectly measure the phase mismatch of waveguides. Finally, they have been studied also in one dimensional photonic crystals and negative index materials. However, all these examples rely on either phase-matching or the availability of photonic resonances. Here we demonstrate that, thanks to the ability of epsilon-near-zero materials to efficiently support nonlinear processes in the absence of phase-matching or resonant conditions, one can control harmonic generation process by altering the phase of two non-collinear counter-propagating beams. We investigate the dynamics of two non-collinear counter-propagating beams impinging on an epsilon-near-zero slab and evaluate the modulation of the second and third harmonic signals as a function of the phase difference between the two sources. The calculations are performed considering a 100nm-thick slab of indium-tin-oxide (ITO). The results confirm that epsilon-near-zero media are exceptional platforms for nonlinear optics, providing a novel path to control these processes, including the possibility to easily characterize optical pulses.
M. A. Vincenti, D. de Ceglia, M. Scalora, and C. De Angelis, "Nonlinear dynamics of counter-propagating beams in epsilon-near-zero films," Proc. SPIE 10672, Nanophotonics VII, 1067206 (Presented at SPIE Photonics Europe: April 22, 2018; Published: 4 May 2018); https://doi.org/10.1117/12.2305862.
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