λ0
propagation
reflection refraction
polarization interference, diffraction
第一节 电磁理论基础
Maxwell’s Equations
AD
dS
V
dV
D E H B/
AB dS 0
CE
dl
t
AB
dS
CH
dl
AJ
dS
and
2 2
x2
1 v2
2 2
t 2
a
2 1
x 2
b
2 2
x 2
a
1 v2
2 1
t 2
b
1 v2
2 2
t 2
2 x 2
(a 1
b 2 )
1 v2
2 t 2
(a 1
b 2 )
If simple harmonic waves are solutions of wave equation, then harmonic wave (linear combination of S.H.W.) is also a solution.
E B
2E 2B
2E
0 0
2E t 2
0,
2B
00
2B t 2
0
• The solutions of Maxwell’s equations are wave-like, with both E and B satisfying the wave equations above.
• Electromagnetic waves travel through vacuum at the speed of
light c = (00)-1/2.
第一节 电磁理论基础
E-M Waves in vacuum
2E
00
2E t 2
0,
2B
0 0
2B t 2
0
(x,t) Asin k(x vt) Asin(kx t)
第一节 电磁理论基础
E-M Waves in vacuum
The Superposition Principle
If 1 and 2 are solutions of wave equation, then (a1 + b2) is also a solution.
2 1
x 2
1 v2
2 1
t 2
t
AD
dS
D
B 0
E
B
H
J
t
D
t
Guass’s law （electric） –– Coulomb’s law Guass’s law （magnetic） –– Biot-Savart law Faraday’s induction law –– Maxwell’s induced electric field Generalized Ampere’s law –– Maxwell’s displacement current
第一节 电磁理论基础
Faraday’s Induction Law
第一节 电磁理论基础
Generalized Ampere’s Law
B dl J da I
C S1
B dl J da 0
C
S2
(0 B) ( J 0)
SJ
da
t
dV
J
t
B
J
E t
c = (00)-1/2
Asin2
(
x
t T
)
A : amplitude
: wavelength (spatial period)
k : wave number (spatial frequency) T : period (temporal period)
: angular frequency
第一节 电磁理论基础
E-M Waves in vacuum
Phase: the argument of the sine and cosine functions
= kx t + 0 Initial phase
Spatial term Temporal term
Rate of change of phase with time
Displacement current
第一节 电磁理论基础
E-M Wave Equations in vacuum
E
B
B
t 0 0
E t
E
B
B t
0 0
2E t 2Βιβλιοθήκη 0 0tE
0 0
2B t 2
E 0
B 0
A A 2A
光学
OPTICS
第一章 光的电磁理论
第一章 光的电磁理论
第一节 电磁理论基础 第二节 光的能量和动量 第三节 光的辐射 第四节 光在介质中传播 第五节 经典理论的局限
Classical Optics at a First Glance
Particle’s aspect
Wave’s aspect
(Geometrical optics) (Physical optics, wave optics)
t x
k
x t
(phase velocity)
x ( / t)x t ( / x)t
x v
t k
Rate of change of phase with distance
第一节 电磁理论基础
E-M Waves in vacuum
• A periodic wave is referred to as harmonic wave. • A sinusoidal wave with a single frequency is known as
第一节 电磁理论基础
E-M Waves in vacuum
The Complex Representation
Im
y r
x
x r cos and y r sin z x iy r(cos i sin) rei
Re
(x, t) A cos(kx t ) Re[ Aei(kxt ) ] (x, t) Asin(kx t ) Im[ Aei(kxt ) ] (x, t) Aei(kxt )
Simple Harmonic Wave (S.H.W.). • A harmonic wave can be composed by a series of S.H.W.
with different frequencies (Fourier series).
sin(t) + 0.3sin(2t) + 0.2sin(4t) + 0.1sin(8t)