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Pseudo-§tark Effect and FM/§tark Double Modulation Spectroscopy for the Detection of
Statistical Fine Structure in Alexandrite
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T.P. Carter, D.E. Horne, and W.E. Moerner "
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1988 June 20 / 21
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Submitted for publication in Chemical Physics Letters
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18. SUBJECv|/ERMS ( Continue on reverse :f necessary and identify by block number)
Statistical Fine Structure > Modulation Spectroscopy^
Alexandrite > FM Spectroscopy—
Stark Effect ; \
19. ABSTRACT (Continue on reverse it necessary and identify by block number) ^
Using laser-FM spectroscopy and transient spectral bole,-burning, the R transition of Cr r
_ _ lm
ions in alexandrite is shown to exhibit a linear pseudo-Stark effect with coefficients of
0.141 MHz-cm^V * and 0.0538 MHz-cm/v"”^ at 1.6 K for 'electric fields along the crystal
a and c axes, respectively. .This result was used to develop a sensitive FM/Stark double
modulation method for the detection of statistical fine structure (SFS) on the inhomo-
geneously broadened R line. While the final signal-to-noise ratio is not much greater
than unity, autocorrelation of the measured spectra provides the first strong evidence
for the presence of SFS in an inorganic material. a r
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Technical Report No. 16
Pseudo-Stark Effect and FM/Stark Double Modulation Spectroscopy
for the Detection of Statistical Fine Structure in Alexandrite
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88 6 28 108
PSEUDO-STARK EFFECT AND FM/STARK DOUBLE
MODULATION SPECTROSCOPY FOR THE DETECTION
OF STATISTICAL FINE STRUCTURE IN ALEXANDRITE
*
T. P. Carter , I). E. Horne, and W. E. Moerner
IBM Research Division
Almadcn Research Center
San Jose, California 95120
ABSTRACT: Using laser-FM spectroscopy and transient spectral hole-burning, the R,m
transition of Cru ions in alexandrite is shown to exhibit a linear pseudo-Stark effect with
coefficients of 0.141 MUz-cm-V 1 and 0.0538 MHz-cm-V ' at 1.6 K for electric fields along
the crystal a and c axes, respectively. This result was used to develop a sensitive FM/Stark
double modulation method for the detection of statistical fine structure (SFS) on the
inhomogeneously broadened Rlm line. While the final signal-to-noise ratio is not much
greater than unity, autocorrelation of the measured spectra provides the first strong evidence
for the presence of SFS in an inorganic material.
•
IBM Visiting Scientist, present address: Chemistry Department, Florida State University,
Tallahassee, FL 32306
I. Introduction
Recently, we reported the first observation of statistical fine structure (SFS) on an
inhomogeneously broadened absorption profile ’ using the S, <— Sn zero-phonon transition
of pentacenc in /Mcrphenyl mixed crystals and the technique of laser frequency-modulation
(FM) spectroscopy. ? SFS is time-independent structure on the inhomogeneous line caused
by fundamental statistical variations (number fluctuations) in the spectral density of absorbers
in each frequency interval. Observation of SFS in the spectra of pentaccne in p-tcrphenyl
“10 2
was facilitated by the large low temperature absorption cross-section (~ 10 cm ) and the
2
very small persistent hole-burning quantum yield. In many ways this system is ideal for the
task of observing SFS, and many other organic mixed crystal systems where the guest has
high oscillator strength and hole-burning is weak will have similarly favorable properties.
However, in order to illustrate the generality of the SFS phenomenon, we report in this paper
the results of our measurements on a transition metal ion (with low oscillator strength) in
an inorganic host crystal.
The system chosen for this study is the lowest energy electronic absorption of Cru ions
in alexandrite (chrysoberyl) crystals. As we will show, this system has very different
properties than pentacenc in /?-terphenyl, and presents challenging experimental problems in
the observation of SFS. The principal problems are that the small oscillator strength in
alexandrite (^ IQ5 compared to « 0.1 for pentacenc) leads to small absolute absorption
changes due to SFS, and that the alexandrite excited state is easily saturated due to the
relatively long excited state lifetime. We chose to detect SFS using a combination of FM
spectroscopy and Stark modulation, and since the pseudo-Stark effect for the electronic
transitions in alexandrite has not been previously reported, it was necessary to perform some
preliminary studies on the electric field behavior of the spectra. We report here our
measurements of the pseudo-Stark effect on transient holes in the spectra of alexandrite and
its use as a method of performing double-modulation spectroscopy for the detection of SFS.
