A New View on Acousto-optic Laser Beam Combining
Konstantin Yushkov
a
and Vladimir Molchanov
National University of Science and Technology “MISIS”, 4 Leninsky Prospekt, Moscow 119049, Russia
Keywords:
Acousto-optics, Coherent Beam Combining.
Abstract:
Coherent combining is a well-known principle of up-scaling the peak power in different types of pulsed lasers.
A new type of acousto-optic beam combiner for pulsed lasers is proposed and discussed. We demonstrate that
phase delay between two laser beams can be controlled and the beams can be combined using one acousto-
optic device. Two cases of degenerate and non-degenerate Bragg diffraction are analyzed and compared. The
experiment with anisotropic Bragg diffraction in paratellurite demonstrated efficiency of combining exceeding
95 %.
1 INTRODUCTION
The principle of coherent combining of laser pulses
underlies the creation of ultrahigh-intensity laser fa-
cilities (S.N. Bagayev et al., 2014) and the forma-
tion of sub-cycle ultrashort optical wave packets (C.
Manzoni et al., 2015). One can also use coherently
combined pulses for secure free-space communica-
tion (G.S. Rogozhnikov et al., 2018). Adding elec-
trical field from several independent sources requires
the simultaneous fulfillment of the following condi-
tions:
1. Synchronization of sources with a common fre-
quency standard;
2. Carrier-to-envelope phase stabilization of each
source;
3. Correction of phase delays of each channel arising
during transport and amplification of beams.
To fulfill the second condition, extra-cavity acousto-
optic (AO) modulators are used in the phase feedback
system (C. Grebing et al., 2009; B. Borchers et al.,
2011; F. L¨ucking et al., 2012; N.A. Koliada et al.,
2016). Often, one master oscillator is used seeding
the pulses that are divided into several independently
amplified channels and recombined at the output of
the amplifiers in front of the compressor (A. Klenke
et al., 2013). This ensures mutual coherence of all
channels.
Two types of coherent combining systems are dis-
tinguished: those with a tiled aperture (S.N. Bagayev
a
https://orcid.org/0000-0001-9015-799X
et al., 2014; V.E. Leshchenko et al., 2015) and with
a commmon aperture (O. Schmidt et al., 2009; A.
Klenke et al., 2013; C. Manzoni et al., 2015). The
beam combining scheme with a tiled architecture is
constructed on an bunch of independent beams each
focused onto a target located in the focal plane. To im-
prove the quality of field distribution in focus, adap-
tive optics systems (F. Li et al., 2017) can be addition-
ally used in such a system.
To combine the beams in a common aperture, po-
larization (A. Klenke et al., 2013), interference (T.Y.
Fan, 2005), or diffraction elements (S.M. Redmond
et al., 2012) are used. Systems based on polar-
ization and interference combining elements usually
have two inputs and one output beam. Combining
of a larger number of beams is achieved by cascad-
ing. The spectral addition (O. Schmidt et al., 2009;
C. Manzoni et al., 2015) is a special case to be con-
sidered separately. In this case, the radiation spectrum
expands, which reduces the Fourier-transform-limited
duration of the ultrashort pulse. Coherent combining
of ultrashort laser pulses directly during AO interac-
Figure 1: General scheme of an acousto-optic coherent laser
pulse combiner.
86
Yushkov, K. and Molchanov, V.
A New View on Acousto-optic Laser Beam Combining.
DOI: 10.5220/0008928200860091
In Proceedings of the 8th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2020), pages 86-91
ISBN: 978-989-758-401-5; ISSN: 2184-4364
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

