Abstract. The analytic expressions for the absorption coefficient (ACF) of a
weak electromagnetic wave (EMW) caused by confined electrons in the presence
of laser radiation modulated by amplitude in doped superlattices (DSL) are
obtained by using the quantum kinetic equation for electrons in the case of
electron–optical phonon scattering. The dependence of the ACF of a weak EMW
on the temperature, frequency and superlattice parameters is analyzed. The results
are numerically calculated, plotted and discussed for n-GaAs/p-GaAs DSL. The
numerical results show that ACF of a weak EMW in a DSL can get negative values.
So, by the presence of laser radiation modulated by amplitude, in some conditions,
the weak EMW is increased. The results also show that in some conditions, the
ability to increase a weak EMW can be enhanced in comparison with the use of
non-modulated laser radiation. This is different from the case of the absence of
laser radiation modulated by amplitude.

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JOURNAL OF SCIENCE OF HNUE
Mathematical and Physical Sci., 2012, Vol. 57, No. 7, pp. 113-123
This paper is available online at
ABILITY TO INCREASE AWEAK ELECTROMAGNETIC WAVE BY
CONFINED ELECTRONS IN DOPED SUPERLATTICES IN THE PRESENCE
OF LASER RADIATIONMODULATED BY AMPLITUDE
Nguyen Thi Thanh Nhan1, Nguyen Vu Nhan2 and Nguyen Quang Bau1
1Faculty of Physics, College of Natural Sciences, Hanoi National University
2Faculty of Physics, Academy of Defence force - Air force
Abstract. The analytic expressions for the absorption coefficient (ACF) of a
weak electromagnetic wave (EMW) caused by confined electrons in the presence
of laser radiation modulated by amplitude in doped superlattices (DSL) are
obtained by using the quantum kinetic equation for electrons in the case of
electron–optical phonon scattering. The dependence of the ACF of a weak EMW
on the temperature, frequency and superlattice parameters is analyzed. The results
are numerically calculated, plotted and discussed for n-GaAs/p-GaAs DSL. The
numerical results show that ACF of a weak EMW in a DSL can get negative values.
So, by the presence of laser radiation modulated by amplitude, in some conditions,
the weak EMW is increased. The results also show that in some conditions, the
ability to increase a weak EMW can be enhanced in comparison with the use of
non-modulated laser radiation. This is different from the case of the absence of
laser radiation modulated by amplitude.
Keywords: Absorption coefficient, doped superlattices, weak electromagnetic
wave, laser radiation.
1. Introduction
In recent times, there has been a growing interest in studying and discovering the
behavior of low-dimensional systems, in particular, DSL. The confinement of electrons
in these systems considerably enhances electron mobility and leads to their unusual
behaviors under external stimuli. As a result, the properties of low-dimensional systems,
especially the optical properties, are very different in comparison with those of normal
Received September 25, 2012. Accepted October 4, 2012.
Physics Subject Classification: 62 44 01 03.
Contact Nguyen Thi Thanh Nhan, e-mail address: nhan_khtn@yahoo.com.vn
113
Nguyen Thi Thanh Nhan, Nguyen Vu Nhan and Nguyen Quang Bau
bulk semiconductors [1, 2]. The linear absorption of a weak EMW by confined electrons
in low-dimensional systems has been investigated using the Kubo-Mori method [3, 4]
and the nonlinear absorption of a strong EMW by confined electrons in low-dimensional
systems has been studied by using the quantum kinetic equation method [5, 6]. The
influence of laser radiation on the absorption of a weak EMW by free electrons in normal
bulk semiconductors has been investigated using the quantum kinetic equation method
[7, 8] and the presence of laser radiation and, in some conditions, the weak EMW is
increased. The influence of laser radiation (non-modulated and modulated by amplitude)
on the absorption of a weak EMW in compositional superlattices has been investigated
using the Kubo-Mori method [9]. The influence of laser radiation on the absorption of a
weak EMW in quantum wells has been investigated using the quantum kinetic equation
method [10]. However, the influence of laser radiation modulated by amplitude on the
absorption of a weak EMW in DSL is still open for study. Researching the influence of
laser radiation on the absorption of a weak EMW plays an important role in experiments
because it is difficult to directly measure the ACF of strong EMW (laser radiation) by
experimental means. Therefore, in this paper, we study the ability to increase a weak EMW
by confined electrons in DSL in the presence of laser radiation modulated by amplitude.
