2. (*) In the Mach-Zehnder interferometer shown below, two input waves denoted by electric fields E1...

  

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2. (*) In the Mach-Zehnder interferometer shown below, two input waves denoted by electric fields E1 and E2 are combined in a 50:50 beam splitter, resulting in a wave EA travelling in the lower arm and a wave EB travelling in the upper arm of the MZI. The two arms have equal length L with the upper arm having an extra phase shift A = /2 relative to the lower arm. The waves in the two MZI arms are combined using another 50:50 beam splitter to give an output wave Eout. The transmitted and reflected waves of the two beam splitters are shown below on the right. mirror L EB = E out EB E, E E A L mirror 2 Ein E in 50:50 beam splitter EA = -Ein Ein (a) Derive an expression for the output electric field Eour in terms of the input fields E1 and E2. (b) If the electric fields of the input waves are given by E = Eejut and E = 2Eoejot, with Eo = 100 V/m, calculate the intensity of the output wave out. Assume free space propagation in the MZI with refractive index n = 1. 2. (*) In the Mach-Zehnder interferometer shown below, two input waves denoted by electric fields E1 and E2 are combined in a 50:50 beam splitter, resulting in a wave EA travelling in the lower arm and a wave EB travelling in the upper arm of the MZI. The two arms have equal length L with the upper arm having an extra phase shift A = /2 relative to the lower arm. The waves in the two MZI arms are combined using another 50:50 beam splitter to give an output wave Eout. The transmitted and reflected waves of the two beam splitters are shown below on the right. mirror L EB = E out EB E, E E A L mirror 2 Ein E in 50:50 beam splitter EA = -Ein Ein (a) Derive an expression for the output electric field Eour in terms of the input fields E1 and E2. (b) If the electric fields of the input waves are given by E = Eejut and E = 2Eoejot, with Eo = 100 V/m, calculate the intensity of the output wave out. Assume free space propagation in the MZI with refractive index n = 1.