Chap. 3 Electromagnetic Theory and Light - PowerPoint PPT Presentation

1 / 19
About This Presentation
Title:

Chap. 3 Electromagnetic Theory and Light

Description:

Chap. 3 Electromagnetic Theory and Light Light possesses both wave-particle manifestations. Classical electrodynamics based on Maxwell s electromagnetic theory ... – PowerPoint PPT presentation

Number of Views:607
Avg rating:3.0/5.0
Slides: 20
Provided by: ComputerC
Category:

less

Transcript and Presenter's Notes

Title: Chap. 3 Electromagnetic Theory and Light


1
Chap. 3 Electromagnetic Theory and Light
Light possesses both wave-particle
manifestations. Classical electrodynamics based
on Maxwells electromagnetic theory unalterably
leads to the picture of a continuous transfer of
energy by way of electromagnetic waves. Quantum
electrodynamics describes electromagnetic
interaction and the transport of energy in terms
of massless elementary particles known as
photons, which are localized quanta of
energy. One of the basic tenets of quantum
mechanics is that both light and material objects
each display both wave-particle properties. In
physical optics light is treated as an
electromagnetic wave. 3.1 Maxwells equations
The simplest statement of Maxwells
equations governs the behavior of the electric
and magnetic fields in free space.
Maxwells equations are generalization of
experimental results.
2
where and are the permeability and
the electric permittivity of free space,
respectively. It should be noted that
except for a multiplicative scalar, the electric
and magnetic fields appears in above equations
with a remarkable symmetry. The mathematical
symmetry implies a good deal of physical
symmetry. Maxwells equations tell us that
a time-varying magnetic field generates an
electric field and a time-varying electric field
generates a magnetic field. Maxwells
equations above can be written in differential
form by using following two theorems from vector
calculus.
3
By applying theorem (3.5) to Eqs. (3.1) and (3.2)
and applying theorem (3.6) to Eqs (3.3) and
(3.4), we obtain the following differential
equations
4
The consequent equations for free space are in
detail as follows
5
3.2 Electromagnetic waves Maxwells
equations for free space can be manipulated into
the form of two vector expressions
Taking the curl of Eq. (3.7)
6
The Laplacian, , operates on each component
of and , so that the two vector
equations (3.18) and (3.19) actually represent a
total of 6 scalar equations. One of these
expressions, in Cartesian coordinates, is
Each component of the electromagnetic field (
) therefore
obeys the scalar differential wave equation
provided that
If we substitute the values of and
into Eq. 3.22, the predicted speed of all
electromagnetic waves travelling in free space
would then be c 3 x 108 m/s. This theoretical
value was in remarkable agreement with the
previously measured speed of light.
7
The experimentally verified transverse character
of light should be explained within the context
of the electromagnetic theory. To that end,
consider the fairly simple case of a plane wave
propagating in the positive x-direction and write
as . Eq. (3.15) is reduced to
For a progressive wave, the solution of (3.23) is
Ex0. So the electric component must be
perpendicular to the propagation direction, x.
Lets orient the coordinate axes so that the
electric field is parallel to the y-axis
. From Eq. (3.13 III), it
follows that
This implies that the time-dependent B-field can
only have a component in the z-direction. Clearly
then, in free space, the plane electromagnetic
wave is indeed transverse, as shown in Fig. 3.1.
Now lets write
Fig. 3.1 Field configuration in a plane harmonic
electromagnetic wave.
8
The associated magnetic field can be found
by directly integrating Eq. (3.25), that is,
(3.26)
Fig. 3.2 Orthogonal harmonic E-field and
B_field.
Clearly, and have the same
time
dependence, and
are in phase at all points in
space. Moreover, and are mutually
perpendicular, and their cross-product,
, points in the propagation direction, as shown
in Fig.3.2. It should be noted that plane
waves are not only solutions to Maxwells
equations. As we saw in the previous chapter, the
differential wave equation allows many solutions
including spherical waves.
9
3.3 Energy
Energy density, , which is the radiant
energy per unit volume, is given by
From Eqs. (3.27) and (3.28), we have
The amount of energy transported during a unit
time and through a unit area perpendicular to the
transport direction is (suppose the wave travels
through an area of A and with a speed of c and
with a time duration of )
The corresponding vector is called Poynting
vector
Its along the wave propagation direction. Its
SI unit is watt per square meter ( ).
10
E and B are so closely coupled to each other that
we need to deal with only one of them. Using
from Eq. 3.26, we can rewrite Eq. 3.30
as
The time-averaged value of the magnitude of
the Poynting vector, symbolized by , is a
measure of the significant quantity known as the
irradiance, .
Where E0 is the peak magnitude of E. Within a
linear, homogeneous, isotropic medium, the
expression for the irradiance becomes
For a point light source, its irradiance is
proportional to . This is well-known
inverse-square law. Fig. 3.3 shows that a point
source emits electromagnetic waves uniformly in
all directions. Let us assume that the energy of
the waves is
11
conserved as they spread from the source. Let us
also center an imaginary sphere of radius on
the source, as shown in Fig. 3.3. If the power of
the source is , the irradiance at the
sphere must then be
Fig. 3.3 A point source emits light isotropically.
In Quantum theory, light possesses quantum energy
is in unit of angstrom, h is Plank constant.
12
3.4 Electromagnetic-photon spectrum
Although all forms of electromagnetic radiation
propagate with the same speed in vacuum, they
differ in frequency and wavelength. Fig. 3.4
plots the vast electromagnetic spectrum. The
frequency range for whole electromagnetic
spectrum is from a few Hz to 1022 Hz. The
corresponding wavelength range is from many
kilometers to 10-14 m. Radiofrequency
waves a few Hz to 109 Hz Microwaves 109
Hz to about 3 x 1011 Hz.
Infrared 3 x 1011 Hz to 4 x 1014 Hz. The
infrared (IR) is often subdivided into four
regions the near IR (780- 3000
nm), the intermediate IR (3000-6000 nm), the far
IR (6000-15,000 nm), and the extreme IR
(15,000 nm-1.0 mm). Light 3.84 x 1014 to 7.69 x
1014 Hz. An narrow band of
electromagnetic waves could be seen by human eye.
Color is not a property of light itself
but a manifestation of the electrochemical
sensing system-eye, nerves, and brain.

