U.S. patent number 5,389,779 [Application Number 08/099,681] was granted by the patent office on 1995-02-14 for method and apparatus for near-field, scanning, optical microscopy by reflective, optical feedback.
This patent grant is currently assigned to AT&T Corp.. Invention is credited to Robert E. Betzig, Igal M. Brener, Stephen G. Grubb, David A. B. Miller.
United States Patent |
5,389,779 |
Betzig , et al. |
February 14, 1995 |
Method and apparatus for near-field, scanning, optical microscopy
by reflective, optical feedback
Abstract
Apparatus and methods of near-field scanning optical microscopy
(NSOM) are described. A sensing technique is used, in which a light
source having an optical cavity is reflectively coupled to the
sample surface. Changes in the surface properties of the sample at
the sensed location alter the optical feedback in the light source.
This leads to detectable changes in the output characteristics of
the light source.
Inventors: |
Betzig; Robert E. (Chatham,
NJ), Brener; Igal M. (Eatontown, NJ), Grubb; Stephen
G. (Warren, NJ), Miller; David A. B. (Fair Haven,
NJ) |
Assignee: |
AT&T Corp. (Murray Hill,
NJ)
|
Family
ID: |
22276123 |
Appl.
No.: |
08/099,681 |
Filed: |
July 29, 1993 |
Current U.S.
Class: |
250/216; 850/30;
850/31; G9B/11.028; G9B/7.125; G9B/7.097 |
Current CPC
Class: |
G11B
11/10541 (20130101); G11B 7/1384 (20130101); B82Y
20/00 (20130101); G11B 7/12 (20130101); G01Q
60/22 (20130101); B82Y 35/00 (20130101) |
Current International
Class: |
G11B
11/105 (20060101); G11B 11/00 (20060101); G12B
21/00 (20060101); G11B 7/12 (20060101); G12B
21/06 (20060101); G11B 7/135 (20060101); H01J
003/14 () |
Field of
Search: |
;250/216,27.26,234,306,307,309,563 ;356/121,5,152,4,124 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Nelms; David C.
Assistant Examiner: Le; Que T.
Attorney, Agent or Firm: Finston; Martin I.
Claims
What is claimed is:
1. Apparatus for collecting information from a surface of a sample,
comprising:
a) a light source that comprises a first optical cavity, and that
further comprises an emissive face portion for emitting
therethrough radiation from the first optical cavity;
b) means for situating the emissive face portion near the sample
surface such that the optical cavity is reflectively coupled to a
spot on the sample surface, relative to at least one wavelength
.lambda. of radiation emitted from the optical cavity;
c) means for scanning the spot over a portion of the sample
surface; and
d) means for detecting changes in an output characteristic of the
light source,
CHARACTERIZED IN THAT:
e) the emissive face portion has a maximum extent L in at least one
dimension parallel to the sample surface that is less than
.lambda.; and
f) the situating means, in use, to situate the emissive face
portion at a distance from the sample surface that is less than or
approximately equal to L.
2. Apparatus of claim 1, wherein:
a) the light source comprises a glass waveguiding body; and
b) at least a portion of said body is doped with a fluorescent
species such that said doped portion can emit radiation when
appropriately stimulated by pump radiation.
3. Apparatus of claim 2, wherein:
a) the glass waveguiding body is an optical fiber having a tapered
terminal portion and an end thereof; and
b) the emissive face portion is defined in the end of the tapered
terminal portion.
4. Apparatus of claim 1, wherein the light source comprises a
laser, the optical cavity is internal to the laser, and at least a
portion of the cavity comprises a gain region of the laser.
5. Apparatus of claim 1, wherein: the light source comprises a
laser having a second optical cavity internal thereto; the first
optical cavity is external to the laser; and the first optical
cavity is optically coupled to the second optical cavity.
6. Apparatus of claim 5, wherein: the light source comprises an
optical fiber optically coupled to the laser and having a tapered
end portion distal the laser; the emissive face portion is defined
in the tapered end portion; and the first optical cavity is defined
within the optical fiber.
7. Apparatus of claim 1, wherein: the light source comprises an
optical amplifier having a second optical cavity internal thereto;
the first optical cavity is external to the optical amplifier; and
the first optical cavity is optically coupled to the second optical
cavity.
