Low-loss reciprocal optical terminals for two-way time-frequency transfer.

We present the design and performance of a low-cost, reciprocal, compact free-space terminal employing tip/tilt pointing compensation that enables optical two-way time-frequency transfer over free-space links across the turbulent atmosphere. The insertion loss of the terminals is ∼1.5 dB with total link losses of 15 dB, 24 dB, and 50 dB across horizontal, turbulent 2-km, 4-km, and 12-km links, respectively. The effects of turbulence on pointing control and aperture size, and their influence on the terminal design, are discussed.

Invited Article: A compact optically coherent fiber frequency comb.

We describe the design, fabrication, and performance of a self-referenced, optically coherent frequency comb. The system robustness is derived from a combination of an optics package based on polarization-maintaining fiber, saturable absorbers for mode-locking, high signal-to-noise ratio (SNR) detection of the control signals, and digital feedback control for frequency stabilization. The output is phase-coherent over a 1-2 µm octave-spanning spectrum with a pulse repetition rate of ∼200 MHz and a residual pulse-to-pulse timing jitter <3 fs well within the requirements of most frequency-comb applications. Digital control enables phase coherent operation for over 90 h, critical for phase-sensitive applications such as timekeeping. We show that this phase-slip free operation follows the fundamental limit set by the SNR of the control signals. Performance metrics from three nearly identical combs are presented. This laptop-sized comb should enable a wide-range of applications beyond the laboratory.

Comb-calibrated laser ranging for three-dimensional surface profiling with micrometer-level precision at a distance.

Non-contact surface mapping at a distance is interesting in diverse applications including industrial metrology, manufacturing, forensics, and artifact documentation and preservation. Frequency modulated continuous wave (FMCW) laser detection and ranging (LADAR) is a promising approach since it offers shot-noise limited precision/accuracy, high resolution and high sensitivity. We demonstrate a scanning imaging system based on a frequency-comb calibrated FMCW LADAR and real-time digital signal processing. This system can obtain three-dimensional images of a diffusely scattering surface at stand-off distances up to 10.5 m with sub-micrometer accuracy and with a precision below 10 µm, limited by fundamental speckle noise. Because of its shot-noise limited sensitivity, this comb-calibrated FMCW LADAR has a large dynamic range, which enables precise mapping of scenes with vastly differing reflectivities such as metal, dirt or vegetation. The current system is implemented with fiber-optic components, but the basic system architecture is compatible with future optically integrated, on-chip systems.

Operation of an optically coherent frequency comb outside the metrology lab.

We demonstrate a self-referenced fiber frequency comb that can operate outside the well-controlled optical laboratory. The frequency comb has residual optical linewidths of < 1 Hz, sub-radian residual optical phase noise, and residual pulse-to-pulse timing jitter of 2.4 - 5 fs, when locked to an optical reference. This fully phase-locked frequency comb has been successfully operated in a moving vehicle with 0.5 g peak accelerations and on a shaker table with a sustained 0.5 g rms integrated acceleration, while retaining its optical coherence and 5-fs-level timing jitter. This frequency comb should enable metrological measurements outside the laboratory with the precision and accuracy that are the hallmarks of comb-based systems.

Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz.

We demonstrate a dual-comb spectrometer using stabilized frequency combs spanning 177 to 220 THz (1360 to 1690 nm) in the near infrared. Comb-tooth-resolved measurements of amplitude and phase generate over 4×10(5) individually resolved spectral elements at 100 MHz point spacing and kilohertz-level resolution and accuracy. The signal-to-noise ratio is 100 to 3000 per comb tooth. Doppler-broadened phase and amplitude spectra of CO(2), CH(4), C(2)H(2), and H(2)O in a 30 m multipass cell agree with established spectral parameters, achieving high-resolution measurements with optical bandwidth generally associated with blackbody sources.

Coherent linear optical sampling at 15 bits of resolution.

Linear optical sampling characterizes a sample by measuring the distortions on a transmitted optical field, thereby quantifying the sample's optical response. By exploiting the high mutual coherence between two phase-locked femtosecond fiber lasers, we achieve very high signal-to-noise ratio measurements of transmitted optical electric fields through coherent averaging. We measure the optical electric fields with 15.16 bits of dynamic range (91 dB in intensity) and with 525 fs timing resolution over a 10 ns time window, in a 5.1 s averaging period.

Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place.

