Observation of Higher-Order Kerr Effect in Thin Epsilon-Near-Zero Films

Highly doped transparent conducting oxide (TCO) thin films with near-zero permittivity can support epsilon-near-zero (ENZ) modes ^1,2, which leads to perfect light absorption and a large electric field intensity enhancement within the film. Extreme nonlinear light-matter interactions in ENZ thin film have led to enhanced high harmonic generation ^3,4 and giant enhancement of the optical Kerr effect (OKE) ^5,6 with ultrafast (sub-picosecond) recovery time. Surprisingly, the self-refraction counterpart of high harmonic generation, i.e., the higher-order Kerr effect (HOKE), in ENZ materials has remained unnoticed until now. Also, all previous works on the giant enhancement of OKE report the saturation of the refractive index change induced by optical nonlinearity with increasing <i>E</i>-field intensity of the incident wave, showing the ultimate limit of self-phase modulation. Although saturation of the imaginary part of the complex refractive index can be understood in terms of saturable absorption-type characteristics of the ENZ thin films, no proper explanation can be found in the existing literature for the observed saturation effect for the real part of the refractive index. Moreover, in the case of extreme nonlinear light-matter interactions, similar to what is observed in gaseous media ⁷, in an ENZ film, HOKE, i.e., the contributions from fifth, seventh, and higher odd-order nonlinearities to self-phase modulation may become prominent. However, no such observation was made to date or perhaps overlooked entirely.<br/>Here, we report the experimental observation of strong HOKE in aluminum-doped zinc oxide (AZO) film grown by atomic layer deposition technique with a thickness of 76 nm and ENZ wavelength of 1590 nm. The Z-scan experiments were performed with femtosecond laser pulses of various wavelengths (1100-1600 nm) and angles of incidence (0-70^o). We observed a substantial contribution from the fifth-order nonlinear process to nonlinear refraction near the ENZ wavelength and at oblique incidence, which resulted in the transition from self-focusing to self-defocusing type OKE. The physical mechanisms leading to this observation are twofold- i) excitation of ENZ modes and the associated field intensity enhancement, and ii) increase of the effective nonlinear light-matter interaction length at an oblique incidence that leads to the enhancement of higher-order nonlinear refraction caused by cascaded third-order processes ⁸. We introduce novel nonlinear metrics to quantify the enhancement of the higher-order nonlinear refraction coefficients.<br/>Finally, our observation of the interplay between the third-order and the fifth-order contributions to the self-phase modulation shows a limited performance of TCO films in all-optical modulators. This observation sheds new light on the optical nonlinearity of TCO films which got overlooked in the past. Many interesting alternative applications can be found based on such a novel observation, where one needs a fast switching from self-focusing to self-defocusing effects. An example is a femtosecond scale switching from an all-optical modulator to an all-optical isolator operation. Additionally, HOKE observed in TCO films could be beneficial for quantum information science. One would be interested in generating &gt;2 photons entangled states via multi-wave (&gt;4) mixing processes that need a significant contribution from HOKE.<br/>References:<br/>1. Campione, S.<i>, et al.</i>, <i>Optics express </i>(2016) <b>24</b> (16), 18782<br/>2. Vassant, S.<i>, et al.</i>, <i>Optics express </i>(2012) <b>20</b> (21), 23971<br/>3. Yang, Y.<i>, et al.</i>, <i>Nature Physics </i>(2019) <b>15</b> (10), 1022<br/>4. Tian, W.<i>, et al.</i>, <i>ACS omega </i>(2020) <b>5</b> (5), 2458<br/>5. Alam, M. Z.<i>, et al.</i>, <i>Science </i>(2016) <b>352</b> (6287), 795<br/>6. Reshef, O.<i>, et al.</i>, <i>Optics letters </i>(2017) <b>42</b> (16), 3225<br/>7. Bache, M.<i>, et al.</i>, <i>Optics letters </i>(2012) <b>37</b> (22), 4612<br/>8. Saltiel, S.<i>, et al.</i>, <i>Optics letters </i>(1997) <b>22</b> (3), 148