An optical clock based on a single trapped 199Hg+ ion

Electronic structure with spin-orbit coupling effect of HfH molecule for laser cooling investigations

The electronic structure, including the spin-orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ - Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission [Formula: see text] , and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.

Low divergence cold-wall oven for loading ion traps

We present a compact cold-wall oven that is simple to build and align for loading miniature ion traps with calcium ions. The cold-wall oven, which is a metal-loaded capillary heated only through a portion of its length by the passage of a current, is described and characterized. An atomic beam with a low divergence of 14 mrad is produced. We perform Doppler-sensitive, resonant fluorescence measurements on the atomic beam to characterize the oven's performance. The emission of atoms from the oven is seen within ∼70 s after turning on the oven at an electric power consumption of <10 W. The flow rate is measured to be 1.5 ± 0.2 × 109 atoms s-1 at a temperature of 702 ± 7 K. The entire oven assembly is mounted on a CF16 feedthrough. This design can be extended to other species for producing a collimated atomic beam.

Photonic chip-based low-noise microwave oscillator

Numerous modern technologies are reliant on the low-phase noise and exquisite timing stability of microwave signals. Substantial progress has been made in the field of microwave photonics, whereby low-noise microwave signals are generated by the down-conversion of ultrastable optical references using a frequency comb1-3. Such systems, however, are constructed with bulk or fibre optics and are difficult to further reduce in size and power consumption. In this work we address this challenge by leveraging advances in integrated photonics to demonstrate low-noise microwave generation via two-point optical frequency division4,5. Narrow-linewidth self-injection-locked integrated lasers6,7 are stabilized to a miniature Fabry-Pérot cavity8, and the frequency gap between the lasers is divided with an efficient dark soliton frequency comb9. The stabilized output of the microcomb is photodetected to produce a microwave signal at 20 GHz with phase noise of -96 dBc Hz-1 at 100 Hz offset frequency that decreases to -135 dBc Hz-1 at 10 kHz offset-values that are unprecedented for an integrated photonic system. All photonic components can be heterogeneously integrated on a single chip, providing a significant advance for the application of photonics to high-precision navigation, communication and timing systems.

Powerful 1-µm 1-GHz optical frequency comb

A self-referenced optical frequency comb is presented based on Kerr-lens mode-locking of ytterbium-doped CALGO. The robust source delivers 3.5 W average power in 44 fs-long pulses at 1 GHz repetition rate. The residual root-mean-square timing jitter of the emitted pulse-train is 146 fs and the residual integrated phase noise of the carrier-envelope offset frequency is 107 mrad, both in a span from 1 Hz to 10 MHz. After stabilization, 2.7 W average power remains for direct application. This work represents the first multi-mode pumped Kerr-lens mode-locked optical frequency comb at gigahertz-level repetition rate.

Kerr-induced synchronization of a cavity soliton to an optical reference

The phase-coherent frequency division of a stabilized optical reference laser to the microwave domain is made possible by optical-frequency combs (OFCs)1,2. OFC-based clockworks3-6 lock one comb tooth to a reference laser, which probes a stable atomic transition, usually through an active servo that increases the complexity of the OFC photonic and electronic integration for fieldable clock applications. Here, we demonstrate that the Kerr nonlinearity enables passive, electronics-free synchronization of a microresonator-based dissipative Kerr soliton (DKS) OFC7 to an externally injected reference laser. We present a theoretical model explaining this Kerr-induced synchronization (KIS), which closely matches experimental results based on a chip-integrated, silicon nitride, micro-ring resonator. Once synchronized, the reference laser captures an OFC tooth, so that tuning its frequency provides direct external control of the OFC repetition rate. We also show that the stability of the repetition rate is linked to that of the reference laser through the expected frequency division factor. Finally, KIS of an octave-spanning DKS exhibits enhancement of the opposite dispersive wave, consistent with the theoretical model, and enables improved self-referencing and access to the OFC carrier-envelope offset frequency. The KIS-mediated enhancements we demonstrate can be directly implemented in integrated optical clocks and chip-scale low-noise microwave generators.

High power optical frequency comb with 10-19 frequency instability

Optical frequency combs with more than 10 W have paved the way for extreme ultraviolet combs generation by interaction with inert gases, leading to extreme nonlinear spectroscopy and the ultraviolet nuclear clock. Recently, the demand for an ultra-long-distance time and frequency space transfer via optical dual-comb proposes a new challenge for high power frequency comb in respect of power scaling and optical frequency stability. Here we present a frequency comb based on fiber chirped pulse amplification (CPA), which can offer more than 20 W output power. We further characterize the amplifier branch noise contribution by comparing two methods of locking to an optical reference and measure the out-of-loop frequency instability by heterodyning two identical high-power combs. Thanks to the low noise CPA, reasonable locking method, and optical path-controlled amplifiers, the out-of-loop beat note between two combs demonstrates the unprecedented frequency stability of 4.35 × 10-17 at 1s and 6.54 × 10-19 at 1000 s.

