Features of third-order optical nonlinearity in carbon disulfide
Degenerate four-wave mixing (DFWM) processes in carbon disulfide have been experimentally studied by applying the wavelength-dependent femtosecond laser source. The quantum mechanical perturbation theory was applied to analyze the experimental data. Third-order optical nonlinearity in carbon disulfi...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2019
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| Zitieren: | Features of third-order optical nonlinearity in carbon disulfide / L.V. Poperenko, S.G. Rozouvan // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 224-230. — Бібліогр.: 23 назв. — англ. |
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| citation_txt | Features of third-order optical nonlinearity in carbon disulfide / L.V. Poperenko, S.G. Rozouvan // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 224-230. — Бібліогр.: 23 назв. — англ. |
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| description | Degenerate four-wave mixing (DFWM) processes in carbon disulfide have been experimentally studied by applying the wavelength-dependent femtosecond laser source. The quantum mechanical perturbation theory was applied to analyze the experimental data. Third-order optical nonlinearity in carbon disulfide has been proposed to consider two- or three-energy levels schemes. Either a two-level or three-level scheme prevails in the nonlinear interaction depending on the symmetry of the participating in the interaction molecular orbitals. These two DFWM schemes have different spatial symmetry of the three wave vectors of the laser beams, which leads to DFWM signal shape variation. Registered DFWM signals demonstrate the presence of a slow decay component for longer light wavelengths, which indicates the availability of a virtual level in carbon disulfide having the same symmetry inherent to the ground state with a 1.12 picoseconds lifetime. The DFWM signal shape based on symmetries of the carbon disulfide ground state and excited states has been analyzed. Quantum mechanics calculations were performed to build wave functions for the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO). Electronic state energies as well as optical transition energy for carbon disulfide were calculated with a few percent accuracy.
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2019. V. 22, N 2. P. 224-230.
© 2019, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
224
Optics
Features of third-order optical nonlinearity in carbon disulfide
L.V. Poperenko, S.G. Rozouvan*
Taras Shevchenko Kyiv National University, Department of Physics
4, Glushkov Ave., 03022 Kyiv, Ukraine
*Corresponding author e-mail: sgr@univ.kiev.ua
Abstract. Degenerate four-wave mixing (DFWM) processes in carbon disulfide have been
experimentally studied applying the wavelength dependent femtosecond laser source. The
quantum mechanical perturbation theory was applied to analyze the experimental data.
Third-order optical nonlinearity in carbon disulfide has been proposed to consider two- or
three-energy levels schemes. Either two-levels or three-levels scheme prevails in the
nonlinear interaction depending on the symmetry of the participating in the interaction
molecular orbitals. These two DFWM schemes have different spatial symmetry of three
wave vectors of the laser beams, which leads to DFWM signal shape variation. Registered
DFWM signals demonstrate the presence of a slow decay component for longer light
wavelengths, which indicates availability of a virtual level in carbon disulfide having the
same symmetry inherent to the ground state with 1.12 picoseconds lifetime. The DFWM
signal shape based on symmetries of the carbon disulfide ground state and excited states
has been analyzed. Quantum mechanics calculus was performed to build wave functions for
the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO).
Electronic states energies as well as optical transition energy for carbon disulfide were
calculated with a few percents accuracy.
Keywords: third-order optical nonlinearity, carbon disulfide, perturbation theory, virtual
levels.
https://doi.org/10.15407/spqeo22.02.224
PACS 31.15.xp, 42.65.An, 42.70.Nq, 82.53.Uv
Manuscript received 14.03.19; revised version received 05.05.19; accepted for publication
19.06.19; published online 27.06.19.
