6.

Laser Frequency Measurements, the Speed of

Light, and the Meter"
K. M. EVENSON and F. R. PETERSEN
With 5 Figures
The spectral characteristics of electromagnetic radiation are determined
by either its vacuum wavelength or its frequency (and, of course, the
speed of light is the product of the two). Before the advent of lasers,
infrared and visible spectra were measured using wavelength techniques.
Lasers have fractional linewidths approaching those of radio and micro-
wave oscillators and have many orders of magnitude more spectral
radiance than incoherent sources, as shown in Fig. 6.1; thus, direct
frequency measuring techniques as well as wavelength techniques can
be used and the frequency techniques provide much more resolution and
accuracy in measuring the spectral characteristics of the radiation.
Frequency measuring techniques are limited only by the accuracy of the
fundamental standard and the stabilities of the sources available and, as
a result, are better by several orders of magnitude. Hence, lasers which
provide intense coherent sources of electromagnetic radiation extending
from the microwave through the visible to the ultraviolet portion of the
electromagnetic spectrum (see Fig. 6.2) can be considered as either
wavelength or frequency sources.
In spite of the fact that lasers provided coherent frequency sources
in the infrared and visible, frequencies could not immediately be measured
because no device capable of generating frequencies of a few THz from
harmonics of cw sources was known to exist. Secondly, the laser frequency
was not very stable; that is, in the case of the gas laser although its
short term linewidth was a few hundred hertz, over a long period, its
frequency could vary within the Doppler and pressure broadened gain
curve of the laser. This gain curve might vary from less than a hundred
to several thousand megahertz depending on the laser. Therefore, even
though the instantaneous frequency of the laser could be measured,
there was no reference point other than the broad gain curve whose center
could not be located very precisely. Happily, solutions to both of these
problems were found: for the first, the extension of frequency measure-
ments into the infrared by means of the metal-on-metal point contact
diode C6.11, and for the second, the development of the technique of
* Contribution of the National Bureau of Standards, not subject to copyright.
350 K. M. EVENSON and F. R. PETERSEN
3000'
Bl ack Body
+
r----- 1
I Monochr omat or 1
L - - - - - J
Charact eri st i cs :
Dri ve Power
Band Wi dth
io3 wat t s
30000 MHz
And k 5 mW/cm
Spect r al Range
Angul ar Div.
Spect r al Radi ance
0.4-3pm
4 ~ S r
i o4 Watts
I MHz
3 W/cm2
0.4 -0.7~
3 x I O - ~ S ~
f or I MHz Bondwi dt h
N= I 0-' W/ cm2/ MHz/ Sr N= IO4 W/cm2/MHz/Sr
N (Laser ) = ioI2 N (Lamp) ! ! !
Fig. 6.1. Comparison of tunable light sources. The laser is characterized by its small spectral
band width and angular divergence resulting in a large spectral radiance per unit band
width. The narrow tuning-range disadvantage of a typical gas laser is to a large extent
being removed by the development of the dye laser
saturated absorption [6.2] (see e.g. Subsect. 1.4.2). These two develop-
ments meant that coherent, highly stable, short wavelength sources of
radiation existed whose frequency and wavelength could be directly
related to the primary frequency and wavelength standards.
With the perfection of highly reproducible and stable lasers, their
wavelength-frequency duality becomes of wider interest. We begin to
think of lasers as frequency references for certain kinds of problems such
as high resolution optical heterodyne spectroscopy [6.3]. The extension
of absolute frequency measurements, linking the cesium standard
(accurate to about 2 x [6.4] to these lasers, provides accuracy
as well as resolution to the absolute frequencies involved. At the same
time, we use the wavelength aspect of the radiation, for example, in
precision long-path interferometry C6.51. Indeed, the increasing resolu-
tion which these new spectroscopic techniques provide may very well
usher in an era of precision and accuracy in frequency and length measure-
ments undreamed of a few years ago.
Laser Frequency Measurements, the Speed of Light, and the Meter 351
G - @ - i c 2 ~
1 - %
KLYSTRONS EWO LASERS
OSCILLATORS
FREQUENCY STANDARDS WAVELENGTH
FREQUENCY
MEASUREMENTS - - I
1 , ACCURAT E LENGTH
MEASUREMENTS
ELECTROMAGNETIC SPECTRUM
Fig. 6.2. The electromagnetic spectrum showing oscillators, frequency and wavelength
standards, and measurement regions. The extension of frequency measurements into the
infrared has produced an overlap of the accurate ( <4 x IO-') wavelength measurement
region and the frequency measurement region for the first time. The frequency standard
is the zero field hyperfine structure separation in the ground state of 133Cs which is de-
fined to be 9 192631 770 Hz. The wavelength standard is the transition between the 2 p , , and
5d, levels of "Kr with the vacuum wavelength of this radiation defined to be1/1650763.73 m.
