High-performance, compact optical standard.

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8×10-13τ-1/2 for times less than 100 s and a flicker noise floor of 1×10-14 out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the ac Stark shift. The retrace was measured to 5.7×10-13 after 30 h of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser.

Effect of atmospheric anisoplanatism on earth-to-satellite time transfer over laser communication links.

The need for an accurate time reference on orbiting platforms motivates study of time transfer via free-space optical communication links. The impact of atmospheric turbulence on earth-to-satellite optical time transfer has not been fully characterized, however. We analyze limits to two-way laser time transfer accuracy posed by anisoplanatic non-reciprocity between uplink and downlink. We show that despite limited reciprocity, two-way time transfer can still achieve sub-picosecond accuracy in realistic propagation scenarios over a single satellite visibility period.

Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser.

We demonstrate self-seeded generation of a broadband comb in a highly nonlinear fiber resonator. When pumped with a cw laser, the fiber cavity generates a comb with two characteristic spacings. Hyperparametric modes spaced by approximately 2 THz create the base structure of the comb, while commensurate Brillouin modes spaced by approximately 10 GHz populate the intermediate frequency gaps. The frequency modes are coherent, and the repetition rate of the comb has been locked to a microwave standard.

Generation of a 20 GHz train of subpicosecond pulses with a stabilized optical-frequency-comb generator.

With a modulator-based 10 GHz optical-frequency-comb generator at 1.55 microm, we report a 20 GHz repetitive train of optical pulses as short as 450 fs. The timing stability of the 20 GHz pulses, in addition to the phase for optical-comb modes, shows a strong dependence on the relative frequency detuning between the comb generator's cavity and the seed cw laser. With a new and simple scheme, the comb generator's cavity resonance was locked to a narrow-linewidth seed laser within an estimated optical-frequency range < or = 6 MHz, enabling high-fidelity 20 GHz subpicosecond pulses and stable optical-frequency-comb generation for indefinite periods.

Toward a low-jitter 10 GHz pulsed source with an optical frequency comb generator.

We demonstrate low residual timing jitter of 10 GHz pulses from a 1.55 ?m optical frequency comb generator based on a doubly-resonant electro-optic modulator. The comb spectral phase is shown to be linear but of different slopes for the two sides of the optical spectrum. The linear phase delay predicts well the measured timing delay of the two pulse trains from the comb generator. The pulse timing jitter is analyzed, and we illustrate that the pump laser's linewidth plays a dominant role in the timing jitter. For Fourier frequencies from 1 Hz to 10 MHz, integrated residual timing jitter at 10 GHz was reduced from approximately 94 fs to approximately 8 fs when the pump laser's linewidth was reduced from approximately 10 MHz to approximately 1 kHz. An electronic servo was then used to stabilize the Fabry-Pérot cavity in the comb generator. Integrated residual timing jitter was further reduced to approximately 6 fs, and the corresponding residual phase noise power density is -105 dBc/Hz at 1 Hz frequency offset from the 10 GHz pulse carrier.

Noise properties of microwave signals synthesized with femtosecond lasers.

We discuss various aspects of high resolution measurements of phase fluctuations at microwave frequencies. This includes methods to achieve thermal noise limited sensitivity, along with the improved immunity to oscillator amplitude noise. A few prototype measurement systems were developed to measure phase fluctuations of microwave signals extracted from the optical pulse trains generated by femtosecond lasers. This enabled first reliable measurements of the excess phase noise associated with optical-to-microwave frequency division. The spectral density of the excess phase noise was found to be -140 dBc/Hz at 100 Hz offset from the 10 GHz carrier which was almost 40 dB better than that of a high quality microwave synthesizer.

Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb.

