Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization
We show the role of nonlinear and acousto-optical phenomena in optical and quantum electronics and the physics of semiconductor lasers. The examples of the use of these phenomena in the optical systems of information processing and the light generation by lasers are presented.
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1186552017-05-31T03:05:51Z Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization Manak, I.S. Karikh, E.D. We show the role of nonlinear and acousto-optical phenomena in optical and quantum electronics and the physics of semiconductor lasers. The examples of the use of these phenomena in the optical systems of information processing and the light generation by lasers are presented. 2008 Article Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization / I.S. Manak, E.D. Karikh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 34-39. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 42.55.Px, 42.65.-k, 78.20.Hp http://dspace.nbuv.gov.ua/handle/123456789/118655 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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We show the role of nonlinear and acousto-optical phenomena in optical and
quantum electronics and the physics of semiconductor lasers. The examples of the use of
these phenomena in the optical systems of information processing and the light
generation by lasers are presented. |
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Manak, I.S. Karikh, E.D. |
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Manak, I.S. Karikh, E.D. Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization Semiconductor Physics Quantum Electronics & Optoelectronics |
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Manak, I.S. Karikh, E.D. |
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Manak, I.S. |
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Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization |
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Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization |
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Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization |
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Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization |
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Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization |
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problems of nonlinear optics and acousto-optics in the curriculum of "quantum electronics" specialization |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Problems of nonlinear optics and acousto-optics in the curriculum of "Quantum Electronics" specialization / I.S. Manak, E.D. Karikh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 34-39. — Бібліогр.: 8 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 34-39.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
34
PACS 42.55.Px, 42.65.-k, 78.20.Hp
Problems of nonlinear optics and acousto-optics
in the curriculum of “Quantum Electronics” specialization
I.S. Manak, E.D. Karikh
Belarusian State University, 4, Nezavisimosti Ave., 220050 Minsk, Belarus
Abstract. We show the role of nonlinear and acousto-optical phenomena in optical and
quantum electronics and the physics of semiconductor lasers. The examples of the use of
these phenomena in the optical systems of information processing and the light
generation by lasers are presented.
Keywords: nonlinear optical phenomena, acousto-optics, integral optics, quantum
electronics, semiconductor laser.
Manuscript received 25.05.07; accepted for publication 07.02.08; published online 31.03.08.
1. Introduction
Acousto-optical and nonlinear optical phenomena are
included in the university curriculum on physical
specialities, namely on “Physical electronics” speciality
and “Quantum electronics” specialization.
The acquaintance with the nature of these
phenomena begins in the course of general natural-
scientific disciplines. The course “Optics” gives the idea
about the reasons of breaking down the linearity of
light’s interaction with the substance through the
nonlinear polarization of the medium under the effect of
light wave’s electrical field.
The next level is concerned with studying the circle
of general professional and special disciplines. The
general methods to study nonlinear phenomena are given
in the course “Theory of wave processes,” where the
nonlinear interactions of waves in electrodynamics and
acoustics, generation of harmonic components, three-
wave interaction, and self-interaction and cross-
modulation of waves are analyzed.
2. Acousto-optics phenomena in optoelectronics
The problems of acousto-optics in the course
“Optoelectronics” are considered from the side of their
use for performing the informational operations over
light beams [1]. One knows that, for the effective
internal modulation of light directly in a radiation
source, it is necessary that the lifetime of the particles at
the upper operating level τ be quite short ( 1 2 fτ < π∆ ,
where f∆ is the required modulation frequency band). It
is about 10–9 s in the case of semiconductor injection
lasers (IL), thus, in these lasers, the internal high-speed
light modulation is available. In solid-state and gas
lasers, the lifetime τ is much longer (about 10–7 s in a
He-Ne laser and about 10–3 s in a YAG:Nd one). So long
lifetimes restrict the direct modulation by so low
frequencies, it loses any practical purpose. Thus, the
radiation of gas and solid-state lasers is modulated
externally with the use of various physical phenomena.
The acousto-optical effect is one of form of
photoelasticity. Under the influence of mechanical
stresses caused by an acoustic wave in the medium, there
appear the alternating regions with different refractive
indices traveling with the sound speed. As a result, the
medium gets characteristics of an optical phase grating
that has a period determined by the acoustic wavelength
and a sharpness determined by the applied acoustic
power. If the grating period Λ is comparable to the light
wavelength λ and the linear aperture of the light beam
Λ>>D , then light diffracts on the acoustic wave.
