‧ Can TEM waves be affected by the presence of electric charges?
‧ We’ve seen role of passive charges → dipoles → dielectrics
‧ Can EM waves/ lights be manipulated meaningfully by
active charges instead?
‧ Exact solution in the presence of still and moving charges
→ useful?
‧ E. T. Whittaker’s two potential general solution → useful?
‧ Feynman’s versatile formula → intuitive and useful?
‧ Scope reduction to steady-state → effect of interfacial & surface active charges
‧ Experiments & results
Unraveling Multimodality with Large Language Models.pdf
On the Possibility of Manipulating Lightwaves via Active Electric Charges
1. On the Possibility of Manipulating Lightwaves
via Active Electric Charges
Chungpin Liao1,2,* Li-Shen Yeh,2 Wen-Bing Lai,1,2 Jyun-Lin Huang,1,2
(廖重賓) (葉立紳) (賴玟柄) (黃均霖)
1Graduate School of Electro-Optic and Materials Science,
National Formosa University (NFU), Huwei, Taiwan 632, ROC.
2Advanced Research & Business Laboratory (ARBL),
Taichung, Taiwan 407, ROC.
*Corresponding Author: cpliao@alum.mit.edu
2015/8/13 1Chungpin Liao et al.
2. 2015/8/13 2Chungpin Liao et al.
Outline
• Can TEM waves be affected by the presence of electric charges?
• We’ve seen role of passive charges dipoles dielectrics
• Exact solution in the presence of still and moving charges
useful?
• Feynman’s versatile formula intuitive and useful?
• Scope reduction to steady-state effect of interfacial & surface
active charges
• Can EM waves/ lights be manipulated meaningfully by
active charges instead?
• Experiments & results
• E. T. Whittaker’s two potential general solution useful?
3. 2015/8/13 Chungpin Liao et al. 3
• Can TEM waves be affected by the presence of electric charges?
The TEM solution is from the source-free wave equation:
Hence, the answer should be YES, especially when
the charges are responsive to the EM wave/ light frequency.
But …
2
2
2
0
E
E
t
02
2
2
t
B
B
4. 2015/8/13 Chungpin Liao et al. 4
Q: How come in fully-ionized dense plasmas, which is full of
positive and negative charges, TEM waves are normal modes?
A: Would the quasi-neutrality property of plasma convince us?
i.e., net charge ~ 0
Q: What about the situations where
charge number density ne falls between
those of vacuum and dense plasma?
?
1. Self-consistent in terms of charges and fields?
2. Even motionless charges, any clue to wave-guiding?
5. 2015/8/13 Chungpin Liao et al. 5
• We’ve seen role of passive charges dipoles dielectrics
Matters respond to impinging lights via passively induced charges,
i.e., induced dipoles, in ways against the incoming EM fields.
Cluster of induced electric dipoles dielectrics
However, there is essentially NO magnetic dipoles responsive to
light frequency.
6. Chungpin Liao et al. 6
• Due to Doyle [1985],* the whole set of Fresnel equations
could be written in its “scattering form”, i.e., D S:
(D – single dipole, S – collective dipoles oscillation pattern)
t
iti
itrrrr
r
p
i
p
t
E
E
sin
sincos2
cos11
(a)
it
it
itrrrr
itrrrr
p
i
p
r
E
E
sin
sin
cos11
cos11
(b)
t
iti
itrrrr
r
s
i
s
t
E
E
sin
sincos2
cos11
(c)
it
it
itrrrr
itrrrr
s
i
s
r
E
E
sin
sin
cos11
cos11
(d)
• S 0, D = 0 for (b), (d) Brewster’s angle, e.g.
1
tan2
rr
rrrp
B
1
tan2
rr
rrrs
B
2015/8/13
rrti nn ,1
* W. T. Doyle, “Scattering approach to Fresnel’s equations and Brewster’s law,” Am. J. Phys. 53 (5), 463-468 (1985).