(a) (b)
Figure 2: Wave vector diagram (a) and frequency-angle characteristic (b) of degenerate off-axis anisotropic diffraction in
paratellurite.
tion has not been previously considered. The paper
considers the design and application features of AO
coherent combiner (AOCC) of laser pulses.
2 SYSTEM ANALYSIS
2.1 Degenerate Double Bragg
Diffraction
Anisotropic Bragg acousto-optic interaction allows
one to obtain high diffraction efficiency of a single
beam at the level of 95–99 % (L.N. Magdich et al.,
2009; J.-C. Kastelik et al., 2009; J.-C. Kastelik et al.,
2018) in one diffraction order. All previously known
coherent combining systems require the use of ad-
ditional phase modulators for fine tuning the phases
of interfering beams. In any acousto-optic device the
phase adjustment can be carried out directly as a re-
sult of diffraction, since the coupled beams belong
to different diffraction orders, for example, +1 and
−1 (V.B. Voloshinov and K.B. Yushkov, 2007), and
the phase of the acoustic signal changes phases dif-
ferently for each of diffraction orders. Thus, it is pos-
sible to reduce the number of optical elements in the
coherent combining system: one acousto-optic devive
instead of two optical elements (phase modulator and
beam splitter).
Double Bragg diffraction in anisotropic case is a
degenerate type of diffraction that takes place when
phase matching condition is simultaneously satisfied
for three optical waves, two of them belonging to
the slow eigenmode and one belonging to the fast
eigenmode (V.B. Voloshinov and A.Yu. Tchernyatin,
2000). The degenerate AO Bragg diffraction is illus-
trated in Fig. 2. There are also two tangential AO
diffraction points: one at a positive Bragg angle and
higher frequency, and another an a negative Bragg an-
gle and lower frequency of ultrasound. Those opera-
tion points are used in AO deflectors (A. Goutzoulis
and D. Pape, 1994). For the degenerate Bragg diffrac-
tion there exists coupling between 0 and ±2 diffrac-
tion orders resulting intensity beatings at double ul-
trasound frequency. For continuous wave beams, av-
erage intensity is distributed more or less equally be-
tween the diffraction orders at high diffraction effi-
ciency (V.B. Voloshinov and K.B. Yushkov, 2007).
However, when one consider pulses laser radiation,
the beatings between the diffraction orders can be
synchronized with the pulse train to reach the peak
of the beatings when the laser pulse arrives.
To describe the operation of the system we use the
first-order coupled wave theory (A. Yariv and P. Yeh,
1984). The equations of coupled modes for double
Bragg scattering have the form:















dA
0
dz
= −
q
2
A
1
(z)exp(iΦ);
dA
1
dz
=
q
2
A
0
(z)exp(−iΦ) −
q
2
A
2
(z)exp(iΦ);
dA
2
dz
=
q
2
A
1
(z)exp(−iΦ),
(1)
The solution for one input beam with initial condi-
tions A
0
(0) = 1, A
1
(0) = A
2
(0) = 0 is well known:















A
0
(z) = cos
2
qz
2
√
2
;
A
1
(z) =
exp(iΦ)
√
2
sin
qz
√
2
;
A
2
(z) = exp(2iΦ)sin
2
qz
2
√
2
.
(2)
In the presence of two incident waves with the same
optical frequency the initial conditions for complex
A New View on Acousto-optic Laser Beam Combining
87

amplitudes must be written as:





A
0
(0) = 1;
A
1
(0) = 0;
A
2
(0) = exp(−2iΩt),
(3)
since complex field representation in slowly-varying
envelope approximation (SVEA) already includes
Doppler shifts between the diffraction orders (V.N.
Parygin and L.E. Chirkov, 1975). The solution of
Eqs. (1) with initial conditions (3) explicitly describes
the beatings:
A
0
(L) = exp(−iΩt + iΦ)[cos(Ωt −Φ)+
icos
qL
√
2
sin(Ωt −Φ)

; (4)
A
1
(L) =
√
2 iexp(−iΩt) sin
qL
√
2
sin(Ωt −Φ); (5)
A
2
(L) = exp(−iΩt −iΦ)[cos(Ωt −Φ)−
icos
qL
√
2
sin(Ωt −Φ)

. (6)
The intensities of the diffraction orders I
p
= |A
p
|
2
are
respectively equal to:
I
0
= I
2
= cos
2
(Ωt −Φ)+
sin
2
(Ωt −Φ)cos
2
qL
√
2
; (7)
I
1
= 2sin
2
(Ωt −Φ)sin
2
qL
√
2
. (8)
The maximum of the diffraction efficiency in the first
order takes place at qL = π/
√
2 and Ωt −Φ = π, and
the sum of the input beam intensities is I
1
= I
0
(0) +
I
2
(0). Since there is no diffracted beam in the first
order when the driving radio-frequency (RF) signal is
switched off, this device can be also used as a pulse
picker or modulator (E.I. Gacheva et al., 2017).
2.2 Non-degenerate Bragg Diffraction
The addition of two beams can also be obtained using
a single Bragg diffraction without degeneracy. In this
case, the equations of coupled modes have the form







dA
0
dz
= −
q
2
A
1
(z)exp(iΦ);
dA
1
dz
=
q
2
A
0
(z)exp(−iΦ),
(9)
with the initial conditions:

A
0
(0) = 1;
A
1
(0) = exp(−iΩt),
(10)
Figure 3: Light intensity of diffracted beams: (a) beatings
for continuous-wave radiation; (b) combining of a synchro-
nized pulse train.
The solution of the system of equations has the form:
A
0
(L) = cos
qL
2
+ exp(−iΩt + iΦ)sin
qL
2
; (11)
A
1
(L) = exp(−iΩt)cos
qL
2
−
exp(−iΦ)sin
qL
2
, (12)
and the intensities are equal to:

I
0
= 1+ sin(qL)cos(Ωt −Φ);
I
1
= 1−sin(qL)cos(Ωt −Φ);
(13)
Such a diffraction geometry has an advantage over
the twofold degenerate geometry considered above,
since the maximum intensity in each of the diffrac-
tion orders is achieved at qL = π/2, that is, at half
the power of the controlling RF signal compared to
a degenerate geometry and four times less power in
compared to diffraction of a single input beam with
maximum efficiency. Moreover, such a configuration
allows one to choose different frequencies of AO in-
teraction, in contrast to degenerate geometry, whose
frequency is uniquely determined by the propagation
direction of the acoustic wave in the AO crystal α and
the wavelength of light λ. Typical ultrasound frequen-
cies in paratellurite are between 20 and 150 MHz with
up to an octave-spanning bandwidth limited by elec-
trical impedance matching of the piezoelectric trans-
ducer (V.Ya. Molchanov and O.Yu. Makarov, 1999).
Note that the tangential geometry of AO interaction
supports wide optical bandwidth exceeding 100 nm in
the visible wavelength region (A. Dieulangard et al.,
2015) that is enough for providing high diffraction
efficiency of ultrashort laser pulses. Non-degenerate
diffraction can be obtained both for isotropic and for
anisotropic AO diffraction that broadens the choice
of acousto-optic materials. In the case of isotropic
diffraction, there will be no group mismatch between
zero and first order, which reduces the diffraction ef-
ficiency of ultrashort laser pulses (K.B. Yushkov and
V.Ya. Molchanov, 2011).
PHOTOPTICS 2020 - 8th International Conference on Photonics, Optics and Laser Technology
88

Figure 4: Oscilloscope traces of coherently combined laser beams: (a) intensity of zero and first diffraction orders at a single
input of the beam in the mode of linear amplitude variation; (b) the intensity of the zero and first diffraction orders for two
input beams in the mode of linear amplitude ramp mode; (c) intensity beats in two output beams; (d) diffraction intensity in
the frequency sweep mode in the range ±2 MHz. Scale bars indicate the measurement units along coordinate axes.
3 EXPERIMENT
The experiment was performed with AOCC based
on paratellurite single crystal with orientation angle
α = 6.4
◦
in (110) plane at the laser wavelength of
λ = 1053 nm. The degeneration frequency is 63.5
MHz for this configuration (see Fig. 2b). In the ex-
periment, non-degenerate diffraction at a frequency
of f = 75 MHz was studied. The single continuous
wave laser beam was split into two arxms and each
arm was aligned to satisfy Bragg phase matching con-
dition independently from another. The radiation in-
tensity was simultaneously recorded by two photodi-
odes in both output diffraction orders. The results are
shown in Fig. 4. Figures 4 (a) and (b) correspond to
linear amplitude ramp of the RF signal. Figure 4 (c)
demonstrates counter-phase beatings in each of the
diffracted beams with more than 95 % of peak effi-
ciency for each of the output beams. The bandwidth
of diffraction demonstrated in Figure 4 (d) using the
frequency swept RF signal. As follows from the so-
lution of the coupled mode equations (13), the max-
imum beat amplitude is achieved when the RF sig-
nal amplitude is half that required to achieve maxi-
mum efficiency in the diffraction of one of the beams.
Moreover, the intensity at the maximum of the beats
is approximately 96 % of the total intensity of the two
input beams.
4 CONCLUSIONS
Efficient coherent combining of continuous radiation
in the considered acousto-optic system is impossi-
ble, since the beatings with the ultrasound frequency
occur between the diffraction orders, and the aver-
age time intensity in each order is approximately 1/2
of the total for non-degenerate geometry and 1/3 of
the total for degenerate geometry (V.B. Voloshinov
and K.B. Yushkov, 2007). This limitation can be
circumvented if one laser beam is first decomposed
into several components using a similar acousto-optic
cell (S.N. Antonov et al., 2007). In this case, the
beams already have shifted frequencies and it is pos-
sible to recombine them at the output obtaining larger
part of the total energy in one of the orders.
In practice, combining of pulsed laser beams is of
great interest since it allows to achieve much higher
A New View on Acousto-optic Laser Beam Combining
89

peak laser power than in continuous wave mode. If
the frequency of the Doppler shift is equal to the in-
termode interval of the optical spectrum, the beat pe-
riod coincides with the interval between two adjacent
pulses. Thus, one can achieve the intensity of the
idler beam to be equal to zero at all times. A simi-
lar approach is used, for example, for stabilized AO-
modulation of ultrashort pulses (O. de Vries et al.,
2015).
ACKNOWLEDGEMENTS
The research was supported by Russian Foundation
for Basic Research (RFBR) under project 18-29-
20019.
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