8. Apparatus of claim 7, wherein: the light source comprises an
optical fiber optically coupled to the optical amplifier and having
a tapered end portion distal the optical amplifier; the emissive
face portion is defined in the tapered end portion; and the first
optical cavity is defined within the optical fiber.
9. Apparatus of claim 1, wherein the light source comprises a
fluorescent body situated within the first optical cavity.
10. Apparatus of claim 9, wherein the first optical cavity has a
length of approximately ##EQU2##
11. Apparatus of claim 1, wherein: the light source comprises a
laser and means for modelocking the laser at a variable modelocking
frequency f.sub.ml ; and the detecting means comprise means for
detecting changes in f.sub.ml.
12. Apparatus of claim 1, wherein: the light source comprises a
laser capable of emitting radiation at the wavelength .lambda. and
frequency ##EQU3## where c is the vacuum velocity of light; and the
detection means comprises means for detecting changes in .nu..
13. Apparatus of claim 1, wherein the detecting means comprise
means for detecting changes in the intensity of radiation emitted
from the light source.
14. A method for collecting information from a surface of a sample,
comprising:
a) operating a light source having an optical cavity such that
electromagnetic radiation is present in the optical cavity, and a
portion of the radiation in the optical cavity is emitted through
an emissive face portion;
b) during (a), situating the emissive face portion near the sample
surface such that the optical cavity is reflectively coupled to a
spot on the sample surface, relative to at least one wavelength
.lambda. of radiation emitted by the light source;
c) during (b), scanning the spot over a portion of the sample
surface; and
d) during (c), detecting changes in an output characteristic of the
light source.
CHARACTERIZED IN THAT step (b) is carried out such that:
e) the spot has a maximum extent L in at least one dimension
parallel to the sample surface that is less than .lambda.; and `f)
the emissive face portion is situated at a distance from the sample
surface that is less than or approximately equal to L.
15. The method of claim 14, wherein: the light source is capable of
emitting radiation at a frequency ##EQU4## where c is the vacuum
velocity of light; and (d) comprises detecting changes in .nu..
16. The method of claim 14, wherein: the light source comprises a
laser; (a) comprises modelocking the laser such that pulses of
radiation are emitted at a modelocking frequency f.sub.ml ; and (d)
comprises detecting changes in f.sub.ml.
17. The method of claim 14, wherein: the light source comprises a
laser having a relaxation oscillation frequency f.sub.rlx ; the
method further comprises, during (a), the step of modulating, at a
modulation frequency, the intensity of radiation in the optical
cavity; and (d) comprises detecting an intensity of radiation
emitted from the laser, and detecting changes in the AC component
of said intensity at the modulation frequency.
18. The method of claim 17, wherein the modulating step comprises
varying the separation between the sample surface and the emissive
face portion.
19. The method of claim 17, wherein the light-source-operating step
comprises pumping the laser at a pump power level, and the
modulating step comprises modulating the pump power level.
20. The method of claim 17, 18, or 19, wherein the modulation
frequency is approximately equal to f.sub.rlx.
21. The method of claim 14, wherein: the light source comprises a
laser having a relaxation oscillation frequency f.sub.rlx ; the
method further comprises providing a sample having a pattern
impressed on a surface thereof, said pattern having spatially
periodic reflectivity variations; step (c) comprises scanning the
spot over the pattern such that said reflectivity variations
modulate radiation in the optical cavity at a modulation frequency;
and step (c) is carried out at a scan rate selected, relative to
the periodicity of said reflectivity variations, such that the
modulation frequency is approximately equal to f.sub.rlx.
22. The method of claim 14, wherein the detecting step comprises
detecting changes in the intensity of radiation emitted from the
light source.
Description
ART BACKGROUND
Recent advances have brought near-field scanning optical microscopy
(NSOM) to the point where it can be applied routinely to a variety
of samples. For example, the design and applications of a probe
based on a metal-coated, tapered optical fiber are described in E.
Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L.
Kostelak, Science 25 1, 1468 (1991); E. Betzig, P. L. Finn, and J.
S. Weiner, Appl, Phys. Lett. 60, 2484 (1992); and E. Betzig and J.
K. Trautman, Science 257, 189 (1992). Nevertheless, further
refinement of near-field probes remains an area of active interest.