7. Chungpin Liao et al. 7
iti
t
it
p
ip
P
E
sincos2
sin
cos
0
iti
t
it
p
rp
P
E
sincos2
sin
cos
0
electric dipole
p-wave
iti
tp
im
M
E
sincos2
sin
0
0
iti
tp
rm
M
E
sincos2
sin
0
0
p-wave
magnetic dipole
Total:
iti
t
it
p
i
MP
E
sincos2
sin
cos
0
0
0
iti
t
it
p
r
MP
E
sincos2
sin
cos
0
0
0
• Induced dipole sources revealed mNMpNP
2015/8/13
p
im
p
ip
p
i EEE
p
rm
p
rp
p
r EEE
8. Chungpin Liao et al. 8
iti
t
it
p
i
MP
E
sincos2
sin
cos
0
0
0
iti
t
it
p
r
MP
E
sincos2
sin
cos
0
0
0
Putting p
tr EP
10 and p
t
r
r
r EM
0
0
1 into:
we obtain:
it
it
itrrrr
itrrrr
p
i
p
r
E
E
sin
sin
)cos(11
)cos(11
(b)
i.e., Scattering form of one of the Fresnel equations
• Checking: p-wave as an example
Source equations
2015/8/13
9. Chungpin Liao et al. 9
• Similarly, for s-wave, with total P and M contributions:
iti
t
it
s
i
MP
E
sincos2
sin
cos
0
0
0
Putting p
tr EP
10 and p
t
r
r
r EM
0
0
1 in, to obtain:
iti
t
it
s
r
MP
E
sincos2
sin
cos
0
0
0
it
it
itrrrr
itrrrr
s
i
s
r
E
E
sin
sin
)cos(11
)cos(11
(d)
i.e., Scattering form of one of the Fresnel equations
Source equations
2015/8/13
10. Chungpin Liao et al. 10
E.g., adding permanent dipoles for novel applications
• By generalization of the types of involved dipoles in
source equations
• Namely, in general, optically-responsive permanent dipoles
(P0 and M0) embedded in the original material can vary
optical properties, such as the Brewster angle.
• This is, now P = P0 + Pind, M = M0 + Mind
(with Pind and Mind as induced dipoles)
• However, still, how exactly do the dipoles affect the
optical properties, physically?
• See e.g., p-wave, unmagnetized case (i.e., P 0, but M = 0)
2015/8/13
11. Chungpin Liao et al. 11
iti
t
it
p
ip
P
E
sincos2
sin
cos
0
iti
t
it
p
rp
P
E
sincos2
sin
cos
0
So, the P (of whatever origin) contributes only its component
along the relevant E.
|| P
All induced P (so || Et)
2015/8/13
itit PP coscos
12. Chungpin Liao et al. 12
• Adding P0 into an unmagnetized host and look at the p-wave case:
2015/8/13
iti
t
iti
p
tr
p
ip
P
EE
sincos2
sin
coscos1 0
0
0
ti
p
tr E cos1~
iti
t
iti
p
ip
PP
E
sincos2
sin
coscos 0
0
0
0
ti
p
tr E cos1
13. 2015/8/13 Chungpin Liao et al. 13
• Can EM waves/ lights be manipulated meaningfully by
active charges instead?
H
E
t
( curl on Faraday’s )
u
=
=
=
=
uniform ε
Ampere’s
Gauss’E
uniform μ
H
E
t
E)E( 2
H
t
u
E
J
t
2
2
2
u uJE
E
tt
The answer should be YES, even though it is nontrivial.
14. 2015/8/13 14Chungpin Liao et al.
• Exact solution in the presence of still and moving charges
useful?
The formal approach is as follows:
A
tt
B
E
AHB
(Faraday’s law)
0
t
A
E
t
A
E
t
J
E
t
E u
2
2
2
15. 2015/8/13 Chungpin Liao et al. 15
Now, according to Ampere’s law: E
t
JH u
t
A
t
u
AA
A
B
E
t
JH
2
uJ
t
A
A
t
A
2
2
2
Now, let
t
A
(Lorentz gauge)
So, we have: uJ
t
A
A
2
2
2
16. 2015/8/13 Chungpin Liao et al. 16
On the other hand, we work on Gauss’ E law: uE
u
t
u A
tt
A
2
We reach:
u
t
2
2
2
So, we have: AHB
t
A
E
uJ
t
A
A
2
2
2
u
t
2
2
2
t
A
Using
(Lorentz gauge)
17. 2015/8/13 17Chungpin Liao et al.
The formal general solution: (see, e.g., Feynman Lecture Notes –II)
2
12
12
4
,2
,1 dV
r
c
r
t
t
u
2
12
2
12
4
,2
,1 dV
rc
c
r
tJ
tA
u
Q: Is it helpful in regard to the purpose of guiding lightwaves?
TEM Light in vacuum
, J 0
?
2’
2
1r’
r12
Position at
t -r’/c
Position at t
q
q
v
Again, self-consistency problem here, unless for motionless charges. Secondly, any practical clue provided for EM wave guiding?
18. 2015/8/13 Chungpin Liao et al. 18
• E. T. Whittaker’s# two potential general solution useful?
2
2
22
22222
1
,
1
,
1
t
F
cz
F
D
tx
G
czy
F
D
ty
G
czx
F
ED zyxx
2
2
2
22222
,
1
,
1
y
G
x
G
H
zy
G
tx
F
c
H
zx
G
ty
F
c
H zyx
),,(
cos,sinsin,cossinˆ
ˆ
,,,
,,,
2
0 0
2
0 0
zyxr
k
rkct
gddtzyxG
fddtzyxF
F & G are:
arbitrary functional of
Nontrivial to put to use
# Whittaker, E. T., "ON AN EXPRESSION OF THE ELECTROMAGNETIC
FIELD DUE TO ELECTRONS BY MEANS OF TWO SCALAR POTENTIAL
FUNCTIONS," Proceedings of the London Mathematical Society, Vol.
