Human development was (and here we argue still is to this day) steered and certainly accelerated by innovation in materials. Indeed, we name human cultural eras after material classes (loosely defined here) such as the stone, bronze, iron ages. And the unique properties and process control of semiconductors, foremost Silicon and III-Vs, have enable the 4^th industrial revolution of digitalization, pivoting into the internet and information era we live in today.

However, such a data-new-world has high demands on next generation computing and in the U.S., already about 7% of all electricity is used for information processing (trend exponentially growing, CARG ~ 45%). Hence, if in less than 8 years we still want to turn on the light or electric heater, something must be done in computing and data processing.

Specialized Computing to the Rescue

The good news is that there is a trend in computing to more efficient, however, more specialized computer systems; a GPU outperforms a CPU and a TPU a GPU (on some tasks, at least). So, if such accelerators, as they are called, are so useful and data is often transferred in the optical domain, why shall we not consider augmenting the menu of accelerators with a PPU (Photonic Process Unit)? Such question is both scientifically interesting, and certainly timely, given that there is an inherent shortage in the chip market (not only since supply chains struggle due to the pandemic). 

Coming back to emerging materials for computing, in our recently published work (Nature Comm. Physics), we report on the first nano-optic metatronic-based integrated analog processor based on a sub-wavelength Epsilon-Near Zero (ENZ) circuitry. Basically, a nanophotonic application-specific integrated circuit.

Analog Nanophotonic Computing

We show that a nanophotonic platform based on epsilon-near-zero materials can solve in the analog domain partial differential equations (PDE), which are universal to the fields of science and engineering. Experimental results of electrically tunable nano-photonic elements confirm the validity of this concept. The meta-morphic (programmable) material indium-tin-oxide (ITO) is commonly routinely used in high-tech such as in touch screens of smart phones and in the solar industry as transparent contact ensures.

In brief, wavelength stretching in zero(optical)-index media enables highly nonlocal interactions within the board based on the conduction of electric displacement current, which can be monitored to extract the solution of a broad class of PDE problems. By exploiting control of deposition technique through process parameters, we demonstrate the possibility of implementing the proposed nano-optic processor using foundry compatible ITO, whose optical properties can be tuned by carrier injection to obtain programmability at high speeds and low energy requirements. This nano-optical analog processor can be integrated at chip-scale, processing arbitrary inputs at the speed of light.

Analog photonic solutions, as discussed in this work, offers unique opportunities to address complex computational tasks and high societal relevance with unprecedented performance in terms of energy dissipation and speeds, overcoming current limitations of modern computing architectures based on electron flows and digital approaches.

Solving Partial Differential Equations with Light

We mathematically prove that the mesh current method of a metatronic circuit, which mimics a lumped-element electrical circuit, can map a finite difference mesh that solves a steady-state Laplacian equation and, by extension, other time-variant second order elliptic partial differential equations. Moreover, in contrast with a resistive network, we numerically show that this technology can be used to solve partial differential equations with high accuracy (90%), while decoupling circuit mesh upscaling from reprogramming speed. Beyond a theoretical framework, we showed through numerical simulation that this metatronic circuit solver can be realized using one single material, exploiting the ability to tailor the optical properties of ITO, sputtered using, experimentally validated, controlled process parameters, thus enabling a high degree of manufacturability.

This analog processor is particularly well-suited to be reprogrammed on both the boundary conditions and network elements, limited in size only by the presence of ohmic losses. Implementing these techniques enables an ultrafast, chip-scale, integrable, and reconfigurable analog computing processor able to solve partial differential equations at the speed of light without lumped circuit capacitance delay. 

In 1000 years, humans will probably not talk about the era of ITO or epsilon-near-zero science. However, this concept is applicable to a broad range of topical areas such as nanooptics- and photonics, metamaterials, metasurfaces, photonic processors, and is posed to show innovations the context of non-von Neumann computer hardware and domain-specific accelerators and co-processors.