Electromagne,c Waves. All electromagne-c waves travel in a vacuum with the same speed, a speed that we now call the speed of light.

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1 Electromagne,c Waves All electromagne-c waves travel in a vacuum with the same speed, a speed that we now call the speed of light.

3 Proper,es of Electromagne,c Waves Any electromagne-c wave must sa-sfy four basic condi-ons: 1. The fields E and B and are perpendicular to the direction of propagation v em.thus an electromagnetic wave is a transverse wave. 2. E and B are perpendicular to each other in a manner such that E B is in the direction of v em. 3. The wave travels in vacuum at speed v em = c 4. E = cb at any point on the wave.

4 Proper,es of Electromagne,c Waves The energy flow of an electromagne-c wave is described by the Poyn,ng vector defined as The magnitude of the Poyn-ng vector is The intensity of an electromagne-c wave whose electric field amplitude is E 0 is

Radia,on Pressure It s interes-ng to consider the force of an electromagne-c wave exerted on an object per unit area, which is called the radia,on pressure p rad.

5 Radia,on Pressure It s interes-ng to consider the force of an electromagne-c wave exerted on an object per unit area, which is called the radia,on pressure p rad. The radia-on pressure on an object that absorbs all the light is energy absorbed Δp = c F = Δp energy absorbed = Δt c ( E = pc) ( ) / Δt = P c where P is the power (joules per second) of the light. where I is the intensity of the light wave. The subscript on p rad is important in this context to dis-nguish the radia-on pressure from the momentum p.

6 Example Solar sailing

7 Intermediate/Advanced Concepts

8 Wave equa-ons in a medium The induced polariza-on in Maxwell s Equa-ons yields another term in the wave equa-on: E z E t 2 2 µε = E 1 E = z v t This is the Inhomogeneous Wave Equa,on. The polariza-on is the driving term for a new solu-on to this equa-on. E z E t 2 2 µε = E 1 E = z c t Homogeneous (Vacuum) Wave Equa,on 0 E ( zt) ikz ( ωt), = Re{ E e } = + 0 ikz ( ωt) * ikz ( ωt) { E e E e } ( kz ωt) = E cos n 2 2 c = = 2 v µε µε 0 0 c v = n

9 Propaga-on of EM Waves

10 Polariza-on and Propaga-on

11 Energy and Intensity S=E H Poyn,ng vector describes flows of E- M power Power flow is directed along this vector (usually parallel to k) Intensity is average energy transfer (i.e. the -me averaged Poyning vector: I=<S>=P/A, where P is the power (energy transferred per second) of a wave that impinges on area A. sin 2 ( kx ωt) = cos 2 ( kx ωt) = 1 2 cε cε S = I E t H t = E = E + E x cε A/ V 0 example E = 1 V / m ( ) ( ) ( 2 2) I =? W / m y hω[ ev ] = λ[ nm] h = Js

12 Polariza-on & Plane of Polariza-on

13 Linear versus Circular Polariza-on

14 Linear polariza-on (frozen -me)

15 Linear polariza-on (fixed space)

16 Circular polariza-on (linear components)

17 Circular polariza-on (frozen -me)

18 Circular polariza-on (fixed space)

r ẑ or t right circular polariza-on Ex r Phase difference è 90 0 (π/2, λ/4) leu circular

19 ŷ E = E x e iδ x ˆx + E y e iδ y ŷ Polariza-on: Summary ŷ E! xˆ xˆ linear polariza-on y- direc-on Phase difference δ = δ x δ y Phase difference = 0 0 Ex r ẑ or t right circular polariza-on Ex r Phase difference è 90 0 (π/2, λ/4) leu circular polariza-on (+: posi-ve helicity ) ẑ Ex r leu ellip-cal polariza-on Phase difference è (π, λ/2) ẑ E! y ẑ E! y ẑ E! y ẑ

20 Polariza-on Applets Polariza-on Explora-on h_p://webphysics.davidson.edu/physlet_resources/dav_op-cs/examples/polariza-on.html 3D View of Polarized Light h_p://fipsgold.physik.uni- kl.de/souware/java/polarisa-on/index.html

21 Quarter wave plate

22 Half wave plate

23 Quiz for the Lab Bonus Credit 0.2 pts

24 Methods for genera-ng polarized light h_p://hyperphysics.phy- astr.gsu.edu/hbase/phyopt/polar.html

25 Polariza-on by Reflec-on h_p://hyperphysics.phy- astr.gsu.edu/hbase/phyopt/polar.html

26 A Polarizing Filter

27 Malus s Law Suppose a polarized light wave of intensity I 0 approaches a polarizing filter. θ is the angle between the incident plane of polariza-on and the polarizer axis. The transmi_ed intensity is given by Malus s Law: If the light incident on a polarizing filter is unpolarized, the transmi_ed intensity is In other words, a polarizing filter passes 50% of unpolarized light and blocks 50%.

28 Malus s Law

29 Polarized sunglasses

30 Brewster Angle

31 Polariza-on by sca_ering (Rayleigh sca_ering/blue Sky)

32 Circularly polarized light in nature

33 Morphology and microstructure of cellular pa_ern of C. gloriosa

34 Reflec-on and dielectric interface

35 Beyond Snell s Law: Polariza-on?

36 Reflec-on and Transmission (Fresnel s equa-ons) Can be deduced from the applica,on of boundary condi,ons of EM waves. An online calculator is available at hjp://hyperphysics.phy- astr.gsu.edu/hbase/phyopt/freseq.html

37 Reflec-on and Transmission of dielectric interfaces

38 Reflec-on and Transmission (Fresnel s equa-ons) Can be deduced from the applica,on of boundary condi,ons of EM waves.

39 Reflec-on and Transmission of dielectric interfaces

40 Energy Conserva-on

41 Normal Incidence

42 Reflectance and dielectric interfaces

Review: Basic Concepts

Review: Basic Concepts Simula5ons 1. Radio Waves h;p://phet.colorado.edu/en/simula5on/radio- waves 2. Propaga5on of EM Waves h;p://www.phys.hawaii.edu/~teb/java/ntnujava/emwave/emwave.html 3. 2D EM Waves