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1/6
CO2 Regenerative Ring Power Amplifiers
C. J. Buczek, R. J. Freiberg, and M. L. Skolnick
Citation: Journal of Applied Physics 42, 3133 (1971); doi:
10.1063/1.1660695
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7/23/2019 1.1660695
2/6
JOURNAL
OF
APPLIED
PHYSICS
VOLUME 42
NUMBER
8
JULY 1971
CO
2
Regenerative Ring Power Amplifiers
C,J, Buczek, R.J. Freiberg, and M.L. Skolnick
United
ircraft Research
Laboratories
East
Hartford Connecticut 06108
Received 29
July
1970; in final
form
14
December
1970)
An unidirectional
regenerative
ring CO
2
power amplifier is
described.
Both below
threshold
unconditionally
stable)
and
above
threshold
conditionally
stable) operation
are
discussed. Analytic expressions
for
a
homogeneously broadened medium
are
presented
for
the
power extracted
from
the active medium, the circulating power, and
the
total output
power
of
the ring amplifier. Experimental results
are
presented in support of the
theoretical analysis and demonstrate the role of gain
saturation
in the performance of CO
2
regenerative ring amplifiers.
I. INTRODUCTION
The frequency and modal stability necessary for ap
plications of CO
2
lasers can be achieved easily
in
relatively short
oscillators
at
power
levels of a few
watts.
1
However,
amplification
is needed to generate
the
higher
powers
required
for
many
present day
laser systems. Conventional power
amplifiers
with
the
necessary 10- to 30-dB gain tend to
be
bulky and
inefficient
at these
low-drive powers
as
a
result
of the
low-gain coefficients
and saturation flux inten
sities associated
with CO
2
laser gain media. 2 In
order
to bridge the gap in
size
and efficiency
be
tween
amplifiers
and
oscillators,
we
have
been
in
vestigating regenerative amplifier techniques. The
purpose of these positive feedback techniques is to
design high-gain CO
2
power amplifiers character
ized by the compactness and effiCiency associated
with
oscillators,
yet
possessing
phase
characteris
tics which will not degrade the
frequency
stability
of
master
oscillator
sources. Regenerative laser
amplification
is not a new problem
area.
Previous
investigators
have
studied
quantum
or
low-level
re
generative amplifiers where gain saturation is not
an
important
phenomenon.
3,4
We, however,
take
into
account
the
very essential role
of gain
satura
tion
which dominates the
performance
of
CO
2
re
generative power
amplifiers. 5
II. GENERAL REGENERATIVE AMPLIFIER
CONSlDERATIONS
In
Fig.
1 some of the general
properties
of
regener
ative amplifiers are considered. In Fig. 1 a) a
simple Fabry-Perot amplifier is
depicted. In
oper
ation
the
amplifier cavity is
tuned to resonance
at
the oscillator
frequency
by
adjusting
its
length.
The
main disadvantage of
the Fabry-
Perot regenerative
amplifier is that it puts an element
in line
with
the
oscillator that
can reflect
power
back
toward the
stable laser to cause deleterious
frequency changes
which would
compromise
the
frequency
stability of
the
system.
Hence, the
Fabry-Perot amplifier re
quires
the
use
of nonreciprocal isolation immedi
ately after
the
master
oscillator.
Unlike the
Fabry- Perot amplifier
above, the
trans
mission ring amplifier
shown in Fig. l b) does not
reflect
power in the
reverse
direction back toward
the
oscillator.
However, this is a two-port
device
3133
employing two
partially
reflecting mirrors.
In
order for
all
the power to be extracted as amplified
transmission from
port
two and no
power
lost
in
re
flection
at
port one the saturated gain of the me
dium G and the
mirror
reflectivities Rl and Ra must
be adjusted to
satisfy
the
relation G
=
Rl/Ra . In
practice
this is often inconvenient to achieve.
The reflective ring
amplifier
shown in Fig. 1 c) is
a Single-port
device
employing only one transmit
ting mirror, thereby permitting all the power to be
extracted from one mirror. Similar to
the
trans
mission
ring amplifier, no
power can
be
directed
back to
the
master oscillator from
the
amplifier to
cause deleterious
frequency changes. This inherent
isolation is a
consequence
of the ring geometry.
In
general, regenerative amplifier operation is con
Sidered in two regions; i) unconditionally stable and
ii) conditionally stable. f
the
product of small
signal
power
gain
Go
and output mirror power re
flection R are less than one
at
all wavelengths, the
ring
is
unconditionally
stable,
1.
e.,
it
does
not
08 -
a)
FABRYPEROT
AMPLIFIER
MASTER
O S I ~ L t T O R
ISOLATOR
I I
POWER
AMPLIFIER
0
PA
\
It Go, G
b) TRANSMISSION RING
AMPLIFIER
P,
el REFLECTIVE RING AMPliFIER
P,
UNCONDITIONAllY STABLE GoRl. GR
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3134
BU CZ E K , FREIBERG
AND
SKOLNICK
Po
POUT
=
o
+
LIP ={G-l P
1
FIG. 2.
Pertinent
power
definitions
for
a reflec
tive
regenerative ring
amplifier.
cillate
and power is
extracted
from the
amplifier
only i f
the
ring is driven by
the
master oscillator.
For
CoR>
1
the
ring can oscillate without drive.
However
under
conditions of
drive
and
proper
tun
ing the
amplifier saturated
gain C
decreases
such
that
CR
< 1.
For
this case power is
extracted
from
the
amplifier
at the deSired
frequency
when the am
plifier
is tuned and locked to the
master oscillator.
Such operation is considered conditionally stable
and
under
conditions of
low-drive
powers,
can be
d e s ~ r i e d
as
classical injection
locking.
6
It
has been
demonstrated
7
that
unidirectional operation
can
be
achieved
above
threshold
by means of a
small direc
tional
anisotropy which is provided by the
master
oscillator
output mirror. The ring
amplifier
con
sequently
does not normally require an additional
nonreciprocal element between
the
source
oscillator
and the
amplifier.
Hence
the inherent isolation
of
the
ring amplifier is preserved in
the conditionally
stable
mode
as
well as
in
the unconditionally
stable
mode of operation. We have achieved satis
factory CO
2
amplifier performance in both modes
of operation by a suitable choice of operating
pa
rameters
such
as
mirror
reflectivity, oscillator
drive
power and gain of
the amplifier
medium.
III. THEORY
Consider a reflective regenerative ring with power
gain C and mirror reflectivity R. Figure 2 illus
trates schematically
the
various
power
quantities
which will be
referred to
throughout
this paper. Po
is
the
drive
power
from the master oscillator.
Pl
is
the
circulating
power inside the
ring amplifier.
t:.P is the power
extracted
from the active medium
of the amplifier. Pout is the total output power from
the
partially
reflecting mirror.
The
boundary
value
problem is
solved
at
the
par
tially reflecting mirror for
unconditionally
stable
operation, Expressions
for Pout, P
b
and t:.p can be
obtained in terms of o and the cavity tuning angle
e where e is related
to the
ring amplifier perime
t ~ r p by e=21fp/ ll.
The
ratio
of the output power
Pout
to the
oscillator
drive
power o can be
written
pout_\r-geiO \
o
- 1 - rge
e
where r
z
and g= C
Z
1)
I f
the small-signal
gain
exceeds the
mirror
reflec-
tion
losses,
this system
can oscillate when tuned to
a
molecular transition
and
saturation
will
decrease
the gain to the value
rg =
1.
I f
we
consider
the
case
rg
