1) Suppose you have two Gaussian laser pulses that have carrier frequencies ml. and w? and the same bandwidth lm. (To he specific, the spectra of the two pulses are e'lw'w''swz. and r3\"\"'_\"'2l2/5\"2). The carrier frequencies are different enough so that. w] w {432' > (in) so that the spectra are well separated. The}; pulses arrive on a fast photodetector at the same time. and the os(':illoseope (also fast) records the time-depenclent intensity. (a) Calculate the functional form for the time dependent intensity of the two overlapped pulses. (1)) Numerical calculations. Assume that the detection system (photodetector and oscilloscope) can measure a maximum frequency of 5 GHz. If we want to he sure to measure the beat frequency from part (a), and an corresponds to A1 = 500nm, what the maximum separation between the input wavelengths that we can use? What constraints does this place on the minimum duration of the pulses? (c) Temporal phase measurement. One of the two pulses passes through a medium that has a rapidly changing refractive index, so that the pulse experiences a temporal phase 0(1) : 3t2.Show how this changes your expression for the measured time dependent intensity. In this scenario, the duration of the individual pulses can be much longer (narrower bandwidth} than the minimum duration calculated in part. (b)