Miniature polarization analyzer based on surface plasmon polaritonsYu-Bo Xie, Zheng-Yang Liu, Qian-Jin Wang, Yong-Yuan Zhu, and Xue-Jin Zhang Citation: Applied Physics Letters 105, 101107 (2014); doi: 10.1063/1.4895517 View online: http://dx.doi.org/10.1063/1.4895517 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Four-level polarization discriminator based on a surface plasmon polaritonic crystal Appl. Phys. Lett. 98, 111109 (2011); 10.1063/1.3561748 Observation of the splitting of degenerate surface plasmon polariton modes in a two-dimensional metallicnanohole array Appl. Phys. Lett. 90, 111103 (2007); 10.1063/1.2713145 Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice Appl. Phys. Lett. 89, 093102 (2006); 10.1063/1.2338886 Nanodot coupler with a surface plasmon polariton condenser for optical far/near-field conversion Appl. Phys. Lett. 86, 181108 (2005); 10.1063/1.1920419 Excitation and direct imaging of surface plasmon polariton modes in a two-dimensional grating Appl. Phys. Lett. 86, 111110 (2005); 10.1063/1.1883334

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Miniature polarization analyzer based on surface plasmon polaritons

Yu-Bo Xie, Zheng-Yang Liu, Qian-Jin Wang, Yong-Yuan Zhu,a) and Xue-Jin Zhangb)

National Laboratory of Solid State Microstructures, Nanjing University, and School of Physics,Nanjing University, Nanjing 210093, China

(Received 7 August 2014; accepted 29 August 2014; published online 11 September 2014)

We investigated a miniature plasmonic polarization analyzer measuring Stokes parameters of a light.

The optical component consists of a 2� 2 polarizer array, three linear polarizers, and one right-

handed circular polarizer. These polarizers are formed with bull’s eye structures on a metal surface.

The measurements of Stokes parameters in a unit radius Poincar�e sphere were demonstrated.

Compact polarization-dependent optical sensing and imaging can be envisioned based on the minia-

ture polarization analyzer. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4895517]

Since the first observation of extraordinary optical trans-

mission (EOT)1 in periodically perforated metal films the

sub-wavelength patterns on metal-dielectric interface have

received much attention. It has proved that this optical phe-

nomenon is attributed to surface plasmon polaritons (SPPs),

an electromagnetic surface waves in the interface between a

dielectric and metal. The highly localized character makes it

possible to miniaturize photonics to nanoscale. Many com-

pact applications have been demonstrated from plasmonic

waveguides to optical sensing.2–5 Among these designs

bull’s eyes that consist of a perforated aperture surrounded

by concentric grooves on metal films have drawn much inter-

est with its excellent properties.6 It can not only control the

optical intensity with extremely high transmission efficiency

and collimate the output light by shaping the wave front but

also can manipulate the state of polarization (SOP) of a light.

It is of vital importance to control the SOP in optical applica-

tions for many optical phenomena are polarization sensitive.

There has been extensive research about the SOP based on

SPPs such as optical activity, optical rotation, and circular

dichroism.7–11 In addition, the most important polarization

elements, linear polarizer and wave plates such as half- and

quarter-wave plates (HWP and QWP), also have been dem-

onstrated based on SPPs12–17 especially using the bull’s eyes

structures. For example, a miniature plasmonic QWP can be

constructed using an elliptical bull’s eye structure,18,19 of

which the kSPP=4 (kSPP is the wavelength of SPPs) difference

of main axes introduce a phase retard after SPPs propagating

through the metal surface. However, a cascade of linear po-

larizer, HWP and QWP, has not been developed, which is

necessary to generate or characterize a light with arbitrary

SOP. For instance, circular polarizer and stokes analyzer all

need a combination of linear polarizer and QWP.

It is well known that Stokes parameters provide the full

information of the SOP. Here, we put forward a miniaturized

Stokes analyzer (MSA) via integration of three differently

oriented plasmonic linear polarizers and one plasmonic

right-handed circular polarizer. The four polarizers are all

developed from the so-called bull’s eye structure;6 each has

a size of about one pixel of charge coupled device (CCD) on

a metallic surface. The SOP can be measured in real time by

MSA. This MSA is expected to be compatible with current

CCD manufacturing process, contributing to polarization-

dependent micro-vision and multichannel sensing.