Highly coherent hybrid dual-comb spectrometer

Dual comb spectroscopy (DCS) is a broadband technique offering high resolution and fast data acquisition. Current state-of-the-art designs are based on a pair of fiber or solid-state lasers, which allow broadband spectroscopy but require a complicated stabilization setup. Semiconductor lasers are tunable, cost-effective, and easily integrable while limited by a narrow bandwidth. This motivates a hybrid design combining the advantages of both systems. However, establishing sufficiently long mutual coherence time remains challenging. This work describes a hybrid dual-comb spectrometer comprising a broadband fiber laser (FC) and an actively mode-locked semiconductor laser (MLL) with a narrow but tunable spectrum. A high mutual coherence time of around 100 seconds has been achieved by injection locking the MLL to a continuous laser (CW), which is locked on a single line of the FC. We have also devised a method to directly stabilize the entire spectrum of FC to a high finesse cavity. This results in a long term stability of 5 × 10^-12 at 1 second and 5 × 10^-14 at 350 seconds. Additionally, we have addressed the effect of cavity dispersion on the locking quality, which is important for broadband comb lasers.

Magneto-optical trapping in a near-suface borehole

Borehole gravity sensing can be used in a number of applications to measure features around a well, including rock-type change mapping and determination of reservoir porosity. Quantum technology gravity sensors, based on atom interferometry, have the ability to offer increased survey speeds and reduced need for calibration. While surface sensors have been demonstrated in real world environments, significant improvements in robustness and reductions to radial size, weight, and power consumption are required for such devices to be deployed in boreholes. To realise the first step towards the deployment of cold atom-based sensors down boreholes, we demonstrate a borehole-deployable magneto-optical trap, the core package of many cold atom-based systems. The enclosure containing the magneto-optical trap itself had an outer radius of (60 ± 0.1) mm at its widest point and a length of (890 ± 5) mm. This system was used to generate atom clouds at 1 m intervals in a 14 cm wide, 50 m deep borehole, to simulate how in-borehole gravity surveys are performed. During the survey, the system generated, on average, clouds of (3.0 ± 0.1) × 105 87Rb atoms with the standard deviation in atom number across the survey observed to be as low as 8.9 × 104.

Phase-stabilized UV light at 267 nm through twofold second harmonic generation

Providing phase stable laser light is important to extend the interrogation time of optical clocks towards many seconds and thus achieve small statistical uncertainties. We report a laser system providing more than 50 µW phase-stabilized UV light at 267.4 nm for an aluminium ion optical clock. The light is generated by frequency-quadrupling a fibre laser at 1069.6 nm in two cascaded non-linear crystals, both in single-pass configuration. In the first stage, a 10 mm long PPLN waveguide crystal converts 1 W fundamental light to more than 0.2 W at 534.8 nm. In the following 50 mm long DKDP crystal, more than 50 µW of light at 267.4 nm are generated. An upper limit for the passive short-term phase stability has been measured by a beat-node measurement with an existing phase-stabilized quadrupling system employing the same source laser. The resulting fractional frequency instability of less than 5×10^-17 after 1 s supports lifetime-limited probing of the ²⁷Al⁺ clock transition, given a sufficiently stable laser source. A further improved stability of the fourth harmonic light is expected through interferometric path length stabilisation of the pump light by back-reflecting it through the entire setup and correcting for frequency deviations. The in-loop error signal indicates an electronically limited instability of 1 × 10^-18 at 1 s.

Dissipative soliton generation and real-time dynamics in microresonator-filtered fiber lasers

Optical frequency combs in microresonators (microcombs) have a wide range of applications in science and technology, due to its compact size and access to considerably larger comb spacing. Despite recent successes, the problems of self-starting, high mode efficiency as well as high output power have not been fully addressed for conventional soliton microcombs. Recent demonstration of laser cavity soliton microcombs by nesting a microresonator into a fiber cavity, shows great potential to solve the problems. Here we study the dissipative soliton generation and interaction dynamics in a microresonator-filtered fiber laser in both theory and experiment. We bring theoretical insight into the mode-locking principle, discuss the parameters effect on soliton properties, and provide experimental guidelines for broadband soliton generation. We predict chirped bright dissipative soliton with flat-top spectral envelope in microresonators with normal dispersion, which is fundamentally forbidden for the externally driven case. Furthermore, we experimentally achieve soliton microcombs with large bandwidth of ~10 nm and high mode efficiency of 90.7%. Finally, by taking advantage of an ultrahigh-speed time magnifier, we study the real-time soliton formation and interaction dynamics and experimentally observe soliton Newton's cradle. Our study will benefit the design of the novel, high-efficiency and self-starting microcombs for real-world applications.

Extending Non-Ambiguity Range of Dual-Comb Ranging for a Mobile Target Based on FPGA

Dual-comb ranging (DCR) is an important method in absolute distance ranging because of its high precision, fast acquisition rate, and large measuring range. DCR needs to obtain precise results during distance measurements for a mobile target. However, the non-ambiguity range (NAR) is a challenge when pushing the dual-comb ranging to the industry field. This paper presents a solution for extending NAR by designing an algorithm and realizing it on a field-programmable gate array (FPGA). The algorithm is robust when facing the timing jitter in the optical frequency comb. Without averaging, the Allan deviation of the results in 1 ms is ∼3.89 μm and the Allan deviation of the results is ∼0.37 μm at an averaging time of 100 ms when the target object is standstill near the NAR. In addition, several ranging experiments were conducted on a mobile target whose speed was from ∼5 mm/s to ∼10 mm/s. The experimental results verify the effectiveness and robustness of our design. The implemented design is an online and real-time data processing unit that shows great industrial potential for using the DCR system.

