Photon

A photon is the elementary excitation of a mode of the electromagnetic field: light is emitted, absorbed and detected in these discrete units. Each photon of frequency $\nu$ carries energy $E = h\nu$ and momentum $p = h/\lambda$, travels at the speed of light, has zero rest mass and has two polarization states. The energy per photon is small on everyday scales: 0.80 eV at 1550 nm and 2.33 eV at 532 nm, where 1 eV is 1.602 × 10⁻¹⁹ J. A 1 mW beam therefore contains an enormous number of photons, about 7.8 × 10¹⁵ per second at 1550 nm and 3.2 × 10¹⁵ per second at 632.8 nm.

Energy and momentum

The energy–wavelength relation, $E\,[\text{eV}] = 1239.84/\lambda\,[\text{nm}]$, and its uses are covered under photon energy. The photon flux of a beam of power $P$ follows directly:

$$\dot N = \frac{P}{h\nu} = \frac{P\lambda}{hc}.$$

For $P = 1$ pW at 550 nm, $\dot N = 2.8 \times 10^6$ photons per second, a level at which individual detection events become countable.

The momentum $h/\lambda$ is 1.25 × 10⁻²⁷ kg·m/s for a 532 nm photon. Summed over a beam it gives radiation pressure: an absorbed beam exerts a force

$$F = \frac{P}{c} = 3.34\ \text{nN per watt},$$

twice that on a perfect mirror. The force is small but measurable, and it underlies optical tweezers, laser cooling of atoms, and the optomechanical coupling in high-finesse cavities.

The two polarization states correspond to helicity $\pm 1$, the circular polarization states; linear polarization is a superposition of the two. A photon is a boson, so many photons can occupy one mode, which is what makes stimulated emission and the laser possible.

Detection

Photodetectors respond to photons individually: each absorbed photon can create at most one electron–hole pair or photoelectron in an ordinary detector, and the fraction that does is the quantum efficiency. At high flux the result is a continuous photocurrent. At low flux, single-photon detectors such as photomultiplier tubes, single-photon avalanche diodes and superconducting nanowire detectors register individual photons as discrete pulses.

The arrival times of photons from a laser follow Poisson statistics, so a measurement that counts $N$ photons on average has a standard deviation of $\sqrt N$. Counting $10^4$ photons gives a signal-to-noise ratio of at most 100 with laser light; this is the origin of shot noise, and the statistics of thermal, laser and single-photon sources are compared under photon statistics.

Where the photon picture matters

Classical wave optics describes interference, diffraction and propagation correctly, and most optical engineering uses it. The photon picture is the natural description when light is absorbed or emitted (the photoelectric effect, semiconductor absorption edges, spontaneous emission), when noise is set by counting statistics, and in quantum technologies. Quantum key distribution with weak laser pulses illustrates the point: with a mean photon number of 0.1 per pulse, 9.5% of pulses contain at least one photon, and 4.9% of those non-empty pulses contain two or more, the fraction exploited by photon-number-splitting attacks. True single-photon sources show antibunching, a second-order correlation $g^{(2)}(0) < 1$ that no classical wave can produce.

Pitfalls

A photon is an excitation of a field mode, and its position is not defined in the way a massive particle's is; picturing it as a small bead travelling along a ray leads to errors. Interference of single photons in a double-slit experiment builds up the same fringe pattern as a classical wave, one detection at a time. Counting rates and photocurrents must be converted with the actual wavelength, since a watt at 405 nm contains fewer than half the photons of a watt at 1064 nm. Dead time and afterpulsing in single-photon detectors distort counting statistics at high rates.

Common questions

Does a photon have mass?

Its rest mass is zero, as far as any experiment has determined. It carries energy and momentum, related by $E = pc$, and so contributes to gravitation and exerts pressure.

Is light a wave or a particle?

Light propagates as a wave, with interference and diffraction, and exchanges energy with matter in discrete quanta. Quantum electrodynamics describes both aspects with a single theory; photons are the quanta of the field modes whose classical limit is the wave.

Can the human eye detect a single photon?

A rod cell responds to a single absorbed photon. In the classic experiment of Hecht, Shlaer and Pirenne, a conscious flash was reported when roughly 5 to 14 photons were absorbed, because neural processing suppresses isolated events.

References: R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, 2000); L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995); B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); S. Hecht, S. Shlaer, M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).