1. Introduction
Carbon disulfide plays a particular role in nonlinear
optics experiments as a standard reference material. It is
an easily available calibration sample with no absorption
bands for popular laser wavelengths, which means
constancy of its nonlinear numbers [1, 2]. Its simple
chemical structure with double chemical bonds seems to
be convenient to understand and demonstrate basic
optical nonlinearity properties. However, carbon
disulfide continues to be a subject of constant
experimental efforts aimed at further studying its optical
nonlinearity origin. The basic inspiration for these
experiments is some gap between quantum-mechanical
understanding of optical nonlinearity and practical
aspects of construction of nonlinear optics based devices
with extra large nonlinear electrical susceptibility tensor
numbers. The basic quantum-mechanical perturbation
theory cannot be applied directly to find a specific
molecule among countless variety of chemical substances
that must have a required nonlinear tensor. The molecule
dipole optical transition moments cannot be presented as
simple analytical expressions for a further analysis and
can only be numerically evaluated using computer-based
calculations, e.g., by applying molecular calculus [3] or
Monte-Carlo approaches [4]. This gap between practical
aspects and the theory limits further practical objectives
of nonlinear optics, e.g., to synthesize a substance with
considerably large nonlinear optical numbers [5]. From
this viewpoint, all recent studies of carbon disulfide have
one objective in common – to study further the optical
nonlinearity fundamentals.
For example, the role of Raman scattering, two- and
three-photon absorption in CS2 nonlinearity was studied
in [6, 7]. Fifth order processes and conditions when
higher order processes exist were discussed in [7].
Particularities of real and imaginary parts of third-order
nonlinear susceptibility as well as electron and nuclear
contributions were studied in [8].
SPQEO, 2019. V. 22, N 2. P. 224-230.
Poperenko L.V., Rozouvan S.G. Features of third-order optical nonlinearity in carbon disulfide
225
In [9], the authors tried to differ nonlinear
properties of liquids and solids. Nonlinear coefficients of
carbon disulfide were taken through microstructures of
liquid phase, in particular, through correlation between
nonlinear properties and different types of molecular
arrangements of clusters surrounding CS2 molecule. CS2
nonlinear numbers were precisely determined using
different approaches, namely: Z-scan, laser radiation and
spectral shear interferometry [10, 11]. Molecular calculus
was performed for determining electronic states, dipole
moments and vibration frequencies of CS2 [12].
The objective of this paper is to analyze the
structure of third-order femtosecond nonlinear optical
degenerate four-wave mixing (DFWM) signal from CS2
by applying the fundamental principles of quantum-
mechanical theory.
2. Theory
Nonlinear optical effects are associated with the terms
of the expansion of induced polarization under influence
of external light wave. Let us apply general
time-dependent perturbation theory [13] for
third-order nonlinear polarization of carbon
disulfide in the DFWM case. The relationship for
induced by three electric monochromatic fields
( )rqp ω=ω=ω ( )tiE pω−β exp , ( )tiE qω−γ exp , and
( )tiE rω−η exp perturbation solution for the third order
nonlinearity dipole moment:
( )
∫∫∫
∞−∞−∞−
α
=
21
321
3
3
ttt
dtdtdt
i
d
h
( ) ( )[ ] ( )[ ] ( )[ ] ( ) ( ) ( )321321 tEtEtEtdtdtdtdSp ηγβηγβα . (1)
Here, ( ) ( )ηγβα ,,td are electric dipole moment
operators and α, β, γ, η indices responsible for light
waves polarizations. Eq. (1) is derived by performing
matrix density consecutive iterations
( ) ( ) ( )( ) ( )( ) ...210 +ρ+ρ+ρ=ρ ttt which are the reaction of
a system on perturbation Hamiltonian ( ) ( )tdEtV −= .
This Hamiltonian represents the time dependent
interaction of the atom with an optical field in the dipole
approximation (a light wave with instantaneous values of
the electric field vector E(t) that induces a dipole d). The
upper limits of integration comply with causality
principle constraints 321 tttt >>> . Integral in Eq. (1) is
taken as a part of approach described in details in [14].
Classical representation of DFWM is two-level scheme
(Fig. 1a), though from the viewpoint of perturbation
theory approach we have to take into consideration all
possible electronic transition schemes induced by three
monochromatic waves. For example, the three-level
scheme (Fig. 1b) satisfies Eq. (1) conditions, namely,
each induced dipole moment arises as a result of an
optical transition between two neighboring levels and
interacts with a wave from three monochromatic waves.
