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Saturation spectroscopy for optically thick atomic samples
Svanberg, Sune; Yan, G.Y.; Duffey, T.P.; Du, W. M.; Hänsch, T. W.; Schawlow, A. L.
Published in:
Journal of the Optical Society of America B: Optical Physics
DOI:
10.1364/JOSAB.4.000462
1987
Link to publication
Citation for published version (APA):
Svanberg, S., Yan, G. Y., Duffey, T. P., Du, W. M., Hänsch, T. W., & Schawlow, A. L. (1987). Saturation
spectroscopy for optically thick atomic samples.
Journal of the Optical Society of America B: Optical Physics
,
4
(4), 462-469. https://doi.org/10.1364/JOSAB.4.000462
Total number of authors:
6
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462 J. Opt. Soc. Am. B/Vol. 4, No. 4/April 1987
Saturation spectroscopy for optically thick atomic samples
S. Svanberg, G.-Y. Yan, T. P. Duffey, W.-M. Du,* T. W. Hansch, and A. L. Schawlow
Department of Physics, Stanford University, Stanford, California 94305
Received Oct 13, 1986; accepted November 25, 1986
Doppler-free saturation spectroscopy in the regime of strong pumping intensities and optically thick atomic
samples is investigated experimentally and theoretically. It is shown that a very high signal-to-background ratio
can be obtained and,
at the same time, subnatural linewidths can be reached. Further contrast and linewidth
improvements can be attained by supplementing the primary depleted pumping beam with a second pumping
beam. By using the signal beam from a first setup as the pumping beam for a second identical arrangement,
extreme values for contrast and linewidth should be attainable.
INTRODUCTION
We have recently' demonstrated how Doppler-free satura-
tion spectroscopy in the regime of strong pumping intensity
and high integrated sample absorption yields strong, narrow
signals on an essentially zero background. In this paper we
present a theoretical description of the phenomena as well as
further experimental data on the technique, which we have
denoted high-contrast transmission spectroscopy. We also
describe how further improvements in signal-to-background
ratio (contrast) and linewidth reduction can be obtained by
injecting an additional pumping beam or by running two
identical setups in series.
The saturation spectroscopy technique employing dye la-
sers was introduced by Hdnsch et al.
2
In order to avoid
power broadening of the Doppler-free signals, normally
modest pump-beam intensities are used. At the line center
only a small fractional change in the transmitted probe-
beam intensity is then obtained for samples typically ab-
sorbing half the probe-beam light. The situation is very
different in the high-intensity, high-absorption regime, in
which the probe-beam transmission can increase from essen-
tially zero to several tens of percent of its unattenuated
value. Because of the exponential nature of the Beer-Lam-
bert law of absorption, the wings of the Doppler-free signal
are more strongly absorbed than the central part. This
effect can be made to dominate over the power broadening,
and linewidths below the natural radiation width limit can
be obtained for isolated signal components.
Two different experimental arrangements for high-con-
trast transmission spectroscopy are shown in Fig. 1. In Fig.
1(a) a conventional setup for saturation spectroscopy is
shown. In the high-contrast version it is important for the
weak probe beam to overlap with the strong pump beam over
the entire length of the absorption cell. Therefore the probe
beam is detected through a semitransparent folding mirror.
In Fig. 1(b) a simplified version of the setup is shown. The
primary beam is sent through a beam splitter and forms a
strong pumping beam traversing the cell. It is strongly
absorbed despite considerable sample bleaching, and the
retroreflected beam forms a weaker probe beam that is re-
flected off the beam splitter. The intensity falloff for the
pump beam traversing the cell is indicated as well as the
gradual change in the absorption coefficient.
As first illustrations, signals obtained for the sodium D, (3
2S,/2-3
2
P1/
2
) and D
2
(3 2S1/2-3
2
P3/
2
) lines in experiments
employing the setup in Fig. 1(a) are shown in Figs. 2(a) and
2(b), respectively. Experimental details will be presented
later. For the samples that are normally almost opaque to
the weak probe beam (linear absorption) in the central parts
of the Doppler-broadened profile, sharp Doppler-free trans-
mission peaks corresponding to hyperfine structure (hfs)
transitions are observed. The relevant hfs of the two D
lines is also given in the figure. For the D, line the excited-
state hfs splitting of 189 MHz is clearly resolved, and the
crossover resonances
3
are also obtained. The upper-state
hfs is too small to be resolved at the power level used for the
D
2
line recording. The favorable signal-to-background ratio
obtained resembles that obtainable in polarization spectros-
copy
4
but is achieved without the use of polarizers. As in
fluorescence monitoring, a strong signal is observed when
the resonance condition is fulfilled, but otherwise no light is
observed.