48 -cm-long room-temperature cavities in vertical and horizontal orientations for Sr optical clock

The development of an optical clock with ultimate accuracy and stability requires lasers with very narrow linewidths. We present two ultrastable laser systems based on 48-cm-long Fabry-Perot cavities made of ultralow expansion glass in horizontal and vertical configurations operating at 698 nm. Fractional frequency instability of the beat signal between the two lasers reaches 1.6×10^-15 at the averaging time of 1 s. We experimentally characterized the contribution of the different noise sources (power fluctuations, residual amplitude modulation, the Doppler noise, and sensitivity to the shock impact) and found that in our case the laser frequency instability to a large extent is determined by an optoelectronic feedback loop. Although the vertical configuration was easier to manufacture and transport, it is much more sensitive to acoustics and horizontal accelerations compared to the horizontal one. Both laser systems were transported over a 60 km distance from the Lebedev Physical Institute to the All-Russian Scientific Research Institute for Physical-Engineering and Radiotechnical Metrology (VNIIFTRI), where they serve as local oscillators for spectroscopy of the clock transition in the recently developed strontium optical clock.

Towards integrated photonic interposers for processing octave-spanning microresonator frequency combs

Microcombs-optical frequency combs generated in microresonators-have advanced tremendously in the past decade, and are advantageous for applications in frequency metrology, navigation, spectroscopy, telecommunications, and microwave photonics. Crucially, microcombs promise fully integrated miniaturized optical systems with unprecedented reductions in cost, size, weight, and power. However, the use of bulk free-space and fiber-optic components to process microcombs has restricted form factors to the table-top. Taking microcomb-based optical frequency synthesis around 1550 nm as our target application, here, we address this challenge by proposing an integrated photonics interposer architecture to replace discrete components by collecting, routing, and interfacing octave-wide microcomb-based optical signals between photonic chiplets and heterogeneously integrated devices. Experimentally, we confirm the requisite performance of the individual passive elements of the proposed interposer-octave-wide dichroics, multimode interferometers, and tunable ring filters, and implement the octave-spanning spectral filtering of a microcomb, central to the interposer, using silicon nitride photonics. Moreover, we show that the thick silicon nitride needed for bright dissipative Kerr soliton generation can be integrated with the comparatively thin silicon nitride interposer layer through octave-bandwidth adiabatic evanescent coupling, indicating a path towards future system-level consolidation. Finally, we numerically confirm the feasibility of operating the proposed interposer synthesizer as a fully assembled system. Our interposer architecture addresses the immediate need for on-chip microcomb processing to successfully miniaturize microcomb systems and can be readily adapted to other metrology-grade applications based on optical atomic clocks and high-precision navigation and spectroscopy.

Hybrid modeling approach for mode-locked laser diodes with cavity dispersion and nonlinearity

Semiconductor-based mode-locked lasers, integrated sources enabling the generation of coherent ultra-short optical pulses, are important for a wide range of applications, including datacom, optical ranging and spectroscopy. As their performance remains largely unpredictable due to the lack of commercial design tools and the poorly understood mode-locking dynamics, significant research has focused on their modeling. In recent years, traveling-wave models have been favored because they can efficiently incorporate the rich semiconductor physics of the laser. However, thus far such models struggle to include nonlinear and dispersive effects of an extended passive laser cavity, which can play an important role for the temporal and spectral pulse evolution and stability. To overcome these challenges, we developed a hybrid modeling strategy by unifying the traveling-wave modeling technique for the semiconductor laser sections with a split-step Fourier method for the extended passive laser cavity. This paper presents the hybrid modeling concept and exemplifies for the first time the significance of the third order nonlinearity and dispersion of the extended cavity for a 2.6 GHz III–V-on-Silicon mode-locked laser. This modeling approach allows to include a wide range of physical phenomena with low computational complexity, enabling the exploration of novel operating regimes such as chip-scale soliton mode-locking.

Direct chip-scale optical frequency divider via regenerative harmonic injection locking

A novel optical frequency division technique, called regenerative harmonic injection locking, is used to transfer the timing stability of an optical frequency comb with a repetition rate in the millimeter wave range (∼300GHz) to a chip-scale mode-locked laser with a ∼10GHz repetition rate. By doing so, the 300 GHz optical frequency comb is optically divided by a factor of 30× to 10 GHz. The stability of the mode-locked laser after regenerative harmonic injection locking is ∼10^-12 at 1 s with a 1/τ trend. To facilitate optical frequency division, a coupled opto-electronic oscillator is implemented to assist the injection locking process. This technique is exceptionally power efficient, as it uses less than 100µW of optical power to achieve stable locking.

Re-evaluation of ortho-para-dependence of self pressure-broadening in the ν1 + ν3 band of acetylene

Optical frequency comb-referenced measurements of self pressure-broadened line profiles of the R(8) to R(13) lines in the ν₁ + ν₃ combination band of acetylene near 1.52 µm are reported. The analysis of the data found no evidence for a previously reported [Iwakuni et al., Phys. Rev. Lett. 117(14), 143902 (2016)] systematic alternation in self pressure-broadened line widths with the nuclear spin state of the molecule. The present work brought out the need for the use of an accurate line profile model and careful accounting for weak background absorptions due to hot band and lower abundance isotopomer lines. The data were adequately fit using the quadratic speed-dependent Voigt profile model, neglecting the small speed-dependent shift. Parameters describing the most probable and speed-dependent pressure-broadening, most probable shift, and the line strength were determined for each line. Detailed modeling of the results of Iwakuni et al. showed that their neglect of collisional narrowing due to the speed-dependent broadening term combined with the strongly absorbing data recorded and analyzed in transmission mode were the reasons for their results.

