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Quantum Optics for Engineers by F.J. Duarte

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9

Laser Oscillators Described via the Dirac Notation

9.1    Introduction

Here we derive the classical linewidth cavity equation

ΔλΔθ(θλ)1

(9.1)

using the Dirac notation approach. First, we notice that in this equation ∆θ is the beam divergence previously related to the uncertainty principle (see Chapter 3):

ΔpΔxh

(9.2)

and (∂θ/∂λ)−1 is the overall cavity angular dispersion (Duarte, 2003).

We should also mention that Equation 9.1 is the single-pass version of the multiple-pass linewidth cavity equation (Duarte and Piper, 1984; Duarte, 1990, 2001):

Δλ=ΔθR(MRλΘG+RλΦP)1

(9.3)

where the multiple-return-pass beam divergence is given by (Duarte, 1989, 1990)

ΔθR=λπw(1+(LRBR)2+(ARLRBR)2)1/2

(9.4)

R is the number of return-cavity ...

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