Time has always had a special status in physics because of its fundamental role in specifying the regularities of nature and because of the extraordinary precision with which it can be measured. This precision enables tests of fundamental physics and cosmology, as well as practical applications such as satellite navigation. Recently, a regime of operation for atomic clocks based on optical transitions has become possible, promising even higher performance. We report the frequency ratio of two optical atomic clocks with a fractional uncertainty of 5.2 x 10(-17). The ratio of aluminum and mercury single-ion optical clock frequencies nuAl+/nuHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 x 10(-17), and systematic uncertainties of 1.9 x 10(-17) and 2.3 x 10(-17) in the mercury and aluminum frequency standards, respectively. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant alpha of alpha/alpha = (-1.6+/-2.3) x 10(-17)/year.

Coherent transfer of an optical carrier over 251 km.

We transfer an optical frequency over 251 km of optical fiber with a residual instability of 6x10(-19) at 100 s. This instability and the associated timing jitter are limited fundamentally by the noise on the optical fiber and the link length. We give a simple expression for calculating the achievable instability and jitter over a fiber link. Transfer of optical stability over this long distance requires a highly coherent optical source, provided here by a cw fiber laser locked to a high finesse optical cavity. A sufficient optical carrier signal is delivered to the remote fiber end by incorporating two-way, in-line erbium-doped fiber amplifiers to balance the 62 dB link loss.

A passively mode-locked fiber laser at 1.54 mum with a fundamental repetition frequency reaching 2 GHz.

We demonstrate a fundamentally mode-locked fiber laser with a repetition frequency in excess of 2 GHz at a central wavelength of 1.535 mum. Co-doped ytterbium-erbium fiber provides the gain medium for the laser, affording high gain per unit length, while a semiconductor saturable absorber mirror (SAM) provides the pulse shaping mechanism in a standing wave cavity. Results are shown confirming cw mode-locking for 1 GHz and 2 GHz repetition frequency systems. The response of the frequency comb output to pump power variations is shown to follow a single pole response. The timing jitter of a 540MHz repetition-rate laser has been suppressed to below 100 fs through phase-lead compensated feedback to the pump power. Alternatively, a single comb line of a 850MHz repetition-rate laser has been phase-locked to a narrow linewidth cw laser with an in-loop phase jitter of 0.06 rad(2). The laser design is compatible with low-noise oscillator applications.

Characterization of frequency noise on a broadband infrared frequency comb using optical heterodyne techniques.

We measure the frequency noise across a Cr:forsterite infrared frequency comb through the optical heterodyne beat of different comb teeth against stable continuous wave (CW) lasers. This sensitive measurement shows strong correlations of the frequency noise between spectral components of the comb, relative to a fixed optical frequency near the 1.3 micron carrier of the Cr:forsterite laser. The correlated frequency fluctuations are shown to arise from amplitude noise on the pump laser. We also report a preliminary comparison of excess noise that occurs during supercontinuum generation in both highly nonlinear fiber and an extruded glass microstructured fiber.

Fiber-laser frequency combs with subhertz relative linewidths.

We investigate the comb linewidths of self-referenced, fiber-laser-based frequency combs by measuring the heterodyne beat signal between two independent frequency combs that are phase locked to a common cw optical reference. We demonstrate that the optical comb lines can exhibit instrument-limited, subhertz relative linewidths across the comb spectra from 1200 to 1720 nm with a residual integrated optical phase jitter of approximately 1 rad in a 60 mHz to 500 kHz bandwidth. The projected relative pulse timing jitter is approximately 1 fs. This performance approaches that of Ti:sapphire frequency combs.

Elimination of pump-induced frequency jitter on fiber-laser frequency combs.

Optical frequency combs generated by femtosecond fiber lasers typically exhibit significant frequency noise that causes broad optical linewidths, particularly in the comb wings and in the carrier-envelope offset frequency (f(ceo)) signal. We show these broad linewidths are mainly a result of white amplitude noise on the pump diode laser that leads to a breathing-like motion of the comb about a central fixed frequency. By a combination of passive noise reduction and active feedback using phase-lead compensation, this noise source is eliminated, thereby reducing the f(ceo) linewidth from 250 kHz to <1 Hz. The in-loop carrier-envelope offset phase jitter, integrated to 100 kHz, is 1.3 rad.

Frequency-resolved coherent lidar using a femtosecond fiber laser.