The Interband Cascade Laser

We review the history, development, design principles, experimental operating characteristics, and specialized architectures of interband cascade lasers for the mid-wave infrared spectral region. We discuss the present understanding of the mechanisms limiting the ICL performance and provide a perspective on the potential for future improvements. Such device properties as the threshold current and power densities, continuous-wave output power, and wall-plug efficiency are compared with those of the quantum cascade laser. Newer device classes such as ICL frequency combs, interband cascade vertical-cavity surface-emitting lasers, interband cascade LEDs, interband cascade detectors, and integrated ICLs are reviewed for the first time.

Ultraviolet to mid-infrared supercontinuum generation in single-crystalline aluminum nitride waveguides

We demonstrate ultrabroadband supercontinuum generation from ultraviolet to mid-infrared wavelengths in single-crystalline aluminum nitride waveguides. Tunable dispersive waves are observed at the mid-infrared regime by precisely controlling the waveguide widths. In addition, ultraviolet light is generated through cascaded second-harmonic generation in the modal phase-matched waveguides. Numerical simulation indicates a high degree of coherence of the generated spectrum at around the telecom pump and two dispersive waves. Our results establish a reliable path for multiple octave supercontinuum comb generation in single-crystalline aluminum nitride to enable applications including precision frequency metrology and spectroscopy.

Optical frequency combs: Coherently uniting the electromagnetic spectrum

Optical frequency combs were introduced around 20 years ago as a laser technology that could synthesize and count the ultrafast rate of the oscillating cycles of light. Functioning in a manner analogous to a clockwork of gears, the frequency comb phase-coherently upconverts a radio frequency signal by a factor of [Formula: see text] to provide a vast array of evenly spaced optical frequencies, which is the comb for which the device is named. It also divides an optical frequency down to a radio frequency, or translates its phase to any other optical frequency across hundreds of terahertz of bandwidth. We review the historical backdrop against which this powerful tool for coherently uniting the electromagnetic spectrum developed. Advances in frequency comb functionality, physical implementation, and application are also described.

Ultralow noise DFB fiber laser with self-feedback mechanics utilizing the inherent photothermal effect

Single frequency laser sources with low frequency noise are now at the heart of precision high-end science, from the most precise optical atomic clocks to gravitational-wave detection, thanks to the rapid development of laser frequency stabilization techniques based on optical or electrical feedback from an external reference cavity. Despite the tremendous progress, these laser systems are relatively high in terms of complexity and cost, essentially suitable for the laboratory environment. Nevertheless, more and more commercial applications also demand laser sources with low noise to upgrade their performance, such as fiber optic sensing and LiDAR, which require reduced complexity and good robustness to environmental perturbations. Here, we describe an ultralow noise DFB fiber laser with self-feedback mechanics that utilizes the inherent photothermal effect through the regulation of the thermal expansion coefficient of laser cavity. Over 20 dB of frequency noise reduction below several tens of kilohertz Fourier frequency is achieved, limited by the fundamental thermal noise, which is, to date, one of the best results for a free-running DFB fiber laser. The outcome of this work offers promising prospects for versatile applications due to its ultralow frequency noise, simplicity, low cost, and environmental robustness.

Quantum-well laser diodes for frequency comb spectroscopy

We demonstrate simple optical frequency combs based on semiconductor quantum well laser diodes. The frequency comb spectrum can be tailored by choice of material properties and quantum-well widths, providing spectral flexibility. We demonstrate the correlation in the phase fluctuations between two devices on the same chip by generating a radio-frequency dual comb spectrum.

High performance quantum cascade laser frequency combs at λ ∼ 6 μm based on plasmon-enhanced dispersion compensation

We demonstrate quantum cascade laser (QCL) optical frequency combs emitting at λ ∼ 6 μm. A 5.5 μm-wide, 4.5 mm-long laser exhibits comb operation from -20 °C up to 50 °C. A maximum output power of 300 mW is achieved at 50 °C showing a robustness of the system. The laser output spectrum is ∼80 cm^-1 wide at the maximum current, with a mode spacing of 0.334 cm^-1, resulting in a total of 240 modes with an average power of 0.8 mW per mode. To achieve frequency comb operation, a plasmonic-waveguide approach is utilized. A thin, highly-doped indium phosphide (InP) layer is inserted in the top cladding design to compensate the positive dispersion of the system (material and waveguide). This approach can be further exploited to design QCL combs at even shorter wavelengths, down to 4 μm. Different ridge widths between 2.8 and 5.5 μm have been fabricated and characterized. All of the devices exhibit frequency comb operation. These observations demonstrate that the plasmonic-waveguide is a robust and reliable method for dispersion compensation of a semiconductor laser systems to achieve frequency comb operation.

Development of a photoelectric phase-locked loop model to better synchronize frequency combs and microwaves

The high phase coherence between ultralow-noise microwaves and ultrahigh-stable optical frequency combs (OFCs) is of both scientific and technological relevance for telecommunication, timekeeping, astronomy, and metrology. Here, a photoelectric phase-locked loop (PLL) model with ultralow phase noise based on the optical-microwave phase detector technique has been proposed and experimentally demonstrated. A detailed mathematical model for tight, real-time phase synchronization of OFCs and microwaves is developed to investigate the feasibility and analyze the characteristics of the phase-coherent system. We fabricate a compact PLL circuit with a proportional-integral-derivative regulator for the synchronization of an OFC to a microwave reference. Once synchronized, the long-term stability of the OFC agrees to 2.4×10^-14 at a 1000 s averaging time, which is enhanced by more than 4 orders of magnitude. Besides, the OFC almost acquires the same frequency stability as the microwave source. The ability to better phase synchronize OFCs and microwaves enables a wide range of applications beyond the laboratory.

