1. INTRODUCTION

An OSA Editor’s request was for me to write on the topic “Why did it take so long for the laser to be invented—since Einstein had discussed stimulated emission some 40 years earlier?” My initial reaction was that this only represents a “textbook author’s” or “theoretical scientist’s” interests and outlook. However, soon I saw in it the chance to express reality—the clear “reality” (according to an experimentalist) is about the slow march of enabling technologies and concepts. I believe real learning comes from the hand–eye–mind coordination used in the lab. There simply is a limit to our imagination—we can only mentally jump so far. Even jigsaw puzzles take some time in any case, and in the lab we have not even yet invented the pieces! A person impatient with the slow pace of history would be asking us to design working laser systems with components and capabilities that still needed clarification (perhaps by presentation on/discussions over a few napkins in a beer garden) and then great ingenuity to create the vast array of facts that are nowadays known to young people still in high school. For example, after amplification was shown by deForest’s 1908 radio tubes, Armstrong, recognizing that evacuation improved the tube’s gain and lifetime, soon had oscillation and oscillators in 1915. The (almost) next step for a modern scientist would be to implement the gain with some semiconductor device, or even with some quantum transitions in a more dilute distributed medium. In fact, there were many, many intermediate steps in the radio and microwave domain, but mostly we must jump over them here, and pick up with quantum system amplifiers.

It seems that Charles Townes’ park-bench inspiration that quantum systems can provide gain had been possible for years, but when it happened [1] in 1951 it was so novel that he got the 1964 Nobel Prize, along with Basov and Prokhorov, who independently invented an equivalent maser scheme. And it is fair to note that the young Professor Townes was advised by his world-famous seniors at the university that he was wasting his time trying to build a quantum-based oscillator, but, just a few months later, in 1954, his group did achieve oscillation. This was nearly 40 years after we had Einstein’s theory that included stimulated emission, and we also had radio oscillators. It is also true that in the 1920s Ladenburg and colleagues had considered the connection between atomic populations and optical absorption. But for brevity we jump to near the 1940s, missing the delicious issues of quantum theory, spectral lines, oscillator strengths, level populations, and lots of other good stuff. Atomic physics was progressing in the universities, but the progress in electrical technology was changing how people lived. Kids could even study their lessons after sunset.

The issues of WWII of course transformed the scene. The subsequent “Cold War” impacted the story of spectroscopic progress rather strongly, especially if one studied in Soviet Russia. There a “Doctor of Science” thesis was presented in 1939 by A. V. Fabrikant on his studies of optical properties of gas discharges, in which he had observed non-absorbing—even amplifying—spectral regions near certain atomic resonance lines. Later, in 1951, he was granted an “Author’s Certificate” for his visionary work, which basically suggested the gas laser concept [2]. But it almost seems as if the Soviet system did not grasp the scientific, commercial, or even future military significance that could develop from a light beam potentially emitted by Fabrikant’s device. Indeed, his work was premature [2] in the West as well, and the Nobel Prize for masers later went to Townes, Prokhorov, and Basov in 1964. This is a negative example of my designer concept for a researcher’s happiness—respect your peers, be loving to your family, and always be ahead of the field, but not too far ahead.

However, in the 1940s in the U.S., Europe, and the Soviet Union, the war and urgently needed RADAR developments ensured a focus on microwaves and their generation and propagation. This brought many technical advances about connecting an amplifying medium (a bunched electron beam) with an electromagnetic resonance in a klystron or magnetron resonant cavity, or in using a voltage-tunable electron beam in a traveling-wave microwave structure. Then the potential for radars with higher spatial resolution led to shorter wavelengths, and the remarkable backward-wave oscillators in the former Soviet Union, remarkable for being near-terahertz in frequency and of surprisingly high power levels [3]. There is a fantastic world of interesting history about microwave developments [4], sources, beam-forming antennas, etc., but our focus here is on the thread leading to modern lasers.

For the war, the developments were step by step: the radar spatial resolution requirement led engineers to think of rebuilding the 8 GHz systems with higher frequencies. A canonical step size of pi would of course be chosen. But water vapor resonances occur near 22 GHz, and are remarkably broadened at atmospheric pressure. So the new radar had a very limited range in cloudy weather, exactly when it was needed to perform well. But that discovery did lead Charles Townes and his brother-in-law, Arthur Schawlow, to look deeply into molecular spectroscopy, and we are all richer by way of that new subject and their wonderful book introducing the topic of Microwave Spectroscopy of Molecules [5].

