wavetrains and coherency. © 2006 walter fendt beats animation
TRANSCRIPT
Wavetrains and Coherency
© 2006 Walter Fendt
Beats Animation
http://www.walter-fendt.de/ph11e/beats.htm
y(x) = Sin x
© SPK
y(x) = [Sin x + Sin (1.08 x)]/2
© SPK
y(x) = [Sin x + Sin(1.04 x) + Sin (1.08 x)]/3
© SPK
0 < x < 200
y(x) = [Sin x + Sin(1.02 x) + Sin (1.04 x) + Sin(1.06 x) + Sin (1.08 x)]/5
© SPK
0 < x < 400
y(x) = [Sin x + Sin(1.01 x) + Sin (1.02 x)+ Sin(1.03 x) + Sin (1.04 x) + Sin (1.05 x) + Sin (1.06 x) + Sin (1.07 x) + Sin (1.08 x)]/9
© SPK
0 < x < 400
y(x) = [Sin x + Sin(1.01 x) + Sin (1.02 x)+ Sin(1.03 x) + Sin (1.04 x) + Sin (1.05 x) + Sin (1.06 x) + Sin (1.07 x) + Sin (1.08 x)]/9
© SPK
Solitary pulse
x
y2
0 cos
0
pE E k x
For
For
LxL
Lx
-L +L
E0
Fourier integral
0 0
1( ) ( )cos( ) ( )sin( )f x A k kx dk B k kx dk
( ) ( )cos( )
( ) ( )sin( )
A k f x kx dx
B k f x kx dx
0
0
( ) cos( )cos( )
sin( ) sin( )
( ) ( )
L
p
L
p p
p p
A k E k x kx dx
k k L k k LE L
k k L k k L
0)k(B
Lkk
Lkk
p
p
)(
)sin(
Lkk
Lkk
p
p
)(
)sin(
kp=2
0 2 4 6 8 10 12 14 16 18-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
2/L
kp=2
k
L=1.5
Wave packet or Wave group
for kp=k
Lk
2
Frequency Bandwidth
Range of frequency k (or ) in wavetrain
(k) (or
t
t
1
4
xk
xk
1
4
Temporal coherence:
Coherence time:
Coherence length:
vtc 1
cc tcl © SPK
Spectral lines from helium gas tube
I
A characteristic Spectral line
20
cl
0
Spectral line broadening
1. Natural linewidth
2. Doppler broadening
3. Collision broadening
4. Pressure broadening
Red Cadmium = 6438 Å
= 1010
Hz, 30 cm
Yellow Sodium
= 109
3 cm= 5893 Å
He-Ne Laser 6328 Å
300 m= 106 Hz,
cl
v
v
v
cl
cl
Hz,
© SPK
Kr discharge lamp has roughly the following intensity distribution at various wavlengths, (in nm),
02 8
36( )
36 ( 605.616) 10
II
Estimate the coherence length of the Kr source.
vtc 1
•Coherence time
•Coherence length
cc tcl