Piezo-electric transducer actuated mirror with a servo bandwidth beyond 500 kHz

We demonstrate a novel system that uses a piezoelectric transducer (PZT)-actuated mirror for laser stabilization. A combination of a simple mechanical design and electronic circuits is used to realize an ultra-flat frequency response, which enables an effective feedback bandwidth of 500 kHz. The PZT also performed well when used in a mode-locked laser with a GHz repetition rate, to which it is difficult to apply an electro-optic modulator (EOM).

Frequency Comb Generation via Cascaded Second-Order Nonlinearities in Microresonators

Optical frequency combs are revolutionizing modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturization through microresonator-based solutions. The combs in such devices are typically generated using the third-order χ^{(3)} nonlinearity of the resonator material. An alternative approach is making use of second-order χ^{(2)} nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or on relatively low-Q waveguide resonators. Here, we present the first such comb that is based on a millimeter-sized microresonator made of lithium niobate, that allows for cascaded second-order nonlinearities. This proof-of-concept device comes already with pump powers as low as 2 mW, generating repetition-rate-locked combs around 1064 and 532 nm. From the nonlinear dynamics point of view, the observed combs correspond to Turing roll patterns.

Possibilities of wide-angle tellurium dioxide acousto-optic cell application for the optical frequency comb generation

The development of the optical frequency comb (OFC) generation and practical application methods is one of the most important and rapidly developing areas of the modern optical electronics. One of the comb types is acousto-optical (AO) OFCs. This type of OFCs is obtained by the multiple passage of an optical signal through a closed loop containing an acousto-optic frequency shifter (AOFS). Despite the fact that AO OFCs have been studied quite intensively lately, the published papers did not focus on the influence of the main element, the AO cell used as AOFS, parameters on the characteristics of the obtained optical comb, primarily on the comb spectral width, number of spectral components and its envelope shape. In this paper, we perform a theoretical analysis of all possiblities in paratellurite crystal wide-angle AO diffraction geometries in order to determine the most suitable for the application as AOFS in a frequency shifting loop.

Phase-coherent lightwave communications with frequency combs

Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. Optical frequency combs can replace the multiple lasers used for the different wavelength channels. Beyond multiplexing, it has been suggested that the broadband phase coherence of frequency combs could simplify the receiver scheme by performing joint reception and processing of several wavelength channels, but an experimental validation in a fiber transmission experiment remains elusive. Here we demonstrate and quantify joint reception and processing of several wavelength channels in a full transmission system. We demonstrate two joint processing schemes; one that reduces the phase-tracking complexity and one that increases the transmission performance.

Frequency combs have the potential to be used as multi-wavelength sources in future optical communications through fiber. Here the authors demonstrate joint phase processing of multi-wavelength comb transmission, and show two schemes to improve performance and reduce complexity.

Electronic Structure with Rovibrational Calculations of the Magnesium Monohalides MgX and Their Cations MgX+ (X = Cl, Br, and I)

Alkaline-earth monohalides are popular compounds that are used in various applications. Little is known, however, in terms of electronic structure, about their cations and their low-lying electronic states. We present in this work electronic structure ab-initio calculations based on multireference configuration interaction plus Davidson correction of three magnesium monohalides and their cations (MgCl, MgBr, MgI, MgCl⁺, MgBr⁺, and MgI⁺). We determine the spectroscopic constants T _e, R _e, ω_e, B _e, and α_e and the dissociation energies D _e for their bound states. Additionally, we investigate their vibrational properties by calculating the vibrational eigenvalue E _v, the rotational constant B _v, and the centrifugal distortion constant D _v. We additionally study the electric charge distribution of several states by determining their permanent dipole moment and transition dipole moment curves. Finally, we calculate the Franck-Condon factors and the radiative lifetimes as precursors for laser cooling experiments.

Silicon nitride/titanium oxide hybrid waveguide design enabling broadband athermal operation

This paper presents a special design of a new kind of silicon nitride/titanium oxide hybrid waveguide with multi-layer materials laminate structure aiming at broadband athermal operation. By incorporating three layers of titanium oxide whose thermo-optic coefficient (TOC) is negative in the waveguide core and upper cladding regions, the thermal drift of the conventional strip waveguide induced by the positive TOC of silicon nitride is fully compensated, with the effective TOC of the hybrid waveguide achieving zero at 1550 nm and only varying extremely slightly within ±6×10^-7/K in the wavelength band from 1350 to 1850 nm. In addition, due to the inherent alternate growth manner of titanium dioxide and silicon nitride thin layers, this new kind of multi-layer material laminate structure waveguide holds the potential of avoiding the challenging growth of low-stress crack-free single-layer silicon nitride film thick enough for realizing an anomalous dispersion waveguide. Furthermore, we numerically demonstrate the different influences of the temperature change on optical frequency comb generation between the traditional waveguide and the hybrid waveguide, and we find that the athermal hybrid waveguide is much more temperature insensitive than the strip waveguide.

