Interview with: Nader Engheta from the University of Pennsylvania about metamaterials and analog computing.

LISTEN NOW**Stewart Bland:**

Please start by introducing yourself and your group, and tell us about your background.

**Nader Engheta: **

Very good, thank you very much, Stewart, and thank you for your interest in my work, and I appreciate your interest, and it’s great to be part of your podcast programme. My name is Nader Engheta, and I’m a professor at the University of Pennsylvania in Philadelphia, and my areas of research interest are on optics, electrodynamics, metamaterials, optical materials, light- matter interaction, in general, physics and engineering of waves. In my group, we are conducting research in a variety of topics related to these fields.

I started actually, my education, in electrical engineering. I did my Batchelor’s degree at the University of Tehran in Iran, and I was born in Iran. I grew up there, and went to my college there. I got my Batchelor’s degree there, and then I came to the United States for my graduate study, so I went to Cal Tech, and I did my Master’s and PhD there, in the area of electrodynamics and electromagnetics. Then, after I got my PhD, I spent one year as a post doc at Cal Tech, and then I started working in a research company, and in those days we were interested in electromagnetic pulses, and the effect of the electromagnetic pulse on materials, and then, after four years in that company, I came to the University of Pennsylvania as the faculty, and since then I’ve been here, having my group interested in the area of optics and optical materials and metamaterials.

Now, at the beginning, when I started my group at the University of Pennsylvania, we were interested in wave interaction with chiral materials. Inspired by what’s going on in the optics of chiral structures, we wanted to see how that would play a role in microwaves, and that got me interested in the fields of wave- matter interactions, and then, over the years, we went to the shorter and shorter wavelengths, and now we’re interested in the various aspects of nanophotonics, optics and metamaterial.

By the way, I have another area of research interest, and that is the optical imaging based, or inspired by the biological visual system of eyes of some of the animal species, particularly with regard to polarisation vision.

So that’s, in a nutshell, about me, and part of the interest that I have in materials.

**Stewart Bland:**

Fantastic, thank you. Now, you’ve recently demonstrated that metamaterials can be designed to perform a kind of analogue computing. So to begin, can you remind us, what is a metamaterial?

**Nader Engheta:**

Sure, I’d be happy to. Meta, the prefix meta in Greek means beyond, and metamaterials are structures that have unusual, beyond the ordinary effect on waves. We need materials to control and manipulate waves around us. We have light around us, we have waves from radio stations around us. You have waves in your microwave oven. All of these are examples of electromagnetic waves, and we need materials to manipulate them, to interact with them. Of course, in nature there are naturally-available materials, that we all are familiar with that, and usually, if you look at ordinary materials, these materials are made of atoms and molecules, and, for example, if you look at a piece of gold or a piece of silver, these materials consist of gold atoms arranged in a specific pattern. This pattern, and these atoms, of course, give the electromagnetic properties of that particular material.

In metamaterials, however, we’re going beyond this natural arrangement, and we’re going to another level of organisation, such that we consider collections of tiny structures, or we call it inclusions, which consist of multiple materials, such that these collections of these inclusions together would make the structure behave with the waves in a very different and unusual way. So that’s why, you know, when you actually can manipulate and control waves with materials, particularly materials that you can engineer to give you properties that you like to have, that necessarily you might not be able to find in nature, then that makes it interesting to see what we can do with this type of manipulation of waves.

**Stewart Bland:**

So what is analogue computing, and how does it differ from the digital variety we’re more used to?

**Nader Engheta:**

A good question. So let me start by saying, what are analogue signals and what are digital signals? If you look at the analogue signal, the analogue signal is a signal that changes continuously as a physical quantity. For example, if you consider a continuously varying electric current, or a continuously varying electric voltage, for example, that’s an analogue signal. Now a digital signal is a series of discrete values, which in the terminology of electrical engineering, we like to call them zeroes and ones, if you will. These zeroes and ones, in a digital system, can relate only to two values, for example, two values of electric current, or two values of electric voltage. Now, an analogue computer is a computer that works with analogue signals. In other words, there, the quantity that’s changing, let’s say for example the electric current or electric voltage, changes continuously with time. However, digital computers, the computers that we are all using every day, those work based on the digital signal, based on these zeroes and ones values. So these are basically like two categories of computers, one can think of.

**Stewart Bland:**

So how do these metamaterials actually perform calculations?