Perhaps the next big event that we seniors and the vigorous athletes among us should be grateful for was the 1945 arrival of Nicolaas Bloembergen in Boston, where in Ed Purcell’s lab he set about measuring relaxation processes in nuclei being resonantly probed. And the equally important part, they published a clear and comprehensive paper, known as BPP [6]. Stimulated emission in nuclear magnetic resonance had been seen by Purcell and Pound, and, from a modern perspective, perhaps the maser idea was basically in the air after the WWII work where the resonator cavity and amplifying media were considered separately. After BPP, Bloembergen then also contributed decisively on the topic of coupled three-level quantum systems, and the possibility of maser amplification by suitable pumping. Ruby was found to be a good material for this application, and these low-noise microwave maser amplifiers gave a huge boost to radar range. Later they have been invaluable in radio astronomy. Then it almost seems that 40 years went by, with chemists using the splittings in such NMR spectra to work out very precise and complete models of various molecules. But later, Richard Ernst wondered about NMR in a maximally inhomogeneous magnetic field, and thereby invented a new and important form of imaging, now known as magnetic resonance imaging (MRI), which was recognized with the Nobel Prize in 1991. And it is well appreciated by us moderns with various pains and ailments.

The physics and optics community had walked away from further NMR research after 1958 due to the invention by Schawlow and Townes of a workable scheme for how to use optical gain of an inverted population, combined with some mirrors to trap the spontaneously emitted light [7]. The multi-pass gain and saturated oscillation amplitude can now be explained to the parents of the precocious primary school kids. But it enabled a really giant breakthrough in 1960 when Theodore Maiman at Hughes Research pursued dilute chromium ions in sapphire as a potential laser medium. “Experts” knew the main problem would be that one had to supply one pumping photon per ion in the crystal just to bleach the red absorption, and then add even more pumping to produce a population inversion and hence gain. After evaluation, Maiman decided to try a ruby with very low chromium concentration, and also to put massively more energy into a xenon-filled flashlamp than would be used in its intended application in photography. The flashlamp’s spiral form provided a natural interior axial space for the ruby rod, which had reflecting coatings on the rod’s end faces. I believe an essential aspect leading to Maiman’s ruby laser success was his lack of respect for the safety limits of the discharge lamp, and that let him be the first person to see the light from a laser [8]. This has led researchers following his path to need occasional afternoons off work, following the incredibly loud explosion and heart-rate test induced by a several kilojoules lamp explosion in the lab.

So, to pick up the Editor’s question about why the laser took so long, it was not that we and our predecessor scientists were just playing video games in the parlor; there simply were many steps to achieve and concepts to expand and to “Velcro” together. You cannot really design until you have a sense of the possibilities. And of course WWII took much of our research team off to other duties.

2. EVEN EARLY RUBY LASERS HAVE APPLICATIONS

Actually, even though dilute, the chromium ions in Maiman’s ruby crystal could store some fraction of a joule in the inverted population, which would then be emitted in a beam of light, lasting nearly a millisecond, more or less as long as the pumping light was brighter than some threshold value. While Maiman could demonstrate his laser’s power by burning a hole in a Gillette razor blade, it was later shown by Professor Schawlow [9] that this emitted pulse of light also could “usefully” vaporize the ink from Washington’s image on a U.S. $1 bill, and thereby erase an eye, for example. Certainly we must note that only seven months after Maiman’s ruby laser, laser action was demonstrated on a continuous basis by a research group at Bell Labs, which had for about four years been working hard to see it. Ali Javan’s invention [10] of the gas laser is interestingly covered in the article by Jeff Hecht [11]. The application of Javan’s ideas for lasers and their heterodyne testing, and finally the idea of the frequency chain, and its successor, the optical frequency comb, is the material covered by the present author in 2000 [12]. But now, a few more stories about pulsed lasers.

The pulsed ruby laser was immediately the hottest topic ever, in several senses, and this quickly led to improvements. One of the really interesting next developments was also from the research group at Hughes. Their colleague, Robert Hellwarth, had the idea to use an electro-optical shutter in the ruby laser cavity to temporarily prevent the ruby from oscillating, and thereby let the excited state population rise to the maximum level provided with the flashlamp pumping pulse. Then, at the moment of maximum gain, an electrical pulse to the shutter would make the optical feedback path available, and the intracavity field would begin circulating back and forth in the cavity, leading to a stair-step succession of amplified intensities, finally providing perhaps ¼ joule of laser output in the last 20 or 30 ns [13]. This power of $\sim 10\mathrm{mW}$ was unprecedented, and came to be known as a “giant pulse.” Cavity loss modulation was called “$Q$-switching.” The study of optical nonlinearities of course blossomed with such a powerful level of excitation. However, the nonlinear epoch really had already jumped forward by the introduction of “designer” phase-matching, by Joe Giordmaine at Bell Labs. He realized that for frequency doubling the ruby light, the normal dispersion with wavelength could be cancelled in suitable birefringent crystals, so that phase-matching could persist over the full crystal length [14]. In the same issue of Phys. Rev. Lett., Paul Maker and his colleagues demonstrated the “Maker fringes” in the second harmonic conversion [15], arising from variation of the phase mismatch as the crystal was rotated. In 1962 Bloembergen and Pershan produced a systematic theory of optical harmonics, which emphasized the symmetries involved in the process [16] and the role of interfaces.