13
Fig. 3.4 Electromagnetic-photon spectrum.
14
Ultraviolet 8 x 1014 Hz to 3.4 x 1016
Hz. X-rays 2.4 x 1016 Hz to 5 x 1019 Hz. Gamma
rays 5 x 1019 Hz to 2.5 x 1033 Hz.
Table 3.1. Frequency and vacuum wavelength ranges
for various colors
15
Fig. 3.6 Emission spectrum of GaInP2
semiconductor under excitation of a He-Cd laser..
Fig. 3.5 Spectra of sunlight and the light from
a tungsten lamp.
16
3.5 Light in matter 3.5.1 Dispersion
In a homogeneous, isotropic dielectric, the phase
velocity of light propagation becomes
The ratio of the speed of electromagnetic wave in
vacuum to that in matter is known as the absolute
index of refraction and is given by
For most materials, is generally equal
to 1. So, the expression of becomes
Actually, n is frequency-dependent, so called
dispersion. When a dielectric is subject to an
applied electric field E, the internal charge
distribution is distorted, which generates
electric dipole moment pLq, with L the position
vector from the negative charge -q to the
positive charge q. The dipole moment per unit
volume is called the electric polarization P.
with
17
Fig. 3.8 shows the dipole formation and a
oscillator model for the vibration of electrons
under an E-field. The negative electrons are
fastened to a stationary positive nucleus. The
natural frequency of the spring is
with k and m being the spring constant and
the electron mass. The force (FE) exerted on an
electron of charge q by a harmonic wave E(t) with
frequency is
Newtons second law provides the equation of
motion with the second term the restoring force.
Fig. 3.8 (a) Distortion of the electron cloud in
response to an applied E-field. (b) The
mechanical oscillator model for an isotropic
medium
For medium with electron density N the electric
polarization P is
18
Eq. (3.44) indicates dispersion. When
ngt1 When nlt1. Fig 3.9 shows
dispersion of materials.
Fig. 3.9 Index of refraction versus wavelength
and frequency for several important optical
crystals.
19
3.5.2 Electric dipole radiation The electric
dipole moment oscillates under the electric filed
as
This oscillation emits radiation. The irradiance
(radiated radially outward from the dipole) is
given by
Fig 3.10 shows the dipole radiation. Notice that
the irradiance is inversely proportional to the
distance r. The maxima occurs in the direction
of . There is no radiation
along the dipole axis ( ).
Fig. 3.10 Field orientation for an oscillating
electric dipole
Write a Comment
User Comments (0)
About PowerShow.com