**Nader Engheta:**

So imagine that you have a block of metamaterial that you designed, in the following way. As the wave enters into this block of metamaterial, let’s say with a certain profile, so the wave enters into this structure with a certain profile, as the wave goes through this structure that you designed specifically, by the time the wave comes out, you would like that exiting wave to have a specific profile, such that that profile would be related to the profile of the input wave that’s coming through a certain mathematical operation. For example, let’s say you have an incoming wave coming at the entrance of your block of metamaterial with a certain profile shape, and you would like, by the time the wave comes out, it would have a shape such that it would be like a derivative of the shape, of the incoming signal to that, or it could be integral of that, or it could be a convolution of that. So that means we need to design materials such that when the wave interacts with these materials, the wave evolves as it goes through it, such that it will give us the profile at the end, which would be based on the mathematical operation we would like that block to do. So essentially it’s becoming like a kind of wave-based analogue computing, because remember, as I mentioned, analogue computers are computers that work with the signals that are analogue, in a sense. Here, our idea is that these signals would be waves, would be optical or microwave, depending whatever wavelength you would like to design your metamaterial that would act on that, so it becomes entirely a wave-based type of analogue computing. One might wonder, by the way, one can say what are the advantages and disadvantages of analogue computers versus digital computers. So if you think about, for example, a digital computer, the computer that we use every day, this sort of computers, for example, because of just using zeroes and ones, digital signal, it’s more immune to noise. Also, a digital computer is an all-purpose computer – you can programme them. The analogue computer, on the other hand, works with the analogue signal, but they’re a specific-purpose computer. They do specific functionality that you design them for. For example, just like what I’ve mentioned, if you design a set of metamaterials that would give you a specific mathematical operation, like differentiation integration, that falls into the category of analogue computers.

**Stewart Bland:**

I see, thank you. So what are the potential applications?

**Nader Engheta:**

calculation, clearly you can see that there would be a variety of applications to consider. One thing that comes to mind is basically, kind of like a very short-term application for this, would be in pattern recognition, would be in image processing. So imagine that, for example, you design these layers of materials, and you would actually send an image at the input of these layers, and you would like, by the time the wave goes through the system and comes out, it will actually give you certain information about that image. For example, something like edge detection, so let’s say you have an image, and you would like, by the time it comes out, you’ll recognise the edges of the object in that image. That would be quite important from the point of view of pattern recognition, from the point of view of image analysis and image processing. Here, in that case, analogue computers could be more advantageous, because these operations would be able to be done on the entire image basically, at the same time, rather than doing it sequentially, in the sense of scanning. Such a structure will allow us to actually have this type of image analysis all at the same time, as the wave of the image going through it.

So that’s one set of applications we are considering, but more of the longer term applications we are considering is the possibility of solving equations using waves in the future. So if, as I mentioned, if one can design a metamaterial slab such that it can do, for example, differentiation on the profile of the wave that’s going through. You can think about, okay, if one can do differentiation, or one can do integration, what would be the next step to actually solve the differential equation, or solve an integral equation? So that requires actually connecting this type of structure with some form of optical system, in order that the wave, as it goes through it, it will actually give out the solution to that equation. This could be quite interesting, that just using waves, in the future we’ll be able to solve equations. That could be quite important, the variety of different areas of engineering and science.

**Stewart Bland:**

That’s fantastic, thank you. So what’s the next step in the project?

**Nader Engheta:**

Well, the next step is, as you have seen from our paper, by the way, so we introduced the concept, we introduced the ideas, we looked at some of the methods of how to design that, and using our simulation, we showed that this is indeed possible, and has a promising direction. So the next step is to, we are working right now on planning and designing experiments to show the proof of the concept, of such wave-based analogue computing. So in our team, right now we are considering three different scenarios for the proof of the concept experimentation. We are looking at different wavelength regimes. As a possible proof of the concept, we are planning and designing experiments in the microwave, as well as in the optical domain. So this will be our next step, to show the proof of the concept, and then we’ll see what are the constraints and what are the design parameters that one needs to take into account, in order to go to the next step of this idea.

**Stewart Bland:**

Fantastic. So finally, I’d like to finish by asking, as always, in your opinion, what are the other hot topics in materials science right now?

**Nader Engheta:**

Well, as somebody who is working in the area of metamaterials, and particularly a different frequency regimes of metamaterials, I’m always interested to see what are the various aspects of exciting material properties can be actually linked to metamaterials. One thing, of course, is the area of graphene. As you know, this has been a very, very exciting area. Many groups are interested in aspects of graphene, both from the point of view of electronics, as well as from the photonics aspect of that. So one of the things my group has been interested in is to see, to merge, the concept of metamaterial with the concept of graphene, to consider the possibility of one atom thick metamaterials, and that can open up quite fascinating directions as to how we’ll have some of the functionalities that metamaterials currently ... I mean basically, suggesting the possible roadmap, could those possibilities be implemented on the one atom thick structures?

Another hot area, by the way, in materials science, is the topological insulators, as you know, so those provide fascinating possibilities for an electronic system, but also one of the things that we are exploring, and looking at, is to see, is there an interesting connection between topological insulators, and the possibility of bringing that into the field of metamaterials.