<s>
Sound	B-Algorithm
amplification	I-Algorithm
by	I-Algorithm
stimulated	I-Algorithm
emission	I-Algorithm
of	I-Algorithm
radiation	I-Algorithm
(	O
SASER	B-Algorithm
)	O
refers	O
to	O
a	O
device	O
that	O
emits	O
acoustic	O
radiation	O
.	O
</s>
<s>
Acoustic	O
radiation	O
(	O
sound	O
waves	O
)	O
can	O
be	O
emitted	O
by	O
using	O
the	O
process	O
of	O
sound	O
amplification	O
based	O
on	O
stimulated	O
emission	O
of	O
phonons	B-Language
.	O
</s>
<s>
Sound	O
(	O
or	O
lattice	O
vibration	O
)	O
can	O
be	O
described	O
by	O
a	O
phonon	B-Language
just	O
as	O
light	O
can	O
be	O
considered	O
as	O
photons	B-Application
,	O
and	O
therefore	O
one	O
can	O
state	O
that	O
SASER	B-Algorithm
is	O
the	O
acoustic	O
analogue	O
of	O
the	O
laser	O
.	O
</s>
<s>
In	O
a	O
SASER	B-Algorithm
device	O
,	O
a	O
source	O
(	O
e.g.	O
,	O
an	O
electric	O
field	O
as	O
a	O
pump	O
)	O
produces	O
sound	O
waves	O
(	O
lattice	O
vibrations	O
,	O
phonons	B-Language
)	O
that	O
travel	O
through	O
an	O
active	O
medium	O
.	O
</s>
<s>
In	O
this	O
active	O
medium	O
,	O
a	O
stimulated	O
emission	O
of	O
phonons	B-Language
leads	O
to	O
amplification	O
of	O
the	O
sound	O
waves	O
,	O
resulting	O
in	O
a	O
sound	O
beam	O
coming	O
out	O
of	O
the	O
device	O
.	O
</s>
<s>
The	O
first	O
successful	O
SASERs	B-Algorithm
were	O
developed	O
in	O
2009	O
.	O
</s>
<s>
Instead	O
of	O
a	O
feedback-built	O
wave	O
of	O
electromagnetic	O
radiation	O
(	O
i.e.	O
,	O
a	O
laser	O
beam	O
)	O
,	O
a	O
SASER	B-Algorithm
delivers	O
a	O
sound	O
wave	O
.	O
</s>
<s>
SASER	B-Algorithm
may	O
also	O
be	O
referred	O
to	O
as	O
phonon	B-Language
laser	O
,	O
acoustic	B-Algorithm
laser	I-Algorithm
or	O
sound	O
laser	O
.	O
</s>
<s>
SASERs	B-Algorithm
could	O
have	O
wide	O
applications	O
.	O
</s>
<s>
Apart	O
from	O
facilitating	O
the	O
investigation	O
of	O
terahertz-frequency	O
ultrasound	B-Application
,	O
the	O
SASER	B-Algorithm
is	O
also	O
likely	O
to	O
find	O
uses	O
in	O
optoelectronics	O
(	O
electronic	O
devices	O
that	O
detect	O
and	O
control	O
light	O
—	O
as	O
a	O
method	O
of	O
transmitting	O
a	O
signal	O
from	O
an	O
end	O
to	O
the	O
other	O
of	O
,	O
for	O
instance	O
,	O
fiber	O
optics	O
)	O
,	O
as	O
a	O
method	O
of	O
signal	O
modulation	O
and/or	O
transmission	O
.	O
</s>
<s>
Using	O
SASERs	B-Algorithm
to	O
manipulate	O
electrons	O
inside	O
semiconductors	O
could	O
theoretically	O
result	O
in	O
terahertz-frequency	O
computer	O
processors	O
,	O
much	O
faster	O
than	O
the	O
current	O
chips	O
.	O
</s>
<s>
Theodore	O
Maiman	O
operated	O
the	O
first	O
functioning	O
LASER	O
on	O
May	O
16	O
,	O
1960	O
at	O
Hughes	O
Research	O
Laboratories	O
,	O
Malibu	O
,	O
California	O
,	O
A	O
device	O
that	O
operates	O
according	O
to	O
the	O
central	O
idea	O
of	O
the	O
"	O
sound	B-Algorithm
amplification	I-Algorithm
by	I-Algorithm
stimulated	I-Algorithm
emission	I-Algorithm
of	I-Algorithm
radiation	I-Algorithm
"	O
theory	O
is	O
the	O
thermoacoustic	O
laser	O
.	O
</s>
<s>
Much	O
like	O
a	O
light	O
laser	O
,	O
a	O
thermoacoustic	O
SASER	B-Algorithm
has	O
a	O
high-Q	O
cavity	O
and	O
uses	O
a	O
gain	O
medium	O
to	O
amplify	O
coherent	O
waves	O
.	O
</s>
<s>
The	O
possibility	O
of	O
phonon	B-Language
laser	O
action	O
had	O
been	O
proposed	O
in	O
a	O
wide	O
range	O
of	O
physical	O
systems	O
such	O
as	O
nanomechanics	O
,	O
semiconductors	O
,	O
nanomagnets	O
and	O
paramagnetic	O
ions	O
in	O
a	O
lattice	O
.	O
</s>
<s>
Finding	O
materials	O
that	O
stimulate	O
emission	O
was	O
needed	O
for	O
the	O
development	O
of	O
the	O
SASER	B-Algorithm
.	O
</s>
<s>
The	O
generation	O
of	O
coherent	O
phonons	B-Language
in	O
a	O
double-barrier	O
semiconductor	O
heterostructure	O
was	O
first	O
proposed	O
around	O
1990	O
.	O
</s>
<s>
Announced	O
in	O
2010	O
,	O
two	O
independent	O
groups	O
came	O
up	O
with	O
two	O
different	O
devices	O
that	O
produce	O
coherent	O
phonons	B-Language
at	O
any	O
frequency	O
in	O
the	O
range	O
megahertz	O
to	O
terahertz	O
.	O
</s>
<s>
The	O
other	O