H. Experimental
4
The alexandrite (BeAl204:Cr3+) crystal structure is orthorhombic Puma with four
molecules per unit cell. There are two crystallographically inequivalent sites occupied by
Al3+ ions in the lattice: one site having inversion (Q) symmetry and the other having mirror
(Cs) symmetry, with the mirror along the crystal ac plane. The Cr34 ions substitute for Al34
ions with about 78% going into the mirror site. 5' 6 The alexandrite crystal used in all
experiments was a highly polished nearly cubic single crystal about 5 mm on a side, with
faces cut parallel to the crystallographic axes. The Cr34 doping level was % 0.03 atom %
Cr/Al.
The Cr34 transition studied in this work was the lower energy component of the
2Fg *-4A2g transition for the mirror site ions, which is split by the distortion to C symmetry
7 8
and is labeled the RIm line. ’ At 1.6 K this zero-phonon line is centered at ss 679.62 nm
(vacuum wavelength measured by a Burleigh WA-10 wavemeter) with a full-width at
half-maximum (FWIIM) of « 2.2 cm' and is strongly 6-axis polarized with a peak optical
density greater than 4 at this Cr3t concentration. In all experiments, the laser polarization
was maintained along the 6-axis and the laser wavelength was located on the long-wavelength
edge of the line.
Laser FM spectroscopy was implemented in the manner described fully in Reference 2.
Figure 1 shows a simplified apparatus diagram: the output of a single-frequency cw dye laser
DL (Coherent 599-21, DCM dye) was sent through an electro-optic phase modulator HO
(Lascrmetrics 1097, LiTaO, ) driven by an rf oscillator and amplifier at 148 MHz, using up
to 16 V rms into 50 £2. This resulted in modulation indices between 0.3 and 1. The laser
beam was first expanded and then focused by a 350 mm focal length lens to give a «
65^m diameter spot throughout the entire 5 mm length of the sample. The sample was held
between polished stainless steel electrodes in a liquid helium immersion cryostat, (7 The
transmitted beam intensity was measured by a Si avalanche photodiode-preamplifier
combination whose output was sent to a double-balanced mixer M referenced to the rf
oscillator. The mixer output near dc was then either applied to the input of a lock-in
amplifier (Princeton Applied Research HR-8) whose output was digitized and averaged by a
digital scope DS (Data Precision 6100 with a 610 plug-in) for double-modulation detection,
or sent to DS directly for ordinary laser- FM detection. In the double-modulation
experiments, a modulated Stark field perpendicular to the propagation direction of the laser
beam was applied to the sample using a unipolar square wave of up to 400 V at 10 kHz.
This was accomplished using a high voltage power supply and an optically coupled high
voltage switcher, II V. A signal synchronous to the high voltage modulation was used as a
reference for lock-in detection. In this way, only those components of the Iascr-FM signal
which were modulated at 10 kHz were detected. Not shown in the diagram are provisions
for switching the FM sidebands and Stark modulation on and off as necessary in synchrony
with the 0.25 s laser scan.
Transient holes were burned and probed by controlling the dye laser scan externally in
the following manner. The laser was held at a fixed frequency a few hundred MIIz from one
end of the scan range for about 200 ms with the FM sidebands and Stark modulation
switched off. This process burned a single hole in the spectrum, uncomplicated by
pseudo-Stark splittings or holes burned by the FM sidebands. The laser was then rapidly
scanned to the near end of its range, the FM and Stark modulations were turned on, and
then the laser was scanned continuously to the opposite end of its range in 250 ms while
digitizing the signal. After this, the laser was scanned rapidly back to the hole frequency,
and a new hole was burned. This sequence was carried out repetitively and successive scans
were averaged by DS. The total scan range was typically 2.5 GHz. No evidence for
persistent hole-burning was observed under any conditions.
For the measurement of SFS spectra (as opposed to the measurement of transient holes),
the laser was scanned forward and backward smoothly and continuously across its range with
the Stark and FM modulations on all the time. This was done to reduce interfering signals
from the turn-on of the FM sidebands and to prevent the formation of transient holes within
the scan range. Even so, weak transient holes arc produced when the laser frequency is
stationary for a brief time at the limits of the scan. To prevent these holes from distorting
the SFS spectra, only the central half of the scan range was digitized and analyzed. The total
scan range in these experiments was typically 1.0 GHz.
