Glossary entry

Wavelength, frequency and wavenumber

Three ways to label the same light. Frequency ν = c/λ; wavenumber in cm⁻¹ is 10⁴ divided by the wavelength in µm; photon energy in eV is 1.23984 divided by the wavelength in µm. 1550 nm is 193.41 THz, 6452 cm⁻¹ and 0.800 eV; near 1550 nm, 100 GHz is 0.80 nm.

Optics fundamentalsUpdated September 2026

Light of one colour can be described by its vacuum wavelength $\lambda$ , its frequency $\nu$ , its wavenumber $\tilde\nu$ or its photon energy $E$ . They are related by

\nu = \frac{c}{\lambda}, \qquad \tilde\nu = \frac{1}{\lambda}, \qquad E = h\nu = \frac{hc}{\lambda},

with $c$ = 299,792,458 m/s and $h$ = 6.62607015 × 10⁻³⁴ J·s, both exact in the SI. Different fields prefer different labels: laser and telecom engineers quote vacuum wavelength in nanometres, the ITU grid and coherent systems use frequency in terahertz, infrared spectroscopists use wavenumber in cm⁻¹, and semiconductor physicists use energy in electronvolts. Frequency and energy do not change when light enters a medium; wavelength does, by the factor $1/n$ , which is why "wavelength" in optics means the vacuum wavelength unless stated otherwise.

Working values

Vacuum wavelength	Frequency	Wavenumber	Photon energy
632.8 nm (HeNe)	473.76 THz	15,803 cm⁻¹	1.959 eV
1310 nm	228.85 THz	7634 cm⁻¹	0.946 eV
1550 nm	193.41 THz	6452 cm⁻¹	0.800 eV
10.6 µm (CO₂)	28.28 THz	943 cm⁻¹	0.117 eV

The shortcuts are $E\,[\mathrm{eV}] = 1.23984/\lambda\,[\mathrm{µm}]$ and $\tilde\nu\,[\mathrm{cm^{-1}}] = 10^4/\lambda\,[\mathrm{µm}]$ , and 1 cm⁻¹ corresponds to 29.98 GHz.

Converting widths

A small spread in one quantity converts to the other through the derivative, $\Delta\nu = c\,\Delta\lambda/\lambda^2$ . Near 1550 nm, 0.8 nm is 99.8 GHz and 100 GHz is 0.80 nm, which is why the 100 GHz DWDM grid is often described as 0.8 nm spacing; at 1310 nm the same 100 GHz is 0.57 nm. A laser linewidth of 100 kHz at 1550 nm is 0.8 fm, far below what a grating spectrometer resolves. Because $\lambda^2$ appears, equal frequency spacings are unequal wavelength spacings across a wide band, and the ITU DWDM grid (G.694.1) is therefore defined in frequency, while the coarse CWDM grid (G.694.2), with 20 nm spacing, is defined in wavelength.

Measurement

Wavelength is measured with a wavemeter, an interferometer that counts fringes against a reference laser, typically to parts in 10⁶ or 10⁷, or with an optical spectrum analyzer to a few picometres. Absolute optical frequency is measured by beating the light against a frequency comb referenced to an atomic clock. Instruments report either vacuum or air wavelength; the two differ by the index of air, about 2.7 × 10⁻⁴, which near 1550 nm is 0.4 nm.

References: BIPM, The International System of Units (SI brochure), 9th ed. (2019); ITU-T G.694.1, Spectral grids for WDM applications: DWDM frequency grid.