The control of the broadband frequency comb emitted from a mode-locked femtosecond laser has permitted a wide range of scientific and technological advances--ranging from the counting of optical cycles for next-generation atomic clocks to measurements of phase-sensitive high-field processes. A unique advantage of the stabilized frequency comb is that it provides, in a single laser beam, about a million optical modes with very narrow linewidths and absolute frequency positions known to better than one part in 10(15) (ref. 5). One important application of this vast array of highly coherent optical fields is precision spectroscopy, in which a large number of modes can be used to map internal atomic energy structure and dynamics. However, an efficient means of simultaneously identifying, addressing and measuring the amplitude or relative phase of individual modes has not existed. Here we use a high-resolution disperser to separate the individual modes of a stabilized frequency comb into a two-dimensional array in the image plane of the spectrometer. We illustrate the power of this technique for high-resolution spectral fingerprinting of molecular iodine vapour, acquiring in a few milliseconds absorption images covering over 6 THz of bandwidth with high frequency resolution. Our technique for direct and parallel accessing of stabilized frequency comb modes could find application in high-bandwidth spread-spectrum communications with increased security, high-resolution coherent quantum control, and arbitrary optical waveform synthesis with control at the optical radian level.

Microfabricated saturated absorption laser spectrometer.

We demonstrate a miniature microfabricated saturated absorption laser spectrometer. The system consists of miniature optics, a microfabricated Rb vapor cell, heaters, and a photodetector, all contained within a volume of 0.1 cm(3). Saturated absorption spectra were measured with a diode laser at 795 nm. They are comparable to signals obtained with standard table-top setups, although the rubidium vapor cell has an interior volume of only 1 mm(3). We discuss the performance and prospects for using such systems as a miniature optical wavelength reference, compatible with transportable instruments.

Magnetic resonance in an atomic vapor excited by a mechanical resonator.

We demonstrate a direct resonant interaction between the mechanical motion of a mesoscopic resonator and the spin degrees of freedom of a sample of neutral atoms in the gas phase. This coupling, mediated by a magnetic particle attached to the tip of the miniature mechanical resonator, excites a coherent precession of the atomic spins about a static magnetic field. The novel coupled atom-resonator system may enable development of low-power, high-performance sensors, and enhance research efforts connected with the manipulation of cold atoms, quantum control, and high-resolution microscopy.

Stable isotopic analysis of atmospheric methane by infrared spectroscopy by use of diode laser difference-frequency generation.

An infrared absorption spectrometer has been constructed to measure the stable isotopic composition of atmospheric methane samples. The spectrometer employs periodically poled lithium niobate to generate 15 microW of tunable difference-frequency radiation from two near-infrared diode lasers that probe the nu3 rotational-vibrational band of methane at 3.4 microm. To enhance the signal, methane is extracted from 25 l of air by use of a cryogenic chromatographic column and is expanded into the multipass cell for analysis. A measurement precision of 12 per thousand is demonstrated for both delta13C and deltaD.

Wavelength references for interferometry in air.

Cavity-mode wavelengths in air are determined by measuring a laser's frequency while it is locked to the mode in vacuum during a calibration step and subsequently correcting the mode wavelength for atmospheric pressure compression, temperature difference, and material aging. Using a Zerodur ring cavity, we demonstrate a repeatability of +/- 2 x 10(-8) (3sigma), with the wavelength accuracy limited to +/- 4 x 10(-8) by knowledge of the absolute helium gas temperature during the pressure calibration. Mirror cleaning perturbed the mode frequency by less than deltav/v approximately 3 x 10(-9), limited by temperature correction residuals.

Study of the excess noise associated with demodulation of ultra-short infrared pulses.

The demodulation of ultra-short light pulses with photodetectors is accompanied by excess phase noise at the pulse repetition rate and harmonics in the spectrum of the photocurrent. The major contribution to this noise is power fluctuations of the detected pulse train that, if not compensated for, can seriously limit the stability of frequency transfer from optical to microwave domain. By making use of an infrared femtosecond laser, we measured the spectral density of the excess phase noise, as well as power-to-phase conversion for different types of InGaAs photodetectors. Noise measurements were performed with a novel type of dual-channel readout system using a fiber coupled beam splitter. Strong suppression of the excess phase noise was observed in both channels of the measurement system when the average power of the femtosecond pulse train was stabilized. The results of this study are important for the development of low-noise microwave sources derived from optical "clocks" and optical frequency synthesis.