Recent advances in stabilizations with saturated absorption techniques
(see Chapter 1) have produced lasers with one-second fractional frequency
instabilities C6.21 as small as 5 x 1 O- I 3 . Although the fractional un-
certainty in frequency reproducibility is somewhat larger, stabilized
lasers are already excellent secondary frequency standards. With ad-
ditional development in laser stabilization and infrared frequency synthesis
some of these devices can be considered as contenders for the primary
frequency standard role; the 3.39 pm He-Ne laser, for example, currently
has a fractional frequency uncertainty in reproducibility [6.2] of less
than one part in 10". The duality implies that the radiation must have
a similar wavelength characteristics, Le., A,?//? z 10- which is more
than 100 times better than the current length standard 16.61. Hence, the
stabilized laser must be considered to have tremendous potential in
wavelength as well as frequency standards applications and perhaps
in both [6.7].
I t has been clear since the early days of lasers that this wavelength-
frequency duality could form the basis of a powerful method to measure
the speed of light. However, the laser's optical frequency was much too
352 K. M. EVENSON and F. R. PETERSEN
high for conventional frequency measurement methods. This fact led to
the invention of a variety of modulation or differential schemes, basically
conceived to preserve the small interferometric errors associated with
the short optical wavelength, while utilizing microwave frequencies which
were still readily manipulated and measured. These microwave fre-
quencies were to be modulated onto the laser output or realized as a
difference frequency between two separate laser transitions C6.81.
Indeed, a proposed major long-path interferometric experiment [6.9]
based on the latter idea has been made obsolete by the recent high-
precision direct frequency measurement [6. IO]. An ingenious modulation
scheme, generally applicable to any laser transition, has recently produced
successfully an improved value for the speed of light C6.1 I]. While this
method can undoubtedly be perfected further, its differential nature
leads to limitations which are not operative in direct frequency measure-
ments.
Recent ultrahigh resolution measurements of both the frequency and
wavelength of the methane stabilized He-Ne iaser yielded a value of the
speed of light 100 times more accurate C6.121 than that of the previously
accepted value C6.131. This significant increase in accuracy was made
possible by the extension of frequency measurements to the region of the
electromagnetic spectrum where wavelength measurements can be
made with high accuracy and by the use of very stable lasers.
It is the purpose of this chapter to describe the stabilization of lasers
by saturated absorption, laser frequency measuring techniques, ex-
perimental details of the speed of light measurement, and some pos-
sibilities for a new standard of length.
6.1. Stabilization of Lasers by Saturated Absorption
Homogeneous as well as inhomogeneous broadening in gas lasers
results in gain curves which are many MHz wide while cavity linewidths
are of the order of only 1 MHz. Therefore, the frequency of a gas laser
is determined within the confines of the gain curve largely by the optical
path length between the mirrors. The fractional frequency instability
is equal to the fractional change in optical path length, and since it is
difficult to keep this parameter less than one part in l op7, passively
stabilized lasers have in general been free to drift many MHz over long
periods of time.
The best short term stability is obtained by taking steps to control
the optical path length between the mirrors. These steps have included
use of cavity materials with near zero expansion coefficients, cavity
Laser Frequency Measurements, the Speed of Light, and the Meter 353
Ampl i f i er Absorber
I
LOOP P l T
FILTER DRI VER
+-DET.
+ I
REF. OSC.
r l
Frequency -
Fig. 6.3aand b. Schematic for laser stabilization by the technique of molecular saturated
absorption. Diagram (a) shows the servo-controlled laser with an internal molecular
absorption cell. Diagram (b) shows I ) the gain curve of the laser without absorber, and
2) the gain curve of the amplifier-absorber combination. The frequency of the laser is
locked to the peak of the narrow emission-type feature shown on curve 2
temperature control, isolation from mechanical and acoustic disturbances,
as well as other ingenious ideas and devices. Also in a discharge excited
gas laser, it is necessary to use a highly stabilized power supply in order
to maintain a constant index of refraction. Some of the most sophisticated
passively stabilized gas lasers have been designed by FREED and the
interested reader is referred there C6.141 for more details. The observed
spectral width is always controlled by environmental perturbations
giving rise to frequency modulation. However, with care, lasers with
short term spectral linewidths of the order of a kHz can be constructed.
