Polarization analysis of birefringence in uniaxially deformed silicon crystals
The birefringence induced by uniaxial compression in low-doped silicon crystals was investigated both theoretically and experimentally. The circular components of the Stokes vector in the transmission and reflectance radiation are measured as a function of external pressure by using the method ba...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2007
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| Zitieren: | Polarization analysis of birefringence in uniaxially deformed silicon crystals / L.I. Berezhinsky, I.L. Berezhinsky, V.I. Pipa, I.Ye. Matyash, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 49-54. — Бібліогр.: 12 назв. — англ. |
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irk-123456789-1177732017-05-27T03:06:05Z Polarization analysis of birefringence in uniaxially deformed silicon crystals Berezhinsky, L.I. Berezhinsky, I.L. Pipa, V.I. Matyash, I.Ye. Serdega, B.K. The birefringence induced by uniaxial compression in low-doped silicon crystals was investigated both theoretically and experimentally. The circular components of the Stokes vector in the transmission and reflectance radiation are measured as a function of external pressure by using the method based on the modulation of radiation polarization. The value of the Brewster constant was obtained for absorption (λ = 0.63 µm) and transparence (λ = 1.15 µm) regions. The obtained experimental data are in a good agreement with calculation results based on the anisotropy model of dielectric properties within the framework of the Hook law. Shown is the practical importance of the polarization analysis in researching anisotropy of dielectric properties of materials. 2007 Article Polarization analysis of birefringence in uniaxially deformed silicon crystals / L.I. Berezhinsky, I.L. Berezhinsky, V.I. Pipa, I.Ye. Matyash, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 49-54. — Бібліогр.: 12 назв. — англ. 1560-8034 PACS 78.20.Fm http://dspace.nbuv.gov.ua/handle/123456789/117773 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
| description |
The birefringence induced by uniaxial compression in low-doped silicon
crystals was investigated both theoretically and experimentally. The circular components
of the Stokes vector in the transmission and reflectance radiation are measured as a
function of external pressure by using the method based on the modulation of radiation
polarization. The value of the Brewster constant was obtained for absorption (λ =
0.63 µm) and transparence (λ = 1.15 µm) regions. The obtained experimental data are in
a good agreement with calculation results based on the anisotropy model of dielectric
properties within the framework of the Hook law. Shown is the practical importance of
the polarization analysis in researching anisotropy of dielectric properties of materials. |
| format |
Article |
| author |
Berezhinsky, L.I. Berezhinsky, I.L. Pipa, V.I. Matyash, I.Ye. Serdega, B.K. |
| spellingShingle |
Berezhinsky, L.I. Berezhinsky, I.L. Pipa, V.I. Matyash, I.Ye. Serdega, B.K. Polarization analysis of birefringence in uniaxially deformed silicon crystals Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Berezhinsky, L.I. Berezhinsky, I.L. Pipa, V.I. Matyash, I.Ye. Serdega, B.K. |
| author_sort |
Berezhinsky, L.I. |
| title |
Polarization analysis of birefringence in uniaxially deformed silicon crystals |
| title_short |
Polarization analysis of birefringence in uniaxially deformed silicon crystals |
| title_full |
Polarization analysis of birefringence in uniaxially deformed silicon crystals |
| title_fullStr |
Polarization analysis of birefringence in uniaxially deformed silicon crystals |
| title_full_unstemmed |
Polarization analysis of birefringence in uniaxially deformed silicon crystals |
| title_sort |
polarization analysis of birefringence in uniaxially deformed silicon crystals |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117773 |
| citation_txt |
Polarization analysis of birefringence in uniaxially deformed silicon crystals / L.I. Berezhinsky, I.L. Berezhinsky, V.I. Pipa, I.Ye. Matyash, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 49-54. — Бібліогр.: 12 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T12:46:36Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 49-54.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
49
PACS 78.20.Fm
Polarization analysis of birefringence
in uniaxially deformed silicon crystals
L.I. Berezhinsky1, I.L. Berezhinsky2, V.I. Pipa1, I.Ye. Matyash1, B.K. Serdega1
1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, prospect Nauky, 03028 Kyiv, Ukraine
Phone: (38 044) 525-5778, e-mail: serdega@isp.kiev.ua
2I. Frantsevich Institute for Problems of Materials Science, NAS of Ukraine
3, Krzhyzhanovsky str., 03142 Kyiv, Ukraine, e-mail: oleggrig@ipms.kiev.ua
Abstract. The birefringence induced by uniaxial compression in low-doped silicon
crystals was investigated both theoretically and experimentally. The circular components
of the Stokes vector in the transmission and reflectance radiation are measured as a
function of external pressure by using the method based on the modulation of radiation
polarization. The value of the Brewster constant was obtained for absorption (λ =
0.63 µm) and transparence (λ = 1.15 µm) regions. The obtained experimental data are in
a good agreement with calculation results based on the anisotropy model of dielectric
properties within the framework of the Hook law. Shown is the practical importance of
the polarization analysis in researching anisotropy of dielectric properties of materials.
