Glossary entry

Photon energy

The energy carried by a single photon, set by its frequency or wavelength. The fundamental quantum unit of optical energy and the basis for all energy-wavelength conversions.

A photon of frequency $\nu$ (or angular frequency $\omega = 2\pi\nu$ , or wavelength $\lambda$ in vacuum) carries energy

E \;=\; h \nu \;=\; \hbar \omega \;=\; \frac{h c}{\lambda},

where $h = 6.626 \times 10^{-34}$ J·s is Planck's constant, $\hbar = h / 2\pi$ , and $c = 2.998 \times 10^8$ m/s.

In practical units, with $\lambda$ in micrometers:

E \, [\text{eV}] \;\approx\; \frac{1.2398}{\lambda \, [\mu\text{m}]}.

The 1.24 conversion constant ( $h c / e$ in eV·μm) is one of the most-used numbers in photonics.

Photon energies at common wavelengths:

Wavelength	Spectral region	Photon energy
100 nm	Extreme UV	12.40 eV
250 nm	UV	4.96 eV
405 nm	Violet (Blu-ray)	3.06 eV
532 nm	Green (Nd:YAG doubled)	2.33 eV
633 nm	Red (HeNe)	1.96 eV
808 nm	NIR (pump diodes)	1.53 eV
850 nm	Datacom multimode	1.46 eV
980 nm	EDFA pump	1.265 eV
1064 nm	Nd:YAG fundamental	1.165 eV
1310 nm	Telecom O-band	0.946 eV
1480 nm	EDFA pump	0.838 eV
1550 nm	Telecom C-band	0.800 eV
3 μm	Mid-IR (HF laser, OPO)	0.413 eV
10.6 μm	CO $_2$ laser	0.117 eV
100 μm	Far-IR / THz	0.0124 eV

For optical power $P$ at wavelength $\lambda$ , the photon flux is

\Phi \;=\; \frac{P}{h\nu} \;=\; \frac{P \lambda}{h c}.

A 1 mW beam at 1550 nm carries $\sim 7.8 \times 10^{15}$ photons per second. The shot-noise floor of any photodetection scales with this number.

The quantum-limited responsivity of a photodetector is $\mathcal{R}_{\max} = e \lambda / hc = \eta \lambda \, [\mu\text{m}] / 1.24$ A/W at quantum efficiency $\eta = 1$ . The bandgap of a photovoltaic absorber must be smaller than the photon energy for the photon to be absorbed; otherwise the semiconductor is transparent at that wavelength.

In single-photon experiments (quantum communications, low-level light detection), the energy of individual photons becomes directly observable, and photon-counting detectors (single-photon avalanche diodes, superconducting nanowire detectors) replace continuous photocurrent measurements.