group	O
from	O
the	O
California	O
Institute	O
of	O
Technology	O
(	O
Caltech	O
)	O
consisted	O
of	O
Ivan	O
S	O
.	O
Grudinin	O
,	O
Hansuek	O
Lee	O
,	O
O	O
.	O
Painter	O
and	O
Kerry	O
J	O
.	O
Vahala	O
from	O
Caltech	O
implemented	O
a	O
study	O
on	O
Phonon	B-Language
Laser	O
Action	O
in	O
a	O
tunable	O
two-level	O
system	O
.	O
</s>
<s>
According	O
to	O
a	O
member	O
of	O
the	O
Nottingham	O
group	O
,	O
the	O
two	O
approaches	O
are	O
complementary	O
and	O
it	O
should	O
be	O
possible	O
to	O
use	O
one	O
device	O
or	O
the	O
other	O
to	O
create	O
coherent	O
phonons	B-Language
at	O
any	O
frequency	O
in	O
the	O
megahertz	O
to	O
terahertz	O
range	O
.	O
</s>
<s>
The	O
differences	O
between	O
the	O
two	O
devices	O
suggest	O
that	O
SASERs	B-Algorithm
could	O
be	O
made	O
to	O
operate	O
over	O
a	O
wide	O
range	O
of	O
frequencies	O
.	O
</s>
<s>
Work	O
on	O
the	O
SASER	B-Algorithm
continues	O
at	O
the	O
University	O
of	O
Nottingham	O
,	O
the	O
Lashkarev	O
Institute	O
of	O
Semiconductor	O
Physics	O
at	O
the	O
National	O
Academy	O
of	O
Sciences	O
of	O
Ukraine	O
,	O
and	O
Caltech	O
.	O
</s>
<s>
SASER	B-Algorithm
's	O
central	O
idea	O
is	O
based	O
on	O
sound	O
waves	O
.	O
</s>
<s>
The	O
set-up	O
needed	O
for	O
the	O
implement	O
of	O
sound	B-Algorithm
amplification	I-Algorithm
by	I-Algorithm
stimulated	I-Algorithm
emission	I-Algorithm
of	I-Algorithm
radiation	I-Algorithm
is	O
similar	O
to	O
an	O
oscillator	O
.	O
</s>
<s>
An	O
oscillator	O
can	O
produce	O
oscillations	B-Algorithm
without	O
any	O
external	O
feed-mechanism	O
.	O
</s>
<s>
The	O
corresponding	O
parts	O
in	O
a	O
SASER	B-Algorithm
device	O
are	O
the	O
excitation	O
or	O
pumping	O
mechanism	O
,	O
the	O
active	O
(	O
amplifying	O
)	O
medium	O
,	O
and	O
the	O
feedback	O
leading	O
to	O
acoustic	O
radiation	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
feedback	O
mechanism	O
into	O
the	O
active	O
medium	O
is	O
the	O
existence	O
of	O
superlattice	B-General_Concept
layers	O
that	O
reflect	O
the	O
phonons	B-Language
back	O
and	O
force	O
them	O
to	O
bounce	O
repeatedly	O
to	O
amplify	O
sound	O
.	O
</s>
<s>
Therefore	O
,	O
to	O
proceed	O
to	O
an	O
understanding	O
of	O
a	O
SASER	B-Algorithm
design	O
we	O
need	O
to	O
imagine	O
it	O
in	O
analogy	O
with	O
a	O
laser	O
device	O
.	O
</s>
<s>
A	O
spontaneously	O
emitted	O
photon	B-Application
inside	O
this	O
interferometer	O
can	O
force	O
excited	O
atoms	O
to	O
decay	O
a	O
photon	B-Application
of	O
same	O
frequency	O
,	O
same	O
momentum	B-Algorithm
,	O
same	O
polarization	O
and	O
same	O
phase	O
.	O
</s>
<s>
Because	O
the	O
momentum	B-Algorithm
(	O
as	O
a	O
vector	O
)	O
of	O
the	O
photon	B-Application
is	O
nearly	O
parallel	O
to	O
the	O
axes	O
of	O
the	O
mirrors	O
,	O
it	O
is	O
possible	O
for	O
photons	B-Application
to	O
repeat	O
multiple	O
reflections	O
and	O
force	O
more	O
and	O
more	O
photons	B-Application
to	O
follow	O
them	O
producing	O
an	O
avalanche	O
effect	O
.	O
</s>
<s>
The	O
number	O
of	O
photons	B-Application
of	O
this	O
coherent	O
laser	O
beam	O
increases	O
and	O
competes	O
the	O
number	O
of	O
photons	B-Application
perished	O
due	O
to	O
losses	O
.	O
</s>
<s>
A	O
SASER	B-Algorithm
device	O
mimics	O
this	O
procedure	O
using	O
a	O
source-pump	O
to	O
induce	O
a	O
sound	O
beam	O
of	O
phonons	B-Language
.	O
</s>
<s>
An	O
example	O
of	O
an	O
active	O
medium	O
is	O
the	O
superlattice	B-General_Concept
.	O
</s>
<s>
A	O
superlattice	B-General_Concept
can	O
consist	O
of	O
multiple	O
ultra-thin	O
lattices	O
of	O
two	O
different	O
semiconductors	O
.	O
</s>
<s>
In	O
the	O
superlattice	B-General_Concept
,	O
a	O
new	O
set	O
of	O
selection	O
rules	O
is	O
composed	O
that	O
affects	O
the	O
flow-conditions	O
of	O
charges	O
through	O
the	O
structure	O
.	O
</s>
<s>
When	O
this	O
set-up	O
is	O
excited	O
by	O
a	O
source	O
,	O
the	O
phonons	B-Language
start	O
to	O
multiply	O
while	O
they	O
reflect	O
on	O
the	O
lattice	O
levels	O
,	O
until	O
they	O
escape	O
from	O
the	O
lattice	O