Fig. 1. DFWM in (a) two- and (b) three- energy level systems.
Standing below are the wave vectors for mutual positions.
Having Eq. (1) integral, we can obtain a relationship
for the three-level case. Here, all three light waves have
the same frequencies (Fig. 1b), which means that we
have third order nonlinearity in the DFWM scheme. The
third-order nonlinear electrical susceptibilities
coefficients may be derived as follows:
( )( )
3
3
2
1
,,,
h
=ω−ωω−ωχ αβλη
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
∑
=αβλη
βαγηηβαγ
γαβηηγαβ
αβγηηαβγ
γβαηηγβα
+−
−+−
−−+
+−
3,2,1
123123
123123
123123
123123
mlnlnm
mnlmmlnm
mnlnml
mnlmmlnm
lmnlnm
mnlmmlnm
mnlnlm
mnlmmlnm
nmnlnm
mnlmmlnm
mnmmml
mnlmmlnm
lmmmnm
mnlmmlnm
mnlnmn
mnlmmlnm
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
. (2)
Here, ( )
ijij
ij
i
T
γ−ω−ω
=
3
13 , ( )
ijij
ij
i
T
γ−ω−ω
=
2
12
and ( )
ijij
ij
i
T
γ−ω−ω
=
11 . γij are damping terms. The
tensor element represents the sum of all possible
polarization indices commutations. Eq. (2) may be
obtained using either Eq. (1) direct integration or
simplifying the relationships for the third-order
nonlinearity in the four-level scheme presented in [15] by
reducing the number of levels from 4 down to 3. In the
spectral region of two-photon absorption
( )( )3
,,, αβληω−ωω−ωχ is equal to zero, because optical
transitions with high value of transition cross section
occur between even and odd orbitals (represented in
Eq. (2) as n and l energy levels). In this case, the m level
has either g or u symmetry, which means that either dnm
SPQEO, 2019. V. 22, N 2. P. 224-230.
Poperenko L.V., Rozouvan S.G. Features of third-order optical nonlinearity in carbon disulfide
226
or dml (which are presented in each component of Eq. (2))
is equal to zero, because the optical transition either
between n and m levels or m and l levels is forbidden.
In frames of the two-level DFWM case (Fig. 1a),
one can obtain a relationship for third-order optical
nonlinearity ( )( )3
,,, αβληω−ω−ωωχ :
( )( )
3
3
2
1
,,,
h
=ω−ω−ωωχ αβλη
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( )
∑
=αβλη
βαγηηβαγ
γαβηηγαβ
αβγηηαβγ
γβαηηγβα
+−
−+−
−−+
+−
3,2,1
123123
123123
123123
123123
mnnnnm
mnnmmnnm
mnmnmn
mnnmmnnm
nmnmnm
mnnmmnnm
mnnnnm
mnnmmnnm
nmnnnm
mnnmmnnm
mnmmmn
mnnmmnnm
nmmmnm
mnnmmnnm
mnnnmn
mnnmmnnm
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
TTT
dddd
. (3)
Eq. (3) may be directly derived from Eq. (2) by
substitution l = n.
3. Experiment and discussion
The set-up that we used in order to perform spectral
DFWM was described in details in [16-18]. To perform
optical wavelength tuning the femtosecond pulses, a light
source consisting of a femtosecond Ti/sapphire oscillator
(Coherent Mira 900F), a regenerative Ti/sapphire
amplifier (Coherent RegA 9000), and an optical
parametric amplifier (OPA) (Coherent 9400) was used.
