Optical frequency synthesizer for precision spectroscopy

Computational multiheterodyne spectroscopy

Dual-comb spectroscopy allows for high-resolution spectra to be measured over broad bandwidths, but an essential requirement for coherent integration is the availability of a phase reference. Usually, this means that the combs' phase and timing errors must be measured and either minimized by stabilization or removed by correction, limiting the technique's applicability. We demonstrate that it is possible to extract the phase and timing signals of a multiheterodyne spectrum completely computationally, without any extra measurements or optical elements. These techniques are viable even when the relative linewidth exceeds the repetition rate difference and can tremendously simplify any dual-comb system. By reconceptualizing frequency combs in terms of the temporal structure of their phase noise, not their frequency stability, we can greatly expand the scope of multiheterodyne techniques.

High-Precision Ramsey-Comb Spectroscopy at Deep Ultraviolet Wavelengths

High-precision spectroscopy in systems such as molecular hydrogen and helium ions is very interesting in view of tests of quantum electrodynamics and the proton radius puzzle. However, the required deep ultraviolet and shorter wavelengths pose serious experimental challenges. Here we show Ramsey-comb spectroscopy in the deep ultraviolet for the first time, thereby demonstrating its enabling capabilities for precision spectroscopy at short wavelengths. We excite ^{84}Kr in an atomic beam on the two-photon 4p^{6}→4p^{5}5p[1/2]_{0} transition at 212.55 nm. It is shown that the ac-Stark shift is effectively eliminated, and combined with a counterpropagating excitation geometry to suppress Doppler effects, a transition frequency of 2 820 833 101 679(103) kHz is found. The uncertainty of our measurement is 34 times smaller than the best previous measurement, and only limited by the 27 ns lifetime of the excited state.

Long-term phase-locking technique for locking the repetition rate of an optical frequency comb laser with 1.67 × 10-19 precision

An ultrahigh stable phase-locked loop system for synchronization of an optical frequency comb to a hydrogen maser has been proposed and experimentally demonstrated. A mathematical model has been set up to investigate the feasibility and steady state of the phase-locking system. The fractional frequency instability is evaluated by measuring the mixed-phase signal of an improved experimental system. Experimental results show that the fractional frequency instability of the phase-locked loop system lies from 8.83×10^-16 at 1 s to 1.67×10^-19 at 1000 s, which indicates our proposed phase-locking system possesses ultrahigh measurement precision with good long-term stabilization performance.

Stabilized chip-scale Kerr frequency comb via a high-Q reference photonic microresonator

We stabilize a chip-scale Si₃N₄ phase-locked Kerr frequency comb via locking the pump laser to an independent stable high-Q reference microresonator and locking the comb spacing to an external microwave oscillator. In this comb, the pump laser shift induces negligible impact on the comb spacing change. This scheme is a step toward miniaturization of the stabilized Kerr comb system as the microresonator reference can potentially be integrated on-chip. Fractional instability of the optical harmonics of the stabilized comb is limited by the microwave oscillator used for a comb spacing lock below 1 s averaging time and coincides with the pump laser drift in the long term.

Hybrid photonic crystal fiber in chemical sensing

Background

In this article, a hybrid photonic crystal fiber has been proposed for chemical sensing. A FEM has been applied for numerical investigation of some propagation characteristics of the PCF at a wider wavelength from 0.7 to 1.7 µm. The geometrical parameters altered to determine the optimized values. The proposed PCF contains three rings of circular holes in the cladding where the core is formulated with microstructure elliptical holes.

Results

The simulation result reveals that our proposed PCF exhibits high sensitivity and low confinement loss for benzene, ethanol and water than the prior PCFs. We have also shown that our proposed PCF shows high birefringence for benzene 1.544 × 10⁻³, for ethanol 1.513 × 10⁻³ and for water 1.474 × 10⁻³ at λ = 1.33 µm.

Conclusion

The proposed PCF is simple with three rings which can be used for the sensing applications of industrially valuable lower indexed chemicals.

Dual-pump Kerr Micro-cavity Optical Frequency Comb with varying FSR spacing

In this paper, we demonstrate a novel dual-pump approach to generate robust optical frequency comb with varying free spectral range (FSR) spacing in a CMOS-compatible high-Q micro-ring resonator (MRR). The frequency spacing of the comb can be tuned by an integer number FSR of the MRR freely in our dual-pump scheme. The dual pumps are self-oscillated in the laser cavity loop and their wavelengths can be tuned flexibly by programming the tunable filter embedded in the cavity. By tuning the pump wavelength, broadband OFC with the bandwidth of >180 nm and the frequency-spacing varying from 6 to 46-fold FSRs is realized at a low pump power. This approach could find potential and practical applications in many areas, such as optical metrology, optical communication, and signal processing systems, for its excellent flexibility and robustness.

Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry

The palette of laser technology has significantly been enriched by the innovations in ultrafast optical pulse generation. Our knowledge of the complex pulse dynamics, which is often highly nonlinear and stochastic in nature, is however limited by the scarcity of technologies that can measure fast variation/fluctuation of the spectral phase (or coherence) and amplitude in real-time, continuously. To achieve this goal, we demonstrate ultrafast interferometry enabled by optical time-stretch for real- time spectral coherence characterization with microsecond-resolution. Accessing the single-shot interferograms continuously, it further reveals the degree of second-order coherence, defined by the cross-spectral density function, at high speed-a capability absent in any existing spectroscopic measurement tools. As the technique can simultaneously measure both the high-speed variations of spectrally resolved coherence and intensity, time-stretch interferometry could create a new arena for ultrafast pulse characterization, especially favorable for probing and understanding the non-repetitive or stochastic dynamics in real-time.

Dual-comb spectroscopy with a phase-modulated probe comb for sub-MHz spectral sampling

We present a straightforward and efficient method to reduce the mode spacing of a frequency comb based on binary pseudo-random phase modulation of its pulse train. As a proof of concept, we use such a densified comb to perform dual-comb spectroscopy of a long-delay Mach-Zehnder interferometer and a high-quality-factor microresonator with sub-MHz spectral sampling. Since this approach is based on binary phase modulation, it combines all the advantages of other densification techniques: simplicity, single-step implementation, and conservation of the initial comb's power.

Frequency comb metrology with an optical parametric oscillator

We report on the first demonstration of absolute frequency comb metrology with an optical parametric oscillator (OPO) frequency comb. The synchronously-pumped OPO operated in the 1.5-µm spectral region and was referenced to an H-maser atomic clock. Using different techniques, we thoroughly characterized the frequency noise power spectral density (PSD) of the repetition rate f_rep, of the carrier-envelope offset frequency f_CEO, and of an optical comb line νN. The comb mode optical linewidth at 1557 nm was determined to be ~70 kHz for an observation time of 1 s from the measured frequency noise PSD, and was limited by the stability of the microwave frequency standard available for the stabilization of the comb repetition rate. We achieved a tight lock of the carrier envelope offset frequency with only ~300 mrad residual integrated phase noise, which makes its contribution to the optical linewidth negligible. The OPO comb was used to measure the absolute optical frequency of a near-infrared laser whose second-harmonic component was locked to the F = 2→3 transition of the ⁸⁷Rb D2 line at 780 nm, leading to a measured transition frequency of ν_Rb = 384,228,115,346 ± 16 kHz. We performed the same measurement with a commercial fiber-laser comb operating in the 1.5-µm region. Both the OPO comb and the commercial fiber comb achieved similar performance. The measurement accuracy was limited by interferometric noise in the fibered setup of the Rb-stabilized laser.

70-fs mode-locked erbium-doped fiber laser with topological insulator

Femtosecond optical pulses have applications in optical communication, astronomical frequency combs, and laser spectroscopy. Here, a hybrid mode-locked erbium-doped fiber (EDF) laser with topological insulator (TI) is proposed, for the first time to our best knowledge. The pulsed laser deposition (PLD) method is employed to fabricate the fiber-taper TI saturable absorber (TISA). By virtue of the fiber-taper TISA, the hybrid EDF laser is passively mode-locked using the nonlinear polarization evolution (NPE), and emits 70 fs pulses at 1542 nm, whose 3 dB spectral width is 63 nm with a repetition rate and transfer efficiency of 95.4 MHz and 14.12%, respectively. Our experiments indicate that the proposed hybrid mode-locked EDF lasers have better performance to achieve shorter pulses with higher power and lower mode-locking threshold in the future.

Octave-spanning coherent supercontinuum generation in a silicon nitride waveguide

We demonstrate the generation of a supercontinuum spanning more than 1.4 octaves in a silicon nitride waveguide using sub-100-fs pulses at 1 μm generated by either a 53-MHz, diode-pumped ytterbium (Yb) fiber laser or a 1-GHz, Yb:CaAlGdO(4) (Yb:CALGO) laser. Our numerical simulations show that the broadband supercontinuum is fully coherent, and a spectral interference measurement is used to verify that the supercontinuum generated with the Yb:CALGO laser possesses a high degree of coherence over the majority of its spectral bandwidth. This coherent spectrum may be utilized for optical coherence tomography, spectroscopy, and frequency metrology.