Consider two limiting diffraction modes depending
on the angle between the wave vectors of the acoustic
SK
r
and optical k
r
waves and the ratio 2/ Λ⋅⋅λ nl , where
l is the length of interaction, and n is the non-disturbed
refractive index of the substance. If the length of
interaction of the acoustic and light waves satisfies the
relation
λΛ⋅<< /2nl ,
and the product 0Sk K⋅ =
r r
(vector k
r
is normally
directed to the vector SK
r
), then the Raman-Nath
diffraction takes place. In this case at the acousto-optical
cell output, there is observed a series of light beams (no
less than three) symmetrically dispersing at the angles of
Θm to the direction of a falling beam, and
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 34-39.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
35
sin m m nΘ = λ Λ ,
where 0, 1, 2,m = ± ± … is the diffraction order.
Physically, relation (1) is the condition of single
light diffraction on an acousto-optical wave. Under the
inverse condition
λΛ⋅>> /2nl ,
the clear diffraction picture at the cell’s output can be
created by the light that falls on it at the angle of ΘB
satisfying the relation
Λλ=Θ n2/sin B .
This is the case of Bragg diffraction, and ΘB is
called the Bragg angle. In contrast to the Raman-Nath
diffraction, the light has multiple diffraction acts in the
Bragg’s mode before it leaves the interaction region. As
the resulting secondary diffraction beams are mutually
coherent, all the diffraction maxima, except the zero and
the first ones, are mutually darkened as a result of the
interference. At the cell’s output are observed the zero
and the first beams. The power of the diffracted (the
first) beam is
( )2
1 sinP P n nl= π ∆ λ ,
where n∆ is a change of the refractive index. As one
can see, if the condition
2n nl∆ = λ
is satisfied, the almost 100 % effectiveness of diffraction
may be achieved.
From the quantum-mechanical point of view, the
Bragg diffraction is explained as a result of the elastic
scattering of photons on phonons [1]. The diffraction
character is determined by the conservation laws of
energy and momentum at the photon-phonon interaction.
Let us consider the use of the acousto-optical effect
for the modulation of the intensity, frequency, and
traveling direction of light beams in the construction of
tunable acousto-optical filters. For the light modulation,
both diffraction modes can be used. It is also worth
noting that acousto-optical modulators can be
constructed in the integrated-optical form. In this case,
light interacts with surface acoustic waves, rather than
with volume ones.
The possibility of frequency modulation of light is
based on its interaction with the moving diffraction
grating and on a change of the output radiation
frequency due to the Doppler effect. As the acoustic
frequencies are many orders less than the optical ones, it
is extremely difficult to observe the effect of frequency
modulation at the direct light detection. To detect the
frequency-modulated light, one uses the optical hetero-
dyne method.
Changing the acoustic wave frequency allows one
to perform the spatial scanning of a light beam. It is
shown that the deflector’s angle resolution (the ratio
between the scanning angle and the angular width of a
light beam) is equal to N f= τ∆ , where aτ = υ is the
time constant determining the deflector’s performance
speed (υ is the speed of an acoustic wave, ∆ f is the
frequency deviation). This means that, at the given
performance speed, the deflector’s angle resolution can
be increased only by increasing ∆f. Because, at the given
values of λ, n , and l, the range of frequency changes is
restricted by condition (1), the Raman-Nath deflector
can operate in a relatively narrow frequency band.
Therefore, the Bragg diffraction mode is more often
used for the spatial scanning. With the help of an
acousto-optical cell, one can perform not only the one-
dimensional light scanning, but also the two-dimensional
one.
3. Integral optics
The practical use of nonlinear and acousto-optical
phenomena is considered in the special courses
“Systems of semiconductor quantum electronics” [2] and
“Semiconductor radiation sources in information-
measurement systems,” where the potentialities of the
application of laser diodes in acousto-optical processors
(AOPs) with the processing of the information in real
time are analyzed. The radiation traveling in a planar
wave guide diffracts on the phase grating that appears
under the influence of acoustic waves excited in an
interdigital transducer (IDT) by the source of radio-
frequency signals. The cases are possible when one
signal is supplied to the IDT input and its spectrum is
analyzed or two signals are supplied with the further
determination of their convolution or correlation.
Schemes including an acousto-optical processor on
planar light-guides, spectrum analyzers with spatial and
time integrations, a correlator, and a convolver are
presented in Figs. 1-4.