For example, the quantity and diversity of applications would be
enhanced through the development of probes having increased photon
flux. In the above-mentioned tapered fiber probe, the flux is
limited, in large part, because the transmitted energy is
exponentially attenuated in evanescent modes within the probe as
the probe diameter tapers to dimensions substantially smaller than
the wavelength. However, rather than imaging the sample directly
via this comparatively weak emitted light, it is possible, in
principle, to measure local properties of the sample by their
influence on the boundary conditions at the emissive aperture of
the probe and their consequent effect on the electromagnetic field
within the probe itself. The problem then becomes one of measuring
these field changes with sufficient speed and sensitivity to permit
high bandwidth NSOM reflection-mode detection.
Reflective feedback probes have, in fact, been demonstrated for
operation at heights greater than one wavelength above the sample
surface. For example, U.S. Pat. No. 4,860,276, issued to H. Ukita,
et al. on Aug. 22, 1989, describes an optical head which can be
used for reading or writing digital data. This head, which is
carded on a flying slider, includes a self-coupled semiconductor
laser situated within several micrometers of the recording surface.
The resulting spot size is about 1 .mu.m in diameter, which,
however,is not substantially smaller than spot sizes attainable
using conventional focusing optics. Thus, the Ukita probe fails to
combine the high resolution of near-field detection with the
relatively high signal-to-noise ratios achievable by reflective
feedback.
SUMMARY OF THE INVENTION
To achieve this, and in that way to achieve high bandwidth NSOM
reflection-mode detection, we have developed a system in which the
tip and aperture region of an NSOM probe serves as one end
reflector of an optical cavity that includes an optically emissive
medium. (For example, the emissive medium may be a Nd.sup.3+ doped
fiber laser continuous with the probe.) The field changes within
the tip are then evidenced as small variations in the complex
reflectivity at one end of the cavity. It is well known that these
variations can result in substantial changes in the optical output
characteristics of the emissive medium. For example, they may
result in large changes in the output power from the opposite end
of a fiber laser, particularly when the laser is operated near
threshold.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 schematically shows an illustrative configuration for a
reflection-mode NSOM system using a fiber laser probe according to
the invention in one embodiment.
FIG. 2 is a graph showing how the output of an illustrative fiber
laser probe depends upon the input power. The illustrative probe
was placed within about 10-20 nm of a reflective gold surface and
vertically oscillated with a peak-to-peak amplitude of about 10 nm.
The upper curve of the figure shows the DC output power of the
probe, and the lower curve shows the near-field-induced AC
modulation.
FIG. 3 is a graph showing how the induced AC modulation depends
upon the separation between the probe tip and a highly reflective
gold surface (upper curve) and a less reflective glass surface
(lower curve).
FIG. 4 is an NSOM image of a chromium test pattern formed on a
glass substrate. The image was made using a fiber laser probe
according to the invention in one embodiment.
FIG. 5 is a shear-force image of the test pattern of FIG. 4. This
image was obtained concurrently with the image of FIG. 4.
FIG. 6 is a graph showing how the modulation gain of an
illustrative fiber laser probe depends upon the modulation
frequency. The modulation gain is expressed as percentage
peak-to-peak output modulation, normalized to a 2% peak-to-peak
variation in pump power. Three curves are shown, corresponding to
three different DC output power levels.
FIG. 7 is a graph showing how the output power of a fiber laser
depends upon the input pump power. Five curves are shown, each
representing different end-reflector conditions. The middle curve
represents an illustrative, fiber-laser NSOM probe.
FIG. 8 is a schematic diagram of an alternate embodiment of the
invention, in which a passive near-field probe is attached to an
emissive face of a laser.
FIG. 9 is a schematic diagram of a light source useful in
connection with an alternate embodiment of the invention. This
light source comprises a fluorescent body situated within a
Fabry-Perot cavity.
FIG. 10 is a schematic diagram of a system, according to one
embodiment of the invention, for detection by modulation of the
laser frequency v.
FIG. 11 is a schematic diagram of a system, according to one
embodiment of the invention, for detection by passively modelocking
the laser.
