Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies

Pseudo-type-II tuning behavior and mode identification in whispering gallery optical parametric oscillators

Wavelength tuning of conventional mirror-based optical parametric oscillators (OPOs) exhibits parabolically-shaped tuning curves (type-0 and type-I phase matching) or tuning branches that cross each other with a finite slope (type-II phase matching). We predict and experimentally prove that whispering gallery OPOs based on type-0 phase matching show both tuning behaviors, depending on whether the mode numbers of the generated waves coincide or differ. We investigate the wavelength tuning of optical parametric oscillation in a millimeter-sized radially-poled lithium niobate disk pumped at 1 μm wavelength generating signal and idler waves between 1.7 and 2.6 μm wavelength. Our experimental findings excellently coincide with the theoretical predictions. The investigated whispering gallery optical parametric oscillator combines the employment of the highest nonlinear-optical coefficient of the material with a controlled type-II-like wavelength tuning and with the possibility of self-phase locking.

Generation of five phase-locked harmonics by implementing a divide-by-three optical frequency divider

We report the generation of five phase-locked harmonics, f₁:2403  nm, f₂:1201  nm, f₃:801  nm, f₄:600  nm, and f₅:480  nm with an exact frequency ratio of 1:2:3:4:5 by implementing a divide-by-three optical frequency divider in the high harmonic generation process. All five harmonics are generated coaxially with high phase coherence in time and space, which are applicable for various practical uses.

Bandwidth-independent linear method for detection of the carrier-envelope offset phase

We propose and demonstrate a novel linear procedure for measurement of the carrier-envelope offset (CEO) phase of femtosecond oscillators. The technique is based on a Mach-Zehnder interferometer, a ring resonator, and a spectrograph. In this scheme, interference between subsequent pulses from a pulse train may frustrate the interference between identical pulses in the Mach-Zehnder, resulting in a modification of interference contrast depending on the CEO phase. We suggest spectrally and spatially resolved interferometry for robust detection of the fringe visibility. It is shown by numerical simulations and experimentally demonstrated that the visibility of such fringes uniquely depends on the CEO phase of the pulse train. Since the method relies only on linear interactions and does not require any nonlinear conversion, it allows characterizing the CEO frequency of mode-locked oscillators with virtually arbitrarily low bandwidth and power levels.

Passion for precision

Optical frequency combs from mode-locked femtosecond lasers have revolutionized the art of counting the frequency of light. They can link optical and microwave frequencies in a single step, and they provide the long missing clockwork for optical atomic clocks. By extending the limits of time and frequency metrology, they enable new tests of fundamental physics laws. Precise comparisons of optical resonance frequencies of atomic hydrogen and other atoms with the microwave frequency of a cesium atomic clock are establishing sensitive limits for possible slow variations of fundamental constants. Optical high harmonic generation is extending frequency comb techniques into the extreme ultraviolet, opening a new spectral territory to precision laser spectroscopy. Frequency comb techniques are also providing a key to attosecond science by offering control of the electric field of ultrafast laser pulses. In our laboratories at Stanford and Garching, the development of new instruments and techniques for precision laser spectroscopy has long been motivated by the goal of ever higher resolution and measurement accuracy in optical spectroscopy of the simple hydrogen atom which permits unique confrontations between experiment and fundamental theory. This lecture recounts these adventures and the evolution of laser frequency comb techniques from my personal perspective.

Defining and measuring optical frequencies: the optical clock opportunity--and more (Nobel lecture)

Four long-running currents in laser technology met and merged in 1999-2000. Two of these were the quest toward a stable repetitive sequence of ever-shorter optical pulses and, on the other hand, the quest for the most time-stable, unvarying optical frequency possible. The marriage of ultrafast- and ultrastable lasers was brokered mainly by two international teams and became exciting when a special "designer" microstructure optical fiber was shown to be nonlinear enough to produce "white light" from the femtosecond laser pulses, such that the output spectrum embraced a full optical octave. Then, for the first time, one could realize an optical frequency interval equal to the comb's lowest frequency, and count out this interval as a multiple of the repetition rate of the femtosecond pulse laser. This "gear-box" connection between the radiofrequency standard and any/all optical frequency standards came just as sensitivity-enhancing ideas were maturing. The four-way union empowered an explosion of accurate frequency measurement results in the standards field and prepared the way for refined tests of some of our cherished physical principles, such as the time-stability of some of the basic numbers in physics (e.g. the "fine-structure" constant, the speed of light, certain atomic mass ratios), and the equivalence of time-keeping by clocks based on different physics. The stable laser technology also allows time-synchronization between two independent femtosecond lasers so exact they can be made to appear as if the source were a single laser. By improving pump-probe experiments, one important application will be in bond-specific spatial scanning of biological samples. This next decade in optical physics should be a blast!

