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.
Light of one color can be described by its vacuum wavelength , its frequency , its wavenumber or its photon energy . They are related by
with = 299,792,458 m/s (the speed of light) and = 6.62607015 × 10⁻³⁴ J·s, both exact in the SI. Different fields prefer different labels: laser and telecom engineers quote vacuum wavelength in nanometers, 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 , which is why "wavelength" in optics means the vacuum wavelength unless stated otherwise.
Wavelength and frequency are inversely proportional: doubling the frequency halves the wavelength, and their product is always the wave speed. For green light at 532 nm, = (299,792,458 m/s) / (532 × 10⁻⁹ m) = 563.5 THz.
Working values
| Vacuum wavelength | Frequency | Wavenumber | Photon energy |
|---|---|---|---|
| 405 nm (violet diode) | 740.23 THz | 24,691 cm⁻¹ | 3.061 eV |
| 532 nm (green) | 563.52 THz | 18,797 cm⁻¹ | 2.331 eV |
| 632.8 nm (HeNe, in air) | 473.61 THz | 15,798 cm⁻¹ | 1.959 eV |
| 1064 nm (Nd:YAG) | 281.76 THz | 9398 cm⁻¹ | 1.165 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 and , and 1 cm⁻¹ corresponds to 29.98 GHz.
Converting widths
A small spread in one quantity converts to the other through the derivative, . 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 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 picometers. 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.
The wavelength calculator converts any one of the four labels to the others, gives the wavelength inside a medium of chosen index, and names the region of the spectrum.
Common questions
What is the relationship between wavelength and frequency?
For any wave, speed = frequency × wavelength. For light in vacuum the speed is fixed at , so and the two are inversely proportional: 1550 nm light oscillates at 193.4 THz and 532 nm light at 563.5 THz. The same relation holds for radio (a 2.4 GHz Wi-Fi signal has a 12.5 cm wavelength) and, with the speed of sound, for sound (440 Hz in air at 343 m/s is 78 cm).
Does the frequency change when light enters glass?
No. The frequency is set by the source and stays the same across an interface; the speed drops to and the wavelength shrinks by the same factor. 532 nm light in glass of index 1.5 has a wavelength of 355 nm inside the glass and still oscillates at 563.5 THz.
How is wavelength converted to wavenumber?
Divide 10⁷ by the wavelength in nanometers to get cm⁻¹: 1550 nm is 6452 cm⁻¹ and 532 nm is 18,797 cm⁻¹. Raman shifts are differences in wavenumber, so a 1332 cm⁻¹ diamond line excited at 532 nm appears at 18,797 − 1332 = 17,465 cm⁻¹, or 572.6 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.