structure	O
in	O
a	O
form	O
of	O
an	O
ultrahigh	O
frequency	O
phonon	B-Language
beam	O
.	O
</s>
<s>
Namely	O
,	O
a	O
concerted	O
emission	O
of	O
phonons	B-Language
can	O
lead	O
to	O
coherent	O
sound	O
and	O
an	O
example	O
of	O
concerted	O
phonon	B-Language
emission	O
is	O
the	O
emission	O
coming	O
from	O
quantum	O
wells	O
.	O
</s>
<s>
A	O
SASER	B-Algorithm
device	O
transforms	O
the	O
electric	O
potential	O
energy	O
in	O
a	O
single	O
vibrational	O
mode	O
of	O
the	O
lattice	O
(	O
phonon	B-Language
)	O
.	O
</s>
<s>
In	O
these	O
wells	O
,	O
electrons	O
can	O
be	O
excited	O
by	O
parcels	O
of	O
ultrasound	B-Application
of	O
millielectronvolts	O
of	O
energy	O
.	O
</s>
<s>
Just	O
as	O
light	O
is	O
a	O
wave	O
motion	O
that	O
is	O
considered	O
as	O
composed	O
of	O
particles	O
called	O
photons	B-Application
,	O
we	O
can	O
think	O
of	O
the	O
normal	O
modes	O
of	O
vibration	O
in	O
a	O
solid	O
as	O
being	O
particle-like	O
.	O
</s>
<s>
The	O
quantum	O
of	O
lattice	O
vibration	O
is	O
called	O
phonon	B-Language
.	O
</s>
<s>
In	O
other	O
words	O
,	O
we	O
need	O
to	O
calculate	O
the	O
energies	O
(	O
or	O
frequencies	O
)	O
of	O
the	O
phonons	B-Language
as	O
a	O
function	O
of	O
their	O
wave	O
vector	O
's	O
k	O
.	O
</s>
<s>
The	O
relationship	O
between	O
frequency	O
ω	O
and	O
wave	O
vector	O
k	O
is	O
called	O
phonon	B-Language
dispersion	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
light	O
we	O
have	O
photons	B-Application
while	O
in	O
sound	O
we	O
have	O
phonons	B-Language
.	O
</s>
<s>
However	O
,	O
at	O
the	O
terahertz	O
frequencies	O
in	O
the	O
regime	O
of	O
phonon	B-Language
laser	O
applications	O
,	O
more	O
difficulties	O
arise	O
.	O
</s>
<s>
Instead	O
of	O
resulting	O
in	O
orderly	O
,	O
coherent	O
phonons	B-Language
,	O
laser	O
structures	O
that	O
can	O
produce	O
terahertz	O
sound	O
tend	O
to	O
emit	O
phonons	B-Language
randomly	O
.	O
</s>
<s>
Scientists	O
in	O
Caltech	O
have	O
overcome	O
this	O
problem	O
by	O
assembling	O
a	O
pair	O
of	O
microscopic	O
cavities	O
that	O
only	O
permit	O
specific	O
frequencies	O
of	O
phonons	B-Language
to	O
be	O
emitted	O
.	O
</s>
<s>
This	O
system	O
can	O
be	O
also	O
tuned	O
to	O
emit	O
phonons	B-Language
of	O
different	O
frequencies	O
by	O
changing	O
the	O
relative	O
separation	O
of	O
the	O
microcavities	O
.	O
</s>
<s>
Briefly	O
,	O
as	O
an	O
electron	O
hops	O
from	O
one	O
quantum	O
well	O
to	O
another	O
neighbouring	O
well	O
it	O
produces	O
a	O
phonon	B-Language
.	O
</s>
<s>
Relaxation	O
of	O
an	O
electron	O
from	O
one	O
of	O
the	O
upper	O
states	O
may	O
occur	O
by	O
emission	O
of	O
either	O
a	O
photon	B-Application
or	O
a	O
phonon	B-Language
.	O
</s>
<s>
This	O
is	O
determined	O
by	O
the	O
density	O
of	O
states	O
of	O
phonons	B-Language
and	O
photons	B-Application
.	O
</s>
<s>
Both	O
phonons	B-Language
and	O
photons	B-Application
are	O
bosons	O
and	O
thus	O
,	O
they	O
obey	O
Bose	O
–	O
Einstein	O
statistics	O
.	O
</s>
<s>
This	O
means	O
that	O
,	O
since	O
bosons	O
with	O
the	O
same	O
energy	O
can	O
occupy	O
the	O
same	O
place	O
in	O
space	O
,	O
phonons	B-Language
and	O
photons	B-Application
are	O
force	O
carrier	O
particles	O
and	O
they	O
have	O
integer	O
spins	O
.	O
</s>
<s>
There	O
are	O
more	O
allowed	O
states	O
available	O
for	O
occupancy	O
in	O
a	O
phonon	B-Language
field	O
than	O
in	O
a	O
photon	B-Application
field	O
.	O
</s>
<s>
Therefore	O
,	O
since	O
the	O
density	O
of	O
terminal	O
states	O
in	O
the	O
phonon	B-Language
field	O
exceeds	O
that	O
in	O
a	O
photon	B-Application
field	O
(	O
by	O
up	O
to	O
~	O
105	O
)	O
,	O
phonon	B-Language
emission	O
is	O
by	O
far	O
the	O
more	O
likely	O
event	O
.	O
</s>
<s>
We	O
could	O
also	O
imagine	O
a	O
concept	O
where	O
the	O
excitation	O
of	O
an	O
electron	O
briefly	O
leads	O
to	O
vibration	O
of	O
the	O
lattice	O
and	O
thus	O
to	O
phonon	B-Language
generation	O
.	O
</s>
<s>
Every	O
one	O
of	O
this	O
"	O
excitation	O
packages	O
"	O
is	O
called	O
phonon	B-Language
