Flow

All optical radiation carries energy. The resulting flow of energy at each instant, per unit time, is called energy flow. We note it \(\phi\) and it is expressed in Watts (W). Electromagnetic theory shows that the energy flow is equal to the flow of its Poynting vector. The time average value of the Poynting vector is given by

⟨ ‖ S ⃗ ‖ ⟩ = 1 2 ε μ ‖ E ⃗ 0 ‖ 2 size 12{ langle ldline { vec {S}} rdline rangle = { {1} over {2} } sqrt { { {ε} over {μ} } } ldline { vec {E}} rSub { size 8{0} } rdline rSup { size 8{2} } } {}

where \(\epsilon\) and \(\mu\) are the permittivity and magnetic permeability of the medium, \(E_{0}\) being the electric field vector. The energy flow is also called power (in particular we speak of the power of a laser).

The energy flow of radiation made up of photons of the same energy is therefore equal to the product of its photon flow (per unit of time) by the individual energy of each photon. The rate of photons per unit time is called photon flux, denoted \(\phi_{p}\) . We have

Φ = E × Φ p = hc λ Φ p size 12{Φ=E times Φ rSub { size 8{p} } = { { ital "hc"} over {λ} } Φ rSub { size 8{p} } } {}

We define a third flux called luminous flux whose unit is the lumen (lm) to quantify the visual simulations of radiation on a standard observer.