# Surface plasmon resonance for in-plane birefringence measurement of
anisotropic thin organic film

Amrit Kumar  Department of Physics, Birla Institute of Technology and Science,
Pilani (BITS Pilani), 333031, India.  Raj Kumar Gupta<EMAIL_ADDRESS>pilani.ac.in Department of Physics, Birla Institute of Technology and Science,
Pilani (BITS Pilani), 333031, India.  Manjuladevi V  Department of Physics,
Birla Institute of Technology and Science, Pilani (BITS Pilani), 333031,
India.  Ashutosh Joshi  Department of Physics, Birla Institute of Technology
and Science, Pilani (BITS Pilani), 333031, India.

###### Abstract

The measurement of in-plane birefringence ($\Delta{n}$) of ultrathin film is
challenging due to a significant deviation of physical properties of materials
in ultrathin regime as compared to that in bulk state. Surface plasmon
resonance (SPR) phenomenon can be employed to measure change in refractive
index of ultrathin film at a very high resolution. This article discusses
simulation of SPR phenomenon in Kretschmann configuration for the measurement
of $\Delta{n}$ in organic thin film exhibiting nematic-like ordering on the
two dimensional gold surface. The distribution of plasmonic field on the gold
surface was found to be anisotropic. This suggested that the coupling
plasmonic field with that of organic thin film exhibiting nematic-like
ordering on the gold surface will be non-isotropic. Therefore, a non-zero
difference in resonance angle (RA) was obtained from SPR measurement performed
along the optic-axis (OA) and orthogonal to OA of the in-plane nematic
ordering ($\Delta\theta$). A calibration surface showing the variation of
($\Delta\theta$) as a function of $\Delta{n}$ and thickness of thin organic
film consisting of shape anisotropic tilted molecules exhibiting nematic-like
ordering on gold surface was obtained. This calibration surface was employed
for the measurement of $\Delta{n}$ of single layer of Langmuir-Blodgett films
of cadmium stearate (CdSA) and 4’-octyl-4-biphenylcarbonitrile (8CB) deposited
on SPR chips. The thickness of the LB films was estimated using X-ray
reflectivity measurement and $\Delta\theta$ was measured using a home built
SPR instrument. The $\Delta{n}$ values were found to be 0.012 and 0.022 for
ultrathin films of CdSA and 8CB molecules, respectively.

Surface plasmon resonance; Kretschmann configuration; In-plane birefringence;
Langmuir-Blodgett film; FDTD simulation

