Optics 430530 week IV Brewster and critical angles

Optics 430/530, week IV • Brewster and critical angles This class notes freely use material from http: //optics. byu. edu/BYUOptics. Book_2015. pdf P. Piot, PHYS 430 -530, NIU FA 2018 1

Conditions on E components (I) • The eqn in medium i gives the condition: in medium t • Likewise, considering the magnetic field gives P. Piot, PHYS 430 -530, NIU FA 2018 2

Condition on E components (II) • sum dif fe ren ce P. Piot, PHYS 430 -530, NIU FA 2018 3

Fresnel’s coefficients (I) P. Piot, PHYS 430 -530, NIU FA 2018 4

Fresnel’s coefficients(II) ni=1, nt=1. 5 ni=1, nt=. 10 P. Piot, PHYS 430 -530, NIU FA 2018 5

Reflectance & Transmittance • P. Piot, PHYS 430 -530, NIU FA 2018 6

Reflectance • Reflectance is defined as • So that and given the previous slides’ power-conservation laws we have: P. Piot, PHYS 430 -530, NIU FA 2018 7

Transmittance • P. Piot, PHYS 430 -530, NIU FA 2018 8

Brewster’s angle (I) • P. Piot, PHYS 430 -530, NIU FA 2018

Brewster’s angle (II) • P. Piot, PHYS 430 -530, NIU FA 2018

Total internal reflection (I) • P. Piot, PHYS 430 -530, NIU FA 2018 11

Total internal reflection (II) • Let’s compute the reflection coefficient with • Which gives and P. Piot, PHYS 430 -530, NIU FA 2018 12

Total internal reflection (III) • It is straightforward to see that both coefficient of reflection have a unity modulus. • So the light is totally reflected. • Reckon that the electric field of the transmitted wave is evanescent wave in z P. Piot, PHYS 430 -530, NIU FA 2018 13

Multiple Parallel Interfaces (chapt. 4) P. Piot, PHYS 430 -530, NIU FA 2018 14

• At the first surface in the direction from medium 0 to 1 we have P. Piot, PHYS 430 -530, NIU FA 2018 15

• P. Piot, PHYS 430 -530, NIU FA 2018 16

• At the second surface in the direction from medium 1 to 2 we have P. Piot, PHYS 430 -530, NIU FA 2018 17

Total field • Forward propagating in region 1: • Backward propagating in region 0: • Forward propagating in region 2: • Backward propagating in region 1: We use the fact that and P. Piot, PHYS 430 -530, NIU FA 2018 18

Edmund Optics www Application: antireflection coating (I) • P. Piot, PHYS 430 -530, NIU FA 2018 19

Application: antireflection coating (II) P. Piot, PHYS 430 -530, NIU FA 2018 20