Tool · Units and conversions

Photonics Unit Converter

What is this power in milliwatts, this wavelength in terahertz or electronvolts, and this linewidth in picometres? Type into any field and the others follow: optical power in dBm, mW, W, µW and dBW; a gain or loss as dB, a linear or field ratio, a percentage or an optical density; a wavelength as frequency, photon energy and wavenumber; and a spectral width as Δν, Δλ and Δσ at that wavelength. Alongside are the photon flux, the responsivity of an ideal detector, the telecom band, the nearest DWDM channel and the coherence length. Background: decibel and dBm, photon energy, and linewidth.

Optical power

dBm

µW

dBW

Power ratio, gain and loss

P₂/P₁

percent

field ratio E₂/E₁

optical density

A loss is a negative number of dB here: 3 dB of loss is −3 dB, P₂/P₁ = 0.501.

Wavelength, frequency and photon energy

wavelength (nm)

wavelength (µm)

frequency (THz)

photon energy (eV)

wavenumber (cm⁻¹)

Vacuum wavelength in nm unless marked. In air at 1550 nm the wavelength is shorter by about 0.43 nm (n ≈ 1.00027).

Linewidth and spacing

Δν

Δλ

Δσ (cm⁻¹)

Converted at the wavelength above. The frequency width is held fixed when the wavelength changes.

Checked against

These checks run in your browser on every load. Each conversion is compared with a value worked out by hand from the exact SI constants, and a round trip through all five wavelength units is checked on 200 random wavelengths.

Check	Expected	Computed	Tolerance

The constants are the exact values of the 2019 SI: c = 299,792,458 m/s, h = 6.62607015 × 10⁻³⁴ J s and e = 1.602176634 × 10⁻¹⁹ C. The band edges follow ITU-T G-series Supplement 39 and the channel grid ITU-T G.694.1. The tolerance is the largest relative difference from Expected that still passes.

The model

Optical power is expressed in decibels relative to one milliwatt, and a ratio of two powers in plain decibels:

P_{\mathrm{dBm}} = 10\log_{10}\frac{P}{1\ \mathrm{mW}}, \qquad G_{\mathrm{dB}} = 10\log_{10}\frac{P_2}{P_1} = 20\log_{10}\frac{E_2}{E_1}

The factor 20 applies to field amplitudes (and to voltages on equal impedances), whose square is the power. Optical density is the same ratio written as $\mathrm{OD} = -\log_{10}(P_2/P_1)$ , so OD 3 is −30 dB. A vacuum wavelength converts to frequency, photon energy and wavenumber through

\nu = \frac{c}{\lambda}, \qquad E = h\nu = \frac{hc}{\lambda}, \qquad E\,[\mathrm{eV}] = \frac{1239.841984}{\lambda\,[\mathrm{nm}]}, \qquad \tilde\nu = \frac{1}{\lambda}

with the exact constants of the 2019 SI. A spectral width converts at the centre wavelength to first order in $\Delta\nu/\nu$ ,

\Delta\lambda = \frac{\lambda^2}{c}\,\Delta\nu, \qquad Q = \frac{\nu}{\Delta\nu}, \qquad \tau_c = \frac{1}{\pi\,\Delta\nu}

and the error of the linear form is about $(\Delta\nu/2\nu)^2$ , which the tool reports once it exceeds 0.01 %. The coherence time is the one for a Lorentzian line with the power-spectrum definition of Saleh and Teich; other line shapes and definitions differ by factors of order one, so the coherence length is an order-of-magnitude figure. The photon flux and the responsivity of a detector with unit quantum efficiency follow from the photon energy,

\Phi = \frac{P}{h\nu}, \qquad \mathcal{R} = \frac{e}{h\nu} = \frac{\lambda\,[\mu\mathrm{m}]}{1.239842}\ \mathrm{A/W}

Wavelengths are vacuum values; in air they are shorter by the refractive index of air, about 1.00027 in the near infrared. The band edges are those of ITU-T G-series Supplement 39, and the DWDM channels are the ITU-T G.694.1 grid, 193.1 THz plus a whole number of 50 or 100 GHz steps.

Worked example

A 1550 nm laser at 3 dBm emits 1.995 mW. Each photon carries 0.7999 eV, or $1.282\times10^{-19}$ J, so the beam carries $1.557\times10^{16}$ photons per second, and a detector with unit quantum efficiency would give 1.250 A/W. After 20 dB of loss, a ratio of 0.01, the power is −17 dBm or 19.95 µW. At 1550 nm the frequency is 193.414 THz; the nearest 100 GHz and 50 GHz channels are both at 193.40 THz, which is 1550.116 nm. A linewidth of 100 kHz is 0.8014 fm, a Q of $1.934\times10^{9}$ , and a Lorentzian line of that width has a coherence length of about 954 m in vacuum.

References: Bureau International des Poids et Mesures, The International System of Units (SI), 9th ed. (2019). ITU-T Recommendation G.694.1, Spectral grids for WDM applications: DWDM frequency grid. ITU-T G-series Supplement 39, Optical system design and engineering considerations. ISO 20473, Optics and photonics: Spectral bands. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed., Wiley (2007).