.	O
</s>
<s>
phonon	B-Language
)	O
it	O
interacts	O
with	O
another	O
excited	O
electron	O
to	O
release	O
its	O
energy	O
too	O
.	O
</s>
<s>
Therefore	O
,	O
we	O
have	O
a	O
stimulated	O
emission	O
,	O
which	O
means	O
a	O
lot	O
of	O
energy	O
(	O
e.g.	O
,	O
acoustic	O
radiation	O
,	O
phonons	B-Language
)	O
is	O
released	O
at	O
the	O
same	O
time	O
.	O
</s>
<s>
A	O
SASER	B-Algorithm
device	O
should	O
consist	O
of	O
a	O
pumping	O
mechanism	O
and	O
an	O
active	O
medium	O
.	O
</s>
<s>
The	O
fact	O
that	O
a	O
SASER	B-Algorithm
operates	O
on	O
principles	O
remarkably	O
similar	O
to	O
a	O
laser	O
,	O
can	O
lead	O
to	O
an	O
easier	O
way	O
of	O
understanding	O
the	O
relevant	O
operation	O
circumstances	O
.	O
</s>
<s>
Instead	O
of	O
a	O
feedback-built	O
potent	O
wave	O
of	O
electromagnetic	O
radiation	O
,	O
a	O
SASER	B-Algorithm
delivers	O
a	O
potent	O
sound	O
wave	O
.	O
</s>
<s>
Sound	O
amplification	O
according	O
to	O
the	O
experiment	O
taken	O
in	O
the	O
University	O
of	O
Nottingham	O
could	O
be	O
based	O
on	O
an	O
induced	O
cascade	O
of	O
electrons	O
in	O
semiconductor	O
superlattices	B-General_Concept
.	O
</s>
<s>
The	O
energy	O
levels	O
of	O
electrons	O
are	O
confined	O
in	O
the	O
superlattice	B-General_Concept
layers	O
.	O
</s>
<s>
As	O
the	O
electrons	O
hop	O
between	O
gallium	O
arsenide	O
quantum	O
wells	O
in	O
the	O
superlattice	B-General_Concept
they	O
emit	O
phonons	B-Language
.	O
</s>
<s>
Then	O
,	O
one	O
phonon	B-Language
going	O
in	O
,	O
produces	O
two	O
phonons	B-Language
coming	O
out	O
of	O
the	O
superlattice	B-General_Concept
.	O
</s>
<s>
This	O
process	O
can	O
be	O
stimulated	O
by	O
other	O
phonons	B-Language
and	O
then	O
give	O
rise	O
to	O
an	O
acoustic	O
amplification	O
.	O
</s>
<s>
Upon	O
the	O
addition	O
of	O
electrons	O
,	O
short-wavelength	O
(	O
in	O
the	O
terahertz	O
range	O
)	O
phonons	B-Language
are	O
produced	O
.	O
</s>
<s>
Since	O
the	O
electrons	O
are	O
confined	O
to	O
the	O
quantum	O
wells	O
existing	O
within	O
the	O
lattice	O
,	O
the	O
transmission	O
of	O
their	O
energy	O
depends	O
upon	O
the	O
phonons	B-Language
they	O
generate	O
.	O
</s>
<s>
As	O
these	O
phonons	B-Language
strike	O
other	O
layers	O
in	O
the	O
lattice	O
,	O
they	O
excite	O
electrons	O
,	O
which	O
produce	O
further	O
phonons	B-Language
,	O
which	O
go	O
on	O
to	O
excite	O
more	O
electrons	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
Eventually	O
,	O
a	O
very	O
narrow	O
beam	O
of	O
high-frequency	O
ultrasound	B-Application
exits	O
the	O
device	O
.	O
</s>
<s>
Semiconductor	O
superlattices	B-General_Concept
are	O
used	O
as	O
acoustic	O
mirrors	O
.	O
</s>
<s>
These	O
superlattice	B-General_Concept
structures	O
must	O
be	O
in	O
the	O
right	O
size	O
obeying	O
the	O
theory	O
of	O
multilayer	O
distributed	B-Device
Bragg	I-Device
reflector	I-Device
,	O
in	O
similarity	O
with	O
multilayer	O
dielectric	O
mirrors	O
in	O
optics	O
.	O
</s>
<s>
Basic	O
understanding	O
of	O
the	O
SASER	B-Algorithm
development	O
requires	O
the	O
evaluation	O
of	O
some	O
proposed	O
examples	O
of	O
SASER	B-Algorithm
devices	O
and	O
SASER	B-Algorithm
theoretical	O
schemes	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
oscillations	B-Algorithm
of	O
the	O
bubbles	O
are	O
self-synchronized	O
and	O
the	O
useful	O
mode	O
amplifies	O
.	O
</s>
<s>
We	O
note	O
that	O
,	O
in	O
the	O
case	O
of	O
the	O
piezoelectric	O
radiators	O
usually	O
used	O
to	O
generate	O
ultrasound	B-Application
,	O
only	O
the	O
working	O
surface	O
radiates	O
and	O
therefore	O
the	O
working	O
system	O
is	O
two-dimensional	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
a	O
sound	B-Algorithm
amplification	I-Algorithm
by	I-Algorithm
stimulated	I-Algorithm
emission	I-Algorithm
of	I-Algorithm
radiation	I-Algorithm
device	O
is	O
a	O
three-dimensional	O
system	O
,	O
since	O
the	O
entire	O
volume	O
of	O
the	O
active	O
medium	O
radiates	O
.	O
</s>
<s>
Hence	O
,	O
the	O
wave	O
amplitude	O
and	O
the	O
bubble	O
