# Photon Statistics of a Coherent Gaussian Beam [closed]

Assume that a 100 pW He-Ne single-mode last emits light at 633 nm in a TEM00 Gaussian beam.

(a)What is the mean number of photons crossing a circle of radius equal to the waist radius of the beam $W_0$ in a time T=100 ns?

(b) What is the root-mean-square value of the number of photon counts in (a)?

(c) What is the probability that no photons are counted in (a)?

Here is my solution. Could somebody please double check it?

A. $h=6.63 \times 10^{-34}$

Photon flux = $(100\times10^{-12})/((h)(4.74\times10^{14}))=3.18\times10^{8}$

Mean number of photons = $3.18\times10^{8} *(100\times10^{-9})=31.8$

B. $\sqrt{((31.8)^2/(100\times 10^{-9})}$

C. probability = 1-.86 = .14

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## closed as too localized by Qmechanic♦, David Z♦Nov 14 '12 at 6:33

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Hi John - generally we discourage questions that just ask for someone to check your work. Once you have identified the specific concept that you're not sure about, that's the point at which it's appropriate to ask a question here. –  David Z Nov 14 '12 at 6:33