Characterization of cellophane birefringence due
to uniaxial strain by focused surface plasmon
microscopy
メタデータ

言語: English
出版者: OSA Publishing
公開日: 2021-07-07
キーワード (Ja):
キーワード (En):作成者: IPSITA, Chakraborty, KANO, Hiroshi
メールアドレス:所属:

URL

http://hdl.handle.net/10258/00010418

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Characterization of cellophane birefringence
due to uniaxial strain by focused surface
plasmon microscopy
I PSITA C HAKRABORTY AND H IROSHI K ANO *Muroran Institute of Technology, 27-1, Mizumoto-cho, Muroran, Hokkaido, 050-8585, Japan* h-kano@mmm.muroran-it.ac.jp

Abstract: In this paper, we study the relationship of local birefringence and stress oriented
inhomogeneous elasticity of a sample from the spatial frequency response of focused surface
plasmon (FSP). The birefringence of the sample varies the propagation constant of surface
plasmon with regard to its direction and produces an elliptic absorption pattern in the reflected
spatial frequency distribution. Birefringence is calculated from the ratio of the propagation
constant along the fast to slow axis of the sample. The change in eccentricity was proportional tothe applied stress on cellophane film. A strong correlation (0.94∼0.97) exists between FSP andphase shifting interferometry results.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1.

Introduction

Propagating surface plasmon (SP) at the flat interface of a conductor and a dielectric are essentially
two-dimensional electromagnetic waves. Confinement on the metal surface is achieved since thepropagation constant (β) is greater than the wave number (k) in the dielectric medium which leads
to the evanescent decay in the dielectric medium [1]. Therefore, SPs cannot be excited directly by
propagating light waves. The principal technique to satisfy the dispersion condition is achievable
by use of a prism coupler as in Kretschmann’s method [2]. In the case of Kretschmann’s method,
β is obtainable as the spatial frequency of the excitation light that gives the reflection minima.
Since β shows strong dependency on the refractive index in the optical near-field from the metal
surface, SPs can be a useful probe for determination of refractive index on the metal. Further, amicroscope objective with high numerical aperture can be used instead of the prism coupler [3].
In this case, the SPs propagating in various directions on the metal surface can be excited and theinterference of the SPs tend to localize/focus over a microscopic region corresponding to theoptical diffraction limit with the introduction of focused laser beam as the source of excitation[4]. Thus, focused surface plasmon (FSP) allows label-free microscopic imaging based on index
of refraction at the metal interface.
In refractive index measurements, dependency on direction of electric field oscillation of theprobe beam appears for samples with anisotropy. Anisotropic samples, especially in thin film form
are an integral part of optical technologies including polymers [5] and bio-medical cellular studies[6]. So, determination of the spatial distribution of anisotropy characteristics over the sample
at specified sites of microscopic regions is a further requirement in bio-physical applications,where the existence of lateral heterogeneity (lipid domains [7], protein domains as amyloid [8],cell-electrode interaction in neuro-biology [9]) convey important (mechano-biological) functional
information in real time. In other words, analysis of retardance essentially indicates quantitative
measurement of the phase difference between the components of the amplitudes emerging fromthe specimen along its principal directions as well as identifying the direction of the fast axis
with respect to a reference coordinate system [10]. The former is referred to as the magnitude
of retardance and the latter as the direction of birefringence. Birefringence measurement havewide applicability in many fields involving polarized light such as electro-optic modulators [11],#417743
Journal © 2021

https://doi.org/10.1364/OSAC.417743
Received 17 Dec 2020; revised 14 Jan 2021; accepted 14 Jan 2021; published 27 Jan 2021

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liquid crystal displays [12], laser resonator [13], non-linear optics [14] and bio-medical optics[15]. The principal technique for characterization of birefringence includes polarization rotation
method with phase shifting interferometry [16] incorporating reconstruction algorithms [17]as potential examples. However, determination of spatially varying retardance calls for special
techniques [18,19,20].
The use of SPs for characterizing anisotropy was also considered [21]. It was suggested
that SPs excited by a similar optical setup for FSP, but with partial coherent light (in order toremove speckle noise, where the localization of SP is not achievable) could potentially provide
the liquid-crystal birefringence by analyzing a reflected spatial frequency distribution.
We report for the first time that near field microscopic birefringence measurement can berealized with an optimized measurement probe. In this paper, we carry out local birefringent
characterization of the anisotropic sample by launching FSP and collecting reflected light througha high numerical aperture microscope objective. In order to obtain birefringence of the sample,
we analyzed the reflected spatial frequency distribution (i.e., the change in shape of the absorption
pattern at the exit pupil). We used cellophane films as a sample and studied the spatial varianceof birefringence due to inhomogeneous elasticity as a result of applied stress by FSP microscopy.
2.

TheoryFor the analysis, we consider the interface of a semi-infinite metal and anisotropic material as
shown in Fig. 1(a). We consider the permittivity of the metal as εm and the anisotropic media
has permittivity tensor in the form of ε. Also, the optic axis is parallel to the interface, i.e., lieson the x-y plane and α denotes the orientation of the optic axis with respect to the x- axis.