1, p. 367-372 (1904).
19. 2015/8/13 19Chungpin Liao et al.
• Feynman’s+ versatile formula intuitive and useful?
'ˆ
1
'
'ˆ'
'
'ˆ
4 2
2
222
r
dt
d
cr
r
dt
d
c
r
r
rq
E
For a charge q in whatever motion
ErBc
'ˆ
Q: How to arrange so many q’s in motion such that the desired
E & B fields are secured for light-guiding purposes?
+ Feynman R., Leighton R. B., Sands M., The Feynman lectures on physics, Vol. II, Sec. 21, Addison-Wesley, Boston, MA, USA (1971).
20. 2015/8/13 Chungpin Liao et al. 20
• Scope reduction to steady-state effect of interfacial
active charges Experiment 1
0
J
t
Charge conservation law:
Steady state: .vv0 ee constEEenJJ eee
At interface between two
conducting media:
0
t
tEtEtE sb
n
a
nn
21. 21
2
0 0 02
0u p uE J
.const
0 0
0
spsu
Pu
no source of E
2
0
Note that the distrib. of ε plays no part in shaping the E lines, but σ can.
Conduction and EQS Charge Relaxation
ba
terminates or originates on it
)1(ˆ 0
b
aa
spsu
En
0 spsu
En
ˆ&
ab
< 0
E excluded from high σ
0 0 up
E
&
terminates or originates on them (it)
20
uup
J
increasing)r(
E attenuates
< 0
2015/8/13 Chungpin Liao et al.
22. V
0
ITO
ZnO
DC current
glass
s < 0
2015/8/13 22Chungpin Liao et al.
• Experiments & results
+
-+
-
Laser beam spot more focused
E direction
23. 2015/8/13 23Chungpin Liao et al.
56.0
58.0
60.0
62.0
64.0
66.0
0.0 5.0 10.0
光功率(µW)
Time (minute)
2015.07.24_measured intensity at edge
DC power supply turned off
Spot bottom edge,
ITO(+)/ZnO(-) 4V
Spot bottom edge,
ZnO(+)/ITO(-) 4V
Residual charges
- undesirable
24. 2015/8/13 24Chungpin Liao et al.
417.5
420.0
422.5
425.0
427.5
430.0
0.0 1.0 2.0 3.0 4.0 5.0
light intensity (µW)
Time (minute)
2015.07.31_Face to face_Top Edge_ITO (+)/ZnO(-)_1.0V to 4.0V
Unbiased reference
4 V
1 V
2 V
3 V
The repeatability was poor so far, possibly due to varying interfacial states.
25. 2015/8/13 Chungpin Liao et al. 25
405.0
410.0
415.0
420.0
425.0
430.0
0.0 1.0 2.0 3.0 4.0 5.0
light intensity (µW)
Time (minute)
2015.07.31_Face to face_Top Edge_ITO(+)/ZnO(-)_4.0 V to 1.0V
reference
1 V
2 V
3 V
4 V
There were likely hysteresis effect due to residual charges.
26. Experiment 2: charge-influenced light reflection
2015/8/13 Chungpin Liao et al. 26
Dielectric: paper
Solid-state
Argon laser,
with E
vertical to the
laser beam
Light power
measurement
per 300 ms
Smooth and shiny
stainless steel
E
Biased
Capacitor
28. 2015/8/13 Chungpin Liao et al. 28
Summary & conclusions
• Active electric charges were found to be responsive to incident
lightwaves and to affect the propagation/reflection of lightwaves.
• Guiding of lightwaves by active charges is valid in principle, but
putting it to work practically would need more creativity and
efforts.
• In the future, such active ingredients may assist the
traditional passive dielectric approach for more meaningful
optical and photonic purposes.
Notas do Editor
Mainly to ask two questions: 1. Will active charges be responsive to incident lightwaves? 2. If so, how to use active charges for the manipulation of lightwaves?
TEM mode is picked up for ease of elaboration only.
The important thing in the light diffraction: E_in, E_ref, and E_tran can all be viewed as results of the induced E and M dipoles, as envisioned from the latter.
We will be talking about nearly vacuum or nearly uniform cases, where the medium is isotropic, linear, and memoryless.
An inhomogeneous wave equation for the vector potential
An inhomogeneous wave equation for the scalar potential
One scalar potential, one vector potential to suffice the full solution; The bottom part: what about self-consistency?
Mathematically easier, but practically harder for our purposes
Again, what about the self-consistency?
To create steady-state interface charges, unpaired and paired.
Residual charge effect might be due to the interface traps.
The results were varying from time to time, but the charge influence on light was obvious.