Carrier-envelope phase stabilization of a 16 TW, 10 Hz Ti:sapphire laser

We propose and demonstrate a simple and promising method for stabilizing the carrier-envelope phase (CEP) of a high-energy ultrashort pulse laser operating at a low repetition rate. The method was successfully applied to a Ti:sapphire laser operating at 10 Hz with 400 mJ pulse energy and 25 fs pulse duration (16 TW). The laser system consists of a 1 kHz front-end preamplifier and a 10 Hz back-end power amplifier. By sampling a 500 Hz reference pulse from a 1 kHz seed pulse, the measured single-shot CEP noise of a 10 Hz amplified pulse is stabilized to 670 mrad rms. Our proposed CEP stabilization concept can be applied to single-shot ultrahigh-power lasers, such as a petawatt laser system.

Microstructure core photonic crystal fiber for gas sensing applications

In this paper, a highly sensitive gas sensor based on the microstructure core and cladding photonic crystal fiber (PCF) is presented over the wavelength range from 1.3 to 2.2 μm, which is advantageous for sensor fabrication. The guiding properties of the proposed structure are dependent on geometrical parameters and wavelengths, which are numerically investigated by using a finite element method (FEM). Introducing the microstructure core makes it possible to obtain higher relative sensitivity and achieves low confinement loss. Moreover, it can be shown that increasing the diameter of the air holes in the microstructure core and decreasing the size of hole to hole space (pitch), the relative sensitivity is enhanced. In addition, the confinement loss is reduced by increasing the value of the diameter of the air holes in the cladding. Simulation results reveal that for the optimum design of the proposed PCF it is possible to obtain the highest relative sensitivity of about 42.27% at the wavelength λ=1.33  μm for the absorption line of methane (CH₄) and hydrogen fluoride (HF) gases. In this case, the confinement loss of the fiber is 4.78345×10^-6  dB/m.

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

We propose a fibre-based approach for generation of optical frequency combs (OFCs) with the aim of calibration of astronomical spectrographs in the low and medium-resolution range. This approach includes two steps: in the first step, an appropriate state of optical pulses is generated and subsequently moulded in the second step delivering the desired OFC. More precisely, the first step is realised by injection of two continuous-wave (CW) lasers into a conventional single-mode fibre, whereas the second step generates a broad OFC by using the optical solitons generated in step one as initial condition. We investigate the conversion of a bichromatic input wave produced by two initial CW lasers into a train of optical solitons, which happens in the fibre used as step one. Especially, we are interested in the soliton content of the pulses created in this fibre. For that, we study different initial conditions (a single cosine-hump, an Akhmediev breather, and a deeply modulated bichromatic wave) by means of soliton radiation beat analysis and compare the results to draw conclusion about the soliton content of the state generated in the first step. In case of a deeply modulated bichromatic wave, we observed the formation of a collective soliton crystal for low input powers and the appearance of separated solitons for high input powers. An intermediate state showing the features of both, the soliton crystal and the separated solitons, turned out to be most suitable for the generation of OFC for the purpose of calibration of astronomical spectrographs.

Mode-resolved frequency comb interferometry for high-accuracy long distance measurement

Optical frequency combs have developed into powerful tools for distance metrology. In this paper we demonstrate absolute long distance measurement using a single femtosecond frequency comb laser as a multi-wavelength source. By applying a high-resolution spectrometer based on a virtually imaged phased array, the frequency comb modes are resolved spectrally to the level of an individual mode. Having the frequency comb stabilized against an atomic clock, thousands of accurately known wavelengths are available for interferometry. From the spectrally resolved output of a Michelson interferometer a distance is derived. The presented measurement method combines spectral interferometry, white light interferometry and multi-wavelength interferometry in a single scheme. Comparison with a fringe counting laser interferometer shows an agreement within <10(-8) for a distance of 50 m.