Deterministic Nonlinear Transformations of Phase Noise in Quantum-Limited Frequency Combs

Optical phase noise of femtosecond lasers is analyzed over various steps of broadband nonlinear frequency conversion. The intrinsic phase jitter of our system originates from quantum statistics in the mode-locked oscillator. Supercontinuum generation by four-wave-mixing processes preserves a noise minimum at the optical carrier frequency. From there, a quadratic increase of the comb linewidth results with mutually anticorrelated phase fluctuations of both spectral wings. Passive phase locking by difference frequency generation strongly enhances the optical phase noise to a level equaling the carrier-envelope phase jitter of the fundamental comb. The same value results from quadratic extrapolation of the optical phase noise to radio frequencies. Our findings are consistent with a fully deterministic transformation of phase noise according to the elastic tape model.

Octave-spanning supercontinuum generation in nanoscale lithium niobate waveguides

We demonstrate octave-spanning supercontinuum generation in unpoled lithium niobate waveguides, which are engineered to possess anomalous dispersion and pumped by a turn-key femtosecond laser centered at 1560 nm. Tunable dispersive waves and strong phase-matched second-harmonic generation are both observed by controlling the widths of the waveguides. The major features of the experimental spectra are reproduced by numerical modeling of the generalized nonlinear Schrödinger equation, which can be used to guide waveguide designs for tailoring the supercontinuum spectrum. Our results identify a path to a simple and integrable supercontinuum source in lithium niobate nanophotonic platform and will enable new capabilities in precision frequency metrology.

High-coherence ultra-broadband bidirectional dual-comb fiber laser

Dual-comb spectroscopy has emerged as an attractive spectroscopic tool for high-speed, high-resolution, and high-sensitivity broadband spectroscopy. It exhibits certain advantages when compared to the conventional Fourier-transform spectroscopy. However, the high cost of the conventional system, which is based on two mode-locked lasers and a complex servo system with a common single-frequency laser, limits the applicability of the dual-comb spectroscopy system. In this study, we overcame this problem with a bidirectional dual-comb fiber laser that generates two high-coherence ultra-broadband frequency combs with slightly different repetition rates (f_rep). The two direct outputs from the single-laser cavity displayed broad spectra of > 50 nm; moreover, an excessively small difference in the repetition rate (< 1.5 Hz) was achieved with high relative stability, owing to passive common-mode noise cancellation. With this slight difference in the repetition rate, the applicable optical spectral bandwidth in dual-comb spectroscopy could attain ~479 THz (~3,888 nm). In addition, we successfully generated high-coherence ultra-broadband frequency combs via nonlinear spectral broadening and detected high signal-to-noise-ratio carrier-envelope offset frequency (f_CEO) beat signals using the self-referencing technique. We also demonstrated the high relative stability between the two f_CEO beat signals and tunability. To our knowledge, this is the first demonstration of f_CEO detection and frequency measurement using a self-referencing technique for a dual-comb fiber laser. The developed high-coherence ultra-broadband dual-comb fiber laser with capability of f_CEO detection is likely to be a highly effective tool in practical, high-sensitivity, ultra-broadband applications.

Trapped Hg+ ion crystal generated by isotope-selective photoionization

We present studies on monoisotopic Hg⁺ ions generation and trapping at room temperature. An ultraviolet laser system, including a frequency-controlled 194 nm laser and a 254 nm laser, is constructed. Mercury atoms are isotope-selectively excited by the 254 nm laser. The spectrum of the 6s²-6s6p transition lines for natural mercury isotopes is measured, and the uncertainty is less than 100 MHz. Then, the selected mercury isotopes are ionized by the 194 nm laser and trapped in a linear Paul trap. The fluorescence of the ion crystal at 194 nm is detected, and the temperature of the ions is estimated to be less than 10 mK.

Frequency comb up- and down-conversion in synchronously driven χ(2) optical microresonators

Optical frequency combs are key to optical precision measurements. While most frequency combs operate in the near-infrared (NIR) regime, many applications require combs at mid-infrared (MIR), visible (VIS), or even ultra-violet (UV) wavelengths. Frequency combs can be transferred to other wavelengths via nonlinear optical processes; however, this becomes exceedingly challenging for high-repetition-rate frequency combs. Here it is demonstrated that a synchronously driven high-Q microresonator with a second-order optical nonlinearity can efficiently convert high-repetition-rate NIR frequency combs to VIS, UV, and MIR wavelengths, providing new opportunities for microresonator and electro-optic combs in applications including molecular sensing, astronomy, and quantum optics.

Video-rate centimeter-range optical coherence tomography based on dual optical frequency combs by electro-optic modulators

Imaging speed and range are two important parameters for optical coherence tomography (OCT). A conventional video-rate centimeter-range OCT requires an optical source with hundreds of kHz repetition rate and needs the support of broadband detectors and electronics (>1 GHz). In this paper, a type of video-rate centimeter-range OCT system is proposed and demonstrated based on dual optical frequency combs by leveraging electro-optic modulators. The repetition rate difference between dual combs, i.e. the A-scan rate of dual-comb OCT, can be adjusted within 0~6 MHz. By down-converting the interference signal from optical domain to radio-frequency domain through dual comb beating, the down-converted bandwidth of the interference signal is less than 22.5 MHz which is at least two orders of magnitude lower than that in conventional OCT systems. A LabVIEW program is developed for video-rate operation, and the centimeter imaging depth is proved by using 10 pieces of 1-mm thick glass stacked as the sample. The effective beating bandwidth between two optical comb sources is 7 nm corresponding to ~108 comb lines, and the axial resolution of the dual-comb OCT is 158 µm. Dual optical frequency combs provide a promising solution to relax the detection bandwidth requirement in fast long-range OCT systems.