## Introduction

The optical phenomenon surface plasmon resonance (SPR) is very popular owing
to its remarkable application in the field of sensors. The phenomenon
facilitates a highly sensitive and label free sensing for a variety of
biological and chemical analytes Homola2008 ; Wu2019 ; Gupta2017 . The
underlying principle for a SPR sensor is based on measurement of changes in
refractive index (RI) at a very high resolution due to molecular interactions.
The surface plasmon polaritons (SPP) can be excited at a metal-dielectric
interface by an incident electromagnetic wave traveling via a coupling medium
with RI greater than 1.0. The resonance can be established by matching the
wavevectors of the incident and the SPP waves. At the resonance, a maximum
energy will transfer from the incident wave to the SPP wave leading to
extinction of the characteristic incident electromagnetic wave from the
spectrum Homolabook2006 ; Abdulhalim2008 ; Prabowo2018 . In the widely
utilized Kretschmann configuration of SPR, a p-polarized monochromatic
electromagnetic wave is allowed to incident on the metal surface via a
coupling prism Krets1968 ; Krets1971 . In order to establish the SPR, the
angle of incidence is varied and the reflected intensity is recorded. At
resonance, the reflected intensity diminishes to minimum. The resonance angle
is unique for the given metal-dielectric interface. Therefore, any adsorption
of analytes at the metal-dielectric interface during sensing can alter the
dielectric nature and hence resonance angle (RA) shifts. The shift in RA can
be measured very precisely and the corresponding change in RI can be
calculated theoretically using the Fresnel’s relations devSNB . In addition to
the traditional sensing applications, the SPR phenomenon can also be used for
the measurement of optical anisotropy in thin films devJMS , temperature
measurement SPR_temp ; SPRtemp2 ; Lu2016  and optical filter wangAPL . A
typical resolution of the Kretschmann configuration based SPR instrument lies
in the range of $10^{-5}$ to $10^{-7}$ RIU devSNB ; resolution1 ; Homola_rev1
. Such a high resolution in the measurement of RI using SPR was successfully
utilized for quantification of optical anisotropy in ultrathin films.
Anisotropy in thin film arises due to tilt of shape anisotropic molecules
(e.g. rod shaped calamitic liquid crystal molecules) with respect to surface
normal which may yield in-plane nematic ordering. In an earlier report by our
group, the optical anisotropy in ultrathin films was estimated experimentally
using the SPR phenomenon by measuring shift in the RA in orthogonal directions
of the films exhibiting different degree of optical anisotropy devJMS . The
reported anisotropy in the ultrathin films was estimated from SPR angle
measurements in randomly chosen orthogonal directions. In order to estimate
the in-plane birefringence ($\Delta{n}=n_{e}-n_{o}$), the SPR measurement has
to be performed along the optic axis (OA) of the thin film and orthogonal to
it. The measured values of RI along OA and orthogonal to it can be treated as
extraordinary ($n_{e}$) and ordinary ($n_{o}$) components, respectively bire .
The shift in RA along OA and orthogonal to OA of a given anisotropic thin film
exhibiting nematic ordering in two dimensional plane can be defined as
$\Delta\theta$. In the present work, we have modified our experimental setup
by integrating a rotating platform (rotation axis along X-axis, Fig. 1 ) with
a resolution of 0.1∘ to rotate the film deposited substrate and measure the
SPR response in-situ as a function of angle of rotation of the film. This
modification ensures alignment of optics for the measurement of $n_{e}$ and
$n_{o}$ and hence $\Delta{n}$ of the ultrathin film. The RI of ultrathin film
will be dependent on several factors including the surface density,
orientation of molecules, surface morphology and the thickness of the film.
Thus the RA measured using SPR phenomenon will be dependent on such factors.
Therefore, a systematic study is needed for the estimation of important
optical parameter related to thin film viz. in-plane birefringence
($\Delta{n}$).

The reports in literature in general provide the value of birefringence of the
bulk material however, due to reduction of dimension of the material, the
physical properties deviate largely from that of bulk. Therefore, measurement
of physical properties of a material at the lower dimension is essential for
material engineering followed by device fabrication. The physical properties
of the low dimensional materials like two dimensional thin film depend on its
thickness. Hence, a calibration curve is essential for quantifying the
dependencies of a physical property on any such parameters. Since, the SPR
phenomenon can be potentially employed for the measurement of RI at a very
high resolution, a small in-plane birefringence due to tilt of shape
anisotropic organic molecules even in a single layer can be measured. Such
film with tilted molecules may exhibit nematic ordering on the surface. In
this article, we present a calibration surface showing the dependency of
$\Delta\theta$ on $\Delta{n}$ and thickness of the thin organic film. The
calibration surface was obtained through simulation and it was utilized for
the estimation of $\Delta{n}$ of single layer of Langmuir-Blodgett (LB) films
of cadmium stearate (CdSA) and 4’-octyl-4-biphenylcarbonitrile (8CB)
molecules. The values of thickness and $\Delta\theta$ of the LB films of CdSA
and 8CB was obtained from X-ray reflectivity and a home built SPR instrument,
respectively and these values were used in the calibration surface for the
estimation of the respective $\Delta{n}$.

## Simulation Setup

A finite difference time domain (FDTD) method was employed for the simulation
of SPR phenomenon in the Kretschmann configuration using a commercial package
of Lumerical lum1 ; lum2 . The FDTD method is highly reliable and advantageous
over other techniques in solving Maxwell’s equations for complex geometries of
materials. The simulation setup is shown in the Figure 1(a).

