TIME: The allowed time period is 180 minutes (3 hours).

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1. The AlGaAs semiconductor lasers used in CD players have a wavelength of 0.78 µm. i) how many photons/sec are produced by the laser if the output power is 3 mW? ii) the new DVD (digital video disc) technology uses InGaAlP semiconductor lasers with a wavelength of 630 nm. At 3 mW output power, will these DVD lasers generate more or less photons than CD lasers?

2. When an electromagnetic wave propagates from one medium with an index of refraction of n1 = 2.5 into a second medium with an index of refraction of n2 = 1.8,

a) only the frequency changes,

b) only the wavelength changes,

c) both the frequency and the wavelength change, and/or

d) the frequency and the wavelength both remain the same.

Briefly explain your answer:

4. Briefly explain material dispersion.

5. Briefly explain waveguide dispersion.

6. Briefly explain modal distortion.

7. A lens system is used to collect the light from a laser diode source (which has an angular spread of 42°) into an optical fiber with an acceptance angle of 8°.

i) what is the resulting magnification of the lens system?

ii) if the diameter of the optical spot at the laser facet is 3 µm, and the core of the fiber is 10 µm, will the image of the optical spot at the facet be larger than, equal to, or less than the core of the fiber?

9. i) what is the critical angle for a ray in AlGaAs (with an index of 3.45) if the material outside the AlGaAs is air?

ii) What is the criteria for a critical angle to exist between two media with indices of refraction n1 and n2?

10. A semiconductor laser emits optical radiation with a free space wavelength of 1.57 µm. What is the i) frequency, ii) velocity, and iii) wavelength of the optical radiation inside the semiconductor laser? Assume that the index of refraction of the semiconductor laser material is 3.47.

11. What is the maximum number of analog phone calls (voice channels) that can possibly be squeezed onto an optical fiber if the light has a wavelength of 1.55 µm? (be sure to state any assumptions.)

13. A lens with a focal length of 0.5 cm is used to focus light with a wavelength of 630 nm to a spot. In one case, light of a uniform intensity (across the lens) is focused. In the second case, light with a Gaussian distribution (across the lens) is focused.

i) describe the distribution of the light at the focus in both cases.

ii) which intensity distribution at the lens results in the smallest spot size at the focus?

14. The index of refraction in an optically transparent material is given by:

a) what is the index of refraction of this material at a wavelength of 1.3 µm?

b) what is the phase velocity of an optical wave propagating in this material if the wavelength of the light is 1.3 µm?

15. For the same optically transparent material described in problem 14, find a mathematical expression for the group index for optical waves with wavelengths between 0.7 µm and 3.0 µm.

17. Consider a symmetric slab waveguide (or a circular step-index fiber waveguide). If all parameters are held constant except the index of the core decreases, will the number of propagating modes increase or decrease? Briefly explain.

18. Consider a symmetric slab waveguide (or a circular step-index fiber waveguide). If all parameters are held constant except the wavelength increases, will the fraction of the energy (of the fundamental propagating mode) in the cladding regions increase, decrease, or remain the same? Briefly explain.

19. The middle layer of a three-layer symmetric slab waveguide has a thickness of 3 µm. The wavelength of light propagating in the waveguide is such that 7 modes can propagate. For this waveguide, a) qualitativley sketch the TE₂ field distribution, and b) qualitativley sketch the TE₄ intensity distribution. c) which mode (TE₂ or TE₄) has the higher effective index?

20. The answer is 2.405. What is the question?

21. Qualitatively sketch a) the index of refraction, b) the first derivative of the index of refraction, and c) the second derivative of the index of refraction as a function of wavelength (over the range 0 to 3 µm) for a typical glass (such as quenched SiO2) that is used in making optical fibers.

22. On the same graph, qualitatively sketch and label both the index of refraction and the group index of refraction for the same glass discussed in problem 21.

23. Find the contribution to pulse spreading in a standard step index fiber (n₁ = 1. 67 and n₂ = 1.57, V = 2.25) which is due to material dispersion if the optical source is a laser operating at a free space wavelength of 1.57 µm. The dfb laser has a spectral emission width of 0.1 Å. The length of the silica fiber is 25 km. The fiber is made from quenched SiO2.

24. Consider the same standard step index fiber (n₁ = 1. 67 and n₂ = 1.57, V = 2.25) described in problem 23.

a) find the amount of pulse spreading in the fiber due only to waveguide dispersion if the optical source is a laser operating at a free space wavelength of 1.57 µm. The dfb laser has a spectral emission width of 0.1 Å. The length of the silica fiber is 25 km. The fiber is made from quenched SiO2.

b) what is the total (material and waveguide) dispersion for this fiber?

25. What is the 3-dB optical bandwidth of the system described in problems 23 and 24?

26. A step-index fiber with a core and cladding index of n₁ = 1. 67 and n₂ = 1.57 has a V number of 25. What is the pulse spread due only to energy being distributed among multiple modes for a 30 km fiber if the optical source is a laser operating at a free space wavelength of 1.57 µm with a spectral width of 0.1 Å? The fiber is made from quenched SiO2.

27. Briefly discuss dispersion-shifted and dispersion-flattened fibers. Indicate a possible index profile for each type.

28. Which of the following waveguides can be designed so that no optical mode can propagate? Another way to ask this question is which waveguides can be designed to have all modes below cut-off? (Assume a finite, non-zero slab or core thickness and that the core or inner region has a higher index than the cladding regions.)

a) symmetric slab waveguides

b) step-index circular fiber waveguides

c) asymmetric slab waveguides

29. An ideal laser diode has a threshold current of 12 mA and a "slope efficiency" of 0.25 mW/mA.

i) Sketch the light (optical output power) versus drive current for this device for a current range of 0 to 100 mA.

ii) How much optical power is emitted at a drive current of 50 mA?

32. For a fiber system that uses Honeywell VCSELs (with a lasing wavelength of 0.85 µm) as optical sources, would you choose a Si, InGaAs, or Ge detector? Explain your choice.

33. An InGaAs PIN photodiode has a responsivity of 0.6 A/W at a wavelength of 1.55 µm. If 80 µW of 1.55 µm radiation are incident on the detector, what current (ideally) flows through the load resistor in a simple PIN circuit?

34. The principle of least time can be used to derive

a) Snell's law,

b) the law of refraction,

c) the law of reflection,

d) the thin lens equation,

e) the graded index profile of a GRIN lens

f) the index profile of a GRIN lens

g) the best path for a lifeguard to rescue a drowning person