Standards of Time and Frequency at the Outset of the 21st Century

After 50 years of development, microwave atomic clocks based on cesium have achieved fractional uncertainties below 1 part in 10(15), a level unequaled in all of metrology. The past 5 years have seen the accelerated development of optical atomic clocks, which may enable even greater improvements in timekeeping. Time and frequency standards with various levels of performance are ubiquitous in our society, with applications in many technological fields as well as in the continued exploration of the frontiers of basic science. We review state-of-the-art atomic time and frequency standards and discuss some of their uses in science and technology.

Optical frequency metrology

Extremely narrow optical resonances in cold atoms or single trapped ions can be measured with high resolution. A laser locked to such a narrow optical resonance could serve as a highly stable oscillator for an all-optical atomic clock. However, until recently there was no reliable clockwork mechanism that could count optical frequencies of hundreds of terahertz. Techniques using femtosecond-laser frequency combs, developed within the past few years, have solved this problem. The ability to count optical oscillations of more than 1015 cycles per second facilitates high-precision optical spectroscopy, and has led to the construction of an all-optical atomic clock that is expected eventually to outperform today's state-of-the-art caesium clocks.

Optical frequency synthesizer for precision spectroscopy

We have used the frequency comb generated by a femtosecond mode-locked laser and broadened to more than an optical octave in a photonic crystal fiber to realize a frequency chain that links a 10 MHz radio frequency reference phase-coherently in one step to the optical region. By comparison with a similar frequency chain we set an upper limit for the uncertainty of this new approach to 5. 1x10(-16). This opens the door for measurement and synthesis of virtually any optical frequency and is ready to revolutionize frequency metrology.

Efficient continuous-wave ultraviolet generation in LiB3O5 and RbD2AsO4

We have demonstrated two continuous-wave nonlinear processes: third-harmonic generation (THG) of 1064-nm radiation with a lithium triborate (LBO) crystal, and second-harmonic generation of 696-nm radiation in deuterated rubidium dihydrogen arsenate. With 34 mW of 1064-nm and 25 mW of 532-nm radiation incident upon the LBO crystal, as much as 60 nW of third-harmonic power has been produced. We present the characteristics that optimize the production of nonlinear power in this sum-frequency generation process. In the second experiment, 15 nW of radiation at 348 nm was produced with 9 mW of 696-nm incident radiation. Both processes will play an important role in the new generation of optical synthesis techniques.

Measurement of the hydrogen 1S- 2S transition frequency by phase coherent comparison with a microwave cesium fountain clock

We report on an absolute frequency measurement of the hydrogen 1S-2S two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in 10(14). Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser.

Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb

We demonstrate a great simplification in the long-standing problem of measuring optical frequencies in terms of the cesium primary standard. An air-silica microstructure optical fiber broadens the frequency comb of a femtosecond laser to span the optical octave from 1064 to 532 nm, enabling us to measure the 282 THz frequency of an iodine-stabilized Nd:YAG laser directly in terms of the microwave frequency that controls the comb spacing. Additional measurements of established optical frequencies at 633 and 778 nm using the same femtosecond comb confirm the accepted uncertainties for these standards.

Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis

We stabilized the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. We confirmed control of the pulse-to-pulse carrier-envelope phase using temporal cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which we used to perform absolute optical frequency measurements that were directly referenced to a stable microwave clock.

Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser

We demonstrate a versatile new technique that provides a phase coherent link between optical frequencies and the radio frequency domain. The regularly spaced comb of modes of a mode-locked femtosecond laser is used as a precise ruler to measure a large frequency gap between two different multiples (harmonics or subharmonics) of a laser frequency. In this way, we have determined a new value of the hydrogen 1S-2S two-photon resonance, f(1S-2S) = 2 466 061 413 187.29(37) kHz, representing now the most accurate measurement of an optical frequency.

Sub-systems for optical frequency measurements: application to the 282-nm (199)Hg(+) transition and the 657-nm Ca line

We are developing laser frequency measurement technologies that should allow us to construct an optical frequency synthesis system capable of measuring optical frequencies with a precision limited by the atomic frequency standards. The system will be used to interconnect and compare new advanced optical-frequency references (such as Ca, Hg(+ ), and others) and eventually to connect these references to the Cs primary frequency standard. The approach we are taking is to subdivide optical frequency intervals into smaller and smaller pieces until we are able to use standard electronic-frequency-measurement technology to measure the smallest interval.