Long term stability of laser oscillators can be attained by servo
controlling the frequency to some more stable reference device. For
354 K . M. EVENSON and F. R. PETERSEN
example, long term stability may be provided by locking the laser to the
resonant frequency of a temperature controlled, mechanically and ther-
mally stable, passive cavity. However, for good resetability a molecular
reference which is less subject to environmental perturbations is more
suitable, provided that Doppler and pressure broadening can be eliminat-
ed or at least greatly reduced. Molecular beam type devices suggest
themselves. However, the molecular saturated absorption technique
attains nearly the same goal and yet avoids most of the experimental
complications of beam devices. With lasers, the technique was first
demonstrated by LEE and SKOLNICK C6.151 with the 6328 A laser and
a 20Ne absorption cell excited by a dc gas discharge. Later a similar
technique was developed by BARGER and HALL C6.161 with the 3.39 pm
He-Ne laser to the point where one second fractional frequency in-
stabilities are now only a few parts in A schematic for laser stabiliza-
tion by the technique of saturated absorption is shown in Fig. 6.3a +b.
Since the linewidths are inversely proportional to the molecular transit
time across the laser beam, HALL and BORDE C6.31, by increasing the
diameter of the laser beam and cooling the absorption cell, have observed
saturated absorption lines which are only 7 kHz wide. This refinement
represents a resolution greater than 10" and is narrow enough for
observation of the methane hyperfine structure. Other lasers of interest
here wich have been stabilized by saturated absorption include the
6328 8, laser which has been locked to various iodine absorption lines
C6.171 and all of the lines in both the 9 and 10pm bands of the C02
laser which have been stabilized to CO, itself C6.18, 191.
Since the wavelength of the radiation coming from an oscillator is
simply related to the frequency through the velocity of propagation, it is
reasonable to assume that the wavelength stability will be the same as the
frequency stability. Moreover, since the coherence length is inversely
proportional to the spectral linewidth of the radiation source, lasers are
excellent wavelength standards. Thus wehave laser oscillators which are
excellent secondary frequency and wavelength standards at a number of
convenient points in the electromagnetic spectrum. The frequencies of all
the aforementioned molecular stabilizing transitions except those at
6328 8, have been measured absolutely [6.10,20] to an accuracy ex-
ceeding that of the length standard.
6.2. Frequency Measurement Techniques
Direct frequency measurements require counting the number of cycles
of electromagnetic radiation in a given period. Modern electronic
circuitry permits direct cycle counting up to about 500 MHz with the
Laser Frequency Measurements, the Speed of Light, and the Meter 355
timing generally provided by a quartz crystal oscillator, or for the
highest accuracy, directly by a cesium clock. A measurement of a higher
frequency requires a heterodyne technique in which two oscillators
(one whose frequency is known) are mixed together so that a countable
frequency difference is generated. The known frequency may be synthe-
sized as an exact harmonic of a directly countable lower frequency by
irradiating an appropriate nonlinear device. To synthesize microwave
frequencies, oscillators of about a hundred MHz irradiating a silicon
diode will generate useful harmonics as high as 40GHz. The desired
harmonic is generally mixed with the unknown frequency in the same
diode so that the heterodyne beat note of a few MHz is finally generated
and can be directly counted.
The above process may be illustrated in the following equation
where v, is the unknown frequency, v, the reference frequency, and
v,, the countable beat note frequency. The harmonic number I is generally
determined by making an approximate frequency determination from a
wavelength measurement. At frequencies from about 40 GHz to 1000 GHz
(1 THz), the silicon diode is still operable; however, several steps are
usually required in a frequency measurement chain extending from some
countable reference frequency. For this purpose, klystrons between 60
and 80GHz are often phase locked to a lower frequency klystron and
these are used to cover the range between 200 and io00 GHz with less
than 15 harmonics in each step. The harmonic number is kept below 15
because at frequencies above a few hundred gigahertz the overall har-
monic generation-mixing process is less efficient and consequently, one
must use a lower harmonic number.
6.3. High-Frequency Diodes
In addition to the silicon diode already mentioned, another type of
harmonic generator mixer, the point contact J osephson junction, is
a much more efficient diode in the generation of high harmonics than
is the silicon diode. Its use has been extended a little higher in frequency
than C6.211 the silicon diode to 3.8 THz by the direct generation of the
401st harmonic from an X-band source. Work is continuing on this
device to determine its high frequency limit.
A third type of harmonic generator-mixer, the metal-metal diode,
is the only device which has been used at frequencies above 3.8 THz.
This metal-metal point contact diode has been the most useful at laser
356 K. M. EVENSON and F. R. PETERSEN
frequencies, and has, thus far C6.221, operated to 88 THz (3.39 pm).