3. NEW KIND OF “LASER” LIGHT GENERATION

At that time there were large area vacuum photodiodes available, designed for a previous national program that resulted in occasional underground strong fast bursts of light (and neutrons). With a cathode diameter $\sim 3\mathrm{cm}$ and a polarizing voltage above 2 kV, peak photocurrents in the low ampere range were linearly available, with sub-nanosecond risetime. Several groups noticed that the diode’s two electrodes were perfect for the laser community—on the collector plate we put a terminated coaxial cable and a fast oscilloscope to view the time-dependent laser power as a fast negative current pulse. On the photocathode, we used a series resistor of some 50 kOhms to the negative HV power supply—and, critically, a coaxial fast capacitor to ground from the photocathode that would have its charge state depleted somewhat by the 30 ns of photocurrent, allowing one to read out (via ac coupling) the fast-rising, slow-decaying pulse of the charge, whose peak mapped the light-pulse’s energy. Of course lab calibration will always be an interesting topic, and laser pulse calorimeters of various designs were developed at NBS and elsewhere. But immediately, a problem arose: when the calibration of the photocell’s electrical amp-seconds per joule of detected light was performed with the regular laser, sensible results were obtained. But if the calibrations were done with the $Q$-switched pulse, the calorimeter usually indicated more energy than the photocell system. Why would that be? It was not nonlinearity. Instead, it was that the very strong light inside the ruby laser cavity—and its nitrobenzene-filled Kerr cell—was exciting stimulated Raman transitions in the liquid. So perhaps a tenth of the light was now emitted, not at the ruby’s 694.3 nm, but at 766 nm, beyond the sensitive range of the vacuum photodiode’s cathode response. My NBS colleague, Don Jennings, and I were really glad to learn of this explanation from the Hughes group, which had detected the offset line spectroscopically [17].

So a puzzle turned into an opportunity: the laser community went from having the single laser wavelength of 694 nm to having lots of red-shifted wavelengths to choose from, according to putting our giant pulses into cells of nitrobenzene, or benzene, or toluene, or carbon tetrachloride, or acetone, etc. Charles Townes and his student, Elsa Garmire, made some nice theoretical discussion of this stimulated Raman scattering effect [18], showing how the mostly coherent laser field and a vacuum field, separated by the Raman excitation energy, gave rise to a cross-term that could virtually excite the molecular vibration state, and lead to optical gain at the Stokes-offset frequency. After a few quanta are scattered, there is a coherent IR vibration superposition state associated with the Raman excitation, with each newly scattered laser photon adding excitation to the vibration. Then one enters a domain of parametric modulation, where one just sees a vibrating index of refraction that makes frequency sidebands on the applied laser light. One of the consequences is that when light has already been shifted once, it can interact with the coherently modulated index of refraction and become scattered again. So multiply-Stokes-shifted light has a unique offset frequency, in contrast to the spontaneous Raman scattering case, in which different transitions to various accessible molecular levels will be displayed.

Of course a vibrating index of refraction should allow scattering of laser light toward higher frequencies as well. These anti-Stokes Raman lines were not initially prominent, but as the lasers became more powerful one could see interesting things, even without focusing, or anyway with softer focusing. At this point one was struck by the fantastic colors on display, but displayed in rings around the original laser beam. This geometrical effect arises because of dispersion in the liquid’s index of refraction, which causes the phase-matching directions associated with the coherent buildup of the scattered anti-Stokes field to have larger and larger cone angles as one considers the higher AS sidebands. To my knowledge, these rings were first described by Robert Terhune’s group of Ford Research Labs. Boris Stoicheff was collaborating with the Townes group on the theory. I had just gotten my $Q$-switched ruby laser to operate in nearly single spatial mode when a visitor to Boulder, Prof Hiroshi Takuma from Tokyo, came by JILA for a discussion of his “off-axis resonator for stimulated Raman oscillation” [19]. In a delicious afternoon’s work, we took this color picture of the stimulated Raman rings with the ever-present Polaroid camera, and that epoch’s approximation to color fidelity [20]. See Fig. 1.

 

Fig. 1. Anti-Stokes rings from ruby laser scattering in nitrobenzene. The angular sharpness of the emitted rings shows that no small filaments were being formed by our nearly single-mode pulses. Later we recorded anti-Stokes lines beyond the doubled ruby’s frequency. These unpublished experiments were performed in collaboration with H. Takuma, who at that time was also a young scientist affiliated with NBS.

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A. Using Laser Sources for Atomic Physics

In what might be the first use of laser light in atomic physics, a JILA group wished to observe nonlinear optical effects on atoms. The idea was to measure the photodetachment of the weakly bound last electron in the Iodine negative ion, ${\mathrm{I}}^{-}$. Lewis Branscomb volunteered his crossed negative ion beam machine, and the ruby laser beam experiment was set up in his lab. Some electrons were indeed detected, and after many calibration steps, the two-photon cross-section was deduced. A first theoretical model, based on plane wave representation of the electrons, gave a result tenfold lower than the observed value [21]. A more realistic calculation was better [22]. Even 23 years later, the experiment was central to resolving the model differences in theoretical work over the role of electron correlations [23].