In a spectrum analyzer with spatial integration at
supplying a harmonic signal ( ) cosS t t= ω to the IDT
input, the phase grating will be a harmonic field of
elastic deformations ( ) cos xS x t= ω , where the spatial
frequency xω = ω υ (υ is the sound speed in the
material of an AOP). The lens performs a Fourier
transformation of the input light field ( )S x , and the
distribution of the light intensity that is proportional to
the input signal spectrum ( )S ω is formed in its focal
plane:
( ) ( ) ( )1 1
xi x
xS S S x e dx
∞
− ω
−∞
ω = ω =
υ υ ∫ .
The spatial frequencies xω are connected with
diffraction angles Θ by the relation
( ) ( )1 1
x f x− −ω = λ Θ = λ , where x is a coordinate of
the spectral component in the Fourier-lens’ focal plane,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 34-39.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
36
1 2S S∫
1 2 3 4 5
S1 S2
Fig. 1. General scheme of an acousto-optical processor: 1 – source of light; 2 – forming system; 3 – acousto-optical processor;
4 – spatial filter; 5 – photodetecting system.
1 2
3
4
5
7
7
7
8
13
12
11 10
10
6
8
9
a
b
c
Fig. 2. Optical scheme of an acousto-optical processor with functions of the spectrum analyzer (a), correlator (b), and convolver
(c): 1 – laser; 2 – collimator; 3 – integral acousto-optical modulator; 4, 5 – surface acoustic wave transducer; 6 – output signal
converters; 7, 9, 12 – objectives; 8, 11 – spatial filters; 10 – CCD; 13 – photodetector.
and f is the lens’ focal distance. Then the spectral
components of an input signal are determined through
the corresponding coordinates of the x-images of the
light source by the following formula:
x
x
f
ω = ω υ = υ
λ
.
By the spatial filter, one of the diffraction orders is
selected and registered by a line of photodetectors. The
position of every sensitive element corresponds to some
definite frequency of the electrical signal.
The frequency resolution of a spectrum analyzer
with spatial integration δf is limited by the size D of the
input aperture of AOP’s sound transducer or by the time
τ of an acoustic wave passing through the optical beam
aperture. At the optical beam divergence restricted by
diffraction, it is equal to
1f
D
υ
δ = =
τ
.
In the correlator, the signals S1(t) and S2(t) are
supplied towards each other to two IDT and the
diffraction field S(x, t) at the AOP output is determined
by the total influence of these signals:
( ) 1 2,
2 2
x D x DS x t S t S t⎛ ⎞ ⎛ ⎞= − − + + −⎜ ⎟ ⎜ ⎟υ υ υ υ⎝ ⎠ ⎝ ⎠
.
Subjecting this field to the direct and inverse
Fourier transformation by lenses and performing the
further time integration of the optical signal by a line of
photodetectors, we get that the variable component of
the output signal
( ) 1 2
0
2Re
2 2
x D x DU x S t S t dt
τ
⎛ ⎞ ⎛ ⎞= − − + −⎜ ⎟ ⎜ ⎟υ υ υ υ⎝ ⎠ ⎝ ⎠∫ , (1)
where τ is the integration time.
If the input signals S1 and S2 are radio signals
modulating the carrier frequency ω, then relation (1) can
be written as
( ) ( ) ( )12 cos 2 xU x R x x⎡ ⎤= ω + θ⎢ ⎥υ⎣ ⎦
, (2)
where ( )12R x is the cross-correlation function of
signals, ( )xθ is a slowly changing quantity
corresponding to the phase of the correlation function.
From (2), one can see that the correlation function is an
envelope of a high-frequency signal with the spatial
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 34-39.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
37
frequency equal to 2ωx. The spatial filter in this scheme
screens the zero-order diffraction. As a matter of fact,
this scheme performs a transformation of the phase
modulation of the light field to the intensity modulation
and also carries the image of acoustic waves’ coverage
(the phase grating) in the plane of photodetector’s
sensitive elements.
In the convolver, the converter performs the
integration of input signals over the AOP space by a lens
and a photodetector. If the spatial filter selects one of the
diffraction orders, then the signal proportional to the
convolution function U(t) of input signals S1(t) and S2(t)
is formed at the photo detector’s output:
( ) 0
2
2
1 2
2
Re
D
t
D
x xU t e S t S t dx
+
− ω
−
⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥≈ − +⎜ ⎟ ⎜ ⎟υ υ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦
∫ .