Figure 1: A schematic of (a) simulation setup showing the major components as
depicted. The plane of polarization is XY. The angle of incidence of the
monochromatic light (L) is $\theta_{i}$, thickness of each material and
detector (D) are shown and (b) a single layer of shape anisotropic molecules
(rod shaped) tilted with respect to X-axis along Y-axis on the YZ plane. The
projection of the molecules is shown in black. Such projection resembles
nematic ordering on 2D plane with optic axis along Y-axis.

The simulation was carried out using a monochromatic plane wave source (L)
having a wavelength of 635 nm. The perfectly matched layer (PML) boundary
condition with steep angle profile of 12 layers was used in order to minimise
reflection from the boundary as the wave enters into the layer. Linear
discrete Fourier transform monitors were used to capture reflected and
transmitted electric field at 350 nm away from the interface. The source was
made to incident on the gold layer via glass medium at an angle of incidence
of $\theta_{i}$. In order to obtain the resonance angle, the incident angle
sweep was generated from 40o\- 48o with 251 iterations. The mesh override was
selected in the propagation direction of the plane wave to get more precise
results. The optical anisotropy was seen in case of a single layer of
materials exhibiting geometrical anisotropy at the molecular level. A common
example of such system is shown schematically in Figure 1(b). A single layer
of rod shaped molecule (calamitic liquid crystal) tilted with respect to
X-axis can have a projection on the YZ plane. If all the molecules are more or
less tilted in the same direction (here it is along Y-axis), they exhibit a
nematic-like ordering with optic axis (OA) parallel to the Y-axis. Another set
of examples are single layer of self-assembled monolayer of rod shaped
octadecanethiol or Langmuir-Blodgett film of fatty acids LBSA . To simulate
such system of anisotropic material, a thin layer of organic material was
added onto the gold layer whose in-plane birefringence $(\Delta{n})$ was
varied systematically to observe the change in the resonance angle for the
same system but measured along the OA (i.e. Y-axis) and orthogonal to it (i.e.
Z-axis) in the SPR simulation model. Since the material is organic, only the
real part of RI is considered in the simulation.

## Experimental

The Kretschmann configured SPR instrument was developed in the laboratory
devSNB . The equipment utilizes 5 mW laser of wavelength 635 nm, coupling
prism (RI=1.51) and a segmented photodiode as detector. The resolution and
sensitivity of the equipment are 1.92 $\mu{RIU}$ and 53${}^{\circ}/RIU$,
respectively. The SPR chip consists of 0.5 mm glass plate (RI=1.51) deposited
with 50 nm thick gold film through sputtering technique. The chemicals,
stearic acid and 4’-octyl-4-biphenylcarbonitrile (8CB) were procured from
Sigma-Aldrich. Both the molecules yield a very stable Langmuir monolayer at
the air-water interface and are ideal systems for utilizing them for
fundamental studies LBSA ; 8CB . A single layer of LB film of CdSA deposited
at 30 mN/m can yield an average molecular tilt of $\sim$10∘ with respect of
surface normal cdsatilt  and similarly, that of 8CB deposited at 4 mN/m yields
an average molecular tilt of $\sim$60∘ with respect to the surface normal
8cbtilt . A single layer of LB films of CdSA and 8CB were deposited onto SPR
chips at target surface pressure of 30 and 4 mN/m, respectively using a LB
trough (KSV-NIMA). The thickness of the LB films were measured by X-ray
reflectivity (XRR) technique using a X-ray diffractometer equipped with thin
film analysis unit (SmartLab, Rigaku).

## Results and Discussion

Figure 2: (a) SPR spectrum of gold-air interface (b) the electric field
profile on the two dimensional gold surface (Y-Z plane) obtained from
simulation.

