Some features of polarization modulation in spectroscopy of optical and photoelectric effects
We analyze usage of modulation of electromagnetic radiation polarization in investigations of optical and photoelectric effects in anisotropic crystals. It is shown that when transmission spectra are studied with the polarization modulation technique, then the results obtained can be represented as...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2004
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| Цитувати: | Some features of polarization modulation in spectroscopy of optical and photoelectric effects / S.V. Kondratenko, I.A. Matyash, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 195-198. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1181742017-05-30T03:03:05Z Some features of polarization modulation in spectroscopy of optical and photoelectric effects Kondratenko, S.V. Matyash, I.A. Serdega, B.K. We analyze usage of modulation of electromagnetic radiation polarization in investigations of optical and photoelectric effects in anisotropic crystals. It is shown that when transmission spectra are studied with the polarization modulation technique, then the results obtained can be represented as a product of two factors. One of them is the derivative of the transmission coefficient with respect to the absorption coefficient, while another characterizes the absorption coefficient anisotropy. Our analysis demonstrates improved information ability of this technique that enables one to explain some previously obtained results. 2004 Article Some features of polarization modulation in spectroscopy of optical and photoelectric effects / S.V. Kondratenko, I.A. Matyash, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 195-198. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS: 78.20.Fm, 78.40.-q http://dspace.nbuv.gov.ua/handle/123456789/118174 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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We analyze usage of modulation of electromagnetic radiation polarization in investigations of optical and photoelectric effects in anisotropic crystals. It is shown that when transmission spectra are studied with the polarization modulation technique, then the results obtained can be represented as a product of two factors. One of them is the derivative of the transmission coefficient with respect to the absorption coefficient, while another characterizes the absorption coefficient anisotropy. Our analysis demonstrates improved information ability of this technique that enables one to explain some previously obtained results. |
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Article |
| author |
Kondratenko, S.V. Matyash, I.A. Serdega, B.K. |
| spellingShingle |
Kondratenko, S.V. Matyash, I.A. Serdega, B.K. Some features of polarization modulation in spectroscopy of optical and photoelectric effects Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kondratenko, S.V. Matyash, I.A. Serdega, B.K. |
| author_sort |
Kondratenko, S.V. |
| title |
Some features of polarization modulation in spectroscopy of optical and photoelectric effects |
| title_short |
Some features of polarization modulation in spectroscopy of optical and photoelectric effects |
| title_full |
Some features of polarization modulation in spectroscopy of optical and photoelectric effects |
| title_fullStr |
Some features of polarization modulation in spectroscopy of optical and photoelectric effects |
| title_full_unstemmed |
Some features of polarization modulation in spectroscopy of optical and photoelectric effects |
| title_sort |
some features of polarization modulation in spectroscopy of optical and photoelectric effects |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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http://dspace.nbuv.gov.ua/handle/123456789/118174 |
| citation_txt |
Some features of polarization modulation in spectroscopy of optical and photoelectric effects / S.V. Kondratenko, I.A. Matyash, B.K. Serdega // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 195-198. — Бібліогр.: 8 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
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| first_indexed |
2025-07-08T13:30:47Z |
| last_indexed |
2025-07-08T13:30:47Z |
| _version_ |
1837085706627842048 |
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195© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 2. P. 195-198.
PACS: 78.20.Fm, 78.40.-q
Some features of polarization modulation in spectroscopy
of optical and photoelectric effects
S.V. Kondratenko*, I.Å. Matyash, B.K. Serdega
V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
45, prospect Nauky, 03028 Kyiv, Ukraine
*Kyiv Taras Shevchenko National University, 64, Volodymyrska str., 01033 Kyiv, Ukraine
E-mail: serdega@isp.kiev.ua
Abstract. We analyze usage of modulation of electromagnetic radiation polarization in inves-
tigations of optical and photoelectric effects in anisotropic crystals. It is shown that when
transmission spectra are studied with the polarization modulation technique, then the results
obtained can be represented as a product of two factors. One of them is the derivative of the
transmission coefficient with respect to the absorption coefficient, while another characte-
rizes the absorption coefficient anisotropy. Our analysis demonstrates improved informa-
tion ability of this technique that enables one to explain some previously obtained results.
Keywords: polarization modulation, absorption coefficient, transmission coefficient.
Paper received 12.02.04; accepted for publication 17.06.04.
