Plane wave reflection 2014mk

Plane Wave Reflection at Oblique Incidence Angles 6.. Plane Wave Reflection at Oblique Incidence Angles 6.. Plane Wave Reflection at Oblique Incidence Angles 6.. Wave Reflection from Mul

Engineering Electromagnetics

Plane Wave Reflection & Dispersion

Nguy ễ n Công Ph ươ ng

I Introduction

II Vector Analysis

III Coulomb’s Law & Electric Field Intensity

IV Electric Flux Density, Gauss’ Law & Divergence

V Energy & Potential

VI Current & Conductors

VII Dielectrics & Capacitance

VIII Poisson’s & Laplace’s Equations

IX The Steady Magnetic Field

X Magnetic Forces & Inductance

XI Time – Varying Fields & Maxwell’s Equations

XII Transmission Lines

XIII The Uniform Plane Wave

XIV Plane Wave Reflection & Dispersion

XV Guided Waves & Radiation

Plane Wave Reflection & Dispersion

1 Reflection of Uniform Plane Waves at Normal

Incidence

2 Standing Wave Ratio

3 Wave Reflection from Multiple Interfaces

4 Plane Wave Propagation in General Directions

5 Plane Wave Reflection at Oblique Incidence Angles

6 Wave Propagation in Dispersive Media

Reflection of Uniform Plane Waves at Normal Incidence (1)

Reflection of Uniform Plane Waves at Normal Incidence (2)

x

x

E E

η η

η η

− +

−

1 2 10

η τ

η η

+ +

Reflection of Uniform Plane Waves at Normal Incidence (3)

10 2 1

2 1 10

η τ

η η

+ +

ωµ η

Reflection of Uniform Plane Waves at Normal Incidence (4)

10 2 1

2 1 10

η τ

η η

+ +

Reflection of Uniform Plane Waves at Normal Incidence (5)

10 2 1

2 1 10

η τ

η η

+ +

1

xs ys

E H

η

+ + =

1 1

1

xs ys

E H

1

( j z j z )

x ys

Reflection of Uniform Plane Waves at Normal Incidence (6)

10 2 1

2 1 10

η τ

η η

+ +

+

Region 1 is dielectric, region 2 is dielectric:

η1 & η2 are positive real values,

Reflection of Uniform Plane Waves at Normal Incidence (7)

Given η1 = 100Ω, η2 = 300Ω, Find the incident, reflected, and transmitted waves.

Reflection of Uniform Plane Waves at Normal Incidence (8)

1 1 Re

1

1 1 Re

ˆ ˆ

Plane Wave Reflection & Dispersion

1 Reflection of Uniform Plane Waves at Normal

Incidence

2 Standing Wave Ratio

3 Wave Reflection from Multiple Interfaces

4 Plane Wave Propagation in General Directions

5 Plane Wave Reflection at Oblique Incidence Angles

6 Wave Propagation in Dispersive Media

Standing Wave Ratio (1)

Standing Wave Ratio (2)

/ 2

λ

2

ϕ π β

+

−

2 2

ϕ π β

+

−

4 2

ϕ π β

+

−

6 2

β

+

−

Standing Wave Ratio (3)

Standing Wave Ratio (4)

xs

xs

E s

E

+ Γ

− Γ

Plane Wave Reflection & Dispersion

1 Reflection of Uniform Plane Waves at Normal

Incidence

2 Standing Wave Ratio

3 Wave Reflection from Multiple Interfaces

4 Plane Wave Propagation in General Directions

5 Plane Wave Reflection at Oblique Incidence Angles

6 Wave Propagation in Dispersive Media

Wave Reflection from Multiple Interfaces (1)

The steady – state has 5 waves:

• Incident wave in region 1

• Reflected wave in region 1

• Transmitted wave in region 3

x

z – l

2

x y

E H

η

+ + =

20 23 20

E − = Γ E +

20 23 20 20

Wave Reflection from Multiple Interfaces (2)

