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, Italyb Ecole Polytechnique Federale 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, Italyd 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

Available online 15 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 quantum dots

(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

www.elsevier.com/locate/photonics

Available online at www.sciencedirect.com

Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 251–255

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

* 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

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

S. Vignolini et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 251–255252

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.

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].

A very 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 SiO2 mask by 100 kVe-beam lithography,

followed by CHF3 plasma etching and transfer into

the GaAs layer by SiCl4/O2/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 10 (2012) 251–255 253

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:

Dvn ¼ �vn

2

Rd3r~E

�nð~rÞ � ðdeð~rÞ~Enð~rÞÞ

Rd3r~E

�nð~rÞ � ðeð~rÞ~Enð~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]:

Dvn ¼ �vn

2

Rd3r~H

�nð~rÞ � ðdmð~rÞ~Hnð~rÞÞ

Rd3r~H

�nð~rÞ � ~Hnð~rÞ

(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

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.

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):

Dvn ¼ aj jvn

2

ð~Hnð~r0ÞÞz��

��2

Rd3r~H

�nð~rÞ � ~Hnð~rÞ

; (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.

A priori, 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. A posteriori 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 from its 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 from the 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 10 (2012) 251–255254

Fig. 3. In (a) and (b) the FDTD calculated 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.

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 NSOM fiber, to end up with a

prevalent magnetic perturbation of the tip. Similar

Fig. 4. Panel (a) and (b) report the FDTD calculations of the magnetic field in

and M2, respectively. In (c) and (d) the experimental spectral shift maps a

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

tensity of the component along the vertical direction for the mode M1

re reported.

S. Vignolini et al. / Photonics and Nanostructures – Fundamentals and Applications 10 (2012) 251–255 255

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.

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