(7.14) Consider a 50:50 beam splitter with input fields of Ei and E2 and output fields of E3 and E4 as shown in Fig. 7.1

[answerhappygod]

7 14 Consider A 50 50 Beam Splitter With Input Fields Of Ei And E2 And Output Fields Of E3 And E4 As Shown In Fig 7 1 1 (109.66 KiB) Viewed 82 times

(7.14) Consider a 50:50 beam splitter with input fields of Ei and E2 and output fields of E3 and E4 as shown in Fig. 7.17. Let the phase shifts of the fields on transmission and reflection be written 4 and 0%, respectively, where i = 1, 2. Assume that Ej and E2 are real. (a) Verify that the output fields must be in the form: E3 = 1a [Ei exp (i$i) + E2 exp (193)], ] E4 € 1 exp (i$i) + E2 exp (101)]. (b) By considering conservation of energy, show that: cos(02 – $i) + cos(01 - 03) = 0. (c) The phase change on transmission is usually taken to be zero, which implies that: cos + cos 61 = 0. Show that this condition is satisfied when there is a relative phase difference of a between the two reflections. 3 ပ်) E EX 50:50 Et Fig. 7.17 The 50:50 beam splitter.