1. Introduction
Modulation of electromagnetic radiation polarization
used in experimental physics is one of the techniques of
differential spectroscopy. These techniques are based on
modulation of different physical quantities (magnetic and
electric field strengths, strain, temperature, radiation
wavelength, etc.). By now they are studied in detail and
generalized (see, e.g., [1�3]). However, such radiation
parameter as polarization differs essentially from other
characteristics of radiation. The distinction is, first of
all, that polarization, being a spatial characteristic of
electromagnetic wave, is described by a set of quantities,
namely, the components of Maxwell Jones or Stokes vec-
tors. Thus, contrary to modulation of other physical quan-
tities (each of which is described by only one parameter),
the polarization modulation (PM) has a two-dimensional
effect on a wave. This feature (being inessential prima
facie) considerably complicates both the experimental
PM technique and interpretation of results obtained with
it. This seems to be the reason for the fact that no atten-
tion has been given to PM, while other differential tech-
niques enjoyed wide popularity. However, there is good
reason to believe that application of PM could increase
information ability of various measuring instruments. For
instance, the PM technique demonstrated high sensitiv-
ity to birefringence when studying the photoelasticity
effect (even in the case of opaque substances) [4]. One
could expect that this could be true also in other cases
because the process of PM covers a set of physical pa-
rameters. So the objective of our work was to study the
PM features bearing in mind the above considerations.
2. Experiment
Let us qualitatively consider a process of measurement
with the PM technique. We take, as an example, study of
linear dichroism in a cubic crystal where anisotropy of
dielectric properties is caused by an oriented external
action. As is well known, dichroism lies in distinction
between absorption coefficients for linearly polarized
radiation when the azimuths of the electric component of
electromagnetic wave are parallel to different axes of the
optical indicatrix of an anisotropic sample. The experi-
mental observation of the effect involves transmission
registration for the above two different polarization
states. This is made in the spectral range where a differ-
ence between the corresponding absorption coefficients
is maximal, i.e., the sample is semitransparent. The tra-
ditional procedure lied in determination of a difference
between the transmission values measured at two
polarizer positions, namely, parallel and perpendicular
to the optical axis. Due to various physical reasons, sen-
sitivity of such measuring instruments to pleochroism is
no less than several percent.
196
SQO, 7(2), 2004
S.V. Kondratenko et al.: Some features of polarization modulation in spectroscopy of �
A considerable (several orders better than the above
value) increase of sensitivity is possible in measuring in-
struments that use modulation of electromagnetic radia-
tion polarization. It is generally considered that such
modulation is a periodic action on a wave that leaves its
energy constant, while changing its polarization state.
This means that modulation frequency is by many orders
lower than that of radiation. In this case the polarization
state can vary due to phase shift between either two
orthogonal components of linearly polarized radiation
or two linear components of circularly polarized radia-
tion [2]. When studying linear pleochroism in optical or
photoelectric effects, the above two approaches are
equivalent to a first approximation. The only important
requirement is that, at modulating action on the electro-
magnetic wave, its polarization be linear in the extreme
phases.
Let radiation go through an anisotropic plate in the
semi-transparency range, i.e., αd ≈ 1. Here α is the ab-
sorption coefficient and d is the plate thickness in the
direction of light propagation. Then an alternating elec-
tric signal at modulation frequency appears at the output
of a photosensitive instrument used for detection of ra-
diation. This signal is proportional to the difference be-
tween the transmission coefficients:
( ) ( )⊥−=∆ αα TTT || , (1)
that are function of the absorption coefficients α|| and α⊥
for radiation whose polarization is, respectively, paral-
lel and normal to the optical indicatrix axes.
Using the expression ∆α = α|| � α⊥ for the difference
between these two absorption coefficients, one can ob-
tain:
( ) ( )
α
α
ααα
∆
∆
−∆+
=∆ ⊥⊥ TT
T . (2)
It should be noted that in most cases ∆α << α⊥, α||. So,
using the definition of derivative, one can transform ex-
pression (2) into
α
α
∆=∆
d
dT
T . (3)
Thus, ∆T is proportional to the derivative dT/d . Ta-
king into account that the absorption coefficient α is
function of photon energy hν, it is convenient to present
the difference ∆T as a product of two partial derivatives,
∂T/∂(hν) and
( )
∂
∂
α
νh
= ( )
1−
∂
∂
ν
α
h
:
α
α
ν
ν
∆
∂
∂
∂
∂
=∆
)(
)(
h
h
T
T . (4)
Let us analyze the physical meaning of Eq.4. First of
all, one can see from it the difference between PM and λ-
modulation [1]. It lies in the fact that the result of λ-modu-
lation appears in expression (4) through the first factor,
)( νh
T
∂
∂
. It can be obtained by graphical or physical dif-
ferentiation of the measured spectral dependence Ò(hν).