A low-phase-noise 18 GHz Kerr frequency microcomb phase-locked over 65 THz

Laser frequency combs are coherent light sources that simultaneously provide pristine frequency spacings for precision metrology and the fundamental basis for ultrafast and attosecond sciences. Recently, nonlinear parametric conversion in high-Q microresonators has been suggested as an alternative platform for optical frequency combs, though almost all in 100 GHz frequencies or more. Here we report a low-phase-noise on-chip Kerr frequency comb with mode spacing compatible with high-speed silicon optoelectronics. The waveguide cross-section of the silicon nitride spiral resonator is designed to possess small and flattened group velocity dispersion, so that the Kerr frequency comb contains a record-high number of 3,600 phase-locked comb lines. We study the single-sideband phase noise as well as the long-term frequency stability and report the lowest phase noise floor achieved to date with -130 dBc/Hz at 1 MHz offset for the 18 GHz Kerr comb oscillator, along with feedback stabilization to achieve frequency Allan deviations of 7 × 10(-11) in 1 s. The reported system is a promising compact platform for achieving self-referenced Kerr frequency combs and also for high-capacity coherent communication architectures.

Dispersive-wave-based octave-spanning supercontinuum generation in InGaP membrane waveguides on a silicon substrate

We demonstrate the generation of an octave-spanning supercontinuum in InGaP membrane waveguides on a silicon substrate pumped by a 1550-nm femtosecond source. The broadband nature of the supercontinuum in these dispersion-engineered high-index-contrast waveguides is enabled by dispersive wave generation on both sides of the pump as well as by the low nonlinear losses inherent to the material. We also measure the coherence properties of the output spectra close to the pump wavelength and find that the supercontinuum is highly coherent at least in this wavelength range.

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.

Frequency comb offset detection using supercontinuum generation in silicon nitride waveguides

We present the first direct carrier-envelope-offset (CEO) frequency detection of a modelocked laser based on supercontinuum generation (SCG) in a CMOS-compatible silicon nitride (Si(3)N(4)) waveguide. With a coherent supercontinuum spanning more than 1.5 octaves from visible to beyond telecommunication wavelengths, we achieve self-referencing of SESAM modelocked diode-pumped Yb:CALGO lasers using standard f-to-2f interferometry. We directly obtain without amplification strong CEO beat signals for both a 100-MHz and 1-GHz pulse repetition rate laser. High signal-to-noise ratios (SNR) of > 25 dB and even > 30 dB have been generated with only 30 pJ and 36 pJ of coupled pulse energy from the megahertz and gigahertz laser respectively. We compare these results to self-referencing using a commercial photonic crystal fiber and find that the required peak power for CEO beat detection with a comparable SNR is lowered by more than an order of magnitude when using a Si(3)N(4) waveguide.

Compact rubidium-stabilized multi-frequency reference source in the 1.55-μm region

Combining light modulation and frequency conversion techniques, a compact and simple frequency-stabilized optical frequency comb spanning over 45 nm in the 1.56-μm wavelength region is demonstrated. It benefits from the high-frequency stability achievable from rubidium atomic transitions at 780 nm probed in a saturation absorption scheme, which is transferred to the 1.56-μm spectral region via a second-harmonic generation process. The optical frequency comb is generated by an electro-optic modulator enclosed in a Fabry-Perot cavity that is injected by the fundamental frequency stabilized laser. Frequency stability better than 2 kHz has been demonstrated on time scales between 1000 s and 2 days both at 1560 nm, twice the rubidium wavelength, and for a comb line at 1557 nm.

One-dimensional frequency-based spectroscopy

Recent developments in optical metrology have tremendously improved the precision and accuracy of the horizontal (frequency) axis in measured spectra. However, the vertical (typically absorbance) axis is usually based on intensity measurements that are subject to instrumental errors which limit the spectrum accuracy. Here we report a one-dimensional spectroscopy that uses only the measured frequencies of high-finesse cavity modes to provide complete information about the dispersive properties of the spectrum. Because this technique depends solely on the measurement of frequencies or their differences, it is insensitive to systematic errors in the detection of light intensity and has the potential to become the most accurate of all absorptive and dispersive spectroscopic methods. The experimental results are compared to measurements by two other high-precision cavity-enhanced spectroscopy methods. We expect that the proposed technique will have significant impact in fields such as fundamental physics, gas metrology and environmental remote sensing.