Fig. 1. (a) Metal-anisotropic interface with arbitrary orientation of birefringence, (b) FSP
excitation with high NA objective lens.

Through, co-ordinate transformation the permittivity tensor for the anisotropic sample can be
written as22⎛ εa cos α + εb sin α (εb − εa ) sin α cos α 0 ⎞⎜⎟ε = ⎜⎜ (εb − εa ) sin α cos α εa sin2 α + εb cos2 α 0 ⎟⎟
(1)
⎜
⎟
0
0
εc ⎠
⎝
where εa , εb and εc are the dielectric constants along the principal directions, respectively.
Since surface plasmons are excited by p-polarized beam, we consider TM mode that propagatesalong the x-axis and its magnetic field along the y-axis of the structure. Applying boundary
conditions for field components at the interface, the propagation constant can be derived as√︄εm εc [εm − (εa cos2 α + εb sin2 α)]
aniso
kSP
= k0
(2)
εm2 − εc (εa cos2 α + εb sin2 α)Research Article

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where k0 is the free space wave-number and εm is the dielectric constant of the metal, and foruniaxial anisotropic material, n0 = (εa )2 and ne = (εb )2 = (εc )2 . Fig. 1(b) depicts the surface
plasmon excitation at the interface of metal and anisotropic media by using the FSP excitation
scheme. The plane wave component involved in the converging light illuminate the interface of
metal and anisotropic medium with a spatial frequency kx that can be expressed bykx = k0 nsubstrate sin θ in(3)

where nsubstrate and θin denote the refractive index of glass substrate and incident angle, respectively.
For coupling the photon to the SP, the dispersion matching condition is required, and it is expressedbyanisokx = kSP(4)
The plane wave component satisfying the dispersion condition and having p-polarization cancouple with SP which decays via heat dissipation during the propagation. Due to the energy
consumption, an absorption minimum is observed in the reflected spatial frequency distributionthat is observable at the exit pupil of the objective lens. The absorption pattern obtained at
the exit pupil plane is elliptical due to the presence of anisotropic sample on the metal layer as
described by Eq. (2).
3.

Focused surface plasmon microscopy

The typical experimental set-up is shown in Fig. 2. The collimated He-Ne laser beam passed
through a radial-polarization converter (RPC) which is placed in the conjugate plane of theentrance pupil of the oil-immersion microscope objective of N.A 1.65. The FSP was generated at
the interface of the metal film and the anisotropic medium. The light reflected from the metal
surface was collected by the same objective lens, and the Fourier transform of the same appearedat the exit pupil of the objective. The reflected spatial frequency distribution was acquired by animage sensor located in the conjugate plane of the pupil.

Fig. 2. Optical set-up with high NA objective lens. [1: He-Ne laser source (632.8 nm), 2:
Beam Expander lenses, 3: Radial Polarization converter, 4: Telecentric lens system, 5: Oilimmersion objective, 6: Sample, 7: Piezo-electric stage, 8: Exit Pupil, 9: Half mirror, 10:
Focusing Lens, 11: CCD]

The substrate (cover slip with a refractive index of 1.78) was coated with a silver film with athickness of 51nm and cellophane was used as anisotropic sample. As seen from Fig. 3(a), thesample when placed on the silver film do not produce any observable birefringence (absorption
arcs are circular in nature) due to the presence of narrow air gap. We used a thin metal stripe
to push the cellophane down to touch the silver thin film as shown in Fig. 3(b). The change in
the nature of the absorption arcs (tending to be elliptical) indicate that the birefringence of thesample can be measured with this technique. The effect of uniaxial stretch on the sample isshown in Fig. 3(c), where the ellipticity of the absorption arcs changes further.

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Fig. 3. Exit pupil image (a) with cellophane, (b) with introduction of metal stripe oncellophane, (c) with uniaxial stretch (blue arrow indicates fast axis of the sample while thered arrow shows the orientation of stretch).

4.

Characterization of birefringence with influence of external factors

We determined the uniaxial strain dependence of refractive index anisotropy of cellophane withthe help of phase shifting interferometry (PSI). For this purpose, we consider the sample to beplaced in one arm of the Mach-Zehnder interferometer and four intensity frames (I1 , I2 , I3 and I4
respectively) are recorded with successive rotation of the polarizer in steps of 45° as shown in
Fig. 4. The resultant retardance can be obtained as shown in Eq. (5).
(︃)︃λI4 (x, y) − I2 (x, y)δ (x, y) =
tan−1
(5)
2π
I3 (x, y) − I1 (x, y)
Since the sample is stretched along its fast axis so the corrected birefringence can be obtained
after the incorporation of the Poisson ratio with the simultaneous corrected thickness.

Fig. 4. Mach Zehnder interferometer with sample subjected to various degrees of stress as
indicated by red arrows, (inset) Local retardance changes as observed at the CCD plane withthe shift in fringes when various degrees of stress was applied to the sample (white arrow
indicates orientation of fast axis of the sample).

