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

Simple route toward efficient frequency conversion for generation of fully coherent supercontinua in the mid-IR and UV range

Fiber supercontinua represent light sources of pivotal importance for a wide range of applications, ranging from optical communications to frequency metrology. Although spectra encompassing more than three octaves can be produced, the applicability of such spectra is strongly hampered due to coherence degradation during spectral broadening. Assuming pulse parameters at the cutting edge of currently available laser technology, we demonstrate the possibility of strongly coherent supercontinuum generation. In a fiber with two zero-dispersion wavelengths a higher-order soliton experiences a temporal breakdown, without any compression or splitting behavior, which leads to nearly complete conversion of input solitonic radiation into resonant nonsolitonic radiation in the dispersive wave regime. As the process is completely deterministic and shows little sensitivity to input noise, the resulting pulses appear to be compressible down to the sub-cycle level and may thus hold a new opportunity for direct generation of attosecond pulses in the visible to near ultraviolet wavelength range.

Optical-frequency transfer over a single-span 1840 km fiber link

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of 2×10(-15) for a gate time τ of 1 s reaching 4×10(-19) in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about 3×10(-19). The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ(-2) slope in the modified Allan deviation, which is also derived theoretically.

A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place

Optical clocks show unprecedented accuracy, surpassing that of previously available clock systems by more than one order of magnitude. Precise intercomparisons will enable a variety of experiments, including tests of fundamental quantum physics and cosmology and applications in geodesy and navigation. Well-established, satellite-based techniques for microwave dissemination are not adequate to compare optical clocks. Here, we present phase-stabilized distribution of an optical frequency over 920 kilometers of telecommunication fiber. We used two antiparallel fiber links to determine their fractional frequency instability (modified Allan deviation) to 5 × 10(-15) in a 1-second integration time, reaching 10(-18) in less than 1000 seconds. For long integration times τ, the deviation from the expected frequency value has been constrained to within 4 × 10(-19). The link may serve as part of a Europe-wide optical frequency dissemination network.

Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal

In supercontinuum generation, various propagation effects combine to produce a dramatic spectral broadening of intense ultrashort optical pulses. With a host of applications, supercontinuum sources are often required to possess a range of properties such as spectral coverage from the ultraviolet across the visible and into the infrared, shot-to-shot repeatability, high spectral energy density and an absence of complicated pulse splitting. Here we present an all-in-one solution, the first supercontinuum in a bulk homogeneous material extending from 450 nm into the mid-infrared. The spectrum spans 3.3 octaves and carries high spectral energy density (2 pJ nm⁻¹–10 nJ nm⁻¹), and the generation process has high shot-to-shot reproducibility and preserves the carrier-to-envelope phase. Our method, based on filamentation of femtosecond mid-infrared pulses in the anomalous dispersion regime, allows for compact new supercontinuum sources.

Broadband coherent light sources are crucial for numerous applications, such as imaging and spectroscopy. Using filamentation of mid-infrared laser pulses in bulk crystals, Silva et al. generate supercontinuum spectra over three octaves, from 4.5 μm to 450 nm, with carrier-envelope phase stability.

Improved measurement of the hydrogen 1S-2S transition frequency

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10)  Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.

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.

Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards with respect to the SI second. We find the transition frequencies to be f(Hg) = 1 064 721 609 899 143(10) Hz and f(Ca) = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).

Accuracy of optical frequency comb generation in optical fiber

We evaluated the accuracy of an optical frequency comb in optical fibers by measuring the frequency shift after a sideband from an electro-optic modulator had passed through the fiber. We found that a frequency drift of a few hertz was due largely to a variation in the ambient temperature that corresponded to an increase in the square root of the Allan variance to 0.66 Hz.