 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2014/paper-2/section-a/a5/solution

For a waveguide mode in a homogeneous nondispersive filling,

ω^{2} = ω_{c}^{2} + v^{2} k_{z}^{2}

v_{p} = ω / k_{z}

v_{g} = d ω / d k_{z} = v^{2} k_{z} / ω

\frac{v _{g}}{v _{p}} = 1 - \frac{ω _{c}^{2}}{ω ^{2}} = 1 - \frac{1}{9} = \frac{8}{9} .

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