Non-reciprocity: The physics of letting waves go one way but not the other Premium

From quantum computing to driverless cars, many technologies benefit from non-reciprocal systems.

Representative photo of a lighthouse. | Photo Credit: Evgeni Tcherkasski/Unsplash

If you can hear someone on the other side of a wall, then that someone can hear you as well. This is something to keep in mind when you’re snooping on your neighbour – but this straightforward statement also embodies a profound principle of physics called reciprocity.

What is reciprocity?

Simply put, the principle asserts that if a signal can be transmitted from Point A (the source) to Point B (the destination), the same signal can also be transmitted from Point B to Point A, simply by exchanging the positions of the source and the destination.

It is an intuitive principle that we often encounter in our daily lives. For example, if you can shine a torchlight at your friend, they can shine the torch back at you as well. The air in between you two that allowed the light to pass one way will have no qualms about letting it pass the other way as well.

(Readers are encouraged to consider some counterintuitive examples of reciprocity as well. For example, in some films, a person being interrogated can’t see the police officers through a window pane but the officers can see the person. Similarly, when you sit in darkness, you can see someone walking under a streetlight, but the other person can’t see you.)

A variety of applications

Scientists and engineers have discovered more exciting applications of this principle. Consider antennas, like the dish-shaped ones used to receive signals for your television, or those erected on Wi-Fi routers and radio sets, or discreetly packed into the body of a smartphone. Antennas can both send and pick up signals in the form of electromagnetic energy. If you want to know how well an antenna is able to receive signals from different directions, you can place multiple sources in different random directions and estimate the reception quality.

Then again, you can make things easier – and cheaper – by using the principle of reciprocity. You just need to feed a single signal into the antenna and then observe how it transmits that signal. Thanks to reciprocity, the antenna should be able to send signals in whichever direction in which it is able to receive signals.

So by studying the way the antenna sends out a signal, we can figure out how well it can pick up signals from that direction – or, in technical parlance, its far-field pattern. This is a handy shortcut that considerably simplifies the testing process and renders it more cost-effective. Engineers use it to test as well as operate radars, sonar, seismic surveys, and magnetic resonance imaging (MRI) scanners as well.

This said, there are various situations where the reciprocal exchange of signals actually causes problems. Consider the example of spying. You would want your antenna to capture all the information from an enemy base, but at the same time, you don’t want your antenna to transmit any signals that could give away your position.

Similarly, imagine you are designing a high-power laser to transmit signals. If there is any imperfection in the transmission line, the laser power could get reflected back towards the laser, and due to reciprocity, can enter the laser. This backreflection could be so strong that it might even damage the laser. In such cases, scientists have need for a device that allows signals to travel in only one direction – like a one-way road for sound, light, or other types of waves.

One-way traffic

Essentially, we need to break the principle of reciprocity and keep it from getting involved. How would we go about this task?

Say you have a device with three components, called A, B, and C, arranged in a straight line from left to right. The function of each component is as follows: A allows only input waves oriented in a specific direction (say, at 90º, parallel with a vertical axis) to pass through. B rotates the direction of the wave by some angle (say, 45º clockwise). C only allows waves oriented at a particular angle (45º) to pass through.

Now, if you send a wave from left to right through these components, some light will go through instead of being fully blocked. Component A will allow the input wave (oriented at 90º) to pass through, and component B will rotate the wave by 45º. Component C will let it pass through as the wave is now oriented at 45º with respect to the vertical axis.

If you try to send a wave in the reverse direction, i.e. from right to left, it won’t get through. Component C will select the wave component oriented at 45º and pass it to component B. B will then rotate it another 45º, leaving it oriented at 0º, i.e. parallel with a horizontal axis. Since component A can only pass waves that are oriented vertically, the incoming wave no longer has a vertical component, A will block everything. As a result, the principle of reciprocity has been broken.

In reality, the components A and B are known as wave plates, and C is called a Faraday rotator. Such a setup, of A, B, and C, is said to achieve magnet-based non-reciprocity for electromagnetic waves (C uses a magnetic material to achieve its effect).

Part of the revolution

There are many technologies that need signals to be amplified, and are thus susceptible to strong back-reflections. They will all benefit from the use of non-reciprocity. Quantum computers, for example, use qubits instead of semiconductors to perform their operations. These qubits are often maintained at 10-100 millikelvin. Their quantum states are determined by measuring their effects on a probe signal. The affected signal needs to be amplified to a significant degree to be sensed. So researchers are also actively exploring non-reciprocal devices that can operate under the specific conditions required for quantum computing.

Apart from the magnet-based example above, there are two other, more complex ways to break reciprocity. Modulation works by continuously changing some parameter of the medium, either in time or in space. The third way, called nonlinearity, is to make the properties of the medium depend on the strength of the incoming signal, which in turn will depend on the direction in which the signal is propagating.

All these methods offer scientists a versatile toolbox with which to control wave transmission and address challenges in signal routing, communication, quantum computing, and machine learning hardware. Each approach has its own advantages and specific applications.

One of the technological revolutions underway around the world is miniaturisation to nanometre and micrometre scales, and non-reciprocal devices are no exception. Some of them are expected to be no bigger than the width of a strand of hair divided by a thousand. Researchers are significantly invested in building these devices; they are eventually expected to be used in, for example, self-driving cars – where the vehicle will need to monitor a large number of signals (from trees, pedestrians, other cars, dividers, and so on) and efficiently to ensure safe-driving.

This is a fascinating and rapidly growing research field today that needs more young minds to explore its depths.

Awanish Pandey is a senior fellow at CERN.