High frequency applications of this diode were first demonstrated in
J avan's laboratory [6. i] by generating and mixing the third harmonic
of a pulsed water vapor laser with a CO, laser. Specifically, the tungsten-
nickel diode has been more useful than many other metal-metal com-
binations which were tested. At these laser frequencies, harmonic
generation, sideband generation, and mixing occur in the same diode,
that is, the harmonics or sidebands are not actually propagated from
diode to diode, but a single diode is radiated with all of the necessary
frequencies. As an example, one of the steps in measuring the frequency
of a CO, laser is to compare the frequency of its 9.3 pm R(i0) line with
the third harmonic of a water vapor laser.
In this case,
where vC02, R( 10) is the unknown frequency (32.134267 THz), and vHP
=10.718069 THz, vkly =0.019958 THz, vbeat =0.000020 THz. In thls
heterodyning, the radiation from all three sources simultaneously
irradiates the diode and the resulting 20MHz beat note is amplified
and measured in a counter or spectrum analyzer.
Some characteristics of this type of diode have been measured C6.231,
and so far, attempts at extending its range to the visible have shown that
it mixes at frequencies as high as 583 THz(5145 A). However, harmonic
generation beyond 88 THz has not been demonstrated. Although the
exact physical mechanism by which the harmonic generation-mixing
occurs is not yet understood, there are at least three different possible
explanations for the phenomena. One is a tunneling process through an
oxide layer C6.241, another is a field emission process C6.251, and a third
is a quantum mechanical scattering model C6.261.
To illustrate the way in which the diode is used in laser frequency
measurement, a direct measurement of the methane transition used to
stabilize the 3.39 pm He-Ne laser will be described. It is this frequency
which is multiplied by the precisely determined methane wavelength to
yield a definitive value of the speed of light.
6.4. The Speed of Light
The speed of light, c, is possibly the most important of all the funda-
mental constants C6.271. It enters into the conversion between elec-
trostatic and electromagnetic units; it relates the mass of a particle
to its energy in the well known equation E =mc2; and it is used as well
Laser Frequency Measurements, the Speed of Light, and the Meter 357
in many relationships connecting other physical constants. In ranging
measurements, very accurately measured transit times for electro-
magnetic waves are converted to distance by multiplying by the speed
of light. Examples are geophysical distance measurepents which use
modulated electromagnetic radiation [6.28], and astronomical mea-
surements such as microwave planetary radar and laser lunar ranging
C6.291. Recent experiments have set very restrictive limits on any possible
speed dependence on direction [6.30] or frequency C6.311.
Because of its importance, more time and effort have been devoted
to the measurement of c than any other fundamental constant. In spite
of this fact, a highly accurate result has remained elusive even in recent
times-mainly because of ever present systematic errors which have
been difficult to properly evaluate. Indeed, the probable value of c has
changed, and the suggestion has been made that the real value may be
changing linearly or even periodically with time C6.321. However, in view
of recent electro-optical measurements, microwave interferometer mea-
surements, spectroscopic measurements, and the laser measurement to be
described here, it appears that the probable value of c is converging to
a constant within the stated errors and that the changing nature of c in
the past was related to unaccounted inaccuracy in previous experi-
ments.
Three different techniques have been used to measure the speed of
light: 1) time of flight techniques; 2) ratio of electrostatic to electro-
magnetic units; and 3) frequency and wavelength measurements (2v =c).
The first quantitative measurement of c was an astronomical one in
which the time of flight of light across the earths orbit around the sun was
measured by ROEMER in 1676. Early time-of-flight terrestrial measure-
ments utilized long accurately-measured base lines and either rotating
toothed wheels or mirrors for measuring the time interval. One of the
most accurate early measurements of c was an electrostatic to electro-
magnetic ratio experiment by ROSA and DORSEY C6.331 in 1906.
Measurements of c in which both the wavelength and frequency of an
oscillator were measured played a significant role in proving that radio
and light radiation were electromagnetic in nature. This method was used
by FROOME C6.131 to obtain the accepted value of c in use since 1958. His
method used a moving reflector type of microwave interferometer
operating at 72 GHz which was used to measure the microwave wave-
length in terms of the length standard. The vacuum wavelength thus
obtained when corrected for diffraction and other systematic effects was
multiplied by the measured frequency to give a value for the speed of light.
The frequency could be related to the primary standard with good
accuracy, but the major estimated experimental error was connected
with uncertainties in the wavelength measurement. At these long wave-
358 K. M. EVENSON and F. R. PETERSEN
lengths the diffraction problem forced the use of a long air path which
resulted in uncertainties in the measurement of the path length and in
the index of refraction.
