Vladimir Bordo

NanoSyd, Mads Clausen Institute

Syddansk Universitet, Denmark

Waveguiding in nanofibers

Contents• Introduction• Fundamentals• Experiments• Theory• Conclusion

Introduction

photoluminescence

waveguiding

optical confinement

InP nanowires / SiO2 p-6P nanofibers / mica

Fundamentals

elementary waves boundary conditions at r = a

arbitrary wave

)( TEnn

n

TMnn ba

zz

zz

HHHH

EEEE

2121

2121

,

,,

normal modes ()

z

2a

1

2

rer

rkH

ck

ck

arerkHe

arerkJe

rkin

tizin

inn

tizin

inn

,1

~)(

,

,)(

,)(

22122

1)1(

2211

221

)1(

222

0),(det

0

n

nn

M

AM

xr

Fundamentals

cutoff

fundamental mode (HE11)

a

a/c

405.22 2

122 nn

aV

A.V. Maslov and C.Z. Ning, Appl. Phys. Lett., 83, 1237 (2003)

Fundamentals

space-decaying (SD) modesr

ir i

time-decaying (TD) modesir

r

i

r

r

waveguide modes

89.2,1 21

89.2,1 21

V.G. Bordo, J. Phys.: Condens. Matter 19, 236220 (2007)

Experiments

Photoluminescence images of para-hexaphenyl nanofibers excited by a mercury lamp ( = 365 nm).

• Measurements of the intensity decay with a fluorescence microscope

F. Balzer, V.G. Bordo, A.C. Simonsen and H.-G. Rubahn, Phys. Rev. B 67, 115408 (2003)

d, m

)(Im20

0)()( zzezIzI

Experiments• Measurements of the intensity decay with a SNOM

set-up distance dependence

T. Tsuruoka, C.H. Liang, K. Terabe and T. Hasegawa, J. Opt. A: Pure Appl. Opt. 10, 055201 (2008)

influence of local defects

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

K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007)

thiacyanine dye molecule

Experiments• Waveguiding & Spatially resolved fluorescence microscopy

K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007) reabsorption

Experiments• Optical cavity effects

K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007)

L

Ld

dL

m

mL

22

Fabry-Perot modesJ-band => anomalous

dispersion

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)

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 betweenexcitons and photons

• Coupling of external light into a nanofiber

T. Voss, G.T. Svacha, E. Mazur, S. Müller, C. Ronning, D. Konjhodzic and F. Marlow, NanoLett., 7, 3675 (2007)

ZnO nanowire

silica fiber

tuning the fiber-nanowire distance

tuning the fiber alignment

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

J. Fiutowski, V.G. Bordo, L. Jozefowski, M. Madsen and H.-G. Rubahn, Appl. Phys. Lett., 92, 073302 (2008)

sin2

sn

phase matching

Experiments

•Rectangular anisotropic nanofiber on a substrate

1

2

3

a

•TE waves do not exist

•TM waves:- dispersion

-cutoff wavelengths

-number of modes

2/12||

||2

2

a

m

c

m

ac

2

3||||

2

a

m

F. Balzer, V.G. Bordo, A.C. Simonsen and H.-G. Rubahn, Phys. Rev. B 67, 115408 (2003)

00

00

00||

2

Theory

Theory•Semi-cylindrical isotropic nanofiber on a substrate

ideally reflecting substrate theory of images

V.G. Bordo, Phys. Rev. B, 73, 205117 (2006)

Theory•Semi-cylindrical isotropic nanofiber on a substrate

V.G. Bordo, Phys. Rev. B, 73, 205117 (2006)

total scattered intensity vs incidence angle

phase matching with a radiative mode

angular distribution of scattered light

vicinity of exciton resonance

•Semi-infinite cylindrical isotropic nanofiber

incident waveguide mode

TETM ba 00000

boundary conditions

ttt

ttt

HHH

EEE

0'''

0'''

=>

fictitious current sheets

V.G. Bordo, Phys. Rev. B, 78, 085318 (2008)

=> '|'|

)'()('||

RdRR

eRKR

RRik

+

02 zz k

)()()( BAM

=>

=>

derzr zi);,(2

1),,(

Theory

tze

tzm

Hec

K

Eec

K

0

0

4

4

Theory•Numerical calculations

silicon nanowire, = 1.5 m

rer

rkH rkin ,

1~)(

22122

1)1(

L. Tong, J. Lou and E. Mazur, Opt. Express, 12,1025 (2004)

Theory•Numerical calculations

L. Tong, J. Lou and E. Mazur, Opt. Express, 12,1025 (2004)

fractional power inside the core

fundamental mode, = 1.5 m

silica nanowiren = 1.45

silicon nanowiren = 3.5

•Numerical calculations

=>FDTDcalculations

top facet

bottom facet

A.V. Maslov and C.Z. Ning, Appl. Phys. Lett., 83, 1237 (2003)

1 2

n

1= 1 2= 6n = 1.8

Theory

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.