Keywords: induced birefringence, polarization analysis, the Stokes vector.
Manuscript received 19.12.06; accepted for publication 26.03.07; published online 01.06.07.
1. Introduction
Birefringence in isotropic materials induced by uniaxial
compression results in the polarization effect named as
photo-elastic [1]. Its essence is that the refractive index
value in the direction of compression and
perpendicularly to it is different. In this case, the
propagation of a light wave in the normal direction to the
deformation axis with the polarization directed at some
angle to this axis can be considered as propagation of
two orthogonally polarized waves with different
velocities. The phase difference between these waves is
observed at the output from medium [2] and can be
expressed by the formula
λϕ Lnn )(π2 || ⊥−=∆ ,
where ||n and ⊥n are the refractive indexes of material
in parallel and perpendicular directions to the
compression axis, respectively, L is the thickness of
medium, λ is the light wavelength. The phase difference
results in the fact that the linearly polarized light at the
input into the medium becomes elliptically polarized at
the output from it at any value of ∆ϕ excepting ∆ϕ = 0,
π/2, π. To determine the polarization state of radiation in
this case, the Stokes vector is very convenient quantity.
The method of Stokes-polarimetry [3] is useful as
components of the Stokes vector are directly measurable
quantities. Stokes-vector components are especially
easily measured by the method of modulation of
radiation polarization.
The polarization modulation (PM) method for
electromagnetic radiation was first used in ellipsometry
[4]. In the work [5], the PM method was successfully
used to study optical anisotropy in solids and liquids.
The PM method allows to observe the photoelastic effect
not only in transmittance, as it was done up to now, but
also in reflection. Moreover, in [6] it was shown that this
method allows to separate elliptically polarized radiation
into the components of the Stokes vector (circular and
linear polarized components). In this work, the
photoelastic effect in crystalline silicon is analyzed using
the Stokes vector components, which were
experimentally measured by the PM method. It is shown
that such description of the photoelastic effect allows to
easily simulate the influence of the external factors
(pressure, temperature etc.) on optical parameters of
crystals, to deal with theoretical calculations and to
compare them with experimental results.
The PM method allows register birefringence by
two ways: (i) measuring the phase difference between
orthogonal components of the linearly polarized
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 49-54.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
50
radiation, and (ii) measuring the difference of reflection
coefficients for s- and p-polarized waves. In this work,
we shall follow the (i)-way, and so we shall consider the
anisotropy of the photoelastic effect as phase anisotropy
contrary to amplitude anisotropy observed by the
reflection absorption spectroscopy (RAS) method [7].