This produced 170 femtosecond pulses were tunable in a
broad spectral range, including the wavelength interval
from 500 to 700 nm. The repetition rate was 150 kHz,
allowing effective lock-in detection in order to improve
the signal-to-noise ratio of the DFWM signal in the
folded box coherent anti-Stocks Raman scattering
(CARS) configuration without generating thermo-optical
effects. The three collinear beams (one is with a tunable
temporal delay) were focused onto the same sample spot
by a lens with 100 mm focal length, leading to a focal
diameter approximately of 20 µm. The fourth deflected
beam as the studied DFWM signal was detected by a
silicon photodiode (Hamamatsu followed by a Stanford
Research preamplifier SR 620). Lock-in techniques
(Stanford Research SR530) were used to improve the
signal-to-noise ratio of the DFWM signal. Two of these
incoming beams were chopped by a mechanical chopper
at different frequencies, and the signal was detected at
the frequency sum.
CS2 liquid was used by us as a reference sample in
numerous spectral DFWM experiments [16-18]. A huge
amount of these data as well as additional measurements
performed for CS2 sample have confirmed existence of
DFWM signal profile development in 600-nm spectral
Fig. 2. DFWM signal in carbon disulfide at various
wavelengths (a) as 3D graph (the curves are gradually shifted in
vertical direction), (b) in logarithmic scale.
region. Our measurements of the DFWM response from
carbon disulfide in 600-nm spectral region found three
distinct components of the signal having different
progress in time. Fig. 2 curves maxima are located in
170 femtoseconds interval which is within OPA pulse
duration. Here, we can put emphasis on distinct spectral
nonlinearity dynamics. The fast component that is
usually called as a “coherent artifact” is basically DFWM
signal either in the two- or three-level scheme. For the
three-level scheme, the DFWM signal maximum arises
by 150 fs later. Longer wavelength signals maxima are
delayed as compared to DFWM signals induced by
shorter wavelength light.
DFWM for two- and three-energy levels.
In two-photon
absorption
spectral
interval
(~600 nm)
DFWM in the two-
level scheme, slow
decay component is
not presented
n(HOMO) – odd
(/even),
m(virtual state) –
even (/odd),
l(LUMO) – even
(/odd)
Outside
two-photon
absorption
spectral
interval
DFWM in the
three-level scheme,
slow decay
component is
presented
n(HOMO) – odd
(/even),
m(virtual state) –
even (/odd),
l(virtual state) – odd
(/even)
Note. HOMO – highest occupied and LUMO – lowest
unoccupied molecular orbitals.
SPQEO, 2019. V. 22, N 2. P. 224-230.
Poperenko L.V., Rozouvan S.G. Features of third-order optical nonlinearity in carbon disulfide
227
In Table, the basic features in these two different
cases, namely, for two-photon spectral absorption region
and for a non-resonant spectral interval outside the two-
photon absorption band are presented. The three-level
scheme DFWM signal disappears for the wavelengths
within two-photon absorption transition spectral interval,
because of the different symmetry for ground and the
upper excited state with zero dipole moment between the
intermediate level and one of two other energy states
(two levels from n, m and l energy levels from Eq. (2)
have the same symmetry). The two- and three-level
schemes that form third-order nonlinear dipole are
simultaneously allowed by symmetry rules (in visible
and near infrared regions below two-photon absorption
bands), but only one three-level scheme is responsible for
curves with the delayed maximum and slow decay
components from Fig. 2. It means that nonzero third-
order nonlinearities cannot exist simultaneously in the
two- and three-energy level schemes either because of
spatial symmetry restrictions or by another reason. Let us
consider the latter moment in details.