After this brief introduction of the basic high-contrast
transmission spectroscopy scheme we will present a simple
theoretical modeling of the experiment in the next section
and also make some qualitative comparisons between ex-
periment and theory; then a repumping scheme for further
contrast enhancement is analyzed theoretically and demon-
strated experimentally. In a further section before the final
discussion, a tandem scheme involving two coupled experi-
mental arrangements is analyzed, illustrating possibilities
for extreme contrast improvement and linewidth reduction.
BASIC SINGLE-CELL VERSION
Theoretical Modeling
We will present here a simple hole-burning description of
the saturation spectroscopy experiment in the regime of
high integrated optical absorption. Effects caused by dy-
namic Stark interaction, self-focusing, etc. are neglected.
We consider a pump (saturating) beam of initial intensity
I(O) impinging upon a Doppler-broadened atomic sample of
length L. The sample, with a particular number density of
atoms of absorption oscillator strength f, exhibits a linear
absorption coefficient ao for weak monochromatic light.
The transition will be saturated for higher intensities, lead-
0740-3224/87/040462-08$02.00 © 1987 Optical Society of America
Svanberg et
al.
Vol. 4, No. 4/April 1987/J. Opt. Soc. Am. B
463
ing to bleaching of the sample; i.e., the absorption coefficient
will be reduced:
a = ao!T1 + 'llsat,
where Isat is the saturation intensity.
5
For a strongly absorbing sample the remaining normalized
intensity I(X)/Isat at a penetration depth x into the cell is
obtained by integration:
ABSORPTION CELL
nflTreTnP
(b)
+
L
0 x L
\ A.??,+. S?, DVO ~~~~. :S,? ..>: ..':.:>:..>.-> . :
RETROREFLECTOR
BEAM SPLITTER
Fig. 1. Experimental arrangements for high-contrast transmission
spectroscopy. (a) Arrangement with separate probe beam of con-
stant power. (b) Simplified arrangement in which the attenuated
pump beam is used as the probe beam.
F
F
3
2
0 2
z
U)
U)
Z ~~1772 MHz
A | < l.'\ --a ' (a)
I 0 1 2
FREQUENCY (GHZ)
Fig. 2. Recordings for the sodium D lines and relevant transition
hyperfine-structure diagrams. (a) D
1
line recording, using a 10-cm
cell at 155
0
C. The probe-beam intensity is 8% of the pump beam
intensity. (b) D
2
line recording, using a 30-cm cell at 141'C. The
probe beam intensity is 0.5% of the pump beam intensity.
I(x)/Ist= I(0)/Isat expL-f Ja(x')dx'] -
(2)
Here a(x') continuously increases through the sample ac-
cording to Eq. (1) as I(x)/Isat is reduced.
The inhomogen-
eously broadened hole in the velocity distribution of the
atoms in a slice Ax of the
sample will be described by a
Lorentzian with a linewidth Av that is larger than the natu-
ral width ALN =
1
/
2
7r ( is the lifetime of the excited state)
because of the power broadening
5
:
Av = /
2
AVN(1 + 1 + '/'sat)
(3)
At the position x along the pump beam the effective frequen-
cy-dependent absorption coefficient for a weak, counter-
propagating beam will be
a
5
(x) = ao- ao
0
- a(x)
Av+ 2
(4)
where a(x) is calculated from Eq. (1) using the I/Isat value
obtained from Eq. (2). The resulting probe-beam transmis-
sion T, through the sample is obtained by integration of Eq.
(4) over the cell length L:
L o-a(X) 1
T, = exp -a0L +\dx
1
- ~Av /2)
(5)
The contrast C is the ratio of the Doppler-free signal peak
transmission (background free) to the background transmis-
sion [far from resonance, Toff-res = exp(-aoL)]:
C = exp[J -a(x)dx + aoL - 1.
(6)
We have calculated the transmission T
5
, the contrast C,
and the resulting linewidth, numerically integrating Eqs.
(2), (5), and (6) by dividing the cell length into 50 equal
intervals. The calculations were performed on an IBM PC
XT, using a FORTRAN program. The results are shown in
Fig. 3 as a function of integrated linear absorption coeffi-
cient aoL for three values of I(O)/Isat: 10, 30, and 100. It is
clearly shown how the probe beam can penetrate the sample
increasingly effectively by using the path bleached by a
pump beam of increasing intensity through the otherwise
optically thick sample. The contrast increases with increas-
ing pump power, increases with optical density, and finally
levels off. For the case of strong initial saturation and very
dense samples, an approximate analytical expression for this
maximum contrast can easily be derived:
Ciim
4 exp(2 1 + I/Isat - 2)
(1 + 1 + IIsat)
(7)
(a)
(1)
Svanberg et al.
464
J.
Opt. Soc.
Am.
B/Vol.
4, No.