2. Theory
As it is known, the polarization state of a light wave in a
general case can be described by the Stokes vector:
],,,[ VUQIS = , (1)
where I is the total intensity of light, Q is the intensity
difference of light polarized across to axes, U is the
intensity of light polarized at the 45° angle to the axes,
and V is the intensity difference of light with right and
left circular polarizations. The Stokes parameters are
expressed through the components ⊥= EEx and
||EEy = of the electrical field of a light wave as [8]
,||||
∗
⊥⊥
∗ += EEEEI
,||||
∗
⊥⊥
∗ −= EEEEQ
,||||
∗
⊥
∗
⊥ += EEEEU (2)
).( ||||
∗
⊥
∗
⊥ −= EEEEiV
Let's consider a plate ( Lz ≤≤0 ) of uniaxial
crystal in vacuum, with optical axis oriented along y
axis. The permeability tensor of a crystal is defined by
the components ⊥ε≡ε=ε zzxx and ||ε≡ε yy . Let the
light wave with the frequency ω and amplitude
)0,,( yx EE=E falls from vacuum in the direction of z
axis onto the surface 0=z of a sample. When refracting
in the crystal, ordinary and extraordinary waves arise,
which are characterized by complex refractive indexes,
accordingly. The oscillations of electric fields of these
waves are mutually orthogonal and independent from
each other. Therefore, reflection (and transmission) of
the waves with amplitudes ixE and iyE occur
independently. It is possible to use for each wave the
reflection νr and transmittance νt coefficients,
respectively, obtained in [2] for an isotropic plate with
the refraction indexes νn~ ( ||,=⊥ν ):
ν
ν
δ
ν
δ
ν
ν
−
−
= i
i
er
er
r
12
2
12
1
)1(
, 2
12
2
12
2
1
)1( ν
ν
δ
δ
ν
ν
ν
−
−
= i
i e
er
rt . (3)
Here, cnL νν ω=δ ~2 and )~1()~1(12 ννν +−= nnr
is the amplitude of reflection from a vacuum-crystal
boundary. The vector amplitudes of the reflected and
transmitted waves are expressed as
yiyxixr ErEr eeE ||+= ⊥ , yiyxixt EtEt eeE ||+= ⊥ . (4)
The complex refractive indexes νn~ are expressed
through real indexes of refraction νn and absorption νχ
as ννν χ+= inn~ .
Under the uniaxial deformation of a crystal, the
refractive index in the direction of pressure ( ||
~n ) and in
perpendicular (to it) direction ( ⊥n~ ) are changed by
different ways. As a model approach, we assume that the
components of the permeability tensor have a linear
dependence on the pressure X :
XaaX µ−ε=ε+ε=ε ⊥ 00|| , . (5)
Here, 2
000 )( χ+=ε in , 0n and 0χ are the indexes
of refraction and absorption in the absence of pressure, µ
is the Poisson constant, aiaa ′′+′= is the complex
parameter depending on the frequency of light. For the
weak absorption ( 00 n<<χ ), from (5) in the linear
approximation on X , we obtain
,10|| XCnn += ,20|| XC+χ=χ
,10 XCnn µ−=⊥ ,20 XCµ−χ=χ⊥ (6)
where n⊥, χ⊥ and ||n , ||χ are the indexes of refraction
and absorption in directions perpendicular and parallel
with respect to the direction of compression,
respectively;
01 2naC ′= , 2
0002 2)( nanaC χ′−′′= .
Thus, in the case of absorbing crystal the
dependence of its optical properties on uniaxial pressure
is described by two parameters: 1C and 2C . The
Brewster constant XnnC )( || ⊥−= is expressed through
1C as 1)1( CC µ+= .
3. Features of the experiment
The circular component of the Stokes vector was
measured in transmittance and reflection for Si crystal as
a function of compressing effort. Measurements were
carried out on the samples prepared from rather pure
silicon single crystal with the concentration of impurities
about 1013 cm–3. The type of crystal conductivity in our
experiments was of no importance, as the contribution of
electrons or holes to permeability, and hence to
birefringence, is very small right up to the concentration
of carriers about ~1017 cm–3 [9]. In the course of
measurements, light fell onto the (010) plane of the
sample. Uniaxial compression was applied along the
crystallographic direction [100], which allowed to avoid
transformation of a crystal into the biaxial one. To
reduce down to a minimum the influence of superficial
defects on results of measurements, the samples were
treated using standard technology including chemical-
dynamic polishing. The thickness of samples in the
direction of light propagation was 0.3 and 1 сm. Their
cross section was 0.8×1.0 сm2 that was stipulated by the
type of the compressing device used.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 49-54.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
51
The optical scheme of the setup was performed as a
Michelson interferometer and described in [5]. Its
operation principle consists of the following. The
linearly polarized radiation )0,,( yx EE=E (azimuth
45° relatively to the direction of pressure applied to the
sample) falls on the splitter and is split by two beams
with equal intensities. One of them is directed onto the
anisotropic reflector R (quarter-wave plate) and another
– on the sample normally to its surface. After reflection,
both beams are reduced together and through the device
analyzing polarization state are directed onto the
photodiode. The block of the photoelastic modulator of
polarization [4] and polarizer (Nicol prism) was used as
an analyzing device. When the scheme operates in the
“transmittance” mode the mirror is put behind the
sample.
