Tool · Detectors and noise

Photon Flux Calculator

How many photons does a beam carry? From the power and wavelength, the calculator gives the photon energy, the photons per second and per pulse, the flux density over a beam area, the same flux in micromoles per second, and the current a detector of given quantum efficiency would produce. Background: photon flux, photon energy and quantum efficiency.

Light

Wavelength (nm)

Average power (mW)

Pulse repetition rate (kHz), 0 for CW

1 µW is 0.001 mW and 1 nW is 10⁻⁶ mW. A repetition rate adds the photons in each pulse.

Area and detector

Beam or spot diameter (mm)

Detector quantum efficiency (%)

The flux density is the average over a circle of this diameter. Quantum efficiency is the share of photons that give a counted electron.

Presets

Readouts

Photons per second in one watt

N/P = λ/(hc) rises in proportion to wavelength: a watt of 1550 nm light carries 2.45 times as many photons as a watt of 632.8 nm light.

Learn with it

Two short experiments. Each one sets the inputs, says where to look, and asks for a prediction before it shows the result.

Checked against

These checks run in your browser on every load. Photon energies, counts and photocurrents are compared with values worked out by hand from the exact SI constants.

Check	Expected	Computed	Tolerance

The expected values follow E = hc/λ, N = P/E and I = ηqN, with h, c, q and N_A exact in the 2019 SI. The tolerance is the largest difference from Expected that still passes, relative to Expected or to 1, whichever is larger.

The model

Each photon carries the energy $E = h c / λ$ , so a beam of power $P$ delivers

N = \frac{P}{E} = \frac{P λ}{h c}

photons per second. With a repetition rate $f_{r e p}$ each pulse holds $N / f_{r e p}$ , and over an area $A$ the flux density is $N / A$ . Dividing by the Avogadro constant gives the flux in moles of photons, the unit of photosynthetic photon flux. A detector that turns a fraction $η$ of the photons into collected electrons gives the current and responsivity

I = η q N, R = \frac{I}{P} = \frac{η q λ}{h c} = η \frac{λ [μ m]}{1.23984} A / W

The constants $h$ , $c$ , $q$ and $N_{A}$ are exact in the SI. The photon numbers are averages: laser light has Poisson photon statistics, so a count of $N$ in a window fluctuates by $\sqrt{N}$ ; that is the shot noise behind the photodiode noise calculator.

Worked example

At 1550 nm $E = 1.2816 \times 10^{- 19} J = 0.7999 e V$ , so 1 mW is $7.8029 \times 10^{15}$ photons per second. A detector with 80 % quantum efficiency turns them into 1.0001 mA, a responsivity of 1.0001 A/W. The same milliwatt at 632.8 nm carries 2.449 times fewer photons, $3.1856 \times 10^{15}$ per second. A 1 W, 80 MHz Ti:sapphire laser at 800 nm puts $5.0341 \times 10^{10}$ photons in each pulse.

Related: the wavelength calculator converts wavelength to photon energy, the responsivity and photon statistics entries go further, and the pulsed laser calculator gives pulse energy and peak power.

References: Bureau International des Poids et Mesures, The International System of Units (SI), 9th ed. (2019). B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed., Wiley (2007), chapters 12 and 18.