Simultaneous near field imaging of electric and magnetic field in photonic crystal nanocavities

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PNFA-264;No.of Pages 5
Please cite this article in press as:S.Vignolini,et al.,Simultaneous near field imaging of electric and magnetic field in photonic
crystal nanocavities,Photon Nanostruct:Fundam Appl (2011),doi:10.1016/j.photonics.2011.04.006
Simultaneous near field imaging of electric and magnetic
field in photonic crystal nanocavities
Silvia Vignolini
a,
*
,Francesca Intonti
a
,Francesco Riboli
a
,Diederik Sybolt Wiersma
a
,
Laurent Balet
b
,Lianhe H.Li
b
,Marco Francardi
c
,Annamaria Gerardino
c
,
Andrea Fiore
d
,Massimo Gurioli
e
a
European Laboratory for Non-linear Spectroscopy and CNR-INO,Via Nello Carrara 1,50019 Sesto Fiorentino,Italy
b
Ecole Polytechnique Fe
´
de
´
rale de Lausanne,Institute of Photonics and Quantum Electronics,Station 3,CH-1015 Lausanne,Switzerland
c
Institute of Photonics and Nanotechnology,CNR,via del Cineto Romano 42,00156 Roma,Italy
d
COBRA Research Institute,Eindhoven University of Technology,5600 MB Eindhoven,The Netherlands
e
European Laboratory for Non-linear Spectroscopy,CNISM and Department of Physics,University of Florence,
Via Nello Carrara 1,50019 Sesto Fiorentino,Italy
Received 25 December 2010;received in revised form 28 February 2011;accepted 9 April 2011
Abstract
The insertion of a metal-coated tip on the surface of a photonic crystal microcavity is used for simultaneous near field imaging of
electric and magnetic fields in photonic crystal nanocavities,via the radiative emission of embedded semiconductor quantumdots
(QD).The photoluminescence intensity map directly gives the electric field distribution,to which the electric dipole of the QD is
coupled.The magnetic field generates,via Faraday’s law,a circular current in the apex of the metallized probe that can be
schematized as a ring.The resulting magnetic perturbation of the photonic modes induces a blue shift,which can be used to map the
magnetic field,within a single near-field scan.
#2011 Elsevier B.V.All rights reserved.
Keywords:Near-field;Magnetic imaging;Photonic crystal
1.Introduction
The ultimate tailoring of the electromagnetic field,
developed in the last years,has have made possible the
storing photonic modes in very small volumes.These
achievements have generated a renewed interest in
nano-optics to gain a detailed knowledge of the spatial
distribution of the optical fields.As a result,different
near field scanning microscopy (NSOM) approaches,
for imaging the fields in photonic structures,have been
developed since the very beginning of the field.
Pioneering works have showed that the nanometer size
dielectric apex of the tip transforms the evanescent
electric field-tail at the sample surface in propagating
waves and thereby maps the electric near-field
intensities [1–4].Therefore the near field intensity
map can be used as a direct measurement of the electric
local density of states (LDOS).Special designs of the
tips have been used to convert the magnetic field to
propagating photons into the tip.Hence the intensity
maps as probe of the magnetic fields [5,6].Devaux et al.
found that with a proper design of the fiber aperture,the
tip plasmon may be resonantly excited by the magnetic
field only for certain structures,radiating light into the
www.elsevier.com/locate/photonics
A
vailable online at www.sciencedirect.com
Photonics and Nanostructures – Fundamentals and Applications xxx (2011) xxx–xxx
* Corresponding author.
E-mail address:sv319@cam.ac.uk (S.Vignolini).
1569-4410/$ – see front matter#2011 Elsevier B.V.All rights reserved.
doi:10.1016/j.photonics.2011.04.006
fiber and obtaining a magnetic image pattern [5].Quite
similarly,Burresi et al.showed that,by fabricating a
metallic split ring resonator at the apex of a near-field
probe,it is possible to image the magnetic field by
measuring the intensity map [6].
Avery different approach,based on the tip induced
spectral shift of the photonic modes,has been developed
for higher fidelity imaging of both electric and magnetic
fields.The interaction of a dielectric tip with the
photonic mode gives a red shift of the resonances
whenever the tip is above a region of high electric fields
[7–11].More recently it has been reported that a