With reference to FIG. 1, a typical NSOM system includes a probe
105, means 102 for situating emissive face portion 103 of the probe
near the sample surface, and means 104 for scanning the probe over
the surface. Emmissive face portion 103 has a maximum extent L in a
least one dimension parallel to the sample surface that is less
than the imaging wavelength .lambda.. The situating means 102, in
use, situate portion 103 at a distance from the sample surface that
is less than or approximately equal to L.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
With further reference to FIG. 1, we created a hybrid, near-field,
fiber laser probe 105 having a laser gain region 107 by drawing a
single mode, Nd.sup.3+ doped optical fiber in a pipette puller and
applying an aluminum coating 110 according to the procedure for
making passive fiber probes described in E. Betzig, J. K. Trautman,
T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251, 1468
(1991). The fiber used had a .DELTA. of about 1%, and a
3.4-.mu.m-diameter core uniformly doped with Nd.sup.3+ ions,
resulting in a measured attenuation at the pump wavelength (753 nm)
of 0.89 dB/cm. Pump light at 753 nm from a Kr.sup.+ laser was
coupled into the cleaved end 120, and the resulting 1060-nm laser
emission was measured at this same end by detector 125 after
isolation from the pump, as shown in the figure. A near-field scan
head incorporating shear force feedback was used to maintain the
tapered end of the probe within the near field, and was controlled
by a set of electronics permitting simultaneous acquisition of
near-field reflection and shear force topographic images. (Shear
force feedback is described in E. Betzig, P. L. Finn, and J. S.
Weiner, Appl. Phys. Lett. 60, 2484 (1992). Low frequency power
fluctuations in the Kr.sup.+ laser necessitated the use of an
active circuit employing an acoustooptic modulator to stabilize the
1060 nm fiber laser emission in a bandwidth from DC to about 10
kHz. Consequently, the near-field signal was generated by imparting
a small vertical dither motion to the sample (approximately 10 nm
peak-to-peak) at a somewhat higher frequency (about 36 kHz) and
demodulating the resultant AC signal imposed on the fiber laser
emission with a lock-in amplifier.
As shown in FIG. 2, the induced AC signal was essentially zero at
pump power levels below threshold, but rose rapidly thereafter to
become a significant fraction of the total laser output power. For
example, we observed a modulation of 22% at an output power of 0.37
mW. This modulation amplitude corresponds to 4.3.times.10.sup.14
photons/sec received at the detector. Together with the observed
sensitivity of this signal to both the sample reflectivity and the
tip-to-sample separation demonstrated in FIG. 3, these results
suggest that data encoded as reflective or topographic bits will be
readable at rates substantially greater than 1 MHz.
To evaluate spatial resolution, we prepared a test pattern
consisting of 11-nm-thick chromium features on a glass substrate
using electron beam lithography. We used NSOM and shear force
microscopy to produce the optical and shear-force images shown,
respectively, in FIGS. 4 and 5. It is desirable to compare these
images when measuring resolution because the topographic data from
the shear force signal can couple into the near-field image,
resulting in the spurious introduction of high-spatial-frequency
information. This is particularly true for the fiber laser probe,
where the sensitivity of the near-field signal to the
aperture-to-sample separation is very high. Because the images of
FIGS. 4 and 5 differ in significant respects, these figures provide
assurance that the optical signal is being evaluated directly. In
particular, the apparent line widths are considerably larger in the
shear force image, since they are determined by a convolution of
the true line width with the outer, metallized diameter of the
probe, whereas the near-field widths result from a convolution of
the true line width with the considerably smaller diameter of the
aperture. Thus, we have concluded that the data in FIG. 4
demonstrate a resolution of 150 nm or better (i.e., 150 nm is the
mean line spacing within the pattern), and in fact contain
information, not exactly correlated with FIG. 5, at spatial
frequencies that correspond to a resolution of 100 nm or better.
This is entirely consistent with the 130-150 nm aperture size used
in the experiments described here.
Our experimental results imply that if the signal-to-noise ratio is
limited only by shot noise, data can be read (from, e.g., a
reflective phase-change medium) at packing densities of about 29
Gbit/in.sup.2 and speeds of about 50 Mbit per second. (This assumes
a power signal-to-noise ratio of about 25 dB, and contrast that is
about half that obtained in our laboratory experiments.)