density	O
vary	O
slowly	O
compared	O
with	O
the	O
period	O
of	O
the	O
oscillations	B-Algorithm
.	O
</s>
<s>
In	O
the	O
theoretical	O
scheme	O
where	O
the	O
usage	O
of	O
resonators	O
is	O
essential	O
,	O
the	O
SASER	B-Algorithm
radiation	O
passes	O
through	O
the	O
resonator	O
walls	O
,	O
which	O
are	O
perpendicular	O
to	O
the	O
direction	O
of	O
propagation	O
of	O
the	O
pump	O
wave	O
.	O
</s>
<s>
According	O
to	O
an	O
example	O
of	O
an	O
electrically	O
pumped	O
SASER	B-Algorithm
,	O
the	O
active	O
medium	O
is	O
confined	O
between	O
two	O
planes	O
,	O
which	O
are	O
defined	O
by	O
the	O
solid	O
walls	O
of	O
the	O
resonator	O
.	O
</s>
<s>
Mathematical	O
analyses	O
have	O
shown	O
that	O
two	O
types	O
of	O
losses	O
must	O
be	O
overcome	O
for	O
generation	O
of	O
oscillations	B-Algorithm
to	O
start	O
.	O
</s>
<s>
Bubbles	O
play	O
the	O
main	O
role	O
in	O
the	O
energy	O
dispersion	O
in	O
a	O
SASER	B-Algorithm
.	O
</s>
<s>
A	O
relevant	O
suggested	O
scheme	O
of	O
sound	B-Algorithm
amplification	I-Algorithm
by	I-Algorithm
stimulated	I-Algorithm
emission	I-Algorithm
of	I-Algorithm
radiation	I-Algorithm
using	O
gas	O
bubbles	O
as	O
the	O
active	O
medium	O
was	O
introduced	O
around	O
1995	O
The	O
pumping	O
is	O
created	O
by	O
mechanical	O
oscillations	B-Algorithm
of	O
a	O
cylindrical	O
resonator	O
and	O
the	O
phase	O
bunching	O
of	O
bubbles	O
is	O
realized	O
by	O
acoustic	O
radiation	O
forces	O
.	O
</s>
<s>
According	O
to	O
other	O
proposed	O
schemes	O
,	O
the	O
electrostriction	O
oscillations	B-Algorithm
of	O
the	O
dispersed	O
particle	O
volumes	O
in	O
the	O
cylindrical	O
resonator	O
are	O
realized	O
by	O
an	O
alternating	O
electromagnetic	O
field	O
.	O
</s>
<s>
However	O
,	O
a	O
SASER	B-Algorithm
scheme	O
with	O
an	O
alternating	O
electric	O
field	O
as	O
the	O
pump	O
has	O
a	O
limitation	O
.	O
</s>
<s>
Hence	O
,	O
a	O
study	O
proposes	O
a	O
SASER	B-Algorithm
scheme	O
without	O
this	O
limitation	O
.	O
</s>
<s>
A	O
proposal	O
for	O
the	O
development	O
of	O
a	O
phonon	B-Language
laser	O
on	O
resonant	O
phonon	B-Language
transitions	O
has	O
been	O
introduced	O
from	O
a	O
group	O
in	O
Institute	O
of	O
Spectroscopy	O
in	O
Moscow	O
,	O
Russia	O
.	O
</s>
<s>
Two	O
schemes	O
for	O
steady	O
stimulated	O
phonon	B-Language
generation	O
were	O
mentioned	O
.	O
</s>
<s>
The	O
first	O
scheme	O
exploits	O
a	O
narrow-gap	O
indirect	O
semiconductor	O
or	O
analogous	O
indirect	O
gap	O
semiconductor	O
heterostructure	O
where	O
the	O
tuning	O
into	O
resonance	O
of	O
one-phonon	O
transition	O
of	O
electron	O
–	O
hole	O
recombination	O
can	O
be	O
carried	O
out	O
by	O
external	O
pressure	O
,	O
magnetic	O
or	O
electric	O
fields	O
.	O
</s>
<s>
The	O
second	O
scheme	O
uses	O
one-phonon	O
transition	O
between	O
direct	O
and	O
indirect	O
exciton	O
levels	O
in	O
coupled	O
quantum	O
wells	O
.	O
</s>
<s>
The	O
magnitude	O
of	O
phonon	B-Language
wave	O
vector	O
in	O
the	O
second	O
proposed	O
scheme	O
,	O
is	O
supposed	O
to	O
be	O
determined	O
by	O
magnitude	O
of	O
in-plane	O
magnetic	O
field	O
.	O
</s>
<s>
Therefore	O
,	O
such	O
kind	O
of	O
SASER	B-Algorithm
is	O
tunable	O
(	O
i.e.	O
</s>
<s>
The	O
reasoning	O
behind	O
that	O
is	O
that	O
a	O
pair	O
of	O
electron	O
and	O
hole	O
near	O
minima	O
of	O
their	O
bands	O
in	O
an	O
indirect	O
gap	O
semiconductor	O
can	O
recombine	O
only	O
with	O
production	O
of	O
a	O
phonon	B-Language
and	O
a	O
photon	B-Application
,	O
due	O
to	O
energy	O
and	O
momentum	B-Algorithm
conservation	O
laws	O
.	O
</s>
<s>
Hence	O
,	O
the	O
lasing	O
transition	O
with	O
production	O
of	O
only	O
one	O
particle	O
–	O
photon	B-Application
–	O
must	O
be	O
resonant	O
.	O
</s>
<s>
This	O
means	O
that	O
the	O
lasing	O
transition	O
must	O
be	O
allowed	O
by	O
momentum	B-Algorithm
and	O
energy	O
conservation	O
laws	O
to	O
generate	O
in	O
a	O
steady	O
form	O
.	O
</s>
<s>
Photons	B-Application
have	O
negligible	O
wave	O
vectors	O
and	O
therefore	O
the	O
band	O
extremes	O
have	O