The electron-optical phonon scattering mechanism is considered. The ACF of a weak
EMW in the presence of a laser radiation field modulated by amplitude are obtained using
quantum kinetic equation for electrons in a DSL. We then estimate numerical values for
the specific n-GaAs/p-GaAs DSL to clarify our results.
2. Content
2.1. The absorption coefficient of a weak EMW in the presence of a laser
radiation field modulated by amplitude in a DSL
2.1.1. The laser radiation field modulated by amplitude
As in [9], here we also assume that the strong EMW (laser radiation) modulated by
amplitude has the form:
~F (t) = ~F1(t) + ~F2(t) = ~F1 sin (Ω1t + α1) + ~F2 sin (Ω2t + α2) (2.1)
where, ~F1 and ~F2 has same direction, Ω1 and Ω2 are a bit different from each other or
Ω1 ≈ Ω2 ; |∆Ω| = |Ω1 − Ω2| ≪ Ω1,Ω2.
After some transformations, we obtain:
~F (t) = ~E01 sin (Ωt + ϕ1) (2.2)
with E01 =
√
F 21 + F
2
2 + 2F1F2 cos(∆Ωt +∆α),∆Ω = Ω1 − Ω2,∆α = α1 − α2,
Ω =
Ω1 + Ω2
2
, ϕ1 = α + α
′
, α =
α1 + α2
2
, tgα
′
=
F1 − F2
F1 + F2
tg
(
∆Ω
2
t+ ∆α
2
)
.
114
Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices...
here, Ω is the reduced frequency (or the frequency of the laser radiation modulated by
amplitude) and |∆Ω| is the modulated frequency. ~E01 is the intensity of the laser radiation
modulated by amplitude.
In the case that ~F1, ~F2, Ω1, Ω2, Ω satisfy the conditions:
~F1
Ω21
=
~F2
Ω22
=
1
2
~F
Ω2
, and
∆α = 0, the above formulas can be approximated as in [9].
When ∆Ω = 0, laser radiation modulated by amplitude becomes non-modulated
laser radiation.
2.1.2. The electron distribution function in a DSL
It is well known that the motion of an electron in a DSL is confined and that
its energy spectrum is quantized into discrete levels. We assume that the quantization
direction is the z direction. The Hamiltonian of the electron-optical phonon system in a
DSL in an EMW field in the second quantization representation can be written as:
H =
∑
n,~p⊥
εn
(
~p⊥ − e
~c
~A(t)
)
a+n,~p⊥an,~p⊥ +
∑
~q
~ω~qb
+
~q b~q
+
∑
n,n′,~p⊥,~q
C~qIn,n′(qz)a
+
n′,~p⊥+~q⊥
an,~p⊥(b~q + b
+
−~q) (2.3)
where n denotes the quantization of the energy spectrum in the z direction (n = 0, 1, 2,
etc.); (n, ~p⊥) and (n′, ~p⊥ + ~q⊥) are electron states before and after scattering, respectively;
~p⊥(~q⊥) is the in plane xOy wave vector of the electron (phonon); a+n,~p⊥ and an,~p⊥ , (b
+
~q and
b~q) are the creation and the annihilation operators of the electron (phonon), respectively;
~q = (~q⊥, qz); ~A(t) =
c
Ω
~E01 cos(Ωt + ϕ1) +
c
ω
~E02 cos(ωt) is the vector potential of
the EMW field (including two EMWs: a strong EMW with the intensity ~E01 and the
frequency Ω; a weak EMW with the intensity ~E02 and the frequency ω); ω~q ≈ ω0 is the
frequency of an optical phonon.C~q is the electron-optical phonon interaction constant [7]:
|C~q|2 = 2πe
2~ω0
V ε0q2
(
1
χ∞
− 1
χ0
)
(2.4)
here V, e, ε0 are the normalization volume, the electron charge and the electronic constant,
χ0 and χ∞ are the static and the high-frequency dielectric constants, respectively. The
electron form factor In,n′(qz) is written as:
In,n′(qz) =
Nd∑
l=1
d∫
0
eiqzzψn(z − ld)ψn′(z − ld)dz (2.5)
In a DSL, the electron energy takes the simple form:
115
Nguyen Thi Thanh Nhan, Nguyen Vu Nhan and Nguyen Quang Bau
εn(~p⊥) =
~2~p2⊥
2m∗
+ ~ωp
(
n+
1
2
)
(2.6)
here, m∗ is the effective mass of electron, ψn(z) is the wave function of the n-th state for
a single potential well which composes the DSL potential, d is the DSL period, Nd is the
number of the DSL period, ωp =
(
4πe2nD
χ0m∗
)1/2
is the frequency plasma caused by donor
doping concentration and Nd is doped concentration.
