Question 9.6: GROUP AND PHASE VELOCITIES Consider a light wave traveling i...

GROUP AND PHASE VELOCITIES   Consider a light wave traveling in a pure SiO_{2} (silica) glass medium. If the wavelength of light is 1300 nm and the refractive index at this wavelength is 1.447, what is the phase velocity, group index (N_{g}), and group velocity (v_{g})?

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The phase velocity is given by

v=\frac{c}{n}=\frac{3 \times 10^{8}  m  s ^{-1}}{1.447}=2.073 \times 10^{8}  m  s ^{-1}

From Figure 9.6, at λ = 1300 nm, N_{g} = 1.462, so

v_{g}=\frac{c}{N_{g}}=\frac{3 \times 10^{8}  m  s ^{-1}}{1.462}=2.052 \times 10^{8}  m  s ^{-1}

The group velocity is ∼0.7 percent smaller than the phase velocity.

9.6

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