One can see that the convolution function is
modulated by the doubled carrier frequency ω0, over
which the input signals are imposed. The convolution
interval is restricted by AOP parameters: t = D / υ in
time and D in space.
Moreover, the requirements to laser diodes about
coherence, divergence, light polarization, facilities of
effective input of the radiation into planar waveguides
are considered as well.
4. Nonlinear phenomena in light-medium interaction
According to the classical approach, the light pro-
pagation through a medium is described by the Maxwell
equations. If these equations are linear, then the waves
travel through the medium irrespective of one another,
i.e. the superposition principle is realized. This picture
corresponds to the linear optics. The intensities of light
fields created by lasers reach the values comparable to
those of intraatomic fields (∼ 108 V/cm). At the inter-
action with substance, the relation between the medium
polarization P and the electrical field strength of a strong
light wave becomes nonlinear:
2 3
1 2 3 ...P E E E= χ + χ + χ + (3)
Here, χ1 is the linear medium susceptibility; χ2, χ3, … are
the nonlinear susceptibilities of the first, second, and
higher orders. As a result of breaking down the
superposition principle, the energy exchange between
different waves occurs. Most nonlinear effects are
related to the quadratic and cubic terms of series (3). The
quadratic term stipulates such phenomena as self-
focusing, second-harmonic generation, optical detection,
parametric generation, etc. Due to the cubic term of the
series, there occur the third-harmonic generation, two-
photon absorption, various kinds of stimulated light
scattering, and others. The great attention in the
“Quantum radiophysics” course is paid to the generation
of the second harmonic (and higher ones) of light and to
the parametric generation.
Consider the interaction between a strong harmonic
light wave with frequency ω and the medium that has a
polarization described by two first terms of series (3).
The nonlinear polarization described by the second term
on the right-hand side of series (3) contains a timely
constant component that can be interpreted as a result of
the “optical detection” of a strong light wave in the
nonlinear medium. The time-depending polarization and,
consequently, the reemitted field oscillate in time with a
frequency of 2ω (the second harmonic of a pumping
light wave). The light wave of the second harmonic gets
the energy from radiation at the basic frequency ω
through the medium polarization component with a
frequency equal to 2ω. It is obvious that the energy
transfer to a light wave with a frequency equal to 2ω will
be efficient if the phase shift between the polarization
wave with frequency 2ω and the second harmonic of the
light wave keeps constant through quite long distances.
If the refractive indices of the medium for the light
waves with frequencies ω and 2ω are different, the phase
shift between them reaches the value of π at a distance lc
that is equal to
( )2/ 4cl n nω ω= λ − .
Consequently, one cannot possibly expect the
power accumulation from the second harmonic at
distances more than lc. The value lc which is called a
coherent length turns to infinity at the equality of the
refractive indices for waves with the basic and doubled
frequencies:
2n nω ω= . (4)
Expression (4) is known as the condition of phase
synchronism. Realization of condition (4) is impeded by
Fig. 3. Scheme of an acousto-optical convolver with spatial
integration.
Fig. 4. Scheme of an acousto-optical correlator with time
integration.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 34-39.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
38
dispersion, i.e. by the dependence of the refractive index
on the frequency, ( )n nω ω= ω . In negative uniaxial
crystals, one can find such a direction, along which the
refractive indices of an ordinary basic wave and an
extraordinary second-harmonic wave are equal, and the
coherent length turns to infinity.
The use of nonlinear optical phenomena allows one
also to get the coherent radiation with a smoothly tunable
frequency. This kind of processes is called the parametric
light generation. Parametric generation is stipulated by the
interaction between a strong pumping light wave with
frequency ω0 and two faint light waves with frequencies
ω1 and ω2 which are induced by self-fluctuations of the
polarization which are inevitably present in the active
medium. As the polarization depends nonlinearly on the
total field intensity in the medium, so the waves with
frequencies ω0, ω1, and ω2 become bound with one
another. The radiation at the frequency ω1 gets the energy
from the strong pumping wave with ω0 while it interacts
with the ω2-wave, and the wave ω2 gets the energy due to
the interaction between the ω0- and ω1-waves.
At the parametric generation, the synchronism
condition looks as
1 2 0k k k+ =
r r r
, (5)
where 1k
r
and 2k
r
are the wave vectors of amplified
waves, 0k
r
is the wave vector of a strong pumping wave.
