20TIMELINEYEARS OF OPTICAL FREQUENCY COMBS

Optical frequency combs are emitted by mode-locked femtosecond lasers. Consecutive

TIME DOMAIN - FEMTOSECOND PULSE TRAIN

pulses of the laser pulse train in the time domain can be described in terms of a Fourier
series, which corresponds to a series of frequency modes in the frequency domain. The
separation between the modes is equal to the repetition frequency fr . The comb modes,
however, are located not at exact integer multiples of the repetition frequency, but areshifted by an arbitrary offset frequency f0 .

∆ϕ Phase ShiftRepetition

fr Frequency

OffsetFrequency
FOURIER
TRANSFORMATION

f0=∆ϕT2nfr + f0

nfr +f0

T= 1frWith a comb spanning more than an octave, it is particularly easy to determine the offset
frequency. A mode with the number n at the red end of the spectrum can be sent through anonlinear crystal to generate its second harmonic frequency, which is now displaced bytwice the offset frequency. A beat note between this frequency doubled mode and an
original comb mode with the number 2n at the blue end of the spectrum directly reveals theoffset frequency 2(nfr + f0 ) – (2nfr + f0 ) = f0 .

“By March 30 of 1997, I had written a confidential six-page proposal for a universal optical frequency
comb synthesizer ‘...which produces a wide comb of absolutely known equidistant marker frequencies
throughout the infrared, visible, and ultraviolet spectral range. To this end, a white light continuum witha pulse repetition rate fr is produced by focusing the output of a mode-locked femtosecond laser into an
optical fiber or bulk medium with a third-order nonlinear susceptibility. The rate of phase slippage of thelaser carrier relative to the pulse envelope, fCEO , is monitored by observing a beat signal between thewhite light continuum and the second harmonic of the laser. The envisioned self-referencing scheme
could find the carrier-envelope offset frequency fCEO without any auxiliary laser.’ I asked Thomas Udemand Martin Weitz in our laboratory to witness and sign every page on April 4, 1997, since this mightbecome important for later patent applications.”– From the Nobel Lecture of Theodor W. Hänsch 2005

FREQUENCY DOMAIN - FREQUENCY COMB

2∆ϕ Phase ShiftTIME

The frequency of each mode can be written as fn = nfr + f0 . This equation maps two radio
frequencies fr and f0 onto the optical frequencies fn . The frequency comb can act as a ruler inthe frequency space once the two critical frequencies, the repetition frequency and theoffset frequency, are known and stabilized. The repetition frequency is readily measureablewith a photodiode and usually lies between a few tens of megahertz and a few gigahertz.

First Envisioned in 1997

SecondHarmonic
Generation2(nfr + f0 )1999

FREQUENCY

2000

Beat Notef0 =2(nfr + f0)-(2nfr + f0)

speed of light in vacuum
c =299,792,458 mslight velocity
c = f ⋅λpulse period
T= 1froffset frequency
f0 = ∆ϕT

bandwidth conversion∆f = c2 ⋅ ∆λ e.g. at 633 nm ∆λ = 1 nm
corresponds to ∆f = 748 GHz
λ2001

frequency comb equation
fcw = n ⋅ frep ± f0 ± fbeat

2005

QUANTUM TECHNOLOGY FOR THE NEXT CENTURY
Menlo Systems’ complete solution for optical lattice clocks
ORScwlaser

sub-Hz linewidth optical output

clocklaser

FC1500-ULNplus Optical Frequency Comb
accuracy: 1 x 10-18 (τ >100 s); stability: 5 x 10-18 in 1 s, 5 x 10-19 in 1000s;
operational range: 500 nm to 2 μm

Sr lattice clock87

P1

first stage cooling

λ=461nmP1

3P03clock transition
λ=698nmsecond stage cooling

λ=689nm
1FC1500-ULNplus

2017

ORS Ultrastable Lasers
state-of-the-art linewidth <1Hz and stability <7 x 10-16 Hz

1

repump coolinglaserlaser

2014

S02019Optical clock transitions for the most accurate definition of the second
strontium clock transitionf = 444.779 THz λ = 674.025 nm
absorbing ion 88Sr+, 5 2S1/2 – 4 2D5/2

calcium clock transitionf = 455.986 THz λ = 657.459 nm
absorbing atom 40Ca, 1S0 - 3P1, ∆mJ = 0

strontium lattice clock transitionf = 429.228 THz λ = 698.446 nm
absorbing atom 87Sr, 5 1S0 – 5 3P0

ytterbium lattice clock transitionf = 518.296 THz λ = 578.420 nmabsorbing atom 171Yb, 6 1S 0 – 6 3P0

First Absolute Optical Frequency Measurement
The measurement of the hydrogen 1S–2S transition frequency using an opticalfrequency comb yielded a new value accurate to 1.8 parts in 1014, surpassing all earlier
optical frequency measurements by more than an order of magnitude.

First Demonstration
With a few weeks difference, John L. Hall at JILA and the team of Hänsch at the Max
Planck Institute for Quantum Optics demonstrated the first octave-spanningself-referencing laser frequency comb.

Menlo Systems
Menlo Systems was founded with the aim toaccelerate the advancement of optical technology for precision measurements and theirapplications from the table tops of research laboratories to standard use incommunication and high technology industries. The first commercial system based on aTi:sapphire laser was delivered in 2001.

Nobel Prize
Hänsch and Hall were awarded the Nobel Prize for their contributions to thedevelopment of laser-based precision spectroscopy, including the optical frequency
comb technique. Menlo Systems released the first fiber based Optical Frequency Comb.

Figure 9® Mode Locking Technology
Menlo Systems’ proprietary figure 9® mode locking technology enabled a newgeneration of reliable, robust, and long term stable metrology equipment forapplications outside the optical laboratory.

