Bandwidth scaling and spectral flatness enhancement of optical frequency combs from phase-modulated continuous-wave lasers using cascaded four-wave mixing

We introduce a new cascaded four-wave mixing technique that scales up the bandwidth of frequency combs generated by phase modulation of a continuous-wave (CW) laser while simultaneously enhancing the spectral flatness. As a result, we demonstrate a 10?GHz frequency comb with over 100?lines in a 10?dB bandwidth in which a record 75?lines are within a flatness of 1?dB. The cascaded four-wave mixing process increases the bandwidth of the initial comb generated by the modulation of a CW laser by a factor of five. The broadband comb has approximately quadratic spectral phase, which is compensated upon propagation in single-mode fiber, resulting in a 10?GHz train of 940?fs pulses.     

High flatness optical frequency comb generator based on the chirping of modulators

A novel scheme for generation of an optical frequency comb (OFC) based on the chirping of two cascaded modulators is proposed. The first modulator is a dual-electrode Mach–Zehnder modulator (MZM), while the other modulator is an integrated MZM composed of two parallel MZMs that increases the number of comb lines. Our modified scheme can generate a large number of frequency lines with excellent flatness by simply modifying the chirp factor, and it is shown that up to 54 frequency lines could be observed. Theoretical analysis and simulation results show that under the variety of conditions that can be used in this scheme, the power fluctuations of the OFC lines are less than 0.5 dB in all cases; these results demonstrate the robustness of our scheme and verify its good accuracy and high stability with perfect flatness. Additionally, our modified scheme has the merit of tunable frequency spacing, which is practical for experimental realization of the OFC.     

Scheme for generation of flat top and high signal-to-noise ratio optical frequency comb

We demonstrate a new scheme for generation of optical frequency comb(OFC) based on cascade modulators, 23 comb lines within 0.5 d B spectral power variation are obtained. An optical finite impulse response(FIR) filter is introduced for suppression of amplified spontaneous emission noise. It is shown that carrier-to-noise-ratio of the OFC generated by this scheme can be as high as 38.8 d B with 12 d B improvement by using a 16-tap FIR filter, and the error vector magnitude performances of loaded Nyquist-16 quadrature amplitude modulation signal is improved from 14.20% to 7.44%.     

Flat optical frequency comb generation using polarization modulator and frequency shifter with double recirculating frequency shifting loops

A scheme to generate ultra-flat and stable optical frequency comb (OFC) based on multi-wavelength optical seed source and polarization-modulator-based complementary frequency shifter (PCFS) has been proposed and demonstrated. The OFC generation scheme includes two stages: 5-carrier light source is generated by utilizing a polarization modulator at the first stage, and the light source is then used as the seed light in the PCFS at the second stage. Compared with the previous flat OFC generator based on a recirculation frequency shifter, the proposed scheme can greatly reduce the recirculation times, and such a property makes the accumulated noise of the system enormously decrease. In order to achieve the frequency comb with the best flatness, the optical amplifier gain, filter stop-band attenuation and modulator drive voltage are optimized. Experiment simulations show that high-quality OFC with hundreds of frequency lines and power fluctuation within 2 dB can be achieved without direct-current bias control and wavelength-selective-switch.     

Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator

We theoretically prove that a conventional Mach-Zehnder modulator can generate an optical frequency comb with excellent spectral flatness. The modulator is asymmetrically dual driven by large amplitude sinusoidal signals with different amplitudes. The driving condition to obtain spectral flatness is analytically derived and optimized, yielding a simple formula. This formula also predicts the conversion efficiency and bandwidth of the generated frequency comb.     

Simulation of a flat optical frequency comb using a single-drive multi-RF Mach–Zehnder modulator in a cascaded intensity modulator chain

We proposed a scheme based on two cascaded lithium niobate intensity modulators to generate an optical frequency comb with very high flatness. Single-drive multi-RF waveforms are used for driving the first intensity modulator, and 9 lines within 1 dB power variation can be obtained. When cascading with another intensity modulator, by specially adjusting the DC bias and the drive amplitudes of the RF signals of the two intensity modulators, 27 or 45 comb lines with a spectral power variation about 1 dB are obtained. The scheme is relatively simple and adjustable, and the frequency interval of the OFC varies with microwave frequency applied on modulators.     

Precision phase control of an ultrawide-bandwidth femtosecond laser: a network of ultrastable frequency marks across the visible spectrum

We demonstrate that the stability of the current optical frequency comb generated by a Kerr-lens mode-locked femtosecond laser is limited by the microwave reference used for phase locking the comb spacing. Hence we implement precision frequency/phase control of the entire comb to the fundamental and second-harmonic frequencies of a stable cw laser without any external microwave reference. The stability of a cw iodine-stabilized laser is transferred to millions of comb lines (with an instability of 3 x 10(-13)) covering more than one octave of the optical frequency spectrum. In addition, the mode spacing of the comb can be used as a stable microwave frequency derived directly from a stable optical oscillator.     