metallic tip produces a magnetic perturbation of the
photonic modes inducing a blue shift of their resonances
which can be used to map the magnetic field [12,13].
The novelty of the present study is to demonstrate
that the two approaches so far used for imaging the
photonic modes (the intensity detection and the tip
induced spectral shift) can be linked together to obtain a
simultaneous measurement of the electric and magnetic
components of photonic modes within a single
measurement.We showed that,by using a commercial
metal-coated tip,we obtain an intensity map,which
gives the imaging of the electric field while the spectral
shift due to the tip perturbation gives a direct measures
of the magnetic field distribution.
2.Experimental details
We study a two-dimensional photonic triangular
lattice of air holes with lattice parameter a = 301 nm
and filling fraction f = 35% fabricated on a suspended
320-nm-thick GaAs membrane embedding three layers
of high-density InAs quantum dots (QDs) grown by
Stranski-Krastanow molecular beam epitaxy.The
photonic crystal microcavity PCMC,denoted D2,
consist in four missing holes in the lattice organized
in a diamond-like geometry (see inset of Fig.1).The
fabrication process consists in patterning a 150-nm-
thick SiO
2
mask by 100 kVe-beam lithography,
followed by CHF
3
plasma etching and transfer into
the GaAs layer by SiCl
4
/O
2
/Ar reactive ion etching.The
membrane is then released by selective etching in an HF
solution.More details on the fabrication can be found in
Ref.[14].One interesting feature of the D2 PCMC is
that the first two resonances M1 and M2 are
characterized by orthogonal near field spatial distribu-
tion of the electric and magnetic intensity,which is
helpful for comparison of the experimental data with
calculated results.An illumination-collection NSOM
setup (Twinsnom,OMICRON) is used with a diode
laser (780 nm),as an excitation source coupled into the
tip that is raster-scanned at a constant height across the
sample’s surface.We use a metal-coated tip in order to
simultaneously probe the electric and magnetic fields.
Photoluminescence (PL) signal is,dispersed by a
spectrometer and detected by a cooled InGaAs array (a
typical spectrum is reported in Fig.1).The overall
spatial resolution,obtained from the experimental data
(as described below) is on the order of 100 nm.All the
data reported in this paper refer to room temperature.
Numerical calculations have been performed with a
commercial three-dimensional (3D) finite-difference
time-domain (FDTD) code (CrystalWave,Photond).
Computational meshes were 15 grid points per period.
3.Tip to sample interaction
Consider a metal-coated probe tip a few nanometers
from the sample.The nanometer-size tip frustrates the
total internal reflected light inside the sample when
scanning close to the surface and thereby maps the near-
field intensities.The electric-field component at the
sample surface induces an electric polarization in the
dielectric core of the probe,generating a propagating
mode that can be detected at the other end of the fiber.
The intensity map of the detected signal is therefore
proportional to the electric field intensity,unless a
special design of the tip strongly enhances the radiative
emission via the magnetic polarization by means of
plasmonic [10] or split ring resonances [11].
In addition to the collected light,we have to take into
account the perturbation of the tip on the frequency of
S.Vignolini et al./Photonics and Nanostructures – Fundamentals and Applications xxx (2011) xxx–xxx2
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PNFA-264;No.of Pages 5
Please cite this article in press as:S.Vignolini,et al.,Simultaneous near field imaging of electric and magnetic field in photonic
crystal nanocavities,Photon Nanostruct:Fundam Appl (2011),doi:10.1016/j.photonics.2011.04.006
Fig.1.Typical PL spectrum collected during the scan with the tip.
The two peaks in the spectra correspond to the two main mode of the
cavity.(I) The inset reports a scanning electron microscope image of
the sample.
the photonic modes.This can be either electric [6,12],or
magnetic [12,13].Inserting a dielectric tip corresponds
to an increase of the dielectric constant (dielectric tip
instead of air) and a red shift of the nth mode is found:
Dv
n
¼ 
v
n
2
R
d
3
r
~
E