A p-polarized electromagnetic wave was allowed to incident at the glass-gold
interface as shown in the Figure 1. The evanescent wave generated in the gold
film can excite the surface plasmon polaritons (SPP). Figure 2(a) shows the
SPR curve for the gold-air interface. It exhibits the RA value of 44∘. The SPR
curve and hence the RA value obtained through the FDTD calculation for the
gold-air interface is in agreement with the literature Gupta2017 . The two
dimensional (2D) electric field profile due to the surface plasmon polaritons
at the resonance angle was obtained and is shown in Figure 2(b). According to
the chosen geometry, the YZ plane corresponds to the gold-air interface and
the plane of polarization is XY. The SPP are excited by the incident
p-polarized electromagnetic wave. Therefore, the electric field of the
incident electromagnetic wave is restricted in the XY plane and has zero
component along the Z-axis. This may lead to surface distribution of the
surface plasmon field to be anisotropic in nature. For a chosen 1000
nm$\times$1000 nm mesh size, the anisotropic nature of the plasmonic field can
be clearly seen in the image. This indicates that the excitation of SPP is
non-isotropic and hence there is an immense possibility that coupling of such
anisotropic field with optically anisotropic material will be direction
dependent. Therefore, the SPR measurement of such anisotropic materials in
different direction with reference to the plane of incidence can yield
different resonance angle. The materials with optical anisotropy can be
obtained either in bulk state or as a single layers of organic molecules
exhibiting some shape anisotropy. The rod shaped calamitic liquid crystal
molecules exhibit a birefringence of $\sim$0.2 in the bulk nematic phase
LCbire ; 5CBbire . The liquid crystal molecules have great technological
importance where such optical anisotropy play significant role in display
device applications. When such shape anisotropic molecules are aligned onto
solid substrate through self-assembly or a controlled Langmuir-Blodgett
deposition technique roberts , the deposited single layer can induce a degree
of optical anisotropy due to a collective tilt of the molecules with respect
to the surface normal. Hence the projections of such tilted molecules can
yield a nematic ordering on the two dimensional surface. In our simulation
setup, we created an organic layer of a given thickness whose RI is chosen to
be anisotropic by assigning different values along X, Y and Z axes. The SPR
spectra were obtained through simulation when the plane of incidence is
parallel and perpendicular to the OA of the in-plane nematic ordering in thin
film of organic material. The difference in RA was noted as $\Delta\theta$
from the SPR spectra obtained in these two geometries.

Figure 3 shows the SPR curves obtained for an anisotropic thin film of 2 nm
thickness having $\Delta{n}$ as 0.1. The corresponding RAs were obtained as
$44.45^{\circ}$ and $44.80^{\circ}$ yielding $\Delta\theta$ to be
$0.35^{\circ}$.

Figure 3: Simulated SPR spectra of a 2 nm thick organic film consisting of
shape anisotropic organic molecules exhibiting an in-plane birefringence of
0.1.

In the simulation, the SPR curves are obtained for different values of
$\Delta{n}$ and thickness of organic film and the corresponding $\Delta\theta$
were obtained. A calibration surface displaying the variation of
$\Delta\theta$ as a function of $\Delta{n}$ and film thickness ($t$) is
plotted in Figure 4.

Figure 4: Calibration surface plot showing the variation of $\Delta\theta$ as
a function of in-plane birefringence ($\Delta{n}$) and thickness of organic
film. The simulated points are shown as filled circle. The surface is
polynomially fitted.

The simulated data are fitted with a surface polynomial curve

$\Delta\theta=P_{1}+P_{2}t+P_{3}\Delta{n}+P_{4}t^{2}+P_{5}\Delta{n}^{2}+P_{6}t\Delta{n}+P_{7}t^{2}\Delta{n}+P_{8}t\Delta{n}^{2}+P_{9}\Delta{n}^{3}$
(1)

where $P_{i},i=1,2,3...9$ are the fit parameters. The fit indicator R-square
was 0.993 which suggests a good fitting. The fitted calibration surface as
represented by the Eq. 1 can be useful for the determination of $\Delta{n}$ of
thin films using SPR phenomenon in the very simple prescribed methodology as
discussed here.