On the other hand, one can treat the spectral depend-
ence of the difference T(hν) between the transmission co-
efficients measured with the PM technique as a result
of concurrent effect of three factors, namely, the deriva-
tive of transmission coefficient with respect to photon
energy, ∂T/∂(hν) (λ-modulation); the inverse derivative
of absorption coefficient with respect to photon energy,
( )
1−
∂
∂
ν
α
h
; and parameter of anisotropy, ∆α. Each of
the above factors has its own physical meaning. Say, ∆α
is due to anisotropy of dielectric properties caused by
external action, and, correspondingly, it contains infor-
mation on the nature of the studied object response to the
external action. This implies that the absorption coeffi-
cients features related to the critical points in energy band
spectrum (e.g., Van Hove singularities) may manifest
themselves in the spectral characteristic of such optical
effect as linear dichroism. The transmission coefficient
derivative has a methodological sense. It points to the
fact that the highest PM signal measured (which is pro-
portional to the dichroism value ∆α) is observed in the
spectral region where the slope of the transmission coef-
ficient curve is maximal.
3. Results
Let us illustrate the above considerations by some ex-
perimental results obtained for a silicon sample that was
uniaxially strained along the [110] direction. Its spectral
dependence of ∆T(hν) was measured with the PM tech-
nique described in [5], while spectral dependence of the
transmission coefficient T(hν) was obtained using stand-
ard technique (Fig. 1). The dichroism value ∆α was found
using the expression ∆α = [(1 � R)2/d] ln(1+ ∆T/T). It
was obtained by transformation of expressions that re-
lated the transmission coefficient to the reflection coeffi-
cient R, sample thickness d and absorption coefficients
for two different polarizations. The derivative ∂T/∂(hν)
was then obtained by differentiating the spectral charac-
teristic of the transmission coefficient, T(hν) . As a result,
one can determine the only unknown factor, ( )
1−
∂
∂
ν
α
h
,
in the right side of Eq.4. Thus, having measured the char-
acteristics ∆T and T(hν), one can determine the spectral
dependencies ∆α(hν) and ( )ν
α
h∂
∂
.
The determination of dichroism could be also done in
another way, if one had a direct technique for physical
differentiation of the spectral dependence of absorption
coefficient. Having calculated the spectral dependence
of absorption coefficient, α(hν), from the well-known ex-
pression for transmission characteristic, and then the in-
verse derivative ( )
1−
∂
∂
ν
α
h
, one could obtain (at the same
function ∂T/∂(hν)) the spectral dependence of ∆α. The
S.V. Kondratenko et al.: Some features of polarization modulation in spectroscopy of �
197SQO, 7(2), 2004
latter characterizes variation of the material permittiv-
ity with external action.
It seems to be of interest to discuss interrelation be-
tween the amplitudes of the factors in the right side of
Eq.4. They are shown in Fig. 2 for the same silicon sam-
ple [5] uniaxially strained along the [110] direction (stress
of 0.3 kbar). To make the situation clearer, all curves are
presented at the comparable scale, in spite of the fact that
their ordinate values differ by an order of magnitude. It
will be recalled that the product of the ordinate values of
these functions gives the curve 2 presented in Fig. 1. This
means that in our case the contributions from these three
factors to ∆T value (that is measured experimentally) are
comparable. The peculiarities and non-monotonic fea-
tures of the same physical origin coincide for the curves 2
and 3 (Fig. 2) only. In particular, the position of the peak
of dichroism curve coincides with that of the minimum of
∂(hν)/∂α function. As to the curve 1, it characterizes the
sample properties, that is, the transmission coefficient
dispersion that depends on the sample thickness. This
means that for such crystals like GaAs (where the ab-
sorption curve edge is not as lengthy as in silicon and,
correspondingly, the slope of the transmission coefficient
curve is greater) the results of measurements obtained
with the PM technique are determined by the transmis-
sion coefficient dispersion to a greater extent, all other
factors being equal.
Let us illustrate the adequacy of the advanced method
of analysis by comparing the results it gives with inde-
pendent data. To this end, we integrate the calculated
function ∂(hν)/∂α (curve 2 in Fig. 2) with respect to the
photon energy. The obtained spectral characteristic of
the absorption coefficient α as a function of photon en-
ergy is shown in Fig. 3 (curve 1) along with the similar
curve from [6]. The agreement between these two curves
is more than satisfactory. This fact seems to be decisive
evidence that our consideration is adequate.
