lecture6 electromagnetism

7/27/2019 Lecture6 Electromagnetism

1/15

Lecture 6:Electromagnetic Theory of Light

ELG 4117

Optoelectronics and Optical Components

September 23, 2013


2/15


Electromagnetic Optics

ray

beam

wave

EM Electromagnetic optics accounts for the

polarization (vector nature) of theelectric and magnetic fields in the lightwaves

Wave optics is scalar approximation toelectromagnetic optics

Ray optics is the approximation to waveoptics when the objects that the lightinteracts with are much larger than thewavelength

Vector nature of light determines the amount of light reflected

and refracted at the boundaries; governs the light propagation

in waveguides and laser resonators.


3/15


Electromagnetic Wave

smkbud4.edu.my


4/15Optoelectronics and Optical Components

Electromagnetic Wave

http://electronicsgurukulam.blogspot.ca/2012/04/how-electro-magnetic-wave-propagates.html

E(r, t)

H(r, t)

Described by coupled electric and magnetic fieldvectors, changing in time and space.



Maxwell's Equations

In free space

H=0E t

E=0H

t

E=0

H=0

c0=1

00

Ex, Ey , Ez

Hx , Hy, Hz

satisfy 2u1

c02

2 u

t2=0

Wave equation stems from Maxwell'sequations: Take to prove.(E)

0(1/36)109 F/m

0(4)107

H /m



Maxwell's Equations

In a mediumIn a medium with no free electric charges or currents, twoadditional vector fields are required:

D(r, t)

B (r, t)

- electric flux density (electric displacement);

- magnetic flux density

H=D t

E=

B

t

D=0

B=0

These two extra vectors include mediumresponse to the electromagnetic field.



Constitutive Relationships

D=0E+P;B=0H+0M

P - polarization density;

M- magnetization density

H=D

t

E=B t

D=0

B=0

In free space:

P=0 ;

M=0 ;

D=0E;

B=0H;

Maxwell's equations reduce tothose in free space.



Boundary Conditions

In a homogeneous medium:

At the Interfaces:

E,H ,D,B are continuous.

Et ,1=Et ,2

Ht ,1=Ht ,2

Dn ,1=Dn ,2Bn ,1=Bn , 2

Tangential components of electric and magnetic fields, and normalcomponents of electric and magnetic flux densities should becontinuous accross an interface between two media.



Intensity, Power, Energy

The flow of electromagnetic power is governed by Poynting vector:

S=EH

The magnitude of time-averaged Poynting vectoris optical intensity:

E

H

S

I(r, t)=S


10/15


Poynting Theorem

Energy Conservation Law

(EH)=(E)H(H)E

Applying the vector product identity

and Maxwell's equations, we arrive at

S= t(

1

20E

2+1

20H

2)+EP t +0HM t

Energy density storedin electric and magnetic field

Power densities deliveredto electric and magnetic

dipolesThe power flow escaping from the surface of

small volume equals the time rate of change of

the energy stored inside the volume.


11/15


Electromagnetic Waves in Dielectrics

The medium is linear, ifP(r,t) depends on E(r,t) linearly. The medium is nondispersive, if response is instantaneous.

The medium is homogeneous, if the relation between Pdepends on E does not depend on position r.

The medium is isotropic, if the relation between P depends on Edoes not depend on the direction of vectorE.

E(r, t) P(r, t)optical medium


12/15


Linear, Nondispersive, Homogeneous, Isotropic

P=0E

- susceptibility of the medium.

E P

- electric permittivity - magnetic permeability

D=E,B=H ,

=0(1+)

=0

H= E t

E=H t

E=0

H=0


13/15


Linear, Nondispersive, Homogeneous, Isotropic

H= E t

E=H t

E=0

H=0

Similar to free-space Maxwell's equations.

Hence, each component of electric andmagnetic fields satisfies the wave equation:

2u1

c2

2 u

t2=0, c=

1

n= c0c= 0 0

=0,Nonmagnetic medium: n=0=1+

Poynting Theorem:

S=W t

W=1

2E2+

1

2H2 - energy density

stored in the medium


14/15


Monochromatic Electromagnetic Waves

E

(r, t

)=Re [E

(r

)exp(i

t

)]H(r, t)=Re [H(r)exp(i t)]

H=iD

E=iBD=0B=0

H=iE

E=iHE=0H=0

in linear isotropichomogeneous

nondispersive medium:

=2

k=n k0=

2U+k2U=0


15/15


Electromagnetic Waves

www.olympusmicro.com

lecture6 electromagnetism

Documents