Manipulation of extinction features in frequency combs through the usage of graphene

Lately, the integration of two-dimensional materials into semiconductor devices has allowed the modification of their effective index by simply applying a modest voltage (between 0 and 3 volts). In this work, we present a device composed of two evanescently coupled silicon microring resonators where both rings have a graphene layer on top. This design is aimed to produce frequency combs with transmission characteristics controlled upon voltage application to the graphene layer. We numerically analyze the device response as a function of the incident wavelength and applied voltage. The results showed a low input intensity (0.6 GW/cm²) needed and a rapid response time (0.1 μs), in comparison to devices controlled by heat injection.

Control of second-harmonic generation in doubly resonant aluminum nitride microrings to address a rubidium two-photon clock transition

Nonlinear optical effects have been studied extensively in microresonators as more photonics applications transitions to integrated on-chip platforms. Due to low optical losses and small mode volumes, microresonators are demonstrably the state-of-the-art platform for second-harmonic generation (SHG). However, the working bandwidth of such microresonator-based devices is relatively small, presenting a challenge for applications where a specifically targeted wavelength needs to be addressed. In this Letter, we analyze the phase-matching window and resonance wavelength with respect to varying microring widths, radii, and temperatures. A chip with precise design parameters was fabricated with phase matching realized at the exact wavelength of a two-photon transition of Rb85. This procedure can be generalized to any target pump wavelength in the telecom band with picometer precision.

Passively mode-locked interband cascade optical frequency combs

Since their inception, optical frequency combs have transformed a broad range of technical and scientific disciplines, spanning time keeping to navigation. Recently, dual comb spectroscopy has emerged as an attractive alternative to traditional Fourier transform spectroscopy, since it offers higher measurement sensitivity in a fraction of the time. Midwave infrared (mid-IR) frequency combs are especially promising as an effective means for probing the strong fundamental absorption lines of numerous chemical and biological agents. Mid-IR combs have been realized via frequency down-conversion of a near-IR comb, by optical pumping of a micro-resonator, and beyond 7 μm by four-wave mixing in a quantum cascade laser. In this work, we demonstrate an electrically-driven frequency comb source that spans more than 1 THz of bandwidth centered near 3.6 μm. This is achieved by passively mode-locking an interband cascade laser (ICL) with gain and saturable absorber sections monolithically integrated on the same chip. The new source will significantly enhance the capabilities of mid-IR multi-heterodyne frequency comb spectroscopy systems.

Counter-rotating cavity solitons in a silicon nitride microresonator

We demonstrate the generation of counter-rotating cavity solitons in a silicon nitride microresonator using a fixed, single-frequency laser. We demonstrate a dual three-soliton state with a difference in the repetition rates of the soliton trains that can be tuned by varying the ratio of pump powers in the two directions. Such a system enables a highly compact, tunable dual comb source that can be used for applications such as spectroscopy and distance ranging.

Localized solutions of Lugiato-Lefever equations with focused pump

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Carrier-envelope offset stabilization of a GHz repetition rate femtosecond laser using opto-optical modulation of a SESAM

We demonstrate, to the best of our knowledge, the first carrier-envelope offset (CEO) frequency stabilization of a GHz femtosecond laser based on opto-optical modulation (OOM) of a semiconductor saturable absorber mirror (SESAM). The 1.05-GHz laser is based on a Yb:CALGO gain crystal and emits sub-100-fs pulses with 2.1-W average power at a center wavelength of 1055 nm. The SESAM plays two key roles: it starts and stabilizes the mode-locking operation and is simultaneously used as an actuator to control the CEO frequency. This second functionality is implemented by pumping the SESAM with a continuous-wave 980-nm laser diode in order to slightly modify its nonlinear reflectivity. We use the standard f-to-2f method for detection of the CEO frequency, which is stabilized by applying a feedback signal to the current of the SESAM pump diode. We compare the SESAM-OOM stabilization with the traditional method of gain modulation via control of the pump power of the Yb:CALGO gain crystal. While the bandwidth for gain modulation is intrinsically limited to ∼250  kHz by the laser cavity dynamics, we show that the OOM provides a feedback bandwidth above 500 kHz. Hence, we were able to obtain a residual integrated phase noise of 430 mrad for the stabilized CEO beat, which represents an improvement of more than 30% compared to gain modulation stabilization.

Power Spectrum Computation for an Arbitrary Phase Noise Using Middleton's Convolution Series: Implementation Guideline and Experimental Illustration

In this paper, we revisit the convolution series initially introduced by Middleton several decades ago to determine the power spectrum (or spectral line shape) of a periodic signal from its phase noise power spectral density. This topic is of wide interest, as it has an important impact on many scientific areas that involve lasers and oscillators. We introduce a simple guideline that enables a fairly straightforward computation of the power spectrum corresponding to an arbitrary phase noise. We show the benefit of this approach on a computational point of view, and apply it to various types of experimental signals with different phase noise levels, showing a very good agreement with the experimental spectra. This approach also provides a qualitative and intuitive understanding of the power spectrum corresponding to different regimes of phase noise.