In order to establish the quantum kinetic equations for electrons in a DSL, we use
the general quantum equation for statistical average value of the electron particle number
operator (or electron distribution function) nn,~p⊥(t) =
〈
a+n,~p⊥an,~p⊥
〉
t
[7]:
i~
∂nn,~p⊥(t)
∂t
=
〈[
a+n,~p⊥an,~p⊥, H
]〉
t
(2.7)
where 〈ψ〉t denotes a statistical average value at moment t and 〈ψ〉t = Tr(Wˆ ψˆ), with Wˆ
being the density matrix operator. Starting from the Hamiltonian in Eq. (2.1) and using
the commutative relations of the creation and the annihilation operators, we obtain the
quantum kinetic equation for electrons in a DSL:
∂nn,~p⊥(t)
∂t
= − 1
~2
∑
n′,~q
|C~q|2 |In,n′(qz)|2
+∞∑
l,s,m,f=−∞
Jl(~a1~q⊥)Js(~a1~q⊥)Jm(~a2~q⊥)Jf(~a2~q⊥)
× exp {i {[(s− l)Ω + (m− f)ω − iδ] t + (s− l)ϕ1}}
×
t∫
−∞
dt2 {[nn,~p⊥(t2)N~q − nn′,~p⊥+~q⊥(t2)(N~q + 1)]
exp
{
i
~
[εn′(~p⊥ + ~q⊥)− εn(~p⊥)− ~ω~q − s~Ω−m~ω + i~δ] (t− t2)
}
+ [nn,~p⊥(t2)(N~q + 1)− nn′,~p⊥+~q⊥(t2)N~q]
exp
{
i
~
[εn′(~p⊥ + ~q⊥)− εn(~p⊥) + ~ω~q − s~Ω−m~ω + i~δ] (t− t2)
}
− [nn′,~p⊥−~q⊥(t2)N~q − nn,~p⊥(t2)(N~q + 1)]
exp
{
i
~
[εn(~p⊥)− εn′(~p⊥ − ~q⊥)− ~ω~q − s~Ω−m~ω + i~δ] (t− t2)
}
− [nn′,~p⊥−~q⊥(t2)(N~q + 1)− nn,~p⊥(t2)N~q]
116
Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices...
exp
{
i
~
[εn(~p⊥)− εn′(~p⊥ − ~q⊥) + ~ω~q − s~Ω−m~ω + i~δ] (t− t2)
}
(2.8)
If we consider a similar problem in normal bulk semiconductors that the authors V.
L. Malevich and E. M. Epshtein published, we will see that Eq. (2.8) has a similarity to
the quantum kinetic equation for electrons in the bulk semiconductor [8].