To our knowledge, the results for Poisson ratio of cellophane were not available in literature andonly known measurements were of cellulose I, cellulose II and cellulose Iβ [22]. We measured
the Poisson ratio by direct mechanical stretching using a micrometer vise. The samples were
cut from various sections of the same cellophane film and were stretched in a micrometer vise
mounted on a micro positioning stage under a microscope. The stretching in the x-direction
was varied from 0 to 25% determined by the micrometer reading. The change in width of thesample was measured using the micro positioning device with the help of the pre-positioned
scale. A typical plot of the thickness versus the length of the sample is shown in Fig. 5. The
slope of a straight-line fit (solid line in Fig. 5) to the data yields the Poisson ratio. Measurements
were repeated on different samples obtained from various positions of the cellophane film. The
average Poisson value was 0.43 and have been used throughout the analysis.

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Fig. 5. Thickness vs length of the cellophane sample undergoing stretching of up to 25%.
The black circles show the recorded data while the solid red line is the linear fit.

Thus, the birefringence of the sample is∆n (x, y) =λ(︂

2πd0 1 − σ ∆LL)︂ tan−1(︃

I4 (x, y) − I2 (x, yI3 (x, y) − I1 (x, y)

)︃

(6)

where, d0 is the thickness of the sample before stretching, σ is the Poisson ratio obtained fromthe ratio of lateral strain to longitudinal strain, L is the length of the sample before stretching, ∆Lis the effective change in length of the sample due to stretching.
Since all the parameters of Eq. (6) are determined we can reconstruct the spatial distributionof birefringence as shown in Fig. 6.

Fig. 6. Reconstructed birefringence map of sample when subjected to various degrees ofstress.
aniso with respect to the fast axis and slow axis of the sample andFurther, we calculate the kSP
the ratio determines the eccentricity of the absorption ellipse at the exit pupil of the microscope
for the four cases considering sample by changing the magnitude of applied stress (no stress,
stress 1, 2, and 3). For this purpose, we best fit an ellipse to the data obtained from the absorption
pattern and obtain the center co-ordinates of the ellipse and then determine the magnitude of
the semi-major and the semi-minor axis pertaining to the oriented direction. The eccentricity
is obtained by the ratio of the semi-major to the semi-minor axis of the ellipse and denotes themagnitude of birefringence. We obtain the values for four different positions of the samples as
indicated by A, B, C, D due to the presence of spatial birefringence generated with stress as shownin Fig. 7 (blue data points). We also determined the birefringence of the samples maintained inprevious conditions with phase shifting interferometry with the help of Eq.6 as discussed in theprevious section for four positions of the sample as A’, B’, C’ and D’, respectively also shownin Fig. 7 (red data points). (The positions of the sample are closely related but are not exact asResearch Article

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in A and A’) We compare these results as obtained by FSP and PSI as shown in Fig. 7. One
can see that there is a strong correlation of the birefringence and the position of the sample asobtained by PSI and FSP data. The Pearson’s correlation co-efficient was obtained as 0.9497,
0.9569, 0.9684 and 0.9748 with root mean square error of 0.000837, 0.0030404, 0.002118 and0.0036822 for no stress, stress 1, 2 and 3 respectively.

Fig. 7. Comparison of stress birefringence with focused surface plasmon (FSP) microscopy
and phase shifting interferometry (PSI).[⋄:Without stretching, *: with stress 1, ◦: with stress2 and ×: with stress 3]

Further to analyze the dependence of the optic axis orientation on the spatial frequency
response of FSP from the exit pupil, we rotate the anisotropic sample in the plane perpendicular
to the optical axis of the objective lens. We find that the rotation of the fast axis of the sample
is manifested as a subsequent rotation of the elliptical absorption pattern in the exit pupil asshown in Fig. 8. We also analyzed the spatial frequency response of the sample when subjected
to various environments such as temperature of 60°C and exposure to ultra-violet radiation(315–400 nm) for 24 hours as shown in Figs. 9(b) and 9(c), respectively. We find that the change
in birefringence is manifested clearly from the change in eccentricity of the absorption ellipse as
1.8% and 10% respectively as shown in Figs. 9(b) and 9(c).

Fig. 8. Effect of rotation of the fast axis (indicated with blue arrow) of the sample on
the exit pupil. Unstretched samples with fast axis orientation at (a) 0° (b) 45° and (c) 90°,
respectively.

Fig. 9. Exit pupil when cellophane film was (b) stretched along its fast axis, (c) subjected totemperature of 60°C and (d) exposed to UV irradiation for 24 hours. The dotted pattern isfor reference to the eye for the change in eccentricity.

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Conclusion

In this paper we studied the change in birefringence of the sample with uniaxial strain byspatial frequency response of focused surface plasmon microscopy. Later we correlated thesemeasurements with phase shifting microscopy when the sample was maintained in previous
conditions. It should be noted that this method can be applied to sub nano-meter thin film samples
as well since confinement of FSP is within (∼ 100 nm) from the metal film. This study can beparticularly helpful for determining low birefringence changes due to certain mechano-biologicalactivity in cellular environment in real time.
Acknowledgments. The first author would like to acknowledge the Ministry of Education, Culture, Sports, Scienceand Technology (MEXT), Japan for the scholarship.

Disclosures. The authors declare no conflicts of interest.
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