Light

This series is about photonic integrated circuits: chips that carry light instead of electric current. Where an electronic chip sends current through metal wires, a photonic chip guides light through narrow channels on its surface, which split it into several paths and bring the paths together again [1]Bogaerts et al. 2020, p. 207.

Understanding such a chip starts with light itself. So what is light, really? Physics settled the answer in the nineteenth century: light is an electromagnetic wave, a pattern of electric and magnetic fields that travels through space [2]Hecht 2017, §1.4, p. 14. This article follows how this answer was found and what it means.

Particles or waves

For a long time it was open whether light is a stream of particles or a wave. Newton, whose prism experiments showed that white light is a mixture of colours, kept both possibilities in view but leaned towards particles, which he called corpuscles, as he grew older. His main objection to waves was that waves spread out behind an obstacle, while light seemed to travel in straight lines [2]Hecht 2017, §1.3, p. 11.

The wave theory returned at the start of the nineteenth century. Between 1801 and 1803 Thomas Young presented his principle of interference to the Royal Society: where two waves meet, their effects combine [2]Hecht 2017, §1.4, p. 12. Augustin Fresnel, working independently in France, developed a wave theory that predicted how light bends around edges, and by 1825 the particle theory had only a few advocates left [2]Hecht 2017, §1.4, p. 13. Interference is the central idea of this series, and the article §Interference returns to it in detail.

What the wave theory could not say was what waves. The answer came from a separate line of research. In 1845 Michael Faraday found that a strong magnetic field changes the light passing through a transparent material, a first sign that light and magnetism are related. James Clerk Maxwell then combined all that was known about electricity and magnetism into a single set of equations and showed from them that electric and magnetic fields can travel through space as a wave. The speed he calculated from electrical measurements equalled the measured speed of light, and he concluded that light is “an electromagnetic disturbance in the form of waves” [2]Hecht 2017, §1.4, pp. 13–14. In 1888 Heinrich Hertz generated and detected such waves, at much longer wavelengths, in the laboratory [2]Hecht 2017, §1.4, p. 14.

For a few decades physicists still assumed a medium for these waves, the aether. With Einstein’s theory of relativity (1905) the aether was abandoned: an electromagnetic wave needs no medium and travels through empty space [2]Hecht 2017, §1.5, p. 15. Unlike sound or waves on water, light reaches us from the Sun through the vacuum of space.

Fields

A field assigns a quantity to every point in space, and it may change with time. A weather map of temperatures is a field of numbers; a map of wind speeds and directions is a field of arrows.

The electric field $\mathbf{E}$ is a field of arrows that describes the force on electric charges. A charge $q$ at a point where the electric field is $\mathbf{E}$ feels the force $\mathbf{F} = q\mathbf{E}$ [2]Hecht 2017, §3.1, p. 46. The electric field is therefore the force per unit charge, and its unit is volts per metre. Charges produce electric fields around them, so the field is how one charge acts on another at a distance.

The magnetic field $\mathbf{B}$ describes a second force, which acts only on moving charges: a charge moving with velocity $\mathbf{v}$ feels $\mathbf{F} = q\mathbf{v} \times \mathbf{B}$ [2]Hecht 2017, §3.1, p. 46. Currents, which are moving charges, produce magnetic fields.

For static charges and steady currents the two fields can be treated separately. Once they change in time, they are coupled: a changing magnetic field produces an electric field, and a changing electric field produces a magnetic field. This coupling is what makes a wave possible, and the article §Maxwell's equations states it precisely.

What oscillates in a light wave

In a light wave, both fields oscillate at every point along the path. In the simplest case, a plane wave in vacuum, the electric field points along one line and grows, falls to zero, reverses and returns; the magnetic field does the same at right angles to it, and both are perpendicular to the direction in which the wave travels. The two oscillate in step, and the strength of the electric field is always $c$ times that of the magnetic field, $E = cB$, where $c$ is the speed of light [2]Hecht 2017, §3.2.1, pp. 55–56, Eq. (3.30). Figure 1 shows such a wave: the electric field in violet, the colour this series uses for light, and the magnetic field in grey, at right angles to it.

What moves along is the pattern of the fields, and with it energy. Nothing material travels with the wave. One way to picture this is a wave in a stadium crowd: each spectator only stands up and sits down again, and yet the wave runs around the stadium.

Because the magnetic field follows from the electric field, one of them is enough to describe the wave. We describe light by its electric field alone, as optics usually does; for a wave in which the electric field oscillates along one fixed direction, the field at each point is then a single number that changes in time [3]Saleh & Teich 2019, ch. 5 introduction, Fig. 5.0-2. The article §Describing a wave sets out how that number depends on position and time.

In vacuum the pattern travels at exactly $c = 299\,792\,458\,\mathrm{m/s}$. The value is exact because the metre has been defined through it since 1983, and the symbol comes from the Latin celer, fast [2]Hecht 2017, §3.2, p. 55. In more familiar units, light travels 30 cm in one nanosecond [3]Saleh & Teich 2019, ch. 2 introduction.

The electromagnetic spectrum

Radio waves, microwaves, X-rays and light are all electromagnetic waves; they differ only in their wavelength, the distance over which the pattern repeats [3]Saleh & Teich 2019, ch. 5 introduction, Fig. 5.0-1. Figure 2 shows the whole range. The wavelengths called optical run from about 10 nm to 300 µm, and the eye sees only a narrow band of them, from 390 nm to 760 nm [3]Saleh & Teich 2019, ch. 2 introduction, Fig. 2.0-1. Wavelengths just longer than the visible band are called infrared.

The light in photonic circuits is infrared, with a wavelength of about 1550 nm, twice the longest wavelength the eye can see. This range became the standard for optical communication because optical fibres lose very little light there and because optical amplifiers exist for it [4]Chrostowski & Hochberg 2015, §1.3.1, p. 9. The violet of the light in the figures of this series and in the lab is therefore a false colour: the real light would be invisible.

Waves and photons

The wave picture is not the whole story. In 1905 Einstein proposed that light is also emitted and absorbed in packets of energy, later called photons, each with an energy proportional to the frequency of the light. Quantum mechanics then showed that light, and indeed electrons and all other particles, has both a wave and a particle aspect [2]Hecht 2017, §1.5, p. 16. The word photon itself was coined only in 1926 [2]Hecht 2017, §1.5, p. 16, footnote.

This series describes light as a classical electromagnetic wave throughout. Its subject is classical integrated photonics, and silicon photonics in particular: circuits that use the interference of light waves travelling along different paths [1]Bogaerts et al. 2020, p. 207. For how light travels through waveguides, splitters and interferometers, the wave nature is the dominant property, and the classical description is sufficient [2]Hecht 2017, ch. 3 introduction, p. 45.

A second field, quantum photonics, uses the quantum nature of light. In photonic quantum computing, for example, the information is carried by quantum states of light that travel through a photonic circuit, such as single photons [1]Bogaerts et al. 2020, Box 1, p. 213. Such circuits need the quantum description of light. Neither this series nor the lab covers them at present.