It is well known that to obtain explicit solutions from Eq. (2.8) is very difficult. In
this paper, we use the first-order tautology approximation method to solve this equation
[7, 8]. In detail, in Eq. (2.8), we choose the initial approximation of nn,~p⊥(t) as:
n0n,~p⊥(t2) = n¯n,~p⊥, n
0
n,~p⊥+~q⊥
(t2) = n¯n,~p⊥+~q⊥, n
0
n,~p⊥−~q⊥(t2) = n¯n,~p⊥−~q⊥
where n¯n,~p⊥ is the balanced distribution function of electrons. We perform the integral
with respect to t2, and then we perform the integral with respect to t of Eq. (2.8). The
expression for the unbalanced electron distribution function can be written as:
nn,~p⊥(t) = n¯n,~p⊥−
1
~
∑
n′,~q
|C~q|2 |In,n′(qz)|2
+∞∑
k,s,r,m=−∞
Js(~a1~q⊥)Jk+s(~a1~q⊥)Jm(~a2~q⊥)Jr+m(~a2~q⊥)
exp {−i {[kΩ + rω + iδ] t+ kϕ1}}
kΩ + rω + iδ{
n¯n′,~p⊥−~q⊥N~q − n¯n,~p⊥(N~q + 1)
εn(~p⊥)− εn′(~p⊥ − ~q⊥)− ~ω~q − s~Ω−m~ω + i~δ
+
n¯n′,~p⊥−~q⊥(N~q + 1)− n¯n,~p⊥N~q
εn(~p⊥)− εn′(~p⊥ − ~q⊥) + ~ω~q − s~Ω−m~ω + i~δ
− n¯n,~p⊥N~q − n¯n′,~p⊥+~q⊥(N~q + 1)
εn′(~p⊥ + ~q⊥)− εn(~p⊥)− ~ω~q − s~Ω−m~ω + i~δ
− n¯n,~p⊥(N~q + 1)− n¯n′,~p⊥+~q⊥N~q
εn′(~p⊥ + ~q⊥)− εn(~p⊥) + ~ω~q − s~Ω−m~ω + i~δ
}
(2.9)
where ~a1 =
e ~E01
m∗Ω2
, ~a2 =
e ~E02
m∗ω2
, ~E01 and Ω are the intensity and the frequency of a strong
EMW (laser radiation), ~E02 and ω are the intensity and the frequency of a weak EMW,
N~q is the balanced distribution function of phonons, ϕ1 is the phase difference between
two electromagnetic waves and Jk(x) is the Bessel function.
117
Nguyen Thi Thanh Nhan, Nguyen Vu Nhan and Nguyen Quang Bau
2.1.3. Calculations of the absorption coefficient of a weak EMW in the presence of
laser radiation modulated by amplitude in a DSL
The carrier current density formula in a DSL takes the form:
~j⊥(t) =
e~
m∗
∑
n,~p⊥
(
~p⊥ − e
~c
~A(t)
)
nn,~p⊥(t). (2.10)
Because the motion of electrons is confined along the z direction in a DSL, we only
consider the in plane xOy current density vector of electrons ~j⊥(t).
The ACF of a weak EMW by confined electrons in the presence of laser radiation
modulated by amplitude in the DSL takes the simple form [7]:
α =
8π
c
√
χ∞E202
〈
~j⊥(t) ~E02 sinωt
〉
t
. (2.11)
Because the strong EMW (laser radiation) is modulated by amplitude, according to
section (2.1.1), it is expressed by Eq. (2.2). According to the hypothesis, due to |∆Ω| ≪ Ω,
then in a small amount of time there are about a few periods T =
2π
Ω
, we can presume
that (∆Ωt +∆α) is changeless. Therefore, we let t get a certain specific value τ in such
a small amount of time. Then, we have:
E01 =
√
F 21 + F
2
2 + 2F1F2 cos(∆Ωτ +∆α) = const;ϕ1 = α + α
′
= const. (2.12)
From the Eqs. (2.9), (2.10), (2.11) and (2.12), we established the ACF of a weak
EMW in the presence of laser radiation modulated by amplitude in DSL:
α =
n0ωpe
4
~ω0
√
π√
2χ∞(m∗kbT )3/2ε0cω3
(
1
χ∞
− 1
χ0
) +∞∑
n,n′=1
IIn,n′ {(D0,1 −D0,−1)
−1
2
(H0,1 −H0,−1) + 3
32
(G0,1 −G0,−1)+1
4
(H−1,1 −H−1,−1 +H1,1 −H1,−1)
− 1
16
(G−1,1 −G−1,−1 +G1,1 −G1,−1) + 1
64
(G−2,1 −G−2,−1 +G2,1 −G2,−1)
}
(2.13)
118
Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices...