III. Results and Discussion
A. Pseudo-Stark effect
9
The ground state pseudo-Stark effect for Cr3+ ions in the mirror site of alexandrite has
been reported previously in ESR spectra at room temperature. '° We demonstrate here that
the Rlm line exhibits a linear pseudo-Stark effect when an electric field is applied along the
crystal a or c axes. This is a pseudo-Stark effect, because there arc two inequivalcnt mirror
sites in an electric field, one of which shifts in one direction with applied field and the other
in the opposite direction. As has been shown before for other zero-phonon transitions, the
Stark effect can be precisely measured at high resolution using hole-burning techniques. ’
Figure 2 shows the results of a Stark experiment with several values for the applied (dc)
Stark field E„ with spectra measured by standard FM spectroscopy (the signal from only
one FM sideband is shown, and the dc Stark field was turned on only during hole scanning).
These spectra were obtained with E, || c ; similar results were obtained for Es || a. Each
spectrum is the average of 64 scans. Trace 2a shows the transient spectral hole with E, = 0
burned at 679.679 nm (= 0 GHz) at 1.6 K with about 6.5 n W on the sample. Traces 2b-2f
were similarly obtained using applied voltages of 50 V, 100 V, 200 V, 300 V, and 400 V,
respectively. As the figure shows, the hole splits symmetrically into two components, each
with approximately the same width as the unshifted line. We have plotted these shifts as a
function of the applied field to determine the pseudo-Stark coefficients for I7., applied along
each of the three axes, as shown in Figure 3. Circles, squares and triangles correspond to
applying E, along the a, b and c axes, respectively. No efTcct was seen for the case of E< ||
b, as expected for the A” — ► A' transition of a 3d ion at a site of C, symmetry. The straight
lines were obtained from least-squares fits to the points, clearly demonstrating a linear
dependence on field. The resulting pseudo-Stark, coefficients for the shift of a single
component are 0.141 Mllz-cm-V 1 and 0.0538 Mllz-cm-V 1 for Es along the a and c axes,
respectively. These coefficients are similar to those for ruby", as expected.
B. EM detection and transient hole behavior
Figure 4a shows a typical trace for lascr-FM only detection of a transient hole burned
at 1.6 K into the Rlm line at 679.684 nm (s 0 MHz) using « 7.5 /AV laser power. For this
experiment, the Stark field was left off. The features at ± 148 MHz are the FM signals of
2
the transient hole using cosine (F, ) detection, and the spacing between these replicas of
the hole allows calibration of of the frequency scale to 1 part in 106. The large transient
at the left edge of the trace is due to a shift of the mixer dc output level caused by dc residual
amplitude modulation'3 (dc-RAM) due to the FM sidebands being turned on at this point
in time. The other, smaller features (which are most obvious between the two signals from
the transient hole) are due to frequency-dependent RAM. This hole was power broadened
considerably due to the conditions chosen for this experiment, and exhibits a width of 14.8
MHz (vide infra). Since the hole is transient and therefore constantly decaying, the two
replicas have different intensities; only a; 60% of the hole intensity seen by the leading
sideband is left at the time when the trailing sideband scans the hole. The time difference
between when the passage of the two sidebands through the hole is 32.7 ms which, together
with the observed hole decay and assuming a single-exponential decay process, implies a
lifetime of « 35 ms. This value is much greater than the 2.3 ms low-temperature lifetime
1 8
of the 2E? state as measured by fluorescence decay. ' However, since the ground state is
degenerate with a splitting 14 of 0.54 cm ', it is reasonable to expect that there might be
ground state cross-relaxation processes occurring which increase the hole recovery time, as
has been observed for transient holes burned in the R line of rubv. 15 No significant
1
difference in width was observed for the two FM components cf a transient hole, implying
there are no important spectral diffusion processes occurring on a time scale faster than
several tens of milliseconds.
Although it is not the principal goal of this paper to provide a careful measurement of
the homogeneous width for the Rlm transition, at lower laser intensities we did observe
shallow transient holes whose widths were v 4.6 MHz, implying an upper limit to the
zero-field homogeneous linewidth of onc-half of this value, or 2.3 MHz. Since this width is
comparable to the laser jitter linewidth for a 250 ms period, we assume that the actual
homogeneous width is smaller. The only other report of the homogeneous width at zero field
for Cr3+ in alexandrite'6 is 44 MHz, as determined by fluorescence line-narrowing techniques.
The difference in the two measurements may be due to the fact that the crystal used in our
measurements is more dilute (0.03 atom % versus 0.05 atom %).
C. FM/Stark double modulation spectroscopy
The purpose of laser- FM/Stark double modulation spectroscopy is to achieve true
zero-background conditions in order to detect the very weak spectral features due to SFS.