In Fig. 2, curves maxima shift gradually with lasing
light wavelengths. Eq. (1) is invariant in respect to
commutations of β, γ, and η indices and as a result the
third-order nonlinear tensor for isotropic media is
commutatively invariant. Technically, commutative
symmetry is valid for paraxial monochromatic waves,
and it was experimentally confirmed in [16]. If the
paraxial approximation is not well satisfying, three laser
beams no longer may be taken as equivalent ones. For
our case of Fig. 2, maxima temporal shifts can be
considered as a result of commutative symmetry
violation. Commutative symmetry is violated because of
non-equivalence of three beams from the viewpoint of
DFWM geometries for two- (Fig. 1a) and three-level
(Fig. 1b) schemes. It may result it DFWM signal maxima
shift. For example, if one takes three pulses delayed in
time (Fig. 3), then it gives the maximum nonlinear signal
based on Eq. (1) scheme. The causality principle is
presented in Eq. (1) as upper limits of integration – each
consecutive pulse affects the system after an influence of
electric field from the previous laser pulse. So, if we for
example decide to exchange the places of the pulses that
propagate along t1 and t3 axes in Fig. 3b, the resulted
third-order nonlinear dipole will be extremely small,
because the third wave that must interact with dipoles
induced by the first two waves is almost passed through
the volume of three beams convergence. The timing
orders of interaction of all three beams are reflected in
Fig. 1 geometries that are different for two- and three-
level schemes. The shift of t2 pulse (which is visible in
Fig. 2 as curves maxima shifts) allows us to apply Fig. 1a
for DFWM in the three-level schemes, too. In this case,
relationships for wave vectors for the two- (upper
relationship) and three-level (bottom relationship)
schemes are still valid:
0=−+− signalpqr kkkk
rrrr
,
0=−−+ signalqpr kkkk
rrrr
. (4)
(a)
(b)
Fig. 3. Pulses mutual temporal arrangement for the (a) two- and
(b) three-level schemes.
Fig. 4. Position of DFWM signals maxima as a function of
wavelength (the left and bottom axes). Carbon disulfide
absorption as a function of wavelength (the right and upper
axes).
Here, the different order of wave vectors subscript
indices reflects Eq. (1) both causality principle and
commutation symmetry. Two different subscript indices
commutations are present in Eq. (4) – ( )pqr ,, and
( )qpr ,, . The latter commutation arises as time delay of
( )pE ω beam, which is visible in Fig. 2 as curves maxima
delays as a function of wavelength. Slow decay compo-
nents are unexpectedly present in Fig. 2 nonlinear signal
curves, though usually it exist in substances with strong
absorption bands due to induced excited states population
gratings. In these schemes, the weak slow decay
component (time constant tvl = 1.12 picoseconds) is
SPQEO, 2019. V. 22, N 2. P. 224-230.
Poperenko L.V., Rozouvan S.G. Features of third-order optical nonlinearity in carbon disulfide
228
a b
Fig. 5. Calculated wave functions for CS2 molecule. (a) wave
functions density (isovalue 0.05) for HOMO (below) and
LUMO molecular orbitals, (b) wave functions density (isovalue
0.01) for the mixed wave function (optical transition between
HOMO and LUMO orbitals).
diffraction of a delayed third beam on population grating
formed by two beams [17], similarly to DFWM in optical
absorption spectral interval. But in our case, the grating
is formed by two-photon absorption on a virtual level
with forbidden one-photon transition to the ground state.
We can only speculate about the origin of the virtual
levels, though it may be related to unpopulated electron-
vibrational levels [19]. Parameter tvl is a few orders of
magnitude less than electronic excited states lifetimes
though it is registered in DFWM setup with 0.1%
measurement error (Fig. 2b). Basically, our experience
shows that the very weak slow decay component is
always present in carbon disulfide within 0.7…1.4 µm
spectral interval. As we can see, the quasi-stable virtual
level in carbon disulfide has a measurable lifetime in
strong light field and therefore may be related to low
populated electron-vibrational level with the energy gap
relatively to HOMO state, which matches the laser light
frequency. We measured 317 nm CS2 absorption band by
using the Hitachi U-3900/3900H spectrophotometer and
a cuvette with a few tens micrometers thickness. The CS2
absorption peak and DFWM signal maxima are presented
in Fig. 4. We can see time evolution of DFWM signal,
which is noticeably correlated to CS2 absorption band in
the doubled optical frequency spectral interval.