Sub 23 μHz instantaneous linewidth and frequency stability measurements of the beat note from an offset phase locked single frequency heterodyned Nd:YAG laser system

We report, what is to the best of our knowledge, the narrowest instantaneous linewidth measurement of the beat frequency between two phase locked heterodyned 1.319 μm Nd:YAG lasers. At both 65 kHz and 31.7 GHz beat frequencies, we measured the instantaneous 3 dB linewidth of the optically-generated microwave tones to be < 22.8 μHz, limited only by the minimum instrument resolution. Allan deviation measurements indicate that the laser system follows a 5 MHz quartz reference oscillator to stability levels of σy (1s) = 8.4 × 10^-12. At 10.24 GHz, the laser system follows a sapphire loaded cavity oscillator to stability levels of σy (1s) = 1.6 × 10^-11. For these measurements, the optical beat note closely follows the linewidth and stability of the driving microwave frequency reference.

Omni-resonant optical micro-cavity

Optical cavities transmit light only at discrete resonant frequencies, which are well-separated in micro-structures. Despite attempts at the construction of planar ‘white-light cavities’, the benefits accrued upon optically interacting with a cavity – such as resonant field buildup – have remained confined to narrow linewidths. Here, we demonstrate achromatic optical transmission through a planar Fabry-Pérot micro-cavity via angularly multiplexed phase-matching that exploits a bio-inspired grating configuration. By correlating each wavelength with an appropriate angle of incidence, a continuous spectrum resonates and the micro-cavity is rendered transparent. The locus of a single-order 0.7-nm-wide resonance is de-slanted in spectral-angular space to become a 60-nm-wide achromatic resonance spanning multiple cavity free-spectral-ranges. The result is an ‘omni-resonant’ planar micro-cavity in which light resonates continuously over a broad spectral span. This approach severs the link between the resonance bandwidth and the cavity-photon lifetime, thereby promising resonant enhancement of linear and nonlinear optical effects over broad bandwidths in ultrathin devices.

Full stabilization and characterization of an optical frequency comb from a diode-pumped solid-state laser with GHz repetition rate

We demonstrate the first self-referenced full stabilization of a diode-pumped solid-state laser (DPSSL) frequency comb with a GHz repetition rate. The Yb:CALGO DPSSL delivers an average output power of up to 2.1 W with a typical pulse duration of 96 fs and a center wavelength of 1055 nm. A carrier-envelope offset (CEO) beat with a signal-to-noise ratio of 40 dB (in 10-kHz resolution bandwidth) is detected after supercontinuum generation and f-to-2f interferometry directly from the output of the oscillator, without any external amplification or pulse compression. The repetition rate is stabilized to a reference synthesizer with a residual integrated timing jitter of 249 fs [10 Hz - 1 MHz] and a relative frequency stability of 10^-12/s. The CEO frequency is phase-locked to an external reference via pump current feedback using home-built modulation electronics. It achieves a loop bandwidth of ~150 kHz, which results in a tight CEO lock with a residual integrated phase noise of 680 mrad [1 Hz - 1 MHz]. We present a detailed characterization of the GHz frequency comb that combines a noise analysis of the repetition rate f_rep, of the CEO frequency f_CEO, and of an optical comb line at 1030 nm obtained from a virtual beat with a narrow-linewidth laser at 1557 nm using a transfer oscillator. An optical comb linewidth of about 800 kHz is assessed at 1-s observation time, for which the dominant noise sources of f_rep and f_CEO are identified.

Ultrafocused Electromagnetic Field Pulses with a Hollow Cylindrical Waveguide

We theoretically show that a dipole externally driven by a pulse with a lower-bounded temporal width, and placed inside a cylindrical hollow waveguide, can generate a train of arbitrarily short and focused electromagnetic pulses. The waveguide encloses vacuum with perfect electric conducting walls. A dipole driven by a single short pulse, which is properly engineered to exploit the linear spectral filtering of the cylindrical hollow waveguide, excites longitudinal waveguide modes that are coherently refocused at some particular instances of time, thereby producing arbitrarily short and focused electromagnetic pulses. We numerically show that such ultrafocused pulses persist outside the cylindrical waveguide at distances comparable to its radius.

Towards fully commercial, UV-compatible fiber patch cords

We present and analyze two pathways to produce commercial optical-fiber patch cords with stable long-term transmission in the ultraviolet (UV) at powers up to ~ 200 mW, and typical bulk transmission between 66-75 %. Commercial fiber patch cords in the UV are of great interest across a wide variety of scientific applications ranging from biology to metrology, and the lack of availability has yet to be suitably addressed. We provide a guide to producing such solarization-resistant, hydrogen-passivated, polarization-maintaining, connectorized and jacketed optical fibers compatible with demanding scientific and industrial applications. Our presentation describes the fabrication and hydrogen loading procedure in detail and presents a high-pressure vessel design, calculations of required H₂ loading times, and information on patch cord handling and the mitigation of bending sensitivities. Transmission at 313 nm is measured over many months for cumulative energy on the fiber output of > 10 kJ with no demonstrable degradation due to UV solarization, in contrast to standard uncured fibers. Polarization sensitivity and stability are characterized yielding polarization extinction ratios between 15 dB and 25 dB at 313 nm, where we find patch cords become linearly polarizing. We observe that particle deposition at the fiber facet induced by high-intensity UV exposure can (reversibly) deteriorate patch cord performance and describe a technique for nitrogen purging of fiber collimators which mitigates this phenomenon.