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Todays summary Polarization Energy / Poyntings vector Reflection and refraction at a dielectric interface: –wave approach to derive Snells law –reflection.

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Presentation on theme: "Todays summary Polarization Energy / Poyntings vector Reflection and refraction at a dielectric interface: –wave approach to derive Snells law –reflection."— Presentation transcript:

1 Todays summary Polarization Energy / Poyntings vector Reflection and refraction at a dielectric interface: –wave approach to derive Snells law –reflection and transmission coefficients –total internal reflection (TIR) revisited

2 Polarization

3 Propagation and polarization In isotropic media (e.g. free space, amorphous glass, etc.) More generally, (reminder :Anisotropic in media, e.g. crystals, one could E not have parallel to D) planar wavefront electric field vector E wave-vector k

4 Linear polarization (frozen time)

5 Linear polarization (fixed space)

6 Circular polarization (frozen time)

7 Circular polarization: linear components

8 Circular polarization (fixed space)

9 /4 plate Linearpolarization Linear polarization birefringent l/4 plate Circularpolarization Circular polarization

10 λ/2 plate Linear (90 o -rotated) polarization Linearpolarization Linear polarization birefringent λ/2 plate

11 Think about that mirror birefringent λ /4 plate Linearpolarization Linear polarization

12 Relationship between E and B Vectors k, E, B form a right-handed triad. Note: free space or isotropic media only

13 Energy

14 The Poynting vector S has units of W/m2 so it represents energy flux (energy per unit time & unit area)

15 Poynting vector and phasors (I) For example, sinusoidal field propagating along z Recall: for visible light, ω~ Hz

16 Poynting vector and phasors (II) Recall: for visible light, ω~ Hz So any instrument will record the average average incident energy flux where T is the period (T=λ/c) irradianceintensity is called the irradiance, aka intensity of the optical field (units: W/m2)

17 Poynting vector and phasors (III) 2 For example: sinusoidal electric field, Then, at constant z:

18 Poynting vector and phasors (IV) Recall phasor representation: complex amplitude or " phasor": Can we use phasors to compute intensity?

19 Poynting vector and phasors (V) two same Consider the superposition of two fields of the same frequency: phasors Now consider the two corresponding phasors:

20 Poynting vector and phasors (V) two same Consider the superposition of two fields of the same frequency: phasors Now consider the two corresponding phasors: and the quantity

21 Poynting vector and irradiance

22 Reflection/Refraction Fresnelcoefficients

23 Reflection & dielectric interface

24

25 I. Polarization normal to plane of incidence

26 Reflection & dielectric interface I. Polarization normal to plane of incidence

27 Reflection & dielectric interface I. Polarization normal to plane of incidence Continuity of tangential electric field at the interface: Since the exponents must be equal for all x, we obtain

28 Reflection & dielectric interface I. Polarization normal to plane of incidence Continuity of tangential electric field at the interface: law of reflection Snells law of refraction so wave description is equivalent to Fermats principle!!

29 Reflection & dielectric interface I. Polarization normal to plane of incidence Incident electric field: Reflected electric field: Transmitted electric field: Need to calculate the reflected and transmitted amplitudes E0r, E0t two i.e. need two equations

30 Reflection & dielectric interface I. Polarization normal to plane of incidence Continuity of tangential electric field at the interface gives us one equation: which after satisfying Snells law becomes

31 Reflection & dielectric interface I. Polarization normal to plane of incidence The second equation comes from continuity of tangential magnetic field at the interface:

32 Reflection & dielectric interface I. Polarization normal to plane of incidence So continuity of tangential magnetic field Bx at the interface y=0 becomes:

33 Reflection & dielectric interface I. Polarization normal to plane of incidence

34 Reflection & dielectric interface II. Polarization parallel to plane of incidence Following a similar procedure...

35 Reflection & dielectric interface

36 energy Reflection & transmission of dielectric interface Recall Poynting vector definition: different on the two sides of the interface

37 Energy conservation

38 energy Reflection & transmission of dielectric interface

39 Normal incidence

40 Brewster angle Recall Snells Law This angle is known as Brewsters angle. Under such circumstances, for an incoming unpolarized wave, only the component polarized normal to the incident plane will be reflected.

41 Why does Brewster happen? elemental dipole radiator excited by the incident field

42 Why does Brewster happen?

43

44

45 Turning the tables Is there a relationship between r, t and r, t ?

46 Relation between r, r and t, t Proof: algebraic from the Fresnel coefficients or using the property of preservation of the preservation of the field properties upon time reversal

47 Proof using time reversal

48 Total Internal Reflection Happens when Substitute into Snells law no energy transmitted

49 Total Internal Reflection Propagating component no energy transmitted

50 Total Internal Reflection Pure exponential decay º evanescent º evanescent wave It can be shown that: no energy transmitted

51 Phase delay upon reflection

52 Phase delay upon TIR

53


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