4. CAN THERE BE EVEN MORE POWER?

You probably already know how this pulsed laser story has evolved. More joules output would be more fun, but the larger size scale means it takes longer for the active system to cool down. And, since it begins to be really expensive if optics are damaged, it takes a little more time to be sure about just what the conditions are. In the Garmire presentation [20] there is an interesting discussion of the formation of “filaments.” Finally, now, about 50 years later, the control of laser pulse shape and duration and timing has become so excellent that one group has built a 192-beam facility in Livermore, California, where more than 1 MJ of optical energy can be delivered on target to a fusion-reaction test pellet [24].

So, like the Editor’s original question of “why did the laser take so long to happen,” we can ask, “why did these high intensity effects take so long to be controlled?” Well, the truth is they were recognized rather early on. Even at my lab’s power scale, if the cavity losses were minimized, the $Q$-switch pulses would develop more rapidly—and be more powerful—and, all too soon, our lab’s very-best-ever ruby rod would be massively damaged—and then have dozens of precisely aligned tubes with a series of internal micro-bubbles. The dreaded filaments! Visually, it looks milky inside. The increase of refractive index with power has led to self-focusing into a number of filaments, and in one very expensive event! Consider that $2500 ruby rod and its perhaps 15 ns pulse duration; that is 166 giga-dollars/s as the spend rate. Compare that with the U.S. GDP, which is “only” about 0.5 M$/s. My best ruby ever, destroyed in nanoseconds at a spend rate 340-thousand-fold greater than even the U.S. GDP rate! A very sad event! And definitely not something to be repeated, never twice in the same lab. (Except for some very well-funded laser fusion labs I have visited in overseas countries.)

5. INCREASING THE REPETITION RATE—NEW “CW” LASERS

Another highway for fun with pulsed lasers would be to have pulses of shorter and shorter durations, and with higher repetition rates. The development of solid-state lasers again had a wonderful surprise for the laser community: this same sapphire host that works so well with chromium doping is also marvelous when doped with titanium ions. It was discovered, again as a happy accident, that if the focusing adjustment of the Ti:sapphire laser is moved away from the ideal tuning for cw operation, there can be an abrupt transition to another state of efficient operation. Wilson Sibbett observed this effect [25], which was finally understood as a transition to a self-mode-locked domain of operation. Essentially, it arises when the cavity is detuned such that the laser beam is diverging slightly more after each pass through the resonator. Then there can be a regime in which a number of modes can be simultaneously operating, and will have a fixed splitting frequency between them. Their phases are self-organizing so that interferences of the multi-wavelength field lead to a longitudinal spatial aspect like a “bullet of light”! The high local intensity, when it is in the laser crystal, induces a Kerr-effect positive lens, sufficient that the transverse beam profile is stabilized, no longer increasing in size after each transit. This increase of the peak intensity is self-stabilizing, as too much focusing will also introduce added losses. (This is in contrast to the planar resonator case, where filament formation ensues.) The spectrum of the laser output abruptly broadens from a few modes to many many modes, thanks to the extremely fast response of the Kerr effect. Finally, the bandwidth is limited by the fact that any sub-portion of the multiple wavelength light can form a spatially limited packet of light, and, considering that the optical cavity has dispersion, the different sub-packets will arrive back at the gain crystal with different time delays, according to their wavelength. The equilibrium spectrum may be $\sim 50\mathrm{nm}$ wide. To broaden the bandwidth more, an excellent solution is to provide an adjustable intracavity physical length, differential according to color, so that all the multiple potential light packets can have the same delay. A beautiful solution was introduced by Fork et al. [26] with two compensating prisms, so that the light was spatially separated according to wavelength when entering the second prism, and thus traversed more or less glass. (Well, actually, it was fused silica, or even ${\mathrm{CaF}}_2$ because, while the dispersion of glass was larger, it was too wavelength sensitive.) The light after prism 2 was retroreflected by a plane mirror, so after double-passing the prism pair, one has produced a differential path-delay with color, depending on the separation of the two prisms. A refinement was to put the retro mirror on a twister PZT, so that a variable delay of some tiny fraction of a wavelength could be controlled electrically. This maps into a fine control of the pulse repetition rate. When optimally adjusted, such a femtosecond titanium-doped sapphire crystal laser (fs laser or Ti:sapphire for short) produces pulses with a few tenths of a watt average power, but the pulse duty factor is near $1:{10}^6$. So the internal cavity peak power is actually several megawatts peak, traveling through the $\sim 12\mathrm{\mu m}$ focal diameter in the crystal. That power, say 3 MW, passing through something like $22{\mathrm{\mu m}}^2$, corresponds to an intensity $\sim 1.3\times {10}^{16}\mathrm{W}/{\mathrm{m}}^2$. This is a strong electric field, only an order of magnitude below the fields that hold the crystal together. No wonder there is a noticeable Kerr-lens effect!

