lecture 14 - university of...
TRANSCRIPT
Lecture 14:
By considering what happens when a sinusoidal plane waveis incident on the surface of a dielectric, and using boundaryconditions, we will obtain the laws of optics and determine the fraction of transmitted / reflected light:
Demonstrate that EM waves incident on a boundary betweentwo dielectrics obey Snell’s law and laws of reflection
Describe total internal reflection and what is meant by evanescent wave
Describe significance of the critical angle, and Brewster angle
Derive Fresnel’s equations, and determine intensity of reflectedand transmitted beams
Last time: Reflection and refraction at dielectric interface
Incident, reflected andtransmitted wave vectorsare in yz plane x=0
Consider plane surfacez=0 separating dielectrics(1) and (2)
incident
reflected
transmitted
µr = 1
How much is reflected and how much transmitted
For simplicity, take plane wave and exclude TIR with n2 > n1
Two cases:1) E perpendicular (transverse) to the plane of incidence, i.e. parallel to the boundary (hence B is in the plane of incidence) TE caseHence wave polarization normal to the scattering plane
2) B perpendicular (transverse) to the plane of incidence, i.e. parallel to the boundary (hence E is in the plane of incidence) TM caseHence wave polarization in the scattering plane
Result for any other polarization can be derived from these two
x
Last time: TM wave polarization
Last time:
TIR
TM
Fresnel’s Laws
Ei
Er
Et
⊗⊗
⊗
Br
Bt
Bi
θtθiθi
(1) (2)
Bi
Br
Bt
ErEt
Ei
θtθiθi
(1) (2)
.
.
.
TM case: magne4cfield transverse toplane of incident – B isparallel to theboundary.
TE case: electric fieldtransverse to plane ofincident – E is parallel tothe boundary.
z
y
z
y
TE polarization
Similar analysis considering E parallel and H parallel produces:
TE(I)
TE(II)
Amplitude transmission and amplitude reflection ratiosfor incident E vector normal to the plane of incidence
θP = θB = Brewster angle
In general, any wave with a random spread of polarizationcan be expressed as linearcombination of TM and TE
At Brewster angle only TEcomponent is reflected, i.e.at this angle the reflected wave is polarized(only TE component)
θi + θt = π/2
ApplicationsPhotographyLaser spectroscopyEtc.
Fresnel’s laws for normal incidence θ =0
Proportions of power transmitted (transmittance) and reflected (reflectance) at the interface can be obtained from time-averaged Poynting vector:
Normal incidence:For example,air(1)-glass(1.5):R(0) = 0.04
Conservation of energy: T + R = 1
Wave impedance
In general, for LIH material:
Can be usedin Fresnel laws
Material with refractive index n (µr = 1):
Units: E (V/m) and H (Amps/m) so E/H has units of Ohms
EM wave in free space, propagating in z direction (E along x):
Worked Example:
a)
b)
a)
b) Left as homework
Summary
The impedance of the medium
Summary
Fresnel Laws
You should beable to derivethese laws
Recommended readings:Grant+Phillips: 11.6.2 11.6.4
Next Lecture:
EM waves in conductors
At the interface between 2 materials, with no free surface charge or current :
LIH materials,wave equation withvelocity
Similarly for B