to	O
be	O
in	O
the	O
same	O
position	O
of	O
the	O
Brillouin	O
zone	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
for	O
devices	O
such	O
as	O
SASERs	B-Algorithm
,	O
acoustic	O
phonons	B-Language
have	O
a	O
considerable	O
dispersion	O
.	O
</s>
<s>
K-space	O
refers	O
to	O
a	O
space	O
where	O
things	O
are	O
in	O
terms	O
of	O
momentum	B-Algorithm
and	O
frequency	O
instead	O
of	O
position	O
and	O
time	O
.	O
</s>
<s>
The	O
conversion	O
between	O
real	O
space	O
and	O
k-space	O
is	O
a	O
mathematical	O
transformation	O
called	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
and	O
thus	O
k-space	O
can	O
be	O
also	O
called	O
Fourier	O
space	O
.	O
</s>
<s>
We	O
note	O
that	O
,	O
the	O
difference	O
in	O
energy	O
of	O
the	O
photon	B-Application
lasing	O
levels	O
has	O
to	O
be	O
at	O
least	O
smaller	O
than	O
the	O
Debye	O
energy	O
in	O
the	O
semiconductor	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
in	O
narrow-gap	O
semiconductors	O
this	O
variation	O
of	O
energy	O
is	O
considerable	O
and	O
therefore	O
external	O
pressure	O
or	O
magnetic	O
field	O
may	O
serve	O
the	O
purpose	O
of	O
tuning	O
into	O
the	O
resonance	O
of	O
one-phonon	O
interband	O
transition	O
.	O
</s>
<s>
The	O
reasoning	O
behind	O
that	O
comes	O
from	O
the	O
fact	O
that	O
,	O
due	O
to	O
the	O
k-selection	O
rule	O
in	O
semiconductors	O
,	O
interband	O
transitions	O
with	O
the	O
production	O
of	O
only	O
one	O
phonon	B-Language
can	O
be	O
only	O
those	O
that	O
produce	O
an	O
optical	O
phonon	B-Language
.	O
</s>
<s>
However	O
,	O
optical	O
phonons	B-Language
have	O
a	O
short	O
lifetime	O
(	O
they	O
split	O
into	O
two	O
due	O
to	O
anharmonicity	O
)	O
and	O
therefore	O
they	O
add	O
some	O
important	O
complications	O
.	O
</s>
<s>
Here	O
we	O
can	O
note	O
that	O
even	O
in	O
the	O
case	O
of	O
multi-stage	O
process	O
of	O
acoustic	O
phonon	B-Language
creation	O
it	O
is	O
possible	O
to	O
create	O
SASER	B-Algorithm
.	O
</s>
<s>
For	O
the	O
same	O
scheme	O
,	O
the	O
usage	O
of	O
a	O
semiconductor	O
heterostructure	O
(	O
layers	O
of	O
different	O
semiconductors	O
)	O
with	O
narrow	O
gap	O
indirect	O
in	O
momentum	B-Algorithm
space	O
between	O
valence	O
and	O
conduction	O
bands	O
may	O
be	O
more	O
effective	O
.	O
</s>
<s>
An	O
essential	O
statement	O
here	O
is	O
that	O
this	O
proposed	O
phonon	B-Language
laser	O
can	O
operate	O
only	O
if	O
the	O
temperature	O
is	O
much	O
lower	O
than	O
the	O
energy	O
gap	O
in	O
the	O
semiconductor	O
.	O
</s>
<s>
Also	O
phonon	B-Language
dispersion	O
law	O
is	O
required	O
to	O
be	O
linear	O
and	O
isotropic	O
too	O
.	O
</s>
<s>
A	O
mathematical	O
analysis	O
,	O
leads	O
to	O
an	O
equation	O
for	O
the	O
average	O
number	O
of	O
electron	O
–	O
hole	O
pairs	O
per	O
one	O
phonon	B-Language
mode	O
per	O
unit	O
volume	O
.	O
</s>
<s>
For	O
a	O
low	O
loss	O
limit	O
,	O
this	O
equation	O
gives	O
us	O
a	O
pumping	O
rate	O
for	O
the	O
SASER	B-Algorithm
that	O
is	O
rather	O
moderate	O
in	O
comparison	O
with	O
usual	O
phonon	B-Language
lasers	O
on	O
a	O
p	O
–	O
n	O
transition	O
.	O
</s>
<s>
Also	O
,	O
indirect	O
exciton	O
has	O
an	O
electric	O
dipole	O
momentum	B-Algorithm
normal	O
to	O
coupled	O
quantum	O
well	O
and	O
thus	O
a	O
moving	O
indirect	O
exciton	O
has	O
an	O
in-plane	O
magnetic	O
momentum	B-Algorithm
perpendicular	O
to	O
its	O
velocity	O
.	O
</s>
<s>
Normal	O
electric	O
field	O
is	O
needed	O
for	O
tuning	O
the	O
transition	O
:	O
direct	O
exciton	O
-->	O
indirect	O
exciton	O
+	O
phonon	B-Language
into	O
resonance	O
and	O
its	O
magnitude	O
can	O
form	O
a	O
linear	O
function	O
with	O
the	O
magnitude	O
of	O
in-plane	O
magnetic	O
field	O
.	O
</s>
<s>
We	O
note	O
that	O
the	O
mathematical	O
analysis	O
of	O
this	O
scheme	O
considers	O
of	O
longitudinal	O
acoustic	O
(	O
LA	O
)	O
phonons	B-Language
instead	O
of	O
transverse	O
acoustic	O
(	O
TA	O
)	O
phonons	B-Language
.	O
</s>
<s>
Generally	O
,	O
the	O
preference	O
in	O
transverse	O
acoustic	O
(	O
TA	O
)	O