Speed of light determinations from wavelength and frequency mea-
surements have traditionally suffered from the problems illustrated by
FROOME'S experiment. To measure the frequency, it is best to do the
experiment at a frequency not too far removed from the primary Cs
frequency where extremely stable oscillators can be made and where fre-
quencies are easily measurable. However, to measure the wavelength, it
is best to do the experiment close to the visible 86Kr wavelength standard
where wavelengths can be more easily compared and where diffraction
problems are not as severe. The extension of frequency measurements
into the infrared portion of the electromagnetic spectrum has in a
sense solved this dilemma, and has been responsible for the 100 fold
increase in the accuracy in the value of c. The frequency of the methane
stabilized helium-neon laser is over 1000 times higher in frequency than
that of the oscillator used in FROOME'S measurement of c. Direct frequency
measurements were recently extended to this frequency [6.22] and
subsequently refined C6.101 to the present accuracy of 6 parts in 10". The
wavelength of this stabilized laser has been compared C6.34-371 with the
krypton46 length standard to the limit of the usefulness of the length
standard (approximately 4parts in lo9) C6.61. The product ofthe measured
frequency and the wavelength yields a new, definitive value for the speed
of light, c. That measurement will now be described.
6.5. Methane Frequency Measurement
To measure the frequency of methane, a chain of oscillators extending
from the cesium frequency standard to the methane stabilized helium-
neon laser was used. The chain is shown in Fig. 6.4. The three saturated-
absorption-stabilized lasers are exhibited in the upper right-hand section,
the transfer chain oscillators are in the center column, and the cesium
frequency standard is in the lower right-hand corner. The He-Ne and
CO, lasers in the transfer chain were offset locked C6.161, that is, they
were locked at a frequency a few megahertz different from the stabilized
lasers. This offset-locking procedure produced He-Ne and CO, transfer
oscillators without the frequency modulation used in the molecular-
stabilized lasers. The measurements of the frequencies in the entire chain
were made in three steps shown on the right-hand side, by using standard
heterodyne techniques [6.22,38-401.
Conventional silicon point-contact harmonic generator-mixers were
used up to the frequency of the HCN laser. Above this frequency, tungsten-
-
Laser Frequency Measurements, the Speed of Light, and the Meter 359
p *
% - 34; - 0 019 938 900
*
V, -12&=0.028 942 00
TRANSFER LASER OSCI LLATOR I l UNEO 1 0 APPROXIMATE tlnt CEWlER1
Fig. 6.4. Stabilized laser frequency synthesis chain. All frequencies are given in THz; those
marked with an asterisk were measured with a transfer laser oscillator tuned to approxi-
mate line center
on-nickel diodes were used as harmonic generator-mixers. These metal-
metal diodes required 50 or more mW of power from the lasers to obtain
optimum signals. The 2-mm-long, 25 pm-diam. tungsten antenna, with
a sharpened tip which lightly contacted the nickel surface, seemed to
couple to the radiation in two separate manners. At 0.89 and 10.7THz
it acted like a long wire antenna [6.41,42], while at 29-88 THz its
concial tip behaved like one-half of a biconical antenna C6.421. Conven-
tional detectors were used in the offset-locking steps.
The methane-stabilized He-Ne laser used in these experiments is
quite similar in size and construction to the device described by HALL
360 K. M. EVENSON and F. R. PETERSEN
C6.21. The gain tube was dc excited, and slightly higher reflectivity mirrors
were employed. The latter resulted in a higher energy density inside the
resonator and consequently a somewhat broader saturated absorption.
Pressure in the internal methane absorption cell was about 0.01 Torr
(1 Torr =133.3 N/mZ).
The two 1.2-m-long CO, lasers used in the experiments contained
internal absorption cells and dc-excited sealed gain tubes. A grating was
employed on one end for line selection, and frequency modulation was
achieved by dithering the 4-m-radius-of-curvature mirror on the opposite
end. CO, pressure in the internal absorption cell was 0.020Torr. The
laser frequency was locked to the zero-slope point on the dip in the 4.3 pm
fluorescent radiation C6.181. The 0.89-, 10.7-, and 88-THz transfer lasers
were 8-m-long linearly polarized cw oscillators with single-mode output
power greater than 50 mW. The Michelson HCN laser has been described
C6.431. The H, 0 laser used a double-silicon-disk partially transmitting
end mirror, and a 0.5-mil polyethylene internal Brewster-angle membrane
polarized the laser beam. The 8-m He-Ne laser oscillated in a single mode
without any mode selectors because of a 4-Torr pressure with a 7 : 1 ratio
of helium to neon. The resultant pressure width was approximately
equal to the Doppler width, and a high degree of saturation allowed only
one mode to oscillate.