Without double modulation, the sensitivity threshold of FM spectroscopy can be limited to
_4 j 7
features greater than 10 in absorbance change due to RAM effects in the modulator.
The approach here is to modulate the spectral features at some low frequency vs far from
the FM modulating frequency, and detect the v, component of the mixer output using lock-in
detection. In this way, none of the RAM background is detected, allowing an increase in the
gain of DS without overload from spurious background signals.
Trace 4b shows a simulation of double modulation detection of a hole similar to the one
shown in Trace 4a, using a Stark shift appropriate for an applied field of 50 V along the
(/-axis. In double modulation detection, the LIA sees an unshiftcd hole in one detection
half-cycle, and two pseudo-Stark-split holes in the other detection half-cycle. When the 1. 1 A
rectifies the signal at the reference input frequency, these two half-cyclcs arc, in effect,
subtracted from each other, resulting in lineshapes similar to those in Trace 4b. This is seen
in the measured data in Figure 4c, which was obtained using Es = 50 V along the a-axis.
Note that the trailing sideband signal at -f 148 MHz is shallower as expected. For this value
of E,. the Stark lines strongly overlap the unshifted line (Stark shift = 14.4 MHz, Iinewidth
= 14.8 MHz’). At higher values of applied field, the Stark components shift farther from
the unshifted hole position, and the signal increases because the oppositely signed
components no longer overlap. As can be seen by comparing traces 4a and 4c, the double
modulation technique very efficiently suppresses the RAM background seen using simple FM
detection, effectively increasing the ultimate detection limit. 17
D. SFS measurements
Acquisition of SFS spectra in alexandrite is complicated by several factors. First of all,
-4
the signal is expected to be small (10 in absorbance change). Usually the laser power is
increased in order to lower the relative contribution of shot noise and improve the sensitivity
to weak signals, but in the present case the laser power had to be kept below a few n W in
order to prevent power broadening. This is the majoi difference between the present FM
measurements and previous studies'7 in gases in which several mW of power could be
presented to the detector. The long lifetime of the transient holes which may be burned in
the spectrum also interferes in the following way. As the laser carrier frequency and the two
sidebands sweep the spectrum, each component excites some of the ions into the excited
state. Because of the lifetime of the transient hole and the scan rates and modulation
frequencies used, the trailing sideband secs a spectrum which has been changed by the
passage of the leading sideband and the carrier center frequency. More importantly, this
"perturbed" spectrum can in principle be different for each laser scan, unless the exact same
ions undergo excitation by the leading sideband and center frequency every time the spectrum
is scanned, which is unlikely. If' such a process is occurring, then successive averages of many
scans can be different, even in the absence of spectral diffusion or persistent hole-burning
and trenching which might cause permanent changes in the "true" shape of the SFS. Also,
if ground or excited state cross-relaxation is occurring, then it is possible that the "true" SFS
spectrum changes after each scan. These effects can be minimized somewhat by lowering the
laser power, but then the overall detection signal-to-noisc would degrade.
Figure 5 shows typical results for attempts to detect SFS in the R,m line of alexandrite
at 1.6 K using laser- FM/Stark double modulation. Trace 5a shows two superimposed
acquisitions of the SFS spectrum, each of v nich is the average of 4096 laser scans (0 GHz
= 679.676 nm). The spectra arc plotted in units of (Aa)F, where a is the absorption
coefficient, I- is the sample length and (Aa)F is a measure of the difference in absorption
between the two FM sidebands. One can see that there arc obvious correlations of both the
narrow and broad features of these two spectra, but even with the large number of averages
taken the signal-to-noise ratio is near unity. Shown in trace 5b is a typical spectrum obtained
when the laser is tuned off the R,m line, again with 4096 averages taken with constant laser
power at the detector. Due to the large noise background from laser shot noise and detector
avalanche noise and to the effects mentioned above, the presence of SFS is not convincing
when observing the raw spectra.
More convincing evidence for the presence of SFS structure is obtained by computing
1 2
the normalized autocorrelations ’ of the spectra. These are shown in Figure 6, where traces
6a and 6b correspond to the spectra in 5a, and trace 6c corresponds to 5b. I he
autocorrelations of spectra taken with the laser in resonance with the R,m line show a
significantly broader origin feature than those taken with the laser off-resonance, suggesting
the presence of underlying homogeneous lincshapcs recurring in the on-line spectra. This
broadening is most likely due to SFS, with the width of the origin feature reflecting the width
of the absorption features producing the SI'S. *' 2 The width at the origin of the
autocorrelation of ofT-resonancc spectra is determined by the bandwidth of the detection
electronics together with the digitization rate of DS. In the previous reports of SFS, the
widths at the origin of (on-resonance) autocorrclatcd spectra were determined principally by
the underlying homogeneous linewidth of the features making up the inhomogeneous band.