High-power multi-megahertz source of waveform-stabilized few-cycle light

Waveform-stabilized laser pulses have revolutionized the exploration of the electronic structure and dynamics of matter by serving as the technological basis for frequency-comb and attosecond spectroscopy. Their primary sources, mode-locked titanium-doped sapphire lasers and erbium/ytterbium-doped fibre lasers, deliver pulses with several nanojoules energy, which is insufficient for many important applications. Here we present the waveform-stabilized light source that is scalable to microjoule energy levels at the full (megahertz) repetition rate of the laser oscillator. A diode-pumped Kerr-lens-mode-locked Yb:YAG thin-disk laser combined with extracavity pulse compression yields waveform-stabilized few-cycle pulses (7.7 fs, 2.2 cycles) with a pulse energy of 0.15 μJ and an average power of 6 W. The demonstrated concept is scalable to pulse energies of several microjoules and near-gigawatt peak powers. The generation of attosecond pulses at the full repetition rate of the oscillator comes into reach. The presented system could serve as a primary source for frequency combs in the mid infrared and vacuum UV with unprecedented high power levels.

Frequency combs have revolutionized the study of electronic structures and dynamics of matter but currently used lasers systems are limited in terms of achievable pulse energies. Here, Pronin et al. demonstrate few cycle pulse emission from a thin-disk laser with 150 nJ pulse energy and 7.7 fs pulse duration.

Repetition rate multiplication of femtosecond light pulses using a phase-locked all-pass fiber resonator

We describe an all-pass fiber resonator with active phase-locking capability for accurate multiplication of the repetition rate of femtosecond light pulses. The cavity length of the resonator is precisely controlled using the Pounder-Drever-Hall phase-locking technique so that the repetition rate is multiplied in stabilization to the Rb atomic clock. Our test result proves the proposed phase-locking scheme is an effective means of generating higher repetition rate pulses with no significant power loss while providing a high degree of long-term stability.

Revealing carrier-envelope phase through frequency mixing and interference in frequency resolved optical gating

We demonstrate that full temporal characterisation of few-cycle electromagnetic pulses, including retrieval of the carrier envelope phase (CEP), can be directly obtained from Frequency Resolved Optical Gating (FROG) techniques in which the interference between non-linear frequency mixing processes is resolved. We derive a framework for this scheme, defined Real Domain FROG (ReD-FROG), for the cases of interference between sum and difference frequency components and between fundamental and sum / difference frequency components. A successful numerical demonstration of ReD-FROG as applied to the case of a self-referenced measurement is provided. A proof-of-principle experiment is performed in which the CEP of a single-cycle THz pulse is accurately obtained and demonstrates the possibility for THz detection beyond optical probe duration limitations inherent to electro-optic sampling.

1-GHz harmonically pumped femtosecond optical parametric oscillator frequency comb

We present the first example of a femtosecond optical parametric oscillator frequency comb harmonically-pumped by a 333-MHz Ti:sapphire laser to achieve a stabilized signal comb at 1-GHz mode spacing in the 1.1-1.6-µm wavelength band. Simultaneous locking of the comb carrier-envelope-offset and repetition frequencies is achieved with uncertainties over 1 s of 0.27 Hz and 5 mHz respectively, which are comparable with those of 0.27 Hz and 1.5 mHz achieved for 333-MHz fundamental pumping. The phase-noise power-spectral density of the CEO frequency integrated from 1 Hz-64 kHz was 2.8 rad for the harmonic comb, 1.0 rad greater than for fundamental pumping. The results show that harmonic operation does not substantially compromise the frequency-stability of the comb, which is shown to be limited only by the Rb atomic frequency reference used.

Frequency-comb-referenced mid-infrared source for high-precision spectroscopy

We report on a tunable continuous-wave mid-infrared optical parametric oscillator (OPO), which is locked to a fully stabilized near-infrared optical frequency comb using a frequency doubling scheme. The OPO is used for 40 GHz mode-hop-free, frequency-comb-locked scans in the wavelength region between 2.7 and 3.4 μm. We demonstrate the applicability of the method to high-precision cavity-ring-down spectroscopy of nitrous oxide (N₂O) and water (H₂O) at 2.85 µm and of methane (CH₄) at 3.2 μm.

Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair

We present a heterodyne absolute distance interferometer with a macroscopic range, based on a promising optical source. The basis of the heterodyne measurement principle, a frequency comb pair with slightly different repetition rates and offset frequencies, is realized coherently by synchronized cavity-enhanced electro-optic frequency comb generators. The unknown distance is determined absolutely from the interferometric phases of distinct comb modes, by a parallel digital lock-in scheme. Comparison experiments with a reference HeNe incremental interferometer show an agreement well within 15 μm, for a range up to 10 m.