In the right-handed Cartesian coordinate system, the

SOP of fully polarized light progress in the positive z direc-

tion can be described by normalized Jones vector ½Ex; Eyeid�,in which Ex, Ey, and d are instantaneous values of electrical

field components and relative phase. In order to deal

with arbitrary polarized light, the Stokes parameters

(S0; S1; S2; S3) are used,20 which can be defined as

S0 ¼ hE2xi þ hE2

yiS1 ¼ hE2

xi � hE2yi

S2 ¼ h2ExEy cos diS3 ¼ h2ExEy sin di; (1)

where h i representing a temporal average on the measure-

ment time. Alternatively, an equivalent experimental defini-

tion can be used

S0 ¼ Ix þ Iy

S1 ¼ Ix � Iy

S2 ¼ 2I45 � ðIx þ IyÞS3 ¼ 2IQ45 � ðIx þ IyÞ; (2)

where Ix, Iy, and I45 are the intensity of the horizontal, verti-

cal, and diagonal (45� clockwise) linear component, respec-

tively. IQ45 is the intensity of right-handed circular

component. The first three intensities can be measured by

linear polarizers with transmitted axis along their light com-

ponent. The measurement of IQ45 can be achieved through a

right-handed circular polarizer which consists of a QWP

with fast axis along the x axis followed by a linear polarizer

with transmitted axis along the diagonal.

In our experiment, we use a setup as shown in Figure

1(a) to characterize the Stokes analyzer. A collimated He-Ne

laser at k¼ 633 nm illuminated on the sample. The diameter

of the laser beam is about 500 lm. The light transmitted

through the sample was collected by an objective (NA¼ 0.9)

and imaged on a CCD camera. The SOP impinging on the

structure was prepared by a SOP controller, comprised of a

linear polarizer (P), a HWP (k/2), and a QWP (k/4), each of

which can be rotated independently. This SOP controller

a)Email: yyzhu@nju.edu.cnb)Email: xuejinzh@nju.edu.cn

0003-6951/2014/105(10)/101107/4/$30.00 VC 2014 AIP Publishing LLC105, 101107-1

APPLIED PHYSICS LETTERS 105, 101107 (2014)

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enables us to perform the experiment with an arbitrary fully

polarized input light.

It is well-known that a narrow slit in a metal film selec-

tively scatters incident light that is polarized perpendicularly

to it, which makes it behave like a linear polarizer.21 This is

also true in the bull’s eye structure if the aperture is replaced

by a narrow slit. A recent theoretical work shows that strong

polarization-dependent transmission22 occurs in a bull’s eye

with a central elliptical aperture. Moreover, the degree of

polarization is only determined by the aspect ratio of the

aperture and an amazing polarization extinction ratio of

1000:1 has been predicted. In our MSA, the linear polarizers

are made of such bull’s eye structures with a perforated slit

surrounded by six concentric periodic grooves. It is milled

by focus-ion-beam (FIB, FEI Helios NanoLab 600i) on a

180 nm thick Au film, which is sputtered on a 0.5 mm thick

silica substrate separated by a 10 nm titanium adhesion layer.

This structure is designed to be resonant at k¼ 633 nm, cor-

responding to kSPP ¼ 606nm. The period, width, and height

of grooves are chosen as 600 nm, 300 nm, and 20 nm. The

width and length of slit is 50 nm and 200 nm. The radius of

innermost circular grooves is R¼ 1.1 lm. We have made

three such bull’s eyes with differently oriented slit as shown

in scanning electron microscopy (SEM) image in Fig. 1(b),

which act as horizontal, vertical, and diagonal linear polar-

izer, respectively. In Fig. 1(c), it shows an enlarged view of

the central slit, which is similar for all four polarizers.

For the right-handed circular polarizer, we just substitute

the circular concentric grooves of diagonal linear polarizer

for elliptical ones with long axis dny ¼ dþ nPþ D and short

axis dnx ¼ dþ nP, as shown in the lower right corner of Fig.

