Part II. Wave Motion. The laser light used in optical fibres has a frequency of about 198 THz while the speed of propagation within the fibre is near 2 x 108 m/s. If we let z be the position along the length of the fibre in meters and t represent time in seconds then the electric field intensity along the fibre is given as,E = Eo * exp(j*(omega*t-beta*z)),which is both a function of position and time. Note that omega is the radian frequency (2*pi*f) and beta is the phase shift coefficient which equals (omega / speed of propagation). Eo is the initial condition and can be set to equal 1.0 V/m. Case A. Plot the field at one instant in time. Plot the real part of this field over the range of z from 0 to 10 ?m at t=0. Label the axis and submit this with your report. Case B. Observe what happens as time advances. The period of a 198 THz wave is about 5 x 10 -15 seconds so to see movement, increment the time in steps of one tenth of a period. In a for loop step time through two periods and watch what happens to the plot. Record your observations. Remember to plot the real part of E. Case C. Propagation in the other direction. A wave traveling in the opposite direction is given by E = Eo * exp(j*(omega*t+beta*z)), note the change in sign. Change the sign in your Case B code above, run it and record the difference. Case D. Interference pattern of two waves. It is a common occurrence in transmission lines, including optical fibre, for there to exist waves propagating in both directions. The total field in the optical fibre is just the sum of the two waves. Generate both waves then add them together to produce the total field. Use the subplot feature to produce three plots in the same figure. Plot the forward wave, the reverse wave and the total wave. Remember to plot the real part of these complex numbers. This interference pattern is known as a standing wave pattern and normally only the amplitude of the pattern is observed. This can be achieved in your plot by taking the abs(real(total field)). Note your observations of the standing wave pattern. Label the axes of these plots and submit one plot at t = 0 as part of the lab report. Case E. An optional challenge. Our optical fibre strain and temperature sensing research instrument uses the interference pattern of two counter propagating lasers to excite and interrogate acoustic waves in the glass. The speed of this acoustic wave is determined by the glass temperature and strain. Observe what happens when one of the lasers is set to a frequency 10 GHz higher than the other. Hint � observe the interference pattern over a much longer time 120 ps instead of 10 fs. Record your observations.