Consequently, we have found that the major limitation on the
bandwidth of our hybrid probe is imposed by the relaxation
oscillation frequency f.sub.rlx of the laser. That is, the time
required for the pump beam to establish a population inversion is
much greater than the time needed for the population inversion to
decay by stimulated emission. This results in a limit f.sub.rlx on
the maximum frequency at which the output power can be modulated,
given approximately by the following theoretical expression:
##EQU1## For a typical NSOM probe, the cavity length L.apprxeq.70
cm, the refractive index n.apprxeq.1.5, the Nd.sup.3+ spontaneous
emission lifetime .rho..apprxeq.500.mu.s, the ratio of pump power
during normal operation to that at threshold r.apprxeq.1.15, and
the reflectivities at the cleaved and tapered ends of the cavity
are R.sub.1 .apprxeq.0.04 and R.sub.2 .apprxeq.0.01, respectively.
These values yield f.sub.rlx .apprxeq.92 kHz, resulting in a limit
on the read rate far lower than would be anticipated on the basis
of shot noise considerations alone.
We determined the frequency response of the probe by plotting the
normalized output power modulation induced by a small AC variation
in the pump power from 10-100 kHz, as shown in FIG. 6. For all
three of the output power levels indicated, f.sub.rlx is of the
same order as predicted above. Furthermore, the sensitivity beyond
f.sub.rlx falls with a very steep slope of about 15 dB/octave. Some
improvement in f.sub.rlx is achieved at higher power levels in
accordance with Equation 1, but even 3.0 mW, as used for the curve
with the fastest response, is sufficient to result in heatinduced
damage to the probe. At a more conservative (and indeed typical)
operating power of 0.38 mW, f.sub.rlx .apprxeq.34 kHz, which
explains the choice of the vertical dither frequency used in the
experimental runs of FIGS. 2-5.
It should be noted, with reference to FIG. 6, that the gain peaking
that occurs at f.sub.rlx can be exploited to achieve optimal
sensitivity. The modulation gain at all frequencies below f.sub.rlx
is somewhat better at 0.38 mW than at 3.0 mW, because it is closer
to the point of optimum sensitivity along the threshold curve. At
an even lower power of 0.12 mW, however, the gain rapidly
diminishes, since it must ultimately vanish in the limit where
threshold is reached.
As noted, above, one way to exploit this gain peaking is to
modulate the separation between the probe and the sample surface at
or near the frequency f.sub.rlx. An alternate method is to modulate
the pump power of the laser at or near this frequency. Yet another
method is possible where the probe is to be used to read a pattern
impressed on the sample surface, such as an array of bits of stored
data in an optical or magneto-optical data storage medium. In such
a case, scanning of the sample can be carded out such that
successive bits (or other surface features) pass beneath the probe
with a frequency at or near f.sub.rlx.
Several schemes are envisaged for improving the bandwidth of the
hybrid probe. For example, with suitably high doping and a
sufficiently short cavity, f.sub.rlx can be increased
substantially. Indeed, pulsed operation at a 2.5 MHz repetition
rate has already been demonstrated in a 1 cm long Nd.sup.3+ doped
fiber laser. (See, e.g., L. A. Zenteno, E. Snitzer, H. Po, R.
Tumminelli, and F. Hakimi, Opt. Lett. 14, 671 (1989).) Second,
other laser systems with much higher f.sub.rlx can be used in place
of fibers. For example, we believe that a passive NSOM probe can be
combined with a semiconductor diode laser to form a system capable
of both high speed and high resolution. In this case, sensitivity
will be a more important issue than bandwidth, since diode lasers
have f.sub.rlx values in the GHz regime.
We have estimated, from data such as those displayed in FIG. 7,
that the effective reflectivity at the near-field end of the cavity
in a typical one of our fiber laser probes is about 1%. Such a low
reflectivity is due to the fact that the taper scatters most of the
back reflected energy into the cladding rather than the core. The
large sensitivity to near-field perturbations then arises from a
redirection of a small part of this scattered light back into the
gain medium and/or from a small change in the phase of the
reflected energy. We believe that it will be desirable to maintain
these characteristics when developing any new hybrid transducer
combining a laser and near-field probe.
The exemplary probes described above were coextensive with optical
fiber lasers. However, it should be noted that such a probe will
typically exhibit gain only in an initial portion, and will not
exhibit substantial gain in the neighborhood of the probe tip. This
will generally be true even if the probe is uniformly doped with
optically emissive ions (provided the total length exceeds the
absorption length for pump radiation). Thus, a terminal portion of
the optical cavity will typically behave as a passive, rather than
as an active, cavity with respect to laser emission.