1(b). Here, d ¼ 1:05 lm is the length of innermost short axis,

D is the increment from short axis to long axis (here,

D ¼ 165nm), P ¼ 600nm is the period of grooves, and n is

an integer going from 0 to 5. The parameters of elliptical

grooves have been optimized to make the structure having a

maximum transmittance and a best performance of filtering

left-handed circular polarization light. The principle of the

circular polarizer can be illustrated by considering simply

that elliptical grooves act as a QWP and central slit act as a

linear polarizer. When transmitting through this structure,

the light seems to go first through a QWP with the fast axis

along the x axis and then through the diagonal linear

polarizer.

The intensities of Ix, Iy, and I45, IQ45 can be obtained

from the diffraction limited Airy spots on the image recorded

by CCD, as shown in Fig. 1(d), where a snapshot of incident

left circularly polarized light case is given. Three linear

polarizers have equal intensity of half of input light. The last

right circular polarizer shows almost zero intensity for reject-

ing the left circularly polarized light. We take the sum of all

pixel values of an Airy spot as the intensity after removing

the background noise. This is different from previous method

to define the intensity by taking the maximum of the Airy

spot.19 But it is a realistic choice for application in nano-

optics.

Figure 2(a) shows the polarization property of the linear

polarizers. The blue, green, and red stand for the data of the

horizontal, diagonal, and vertical linear polarizer, respec-

tively. In the beginning, we checked the depolarization of

setup with and without the sample, both showing little

FIG. 1. (a) Sketch of experimental

setup. (b) SEM image of the Stokes an-

alyzer. The scale bar is 5 lm long. (c)

Enlarged view of the central slit of cir-

cular polarizer. (d) A typical image of

diffraction-limited Airy spots corre-

sponding to four bull’s eye elements in

the SEM image in (b) with left circu-

larly polarized input light. Three linear

polarizers have equal intensity of half

of the input light. The last right circu-

lar polarizer shows almost zero inten-

sity for filtering the left circularly

polarized light.

FIG. 2. (a) Normalized theoretical (continuous curves) and experimental

(dot curves) transmission intensity of three linear polarizers. The polariza-

tion angle of linearly polarized input light varies from 0� to 180� with regard

to the y axis. (b) Normalized transmission of elliptical bull’s eyes with vary-

ing increment D. Successive curves have been offset by 0.5 units for clarity.

Input polarization varies from 0� to 360�every 10�one step along the blue

circle shown in the inset (The origin and direction is marked as a red

arrow.).

101107-2 Xie et al. Appl. Phys. Lett. 105, 101107 (2014)

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depolarization. Consequently, we can represent the bull’s

eye by a Jones matrix. Then the normal transmission (dotted

curves) is measured for each linear input light with polariza-

tion angle varying from 0� to 180� every 5� one step relative

to the y axis. The experimental results are in good agreement

with the theoretical results (continuous curves) deduced

from the Jones matrix JL ¼1 0

0 0

� �. It demonstrates clearly

that these polarizers keep optical coherence and follow the

Malus law of absorption very well. Furthermore, their extinc-

tion ratio is too large to be recognized in our current accuracy

of measurement, making them as perfect linear polarizers.

In general, the periodic grooves act as a coupling grating

to convert the input light to SPPs, which travel inwardly and

would excite the central nanoslit when across it. SPPs launched

by one side of a circular groove would be reflected weakly by

its opposite side. The reflected SPPs would excite the central

nanoslit, too. Thus, each circular groove behaves as a low-Q

Fabry-Perot (F-P) cavity almost independently. In addition, the

central nanoslit can be excited directly by the incident light,

which is another channel. Usually this direct channel is much

weaker than the SPPs-excited channel in all EOT. The interfer-

ence between these two channels leads to the so-called Fano

resonance, whose intensity is dependent on the phase differ-

ence of these two channels.23 Here, for a low-Q F-P cavity, the

phase difference is mainly determined by the innermost radius

(R) of grooves. In our design, R ¼ 1:1 lm is a good choice

with transmission almost equal to the circular polarizer. For

both channels, only the light or SPPs polarized perpendicularly

to the nanoslit can excite it. We can conclude that this bull’s

eye behaves as a linear polarizer with high transmission.

