Investigation of light polarization in CdS in the presence of two-photon absorption
It is shown that, under the two-photon absorption in CdS, the increase in the azimuth of polarization causes a smooth change of the large semi-axis angle rotation, ellipticity, focal parameter, and eccentricity of the polarization ellipse. When the angle of phase lag δ = 40⁰, the minimum value of...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2007
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| Цитувати: | Investigation of light polarization in CdS in the presence of two-photon absorption / M.R. Kulish, M.P. Lisitsa, N.I. Malysh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 72-75. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1179182017-05-28T03:04:06Z Investigation of light polarization in CdS in the presence of two-photon absorption Kulish, M.R. Lisitsa, M.P. Malysh, N.I. It is shown that, under the two-photon absorption in CdS, the increase in the azimuth of polarization causes a smooth change of the large semi-axis angle rotation, ellipticity, focal parameter, and eccentricity of the polarization ellipse. When the angle of phase lag δ = 40⁰, the minimum value of ellipticity and the maximal values of focal parameter and eccentricity will be realized. 2007 Article Investigation of light polarization in CdS in the presence of two-photon absorption / M.R. Kulish, M.P. Lisitsa, N.I. Malysh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 72-75. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 42.25.Bs, 42.65.-K http://dspace.nbuv.gov.ua/handle/123456789/117918 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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It is shown that, under the two-photon absorption in CdS, the increase in the
azimuth of polarization causes a smooth change of the large semi-axis angle rotation,
ellipticity, focal parameter, and eccentricity of the polarization ellipse. When the angle of
phase lag δ = 40⁰, the minimum value of ellipticity and the maximal values of focal
parameter and eccentricity will be realized. |
| format |
Article |
| author |
Kulish, M.R. Lisitsa, M.P. Malysh, N.I. |
| spellingShingle |
Kulish, M.R. Lisitsa, M.P. Malysh, N.I. Investigation of light polarization in CdS in the presence of two-photon absorption Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kulish, M.R. Lisitsa, M.P. Malysh, N.I. |
| author_sort |
Kulish, M.R. |
| title |
Investigation of light polarization in CdS in the presence of two-photon absorption |
| title_short |
Investigation of light polarization in CdS in the presence of two-photon absorption |
| title_full |
Investigation of light polarization in CdS in the presence of two-photon absorption |
| title_fullStr |
Investigation of light polarization in CdS in the presence of two-photon absorption |
| title_full_unstemmed |
Investigation of light polarization in CdS in the presence of two-photon absorption |
| title_sort |
investigation of light polarization in cds in the presence of two-photon absorption |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117918 |
| citation_txt |
Investigation of light polarization in CdS in the presence of two-photon absorption / M.R. Kulish, M.P. Lisitsa, N.I. Malysh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 72-75. — Бібліогр.: 10 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT kulishmr investigationoflightpolarizationincdsinthepresenceoftwophotonabsorption AT lisitsamp investigationoflightpolarizationincdsinthepresenceoftwophotonabsorption AT malyshni investigationoflightpolarizationincdsinthepresenceoftwophotonabsorption |
| first_indexed |
2025-07-08T13:01:03Z |
| last_indexed |
2025-07-08T13:01:03Z |
| _version_ |
1837083828687994880 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 72-75.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
75
PACS 42.25.Bs, 42.65.-K
Investigation of light polarization in CdS
in the presence of two-photon absorption
M.R. Kulish, M.P. Lisitsa, N.I. Malysh
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: n_kulish@yahoo.com
Abstract. It is shown that, under the two-photon absorption in CdS, the increase in the
azimuth of polarization causes a smooth change of the large semi-axis angle rotation,
ellipticity, focal parameter, and eccentricity of the polarization ellipse. When the angle of
phase lag δ = 40о, the minimum value of ellipticity and the maximal values of focal
parameter and eccentricity will be realized.
Keywords: CdS, two-photon absorption, ellipticity, ellipse of polarization.
Manuscript received 24.04.07; accepted for publication 24.04.07; published online 19.10.07.
1. Introduction
As usual, the two-photon absorption coefficient is
measured for the orientation of the electric vector Е of an
electromagnetic wave in parallel to the optical axis С of a
uniaxial crystal or at the right angle to it [1-3]). Influence
of the polarization azimuth on the light intensity in
uniaxial crystals was studied in articles [4-6]. However,
the polarization ellipse form was not studied in these and
other articles. We have investigated the influence of the
polarization azimuth on the large semi-axis angle rotation,
ellipticity, focal parameter, and eccentricity of the
polarization ellipse of light traveling in CdS and have
found equations describing the polarization mode in CdS
in the presence of two-photon absorption.