n
ð
~
rÞ  ðdeð
~

~
E
n
ð
~
rÞÞ
R
d
3
r
~
E

n
ð
~
rÞ  ðeð
~

~
E
n
ð
~
rÞÞ
:(1)
In this case the shift is proportional to the intensity of
the electric field at the position of the nano-object and,
therefore,it can be used for mapping the electric field
intensity distribution (i.e.LDOS) on the sample.In a
very similar manner,we can consider the perturbation
on the PCMC due to a magnetic tip.From perturbation
theory (not reported here) we have found that the
frequency shift of the mode is given by a relationship
identical to the dielectric case,as shown in Eq.(2),
where the dielectric constant and the electric field are
substituted with the magnetic susceptibility and the
magnetic field [12]:
Dv
n
¼ 
v
n
2
R
d
3
r
~
H

n
ð
~
rÞ  ðdmð
~

~
H
n
ð
~
rÞÞ
R
d
3
r
~
H

n
ð
~
rÞ 
~
H
n
ð
~

(2)
As shown in Refs.[12,13],the simplest magnetic
nano-object is a metallic ring (in our case the aperture of
the metallic coated tip),which interacts with the
magnetic field normal to the ring plane (z axis).In this
case,an electric current is induced along the ring and
the corresponding magnetic moment turns out to be
antiparallel to the magnetic field (see Fig.2).Therefore,
the magnetic susceptibility of the ring is a tensor with
only one diagonal component (zz),whose real part is
negative.The resulting shift of the mode frequency is
towards higher frequencies and is proportional to the
intensity of the z-component of the magnetic field,as
stated by Eq.(3):
Dv
n
¼ a
j j
v
n
2
ð
~
H
n
ð
~
r
0
ÞÞ
z