Phase-predictable tuning of single-frequency optical synthesizers

We investigate the tuning behavior of a novel type of single-frequency optical synthesizers by phase comparison of the output signals of two identical devices. We achieve phase-stable and cycle-slip free frequency tuning over 28.1 GHz with a maximum zero-to-peak phase deviation of 62 mrad. In contrast to previous implementations of single-frequency optical synthesizers, no comb line order switching is needed when tuned over more than one comb line spacing range of the employed frequency comb.

Gigahertz self-referenceable frequency comb from a semiconductor disk laser

We present a 1.75-GHz self-referenceable frequency comb from a vertical external-cavity surface-emitting laser (VECSEL) passively modelocked with a semiconductor saturable absorber mirror (SESAM). The VECSEL delivers 231-fs pulses with an average power of 100 mW and is optimized for stable and reliable operation. The optical spectrum was centered around 1038 nm and nearly transform-limited with a full width half maximum (FWHM) bandwidth of 5.5 nm. The pulses were first amplified to an average power of 5.5 W using a backward-pumped Yb-doped double-clad large mode area (LMA) fiber and then compressed to 85 fs with 2.2 W of average power with a passive LMA fiber and transmission gratings. Subsequently, we launched the pulses into a highly nonlinear photonic crystal fiber (PCF) and generated a coherent octave-spanning supercontinuum (SC). We then detected the carrier-envelope offset (CEO) frequency (f(CEO)) beat note using a standard f-to-2f-interferometer. The f(CEO) exhibits a signal-to-noise ratio of 17 dB in a 100-kHz resolution bandwidth and a FWHM of ≈10 MHz. To our knowledge, this is the first report on the detection of the f(CEO) from a semiconductor laser, opening the door to fully stabilized compact frequency combs based on modelocked semiconductor disk lasers.

Intrinsic power oscillations generated by the backaction of continuum on solitons and its implications on the transfer functions of a mode-locked laser

Soliton mode locking is an essential technique for building compact mode-locked lasers with multigigahertz repetition rates. In this scheme, pulses behave like dissipative solitons due to the presence of gain, loss, frequency filtering, and nonlinear absorption in the cavity. The continuum waves that radiate from the perturbed soliton act back on the soliton, resulting in periodic changes in the electric field of the pulse. We find that, in the presence of gain filtering or two-photon absorption, this field modulation is converted to power modulation, which is observable from the radio-frequency spectrum of the laser's output power. We investigate its physical origin in the context of soliton perturbation theory. For comparison, we also perform numerical simulations and experiments.

High-power mid-infrared frequency comb from a continuous-wave-pumped bulk optical parametric oscillator

We demonstrate that it is possible to obtain a mid-infrared optical frequency comb (OFC) experimentally by using a continuous-wave-pumped optical parametric oscillator (OPO). The comb is generated without any active modulation. It is based on cascading quadratic nonlinearities that arise from intra-cavity phase mismatched second harmonic generation of the signal wave that resonates in the OPO. The generated OFC is transferred from the signal wavelength (near-infrared) to the idler wavelength (mid-infrared) by intracavity difference frequency generation between the OPO pump wave and the signal comb. We have produced a mid-infrared frequency comb which is tunable from 3.0 to 3.4 µm with an average output power of up to 3.1 W.

Low-noise parametric frequency comb for continuous C-plus-L-band 16-QAM channels generation

A low phase noise frequency comb generated from a continuous-wave seed is experimentally demonstrated across continuous C- and L-bands. Parametrically generated carriers with optical signal-to-noise ratio in excess of 45 dB were used to generate 16-ary quadrature amplitude modulated signals. We characterize 20 GBaud channels' performance that was varied by only 1.7 dB across the combined C/L band.

Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling

A dual-comb nonlinear asynchronous optical sampling method is proposed to simplify determination of the time interval and extend the non-ambiguity range in absolute length measurements. Type II second harmonic generation facilitates curve fitting in determining the time interval between adjacent pulses. Meanwhile, the non-ambiguity range is extended by adjusting the repetition rate of the signal laser. The performance of the proposed method is compared with a heterodyne interferometer. Results show that the system achieves a maximum residual of 100.6 nm and an uncertainty of 1.48 μm in a 0.5 ms acquisition time. With longer acquisition time, the uncertainty can be reduced to 166.6 nm for 50 ms and 82.9 nm for 500 ms. Moreover, the extension of the non-ambiguity range is demonstrated by measuring an absolute distance beyond the inherent range determined by the fixed repetition rate.