After the existence of Kerr-lens self-mode-locking became known, it was possible to extend this idea to other laser ions in other crystal hosts. But the broad bandwidth of the optimized Ti:sapphire laser ($\sim 750–900\mathrm{nm}$) also represents a really good hint for how to proceed further—this time with materials outside a laser cavity. We just need a slightly smaller mode in the material, and some way to organize such that all the generated colors propagate at the same speed. This would be a purpose-designed special optical fiber. Then this extreme phase-modulation activity, with a modulation index of a few units, can successively broaden the spectrum, to the point where dimly visible red light entering into the fiber is converted into rainbow light at the exit, extending beyond our visual range in both directions. This is the so-called Magic Rainbow Fiber, described by Jinendra Ranka and his colleagues in 1999 [27], and was the last key element for beginning the age of the optical frequency comb. Interestingly, this “holey” fiber had been proposed in 1991 by Philip Russell, and had been developed by his Photonic Crystal Fibers group exactly for its “designer” choice of dispersion curves, potential broadband single-mode transmission, and strong polarization filtering capabilities [28]. But the fs rainbows had to wait until the late 1990s when fs lasers became commercially available.

So on the question of why it takes so long, I believe it is again that the needed technology and theoretical understanding were not available. At least it was a long time before the wonderful progress of the pulse laser community got its proper recognition. When my ruby burned in 1965 or 1966, it seemed to be time for “something completely different,” as they now say. (Of course it had been fun to focus that almost single spatial mode laser with a good 10 or 15 cm lens—the sound of the air spark left one’s ears ringing for several days. Like a large caliber pistol at the firing range!) What was needed was some way to have a repeated, stable kind of pulse. It does not need to be so energetic, because most of the nonlinear things to study care more about power rather than energy. So instead of ½ joule once in 10 min, could we please have something at 10 Hz? Maybe a watt average power. But wouldn’t it be better to have a 100 kHz repetition rate, since then the environment for my experiment will be pretty stable between pulses? A natural next rate is the c/2L cavity repetition rate, perhaps 100 MHz. But certainly we cannot expect even millijoules per pulse. How about 10 nJ per pulse at 100 MHz? That is 1 W average. Now it makes a real difference if your spectroscopy is linear or quadratic in power. Lots of the new phenomena are nonlinear, so we would like really short pulses, such that the associated peak power would be not a single watt, but something $\sim \mathrm{kW}$ scale, for example. Still, perhaps we citizens of the cw laser metrology community can be forgiven for not being up to date about how our pulse-admiring colleagues were coming along. Left to our own devices, the best we could do was Kourogi’s rf phase modulator in a cavity, with the microwaves and cavity length synchronized so that all the frequency-shifted components—the multi-generation children of a single frequency-shifting passage—could remain synchronized, and continue jumping away in frequency [29]. The optical output was a comb of optical frequencies, with mutual coherence assured by the low phase noise of the microwave source. Of course, after hundreds of passes the phase noise is hundreds of times larger. Larger phase noise converts more carrier power into noise sidebands, and eventually there is just broadband spectral noise remaining. This is the basic reason the synthesis from the rf time/frequency standards was so slow in achieving the phase-coherent contact between our stable optical frequency standards and the rf standards at the NBS. Eventually 12 intermediate optical-style oscillators were used to perform the multiply and filtering needed to build a frequency chain [30]. This coherent connection from microwaves to the optical domain was achieved first in 1972, and extended finally to visible light [31] in 1982, based on a suggestion by Venia Chebotayev [32]. Teams from many nations’ metrology labs contributed to the technology and electronic tricks needed to have a traceable and precise connection between rf and optical domains. The actual measurement of light frequency—when its wavelength was known—initially could be seen as a measurement of the speed of light. Many laboratories contributed their own measurements, and in 1983 it was possible to invert this process: let us adopt a conventional number such as 299,792,458 m/s as the exact, defined value for the speed of light. Then we can use any/all of these different (measurable) lasers to represent accurate realizations of the International Metre [33]. But the frequency-measuring business was expensive, and needed a team of specialists to maintain the chain of lasers that extended the rf frequency standard to known multiples and, finally, even to visible light.