The 1.12 picosecond slow decay component
indicates on quasi-stable virtual level l which appears as
a result of DFWM interaction in CS2 nonresonant
spectral region. This level with relatively low (comparing
to virtual level m) dumping term is responsible for
resonant enhancement of nonlinear dipole induced in the
three-level scheme comparing to the two-level scheme
case. The enchancement is a result of low denominators
in Eq. (1) terms ( )
lmlm
lm
i
T
γ−ω−ω
=
11 because of relatively
stable upper virtual level m in the three-level scheme and
relatively small dumping terms γlm. The denominators in
the relevant terms for the two-level case are higher,
because of the negligibly small virtual level lifetimes. If
trying to analyze Fig. 2b signal behavior, one can see
smooth rise in the slow decay component intensity as
well as evolution of curves maximum positions as a
function of wavelength numbers. It means that three-
level DFWM have a higher efficiency as compared to the
two-level scheme in the nonresonant region. The position
of two-photon absorption line in the 630-nm spectral
region marks the boundary between these two DFWM
schemes. The curves from Fig. 2a are normalized taking
into account the photodiode due to experimental setup
spectral sensitivity, which indicates constant CS2 third-
order nonlinearity numbers in the 548…668-nm spectral
range. We believe that the constancy of the nonlinearity
tensor independently of two different energy level
schemes indicates existence of a more general equation
for optical nonlinearity that should include Eqs. (1), (2)
as invariant forms.
To illustrate these considerations, we have
performed molecular calculus on carbon disulfide
molecule by applying excitation energies in the frame of
TD-DFT (Time-Dependent Density Functional Theory)
approach by using GAMESS software [20]. The energy
of the lowest dipole transition was determined in our
calculations as 4.159 eV (which corresponds to the
wavelength of 298.11 nm). The results of numerical
calculations are in sufficiently good correlation with the
measured CS2 absorption peak position (Fig. 4). Spatial
distributions of electron density in the ground and excited
states are presented in Fig. 5. The distributions for
LOMO and HUMO molecular orbitals are typical for
these linear three-atomic molecules [21]. We have also
presented the mixed state electron density distributions
for the case ( )2
nl ϕ−ϕ and ( )2nl ϕ+ϕ , which illustrate
the density in times 0 and T/2 (T is the period of
oscillation with Bohr frequency ħωnl) depicted in grey
and black colors. They form a dipole that arises during
optical transition in dipole approximation.
The transition seems to be identified earlier [22] as
a transition between u∆1 and
+Σg
1
energy levels, though
it was determined as being complex and not well
understood. Detailed studies of CS2 spectrum [23]
revealed this region absorption band contains five
different bands related to different equilibrium
geometries of CS2 molecule.
4. Conclusions
In this paper, we have presented the data on spectral
evolution of third-order nonlinear properties inherent to
carbon disulfide. The degenerate four-wave mixing
experiments were performed with visible wavelengths
femtosecond laser pulses and were analyzed applying
general time-dependent perturbation theory. The major
points of our research are summarized below.
1. We proposed to consider degenerate four-wave
mixing interaction as a process with four optical
transitions of the same frequency in two basic schemes,
namely, with three or two energy levels. These two
SPQEO, 2019. V. 22, N 2. P. 224-230.
Poperenko L.V., Rozouvan S.G. Features of third-order optical nonlinearity in carbon disulfide
229
presented schemes are a consequence of probabilistic
nature of quantum mechanics, and we have to take into
account all possible transitions induced by
monochromatic laser light.
2. Two- and three-level DFWM interactions have
different cross-sections and basically cannot be active
simultaneously. The efficiency of each scheme depends
on symmetry of the molecular orbitals participating in the
interaction. The presence of absorption bands and the
two-photon ones influences the symmetry of electron and
virtual DFWM energy levels and make then a specific
DFWM format to be active or nonactive in some spectral
interval.
3. Two- and three-level DFWM interactions have
different spatial symmetry of their wave vectors, which
results in DFWM signal shape variation due to causality
principle for three interacting light waves.
4. Carbon disulfide exhibits the presence of virtual
levels with relatively high lifetimes of 1.12 picoseconds,
which are responsible for the existence of slow decay
component in the DFWM signals. The slow decaying
part of DFWM signal is a result of third delayed beam
diffraction on a population grating. The grating that is
noticeable in the femtosecond time scale appears because
of a populated virtual level having the same symmetry as
the ground state. The intensity of the slow component is
relatively low as compared to the DFWM signal at its
maximum, because of low numbers for two-photon
transition cross-sections.