phonons	B-Language
is	O
better	O
because	O
TA	O
phonons	B-Language
have	O
lower	O
energy	O
and	O
the	O
greater	O
life-time	O
than	O
LA	O
phonons	B-Language
.	O
</s>
<s>
A	O
further	O
analysis	O
of	O
the	O
scheme	O
can	O
help	O
us	O
to	O
establish	O
differential	O
equations	O
for	O
direct	O
exciton	O
,	O
indirect	O
exciton	O
and	O
phonon	B-Language
modes	O
.	O
</s>
<s>
The	O
solution	O
of	O
these	O
equations	O
gives	O
that	O
separately	O
phonon	B-Language
and	O
indirect	O
exciton	O
modes	O
have	O
no	O
definite	O
phase	O
and	O
only	O
the	O
sum	O
of	O
their	O
phases	O
is	O
defined	O
.	O
</s>
<s>
The	O
aim	O
here	O
is	O
to	O
check	O
if	O
the	O
operation	O
of	O
this	O
scheme	O
with	O
a	O
rather	O
moderate	O
pumping	O
rate	O
can	O
hold	O
against	O
the	O
fact	O
that	O
excitons	O
in	O
coupled	O
quantum	O
wells	O
have	O
low	O
dimensionality	O
in	O
comparison	O
to	O
phonons	B-Language
.	O
</s>
<s>
Hence	O
,	O
phonons	B-Language
not	O
confined	O
in	O
the	O
coupled	O
quantum	O
well	O
are	O
considered	O
.	O
</s>
<s>
An	O
example	O
is	O
longitudinal	O
optical	O
(	O
LO	O
)	O
phonons	B-Language
that	O
are	O
in	O
AlGaAs/GaAs	O
heterostructure	O
and	O
thus	O
,	O
phonons	B-Language
presented	O
in	O
this	O
proposed	O
system	O
are	O
three-dimensional	O
.	O
</s>
<s>
Differences	O
in	O
dimensionalities	O
of	O
phonons	B-Language
and	O
excitons	O
cause	O
upper	O
level	O
to	O
transform	O
into	O
many	O
states	O
of	O
phonon	B-Language
field	O
.	O
</s>
<s>
There	O
is	O
no	O
additional	O
requirement	O
for	O
the	O
laser	O
pumping	O
despite	O
the	O
difference	O
in	O
phonon	B-Language
and	O
exciton	O
dimensionalities	O
.	O
</s>
<s>
Phonon	B-Language
laser	O
action	O
has	O
been	O
stated	O
in	O
a	O
wide	O
range	O
of	O
physical	O
systems	O
(	O
e.g.	O
</s>
<s>
Hybridized	O
orbitals	O
of	O
an	O
electrical	O
system	O
are	O
replaced	O
by	O
optical	O
supermodes	O
of	O
this	O
photonic	O
molecule	O
while	O
the	O
transitions	O
between	O
their	O
corresponding	O
energy	O
levels	O
are	O
induced	O
by	O
a	O
phonon	B-Language
field	O
.	O
</s>
<s>
The	O
medium	O
becomes	O
purely	O
optical	O
and	O
the	O
laser	O
field	O
is	O
provided	O
by	O
the	O
material	O
as	O
a	O
phonon	B-Language
mode	O
.	O
</s>
<s>
An	O
inversion	O
produces	O
gain	O
,	O
causing	O
phonon	B-Language
laser	O
action	O
above	O
a	O
pump	O
power	O
threshold	O
of	O
around	O
7	O
μW	O
.	O
</s>
<s>
Viewed	O
as	O
Brillouin	O
process	O
,	O
the	O
system	O
accesses	O
a	O
regime	O
in	O
which	O
the	O
phonon	B-Language
plays	O
the	O
role	O
of	O
Stokes	O
wave	O
.	O
</s>
<s>
For	O
this	O
reason	O
it	O
should	O
be	O
also	O
possible	O
to	O
controllably	O
switch	O
between	O
phonon	B-Language
and	O
phonon	B-Language
laser	O
regimes	O
.	O
</s>
<s>
These	O
controls	O
impact	O
both	O
phonon	B-Language
laser	O
action	O
and	O
cooling	O
and	O
define	O
some	O
finely	O
spaced	O
optical	O
levels	O
whose	O
transition	O
energies	O
are	O
proportional	O
to	O
phonon	B-Language
energies	O
.	O
</s>
<s>
The	O
approach	O
uses	O
intermodal	O
coupling	O
,	O
induced	O
by	O
radiation	O
pressure	O
and	O
can	O
also	O
provide	O
a	O
spectrally	O
selective	O
mean	O
to	O
detect	O
phonons	B-Language
.	O
</s>
<s>
In	O
a	O
two	O
level	O
system	O
,	O
the	O
particles	O
have	O
only	O
two	O
available	O
energy	O
levels	O
,	O
separated	O
by	O
some	O
energy	O
difference	O
:	O
ΔΕ	O
=	O
E2	O
−	O
E1	O
=	O
hv	O
,	O
where	O
ν	O
is	O
the	O
frequency	O
of	O
the	O
associated	O
electromagnetic	O
wave	O
of	O
the	O
photon	B-Application
emitted	O
and	O
h	O
is	O
the	O
Planck	O
constant	O
.	O
</s>
<s>
When	O
a	O
particle	O
in	O
the	O
upper	O
state	O
interacts	O
with	O
a	O
photon	B-Application
matching	O
the	O
energy	O
separation	O
of	O
the	O
levels	O
,	O
the	O
particle	O
may	O
decay	O
,	O
emitting	O
another	O
photon	B-Application
with	O
the	O
same	O
phase	O
and	O
frequency	O
as	O
the	O
incident	O
photon	B-Application
.	O
</s>
<s>
In	O
a	O
two-level	O
atom	B-Language
the	O
pump	O
is	O
,	O
in	O
