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Assignment 1 (5 points + 1 bonus point) [Due on Tuesday, Feb. 7, hand-in at the class] 1. Derive the wave equation in a source-less free-space from the Maxwell equations and find the general solution. (1 point) 2. Find the fundamental (TE) mode electric field distribution in a triple-layer slab waveguide: the quartz (SiO2) substrate has a refractive index of 1.5, the core layer in 1μm thick is made of lead glass (PbO-SiO2) with a refractive index of 1.7, the cladding is simply air with a refractive index of 1. Find the associated magnetic field distribution. (2 points) Assuming the operating wavelength is 650nm (the red light), how to make this waveguide single-moded? (1 bonus point) 3. Find the core radius necessary for single-mode operation at 1550nm of a step-index fibre with n1 =1.480 and n2 =1.478. What is the numerical aperture? If the optical signal has a lost of 55 percent of its power after traversing 20km of this fibre, what is the attenuation in dB/km? (1 point) 4. A certain optical fibre has an attenuation of 0.6dB/km at 1300nm and 0.3dB/km at 1550nm. Suppose the following two optical signals are launched simultaneously into the fibre: an optical power of 250W at 1300nm and an optical power of 100W at 1550nm. What are the power levels in W of these two signals at (a) 8km and (b) 20km? (1 point) 1

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