where:
Ds,m = e
−
ξs,m
2kBT
(
4m∗
2
ξ2s,m
~4
)1/4
K1/2
( |ξs,m|
2kBT
)[
e
−
εn
kBT (Nω0 + 1)− e−
ε
n′
−ξs,m
kBT Nω0
]
Hs,m = a
2
1
(
1
2
+
1
4
cos 2γ
)
e
−
ξs,m
2kBT
(
4m∗
2
ξ2s,m
~4
)3/4
K3/2
( |ξs,m|
2kBT
)[
e
−
εn
kBT (Nω0 + 1)− e−
ε
n′
−ξs,m
kBT Nω0
]
Gs,m = a
4
1
(
3
8
+
1
4
cos 2γ
)
e
−
ξs,m
2kBT
(
4m∗
2
ξ2s,m
~4
)5/4
K5/2
( |ξs,m|
2kBT
)[
e
−
εn
kBT (Nω0 + 1)− e−
ε
n′
−ξs,m
kBT Nω0
]
εn = ~ωp
(
n+
1
2
)
, εn′ = ~ωp
(
n′ +
1
2
)
, Nω0 =
1
e
~ω0
kBT − 1
, IIn,n′ =
+∞∫
−∞
|In,n′(qz)|2 dqz
a1 =
eE01
m∗Ω2
, a2 =
eE02
m∗ω2
, E01 =
√
F 21 + F
2
2 + 2F1F2 cos(∆Ωτ +∆α)
ξs,m = ~ωp (n
′ − n) + ~ω0 − s~Ω−m~ω,with s = −2,−1, 0, 1, 2;m = −1, 1.
γ is the angle between the two vectors ~E01 and ~E02. ~F1 and ~F2 are the intensities of two
laser radiations that creates laser radiation modulated by amplitude (with the intensity ~E01
and the frequency Ω).
Equation (2.13) is the expression of the ACF of a weak EMW in the presence of
external laser radiation modulated by amplitude in a DSL. From the expression of the ACF
of a weak EMW, we see that ACF of a weak EMW is independent of E02 and dependent
only on E01 , Ω, ω, T, d,Nd, nD.
When ∆Ω = 0, the above results will come back the case of absorption of a weak
EMW in the presence of non-modulated laser radiation.
From epression (2.13), when we set E01 = 0, we will receive an expression of the
ACF of a weak EMW in the absence of laser radiation in a DSL that has been investigated
in [4] but by using the Kubo-Mori method.
Expression (2.13) is similar to the expression of the ACF of a weak EMW in the
presence of laser radiation in a quantum well that has been investigated in [10], but
different from [10] in wave function, the energy spectrum and the electron form factor
In,n′(qz), in addition to the laser radiation which in this case is modulated by amplitude.
Here it is very difficult to calculate IIn,n′ =
+∞∫
−∞
|In,n′(qz)|2 dqz by hand as in [10], so we
have to program the calculation to be done on a computer.
119
Nguyen Thi Thanh Nhan, Nguyen Vu Nhan and Nguyen Quang Bau
2.2. Numerical results and discussion
In order to clarify the mechanism for the absorption of a weak EMW in a DSL in
the presence of laser radiation modulated by amplitude, in this section we will evaluate,
plot and discuss the expression of the ACF for the case of a DSL with equal thickness
dn = dp of the n-doped and p-doped layers, equal and constant doped concentration
nD = nA: n-GaAs/p-GaAs. The parameters used in the calculations are as follows [4, 7]:
χ∞ = 10.9, χ0 = 12.9, m = 0.067m0, m0 being the mass of free electron, d = 80 nm,
n0 = 10
23m−3, ~ω0 = 36.25meV , γ = π3 .
Figure 1. The dependence of α on T Figure 2. The dependence of α on ∆Ω
Figure 1 describes the dependence of α on temperature T, with Nd = 15, nD =
1023m−3, Ω1 = 3.1013 Hz, Ω2 gets five different values: 2.6.1013 Hz, 3.1013 Hz, 3.4.1013
Hz, 3.8.1013 Hz, 4.1013 Hz; α1 =
π
3
, α2 =
π
6
, F1 = 10.10
6V/m, F2 = 15.10
6V/m,
ω = 1013Hz. The five different values of Ω2 correspond to the five different values of
∆Ω: 0.4.1013 Hz, 0 Hz, -0.4.1013 Hz, -0.8.1013 Hz, -1013 Hz. Figure 1 shows that when
the temperature T of the system rises from 30K to 400K, its ACF decreases, and then
gradually increases to 0. From Figure 1 we also see that when T gets a value which is
under 80K, the ACF of a weak EMW in the presence of non-modulated laser radiation is
greater than one in the presence of laser radiation modulated by amplitude. This means
that the absorption of a weak EMW is reduced when a strong EMW is modulated by
amplitude and, when T gets a value which is over 100K, the ACF of a weak EMW gets
values greater than one for the case of a non-modulated strong EMW. In addition, the ACF
also gets negative values, i.e. the ACF of a weak EMW becomes increased coefficient of
a weak EMW. So, when T gets a value which is over 100K, the ability to increase a
weak EMW in the presence of laser radiation modulated by amplitude is decreased in
comparison with that in the presence of non-modulated laser radiation; and when T gets
the value about from 80K to 100K, the ACF of a weak EMW in the presence of laser
radiation modulated by amplitude can be greater or smaller than one in the presence of
non-modulated laser radiation.