a	O
way	O
,	O
the	O
laser	O
itself	O
.	O
</s>
<s>
The	O
amplification	O
of	O
coherent	O
terahertz	O
sound	O
in	O
a	O
Wannier	O
–	O
Stark	O
ladder	O
superlattice	B-General_Concept
has	O
been	O
achieved	O
in	O
2009	O
according	O
to	O
a	O
paper	O
publication	O
from	O
the	O
School	O
of	O
Physics	O
and	O
Astronomy	O
in	O
the	O
University	O
of	O
Nottingham	O
.	O
</s>
<s>
Wannier	O
–	O
Stark	O
effect	O
,	O
exists	O
in	O
superlattices	B-General_Concept
.	O
</s>
<s>
Electron	O
states	O
in	O
quantum	O
wells	O
respond	O
sensitively	O
to	O
moderate	O
electric	O
fields	O
either	O
by	O
the	O
quantum	O
confined	O
Stark	O
effect	O
in	O
the	O
case	O
of	O
wide	O
barriers	O
or	O
by	O
Wannier-Stark	O
localization	O
in	O
the	O
case	O
of	O
a	O
superlattice	B-General_Concept
.	O
</s>
<s>
Namely	O
,	O
in	O
a	O
mathematical	O
point	O
of	O
view	O
,	O
if	O
an	O
electric	O
field	O
is	O
applied	O
to	O
a	O
superlattice	B-General_Concept
the	O
relevant	O
Hamiltonian	O
exhibits	O
an	O
additional	O
scalar	O
potential	O
.	O
</s>
<s>
In	O
the	O
proposed	O
scheme	O
,	O
an	O
application	O
of	O
an	O
electrical	O
bias	O
to	O
a	O
semiconductor	O
superlattice	B-General_Concept
is	O
increasing	O
the	O
amplitude	O
of	O
coherent	O
folded	O
phonons	B-Language
generated	O
by	O
an	O
optical	O
pulse	O
.	O
</s>
<s>
This	O
increase	O
of	O
the	O
amplitude	O
is	O
observed	O
for	O
those	O
biases	O
in	O
which	O
the	O
energy	O
drop	O
per	O
period	O
of	O
the	O
superlattice	B-General_Concept
is	O
greater	O
than	O
the	O
phonon	B-Language
energy	O
.	O
</s>
<s>
If	O
the	O
superlattice	B-General_Concept
is	O
biased	O
such	O
that	O
the	O
energy	O
drop	O
per	O
period	O
of	O
the	O
superlattice	B-General_Concept
exceeds	O
the	O
width	O
of	O
electronic	O
minibands	O
(	O
Wannier	O
–	O
Stark	O
regime	O
)	O
,	O
the	O
electrons	O
become	O
localized	O
in	O
the	O
quantum	O
wells	O
and	O
vertical	O
electron	O
transport	O
takes	O
place	O
via	O
hopping	O
between	O
neighboring	O
quantum	O
wells	O
,	O
which	O
may	O
be	O
phonon	B-Language
assisted	O
.	O
</s>
<s>
As	O
it	O
had	O
been	O
shown	O
previously	O
,	O
under	O
these	O
conditions	O
stimulated	O
phonon	B-Language
emission	O
can	O
become	O
the	O
dominant	O
phonon-assisted	O
hoping	O
process	O
for	O
phonons	B-Language
of	O
an	O
energy	O
value	O
close	O
to	O
the	O
Stark	O
splitting	O
.	O
</s>
<s>
Thus	O
,	O
coherent	O
phonon	B-Language
amplification	O
is	O
theoretically	O
possible	O
in	O
this	O
type	O
of	O
system	O
.	O
</s>
<s>
Together	O
with	O
the	O
increase	O
in	O
amplitude	O
,	O
the	O
spectrum	O
of	O
the	O
bias-induced	O
oscillations	B-Algorithm
is	O
narrower	O
than	O
the	O
spectrum	O
of	O
the	O
coherent	O
phonons	B-Language
at	O
zero	O
bias	O
.	O
</s>
<s>
This	O
shows	O
that	O
coherent	O
amplification	O
of	O
phonons	B-Language
due	O
to	O
stimulated	O
emission	O
takes	O
place	O
in	O
the	O
structure	O
under	O
electrical	O
pumping	O
.	O
</s>
<s>
A	O
bias	O
voltage	O
is	O
applied	O
to	O
a	O
weakly	O
coupled	O
n-doped	O
GaAs/AlAs	O
superlattice	B-General_Concept
and	O
increases	O
the	O
amplitude	O
of	O
the	O
coherent	O
hypersound	O
oscillations	B-Algorithm
generated	O
by	O
a	O
femtosecond	O
optical	O
pulse	O
.	O
</s>
<s>
An	O
evidence	O
of	O
hypersound	O
amplification	O
by	O
stimulated	O
emission	O
of	O
phonons	B-Language
emerges	O
,	O
in	O
a	O
system	O
where	O
the	O
inversion	O
of	O
the	O
electron	O
populations	O
for	O
phonon-assisted	O
transitions	O
exists	O
.	O
</s>
<s>
This	O
evidence	O
is	O
provided	O
by	O
the	O
bias-induced	O
amplitude	O
increase	O
and	O
experimentally	O
observer	O
spectral	O
narrowing	O
of	O
the	O
superlattice	B-General_Concept
phonon	B-Language
mode	O
with	O
a	O
frequency	O
of	O
441GHz	O
.	O
</s>
<s>
The	O
THz	O
stimulated	O
phonon	B-Language
induced	O
transitions	O
between	O
the	O
electron	O
superlattice	B-General_Concept
states	O
lead	O
to	O
this	O
coherent	O
amplification	O
while	O
processing	O
a	O
population	O
inversion	O
.	O
</s>