Figure 2(b) shows the experimental optimization of circu-

lar polarizer. There are 10 normalized transmittance curves

(offset by 0.5) of different elliptical bull’s eyes with d ¼1:05 lm and increment D ¼ dn

y � dnx varying from 75 nm to

210 nm every 15 nm one step. In the experiment, the input

polarization representing by Stokes parameters varies from 0�

to 360� every 10� one step along the blue circle shown in the

inset (the origin and direction is marked as a red arrow). The

Jones matrix of these structures can be expressed as

JC ¼ JLJQ, where JL ¼1 0

0 0

� �and JQ ¼ qeid 0

0 1

� �are

in the principal axis system. JL is the same as the one before,

for that the linear polarization property is only controlled by

the slit shape. JQ is the Jones matrix of wave plate determined

by the increment D and innermost short axis d of grooves,

where q is the dichroism and d is the phase retard. For these el-

liptical polarizers, measured data (dotted curves) have a good

agreement with the theoretical results (continuous curves).

In our design, we choose d ¼ 1:05 lm as the innermost

short axis, making each elliptical groove just have a little de-

formation with respect to the circular one. It is reasonable to

use the conclusion of the linear polarizer and to decompose

the arbitrary polarization to two linear polarizations along

the main axis. Considering two Fano interferences along the

short axis and long axis, different lengths of two main axes

give rise to different transmittance, resulting in dichroism q.

There is an approximate linear relationship d ¼ 2pD=kSPP

between phase retard d and increment D. This linear

relationship can be understood clearly by neglecting the

direct channel and the reflection of SPPs because they are all

weak in bull’s eye. A phase difference between SPPs propa-

gating along two main axes is introduced after arriving at the

central slit. However, Fano resonance would introduce a lit-

tle deviation from this linear relationship. From the red line,

we can get a quick view of the linear variation of the phase

retard d vs. the increment D. For d ¼ 1:05 lm and

D ¼ 165nm, we obtained the best results with d ¼ 82� and

q � 0:9 by data fitting.

Figure 3(a) shows measured intensities (dotted curves)

of four Stokes analyzer elements: Ix (blue), Iy (red), I45

(green), IQ45 (black), as well as theoretical results (continu-

ous curves) deduced from the Jones matrice JC; JL. Only

IQ45 have a visible deviation from original input SOP (brown

curves with x markers), which is mainly caused by a non-

perfect circular polarizer with phase retard of 82�. As input

light is full polarized the temporal average h i in Eq. (1) have

no effect. This means that a simple correction method can be

deduced from Eq. (1) to remove the error from phase devia-

tion in circular polarizer

S3 ¼ ðSu3 � S2 cos uÞ=sinu: (3)

Here, u ¼ 90� � d is the phase deviation from a standard cir-

cular polarizer, Su3 is the measured Stokes parameter, and S3

is the corrected value. After using Eq. (3), the systematic

error has been removed so that theoretical Stokes parameters

(continuous curves, S0 (blue), S1 (red), S2 (green), and S3

(black)) superposed with the original input value (dashed

curves), as shown in Fig. 3(b). The corrected result is also

shown in a Poincar�e sphere in Fig. 3(c). Only half of the data

is given for clarity. Here, the red, green, and blue circle cor-

respond to the section line of plane S1S2, S1S3, and S2S3 in

the unit radius Poincarehe unit radius Poincaref�e sphere. The

measured results are consistent with the input SOP very

FIG. 3. (a) Intensity measurement of four Stokes analyzer elements: Ix

(blue), Iy (red), I45 (green), and IQ45 (black). (b) Stokes parameters after cor-

rected using Eq. (3): S0 (blue), S1 (red), S2 (green), S3 (black). (c)

Comparison between measured Stokes parameters using our miniature

Stokes analyzer and input polarization in a Poincar�e sphere. In experiments,

input polarization varying from 0� to 360� every 10�one step along the blue

circle. The origin and direction is marked as a red arrow.

101107-3 Xie et al. Appl. Phys. Lett. 105, 101107 (2014)

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well. Our miniature Stokes analyzer can give a good mea-

surement of SOP of light.

In summary, we have proposed a miniature Stokes ana-

lyzer basing on SPPs. This component is as small as ten

micrometers and could be fabricated in arrays. Combining

with current CCD manufacturing techniques a CCD-liked

polarization device can be made. This will provide a wide

application in polarization-dependent optical sensing and

imaging.

This work was supported by the State Key Program for

Basic Research of China (Grant Nos. 2010CB630703 and

2012CB921502), by the National Natural Science

Foundation of China (Grant Nos. 11274159, 11174128, and

11374150) and by PAPD.

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