Generation of flat optical frequency comb by fiber loop modulation

We propose a novel flat optical frequency comb generation system that employs fiber loop modulation and experimentally demonstrate its operation. Generally, when an external laser beam is injected into a fiber loop system including an optical modulator and an amplifying medium, multiple sidebands are generated exponentially. On the other hand, the fiber loop starts mode-locked oscillation at a center frequency to maximize the round-trip gain in the fiber loop from the seeds of the injected laser sidebands. By locking the sidebands from fiber loop modulation with the mode-locked oscillation in the fiber loop, the synchronous spectrum between the mode-locked oscillation and the sidebands can be shaped into a flat spectrum. Thus, a flat optical frequency comb with a flatness of about ±1 dB is obtained in the spectral bandwidth of about 1 THz.     

Roughness of organ pipe sound due to frequency comb

In the sound spectrum of flue organ pipes in addition to the usual harmonic partials, sometimes a series of equidistant but not harmonic lines can be found. This phenomenon has been observed in the recorded sound of pipes from different pipe ranks. The second set of spectral lines is similar to "frequency combs" used in optics for accurate measurement of optical frequencies. Analysis of measured sound spectra with and without frequency comb and simulations are presented and discussed in the paper. The appearance of frequency combs in the sound spectrum is explained by a model that assumes the presence of a mouth tone in addition to the pipe sound. Mouth tone bursts are generated when the oscillating air jet passes the upper lip. The burst repetition frequency is locked to the fundamental frequency of the pipe and the bursts are coherent with a pulse-to-pulse phase shift. The phase shift explains the observed frequency offset of the frequency comb to the harmonic frequencies. The simulations also show that weak and fluctuating mouth tones cannot generate frequency comb due to a lack of coherence.     

High-Q microwave photonic filter with self-phase modulation spectrum broadening and third-order dispersion compensation

We propose and experimentally demonstrate a scheme of high-Q microwave photonic filter （MPF） using the techniques of self-phase modulation （SPM） spectrum broadening and third-order dispersion （TOD） compensation. The optical pulses from a mode-locking laser are spectrally broadened by the SPM in the highly nonlinear fiber. A wideband optical frequency comb with 365 spectral lines within 10-dB power variation from the highest spectral power is obtained. By applying a cubic phase modulation via a waveshaper, the effect of TOD which broadens the MPF passband is eliminated. The final implemented MPF has a Q-value as high as 296 and a tuning range of 700 MHz.     

Octave-spanning frequency comb generation in a silicon nitride chip

We demonstrate a frequency comb spanning an octave via the parametric process of cascaded four-wave mixing in a monolithic, high-Q silicon nitride microring resonator. The comb is generated from a single-frequency pump laser at 1562?nm and spans 128?THz with a spacing of 226?GHz, which can be tuned slightly with the pump power. In addition, we investigate the RF amplitude noise characteristics of the parametric comb and find that the comb can operate in a low-noise state with a 30?dB reduction in noise as the pump frequency is tuned into the cavity resonance.     

All optical arbitrary waveform generation by optical frequency comb based on cascading intensity modulation

We propose and experimentally demonstrate an all optical arbitrary waveform generation by optical frequency comb (OFC) based on cascading intensity modulation. By selecting spectral lines of interest from OFC through optical filters, 10 GHz, 20 GHz, and 60 GHz sinusoidal signals with low phase noise and more complex waveforms, including ultra-short pulse, half-wave cosine, and single frequency modulated MMW signals, are generated easily.     

Cavity-enhanced direct frequency comb spectroscopy

Cavity-enhanced direct frequency comb spectroscopy combines broad spectral bandwidth, high spectral resolution, precise frequency calibration, and ultrahigh detection sensitivity, all in one experimental platform based on an optical frequency comb interacting with a high-finesse optical cavity. Precise control of the optical frequency comb allows highly efficient, coherent coupling of individual comb components with corresponding resonant modes of the high-finesse cavity. The long cavity lifetime dramatically enhances the effective interaction between the light field and intracavity matter, increasing the sensitivity for measurement of optical losses by a factor that is on the order of the cavity finesse. The use of low-dispersion mirrors permits almost the entire spectral bandwidth of the frequency comb to be employed for detection, covering a range of ～?10% of the actual optical frequency. The light transmitted from the cavity is spectrally resolved to provide a multitude of detection channels with spectral resolutions ranging from several gigahertz to hundreds of kilohertz. In this review we will discuss the principle of cavity-enhanced direct frequency comb spectroscopy and the various implementations of such systems. In particular, we discuss several types of UV, optical, and IR frequency comb sources and optical cavity designs that can be used for specific spectroscopic applications. We present several cavity-comb coupling methods to take advantage of the broad spectral bandwidth and narrow spectral components of a frequency comb. Finally, we present a series of experimental measurements on trace gas detections, human breath analysis, and characterization of cold molecular beams. These results demonstrate clearly that the wide bandwidth and ultrasensitive nature of the femtosecond enhancement cavity enables powerful real-time detection and identification of many molecular species in a massively parallel fashion.     

