Transcript Waveguiding in nanofibers

Waveguiding in nanofibers
Vladimir Bordo
NanoSyd, Mads Clausen Institute
Syddansk Universitet, Denmark
Contents
•Introduction
•Fundamentals
•Experiments
•Theory
•Conclusion
Introduction
InP nanowires / SiO2
p-6P nanofibers / mica
waveguiding
photoluminescence
optical confinement
Fundamentals
1
r
2a
2
z
elementary waves
boundary conditions at r = a
 n  e in J n ( k 22   2 r )e iz it , r  a
in
 n  e H ( k   r )e
k1 

(1)
n
2
1
1 , k2 
c
H n(1) ( k12   2 r ) ~
 x
2

c
1
r
iz it
, ra
2
e
i k12   2 r
, r 
E1  E2 , E1z  E2 z ,
H1  H 2 , H1z  H 2 z
  
M n An  0

det M n (  ,  )  0
arbitrary wave
   (an nTM  bn nTE )
n
normal modes ()
a
Fundamentals
cutoff
V 
2a

a/c
n 22  n12  2.405
fundamental mode (HE11)
A.V. Maslov and C.Z. Ning,
Appl. Phys. Lett., 83, 1237 (2003)
Fundamentals
1  1,  2  2.89
  r
 
waveguide
modes
r
   r  i i
 
r
  r
    i
r
i
space-decaying
(SD) modes
time-decaying
(TD) modes
V.G. Bordo, J. Phys.: Condens. Matter 19, 236220 (2007)
 1  1,  2  2.89
Experiments
• Measurements of the intensity decay with a fluorescence microscope
d, m
I ( z)  I ( z0 )e 2 Im  ( z  z0 )
Photoluminescence images of parahexaphenyl nanofibers excited by a mercury
lamp ( = 365 nm).
F. Balzer, V.G. Bordo, A.C. Simonsen and H.-G. Rubahn, Phys. Rev. B 67, 115408 (2003)
Experiments
• Measurements of the intensity decay with a SNOM
set-up
distance dependence
influence of
local defects
T. Tsuruoka, C.H. Liang, K. Terabe and T. Hasegawa, J. Opt. A: Pure Appl. Opt. 10, 055201 (2008)
Experiments
• Waveguiding at different wavelengths
T. Tsuruoka, C.H. Liang, K. Terabe and T. Hasegawa, J. Opt. A: Pure Appl. Opt. 10, 055201 (2008)
Experiments
• Waveguiding & Spatially resolved fluorescence microscopy
thiacyanine dye molecule
K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007)
Experiments
• Waveguiding & Spatially resolved fluorescence microscopy
K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007)
reabsorption
Experiments
• Optical cavity effects
Fabry-Perot modes
J-band => anomalous
dispersion
  2 L  2m
m

L
d

 
 
d
L
L
K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007)
Experiments
• Optical cavity effects
ZnSe nanowire
PL spectra from nanowires
of different lengths
L.K. van Vugt, B. Zhang, B. Piccone, A.A. Spector and R. Agarwal, NanoLett.. 9, 1684 (2009)
Experiments
TE01 mode excitation
HE11 mode excitation
L.K. van Vugt, B. Zhang, B. Piccone, A.A. Spector and R. Agarwal, NanoLett., 9, 1684 (2009)
Experiments
two-mode excitation
”slow light” (vg = c/8)
near the band-edge
(2.69 eV)
strong coupling between
excitons and photons
L.K. van Vugt, B. Zhang, B. Piccone, A.A. Spector and R. Agarwal, NanoLett., 9, 1684 (2009)
Experiments
• Coupling of external light into a nanofiber
silica fiber
tuning the fiber alignment
ZnO nanowire
tuning the fiber-nanowire distance
T. Voss, G.T. Svacha, E. Mazur, S. Müller, C. Ronning, D. Konjhodzic and F. Marlow,
NanoLett., 7, 3675 (2007)
Experiments
•Optical mode launching in nanofibers
set-up
light scattering
photoluminescence
J. Fiutowski, V.G. Bordo, L. Jozefowski, M. Madsen and H.-G. Rubahn, Appl. Phys. Lett., 92, 073302 (2008)
Experiments
•Optical mode launching in nanofibers
phase matching

2

n s sin 
J. Fiutowski, V.G. Bordo, L. Jozefowski, M. Madsen and H.-G. Rubahn, Appl. Phys. Lett., 92, 073302 (2008)
Theory
•Rectangular anisotropic nanofiber on a substrate
•TE waves do not exist
a 1
2
3
•TM waves:
- dispersion
1/ 2
 2
 ||  m  2 
   2  || 

 
   a  
 c
-cutoff wavelengths
c 
2  a
m
-number of modes
  ||

2   0
0


0

0
0

0
  
m
2a


 ||
 ||   3
F. Balzer, V.G. Bordo, A.C. Simonsen and H.-G. Rubahn, Phys. Rev. B 67, 115408 (2003)
Theory
•Semi-cylindrical isotropic nanofiber on a substrate
ideally reflecting substrate
V.G. Bordo, Phys. Rev. B, 73, 205117 (2006)
theory of images
Theory
•Semi-cylindrical isotropic nanofiber on a substrate
phase matching with
a radiative mode
angular distribution
of scattered light
total scattered intensity
vs incidence angle
V.G. Bordo, Phys. Rev. B, 73, 205117 (2006)
vicinity of exciton resonance
Theory
•Semi-infinite cylindrical isotropic nanofiber
=>

1 
 (r , , z ) 
 (r ,  ;  )e iz d
2 



M ( ) A( )  B( )
=>
incident waveguide mode
0  a0 0TM  b0 0TE
z  k 2 z  0
boundary conditions



Et''  Et'  E 0t



H t''  H t'  H 0t
=>


c 
Km  
e z  E 0t
4
e

c 
K 
e z  H 0t
4
+
 
fictitious
=>
current sheets
V.G. Bordo, Phys. Rev. B, 78, 085318 (2008)
 
  e ik|R R '| 
  ( R)   K  ( R' )   dR'
| R  R' |
Theory
•Numerical calculations
silicon nanowire,  = 1.5 m
H n(1) ( k12   2 r ) ~
1
r
e
i k12   2 r
, r 
L. Tong, J. Lou and E. Mazur, Opt. Express, 12,1025 (2004)
Theory
•Numerical calculations
fundamental mode,  = 1.5 m
fractional power inside the core
silica nanowire
n = 1.45
L. Tong, J. Lou and E. Mazur, Opt. Express, 12,1025 (2004)
silicon nanowire
n = 3.5
Theory
•Numerical calculations
top facet
1= 1
2= 6
n = 1.8
=>
1 2
n
FDTD
calculations
A.V. Maslov and C.Z. Ning,
Appl. Phys. Lett., 83, 1237 (2003)
bottom facet
Conclusion
•Waveguiding is characterized by optical confinement.
•Electromagnetic fields in a nanofiber can be described in terms of wavegiude
modes as well as transient modes. The latter ones can be radiative.
•Waveguide modes have frequency cutoffs below which they can not
propagate to the exclusion of the fundamental mode.
•Waveguiding in nanofibers can be observed in both photoluminescence and
propagation of incident light.
•A nanofiber can act as an optical resonator. The waveguide modes can be
enhanced if the waves travelling back and forth interfere constructively.
•The launching of the nanofiber modes can be observed in the far field as
peaks in light scattering or photoluminescence.
•As the nanofiber diameter increases, the optical confinement becomes better.