Question

Question 1 (25 marks) (a) Using a diagram, derive an expression for numerical aperture assuming light is incident on a step-index fiber. Briefly explain the significance of numerical aperture. (b) A source emits light with an optical power $P_0$. If the emitted power distribution per solid angle in the direction making an angle $\theta$ with a fiber axis is given by $$I(\theta) = \frac{1}{\pi}P_0 \cos(\theta),$$ show that the power collected by the fiber is $$P = (NA)^2 P_0$$ where NA is the numerical aperture of the fiber. (c) Using the definition of group velocity show that the group velocity can be written as $$v_g = v - \lambda \frac{dv}{d\lambda},$$ where $v$ is the phase velocity. (d) Explain what is meant by cut-off wavelength in an optical fiber. (e) A step-index fiber which has a diameter of 10 µm with a cladding refractive index $n_2 = 1.443$ operates at 1.55 µm. Determine the core index at which the fiber V parameter is 10.

          Question 1 (25 marks)
(a) Using a diagram, derive an expression for numerical aperture assuming light is incident
on a step-index fiber. Briefly explain the significance of numerical aperture.
(b) A source emits light with an optical power $P_0$. If the emitted power distribution per
solid angle in the direction making an angle $\theta$ with a fiber axis is given by
$$I(\theta) = \frac{1}{\pi}P_0 \cos(\theta),$$
show that the power collected by the fiber is
$$P = (NA)^2 P_0$$
where NA is the numerical aperture of the fiber.
(c) Using the definition of group velocity show that the group velocity can be written as
$$v_g = v - \lambda \frac{dv}{d\lambda},$$
where $v$ is the phase velocity.
(d) Explain what is meant by cut-off wavelength in an optical fiber.
(e) A step-index fiber which has a diameter of 10 µm with a cladding refractive index
$n_2 = 1.443$ operates at 1.55 µm. Determine the core index at which the fiber V parameter
is 10.

$Question 1 (25 marks) (a) Using a diagram, derive an expression for numerical aperture assuming light is incident on a step-index fiber. Briefly explain the significance of numerical aperture. (b) A source emits light with an optical power P0. If the emitted power distribution per solid angle in the direction making an angle θ with a fiber axis is given by I(θ) = (1)/(π)P0 cos(θ), show that the power collected by the fiber is P = (NA)^2 P0 where NA is the numerical aperture of the fiber. (c) Using the definition of group velocity show that the group velocity can be written as vg = v - λ(dv)/(dλ), where v is the phase velocity. (d) Explain what is meant by cut-off wavelength in an optical fiber. (e) A step-index fiber which has a diameter of 10 µm with a cladding refractive index n2 = 1.443 operates at 1.55 µm. Determine the core index at which the fiber V parameter is 10.$

Added by Cody F.

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