2. Samples and measuring method
Plane-parallel uniaxial single crystals CdS of 5 mm in
thickness were used. Light flux falls at the right angle to
the input surface of these crystals (Fig. 1). The optical
axis in these crystals is parallel to the input surface
(Fig. 1, insert a). Single crystals CdS were positioned
between a polarizer and an analyzer. A fixed angle ϕ
(polarization azimuth) between the optical axis and the
vector Е was set by crystal rotation. A ruby laser with
20-ns pulse duration and 1-pm half-width was a light
source. ELU-FT photomultipliers served as light
detectors. Intensity of light on the input (I0) and on the
output (I) of a sample was determined with an error of at
most 10 %. A variation of the intensity was fulfilled by
rearrangement of neutrally grey filters from a set located
before a sample into the set located after a sample.
In the presence of two-photon absorption, the
reciprocal transmission 1/T of the sample linearly
depends on I0 [1, 3]:
[ ]
002
0
)1(
1)(exp
)1(
)exp(1
BIAI
RK
Kd
R
Kd
I
I
T
+=
−
−β
+
−
== , (1)
where K and β are the coefficients of one-photon and
two-photon absorption, d and R is the thickness and
reflection coefficient of the sample, and A and B are
constants. Using the experimentally determined values I
and I0, we plot a dependence 1/T = f(I0) (Fig. 2, points),
where every point was averaged over 20-30
measurements. The empiric dependence of 1/T on I0 is
approximated by a straight line by the method of least
squares. The point, where this line crosses the ordinate
axis, gives the constant A, and the line slope gives the
constant B. Inserting A and B in the formulas
])1(ln[
1 2RA
d
K −= , (2а)
1)1(
)1(
2 −−
−
=β
RA
RBK , (2b)
we estimated K (K = 1.8 cm−1) and β. The error of
estimation of K is ±10 %, and that of β equals ±20 %.
Fixing the polarization azimuth ϕ for the set of values
ψ, we evaluated the dependence of 1/Т = f(I0) and then
the value of I which corresponds to a certain fixed value
of I0 (Fig. 2). Estimating the values of I and ψ in this
way, we obtained the dependence I = f(ψ) (Fig. 3a,
points).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 72-75.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
75
Fig. 1. Experimental setup used for the research of the influence
of two-photon absorption on light polarization: a ruby laser (1);
sets of calibrated neutrally grey filters (2) and (6); polarizer (3)
(Glan prism); single crystal CdS, optical axis of which is parallel
to the y axis (4); analyzer (5) (Glan prism); photomultiplier
ELU-FT (7). In insert a, we show the orientation of the
polarization vector of an electromagnetic wave E relative to the
optical axis C on the input surface of the uniaxial crystal, and ϕ
is the polarization azimuth. In insert b, we display the form of
the polarization ellipse on the output surface of the crystal, ψmax
is the angle, on which the major semi-axis of the polarization
ellipse will rotate relative to the optical axis C after the
transmission of light through the crystal.
2. Influence of two-photon absorption on light
polarization
Let a monochromatic linearly polarized light flux fall
onto the surface of a uniaxial crystal at the right angle
(Fig. 1). It is possible to consider that, in such a crystal,
two components of the light flux are traveling along one
way, if the azimuth ϕ ≠ nπ/2, (n = 0, 1, 2, 3,…). In one
of the components, Е⊥С, and Е||C in the other one.
Immediately after the input surface of the crystal, the
intensities of these components are as follows:
ϕ=⊥
2
00 cosII , ϕ= 2
00 sinII . (3)
On the output surface of the crystal, these
intensities are equal to
( )dK
dK
e
K
RI
eRI
I
⊥
⊥
−
⊥
⊥⊥
−
⊥
⊥
−
ϕ−β
+
ϕ−
=
1
cos)1(
1
cos)1(
2
0
22
0 , (4)
( )dK
dK
e
K
RI
eRI
I
||1
sin)1(
1
sin)1(
||
2
||0
22
||0
−
−
−
ϕ−β
+
ϕ−
= . (5)
On the output from an analyzer, the intensity of
light equals
δψ+ψ+ψ= ⊥⊥ cos)2(sinsincos ||
2
||
2 IIIII , (6)
where δ is the phase lag angle.
0 10 20 30 40 50 60
3.8
4.0
4.2
4.4
4.6
4.8
5.0
1/
T
I0, MW\cm2
Fig. 2. Dependence of the reciprocal transmission 1/Т versus
intensity I0 of a linearly polarized light which falls onto the
input surface of a crystal CdS of 5 mm in thickness at the right
angle. The azimuth of polarization ϕ = −15º, ψmax is the angle
between the orientation of the polarization vector of an
electromagnetic wave after an analyzer and the optical axis C.
Points present the experiment data, and the solid line is the
result of calculations by formula (1). ψmax = −60º. Arrows
show the method of determination of the intensity on the
output of a sample.