The feature of this scheme is use of a polarization
modulator. The latter is a dynamic phase plate that
changes polarization of a transmitted light wave without
changing its intensity. The action of the system of
modulator-polarizer has been analyzed in the work [6] in
detail. It was shown that, after passing through the
modulator and connected with it polarizer (Nicol prism),
radiation with elliptic polarization generates in the
photodiode a signal containing two components that
differ by their frequencies. The first component with the
modulation frequency f corresponds to the intensity of a
circular component of elliptically polarized radiation,
and with the frequency 2f – to a linearly polarized
component. Therefore, it is possible to fix the intensity
of a circular or linear component simultaneously by
using the appropriate selective recording device. It is
very important to note that in this case the magnitude of
the linearly polarized component is the sum of Q and U
(two components of the Stokes vector) which are
orientated at the angle of ±45° relatively to each other.
So, it is possible to measure the Q and U components by
registration of an azimuth and magnitude of I component
of the Stokes vector.
All these measurements were carried out at the
room temperature. The He-Ne laser ЛГ-126 (λ =
0.63 µm and 1.15 µm) was used as a source of radiation.
The pure Si crystals weakly absorb at the wavelength
1.15 µm (absorption coefficient is close to 10–1 сm–1)
and strongly absorb at the wavelength 0.63 µm
(absorption coefficient is 3·103 сm–1) [10]. The Ge
photodiode was used as a photodetector, signal of which
was registered using a lock-in selective amplifier.
4. Results and discussion
Fig. 1 shows the comparison of calculated and
experimentally observed circular component Vt of the
Stokes vector for the thick sample (L = 1 cm) with weak
light absorption. To estimate the parameters 1C and 2C ,
in the function )(XVt , we can neglect the weak
dependence of reflection amplitudes 12νr on pressure.
So, we can write
))(2exp()
2
sin()( ||
||
0 ⊥
⊥ χ+χ
λ
π
−
δ−δ
=
LVXVt , (7)
where 0V practically does not depend on pressure and
ϕ=δ−δ ⊥ 2)( || . The cross-points of the function
)(XVt with the x-axis correspond to the pressure mX , at
which the phase difference ∆ϕ = mπ (m = 0, 1, 2, …).
For 1=m , the Brewster constant is expressed through
the pressure 1X as )2( 1LXC λ= . The constant 2C
defines a reduction of oscillation amplitudes with an
increase of pressure.
The constant С2 = 1.3·10–7 bar–1 was determined
from the experimental curve in Fig. 1 taking into account
the attenuation of enveloping curve drawn around the
oscillation function. The Brewster constant С =
= 2.6·10–6 bar–1 (appropriate constant С1 = 2·10–6 bar–1)
was determined from the same experimental curve in the
point Х1, in which the amplitude of a signal is equal to
zero, i.e. Vt = 0, and the phase difference ( ||δ – ⊥δ ) =
= π (m = 1).
The damping character of intensity of circular
polarized component is explained by an increase of the
absorption coefficient ||χ and decrease of the absorption
coefficient ⊥χ with growing the pressure according to
(6). In fact, it displays the action of birefringence and
dichroism effects simultaneously.
