In our first article, we talked about the basic ideas behind our optical Fourier Transform chip and why

In our first article, we talked about the basic ideas behind our optical Fourier Transform chip and why we made it a reality. In the next few articles, we’ll be going into greater depth on our system and how it works. We begin here by describing how we can take digital data and encode it into an optical field that can be processed at the speed of light.
Why use light?
Our technology is designed to perform a mathematical function called a 2-dimensional Fourier transform at very high speed. In our system, this calculation is performed through a combination of optical interference and the properties of simple convex lenses. The physical result of that calculation is a 2D pattern of light of varying intensity and phase. To make the system useful, we need to be able to:
Convert information from a digital representation into an optical field

https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv01.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv02.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv03.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv04.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv05.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv06.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv07.html
https://wordpress-177471-904978.cloudwaysapps.com/qaz/edc/video-les-championnats-de-france-de-cyclo-cross-en-direct-tv08.html
https://www.bhakticharuswami.com/tgb/yhn/video-ach-hip01.html
https://www.bhakticharuswami.com/tgb/yhn/video-ach-hip02.html
https://www.bhakticharuswami.com/tgb/yhn/video-ach-hip03.html
https://www.bhakticharuswami.com/tgb/yhn/video-ach-hip04.html
https://www.bhakticharuswami.com/tgb/yhn/video-ach-hip05.html
https://www.bhakticharuswami.com/tgb/yhn/video-aust-cyclo-cross-che01.html
https://www.bhakticharuswami.com/tgb/yhn/video-aust-cyclo-cross-che02.html
https://www.bhakticharuswami.com/tgb/yhn/video-aust-cyclo-cross-che03.html
https://www.bhakticharuswami.com/tgb/yhn/video-aust-cyclo-cross-che04.html
https://www.bhakticharuswami.com/tgb/yhn/video-aust-cyclo-cross-che05.html
https://www.bhakticharuswami.com/tgb/yhn/video-aust-cyclo-cross-che06.html
https://www.bhakticharuswami.com/tgb/yhn/video-ciclo-ing-01.html
Allow that field to interfere with itself and pass through a lens, a process which separates out light of different phases
Detect the result, and then convert that signal back into a digital representation.
This method sounds like a lot of extra work, but there are some significant advantages to it that make it worth the effort.
The first is that our optical calculations are performed in parallel through interference, so performing a calculation on more data by adding more optical components doesn’t increase the runtime. In fact, adding more data increases the effective performance of our system, as we carry out the equivalent of n log(n) electronic operations for n data elements.
The second is that this process can be performed at incredible speed, as light (in vacuum) travels at a velocity of nearly 300 million meters per second. Almost all of the time taken in performing a sequence of optical calculations lies in adjusting the optical elements that write data into the light; the actual calculation itself takes place nearly instantaneously.
The third is that light can carry a phenomenal amount of information because of the wave-like nature of photons.
A simple way of transmitting digital information using waves is called “On-Off Keying” (OOK). In very basic terms, this is where you turn a signal on and off to create a sequence of pulses that correspond to the binary digital information (bits) that you want to send. The maximum amount of information per unit time that you can send using this method, the “bandwidth” of the channel, is governed by the frequency of the carrier wave.
The light we use in our system has a wavelength of 1550 nanometers. While this is quite a long wavelength for light (in the infra-red), the photons that make up this light are still completing a full wave oscillation over a very short distance. As light travels a phenomenal distance in a single second, the photons are oscillating very quickly, at about 193 Terahertz.
An optical signal with a frequency of 193 Terahertz has an enormous bandwidth and can be used to transmit a vast amount of information per second. This is why modern fibre-optic broadband communications (which also use 1550 nm light) are so much faster than their electronic counterparts, but it also means that optical computing systems can work at much greater speeds than electronic ones. Not only is the calculation itself performed at the speed of light, but the rate at which we can perform new calculations is limited only by:
How quickly we can alter the information contained in the optical field
The speed at which the detectors can reliably detect the Fourier transform data
In this article, we’re talking about how we address the first of these limits using Silicon Photonics.
Silicon Photonics
What is Silicon Photonics? If you’re familiar with modern computers, you’ll know that calculations are performed with what are known as “integrated circuits”, complex systems of transistor-based logic gates that make use of the semiconducting properties of silicon to control the flow of electrical current.
Silicon is transparent, so in a silicon photonic system, light can be made to travel along special channels called “waveguides”. These can be cut or “etched” into a flat piece of pure silicon using the same technology used to create electronic processors, but with a much simpler design that is easier to manufacture. Because of the angle between the direction in which the light is travelling and the walls of the waveguide, light can’t escape from these channels, so it follows the path etched into the silicon. This is the same principle of total internal reflection that keeps light from escaping from fibre-optic cables.
Not only can we etch waveguides into silicon to transmit light, but we can also use the same approach to make components that allow us to adjust the properties of that light. A silicon photonic system is therefore also an integrated circuit, but one built with the aim of carrying and manipulating light instead of electrical signals. In our system, the components we use to write information into light are called interferometers.
Interferometers
Interferometers are a common tool in experimental physics and are usually used to detect very small changes in distance. This can be as simple as measuring the expansion or contraction of an object due to thermal effects, or it can be as ground-breaking as detecting the tiny variations in the structure of space itself due to gravitational waves.
For interferometers which operate using lasers, the idea is to split a coherent beam of light into two, allow each beam to travel along a different path, and then recombine the beams. If the paths are the same length, then the phase of the individual beams remains the same, and recombining them produces a single beam of the same intensity and phase as the original source.
Image for post
Two in-phase waves with the same frequency and amplitude, when added together, will constructively interfere to produce one wave of the same phase and frequency with greater amplitude
Light of a specific frequency performs a fixed number of oscillations over a given distance. If the paths are not the same length, then when the beams are recombined the relative phase will be different and the recombined beam will show the effects of interference.
Image for post
Two waves with the same amplitude and frequency but different phases destructively interfere to produce a new wave with a smaller amplitude and a different phase to both. By controlling the phase and amplitude of each wave, we can create a new wave with different properties. This is the fundamental principle by which we can encode information into a beam of light.
Because light has such a short wavelength, even tiny changes in distance along each path will produce detectable changes in phase. Interferometers come in many different forms; some are huge (the LIGO gravitational wave detectors are 4km long along each path or “arm” of the detector), and some are tiny. In our system, we cut micro-scale components called Mach-Zehnder interferometers (MZIs) into the silicon.
The Mach-Zehnder Interferometer
The phase-altering property of interferometers isn’t just useful for detecting changes in distance; they can also be used as a means of controlling the properties of light. We use MZIs to control the phase and amplitude of light passing through our silicon photonic circuit.
A silicon photonic MZI has a very simple structure. It starts when a single waveguide is split into two paths, each representing one of the arms of an interferometer. When we split the waveguide in two, light is distributed equally along each arm.
The amplitude of the optical field in each arm is equal to the input field divided by ​the square root of 2. This factor ensures that the total energy, proportional to the squared amplitude of the field, is conserved. This is illustrated in the diagram below. If we say that the original field has an amplitude equal to 1, the field in each branch has an amplitude ​1/√2:
Image for post
When two branches merge, the amplitude of the field is the sum of the amplitudes in each branch divided