Conventional klystrons used to generate the four difference fre-
quencies between the lasers were all stabilized by standard phase-lock-
techniques, and their frequencies were determined by cycle counting
at X-band.
An interpolating counter controlled by a cesium frequency standard of
the NBS Atomic Time Scale [6.44,45] counted the 10.6-GHz klystron
in the transfer chain. This same standard was used to calibrate the other
counters and the spectrum-analyzer tracking-generator.
I n step 1, a frequency synthesis chain was completed from the cesium
standard to the stabilized R(10) CO, laser. All difference frequencies in
this chain were either measured simultaneously or held constant. Each
main chain oscillator had its radiation divided so that all beat notes in the
chain could be measured simultaneously. For example, a silicon-disk
beam splitter divided the 10.7-THz beam into two parts: one part was
focused on the diode which generated the i2th harmonic of the HCN
laser frequency, the remaining part irradiated another diode which mixed
the third harmonic of 10.7-THz with the output from the 9.3 pm CO,
laser and the 20-GHz klystron.
Figure 6.4 shows the two different ways in which the experiment was
carried out. In the first scheme (output from mixers in position A), the
HCN laser was frequency locked to a quartz crystal oscillator via the
148- and 10.6-GHz klystrons, and the frequency of the 10.6-GHz klystron
Laser Frequency Measurements, the Speed of Light, and the Meter 361
was counted. The H,O laser was frequency locked to the stabilized
CO, laser, and the beat frequency between the H,O and HCN lasers was
measured on the spectrum analyzer. In the second scheme (output from
mixers in position B), the 10.6-GHz klystron was phase locked to the
74-GHz klystron, which in turn was phase locked to the free-running
HCN laser. The 10.6-GHz klystron frequency was again counted. The
free-running H, 0 laser frequency was monitored relative to the stabilized
CO, laser frequency, and the beat frequency between the H,O and HCN
lasers was measured as before on the spectrum analyzer.
In step 2, the difference between the two CO, lines was measured.
The HCN laser remained focused on the diode used in step 1, which now
also had two CO, laser beams focused on it. The sum of the third har-
monic of the HCN frequency, plus a microwave frequency, plus the
measured rf beat signal is the difference frequency between these two CO,
lines. The two molecular-absorption-stabilized CO, lasers were used
directly, and the relative phase and amplitudes of the modulating
voltages were adjusted to minimize the width of the beat note. The beat
note was again measured on a combination spectrum analyzer and
tracking-generator-counter. The roles of the CO, lasers were inter-
changed to detect possible systematic differences in the two laser-
stabilization systems.
In step 3, the frequency of the P(7) line in methane was measured
relative to the 10.18 pm R(30) line of CO,. Both the 8-m 3.39 pm laser
and the CO, laser were offset locked from saturated-absorption-stabilized
lasers and thereby not modulated. The 10- to 100-MHz beat note was
again measured either on a spectrum analyzer and tracking generator, or
in the final measurement when the SIN ratio of the beat note was large
enough (about loo), directly on a counter.
The measurements were chronologically divided into four runs, and
values for each of the steps and for v4, v 5 , and v6 were obtained by
weighting the results of all runs inversely proportional to the square of
the standard deviations. The largest uncertainty came in step 1 ; however,
a recent measurement by NPL [6.46] gave a value of the R(12) line which
was only 2 x lo-'' (7 kHz) different from the number obtained by adding
the R(12kR(10) difference C6.201 to the present R(i 0) value. Thus, the
first step of the experiment has been verified.
The final result is:
Molecule Line I [ P I Frequency [THz]
2 ~( 30) 10.18 29.442483 315(25)
2 R(10) 9.3 32.134266891 (24)
l 2CI 60
1 2 ~ 1 6 0
"CH, P( 7) 3.39 88.376 181 627(50)
362 K. M. EVENSON and F. R. PETERSEN
r
1 2 68 70
Fig. 6.5. Accurate speed of light values in meters per second since 1958. The value recom-
mended by CCDM is 299792.458 m/s with an uncertainty of about 4 parts in lo9. This
value maintains continuity in the meter and may be used when the meter is redefined
The numbers in parentheses of the right column are i-standard-devia-
tion-type errors indicating uncertainties in the last two digits.