4/April
1987
106
10
5
U)
cr:
z
0
0
10
4
102
l0o
z
0
U)
cl:
H
'0-I
10-2
1o-3
z
I
0 I I I 1 1' 1 1'
0 3
6 9
12 15
18 21
(2 L .
Fig. 3. Theoretical
values for the contrast C, the probe-beam peak
transmission To, and the Doppler-free
signal half-width (solid lines)
as functions
of the integrated absorption lengths for different values
of I/Isat
The dashed lines show the theoretical linewidth for
the
tandem cell case.
According
to this equation the attainable contrast increases
from about 20 to
about 2 X 106 when I/Isat varies from 10 to
100, which is in
accordance with the computer results in Fig.
3. Since the contrast is high
in the regime studied, the probe
peak transmission value
To is almost the same as the trans-
mission of the Doppler-free signal
(without background).
In the lower part of the diagram the signal
half-width, ex-
pressed in terms of the natural linewidth AN,
is plotted
(solid lines). For a sample of low optical density
a substan-
tial power
broadening is obtained. However, for more dense
samples the wing absorption
narrows down the linewidth
and brings it down below the natural
one. The details of the
line-shape alteration are shown in Fig. 4 for
different a
0
L
values in the case of I/Isat
= 30. Here the Doppler-free
signal amplitude has been normalized
to 1. A Lorentzian
corresponding to the natural line shape is indicated
with a
dashed line. The narrowing effect,
related to the preferen-
tial wing absorption at increasing
optical densities, can be
clearly
seen. It is interesting to note that, e.g., for I/Isat
= 30
the natural linewidth
can be obtained
with T as
high as 12%
and
C = 100.
Experiments
Most of
our experiments
were
performed
on the sodium
D
1
line
(3
2
S
1
/
2
-
3
2
P
1
/
2
, X =
5896 A), using
both experimental
arrangements
shown
in Fig. 1. A
Coherent Radiation
Model
599-21 single-mode
dye
laser, pumped
by an
argon-ion
laser,
was
used. This
laser has a stabilized
linewidth
of about ,1
MHz. An air
track wavemeter
was used to
facilitate setting
of the correct laser
wavelength.
Sodium cells of diameter
15
mm
and of lengths
up to 30
cm were
used. Cells
were placed
in a piece of straight copper
tubing wrapped with heating
tape,
and the temperature
was
measured
with a thermocou-
ple that was
placed in contact with the
cell. It is advanta-
geous to
use long cells
in the present
technique,
since a high
integrated absorption
can then
be obtained without
operat-
ing at
such a high vapor pressure that collisional broadening
of the
lines causes
a serious problem.
A simple
silicon
detec-
tor without
any bias voltage was
used to detect the
transmit-
ted beam. Frequently, strong attenuation
filters had to be
inserted in front
of the detector in
order to ensure operation
in the linear regime. Laser beam diameters were
typically 1
to 2 mm and were
not determined accurately.
The signals
were
recorded directly on an X-Y recorder synchronized
with
the slow
laser wavelength
sweep,
In Fig. 2, first
examples of high-contrast
recordings with
the standard setup [Fig. 1(a)] are
shown. Results from a
detailed experimental
investigation
of the Fgr =
1 - Fexc = 2
line component
[the highest-frequency component in
Fig.
2(a)]
are shown in Fig. 5. The primary pump power was
0.9
mW, and the
probe-beam power was 0.004 mW.
The signal
intensity
(probe-beam transmission), contrast,
and
linewidth are plotted. The data were
obtained with a cell 30
1.0
z
0
Un
Un
U)
z
a:
Li
I-
I_
-J
Lii
a:
0.5
0
0
2
Au//Az/N
Fig. 4. Theoretical
curves for the probe-beam
transmission T for
different absorption lengths a
0
L. All curves are normalized
to 1 at
the
line center. The dashed line corresponds
to a Lorentzian with
the natural linewidth.
Svanberg et
al.
Vol.
4,
No.
4/April
1987/J.
Opt.
Soc.
Am.
B
465
0
2
4
INTEGR.
NO.
DENSITY
I
I
I
6
(X
10
12
/cm
2
)
40
-10.5
30
_
N
N
C
0.1
_
-I
I
20
-
90.05
C]
I
LdI
I
Z I
lo0
I
I
90.01
0
-j
0.005
120
130
140
150
155
CELL
TEMPERATURE
(C)
Fig.
5. Experimental
results
for the
Fgr
- Fex
= 2
component.
Data
were
obtained
with
a 30-cm
cell,
using
the
arrangement
given
in
Fig.
1(a)
with
0.9 mW
for
the
pump
beam
and
0.004
mW
for
the
probe
beam.
A, Linewidth;
, transmission.
1o
2
-
IO U
l0o-
0
2
4
0
6
INTEGR.
NO.