23( )

η1 η2 η3

ηin

Incident energy

10 1

1 10

,

in w z l in

η1 η2 η3

ηin

Incident energy

Wave Reflection from Multiple Interfaces (4)

0

x

z – l

Wave Reflection from Multiple Interfaces (5)

λ

=

22

3

in

η η

Wave Reflection from Multiple Interfaces (6)

It is required to coat a glass surface with an appropriate dielectric layer to provide total

transmission from air to the glass at a wavelength of 570 nm The glass has dielectric constant,

εr = 2.1 Find the required dielectric constant for the coating and its minimum thickness.

2

377

1.45 313

r

η ε

µ ε

×

22

Wave Reflection from Multiple Interfaces (7)

The reflected power fraction: |Γ| 2

The fraction of the power transmitted into region 4: 1 – |Γ| 2

Plane Wave Reflection & Dispersion

1 Reflection of Uniform Plane Waves at Normal

Incidence

2 Standing Wave Ratio

3 Wave Reflection from Multiple Interfaces

4 Plane Wave Propagation in General Directions

5 Plane Wave Reflection at Oblique Incidence Angles

6 Wave Propagation in Dispersive Media

Plane Wave Propagation in General Directions (1)

k k

Plane Wave Propagation in General Directions (2)

Given a 50 MHz uniform wave, it has electric field amplitude 10 V/m The medium is

lossless, εr = ε’r= 9.0; μr= 1.0 The wave propagates in the x, y plane at a 30o angle to the

x axis, & is linearly polarized along z Find the phasor expression of the electric field.

Ex.

6

1 8

Plane Wave Reflection & Dispersion

1 Reflection of Uniform Plane Waves at Normal

Incidence

2 Standing Wave Ratio

3 Wave Reflection from Multiple Interfaces

4 Plane Wave Propagation in General Directions

5 Plane Wave Reflection at Oblique Incidence Angles

6 Wave Propagation in Dispersive Media

Plane Wave Reflection at Oblique Incidence Angles (1)

s – polarization, TE

Plane Wave Reflection at Oblique Incidence Angles (2)

Plane Wave Reflection at Oblique Incidence Angles (3)

Plane Wave Reflection at Oblique Incidence Angles (4)

Plane Wave Reflection at Oblique Incidence Angles (5)

E E E E

η τ

− +

Plane Wave Reflection at Oblique Incidence Angles (6)

− +

η τ

1

cos

s

η η

θ

=

2 2

2

cos

s

η η

s – polarization, TE

Plane Wave Reflection at Oblique Incidence Angles (7)

n

η η

1 2

Plane Wave Reflection at Oblique Incidence Angles (8)

Plane Wave Reflection at Oblique Incidence Angles (9)

1 1

P

Ex 1

A uniform plane wave is incident from air onto glass at an angle of 30o from the

normal Find the fraction of the incident power that is reflected and transmitted for

(a) p – polarization, & (b) s – polarization Given glass refractive index n2 = 1.45.

p – polarization, TM

Plane Wave Reflection at Oblique Incidence Angles (10)

θ θ

Plane Wave Reflection at Oblique Incidence Angles (11)

Compute n1 so that total reflection occurs at the back

Plane Wave Reflection at Oblique Incidence Angles (12)

1

cos

s

η η

2

cos

s

η η

 

2 1

Plane Wave Reflection at Oblique Incidence Angles (13)

Plane Wave Reflection & Dispersion

1 Reflection of Uniform Plane Waves at Normal

Incidence

2 Standing Wave Ratio

3 Wave Reflection from Multiple Interfaces

4 Plane Wave Propagation in General Directions

5 Plane Wave Reflection at Oblique Incidence Angles

6 Wave Propagation in Dispersive Media

Wave Propagation in Dispersive Media (1)

Wave Propagation in Dispersive Media (2)

Wave Propagation in Dispersive Media (3)

β ω