Review questions for HW 4

1. What effect is the operation of optical fiber based on?

Totally internal reflection.

2. What are the 2 major factors that control the coupling of light into a fiber?

area of core > area of the beam, acceptance angle of the fiber < 0.5*divergence angle.

3. Which factor does numerical aperture (NA) determine?

The maximum input angle.

4. If n_1 is almost equal to n_2 and assumes typical value of n for glass, what is the value of percentage change in refractive index for a fiber with NA=0.1.

NA = n sqrt(2 * Delta) => Delta = 1/2 ({NA} /n)^2 = 1/2 (0.1/1.5)^2 = 0.222%

5. Consider a fiber with n_1=1.49, n_2=1.48 lambda = 1 micron, a = 2.5 micron.
a) Find NA and V.
b) Is this a single mode fiber?
c) Find the cutoff wavelength (the shortest wavelength) at which the fiber supports only a single mode.

a) NA = sqrt (n_1^2-n_2^2) = 0.1723, V = ( 2 pi ) / lambda a NA = 2.707
b) V > 2.405 => not single mode operation.
c) 2.405 = 2 pi {a NA} / lambda_c => lambda_c = 1.125 micron

6. For the fiber in 5., we try to couple a Gaussian (laser) beam with beam waist of 1 micron at wavelength of 1 micron.
a) Find the divergence angle of the beam.
b) Could the beam be optimally coupled into the fiber?

a) divergence angle = 2 lambda / ( pi w_o ) = 2/pi (radian)
b) acceptance angle = sin^{-1} (0.1723) = 0.173 < 0.5*divergence angle => not good
w_o < a => good
Overall, the coupling will not be optimal.

7. Repeat 6. with a Gaussian beam with beam waist of 2.6 micron. If the beam cannot be optimally coupled into the fiber, suggest a way to achieve this.

Divergence angle = 0.2449
2 times acceptance angle > divergence angle => good
w_o > a => not good.
we can use a lens to focus the beam to smaller size but need to re-check the divergence angle and make sure the distance between the fiber and the focus is less than z_o.

8. If we increase core radius of the fiber in 5. to 25 micron, how many modes can be supported by the fiber?

NA = sqrt (n_1^2-n_2^2) = 0.1723, V = (2 pi a NA) / lambda =27.06
Number of modes M = int (V^2/2) = 336

9. For a step index fiber, what are the two major types of dispersion? List them in order of increasing magnitude.

$D_{intra} < D_{modal}$

10. At what wavelength does the glass fiber have zero chromatic dispersion?

1.3 micron

11. Why single mode fiber is better than multimode ones?

It eliminates $D_{modal}$ by limiting the number of paths.

12. One of the drawbacks of single fiber system is cost. Why a single mode fiber system incurs higher cost?

Single mode fiber requires a laser to couple light into the system and alignment is very important.