Electro-optic modulation is a key function in optical data communication and possible future optical compute engines. The performance of modulators intricately depends on the interaction between the actively modulated material and the propagating waveguide mode. While a variety of high-performance modulators have been demonstrated, no comprehensive picture of what factors are most responsible for high performance has emerged so far. Here we report the first systematic and comprehensive analytical and computational investigation for high-performance compact on-chip electro-optic modulators by considering emerging active materials, model considerations and cavity feedback at the nanoscale. We discover that the delicate interplay between the material characteristics and the optical mode properties plays a key role in defining the modulator performance. Based on physical tradeoffs between index modulation, loss, optical confinement factors and slowlight effects, we find that there exist combinations of bias, material and optical mode that yield efficient phase or amplitude modulation with acceptable insertion loss. Furthermore, we show how material properties in the epsilon near zero regime enable reduction of length by as much as by 15 times. Lastly, we introduce and apply a cavity-based electro-optic modulator figure of merit, Δλ/Δα, relating obtainable resonance tuning via phase shifting relative to the incurred losses due to the fundamental KramersKronig relations suggesting optimized device operating regions with optimized modulation-to-loss tradeoffs. This work paves the way for a holistic design rule of electrooptic modulators for high-density on-chip integration.

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Here, we demonstrate a spectrally broadband, GHz-fast Mach-Zehnder interferometeric modulator, exhibiting a miniscule VpL of 95 V•µm, deploying a sub-wavelength short electrostatically tunable plasmonic phase-shifter, based on heterogeneously integrated ITO thin films into silicon photonics.Indium tin oxide (ITO), belonging to the class of transparent conductive oxides, is a material extensively adopted in high-tech industry such as in touchscreen displays of smartphones or contacts for solar cells. Recently, ITO has been explored for electro-optic modulation using its free-carrier dispersive effect enabling unity-strong index modulation [1][2][3][4]. However, GHz-fast modulation capability using ITO is yet to be demonstrated -a feature we show herein. Given the ubiquitous usage of phase-shifter technologies, such as in data communication, optical phased arrays, analog and RF photonics, sensing etc.; here we focus on a Mach-Zehnder interferometer (MZI) based modulator to demonstrate a comprehensive platform of heterogeneous integration of ITO-based opto-electronics into silicon photonic integrated circuits (PIC). Since for phaseshifters only the real-part of the optical refractive index (n) is of interest, in previous studies we have shown the interplay between a selected optical mode (e.g. photonic bulk vs. plasmonic) and the material's figure of merit (Dn/Da), where a is the optical loss, directly resultant form Kramers-Kronig relations [5]. Additionally, ITO can be selectively prepared (via process conditions [6]) for operating in either an n-dominant or adominated region [5]. Using this approach, we recently showed a photonic-mode ITO-oxide-Si MZI on silicon photonics characterized by a VpL = 0.52 V•mm [3], and a plasmonic version deploying a lateral gate exhibiting a VpL = 0.063 V•mm [7]. Indeed, a plasmonic mode enables a strong light-matter-interaction (e.g. extrinsic slow-light effect), which, when superimposed with ITO's intrinsic slow-light effect, proximal epsilon-near-zero (ENZ) effects [8], enables realization of just 1-5 µm short phase-shifters [5]. The device-advantage of such micrometer-compact opto-electronics are small capacitances, in the order of ~fF, enabling low power

Densely integrated active photonics is key for next generation on-chip networks for addressing both footprint and energy budget concerns. However, the weak light-matter interaction in traditional active Silicon optoelectronics mandates rather sizable device lengths. The ideal active material choice should avail high index modulation while being easily integrated into Silicon photonics platforms. Indium tin oxide (ITO) offers such functionalities and has shown promising modulation capacity recently. Interestingly, the nanometer-thin unity-strong index modulation of ITO synergistically combines the high group-index in hybrid plasmonic with nanoscale optical modes. Following this design paradigm, here, we demonstrate a spectrally broadband, GHz-fast Mach–Zehnder interferometric modulator, exhibiting a high efficiency signified by a miniscule VπL of 95 V μm, deploying a one-micrometer compact electrostatically tunable plasmonic phase-shifter, based on heterogeneously integrated ITO thin films into silicon photonics. Furthermore we show, that this device paradigm enables spectrally broadband operation across the entire telecommunication near infrared C-band. Such sub-wavelength short efficient and fast modulators monolithically integrated into Silicon platform open up new possibilities for high-density photonic circuitry, which is critical for high interconnect density of photonic neural networks or applications in GHz-fast optical phased-arrays, for example.

Tunable optical material properties enable novel applications in both versatile metamaterials and photonic components including optical sources and modulators. Transparent conductive oxides (TCOs) are able to highly tune their optical properties with applied bias via altering their free carrier concentration and hence plasma dispersion. The TCO material indium tin oxide (ITO) exhibits unity-strong index changes, and epsilon-near-zero behavior. However, with such tuning the corresponding high optical losses, originating from the fundamental Kramers-Kronig relations, result in low cavity finesse. However, achieving efficient tuning in ITO-cavities without using light matter interaction enhancement techniques such as polaritonic modes, which are inherently lossy, is a challenge. Here we discuss a novel one-dimensional photonic crystal nanobeam cavity to deliver a cavity system offering a wide range of resonance tuning range, while preserving physical compact footprints. We show that a vertical Silicon-slot waveguide incorporating an actively gated-ITO layer delivers ~3.4 nm of tuning. By deploying distributed feedback, we are able to keep the Q-factor moderately high with tuning. Combining this with the sub-diffraction limited mode volume (0.1 (λ/2n) 3 ) from the photonic (non-plasmonic) slot waveguide, facilitates a high Purcell factor exceeding one thousand. This strong light-matter-interaction shows that reducing the mode volume of a cavity outweighs reducing the losses in diffraction limited modal cavities such as those from bulk Si 3 N 4 . These tunable cavities enable future modulators and optical sources such as tunable lasers.