In a coordinated effort, the wavelength of the 3.39 pm line of methane
was measured with respect to the 86Kr 6058A primary standard of
length by BARGER and HALL C6.341. Using a frequency-controlled
Fabry-Perot interferometer with a pointing precision of about 2 x
orders, a detailed search for systematic offsets inherent in the experiment,
including effects due to the asymmetry of the Kr standard line, was made.
Offsets due to various experimental effects (such as beam misalignments,
mirror curvatures and phase shifts, phase shift over the exit aperture,
Laser Frequency Measurements, the Speed of Light, and the Meter 363
Table 6.1. Speed of light measurements since 1958
Year Author Ref. Method
1958 FROOME
196 1 CUTKOSKY and
THOMAS
1965 KOLIBAYEV
1965 RANK et al.
1966 KAROLUS
1967 GROSSE
1967 SIMKIN et al.
197 1 BJERHAMMAR
1972 BAY et al.
1972 BAIRD et al.
1972 EVENSON et al.
1973 GUELACHVILI
1973 BARD and
BLANEY et al.
1973 CCDM
C6.131
[6.48]
16.491
C6.511
C6.521
C6.531
C6.541
[6.1 I ]
C6.471
16.121
16.551
[6.50]
[6.47,461
16.6, 101
Radio interferometer
Ratio of units
Electro-optical
Spectroscopic
Electro-optical
Electro-optical
Radio interferometer
Electro-optical
He-Ne I v (0.633 pm)
CO, I v (9 and 10 pm, avg.)
He-Ne i . v (3.39 pm) c.g.
Spectroscopic
CO, Iv (9.32 pn)
He-Ne Iv (3.39 pm)
peak
299792.5 0.1
299791.96 0.8
29 9792.6 0.06
299792.8 0.4
299792.44 0.2
299792.5 0.05
29 9792.56 0.1 I
299792.375 0.060
299792.462 0.018
299792.460 0.006
299792.4562 0.001 1
299792.4587 0.001 1
29 9792.46 0.07
299192.457 0.006
29 9792.458 0.001 2
diffraction, etc.) were carefully measured and then removed from the data
with an uncertainty of about 2 parts in lo9. Their results indicate an
asymmetry in the krypton line which resulted in two different values of
,ICH4. One value arises if the center of gravity of the krypton line is used
to define the meter, and another if the peak value is used. This repro-
ducibility for a single wavelength measurement illustrates the high
precision which is available using the frequency-controlled interferom-
eter.
At the 5th session of the consultative committee on the definition of
the meter (CCDM) C6.61, results of BARCER and HALL as well as measure-
ments made at the International Bureau of Weights and Measures C6.361,
the National Research Council C6.371, and the National Bureau of
Standards at Gaithersburg C6.351 were all combined to give a recom-
mended value for the wavelength of the transition of methane used to
stabilize the He-Ne laser. The recommended value is
&. H4[P(7, , bandvzl =3392231.40 x lo- m .
(6.3)
Multiplying this recommended wavelength of methane by the
measured frequency yields the value for the speed of light:
c =299792458 m/sec ( Ac/ c = 4 x W9) , (6.4)
364 K. M. EVENSON and F. R. PETERSEN
which was also recommended by the CCDM C6.61 to be used in distance
measurements where time-of-flight is converted to length and for
converting frequency to wavelength and vice versa.
This result is in agreement with the previously accepted value of
c =299 792 500( 100) m/sec and is about 100 times more accurate. A
recent differential measurement of the speed of light has been made by
BAY et al. C6.111; their value is 299792462(18) m/sec, which is also in
agreement with the presently determined value. A third recent, highly
accurate value may be obtained by multiplying the frequency of the R( 12),
9.3 pm line of CO, measured by BLANEY et al. C6.461 by the wavelength
measured by BAIRD et al. C6.471 which yields the value of 299 792458 (6) m/
sec for c. Also shown is another value by BAIRD C6.471, however, it used
the CO, frequencies which were measured in this experiment, and hence,
does not represent an independent value.
arises from the interferometric measurements with the incoherent
krypton radiation which defines the international meter. This limitation
is indicative of the remarkable growth in optical physics in recent years;
the present krypton-based length definition was adopted only in 1960.
Various measurements of c since FROOMES work are listed in Table 6.1
and are plotted in Fig. 6.5. One sees a remarkable convergence of the
values of c for the first time in history!
Thefractionaluncertaintyin thisvaluefor thespeedoflight, k 4 x
6.6. Possible New Standard of Length
In addition to the recommended values of the wavelength of methane
and the value of the speed of light made at the 5th CCDM meeting C6.61,
a value for the wavelength of iodine was also recommended:
These recommended values are in agreement with wavelength measure-
ments to the limits possible with the krypton length standard (that is,
about +4 x It is recommended that either of these values be
used to make length measurements using these stabilized lasers in the
interim before the meter is redefined.