We have utilized the calibration surface (Eqn. 1) for the estimation of in-
plane birefringence of ultrathin films fabricated using the standard Langmuir-
Blodgett (LB) technique. We fabricated a single layer of LB films of cadmium
stearate (CdSA) and 8CB molecules on the SPR chips at the target surface
pressure of 30 and 4 mN/m, respectively LBSA ; 8CB . The molecules in a single
layer of LB films of CdSA and 8CB were tilted by $\sim$10 and 60∘ with respect
to the substrate normal cdsatilt ; 8cbtilt . Hence, they can offer anisotropy
in the refractive indices and therefore can exhibit non-zero values of
$\Delta{n}$. The thickness of the LB films were obtained from X-ray
reflectivity measurement (Figure 5). The experimental curve was fitted using
Parrat’s formulation Parratt  and the thickness of the film was estimated
therefrom. The thickness of gold film deposited over the glass plate, LB films
of CdSA and 8CB deposited over such gold substrates were estimated as 49, 2.4
and 2.0 nm, respectively.

Figure 5: X-ray reflectivity curves obtained from (a) thin films of gold, (b)
LB films of cadmium stearate (CdSA) and (c) 4’-octyl-4-biphenylcarbonitrile
(8CB). The theoretical fitting yields the thickness of gold, CdSA and 8CB
films to be 49, 2.4 and 2.0 nm, respectively.

The LB films of CdSA and 8CB were scanned using the SPR instrument. The change
in RA along the such orthogonal directions ($\Delta\theta$) were found to be
24 and 71 millidegree, respectively. Such non-zero values suggest the
anisotropy in the ultrathin films. The values of thickness and $\Delta\theta$
were substituted in the calibration surface and $\Delta{n}$ of the ultrathin
films of CdSA and 8CB were estimated as 0.012 and 0.022, respectively.

Our analysis give a strong foundation for the measurement of in-plane
birefringence of ultrathin films of organic molecules. Such information are
essential for the development of optical devices.

## Conclusion

The measurement of physical properties at a lower dimension is challenging due
to large dependencies of the properties on other parameters e.g. thickness of
the thin film, aspect ratio of nanomaterials, morphology etc. In this article,
we simulated the SPR phenomenon in Kretschmann configuration to measure the
in-plane birefringence of thin organic film. The thin film consists of rod
shaped organic molecules tilted on the gold surface and thus exhibited in-
plane nematic ordering. We performed simulation to obtain a calibration
surface showing the variation of $\Delta\theta$ as a function of $\Delta{n}$
and thickness of the film. Such calibration surface was employed for the
estimation of $\Delta{n}$ in single layer of LB films of CdSA and 8CB. This
study provides a vital methodology for the measurement of very small value of
$\Delta{n}$ even in case of a single layer of ultrathin organic film. Further
studies involve the role of percolation in quasi-two dimensional film on the
optical properties.

## Acknowledgements

We are thankful to BITS Pilani for providing Lumerical software. We are
thankful to Department of Science and Technology, India for providing the XRD
facility through FIST programme. Thanks are also due to DST India for
supporting SPR instrument from project (IDP/SEN/06/2015) and LB trough from
(CRG/2018/000755). This is a post-peer-review, pre-copyedit version of an
article published in Plasmonics. The final authenticated version is available
online at: https://doi.org/10.1007/s11468-021-01373-1.

## Funding

Not applicable.

## Conflicts of interest/Competing interests

There are no conflicts of interest/competing interests to declare.

## Availability of data and material

The datasets generated during and/or analysed during the current study are
available from the corresponding author on reasonable request.

## Code availability

Lumerical is GUI based commercial simulation package. As such code
availability is not applicable. However, some scripts can be made available on
reasonable request to corresponding author.

## Authors’ contributions

Simulation and part of experiments were done by Amrit Kumar.
Conceptualization, data analysis, manuscript preparation were done by Raj
Kumar Gupta. Data analysis and manuscript preparation were done by
Manjuladevi. SPR measurements and part of experiments were done by Ashutosh
Joshi.

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