Toward a 3:1 frequency divider based on parametric oscillation using AgGaS(2) and PPLN crystals

Frequency divide-by-two (2:1) and divide-by-three (3:1) optical parametric oscillators (OPOs) are basic devices for the implementation of future accurate optical frequency division chains. We report our latest development toward a phase-locked 3:1 frequency division of a radiation at lambda(p) approximately 843 nm (355.9 THz), using doubly resonant oscillators (DROs) based on silver gallium sulfide (AgGaS(2 ) or AGS) and multigrating periodically poled lithium niobate (PPLN). Although stable single-mode pair operation is achievable without any active cavity length servo with the AGS-DRO, because of a strong passive thermal feedback servo, the PPLN-DRO requires an active intensity side-of-fringe locking servo to maintain long-term, single-mode pair operation. To overcome the limited idler output power (<1 mW) due to the weak mirror transmissivity at 2.53 mum, a CaF (2) Brewster-oriented plate was inserted in a longer-cavity PPLN-DRO as a variable output coupler. About 3 mW of idler wave is thus coupled outside the cavity, yielding 15 nW of doubled-idler. We obtained a 30 dB signal-to-noise ratio beatnote in a 100 kHz resolution bandwidth of a spectrum analyser. This beat signal will be used to phase-lock the divider.

Accurate measurement of large optical frequency differences with a mode-locked laser

We have used the comb of optical frequencies emitted by a mode-locked laser as a ruler to measure differences of as much as 20 THz between laser frequencies. This is to our knowledge the largest gap measured with a frequency comb, with high potential for further improvements. To check the accuracy of this approach we show that the modes are distributed uniformly in frequency space within the experimental limit of 3.0 parts in 10(17) . By comparison with an optical frequency comb generator we have verified that the mode separation equals the pulse repetition rate within the experimental limit of 6.0 parts in 10(16).

Accurate relative frequency cancellation between two independent lasers

For high-precision frequency-based applications of lasers, the frequency difference between two independent lasers is accurately stabilized and maintained. We describe a simple and novel feed-forward method with an acousto-optic modulator. This method can be used in optical phase-locked loops.

Accuracy of optical frequency comb generators and optical frequency interval divider chains

We compared two methods for measuring large optical frequency differences: an optical frequency comb generator, which creates a large number of sidebands from a single-mode laser through electro-optic modulation, and an optical frequency interval divider chain, which divides a frequency gap successively by two until it becomes accessible to a radio-frequency counter. By locking two diode lasers to two modulation sidebands of a comb generator, ~1 THz apart, and measuring this interval with a chain of four phase-locked interval dividers, we demonstrate for the first time to our knowledge the accuracy of both techniques within an experimental limit of 6.8 x 10(-15).

Optical frequency division by 3 of 532 nm in periodically poled lithium niobate with a double grating

Optical frequency division by 3 of 532 nm is demonstrated by back-to-back difference-frequency generation in a periodically poled lithium niobate crystal with a double grating. The first grating generates 1596-nm light from 532- and 798-nm inputs, and the second grating mixes the 798-nm input and the 1596-nm output from the first grating to produce a second 1596-nm output. The beat signal between the two 1596-nm outputs is detected and frequency stabilized to yield the 3:1 frequency ratio.

Highly selective terahertz optical frequency comb generator

Using a 10.5-GHz resonant electro-optic modulator placed inside a resonant optical cavity, we generated an optical frequency comb with a span wider than 3 THz. The optical resonator consists of three mirrors, with the output coupler being a thin Fabry-Perot cavity with a free spectral range of 2 THz and a finesse of 400. Tuning this filter cavity onto resonance with a particular high-order sideband permits efficient output coupling of the desired sideband power from the comb generator, while keeping all other sidebands inside for continued comb generation. This spectrally pure output light was then heterodyne detected by another laser with a frequency offset of the order of 1 THz.

Frequency metrology by use of quantum interference

Quantum interference in the rate of two-photon excitation of the 6S((1/2)) ?6P(3/2) ? 6D(5/2) transition in atomic cesium is exploited to demonstrate phase-sensitive frequency demodulation for an optical interval of +/- 12.5 THz. By thus using atoms as ultrafast nonlinear mixing elements, we suggest and analyze a new avenue for absolute comparisons of a dense set of frequencies over the range of 200-2000 nm.

Division by 3 of optical frequencies by use of difference-frequency generation in noncritically phase-matched RbTiOAsO(4)

A new scheme for coherently connecting optical frequencies in a 3:1 ratio has been demonstrated. To phase lock a Nd:YAG laser at 1064 nm with a CO overtone laser at 3192 nm, we generated their difference frequency in RbTiOAsO(4) (RTA) and beat it against the second harmonic of 3192 nm that was generated in AgGaSe(2).