DENSITY
(x
1012
/cm
2
)
I I I'
I I
120
130
140
150
155
CELL
TEMPERATURE
(C)
Fig. 6.
Experimental
results
for
the
crossover
signal
connecting
the
Fgr
= 1
level
to the
Fex
=
2 and
Fex
=
1 levels.
Data
were
obtained
with
a
30-cm
cell
in
the arrangement
shown
in Fig.
1(b).
The
primary
pump-beam
power
was
0.9
mW.
Note
the
subnatural
linewidth
obtained.
cm
long.
As the
signal
goes
to
zero
for
very
dense
samples,
a
constant
background
level
remains.
This
background
is
due
to
scattering
of
the
pump
light
in
the
beam
splitter
in
front
of
the
detector
and
to
fluorescence
from
the
cell.
Clearly,
this
background,
which
is incoherent,
could
be
eliminated
by
spatial
filtering
or by
moving
the
detector
farther
away.
In
calculating
the
contrast
we
have
first
subtracted
the
artifi-
cial
background
produced
by
the
scattering.
It can
be seen
that
the
contrast
increases
and
the
linewidth
decreases
for
denser
samples,
as predicted
by
the
curves
in Fig.
3.
The
sodium
atom
is
clearly
not
a two-level
system.
The
saturation
is
brought
about
by hyperfine
pumping
that
de-
pletes
a particular
lower
level
by
pumping
the
atoms
over
into
the
other
ground-state
sublevel.
5
It is
hard
to
estimate
the
effective
value
of I/Isat
for
the
transition
studied.
The
data
in
Fig.
5
correspond
roughly
to
the
case
I/Isat
=
15
for
a
0
L values
increasing
up
to
8. Detailed
comparisons
are
not
meaningful,
since
the
experimental
beams
are
Gaussian,
whereas
the
theory
was
developed
for
"top-hat"
beam
pro-
files.
The
theory
predicts
linewidths
below
the
natural
one
(AvN
=
/27rr
=
9.7
MHz
6
for
our
case),
but
this
was
not
observed
in this
experiment,
probably
because
of
collision
effects
in the
cell.
In
our
previous
work,'
detailed
data
were
presented
that
had
been
obtained
with
the
simplified
arrangement
shown
in
Fig.
1(b).
Here
we
show
instead
corresponding
data
for
the
crossover
signal
connecting
the
Fexc
=
2 and
Fexc
= 1
sublev-
els
with
the
common
Fgr
= 1 level.
Data
for a
cell
30 cm
long
are
shown
in Fig.
6.
In
this
case
extremely
high
contrasts
(corrected
for
the
constant-background
level
corresponding
to about
0.003%
transmission)
are
obtained,
and
linewidths
well
below
the
natural
one
are
observed.
The
presented
data
match
a
I/Ihat
value
of
about
35
and
a aL
product
increasing
up
to about
8.
Since
the
probe
beam
in the
case
of the
experimental
arrangement
of Fig.
1(b)
is
obtained
from
the
pump
beam
after
its
passage
through
the
cell,
its
primary
intensity
is
not
constant,
as for
the
setup
shown
in
Fig.
1(a).
This
means
that
the
Doppler-free
signal
trans-
mission
in
terms
of
the
transmission
(100%)
measured
when
the
laser
is tuned
completely
off
the
line
is lower
than
if
the
arrangement
in
Fig.
1(a)
had
been
used.
Since
the
transmis-
sion
curves
of
Fig.
3 are
given
for
the
standard
arrangement,
we
do
not
include
the
transmission
data
in Fig.
6. Note
that
the
calculated
values
for
the
contrast
and
linewidth
pertain
to
both
experimental
arrangements.
CASE
OF
SAMPLE
REPUMPING
In
saturation
spectroscopy
experiments
in the
regime
of
high
integrated
absorption
discussed
above,
the
intensity
of the
pump
beam
is
strongly
reduced
when
passing
the
sample.
Thus
it
saturates
much
less
efficiently
in the
back
part
of the
cell
than
in
its
front
part.
(The
intensity
curve
included
in
Fig.
1 is
calculated
for
the
case
I/Iat
=
30
and
aoL
=
9.)
Thus
the
contrast
obtained
is mainly
due
to
differences
in
transmission
on
and
off
resonance
in
the
front
path
of
the
cell,
whereas
the
back
part
is
less
active.
This
situation
can
be
changed
by focusing
the
pumping
beam
through
the
cell.
However,
the
effect
of
keeping
the
pumping
intensity
high
through
the
cell
can
more
readily
be demonstrated
by
inject-
ing
a
second
pump
beam
of
the
same
intensity
as
the original
A
/
A
\A
*
A
_*'
AZ/N
-------
=
/
A
A l l
**
LŽ V[1
-A
.
.
.
.
.
.
.
Svanberg
et
al.
l
I
I