2
R
d
3
r
~
H

n
ð
~
rÞ 
~
H
n
ð
~

;(3)
where a is a parameter which depends on the R-L
characteristics and geometry of the ring.The perturba-
tion of the magnetic susceptibility of the PCMC would
produce a high frequency shift of the photonic eigen-
modes.In principle,for a metal-coated dielectric tip
both magnetic and electric perturbations could occur.
The sign of the mode shift is therefore a fingerprint of
the electric or magnetic interaction.
Apriori,deciding whether the dielectric or magnetic
perturbation dominates for a specific metallic coated tip
is a complicated problem,which depends on the details
of the tip and/or of the photonic modes that the tip is
perturbing.Aposteriori there is,however,a very simple
way to distinguish between the two interactions the sign
of the induced shift of the photonic resonances:a blue
(red) shift is the fingerprint of a magnetic (electric)
perturbation.
4.Imaging
In Figs.3(a) and (b) the calculated electric field
distribution associated with the two main modes of the
cavities is compared with the map of PL intensity,in
panels (c) and (d).The PL intensity maps of each mode
are obtained by reporting as function of the position of
the tip the intensity of the peak associated to the mode.
In previous works we used a dielectric tip in a similar
SNOM experiment and we found that the uncoated tip
also collected photons fromits sides [15],resulting in a
poor spatial resolution and low fidelity mapping of the
electric LDOS [9,15].Here we find that using a metal-
coated tips the PL intensity maps,reproduce with high
fidelity the electric field intensity distribution,with a
resolution that is comparable to the tip aperture
(100 nm).
In order to provide a map of the magnetic field
intensity along the vertical direction the spectra are
fitted using a Lorentzian curve,and the wavelength of
the peak extrapolated fromthe fit is reported as function
of the position of the tip during the scan.We observe
that the values obtained for the peak are position-
dependent,and the peak frequency is always larger than
the frequency of the unperturbed mode,revealing a
magnetic interaction as described in the previous
S.Vignolini et al./Photonics and Nanostructures – Fundamentals and Applications xxx (2011) xxx–xxx 3
+ Models
PNFA-264;No.of Pages 5
Please cite this article in press as:S.Vignolini,et al.,
Simultaneous near field imaging of electric and magnetic field in photonic crystal nanocavities,Photon Nanostruct:Fundam
Appl (2011),doi:10.1016/j.photonics.2011.04.006
Fig.2.Schematic representation of the interaction between the tip and
the sample.The active region of the tip consists in its aperture that
interacts with the magnetic field normal to the ring plane.
section.As discussed above,the sign of the shift means
that the magnetic perturbation has overcome the
dielectric perturbation.We do not claim that this result
is a general feature of all metal-coated fibers,on the
contrary it is quite likely that the dominance.Of the
magnetic perturbation with respect to the dielectric
perturbation would depend on the details of the tip.We
simply demonstrate that it is possible,by using a
commercial metal-coated NSOMfiber,to end up with a
prevalent magnetic perturbation of the tip.Similar
results have been shown in Refs.[12,13].In Fig.4(a)
and (b) the calculated intensity distribution of the
magnetic field component along the vertical axis is
compared with the experimental spectral shift map
reported in panels (c) and (d).In this case,the resolution
and,consequently,the fidelity are slightly worse than in
the case of the electric field mapping,when indicates,as
expected,that the active area of the tip that provides the
interaction is larger than the aperture of the tip into
which the signal is collected.However,the obtained
S.Vignolini et al./Photonics and Nanostructures – Fundamentals and Applications xxx (2011) xxx–xxx4
+ Models
PNFA-264;No.of Pages 5
Please cite this article in press as:S.Vignolini,et al.,Simultaneous near field imaging of electric and magnetic field in photonic
crystal nanocavities,Photon Nanostruct:Fundam Appl (2011),doi:10.1016/j.photonics.2011.04.006
Fig.3.In (a) and (b) the FDTDcalculated electric field distribution associated to the two main modes of the cavities M1 and M2,respectively.(c and