In fact, as noted above, an emissive face of a laser or other light
source can be coupled to the sample through a purely passive
near-field probe attached to the emissive face. Such a combined
assembly is shown in FIG. 8. The reflectivity of the interface
between, e.g., laser diode 200 and passive probe 210 can be varied
from near zero to near 100% by, for example, applying appropriate
anti-reflective coatings. This reflectivity affects the optical
feedback, and thus affects the operation of the light source. For
example, when the reflectivity is high enough for the diode to lase
even without the attached probe, the combined assembly may be
described as a laser coupled to a passive cavity external to the
laser itself. On the other hand, the reflectivity may be too low
for the isolated diode to lase. In that case, the combined assembly
may be described as an optical amplifier coupled to an external,
passive cavity or cavity portion.
It should be noted that the reflectivity at the probe tip can be
selected to maximize the sensitivity of the probe. For example, the
tip reflectivity of a drawn optical fiber probe can be changed by
changing the material with which the tip is coated.
It will be appreciated that the optical output characteristics of
still other kinds of light sources can be altered by the near field
of a sample surface. It is intended for these, too, to be included
within the scope of the invention. By way of example, a suitable
light source may be provided, as shown in FIG. 9, by a fluorescent
body 300 contained within a Fabry-Perot resonator of such a small
length that the fluorescent emission of the body is substantially
confined to a single resonant mode. We expect that the tuning of
such a cavity will be sensitive to the near field of the sample
surface sensed, for example, through a sub-wavelength aperture 3 10
in one of the end-reflectors 320 of the cavity. Changes in the
tuning of the cavity will result in detectable changes in, e.g.,
the intensity of the fluorescent emission. Fluorescent body 300 is
exemplarily a half-wavelength-thick layer of silicon dioxide doped
with a suitable fluorescent species such as erbium, and enclosed
within distributed Bragg reflectors comprising alternate,
quarter-wavelength-thick layers 330, 340 of silicon and silicon
dioxide. Alternatively, the fluorescent body is a gallium arsenide
quantum well embedded in the center of a half-wavelength layer of
AlGaAs, and layers 330 and 340 comprise AlGaAs and AlAs in
alternation. These and similar structures are readily fabricated by
well-known methods, such as vacuum evaporation and molecular beam
epitaxy.
In at least some cases, it may be useful to detect imaging signals
by frequency modulation rather than by amplitude modulation, either
by optical heterodyning or by passively mode locking the
laser-probe system. Such methods are expected to retain sensitivity
well beyond threshold. Optical heterodyning is a useful detection
method where what is modulated is the frequency .nu. of the laser
radiation. By contrast, the mode-locking method leads to modulation
of the output pulse frequency f.sub.ml of the laser. Both of these
frequencies can be affected by effective changes in the phase of
the reflected wave from the probe tip as the tip is moved relative
to the sample surface or as the reflectivity of the sample surface
changes.
As shown in FIG. 10, a laser exemplarily formed by near-field
optical microscope tip 400, gain medium 410 and output coupler 420
emits light into laser frequency measuring system 430 which is, for
example, an optical heterodyne detector. As the reflectivity or
height of the sample surface changes, consequent changes in the
laser frequency v will be detected.
In the alternative detection scheme of FIG. 11, saturable absorber
500 is added to the cavity to cause passive modelocking. Passive
modelocking causes the laser to emit a train of optical pulses
whose repetition frequency f.sub.ml depends on the optical length
of the laser cavity. Thus, as the reflectivity or the height of the
sample surface is changed, the effective optical length of the
cavity is also changed, and this change will result in a change in
the frequency f.sub.ml. The modelocked pulse train is fed to
pulse-frequency measuring system 510. A suitable such system is
described, e.g., in W. H. Knox, "In situ Measurement of Complete
Intracavity Dispersion in an Operating Ti:Sapphire Femtosecond
Laser," Optics Letters 17, (1992) 514-516. This article by Knox
also demonstrates explicitly that the method of measuring the pulse
repetition rate from a passively modelocked laser is very sensitive
to optical processes in laser cavities. Significantly, the pulse
repetition frequency is readily chosen to be within a range that
can be measured electronically .
* * * * *