5. Carbon disulfide demonstrates constancy of its
third-order nonlinearity numbers despite distinct
variations in DFWM specifics across the broad spectral
range. From our viewpoint, it indicates the possibility of
some integral solution for optical nonlinearities, which
should include particular solutions of general time-
dependent perturbation theory as its parts.
Molecular calculus has allowed to receive
numerical solution for time-independent Schroedinger
equation, which illustrates coincidence of the theory
approach and the experimental results. The approach may
be proposed in order to analyze the spectral femtosecond
DFWM data for broad variety of substances.
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Authors and CV
Leonid Poperenko, born in 1950,
defended his Doctoral Dissertation in
Physics and Mathematics in 1992 and
became full professor in 1996. Head
of Department of Optics at the Taras
Shevchenko National University of
Kyiv. Authored over 200 publica-
tions, 15 patents, 7 textbooks. The
area of his scientific interests includes
spectral ellipsometry of metals and
surface science.
Stanislav Rozouvan, born in 1961,
defended his PhD thesis in optics and
laser physics in 1995. Scientist at the
Department of Optics of Taras
Shevchenko National University of
Kyiv. Authored over 70 publications,
3 patents. The area of his scientific
interests includes scanning tunneling
microscopy and third-order nonlinear
optics.
|
| id | nasplib_isofts_kiev_ua-123456789-215461 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:52:36Z |
| publishDate | 2019 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Poperenko, L.V. Rozouvan, S.G. 2026-03-18T11:38:38Z 2019 Features of third-order optical nonlinearity in carbon disulfide / L.V. Poperenko, S.G. Rozouvan // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 224-230. — Бібліогр.: 23 назв. — англ. 1560-8034 PACS: 31.15.xp, 42.65.An, 42.70.Nq, 82.53.Uv https://nasplib.isofts.kiev.ua/handle/123456789/215461 https://doi.org/10.15407/spqeo22.02.224 Degenerate four-wave mixing (DFWM) processes in carbon disulfide have been experimentally studied by applying the wavelength-dependent femtosecond laser source. The quantum mechanical perturbation theory was applied to analyze the experimental data. Third-order optical nonlinearity in carbon disulfide has been proposed to consider two- or three-energy levels schemes. Either a two-level or three-level scheme prevails in the nonlinear interaction depending on the symmetry of the participating in the interaction molecular orbitals. These two DFWM schemes have different spatial symmetry of the three wave vectors of the laser beams, which leads to DFWM signal shape variation. Registered DFWM signals demonstrate the presence of a slow decay component for longer light wavelengths, which indicates the availability of a virtual level in carbon disulfide having the same symmetry inherent to the ground state with a 1.12 picoseconds lifetime. The DFWM signal shape based on symmetries of the carbon disulfide ground state and excited states has been analyzed. Quantum mechanics calculations were performed to build wave functions for the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO). Electronic state energies as well as optical transition energy for carbon disulfide were calculated with a few percent accuracy. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Optics Features of third-order optical nonlinearity in carbon disulfide Article published earlier |
| spellingShingle | Features of third-order optical nonlinearity in carbon disulfide Poperenko, L.V. Rozouvan, S.G. Optics |
| title | Features of third-order optical nonlinearity in carbon disulfide |
| title_full | Features of third-order optical nonlinearity in carbon disulfide |
| title_fullStr | Features of third-order optical nonlinearity in carbon disulfide |
| title_full_unstemmed | Features of third-order optical nonlinearity in carbon disulfide |
| title_short | Features of third-order optical nonlinearity in carbon disulfide |
| title_sort | features of third-order optical nonlinearity in carbon disulfide |
| topic | Optics |
| topic_facet | Optics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215461 |
| work_keys_str_mv | AT poperenkolv featuresofthirdorderopticalnonlinearityincarbondisulfide AT rozouvansg featuresofthirdorderopticalnonlinearityincarbondisulfide |