6. COMB ARRIVES

But earlier I was describing that another community of laser experts was making lasers that were faster and spectrally vaster, and that some effort was being applied to have them function stably. One could even servo-control the repetition rate, so that it was stable and accordingly could be known in terms of the Cs-clock definition of the second. This process was begun already in 1978 by Ted Hänsch’s Stanford group, using the synch-pumped mode-locked pulses of a dye laser to introduce the technique of frequency comb spectroscopy [34]. Then, finally, came the wonderful Ti:sapphire laser, and then the incredible Magic Rainbow Fiber from Bell Labs, which delivered synchronously pulsed light with over a factor of two in fractional bandwidth! Theoreticians thinking about such repeating pulses recognized the connection with Mr. Fourier’s ideas, but there was a bit of a new factor at work. Because the pulses are so brief, they actually contain only a few cycles of the electromagnetic field. So then it might make a difference in a nonlinear experiment whether the underlying optical cycle reaches its peak exactly when the envelope’s peak is achieved. Also, there could be a slow drift of the cycle’s peak under the envelope, from cycle to cycle. This repeating phase slip per cycle came to be known as the carrier-envelope offset phase. Impressively, the 1978 Stanford thesis of J. N. Eckstein already contained this analysis. So even with the newly added bandwidth factor of $\sim 1$ E5, this new optical source was a lot like Mr. Fourier had foreseen: a vast comb of frequencies, all separated by the same frequency interval. A little algebra will show the comb’s frequency splitting is exactly the pulse repetition rate. And the actual laboratory waveform gathers optical phase basically in this way, $N*f_{\text{rep}}$. However, there is the additional carrier-envelope offset phase slip per each pulse interval, $\mathrm{\Delta }\mathrm{\Phi }$, which will just appear as an added carrier-envelope offset frequency, $f_{\text{ceo}}=\mathrm{\Delta }\mathrm{\Phi }*f_{\text{rep}}$, that is added to all the comb lines. So with the start of a new millennium, the marvelous Ti:sapphire laser was now invited into all frequency metrology labs, and we cw laser folks got to see a vastly broader universe: any comb line is described by its order number and two frequencies. The simple formula is $f_{\text{optical}}=N*f_{\text{rep}}+f_{\text{ceo}}$, and this formula gives the optical frequency to 16 digits accuracy and more, in spite of having the integer $N\sim 1\mathrm{E}6$ factor in the formula. It seems absolutely incredible, but the comb formula has been tested to be valid to 19 digits [35]. [However, it is important to note that until we change the definition of time (and so its inverse, frequency), absolute frequencies cannot be stated to better than $\sim 3\mathrm{E}-16$, which is the apparent accuracy limit of the atomic-fountain Cs clocks in realizing the as-defined SI second.]

Now, compared with the days of the dinosaur frequency chains [36], with the comb we can go between the optical and the rf frequency standards in a single step. But before the comb epoch, this was not possible because of the multiplied phase noise: so how can that connection be possible now? The answer is another epoch-defining physics fact: the optical frequency reference system can have much less phase noise to start with (compared with any rf source), and the initial comb from the fs laser has essentially tight coupling from one end of its spectrum to the other. (Otherwise, some straggling color will be arriving at the Ti:sapphire crystal just after the main “bullet” has passed, and the necessary added focusing lens power will not be available. When the big pulse is entering the crystal, there is a huge change of integrated refractive index during the few-cycles event. So this phase chirp can feed power into the front or the back of a potentially straggling packet formed by frequencies near the edges of the interacting bandwidth. In this way synchronization is preserved, until finally it cannot be. Indeed, the comb power per unit bandwidth drops quite abruptly at the edge of the comb’s bandwidth.)

It is worth noting how Mr. Fourier’s limits are still present, but here are a little different. We used to carelessly speak that a pulsewidth that was narrow meant a frequency width that was broad. But that single pulse is not our present case: we have a continuing supply of essentially identical pulses coming from the laser, and with a timing even more regular than any clockwork tied to a National Laboratory frequency standard! If we measure wisely with this train for 1 s, we deserve to have a 1 Hz imprecision, at the most. (Actually the S/N with the combs is so high one can have 12 digits in 1 s, at least, not just the ${10}^8$ corresponding to the number of pulses emitted by the laser. And because the laser is so stable, the factor can be much larger.) Every one of the comb’s spectral lines can potentially carry a few millihertz kind of linewidth, limited by the measuring duration if we have an ideal laser. So this new kind of “continuous” laser is actually off most of the time, but has very strong temporal peaks, and offers a frequency definition fully as precise as would be possible with a truly continuous, single frequency of light. This comb is really something like 1 million lasers of millihertz linewidths, all mutually collimated and synchronized.

7. COMB’S ARRIVAL—WHAT SET THE DATE?

So why did the optical comb come when it did? In this case, after the 1978 comb introduction by the Hänsch and Chebotayev groups, the potential metrological users of such a technology were primed for its use, and were busy trying out various temporizing and partial solutions put together from their own tool chests [37]. The breakthrough came because an entirely different cohort of laser scientists was pushing to get higher peak powers and shorter pulses for their own purposes, such as pump-probe experiments with femtosecond time resolution. And abruptly, the bandwidth-expanding Magic Rainbow Fiber was available, because a small community of optical fiber designers was checking what kind of dispersion controls and what bandwidths could be carried single-mode in fibers of novel design. By designing fibers with internal microstructure, the optical core does not carry all the light. Indeed, a different fraction of evanescent power would be outside the main solid core, depending on the wavelength, and so could interact with the structure components in a wavelength-sensitive manner. In fact, wavelengths spanning a factor of 2 can have single-mode propagation, as obtained by the fiber design.