Here however, the width at the origin for traces 6a and 6b is comparable to the short-time
laser jitter linewidth, ss 1-2 MIIz. We therefore interpret our data as showing that the zero
(magnetic) field homogeneous width of the Cru ions in the R,m line of alexandrite is less than
2 MHz, limited in our experiment by the laser linewidth. This result is consistent with the
transient hole widths reported in Sect. III.B. above.
IV. Conclusion
Using lascr-FM spectroscopy and transient spectral hole-burning, we have measured the
Stark coefficients for Cr3f ions in alexandrite for laser light polarized along the b-axis and
find a linear pseudo-Stark splitting for the mirror site ions. Using this information, we have
developed a FM/Stark double modulation detection technique that removes the interfering
background due to residual amplitude modulation. We have used this technique and
autocorrelation analysis to provide strong evidence for the existence of statistical fine
structure in the R,m transition of alexandrite at 1.6 K. This is the first evidence for SFS in
an inorganic material and suggests that SFS will be a general feature of all inhomogcncously
broadened transitions. In order to improve the signal-to-noisc ratio of SFS measurements
on weakly allowed transitions where excitc-statc saturation may be a problem, a detection
technique is required that will provide higher laser power on the detector while maintaining
the laser power on the sample below levels that produce power broadening. One technique
that may achieve this is heterodyne FM spectroscopy, where the optical carrier is produced
by a separate, higher power beam that does not pass through the sample.
ACKNOWLEDGEMENT
The authors thank Dr. R. C. Morris of Allied Corporation, Corporate Technology
Division, for the generous loan of the alexandrite crystal, Dr. R. M. Macfarlanc for the use
of the Stark effect sample holder, and Dr. R. S. Meltzcr for stimulating discussions. This
work was supported in part by the U.S. Office of Naval Research.
REFERENCES
1. W. E. Mocrner and T. P. Carter, Phys. Rev. Lett. 59 , 2705 (1987); W. 11. Moerner
and T. P. Carter, Bull. Am. Phys. Soc. 32, 1630 (1987).
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1988.
3. G. C. Bjorklund, Opt. Lett. 5, 1.5 (1980); G. C. Bjorklund, M. D. Levenson, W.
Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
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(1985).
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Lumin. 37, 29 (1987).
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J. Quantum Electron. QE-16, 1302 (1980).
15. A. Szabo, Phys. Rev. B ]^, 4512 (1975).
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-12-
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FIGURE CAPTIONS
Figure I. Simplified apparatus diagram. See text for description of symbols. A detailed
description of the FM apparatus is presented in Ref. 2.
Figure 2. Pseudo-Stark efTect on transient holes burned into the R)m line of alexandrite at
1.6K, detected using laser-FM spectroscopy. The signal from only one FM sideband is shown
here. Traces a) through Q correspond to applied voltages of 0, 50, 100, 200, 300 and 400
V, respectively.
Figure 3. Pseudo-Stark splittings as a function of applied electric field. The laser polarization
is always along the crystal b axis. Circles, squares, and triangles correspond to applied
electric fields along the ax and b axes, respectively. The straight lines are least-square fits
to the data. No splitting was observed for electric fields applied along the b axis.
Figure 4. Transient hole burning and laser- FM/Stark double modulation detection in the
Rlm line of alexandrite at 1.6K. Trace a) is the signal from a transient hole detected with
laser-FM spectroscopy; trace b) is a simulation of the lineshape expected for double
modulation detection; trace c) is the actual double modulation signal of a transient hole
obtained using identical conditions to those used to produce trace a).
Figure 5. SFS in alexandrite at 1.6 K using double modulation detection with a 10 kHz signal
at 200 V applied along the a axis. Trace a) shows the superimposed results of successive
averages of 4096 laser scans across a small portion of the R,m line. Trace b) is an average
of 4096 scans, with the laser tuned off of the line.
Figure 6. Normalized autocorrelations of the SFS data presented in Figure .5. Traces a) and
b) were obtained from the on-line SFS spectra, trace c) was obtained From the ofT-linc
spectrum.
DL/1113/87/2
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Attn: Dr. S. Yamamoto
Marine Sciences Division
San Diego, California 91232