d) Maps of PL intensity for the two modes M1 and M2,respectively.
Fig.4.Panel (a) and (b) report the FDTDcalculations of the magnetic field intensity of the component along the vertical direction for the mode M1
and M2,respectively.In (c) and (d) the experimental spectral shift maps are reported.
spatial resolution is far behind the diffraction limit
(200 nm).
5.Conclusion
The sub-wavelength nature of the structures and
fields involved in photonic and metamaterial systems
require the development of novel nano-optical techni-
ques.We demonstrate that,by using a simple metallic
tip it is possible to measure simultaneously the magnetic
and electric field of a photonic mode.The spectral shift
of the photonic mode is due to magnetic perturbation,
while the detection of PL signal is due to the electric
interaction.The subtle interplay of these two experi-
mental effects may open the route for testing a famous
and interesting variant of Heisenberg’s uncertainty
principle which relates the electric and magnetic fields.
References
[1] N.Louvion,D.Ge
´
rard,J.Mouette,F.de Fornel,C.Seassal,X.
Letartre,A.Rahmani,S.Callard,Local observation and spec-
troscopy of optical modes in an active photonic-crystal micro-
cavity,Phys.Rev.Lett.94 (2005) 113907.
[2] S.I.Bozhevolnyi,V.S.Volkov,J.Arentoft,A.Boltasseva,T.
Sondergaard,M.Kristensen,Direct mapping of light propaga-
tion in photonic crystal waveguides,Opt.Commun.212 (2001)
51.
[3] P.Kramper,M.Kafesaki,C.M.Soukoulis,A.Birner,F.Mu
¨
ller,
U.Go
¨
sele,R.B.Wehrspohn,J.Mlynek,V.Sandoghdar,Near-
field visualization of light confinement in a photonic crystal
microresonator,Opt.Lett.29 (2004) 174.
[4] H.Gersen,T.J.Karle,R.J.P.Engelen,W.Bogaerts,J.P.Korterik,
N.F.van Hulst,T.F.Krauss,L.Kuipers,Local observation and
spectroscopy of optical modes in an active photonic-crystal
microcavity,Phys.Rev.Lett.94 (2005) 073903.
[5] E.Devaux,A.Dereux,E.Bourillot,J.-C.Weeber,Y.Lacroute,
J.-P.Goudonnet,C.Girard,Phys.Rev.B 62 (2000) 10504.
[6] M.Burresi,D.van Oosten,T.Kampfrath,H.Schoenmaker,R.
Heideman,A.Leinse,L.Kuipers,Science 326 (2009) 550.
[7] A.F.Koenderink,R.Wu
¨
est,B.C.Buchler,S.Richter,P.Strasser,
M.Kafesaki,A.Rogache,R.B.Wehrspohn,C.M.Soukoulis,D.
Ernig,F.Robin,H.Ja
¨
ckel,V.Sandoghdar,Near-field optics and
control of photonic crystals,Photonics Nanostruct.Fundam.
Appl.3 (2005) 63.
[8] A.F.Koenderink,M.Kafesaki,B.C.Buchler,V.Sandoghdar,
Controlling the resonance of a photonic crystal microcavity by a
near-field probe,Phys.Rev.Lett.95 (2005) 15390.
[9] S.Mujumdar,A.F.Koenderink,T.Su
¨
nner,B.C.Buchler,M.
Kamp,A.Forchel,V.Sandoghdar,Near-field imaging and
frequency tuning of a high-Qphotonic crystal membrane micro-
cavity,Opt.Express 15 (2007) 17214.
[10] L.Lalouat,B.Cluzel,P.Velha,E.Picard,D.Peyrade,J.P.
Hugonin,P.Lalanne,E.Hadji,F.de Fornel,Near-field interac-
tions between a subwavelength tip and a small-volume photonic-
crystal nanocavity,Phys.Rev.B 76 (2007) 041102(R).
[11] F.Intonti,S.Vignolini,F.Riboli,A.Vinattieri,D.S.Wiersma,M.
Colocci,L.Balet,C.Monat,C.Zinoni,L.H.Li,R.Houdre,M.
Francardi,A.Gerardino,A.Fiore,M.Gurioli,Spectral tuning
and near-field imaging of photonic crystal microcavities,Phys.
Rev.B 78 (2008) 041401(R).
[12] S.Vignolini,F.Intonti,F.Riboli,L.Balet,L.H.Li,M.Francardi,
A.Gerardino,A.Fiore,D.S.Wiersma,M.Gurioli,Magnetic
imaging in photonic crystal microcavities,Phys.Rev.Lett.105
(2010) 123902.
[13] M.Burresi,T.Kampfrath,D.van Oosten,J.C.Prangsma,B.S.
Song,S.Noda,L.Kuipers,Magnetic light-matter interactions in
a photonic crystal nanocavity,Phys.Rev.Lett.105 (2010)
123901.
[14] M.Francardi,L.Balet,A.Gerardino,C.Monat,C.Zinoni,L.H.
Li,B.Alloing,N.Le Thomas,R.Houdre,A.Fiore,Phys.Stat.
Sol.C 3 (2006) 3693.
[15] S.Vignolini,F.Intonti,F.Riboli,D.S.Wiersma,L.Balet,L.H.
Li,M.Francardi,A.Gerardino,A.Fiore,M.Gurioli,Polariza-
tion-sensitive near-field investigation of photonic crystal micro-
cavities,Appl.Phys.Lett.94 (2009) 163102.
S.Vignolini et al./Photonics and Nanostructures – Fundamentals and Applications xxx (2011) xxx–xxx 5
+ Models
PNFA-264;No.of Pages 5
Please cite this article in press as:S.Vignolini,et al.,Simultaneous near field imaging of electric and magnetic field in photonic
crystal nanocavities,Photon Nanostruct:Fundam Appl (2011),doi:10.1016/j.photonics.2011.04.006