8. PROGRESS COMES IN JUMPS

So we can return to and expand the OSA Editor’s basic idea: it is really interesting to reflect more generally on this issue of how do the big technical jumps happen? Charles Townes has a nice reflection on the origin of the maser and “how the laser happened” [1]. For the frequency comb, it may seem remarkable that the U.S. produced tens of thousands of BC-221 frequency-measurement sets (based on rf combs) for their armies in Europe in the context of WWII. I believe the issue was secure information transfer within the local area of combat. The ability to measure frequency quite accurately before going on-air would have made it feasible to have pre-arranged low-power radio meetings at, e.g., 07:00 hours, and for the troops of one team to be bidirectionally informed about the local circumstances. Another international team’s model was to have a superbly effective encoder/decoder system. However, we can see that its strategic value would be so great that the use would likely be in a non-reciprocal manner, from chiefs to workers, with the Enigma device itself safely far away from the contact zone. (I know nothing about the actual facts of this story—this is just a private way of understanding what I have seen and read about. One fact is that on eBay there are BC-221s offered with serial numbers above 24,000).

A second thing that is shocking about the technology/human interface is that long ago, in the late 1950s, I actually used one of these BC-221 Signal Corps frequency meters for my thesis. And I was well aware that there were frequency markers available at every 1 MHz mark, and separately at every 100 kHz mark. This system relies on having an rf comb from either of two precision crystal oscillators, in combination with a beautifully executed variable capacitor-based oscillator for the interpolation tuning at the sub-kilohertz level. I admired how powerfully that BC-221 enabled my NMR frequencies to be measured, before our lab received its first HP frequency counter, with its vertically organized digit lights for the user to sum up mentally, column by column.

Almost 40 years later, Kourogi demonstrated his EOM-generated optical combs [29], and their bandwidth extension by nonlinear optical means. But, as noted before, these optical combs were intrinsically limited because there were no rf sources of such low phase noise that one would have an optical sinewave signal after the required multiplication. So a working strategy would be a stable optical source to provide the main part of the frequency, and then feed that into Kourogi’s iteratively shifted cavity modulator system. This approach was used both in Boulder and in Munich in various frequency-measuring programs. That is a good tool, especially now that it can be done in chip-scale lithographically formed ring “fiber” oscillators [38].

9. LOOK TO THE FUTURE

As a brief look to the future, let us consider a new potential (BIG) technical business: this is a versatile accurate optical frequency source and measurement system with optical and microwave outputs/inputs.

We can measure frequency differentials, up to a terahertz or even a dozen, between optical lines. But lacking the classic frequency chain, there seemed to be no way to get the integer between optical and microwave sources before the optical frequency comb. This was so particularly before combs could have octave-scale bandwidth, which was believed necessary to separately learn the harmonic number and the frequency offset from the strict rf harmonic, the so-called carrier-envelope phase drift rate. More simply put, the carrier-envelope offset frequency, fceo, could be measured with an $f\text{-}2f$ interferometer [39].

So what are these elegant integrated comb generators? They work by having an input optical field resonating with a cavity resonance mode. Think of light going circumferentially around in little bulges formed onto a rod of low-loss fused silica. Power can be coupled into the whispering gallery modes by a focused tangential laser beam [38]. Resonant optical power builds up, and the vacuum noise field in a neighboring mode can interact with the strong mode to produce sideband amplifications, and ultimately full parametric splitting of the input field into blue and red coherent sidebands. And a moment later a full spectrum of sidebands exists, with its coherent spectral width ultimately limited by material and waveguide dispersion [38]. A few groups have shown it is possible to control the system’s progress through this rich behavioral landscape, to the place where there is but one offset frequency for the whole comb [40,41]. Of course there is dispersion across such a bandwidth, so one can wonder if the comb lines will necessarily have the original single frequency input line as a component.

I believe we are at an interesting place on the highway toward the convenient, practical—but accurate—measurement of optical frequencies. I expect we can agree it is not too meaningful to ask for a 14-digit measurement of an oscillator that is only stable to 11 or 12 digits. But it would be wonderful to have the comb technology available, ideally in some simplified way, to provide fast convenient frequency measurements at any level of resolution. So how could we do this?

Let us think about a stable optical source between, say, 3 μm and 300 nm wavelength. Its frequency is then 100 to 999 THz, say 300 THz, $\pm$ a factor of 3. We can make combs with repetition rates up to $\sim 10\mathrm{GHz}$ by a really short femtosecond laser, or much higher with a nonlinear monolithic resonator, such as that considered above. With such a 10 GHz repetition rate, the integer ratio of optical frequency/reference frequency is $\sim 1\mathrm{E}5$ $\pm$ a factor of 3. So one can see a plan developing in which we change the repetition rate just a bit, a mere 10 ppm, and that will change the integer label of local comb teeth by unity. Now, if we could measure that repetition-rate change a lot better than 10 ppm, would we be in a position to determine the exact integer number? And then one could give the actual optical frequency? Well, this is the idea, the dream, at least, but we first have to deal with two additional frequencies. One is just the actual beat frequency between the high comb’s tooth’s frequency and the actual optical source of interest—we can normally have much better sensitivity and measurement flexibility if this difference frequency is in the rf domain. For the hardest case, using the 10 GHz repetition rate (tooth spacing) we might have to deal with frequencies up to $\pm 5\mathrm{GHz}$, if we have no flexibility with the reference and target sources. For this, commercial photodetectors from the telecom business are available.