Optical frequency measurements with the global positioning system: tests with an iodine-stabilized He-Ne laser.

Global positioning system- (GPS-) referenced optical frequency combs based on mode-locked lasers offer calibrations for length metrology traceable to international length standards through the SI second and the speed of light. The absolute frequency of an iodine-stabilized He-Ne laser [127I2 R(127) 11-5 f component] was measured with a femtosecond comb referenced to a multichannel GPS timing receiver. The expected performance and limitations of GPS-referenced comb measurements are discussed.

Optical frequency synthesis and comparison with uncertainty at the 10(-19) level.

A femtosecond laser-based optical frequency synthesizer is referenced to an optical standard, and we use it to demonstrate the generation and control of the frequency of electromagnetic fields over 100 terahertz of bandwidth with fractional uncertainties approaching 1 part in 10(19). The reproducibility of this performance is verified by comparison of different types of femtosecond laser-based frequency synthesizers from three laboratories.

Dark-line atomic resonances in submillimeter structures.

We present measurements of dark-line resonances excited in cesium atoms confined in submillimeter cells with a buffer gas. The width and contrast of the resonances were measured for cell lengths as low as 100 microm. The measured atomic Q factors are reduced in small cells because of frequent collisions of atoms with the cell walls. However, the contrast of coherent population trapping resonances measured in the small cells is similar in magnitude to that obtained in centimeter-sized cells, but substantially more laser intensity is needed to excite the resonance fully when increased buffer-gas pressure is used. The effect of the higher intensity on the linewidth is reduced because the intensity broadening rate decreases with buffer-gas pressure.

Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers.

We link the output spectra of a Ti:sapphire and a Cr:forsterite femtosecond laser phase coherently to form a continuous frequency comb with a wavelength coverage of 0.57-1.45 microm at power levels of 1 nW to 40 microW per frequency mode. To achieve this, the laser repetition rates and the carrier-envelope offset frequencies are phase locked to each other. The coherence time between the individual components of the two combs is 40 micros. The timing jitter between the lasers is 20 fs. The combined frequency comb is self-referenced for access to its overall offset frequency. We report the first demonstration to our knowledge of an extremely broadband and continuous, high-powered and phase-coherent frequency comb from two femtosecond lasers with different gain media.

Experimental study of noise properties of a Ti:sapphire femtosecond laser.

The fidelity of a coherent link between optical and microwave frequencies is largely determined by noise processes in a mode-locked femtosecond laser. This work presents an experimental study of the noise properties of a Ti:sapphire femtosecond laser. It includes measurements of pulse repetition rate fluctuations and shot noise exhibited by the Ti:sapphire femtosecond laser. Based on the results of noise measurements, the fractional frequency stability of a microwave signal produced by the femtosecond laser has been evaluated.

Chromium-doped forsterite: dispersion measurement with white-light interferometry.

Using a Michelson white-light interferometer, we measure the group-delay dispersion and third-order dispersion coefficients, d2(phi)/d(omega)2 and d3(phi)/d(omega)3, of chromium-doped forsterite (Cr:Mg2SiO4) over wavelengths of 1050-1600 nm for light polarized along both the c and b crystal axes. In this interval, the second-order dispersion for the c axis ranges from 35 fs2/mm to -14 fs2/mm, and the third-order dispersion ranges from 36 fs3/mm to 142 fs3/mm. For the b axis the second-order dispersion ranges from 35 fs2/mm to -15 fs2/mm and the third-order from 73 fs3/mm to 185 fs3/mm. Our data are relevant for the development of optimized dispersion compensation tools for Cr:Mg2SiO4 femtosecond lasers. These measurements help to clarify previously published results and show some significant discrepancies that existed, especially in the third-order dispersion. Our results should furthermore be useful to build up an analytic expression for the index of refraction of chromium forsterite.