4. Conclusions
The above approach to treatment of spectral characteris-
tics taken with the PM technique was used when consid-
ering linear dichroism. It seems obvious that the same
approach can be applied to consideration of circular di-
chroism. For its measurement a modulator based on the
photoelastic effect [7] can be used. This instrument can
periodically vary direction of circular polarization of
electromagnetic wave. Similar argumentation can be ex-
tended to usage of this PM technique for measurements
of other effects related to radiation absorption in semi-
conductors, such as photoconductivity, photovoltaic ef-
Photon energy, eV
T
ra
n
sm
is
si
o
n
,
a
r
b
.
u
n
it
s
D
T
,
a
r
b
.
u
n
it
s
1 2
0.0 0.0
1.41.31.21.11.0
0.3 0.01
Fig. 1. The transmission coefficient (1) and its variations due to
strain (2) as function of photon energy for a Si sample 0.38 mm
thick uniaxially strained along the [110] direction (stress of 0.3
kbar).
Photon energy, eV
�1
�1 *�1
Da, cm
¶ ¶ nT h/ , eV ( / ) , eV cm¶a ¶ nh
2
1 3
1.41.31.21.11.0
10
10
10 10
10
10
�0
�1
�2 �3
�2
�1
Fig. 2. The spectral dependencies of: the partial derivative of
the transmission coefficient,∂T/∂(hν) (1); inverse partial deriva-
tive of the absorption coefficient, ( )
1−
∂
∂
ν
α
h
(2); difference ∆α
between the absorption coefficients for two orthogonal states of
linear polarization (3). (Calculated from the expressions given in
the text, with use of the experimental results from Fig.1.)
Fig. 3. The absorption coefficient α as function of photon energy
hν (calculated by integration of ∂α/∂(hν)) (1)) as compared to the
results obtained in [6] (2).
Photon energy, eV
A
b
so
r
p
ti
o
n
c
o
ef
f.
,
cm
�
1
1
2
1.41.31.21.11.0
0.01
0.1
1
10
100
10000
198
SQO, 7(2), 2004
S.V. Kondratenko et al.: Some features of polarization modulation in spectroscopy of �
fects, etc. For instance, photoconductivity is measured
with the PM technique, then the transmission coefficient
T in Eq. (3) should be replaced by photocurrent Ipc(α).
The results of photopleochroism studies [8] can serve
as support of the above statements. In this work, a spec-
tral characteristic of photopleochroism for a crystal with
intrinsic natural anisotropy is presented. In the first ap-
proximation, this characteristic looks like a derivative of
the photoconductivity spectral curve. The latter curve has
a peak at big values of the surface recombination veloc-
ity, so its derivative must be alternating. And just this
tooks place in [8]. Contrary to the λ-modulation spectra,
the characteristic obtained with PM technique has a fine
structure, which (according to the above expression (4))
carries information on the anisotropy parameter ∆α(hν).
One can separate these two functions that are contained
in the presented spectral dependence, if one invokes the
results of additional measurements (say, those performed
with λ-modulation).
Thus, we have shown that the results of any polariza-
tion effect measurement performed with PM technique
contain (contrary to those obtained with all other modu-
lation types) not one, but two functional dependencies
(to say nothing of the dichroism parameter that is an es-
sential characteristic of anisotropic crystals).
References
1. Ì. Cardona, Ìîdulation Spectroscopy. Academic Press,
New York and London, 1969.
2. K.G. Gusev, A.D. Filatov, A.P. Sokolov, Polarization Modu-
lation. Sovetskoe Radio, Moscow, 1974 (in Russian).
3. V.A. Tyagai, O.V. Snitko, Electroreflectance of Light in Semi-
conductors. Naukova Dumka, Kiev, 1980 (in Russian).
4. I.I. Boiko, Ye.F. Venger, E.V. Nikitenko, B.K. Serdega //
Semiconductor Physics, Quantum Electronics & Optoelec-
tronics, 2(2), pp. 54-58 (1999).
5. E.F. Venger, I.E. Matyash, B.K. Serdega // Opt. Spectrosc.,
94, No 1, pp. 38-42 (2003) (in Russian).
6. W.C. Dash, F. Newman // Phys. Rev., 99, pp. 1151-1155, 1955.
7. S.N. Jasperson, S.E. Sahnatterly // Rev. Sci. Instrum., 40,
No 6, pp. 761 (1969).
8. G.A. Medvedkin // Fiz. Tekh. Poluprov., 34, No 6, pp. 533-
536 (2000) (in Russian).
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