‧ 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

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

27. 0.00174
0.00176
0.00178
0.0018
0.00182
0.00184
0.00186
0.00188
0 2 4 6 8 10 12 14 16 18 20
W
Time(min)
No bias
Biased at -15V
Turning off -15V
Biased at +15V
Turning off +15V
Measured results:
2015/8/13 Chungpin Liao et al. 27

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.