As a first year graduate student, you are assigned to assist a 3d year ph. d. student with his thesis project -working with optical communications devices. the senior student tells you to characterize a waveguide that is 10 m long and lossless. the waveguide can be treated as a parallel plate waveguide filled with a spacing of 2.5 mm between the plates (which can be treated as perfect conductors). inside the waveguide is a dielectric with & 9eo and does not depend on frequency. you will be sending pulses at the frequencies 27 ghz, 30 ghz, 35 ghz and 39.5 ghz a) which modes will propagate in the waveguide? b) what are the group velocities for the pulse in each mode? what are the phase velocities? c) for each mode higher than tem, calculate group delay of each pulse at the end of the waveguide. d) what type of dispersion, if any, does each pulse experience in each mode? partial solution: (b) tm: v c/n=1 x 10 m/s. tmi, te: v67.2x 10 m/s, 74.5 x 10 m/s, 82.1 x 10 m/s, 86.2 x 10°m/s; v149 x 10 m/s, 1.34 x 10 m/s, 1.22 x 10 m/s, 1.16 x 10 m/s. (c) tmo: 33.3 ns. tm, te: 149 ns, 134 ns, 122 ns, 116 ns.