Influence of two-photon absorption on the
polarization of light that travels in CdS is studied at I0=
50 MW/cm2 for a few polarization azimuths. For all
values of φ, the dependence I = f(ψ) looks like such that
is presented in Fig. 3a. The dependence (solid line)
calculated by formula (6) is put in agreement with
experimental data (points) by the choice of δ. At the
optimum value δ = −40o, the error of approximation is
less than 5 %. Values of the minimum (I = Imin) and
maximal (I = Imax) intensities, and the angle ψ = ψ max, on
the achievement of which I = Imax were easily found
using the information from Fig. 3. Then, by using the
well-known correlation between the intensity I and the
electric field strength E [7],
E[V/cm] = 27.46⋅I 0.5 [W/cm2], (7)
we obtained the form of the polarization ellipse
(Fig. 3b).
We can characterize any ellipse by the angular
position of its major half-axis relative to the Carthesian
coordinates, by the contraction factor, eccentricity, and
focal parameter, and each of these parameters depends
on the coefficient of two-photon absorption.
The angular position of the major semi-axis ψmax
depends on the polarization azimuth ϕ in the following
way:
δ
−
=ψ
⊥
⊥
cos
2
)(2tg
5.05.0
max II
II
. (8)
While approximating the empiric dependence
ψmax= f(φ) in Eq. (8), we used the values R⊥ = R|| = 0.2,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 72-75.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
75
-150 -100 -50 0 50 100 150 200
0
5
10
a
Ψmax
min
max
I
I
I,
M
W
/c
m
2
ψ, degree
-100 -50 0 50 100
-100
-50
0
50
100 2a
2b
b
E y,
KV
/c
m
Ex, KV/cm
Fig. 3. Light intensity I going out of a CdS crystal versus the
rotation angle of an analyzer ψ (a) and the form of a
polarization ellipse (b). Points are the experimental data, and
the solid line is the result of calculations by formula (5). The
polarization azimuth φ = −15o, and I0 = 50 MW/cm2. 2a and
2b stand for the lengths of the major and minor axes of the
polarization ellipse, respectively.
and I0 = 50 MW/cm2, as well as the values of К⊥, К||, β⊥,
and β|| determined from the dependences 1/Т = f(I0)
measured at φ = 0 and φ = 90o. It is shown that the
calculated (Fig. 4a, solid line) and empiric (Fig. 4a,
points) dependences numerically agree with each other.
The deviation of an ellipse from a circle is
characterizes by the contraction factor or the ellipticity
max
min
I
I
a
b
=χ , (9)
where b and a are the lengths of the minor and major
semi-axes of the polarization ellipse (Fig. 3b), Imin and
Imax is the minimum and maximal intensities on the
analyzer output (Fig. 3a). The intensities Imin and Imax are
estimated by formula (6), in which the known values of
К⊥, К||, β⊥, and β|| were inserted. The angle ψmax was
estimated by formula (8) and also was inserted in
formula (6). In total accordance with formula (9) at
ϕ = 0º and ϕ = 90º, the ellipse degenerates into a straight
line. The maximal approaching to a circle is achieved at
ϕ = − 45о (Fig. 4b).
-100 -80 -60 -40 -20 0
-100
-80
-60
-40
-20
0
a
ψ
m
ax
, d
eg
re
e
ϕ, degree
-100 -80 -60 -40 -20 0
0.0
0.1
0.2
0.3
0.4
b
χ
ϕ, degree
-100 -80 -60 -40 -20 0
0.92
0.94
0.96
0.98
1.00
c
ξ
ϕ, degree
-100 -80 -60 -40 -20 0
2
4
6
8
10
12
d
p,
K
V
/c
m
ϕ, degree
Fig. 4. Rotation angle ψmax of the major semi-axis of the
polarization ellipse relative to the optical axis C (a), ellipticity
χ (b), eccentricity ξ (c), and focal parameter p (d) vs the
polarization azimuth ϕ. Pumping intensity I0 = 50 MW/cm2,
and λ = 694.3 nm. Solid curves were calculated by formulas
(8) – (a), (9) – (b), (10) – (c), (11) – (d).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 72-75.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
75
The ellipse eccentricity reads
max
minmax
22
I
II
a
ba −
=
−
=ξ . (10)
In accordance with the data of Fig. 4c, there is the
quantitative correspondence between of the empiric
dependence ξ on ϕ and that calculated by formula (10).
The minimum value of ξ will be realized on the
achievement of the value of φ = − 45º.
min
min
2
2
46.27
I
I
a
bp == . (11)
A focal parameter characterizes a change of the
polarization ellipse at points crossing the perimeter by a
chord which passes through the focus and is parallel to
the minor axis. Dependences р on ϕ calculated by
formula (11) and the empiric data are given in Fig. 4d.
3. Conclusions
We have established the relations describing the
influence of two-photon absorption on light polarization
in uniaxial crystals. They describe quantitatively the
experimentally measured changes of the light
polarization under its distribution in CdS. The features
of the influence of two-photon absorption on light
polarization should by taken into account in the
development of high-efficiency second-harmonic
generators [8]; transformers of the pulse width into a
current [9]; polarization modulator and demodulator of
light, and the information transfer by pulses of femto-
second duration [10].
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