If this condition is realized, then the waves with
frequencies ω1 and ω2 are amplified in the nonlinear
medium due to the energy of the pumping wave ω0. To
attain the generation, the nonlinear medium is put into a
complicated resonator that provides the positive feed-
back for the waves with ω1 and ω2. As relation (5) is
vectorial, the smooth tuning of the frequencies ω1 and ω2
of the generated waves is attained by turning the axis of
two system-composing resonators, which results in
changing the direction and length of the vectors
1 1 1k n c= ω
r
and 2 2 2k n c= ω
r
. It should be noted that,
to get a coherent radiation with smoothly tunable
frequency, one can also use a single-resonator scheme
that provides an output signal of higher stability.
5. Nonlinear optics of semiconductor lasers
Some courses of the specialization “Quantum elec-
tronics” are concerned with the consideration of the
nonlinear optics of semiconductor media and structures,
including the optical bistability and other effects [3].
In the special course “Semiconductor lasers” [4], it is
shown that, due to the strong nonlinear dependence of the
amplification coefficient on the concentration of excess
charge carriers, the pumped medium has characteristics of
an antireflecting filter. The phenomenon of undamped
pulses in semiconductor lasers is explained as the
relaxation vibrations appearing due to the influence of
some nonlinear mechanism resulting in an instability of
the steady-state mode. The instability criterion is generally
brought to the condition of positive nonlinear losses in a
resonator. The following phenomena are typical of the
complex dynamics of injection lasers:
1) hard self-excitation resulting in a fast increase
of the light intensity at reaching the generation
threshold;
2) hysteresis of the watt-ampere characteristic;
3) automodulation of the light intensity with
typical times of 10–10 s, determining the complicated
time structure of light pulses;
4) generation of single coherent pulses with the
rise and fall times not more than 10–10 s (analog of the
generation of monopulses by lasers on ruby and glasses);
5) emission of a regular sequence of short light
pulses of length ∼10–10s and the repetition frequency of
∼109s–1 at synchronizing the laser by a periodic signal;
6) self-synchronization of the longitudinal modes
with the emission of a sequence of short light pulses
with repetition frequencies of 108 Hz (with an external
resonator) and 1011 Hz (with a resonator formed by crys-
tal facets);
7) competition and anticompetition of modes
consisting in their mutual damping and excitation.
The variety of instable phenomena in IL is closely
related to its properties as a pulse system. By
approaching the study of the dynamics of IL from
positions of the theory of oscillations, except the basic
process – the induced emission of electromagnetic
waves, one should also remember two important
periodic processes typical of any type of lasers. The first
one is that any disturbance of the electromagnetic field
in a resonator is repeated many times with the period
2T L= υ , where L is the resonator length and υ is the
speed of light in the medium. This results in periodic
oscillations of the amplification coefficient and the
intensity of pulses (interaction in the “electron–photon”
system). The fundamental source of these oscillations is
the shot noise of a quantum transition that is responsible
for the spontaneous radiation and the induced one. At a
quite strong feedback and at the impact of an exterior
resonance disturbance, the oscillations can become
undamped (light auto-modulation).
Experiments show that, as a rule, only one mode is
generated continuously. In this case, the laser beam
intensity and frequency just slightly fluctuate near their
average values. If several modes are simultaneously
generated, then the laser radiation becomes unsteady as a
result of the competition between them. In this case, the
radiation consists of a set of chaotic pulses.
At the pulse excitation, the time interval from the start
of generation to its end can be divided into four parts:
1) delay time, when the substance is excited and
there is no generation;
2) transient mode from the start of generation to
reaching the quasisteady operation;
3) quasisteady operation is the continuous gene-
ration with auto-modulation phenomena;
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 34-39.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
39
4) in the absence of pumping, the generation
power relaxes to zero.
The facilities of the formation of a radiation pulse
with extremely short length and large amplitude by laser
diodes in the modes of free generation and modulation
of the Q-factor of a resonator are analyzed.
