where k p = ω ω p / c , ω ω p is the light frequency, j = … … , − − 1 , 0 , 1 , … … is the pulse number and ϕ ϕ ^ ^ j is the initial (random) phase of the j -th pulse. We assume that the mean value of all these phases is equal to zero, ⟨ ⟨ ϕ ϕ ^ ^ j ⟩ ⟩ = 0 , and their root mean square (RMS) uncertainty ( ⟨ ⟨ ϕ ϕ 2 ^ ^ ⟩ ⟩ − − ⟨ ⟨ ϕ ϕ ^ ^ ⟩ ⟩ 2 ) 1 / 2 is equal to Δ Δ ϕ ϕ .