Consider an LCD pixel as shown in the Figure 2. Assume the incident light is (left-hand) circularly polarized. The first (left) polarizer is vertical along the direction 'x', while the second (right) polarizer is horizontal along the direction 'y'. Assume the LC acts like a polarization rotator and has a twist coefficient a = 10 m- in um its natural state (no electric field applied). a. Write an expression for the Jones vector of the incident light Jin. b. Write an equation to represent the Jones matrix of the polarizers P1 and P2. c. Write an equation to represent the Jones matrix of the LC assuming its thickness is 0.5mm and the applied voltage is OV (Fig. 2a). d. Calculate the Jones vector of the transmitted light Jout for the case of part (c). e. Write an equation to represent the Jones matrix of the LC assuming the applied voltage modifies the twist coefficient to a, = 0.5 x 10 3n rad/um (Fig. 1b). f. (BONUS 2 points) Calculate the Jones vector of the transmitted light Jout for the case of part (e). g. (BONUS 3 points) Calculate the output intensity relative to the incident intensity for the case of part (e). (a) Polarizer Twisted nematic cell in natural state Polarizer ransmitted light Incident light P1 P2 (b) Polarizer Twisted nematic cell in presence of electric field Polarizer Incident light Blocked light Electric field Figure 2: A twisted nematic liquid crystal (LC) between crossed polarizers. Hint: The Jones matrix of a polarization rotator that rotates the angle of linear polarization by an angle 0 is T = cos 0 - sin 0] sin 0 cos 0