The influence of saturation effects on the
generation dynamics in a single-mode injection laser,
including spectral and spatial burn-out dips [5], is
studied. It is shown that the generation mode induces
transitions between the conduction band and the valence
one by breaking the quasiequilibrium in bands. The
amplification coefficient stops to be a single-valued
function of the concentration of carriers. The higher the
density of photons in a resonator, the greater is the
deviation from the equilibrium. To take this effect into
account in the kinetic equations, the amplification
coefficient is multiplied by the factor
( ) 1
sat/1 −+=γ SS ,
where S and Ssat are, respectively, the density of photons
in the resonator and the saturating density. This
approach means that the amplification instantly follows
a change in the density of photons. It is based on the fact
that the time of establishing the equilibrium in the bands
is much less than the times typical of the transient
processes in a laser.
The radiation kinetics of semiconductor sources is
studied in specialized laboratory practices [6].
The special course “Electromagnetic theory of
semiconductor lasers” [7] considers the phenomena
concerned with nonlinear refraction and the influence of
carriers on the refractive index of a semiconductor. As
known, the concentration of carriers depends on the
radiation intensity. At the photoelectric absorption, the
concentration increases, whereas it decreases under the
induced radiation. This results in the nonlinear refraction
of two types. In a laser medium, it has the properties of
auto-focusing and causes non-homogeneities and
instabilities. At the use of external resonators, nonlinear
refraction allows one to get bistable modes, as it occurs
in nonlinear resonators. But, in this case, external
sources aren’t necessary, and the continuous mode is
possible at room temperature [3, 7].
Another important aspect of the use of nonlinear
refraction consists in damping the unwanted modes in
the spectral surrounding of a laser line in the single-
frequency mode by the parametric interaction between
modes. The space-time (dynamical) grating of medium’s
optical parameters, which appears at the beating of
modes, causes the energy exchange between interfering
modes. The process involves two or three modes that
produce the beating at the total frequency Ω. At the two-
mode interaction, a sharp spectral asymmetry with the
transmission of energy to the long-wave mode is found.
The exceptions are given by small values of 1Ω ≤ τ ,
where τ is the relaxation time of an induced dynamical
grating. In those cases, the damping of side modes on
both sides of the “strong” mode prevails. If the Q-factor
of a resonator provides the damping of “far” modes, then
the internal mechanism of stabilizing the single-
frequency mode works in a laser with such a resonator.
In this case, due to the optical nonlinear scattering on the
dynamical grating, the antiphase oscillations appear at
the side frequency (phase inversion), which leads to the
damping of oscillations and fluctuations at the side
frequencies.
In a special course “Quantum-well lasers and
integrated-optical elements,” the effects of dimensional
quantization, possibilities of optical transitions and rules
of selection, nonlinear amplification effects, new laser
structures including ones with optical bistability and
laser amplifiers are considered [3].
In a special course “Kinetic theory of semi-
conductor injection lasers” for magisters [8], the
dynamics and peculiarities of light generation in various
types of injection lasers including the influence of
nonlinear amplification effects on the transient and
modulation characteristics of injection lasers, the nature
of a nonlinear interaction between modes, and its
influence on laser radiation dynamics are analyzed.
6. Conclusion
We have considered the questions of nonlinear and
acoustic optics included in the curriculum of general and
special courses for university’s students specializing in
quantum electronics. Along with general questions, a
special attention is paid to the use of acousto-optical
methods in the analysis and the processing of optical
signals in integrated optoelectronics and to nonlinear
optics of semiconductor injection lasers.
References
1. E.D. Karikh, Optoelectronics. BSU, Minsk, 2000
(in Russian).
2. I.S. Manak, V.A. Firago, Systems of Semiconductor
Quantum Electronics. BSU, Minsk, 2006 (in
Russian).
3. Nonlinear Optics of Semiconductor Lasers // Proc.
of Lebedev Phys. Inst. of RAS, vol. 166. Nauka,
Moscow, 1986 (in Russian).
4. E.D. Karikh, I.S. Manak, Semiconductor Lasers.
BSU, Minsk, 1999 (in Russian).
5. A.A. Afonenko, V.K. Kononenko, I.S. Manak,
Theory of Semiconductor Lasers. BSU, Minsk, 1995
(in Russian).
6. A.L. Gurskii, E.V. Lutsenko, I.S. Manak, Physics of
Semiconductor Light Sources. Practical Course.
BSU, Minsk, 2002 (in Russian).
7. A.A. Afonenko, I.S. Manak, Electromagnetic
Theory of Semiconductor Lasers. BSU, Minsk, 1997
(in Russian).
8. A.A. Afonenko, I.S. Manak, Kinetic Theory of
Semiconductor Injection Lasers. BSU, Minsk, 1998
(in Russian).
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