Compact Optical Frequency Comb
The fully autonomous SmartComb in a 19” housing makes Hänsch’s 2001 vision of acompact and portable Optical Frequency Comb reality, a mile stone for field applicationsin frequency metrology.

World’s Most Precise Optical Frequency Comb
With the FC1500-250-ULNplus Menlo Systems provides an Optical Frequency Comb witha demonstrated accuracy at the 20th decimal place.

APPLICATIONSImage courtesy of Christian Lisdat, PTB, Germany

Optical clocks
The formal SI definition of the second is currently the9,192,631,770 multiple of a transition between two
hyperfine states in a cesium atom. With an accuracyof one part in 1016 latest generation cesium clocks err
by less than one second in 30 million years. By
increasing the oscillation frequency from themicrowave to the optical region of theelectromagnetic spectrum the accuracy is improvedby several orders of magnitude. Today’s mostaccurate optical lattice clocks with a precision in therange of 10-18 reduce the error to less than 1 second in
15 billion years, the estimated age of the universe. In
the hunt for the highest precision, optical frequency
combs are an indispensable tool for the comparisonof different optical clocks. They provide the gear forthe conversion between optical and microwave
frequencies in order to make them measurable. Withan accuracy and stability of 10-18 or better theypresent a suitable clockwork operating in the testingof physical theories or in relativistic geodesy.

Dimensional metrology

High-resolution spectroscopy

Frequency metrology in space

According to the SI definition, the meter is the lengthof the path traveled by light in vacuum during a timeinterval of 1/299,792,458 of a second. In a practicalrealization of the meter, a stable metrology laser withan accurately determined frequency is used toconvert its wavelength into a path length by meansof optical interferometry. Besides uncertainties
arising from the interferometer resolution and therefractive index determination, the uncertainty in thelaser frequency is limiting the accuracy of the length
measurement. Since an optical frequency comb
allows for a direct and absolute frequency
measurement with highest accuracy, this uncertainty
is decreased to a non-relevant value in the length
determination.
Cumbersome
periodicintercomparison campaigns of the optical laser
frequency used in different national metrology
laboratories have become obsolete.

Precision laser spectroscopy of atomic transitions is
the most powerful tool for accurate testing ofphysical theories and for determining the values andconceivable drifts of fundamental constants.
Sophisticated techniques for laser stabilization andsample preparation allow for probing of ultra narrowtransitions with smallest systematic error andpotentially very high relative accuracy. Theseexperiments naturally require the comparison of theprobing laser light either against some opticalreference or against the SI second realized by atomic
clocks. Optical frequency comb synthesis is theenabling technique for this comparison, ensuring
highest spectral purity in the transfer of the reference
stability to the spectroscopy laser. The advantage ofthe several hundred thousand ultra stable andprecisely tuned cw lasers operating at once in afrequency comb also facilitates experiments withsensitivity for the tiniest amounts of molecules in thegas phase, such as performed e.g. for atmospheric
trace gas monitoring.

State-of-the-art optical frequency combs are
qualified for operation under microgravity andvacuum conditions, which are essential requirements
for their mission in space. Satellites flying information need to hold their relative position
accurate to few microns. The European Space Agency
is investigating frequency combs as a unique
technology to measure distances of several hundred
meters with micrometer and even nanometer
accuracy. Likewise global navigation systems willprofit from increased precision of their on-board
atomic clocks, while space-born or lunar
observatories would enable high resolution
astronomical spectroscopy free of atmospheric
impact such as absorption, blurring, wind loading orvibrations. In fundamental research experiments
optical frequency combs perform absolute frequency
measurements on space missions probing theequivalence principle.

Image courtesy of Baxley/JILA

Molecular fingerprinting in
the mid-infrared
Rotational and vibrational transitions of molecules
are energetically located in the mid-infrared region of
the electromagnetic spectrum. By exactly
determining position and intensity of theirabsorption lines, molecular species and theirconcentrations within a mixture are unambiguously
identified. The accuracy and sensitivity of such
spectroscopic measurements were limited by the lackof suitable light sources in the past. Optical frequency
combs covering a broad spectrum extended into themid-IR region enable novel spectroscopic
approaches for the direct and absolute measurementof molecular fingerprints. Methods such as Fouriertransform spectroscopy or cavity enhanced detection
achieve the high sensitivity necessary for the analysisof chemical trace amounts. Dual comb spectroscopy
further enhances sensitivity and precision, at thesame time decreasing the recording time and therequirements for optical detectors.

Image courtesy of ESO/B. Tafreshi (twanight.org)

Astro-combs
The extremely accurate and fine grid of the frequency
ruler provided by an optical frequency comb is usedtocalibrate
highresolution
astronomical
spectrographs. With the laser lines superimposed on
the star's spectral lines the latter are readily measured
with the accuracy of an atomic clock. At the sametime, uncertainties from practical spectroscopic
experiments are eliminated. As the calibration isabsolute, even if different combs are used to calibrate
spectra from different telescopes at different epochs,
those spectra can be compared. Astro-combs enable
observations that previously were unachievable, suchas the quest for exoplanets or the characterization ofquasars. They also facilitate the investigation whether
the expansion of the universe is accelerating. Such a
direct observation could be decisive on whether or
not dark energy, together with general relativity,
constitute the proper model, or if we have to seek out
new explanations.

PRECISION IN PHOTONICS. TOGETHER WE SHAPE LIGHT.

MenloSystems
Image courtesy of ESA

Menlo Systems is a leading developer and global supplier of instrumentation for high-precision metrology.
If you want to find out more about our frequency comb technology call us at +49 89 189 166 0, email us atsales@menlosystems.com or visit our website www.menlosystems.com.