Abstract
For decades, nonlinear optics has been used to control the frequency and propagation of light in unique ways enabling a wide range of applications such as ultrafast lasing, sub-wavelength imaging, and novel sensing methods. Through this, a key thread of research in the field has always been the development of new and improved nonlinear materials to empower these applications. Recently, epsilon-near-zero (ENZ) materials have emerged as a potential platform to enhanced nonlinear interactions, bolstered in large part due to the extreme refractive index tuning (Δn∼ 0.1 - 1) of sub-micron thick films that has been demonstrated in literature. Despite this experimental success, the theory has lagged and is needed to guide future experimental efforts. Here, we construct a theoretical framework for the intensity-dependent refractive index of the most popular ENZ materials, heavily doped semiconductors. We demonstrate that the nonlinearity when excited below bandgap, is due to the modification of the effective mass of the electron sea which produces a shift in the plasma frequency. We discuss trends and trade-offs in the optimization of excitation conditions and material choice (such material loss, band structure, and index dispersion), and provide a figure of merit through which the performance of future materials may be evaluated. By illuminating the framework of the nonlinearity, we hope to propel future applications in this growing field.
Highlights
Nonlinear optics studies the reaction of materials to intense light and has long been an avenue of interest for controlling the flow of light [1,2]
[13] For low-loss ENZ materials, the real index is less than unity – a condition termed near-zero index (NZI) – and such materials have demonstrated an enhancement of nonlinear processes including the intensity-dependent refractive index (IDRI) [20,22,23,24,25] and frequency conversion [14,26,27,28] through electric field confinement and slow light effects [29,30], thereby opening a breadth of applications in light manipulation [25]
Examining the limits of the nonlinearity, we find that the max variation in the refractive index is achieved when the change in effective mass is maximized, δ= n ε − n, essentially resulting in complete suppression of the max
Summary
Nonlinear optics studies the reaction of materials to intense light and has long been an avenue of interest for controlling the flow of light [1,2]. Recent success has been found working with epsilon-near-zero (ENZ) materials – media that exhibit a spectral range where | Re{ε (ω)} |< 1 [11,12,13,14,15,16,17,18,19,20,21] This condition may be satisfied in bulk materials near resonances or through free carriers, as well as in nanostructured materials as an effective property by mixing both metals and dielectrics. A prominent subset of ENZ materials is the transparent conducting oxides (TCOs) [31,32,33,34], such as indium tin oxide (ITO) or aluminum-doped zinc oxide (AZO) These materials provide a carrier concentration of up to 1020 – 1021 (cm3) due to the high fraction of donor atoms In3+ in ITO or Al3+ in AZO, and produce an ENZ region in the telecommunication spectrum (1.3 – 1.5 (μm)). Index modulation in NZI materials is of interest for potential applications in alloptical switching
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