Using expressions (3)–(5), we have calculated all
the components of the Stokes vector. The Stokes vector
components as the function of pressure in transmittance
are shown in Fig. 2. Let’s pay attention to the following
fact: the total intensity weakly oscillates with a change
Fig. 1. Vt component of transmitted light as a function of
the uniaxial compression Х for the sample with the
thickness L = 0.3 сm: dashed line – experiment, solid line –
calculation by using (3)-(5) for the values: ω =
1.6·1015 Hz; n0 = 3.5; χ0 = 5·10–5.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 49-54.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
52
of pressure. At the same time, the oscillation of the It
component is synchronous with oscillation of the linear
component Qt. These oscillations are due to multibeam
interference that inevitably occurs when using the
parameters of silicon. Our calculation showed that these
oscillations disappear, if the absorption index increases
up to χ0 =2·10–4. The explanation of behaviour of the Ut
and Vt components is not difficult, too. Let's remember
that the Ut component characterizes a linear polarization
of the electric field of the light wave with the azimuths
±45° relatively to the deformation direction. The
incident light wave has just this polarization. The sample
takes the form of a phase plate under compression, and
accordingly with its properties, it transforms the incident
linear polarized wave into the elliptically polarized one
in a general case. Fig. 2 illustrates this situation. One can
see that the Vt component grows at the expense of a
decrease of the Ut component when the pressure
increases. At the argument Х = 48 bars, the Ut
component is zero and the Vt component achieves its
peak value. It means that the light wave leaving the
sample is completely circular polarized because the
phase difference ϕ between orthogonal components of
the linearly polarized radiation achieves π⁄2. The further
increase of the pressure results in appearance of the Ut
component again but with another sign. At the same
time, the intensity of the Vt component decreases. At X =
= 85 bars, Vt = 0 and the Ut component has its peak
value. In this point, the phase difference ϕ = π, and the
light wave leaving the sample has linear polarization but
orthogonally to polarization of the incident wave. The
further increase in pressure after the point X = 85 bars
results in growth of the circular Vt component and
decrease of the Ut component. However, the circular Vt
component has another sign that means changing of the
rotation direction. The same situation is observed at the
point X = 176 bars and other appropriate points.
Fig. 2. Components of the Stokes vector for transmitted light as
a function of the uniaxial compression Х calculated using (3)-(5):
1 – It, 2 – Ut, 3 – Qt, 4 – Vt for the values: ω = 1.6·1015 Hz, n0 =
= 3.5; L = 0.3 сm; χ0 = 5·10–5; C = 2.6·10-6 bar–1.
It is unexpected that Qt components of the Stokes
vector appear, i.e. the linearly polarized wave with the
azimuth parallel to the optical axis of the sample (direc-
tion of deformation), which is absent in the structure of
initial radiation at Х = 0. The appearance of this
component is undoubtedly connected with a combination
of the Ut and Vt components, which takes place at the
multiple reflection of radiation inside the sample.
Appearance of the Qt component is a reverse process
relatively to resolution of the elliptically polarized wave
by linear and circular components, which are carried out
by means of the used technique. It is confirmed by the
fact that the Qt component is present when Vt ≠ 0 and
Qt = 0 at Vt = 0 (excluding the first period). Moreover,
the calculation showed and experiment confirmed that
the Qt component disappears when the absorption
coefficient or thickness of the sample increases, i.e.
when multireflections are absent due to a complete
damping of radiation along the sample.
Let's note the important feature of the PM method
in measurements of the photoelastic effect. The non-
polarized component of a light flow is always present
after passage through the modulator and polarizer,
because these elements are not ideally perfect.
Therefore, this component is a handicap in measure-
ments of small anisotropy, because it will create a noise
current in the photodiode. In the case of PM, this non-
polarized component does not contribute to the
modulated signal and consequently does not limit the
sensitivity of the used selective amplifier. Thus, the
range of measured signals (and hence measured
anisotropy) can reach some orders as is shown in
Fig. 3. It shows the first half of the period of an
oscillation function for the circular component of the
Stokes vector submitted in Fig. 2. The curve in Fig. 2 is
bounded below by a noise of the measuring circuit and
light source.
Fig. 3. Experimental illustration for detectability of PM in
relation to the value of compression obtained from the first
half-period of the Vt oscillation function in Fig. 2.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 49-54.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
53
The investigations of induced birefringence in
silicon was carried out earlier only in transmittance by
means of the traditional optical-polarization schemes.
So, it is interesting to compare the magnitude of this
constant obtained earlier, for example in the work [11],
where C = 1.95·10–6 bar–1, and that of our PM method.
The value of the Brewster constant at λ = 1.15 µm
determined in our experiments is С = 2.6·10–6 bar–1.
