Exercise 4.1 (Transmission grating) Consider a transmission diffraction grating. Suppose that we wish to use this grating to separate out different wavelengths of information in a WDM signal at 1550 nm transmitted through an optical fiber (WDM stands of wavelength division multiplexing.) Suppose that the diffraction grating has a periodicity of 2 Î¼m. The angle of incidence is 0Â° with respect to the normal to the diffraction grating.
(a) Describe in not more than 50 words what is WDM.
(b) What is the angular separation of the intensity peaks associated with the first order diffraction peaks, for two different wavelength components at 1.550 Î¼m and 1.540 Î¼m?
(c) If a CCD camera with a pixel size of 5 Î¼m is used to detect the signals, how far away from the diffraction grating should the CCD camera be placed to ensure that the pixels detecting the two wavelengths are separated by at least 10 other pixels to avoid cross-talk between the signals.

Exercise 4.2 (Coherence lengths) Find the coherence length of the following light sources that can be used for optical fiber communication.
(a) An LED emitting at 1550 nm with a spectral width 150 nm.
(b) A semiconductor laser diode emitting at 1550 nm with a spectral width 3 nm.
(c) A quantum well semiconductor laser diode emitting at 1550 nm with a spectral with of 0.1 nm.

Exercise 4.3 (Single mode fiber) Consider a fiber with a core of diameter
of 8Î¼m and refractive index of 1.468 and a cladding with refractive index of 1.464 (both at 1300 nm where the fiber is operated).
(a) Calculate the V-number for the fiber. Is this a single mode fiber?
(b) Calculate the wavelength below which the fiber becomes multimode.
(c) Calculate the numerical aperture.
(d) Calculate the maximum acceptance angle.
(e) Using the dispersion graph from Figure 2.22, page 125 (â€œOptoelectronics and Photonics 2nd editionâ€ by S.O. Kasap; Note: in the 1st edition the corresponding figure is Figure 2.21 page 77), calculate the bit rate x distance product (B x L) of the fiber, if the laser source use has a full width at half maximum (FWHM) of 3nm.

Exercise 4.4 (GRIN Lenses) Problem 2.29, Page 174, â€œOptoelectronics and Photonics 2nd editionâ€ by S.O. Kasap (Note: in the 1st edition the problem is Problem 2.16, Page 105).

Exercise 4.1 (Transmission grating) Consider a transmission diffrac...