We demonstrate a coherent lidar that uses a broadband femtosecond fiber laser as a source and resolves the returning heterodyne signal into N spectral channels by using an arrayed-waveguide grating. The data are processed incoherently to yield an N-times improvement in the Doppler measurement of a surface vibration. For N=6, we achieve a sensitivity of 153 Hz, corresponding to a 0.12 mm/s motion, in 10 ms despite a signal that is speckle broadened to 14 kHz. Alternatively, the data are processed coherently to form a range image. For a flat target, we achieve a 60 microm range resolution, limited mainly by the source bandwidth, despite the dispersion of 1 km of optical fiber in the signal path.

Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser.

A frequency comb is generated with a Cr:forsterite femtosecond laser, spectrally broadened through a highly nonlinear optical fiber to span from 1.0 to 2.2 ,m, and stabilized using the f-to-2f self-referencing technique. The repetition rate and the carrier-envelope offset frequency are stabilized to a hydrogen maser, calibrated by a cesium atomic fountain clock. Simultaneous frequency measurement of a 657-nm cw laser by use of the stabilized frequency combs from this Cr:forsterite system and a Ti:sapphire laser agree at the 10(-13) level. The frequency noise of the comb components is observed at 1064, 1314, and 1550 nm by comparing the measured beat frequencies between cw lasers and the supercontinuum frequency combs.

Response dynamics of the frequency comb output from a femtosecond fiber laser.

The frequency comb from a mode-locked fiber laser can be stabilized through feedback to the pump power. An understanding of the mechanisms and bandwidth governing this feedback is of practical importance for frequency comb design and of basic interest since it provides insight into the rich nonlinear laser dynamics. We compare experimental measurements of the response of a fiber-laser frequency comb to theory. The laser response to a pump-power change follows that of a simple low-pass filter with a time constant set by the gain relaxation time and the system-dependent nonlinear loss. Five different effects contribute to the magnitude of the response of the frequency comb spacing and offset frequency but the dominant effects are from the resonant contribution to the group velocity and intensity-dependent spectral shifts. The origins of the intensity-dependent spectral shifts are explained in terms of the laser parameters.

Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser.

A frequency comb is generated with a chromium-doped forsterite femtosecond laser, spectrally broadened in a dispersion-shifted highly nonlinear fiber, and stabilized. The resultant evenly spaced comb of frequencies ranges from 1.1 to beyond 1.8 microm. The frequency comb was referenced simultaneously to the National Institute of Standards and Technology's optical frequency standard based on neutral calcium and to a hydrogen maser that is calibrated by a cesium atomic fountain clock. With this comb we measured two frequency references in the telecommunications band: one half of the frequency of the d/f crossover transition in 87Rb at 780 nm, and the methane v2 + 2v3 R(8) line at 1315 nm.

420-MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2-micrometre range.

We demonstrate a chromium-doped forsterite femtosecond ring laser that generates 30-fs pulses at a 420-MHz repetition rate with nearly 500 mW of average power. The compact solid-state design and broad spectral output make this laser attractive for telecommunications applications in the 1.3-1.5-micrometre region. Additional spectral broadening of the laser output in highly nonlinear optical fiber leads to octave-spanning spectra ranging from 1.06 to 2.17 micrometre. The octave is reached at a level of 18 dB below the peak. The underlying optical frequency comb can be linked to existing optical frequency standards.

Noise amplification during supercontinuum generation in microstructure fiber.

Supercontinua generated by femtosecond pulses launched in microstructure fiber can exhibit significant low-frequency (<1-MHz) amplitude noise on the output pulse train. We show that this low-frequency noise is an amplified version of the amplitude noise that is already present on the input laser pulse train. Through both experimental measurements and numerical simulations, we quantify the noise amplification factor and its dependence on the supercontinuum wavelength and on the energy and duration of the input pulse. Interestingly, the dependence differs significantly from that of the broadband white-noise component, which arises from amplification of the input laser shot noise.

Fundamental noise limitations to supercontinuum generation in microstructure fiber.

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50% for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schrödinger equation, finding good quantitative agreement over a range of input-pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input-pulse shot noise and the spontaneous Raman scattering down the fiber.

Raman gain: pump-wavelength dependence in single-mode fiber.

The magnitude of the stimulated Raman gain spectrum will depend on the absolute pump wavelength. Measurements of the pump-wavelength scaling of the stimulated Raman gain of several single-mode fibers are presented. The measurements were obtained by use of two techniques: a brute-force comparison of gain versus pump wavelength and a more elegant comparison of the asymmetry in the Stokes and anti-Stokes Raman gain spectrum at a fixed pump wavelength. This second asymmetry technique has the advantage that it is independent of the uncertainties typically associated with relative measurements of optical power.