Highly selective terahertz optical frequency comb generator

Using a 10.5-GHz resonant electro-optic modulator placed inside a resonant optical cavity, we generated an optical frequency comb with a span wider than 3 THz. The optical resonator consists of three mirrors, with the output coupler being a thin Fabry-Perot cavity with a free spectral range of 2 THz and a finesse of 400. Tuning this filter cavity onto resonance with a particular high-order sideband permits efficient output coupling of the desired sideband power from the comb generator, while keeping all other sidebands inside for continued comb generation. This spectrally pure output light was then heterodyne detected by another laser with a frequency offset of the order of 1 THz.     

Noise-induced linewidth in frequency combs

Frequency combs generated by trains of pulses emitted from mode-locked lasers are analyzed when the center time and phase of the pulses undergo noise-induced random walk, which broadens the comb lines. Asymptotic analysis and computation reveal that, when the standard deviation of the center-time jitter of the nth pulse scales as n(p/2) where p is a jitter exponent, the linewidth of the kth comb line scales as k(2/p). The linear-dispersionless (p=1) and pure-soliton (p=3) dynamics in lasers are derived as special cases of this time-frequency duality relation. In addition, the linewidth induced by phase jitter decreases with power P(out), as (P(out))(-1/p).     

10 GHz, 2.4 ps pulse generation using a single-stage dual-drive Mach-Zehnder modulator

This Letter reports on picosecond pulse generation at a repetition of 10 GHz by using a single-stage electro-optic LiNbO(3) Mach-Zehnder modulator, stressing the simplicity of its setup. It is analytically and experimentally proved that dual-arm modulation with in-phase sinusoidal signals having slightly different amplitudes generated a highly coherent optical comb with a great spectral flatness and a parabolic phase relationship in its spectrum. The generated comb was Fourier synthesized and shaped into an ultrashort pulse train with an optical bandpass filter and a dispersive fiber. The pulse source was highly stable, exhibiting an ultralow timing jitter of less than 130 fs.     

基于双环混频光电振荡器的可调谐微波频率梳产生

随着无线通信的速率提升和微蜂窝趋势,光载微波技术已经成为重要的发展趋势,而光生多载波系统是光载微波的最重要的技术之一.本文提出了一种基于双环混频光电振荡器（OEO）的可调谐光载微波频率梳产生方案,可同时实现多频段微波信号产生,从而高效低成本地为无线节点提供光生微波载波.方案采用混频双环OEO系统,通过工作在增益开关状态的直调激光器,利用其非线性动态特性产生多频率光载微波频率梳信号,并采用双路微波滤波器分别滤出两个相邻频率的微波信号,并利用二者的差频反馈注入直调激光器构成光电谐振.利用偏振双环结构抑制长谐振腔引起的边模问题,提高了输出信号的噪声特性.经过实验分析,得到了低相噪的多路微波信号,并最终实现了间隔797.4 MHz的稳定的微波频率梳信号,一阶载波相位噪声低于-101.7 dBc/Hz@10 kHz,-115.2 dBc/Hz@50 kHz.因此该方案产生的光载微波频率梳信号具有低噪声的优点,适用于光载微波通信系统.     

High resolution atomic coherent control via spectral phase manipulation of an optical frequency comb

We demonstrate high resolution coherent control of cold atomic rubidium utilizing spectral phase manipulation of a femtosecond optical frequency comb. Transient coherent accumulation is directly manifested by the enhancement of signal amplitude and spectral resolution via the pulse number. The combination of frequency comb technology and spectral phase manipulation enables coherent control techniques to enter a new regime with natural linewidth resolution.     

Fiber-laser frequency combs with subhertz relative linewidths

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

Interferometric selection of frequency comb modes

We demonstrate a scheme to split an optical frequency comb into four separate frequency combs, each with four times the repetition rate of the original, but which are offset in frequency from each other. These spectrally rarified “daughter” combs are generated using fibre interferometers that are actively stabilised. We describe how these “daughter” combs can be used to resolve ambiguities that occur when comparing an arbitrary frequency continuous-wave signal against an optical frequency comb.