Distinction with the result obtained in the work [11] is
close to 30 %.
The measurement of the photoelastic effect in
reflection was carried out at λ = 1.15 µm (case of weak
absorption) and λ = 0.63 µm (case of strong absorption).
The effect of multireflection with participation of the
sample back wall plays an important role in formation of
the reflected wave in the first case, but is insignificant in
the second case. Fig. 4 shows the results of calculations
of· the I r , Ur , Qr , Vr components as a function of the
pressure X for the case of weak absorption. As well as in
transmittance, multibeam interference takes place in this
case, and then all the components I r , Ur , Qr , Vr are
the oscillation functions versus X. Notice that the optical
path is increased twice at participation of a back wall in
formation of the reflected wave. It means that, within the
framework of the accepted model (6), in the same range
of pressures the oscillation period for the reflected wave
should decrease twice in comparison with the
transmitted wave, as is observed in Fig. 4.
The curve R = f(X) of the photoelastic effect in the
case of strong light absorption (Fig. 5) essentially differs
from that of the transmittance case. This difference is
observed both in the shape and in absolute value. First of
all, it is caused by the fact that the crystal thickness d
forming a reflected wave (d = 1/α ≈ 3.3·10–4 сm for λ =
0.63 µm) is some orders less than the geometric crystal
thickness of 0.3 mm. Hence, in this case, the phase
difference ϕ = (2π⁄λ)∆(nL) between orthogonal
components of a light wave should be L/2d times less
than in the transmittance case at the same anisotropy of
∆n. The real situation is still more complex. For
example, Fig. 5 shows the calculated and experimental
curves of the Vr component of the Stokes vector. The
analysis of the experimental curve has shown that this
curve is not described by a sine function, as it is
observed in transmittance, but rather it is some power
function. Moreover, the value of the Brewster constant,
at which the best coincidence of the experimental and
calculated curves takes place, also differs from the
meaning of that in the transparency region. This result is
in a good agreement with those of the work [12], where
by means of the Raman scattering in silicon shown is
that the Brewster constant sharply grows when
approaching to the absorption edge.
5. Conclusions
The use of polarization analysis to study birefringence
shows that the characteristics and peculiarities of the
photoelastic effect are well displayed by two
components of the Stokes vector, namely, Ut and Vt.
However, the use of the circular component Vt for
measurements of any specific quantities (for example,
the Brewster constant or anisotropy value) represents the
most optimum variant. It is explained by the fact that the
function Vt(X) has linear dependence on the
birefringence value, at least, for small meanings of the
argument, and it can be measured within a wide range of
signals. It is advantages of the Vt(X) function. As signals
measured by standard devices have a noise level of 5-6
orders less than the maximal value of the Vt component,
the sensitivity of the measuring PM-devices to the
quantity of anisotropy is some orders higher than
traditional optical-polarization methods. So, investi-
gating anisotropy of refraction indexes is enough to be
limited by such value of the product (n||–n⊥)L, until the
function Vt = f(Х) has linear dependence, i.e. ϕ < π/2.
Fig. 4. Components of the Stokes vector (1 – Ir, 2 – Ur, 3 –
Qr, 4 – Vr) as a function of the uniaxial compression Х
calculated using (3)-(5) for radiation reflected from the
sample for the values: L =0 .3 cm; ω = 1 .6 ·10 1 5 Hz;
n 0 = 3 .5 ; χ0 = 5 ·10–5; C = 2 .6 ·10–6 bar–1.
Fig. 5. Vr component of the Stokes vector as a function of
the uniaxial compression Х: dashed line – experiment,
solid line – calculation by using (3)-(5) for the values: L =
= 0.3 cm; ω = 3·1015 Hz; n0 = 3.8; χ0 = 3.5·10–3; C =
= 4 ·10 – 6 ba r – 1 .
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 49-54.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
54
Concerning to reflection, the results obtained by
means of the PM method testify that this method is very
promising to investigate birefringence induced in opaque
substances. The nonlinearity observed in the deforma-
tion curve Vr = f(X) is a lack what reduces metrological
importance of this effect. But this lack can be easily
eliminated by application of calibration.
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