It is also significant that no further work was recommended on the
present length standard, the krypton lamp, which is far inferior to a
laser and will probably soon be replaced by one.
As a result of the recommendations made by CCDM, two different
definitions of a new length standard must be considered. First, we can
continue as before with separate standards for the second and meter, but
Laser Frequency Measurements, the Speed of Light, and the Meter 365
with the meter defined as the length equal to 1//2 wavelengths in vacuum
of the radiation from a stabilized laser instead of from a 86Kr lamp.
Either the methane-stabilized C6.2, 161 He-Ne laser at 3.39 pm (88 THz)
or the 1,-stabilized C6.171 He-Ne laser at 0.633 pm (474 THz) appear to
be suitable candidates. The 3.39 pm laser is already a secondary fre-
quency standard in the infrared, and hopefully, direct measurements of
the frequency of the 0.633 pm radiation will give the latter laser the same
status in the visible. The 3.39 pm laser frequency is presently known to
within 6 parts in lo", and the reproducibility and long term stability
have been demonstrated to be better by more than two orders of magni-
tude. Hence, frequency measurements with improved apparatus in the
next year or two are expected to reduce this uncertainty to a few parts
in 10". A new value of the speed of light with this accuracy would thus be
achievable if the standard of length were redefined in terms of the wave-
length of this laser.
Alternately, one can consider defining the meter as a specified fraction
of the distance light travels in one second in vacuum (that is, one can fix
the value of the speed of light). The meter would thus be defined in terms
of the second and, hence, a single unified standard would be used for
frequency, time, and length. What at first sounds like a rather radical and
new approach to defining the meter is actually nearly one hundred years
old. It was first proposed by Lord Kelvin in 1879 r6.561. With this def-
inition, the wavelength of all stabilized lasers would be known to the
same accuracy with which their frequencies can be measured. Stabilized
lasers would thus provide secondary standards of both frequency and
length for laboratory measurements, with the accuracy being limited
only by the reproducibility, measurability, and long term stability. It
should be noted that an adopted nominal value for the speed of light is
already in use for high-accuracy astronomical measurements C6.571,
thus, there are currently two different standards of length in existence :
one for terrestrial measurement and one for astronomical measurements.
A definition which fixes c and unites these two values of c would certainly
be desirable from a philosophical point of view.
Independent of which type of definition is chosen we believe that
research on simplified frequency synthesis chains bridging the micro-
wave-optical gap will be of great interest, as will refined experiments
directed toward an understanding of the factors that limit optical fre-
quency reproducibility. No matter how such research may turn out, it is
clear that ultraprecise physical measurements made in the interim can be
preserved through wavelength or frequency comparison with a suitably
stabilized laser such as the 3.39 pm methane device.
Frequencies are currently measurable to parts in l Ol 3 , and hence
the over-all error of about six parts in 10" for the frequency measure-
366 K. M. EVENSON and F. R. PETERSEN
ment can be reduced. This measurement was performed fairly quickly
to obtain a frequency of better accuracy than the wavelength. It should
be possible to obtain considerably more accuracy by using tighter
locks on the lasers. For example, the 8-m HCN laser has recently been
phase locked [6.58,59] to a multiplied microwave reference which
currently determines the HCN laser linewidths. An improved microwave
reference could be a superconducting cavity stabilized oscillator C6.601
for best stability in short term (narrowest linewidth) coupled with a
primary cesium beam standard for good long term stability.
The relative ease with which these laser harmonic signals were
obtained in these frequency measurements indicates that the measure-
ment of the frequencies of visible radiation now appears very near at hand.
Even if the point contact metal-on-metal diode is inoperable above
88 THz, conventional nonlinear optical techniques (i.e., 2nd harmonic
generation in crystals) could still be used to extend direct frequency
measurements to the visible. Such measurements should greatly facilitate
ones ability to accurately utilize the visible and infrared portion of the
electromagnetic spectrum.
Acknowledgement
The authors which to acknowledge J . S. WELLS, B. L. DANIELSON, and
G. W. DAY who participated in the measurement of the frequency of the
methane stabilized He Ne laser and R. L. BARGER and J . L. HALL who
first stabilized the laser and measured its wavelength. We also express our
gratitude to D. G. MCDONALD and J . D. CUPP whose work with the
J osephson junction was a parallel effort to ours in trying to achieve near-
infrared frequency measurements. We note here that experiments using
the J osephson junction to measure laser frequencies are continuing, and
may well lead to better methods for near-infrared frequency synthesis
in the future.
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