30-THz upconversion of an AlGaAs diode laser with AgGaS(2): bridging the several-terahertz frequency gap in the near infrared

We report as much as 6-micro W upconverted cw radiation at lambda = 778 nm from the sum-frequency mixing of a 50-mW diode laser at lambda = 842 nm and a 200-mW CO(2) laser at lambda = 10.2 microm by use of a 15-mm-long silver thiogallate crystal. This nonlinear material provides a convenient connection between IR and visible/near-IR optical standards. We describe simple frequency chains based on this upconversion process that permit the absolute frequency measurement of many visible or near-IR possible standards at the 10(-12) accuracy level. Transposition of terahertz-scale frequency-difference measurements from the near IR to the 10-microm domain is also proposed.

Proposed sum-and-difference method for optical-frequency measurement in the near infrared

We propose a method for the determination of optical frequencies in the near infrared that is based on the nonlinear generation of the optical sum and difference frequencies of two near-infrared lasers followed by the comparison of the sum and difference frequencies with standards in the visible and in the far infrared, respectively. We also address questions of practicability and discuss some examples open to the method.

Optical heterodyning with a frequency difference of 1 THz in the 850-nm range

We report our recent progress on detection of large frequency difference (up to 1.028 THz, Deltalambda = 2.5 nm) between two laser diodes at 852 nm, using a Schottky diode as harmonic mixer/detector. Using the 11th harmonic of a klystron operating at 93.5 GHz or the 991-GHz line of an optically pumped HCOOH far-infrared laser, we were able to observe a signal-to-noise ratio of 2 dB in a 1-MHz-resolution bandwidth.

Coherent bisection of optical frequency intervals as large as 530 THz

We demonstrate the coherent bisection of a 530-THz frequency interval between two lasers by phase locking a third laser to the midfrequency point of the first two by using the nonlinear phase-locking scheme. This is done by comparing the sum frequency of the first two lasers with the second harmonic of the third laser. We also examine the properties of such a frequency divider for the important practical case of a few-terahertz intervals in the 850-nm diode-laser regime.

Optical frequency counting from the UV to the near IR

A method for measuring optical frequencies from the UV to the near IR relative to a microwave frequency standard is proposed. The concept is to measure the frequency difference of two known ratios ((1/2) and ?) of an optical frequency f relative to the cesium clock. By employing optical parametric oscillators and wideband modulators to link the ((1/2))f and (?)f frequencies, a precise and accurate optical frequency comb can be provided in the ~1-2-microm wavelength region. By using this comb, most optical frequencies from the UV to the near IR can be measured or synthesized. A configuration for measuring the frequency of the hydrogen 1S-2S transition is described.

Tunable optical frequency division using a phase-locked optical parametric oscillator

We report the experimental demonstration of a novel optical parametric oscillator approach to tunable optical frequency division. The beat frequency of the signal and idler subharmonic outputs of a tunable cw KTP optical parametric oscillator was phase locked to a microwave reference frequency source, which thus permitted precise determination of the output frequencies at approximately half the input pump frequency.

Injection locking of a highly coherent and high-power diode laser at 1.5 microm

Injection locking has been employed to improve the coherence of a high-power diode laser at 1.5 microm. The injected high-power laser emitted in a single mode with a side-mode suppression ratio of larger than 30 dB and an output power of 40 mW. The FM noise of the slave laser was nearly the same as that of the submegahertz-linewidth master laser. We have also demonstrated the coherent addition of the master and the injection-locked slave laser with a residual phase error of deltaø < 0.2 rad.

Stable semiconductor laser with a 7-Hz linewidth by an optical-electrical double-feedback technique

A semiconductor laser with a linewidth of 7 Hz locking to a supercavity was achieved by using an optical-electrical double-feedback technique. The emitted power concentration within the stabilized field spectrum was 81%. The minimum value of the square root of the Allan variance for the frequency stability was 2.4 x 10(-14) at the integration time of 70 msec.

Progress at NIST toward absolute frequency standards using stored ions

Experiments directed toward the realization of frequency standards of high accuracy using stored ions are briefly summarized. In one experiment, an RF oscillator is locked to a nuclear spin-flip hyperfine transition (frequency approximately 3.03x10(8) Hz) in (9 )Be(+) ions that are stored in a Penning trap and sympathetically laser-cooled. Stability is better than 3x10(-12)tau(-(1/2)) and uncertainty in Doppler shifts is estimated to be less than 5x10(-15). In a second experiment, a stable laser is used to probe an electric quadrupole transition (frequency approximately 1.07x10(15) Hz) in a single laser-cooled (199)Hg(+) ion stored in a Paul trap. The measured Q value of this transition is approximately 10(13). Future possible experiments are discussed.