120
Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices...
Figure 2 describes the dependence of α on∆Ω (|∆Ω| is the modulated frequency),
and also with the above conditions and seven different values of T. From Figure 2 we see
that the curves can have a maximum or a minimum in the investigative interval.
Both Figures 1 and 2 show that in the high temperature region, the ACF is almost
independent of ∆Ω, i.e. the amplitude modulation of laser radiation hardly affects the
ability to increase a weak EMW in the presence of laser radiation.
Figure 3. The dependence of α on Ω Figure 4. The dependence of α on ω
Figure 3 describes the dependence of α on Ω (reduced frequency), with Nd = 15,
nD = 10
23m−3, Ω1 = 2.5.1013Hz ÷ 8.1013Hz, ∆Ω = 0.5.1013Hz , α1 = π
3
, α2 =
π
6
,
F1 = 3.10
6V/m, F2 = 10.10
6V/m , ω = 1013Hz and five different values of T. The
curves in this figure can have a minimum or no minimum in the investigative interval.
Figure 4 describes the dependence of α on the frequency ω of the weak EMW, with
Nd = 15, nD = 10
23m−3, Ω1 = 3.1013Hz, α1 =
π
3
, α2 =
π
6
, and five different values of
Ω2 corresponding to the five different values of∆Ω, ω = 0.5.10
13Hz ÷ 20.1013Hz. This
figure includes two subplots: the first subplot with F1 = 4.10
5V/m, F2 = 8.10
5V/m,
T = 30K, the second subplot with F1 = 10.10
6V/m, F2 = 15.10
6V/m, T = 90K.
From Figure 4 we see that the curves in the first subplot have a maximum where ω = ω0
while the curves in the second subplot have no maximum and can have a minimum or no
minimum in the investigative interval.
Figure 5 shows the ACF as a function of the number of DSL period Nd, with
Ω1 = 3.10
13Hz, nD = 10
23m−3, α1 =
π
3
, α2 =
π
6
, F1 = 6.10
6V/m, F2 = 10.10
6V/m,
T = 100K, ω = 1013Hz and five different values ofΩ2 corresponding to the five different
values of ∆Ω. From this figure, we see that when ∆Ω = 0Hz, the ACF gets a negative
value and smaller than one for the cases of ∆Ω = 0.4.1013Hz,−0.8.1013Hz,−1013Hz,
and greater than one for the case of ∆Ω = −0.4.1013Hz. So, the ability to increase
a weak EMW is enhanced when laser radiation is modulated by amplitude with
∆Ω = −0.4.1013Hz; and when laser radiation is modulated by amplitude with ∆Ω =
121
Nguyen Thi Thanh Nhan, Nguyen Vu Nhan and Nguyen Quang Bau
0.4.1013Hz,−0.8.1013Hz,−1013Hz, the ability to increase a weak EMW is not enhanced
in comparison with the case of non-modulated laser radiation (∆Ω = 0Hz), but is
decreased.
Figure 5. The dependence of α on Nd Figure 6. The dependence of α on nD
Figure 6 describes the dependence of α on the Nd, with Nd = 15, Ω1 = 3.10
13Hz
, α1 =
π
3
, α2 =
π
6
, F1 = 6.10
6V/m, F2 = 10.10
6V/m , T = 100K, ω = 1013Hz
and five different values of Ω2 corresponding to the five different values of ∆Ω. From
this figure, we also see that the ability to increase a weak EMW is enhanced when laser
radiation is modulated by amplitude with ∆Ω = −0.4.1013Hz, and when laser radiation
is modulated by amplitude with ∆Ω = 0.4.1013Hz,−0.8.1013Hz,−1013Hz, the ability
t