Supercontinuum generation by multiple scatterings at a group velocity horizon

A new scheme for supercontinuum generation covering more than one octave and exhibiting extraordinary high coherence properties has recently been proposed [Phys. Rev. Lett. 110, 233901 (2013)]. The scheme is based on two-pulse collision at a group velocity horizon between a dispersive wave and a soliton. Here we demonstrate that the same scheme can be exploited for the generation of supercontinua encompassing the entire transparency region of fused silica, ranging from 300 to 2300nm. At this bandwidth extension, the Raman effect becomes detrimental, yet may be compensated by using a cascaded collision process. Consequently, the high degree of coherence does not degrade even in this extreme scenario.

Two-stage system based on a software-defined radio for stabilizing of optical frequency combs in long-term experiments

A passive optical resonator is a special sensor used for measurement of lengths on the nanometer and sub-nanometer scale. Astabilized optical frequency comb can provide an ultimate reference for measuring the wavelength of a tunable laser locked to the optical resonator. If we lock the repetition and offset frequencies of the comb to a high-grade radiofrequency (RF) oscillator its relative frequency stability is transferred from the RF to the optical frequency domain. Experiments in the field of precise length metrology of low-expansion materials are usually of long-term nature so it is required that the optical frequency comb stay in operation for an extended period of time. The optoelectronic closed-loop systems used for stabilization of combs are usually based on traditional analog electronic circuits processing signals from photodetectors. From an experimental point of view, these setups are very complicated and sensitive to ambient conditions, especially in the optical part, therefore maintaining long-time operation is not easy. The research presented in this paper deals with a novel approach based on digital signal processing and a software-defined radio. We describe digital signal processing algorithms intended for keeping the femtosecond optical comb in a long-time stable operation. This need arose during specialized experiments involving measurements of optical frequencies of tunable continuous-wave lasers. The resulting system is capable of keeping the comb in lock for an extensive period of time (8 days or more) with the relative stability better than 1.6 × 10⁻¹¹.

Strong enhancement of parity violation effects in chiral uranium compounds

A new generation of molecular candidates for parity violation measurements. The chiral UNXYZ compounds are predicted to exhibit strong parity violating effects which are up to an order of magnitude larger than for any of the previously suggested candidates.

CEO stabilization of a femtosecond laser using a SESAM as fast opto-optical modulator

We present a new method for intra-cavity control of the carrier-envelope offset (CEO) frequency of ultrafast lasers that combines high feedback bandwidth with low loss, low nonlinearity, and low dispersion. A semiconductor saturable-absorber mirror (SESAM) inside a modelocked laser is optically pumped with a continuous-wave (cw) laser. In this way, the SESAM acts as intra-cavity opto-optical modulator (OOM): the optical power of the cw-laser corresponds to a high-bandwidth modulation channel for CEO frequency control. We experimentally verified this method for a femtosecond Er:Yb:glass oscillator (ERGO), in which one SESAM is in parallel used for modelocking and as intra-cavity OOM for achieving a tight CEO lock. This laser can also be CEO-stabilized in the usual scheme, in which the laser pump current is modulated, i.e., the gain element acts as intra-cavity OOM. We compare the performance with gain and SESAM OOM measuring CEO transfer function, frequency noise power spectral density (PSD), and Allan deviation for integration times up to 1000 s. In the case of the gain OOM, the millisecond upper-state lifetime of the Er:Yb:glass limits the achievable CEO-control bandwidth to <10 kHz. The feedback bandwidth of the SESAM OOM was more than a factor of 10 higher than the gain OOM bandwidth and was mainly limited by the used current driver. The residual integrated phase noise (1 Hz - 100 kHz) of the ~20-MHz CEO beat was improved by more than an order of magnitude (from 720 mrad to less than 65 mrad), and the fractional frequency stability by a factor of 4 (from 1∙10<su⁻⁸ to 2.5∙10⁻⁹ at 1 s).

Complete analog control of the carrier-envelope-phase of a high-power laser amplifier

In this work we demonstrate the development of a complete analog feedback loop for the control of the carrier-envelope phase (CEP) of a high-average power (20 W) laser operating at 10 kHz repetition rate. The proposed method combines a detection scheme working on a single-shot basis at the full-repetition-rate of the laser system with a fast actuator based either on an acousto-optic or on an electro-optic crystal. The feedback loop is used to correct the CEP fluctuations introduced by the amplification process demonstrating a CEP residual noise of 320 mrad measured on a single-shot basis. The comparison with a feedback loop operating at a lower sampling rate indicates an improvement up to 45% in the residual noise. The measurement of the CEP drift for different integration times clearly evidences the importance of the single-shot characterization of the residual CEP drift. The demonstrated scheme could be efficiently applied for systems approaching the 100 kHz repetition rate regime.