Another little issue about the combs is that it is the repetition rate of the pulses that we know, and Mr. Fourier maps that into the frequency separation of the comb’s teeth. We actually do not initially know what the offset frequency between harmonics of the repetition rate and the actual optical frequency comb teeth will be. This is again our carrier-envelope offset frequency, considered earlier. But here we have the perfect tools to explore this: a single frequency source to be measured and a narrowly but precisely tunable comb separation frequency (the repetition rate), and so a measurable family of beat frequencies between the stable unknown and the local family of a nearby comb’s teeth. Actually the repetition frequency and one of the beat frequencies—and its sign!—are the useful measurables. Now the best case for us will be if we have a knob that beautifully and unambiguously changes the fceo for the comb laser. I mean, only changes fceo. But as noted earlier, within the last year or so, something new has come into our tool box, in that it is possible to start with a cw reference laser and have a nonlinear ring resonator produce the comb sidebands. I think it does not need to be anything like an octave span. Following [40,41], let us shift the stable reference laser with an AOM, driven by a frequency synthesizer. We follow their procedure to ensure there is only one comb being generated. Then we can change the temperature of the nonlinear ring resonator, while keeping the resonance condition by appropriately changing the synthesizer for the AOM. Now we have a second optical beat frequency of the comb with the stable, unknown optical source, and the comb integer has been shifted by unity. And we have the capability to measure very precisely the new comb repetition rate. It seems that the number of unknowns is limited, but we can make any large number of precise measurements covering many orders, as we need. First we can guess/search for an integer order number that behaves properly. Then we need to figure out the fceo. But if we change the comb repetition rate thermally by a tiny amount, it seems reasonable to expect the comb’s fceo to have only a small change also. I feel that with experience and patience, it should be possible to find the integer and the fceo for one set of conditions. We also will want a few Taylor expansion coefficients relating changes of the fceo to repetition-rate changes of the comb. Certainly if one set up the canonical Ti:sapphire laser with the prism-pair dispersion controller, the swivel action of my PZT actuator might have a small impact on the repetition rate, while mostly changing the fceo. But if one displaces the light beam or the swivel mirror transversely, one can “dial in” a happy position where the fceo and frep changes are essentially orthogonal. Now we have an optical frequency-measuring apparatus almost suitable for an undergraduate laboratory!

10. SUMMARY AND CONCLUSIONS

So to conclude the story about why real progress takes such a long time from a theoretical first insight until there is a real working apparatus, I believe that it is the reality in the lab—the toolbox and the related theoretical constructs—that controls the research progress, and the rate of invention of “really cool stuff” that might transform the world. Of course, we do also need the big dream, AND the talented researchers to have this chance. What a pity it is that the U.S. businesses have folded up their research labs. Still, the legacy of Bell Labs may not yet be fully concluded: that was the best “idea factory” that I have ever heard about [42]. It is important that the creative scientists and engineers of that organization recognized that vacuum tubes could not be central to their future systems, and that the ultimate purpose of their research effort (in our current language) was to find the solid-state, miniature, wide bandwidth, and power-conserving amplifiers of the future, and to push communication to higher frequencies, and to develop more dense coding schemes, etc. Of course, at the time, they had no clue about which directions nature would make available. The direction to avoid was more clear than the exact objective.

So for some topics, mostly ones where technical infrastructure needs are minimal (or standardized), we can still plan and make good progress, and develop useful objects and capabilities. But there is no way to efficiently plan for seriously important breakthroughs—they come exactly from fresh contact between communities who have prospered from their independent development of tools for their own works. As an example, speaking for the precision metrology aspects of these laser works, who could have ever imagined that developing pulse lasers that can drill holes through metal and create bubbles inside glass could ever ever have any utility in precision measurements involving precisions of 16 digits, and beyond [43]? It seems to me that the big advances happen “accidentally” and when least expected. Planning and funding research programs to maximize the likelihood of small success is almost sure to succeed in giving us a least-publishable quantum of science advance. But it is also almost sure to deny us the epoch-changing breakthroughs such as lasers, optical frequency combs, and cellphones. Pity the young scientists of the future who set up Google filters so they will only read about things that are relevant to their current work and interests!

Apologies and a Warning Note to the Reader. Of course, the above words and opinions represent only my personal knowledge and so can only approximate reality. Your comments (in moderation) would be useful in refining this discussion: jhall@jila.colorado.edu.

I also hasten to apologize to colleagues whose cool advances have been misunderstood, poorly represented, or not even mentioned. Of course, these failings are mine alone.