(for the sake of brevity, negative frequency components are omitted). The electric field is now expressed as a function of frequency, Δω and Δt are related through the uncertainty relation1

ΔωΔt=4ln(2),

and the spectral phase, φ(ω), describes the relationship between the frequency components of the pulse. In equation (2), ω as well as Δω represent angular frequencies. Angular frequency can be converted to linear frequency, ν (i.e. the observable quantity), by dividing it by 2 π,

ν = ω/2 π

In terms of the linear frequency, the uncertainty principle is given by,

c_{B} = ΔνΔτ = 2ln(2)/ π

When an input pulse, E_{in}(ω), passes through a dispersive medium, the phase added by the material is given simply by the product of the input field with the transfer function of the material. The emerging pulse E_{out}(ω), is given by,