Generation of ultra-narrow, stable and tunable millimeter- and terahertz- waves with very low phase noise

The interference between two spectral lines of the frequency comb of a fiber femtosecond laser is used to generate millimeter-wave and terahertz tones. The two lines are selected by stimulated Brillouin scattering (SBS) amplification. All other modes are strongly rejected based on polarization discrimination, using the polarization-pulling effect that is associated with SBS. The inherent high spectral quality of a femtosecond fiber laser comb allows generation of millimeter- and terahertz waves with linewidths below 1 Hz, and a phase noise of -105 dBc/Hz at 10 kHz offset. The generation, free-space transmission and detection of continuous waves at 1 THz are demonstrated as well. Lastly, the generated millimeter-wave carriers are modulated by 40 Gbit/s data. The entire system consists of a fiber laser and standard equipment of optical telecommunications. Besides metrology, spectroscopy and astronomy, the method can be utilized for the emergent field of wireless millimeter-wave and THz-communications at ultra-high data rates.

Femtosecond laser pulses for fast 3-D surface profilometry of microelectronic step-structures

Fast, precise 3-D measurement of discontinuous step-structures fabricated on microelectronic products is essential for quality assurance of semiconductor chips, flat panel displays, and photovoltaic cells. Optical surface profilers of low-coherence interferometry have long been used for the purpose, but the vertical scanning range and speed are limited by the micro-actuators available today. Besides, the lateral field-of-view extendable for a single measurement is restricted by the low spatial coherence of broadband light sources. Here, we cope with the limitations of the conventional low-coherence interferometer by exploiting unique characteristics of femtosecond laser pulses, i.e., low temporal but high spatial coherence. By scanning the pulse repetition rate with direct reference to the Rb atomic clock, step heights of ~69.6 μm are determined with a repeatability of 10.3 nm. The spatial coherence of femtosecond pulses provides a large field-of-view with superior visibility, allowing for a high volume measurement rate of ~24,000 mm3/s.

Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip

We report a novel geometry for OPOs based on nonlinear microcavity resonators. This approach relies on a self-locked scheme that enables OPO emission without the need for thermal locking of the pump laser to the microcavity resonance. By exploiting a CMOS-compatible microring resonator, we achieve oscillation featured by a complete absence of "shutting down", i.e. the self-terminating behavior that is a very common and detrimental occurrence in externally pumped OPOs. Further, our scheme consistently produces very wide bandwidth (>300nm, limited by our experimental set-up) combs that oscillate at a spacing equal to the FSR of the micro cavity resonance.

Endless frequency shifting of optical frequency comb lines

The functional principle of a novel technique for frequency shifting lines of an optical frequency comb is demonstrated. The underlying principle is to shift the carrier frequency by changing the carrier phase within the time span between subsequent pulses of a mode-locked laser used as comb generator. This universal frequency shifter does not require intrusion into the comb generator and provides high agility for arbitrary temporal frequency evolutions.

Multi-wavelength generation by self-seeded four-wave mixing

A cost effective method of generating multi-wavelength based on the cascaded four wave mixing effect is experimentally demonstrated. The proposed scheme is free from external tunable laser sources and pump modulators, resulting from the use of a broadened linewidth tunable dual wavelength erbium-doped fiber laser as intracavity pump. In this configuration, the number of four wave mixing cascades becomes larger in tandem with the increment of erbium-doped fiber amplifier output power. When its output power is set at 20.57 dBm, six waves having optical signal to noise ratio larger than 10 dB are generated. The six waves are stable with peak power fluctuations less than 1 dB within 30 minutes period and tunable with wavelength spacing ranging from 1.03 nm to 11.31 nm.

Multi-delay, phase coherent pulse pair generation for precision Ramsey-frequency comb spectroscopy

We demonstrate the generation of phase-stable mJ-pulse pairs at programmable inter-pulse delays up to hundreds of nanoseconds. A detailed investigation of potential sources for phase shifts during the parametric amplification of the selected pulses from a Ti:Sapphire frequency comb is presented, both numerically and experimentally. It is shown that within the statistical error of the phase measurement of 10 mrad, there is no dependence of the differential phase shift over the investigated inter-pulse delay range of more than 300 ns. In combination with nonlinear upconversion of the amplified pulses, the presented system will potentially enable short wavelength (<100 nm), multi-transition Ramsey-frequency comb spectroscopy at the kHz-level.