Materials with a spatially uniform but temporally varying optical response have applications ranging from magnetic field-free optical isolators to fundamental studies of quantum field theories. However, these effects typically become relevant only for time variations oscillating at optical frequencies, thus presenting a significant hurdle that severely limits the realization of such conditions. Here we present a thin-film material with a permittivity that pulsates (uniformly in space) at optical frequencies and realizes a time-reversing medium of the form originally proposed by Pendry [Science 322, 71 (2008)SCIEAS0036-807510.1126/science.1162087]. We use an optically pumped, 500 nm thick film of epsilon-near-zero (ENZ) material based on Al-doped zinc oxide. An incident probe beam is both negatively refracted and time reversed through a reflected phase-conjugated beam. As a result of the high nonlinearity and the refractive index that is close to zero, the ENZ film leads to time reversed beams (simultaneous negative refraction and phase conjugation) with near-unit efficiency and greater-than-unit internal conversion efficiency. The ENZ platform therefore presents the time-reversal features required, e.g., for efficient subwavelength imaging, all-optical isolators and fundamental quantum field theory studies.

Time-varying metasurfaces are emerging as a powerful instrument for the dynamical control of the electromagnetic properties of a propagating wave. Here we demonstrate an efficient time-varying metasurface based on plasmonic nano-antennas strongly coupled to an epsilon-near-zero (ENZ) deeply sub-wavelength film. The plasmonic resonance of the metal resonators strongly interacts with the optical ENZ modes, providing a Rabi level spitting of ∼ 30%. Optical pumping at frequency ω induces a nonlinear polarisation oscillating at 2ω responsible for an efficient generation of a phase conjugate and a negative refracted beam with a conversion efficiency that is more than four orders of magnitude greater compared to the bare ENZ film. The introduction of a strongly coupled plasmonic system therefore provides a simple and effective route towards the implementation of ENZ physics at the nanoscale.Introduction. Time-varying systems and metasurfaces are of interest in view of the fundamental physics questions that have arisen [1][2][3][4][5][6][7] and also in view of the potential applications ranging from perfect lenses to spectral and temporal shaping of light fields [8][9][10][11][12][13][14][15][16][17]. Recent results have shown that thin films of epsilon-near-zero (ENZ) materials with a dielectric permittivity close to zero [18,19] at optical wavelengths in the visible or near-infrared spectral regions are promising candidates to achieve rapid (on the optical wave oscillation timescale) temporal changes of the optical properties [7]. The very large order-of-unity refractive index changes that can be induced optically [20][21][22][23] makes it possible to achieve efficient temporal modulation uniformly across the medium [10, 24] even in deeply subwavelength thin films [25][26][27], resulting in optically-induced negative refraction with unity efficiency [7]. However, the results demonstrated so far rely on high-intensity optical pumping of the ENZ film in order to achieve such large changes in the refractive index. Recently, the combination of ENZ films with plasmonic structures has led to a significant reduction of the required optical powers for the Kerr nonlinear contribution to the refractive index [28]. Coupling between light and matter can be enhanced when two resonant systems with the same optical resonant frequency are brought into close contact [29]. Strong coupling occurs when the strength of the coupling mech- * daniele.faccio@glasgow.ac.uk, r.sapienza@imperial.ac.uk, sha-laev@purdue.edu: † These authors contributed equally. anism (measured by the splitting of the two resonant frequencies [30]) dominates the intrinsic losses in the system thus resulting in a double peaked structure in the absorption spectrum or equivalently, in two well-separated polariton branches in the spectral domain. In the temporal domain, this will give rise to Rabi oscillations between the populations on these two branches and the combination of light-matter states where the matter component can contain a large fraction of the total ener...

We investigate adiabatic frequency conversion using epsilon near zero (ENZ) materials. We show that, while the maximum frequency conversion for a given change of permittivity does not exhibit an increase in the vicinity of the Re[εr]=0 condition, the change in permittivity can be achieved in a shorter length and, if the pump is also in the ENZ region, at a lower pump intensity. This slow propagation effect makes the conversion efficiency in the ENZ material comparable to that in micro-resonators and other structured slow light schemes, but unlike the latter, no nanofabrication is required for ENZ materials which constitutes their major advantage over alternative frequency conversion approaches. Our results, supported by experimental measurements, indicate that transparent metal oxides operating near the ENZ point are good candidates for future frequency conversion schemes. INTRODUCTIONFrequency conversion is a signature characteristic and a key application of nonlinear optics [1]. It can be attained using both second and third order nonlinearities in various media. Second order processes require noncentrosymmetric media and include the well-known effects of sum and difference frequency generation while third order phenomena, which occur in any medium, include four-wave mixing processes as well as Raman effects. All of these frequency conversion schemes can be characterized as parametric processes where the optical properties are modulated with a certain frequency which causes the generation of oscillations at new frequencies. Typically, frequency conversion is well described by the coupled wave formalism [2] in which the energy flows back and forth between waves of different frequencies (often characterized as pump, signal and idler) depending on the phase relations between the waves (phase matching conditions).While the field of frequency conversion is well established, the development of powerful ultra-fast light sources has led to the observation of different effects where the entire spectrum of the incoming light wave shifts adiabatically in the presence of a rapid change of the refractive index, typically induced by a strong optical pump (although other methods are possible). These effects have been observed both in high-Q resonant dielectric structures (Fig. 1a) [3][4][5][6] and in free propagating waves inside nonlinear epsilon-near zero (ENZ) media [7][8][9]. Although several nonlinear processes have been shown to be enhanced in ENZ materials (Fig. 1b) [10][11][12], driving intense research [13,14], rapid and complete frequency conversion/ modulation represents a unique opportunity to explore novel applications, especially in imaging, sensing, and telecommunications. Currently, the research on adiabatic frequency conversion (AFC) is ongoing and it is not clear which approach (i.e. high-Q resonators or ENZ) is the most appropriate. With that in mind, we explore what characteristics are needed to achieve efficient AFC, giving special attention to ENZ materials, were we find the potential for large frequency...

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The ultrafast changes of material properties induced by short laser pulses can lead to frequency shift of reflected and transmitted radiation. Recent reports highlight how such a frequency shift is enhanced in the spectral regions where the material features a near-zero real part of the permittivity. Here we investigate the frequency shift for fields generated by four-wave mixing with a nonlinear polarisation oscillating at twice the pump frequency. In our experiment we observe a frequency shift of more than 60 nm (compared to the pulse width of ∼40 nm) for the phase conjugated radiation generated by a 500 nm Aluminium-doped Zinc Oxide (AZO) film pumped close to the epsilon-near-zero wavelength.Our results indicate applications of time-varying media for nonlinear optics and frequency conversion.