Stable Repetition Rate Research Articles

Electro-optic frequency comb generation via cascaded modulators driven at lower frequency harmonics

Electro-optical modulation of a continuous wave laser is a highly stable way to generate frequency combs, gaining popularity in telecommunication and spectroscopic applications. These combs are generated by modulating non-linear electro-optic crystals with radio frequencies, creating equally spaced side-bands centered around the single-frequency seed laser. Electro-optic frequency comb architectures often choose between optical bandwidth (cascaded GHz combs) or higher mode density (chirped RF generation). This work demonstrates an electro-optic frequency comb with > 120 GHz of bandwidth and an 80 MHz repetition rate. The comb has three cascaded electro-optic modulators driven at sequentially lower harmonics, the last megahertz modulation dictating the repetition rate. This architecture can modulate at any individual harmonic and repetition rate without changes to the components. This comb can be used in any applications where a stable and tunable repetition rate is needed.

Optical frequency comb significantly spanned to broadband by an optomechanical resonance

An optical frequency comb, as a spectrum made of discrete and equally spaced spectral lines, is a light source with essential applications in modern technology. Cavity optomechanical systems were found to be a feasible candidate for realizing an on-chip frequency comb with low repetition rate. However, it was difficult to increase the comb line numbers of this type of frequency combs because the mechanical oscillation amplitude of such a system, which determines the frequency comb bandwidth, cannot quickly increase with pump laser power. Here, we develop a new approach to generate a broadband optomechanical frequency comb by employing a different mechanism to enhance the mechanical oscillation. Two pump tones with their frequency difference matching the mechanical frequency will drive the system into a self-organized nonlinear resonance and thus tremendously transfer the energy to the mechanical resonator. As a result, more than 10,000 or even more comb lines become available under the pump laser power of the order of milliwatts. A unique feature of the self-organized resonance is the mechanical frequency locking so that, within a certain range of the frequency difference between two drive tones, the distance between comb teeth can be locked by the two drive tones and becomes independent of any change of pump power. This property guarantees a stable repetition rate of the generated frequency comb.

Integer-locking condition for stable dual-comb interferometry in situations with fluctuating frequency-comb repetition rates

To make dual-comb interferometry usable in a wide range of applications, it is important to achieve reproducible measurement results even in non-ideal environments that affect the repetition-rate stability. Here, we consider dual-comb interferometry based on a pair of fully referenced optical frequency combs (OFCs) and investigate the impact of fluctuations in the OFC repetition frequencies on the peak position of the center burst in the interferogram. We identify a phase-locking scheme that minimizes the impact of these fluctuations through choosing a special combination of phase-locked frequencies, and the resulting type of operating condition is termed integer-locking condition. Under the integer-locking condition, the number of sampling points in each interferogram remains constant regardless of repetition-rate variations, and this enables more stable phase-resolved measurements in non-ideal environments. We demonstrate the application of this approach using absolute path-length measurements and discuss the accuracy limit imposed by the integer-locking condition. Our findings offer a strategy for robust dual-comb interferometry outside metrology laboratories.

Nonlinear Generation, Compression and Spatio‐Temporal Analysis of sub‐GV/cm‐Class Femtosecond Mid‐Infrared Transients

AbstractA Yb:YAG thin‐disk regenerative amplifier with 3 kHz repetition rate pumps a second‐order nonlinear mixing scheme providing femtosecond transients of maximum electric field strength beyond 330 MV cm−1 at a center frequency of 45 THz. This value surpasses field conditions present at submolecular dimensions of matter. The inherent competition between efficiency and bandwidth in parametric downconversion is overcome with a third‐order nonlinear step of self‐phase modulation (SPM). The high repetition rate, versatility, beam quality, and passive phase stability of our system support advanced spectroscopic approaches like electro‐optic sampling (EOS). With this technique, solitonic self‐compression and octave‐spanning supercontinua directly on a subcycle scale are studied.

Repetition rate difference, stability and polarization extinction ratio of single-cavity polarization-multiplexed fiber laser with weak birefringence

We investigated a stable single-cavity polarization-multiplexed ring fiber laser with weak birefringence. The feasibility of the weak intrinsic residual birefringence to induce polarization-multiplexed pulses with low repetition rate difference under dual/triple-comb modes is experimentally verified. The significant evolution of the relative stability and polarization extinction ratio, and its physical mechanism are revealed when adjusting the linear intracavity loss. These results provide further understanding of the influence of birefringence amount, loss, dispersion, and multiple pulse interaction on the polarization-multiplexed pulses. Meanwhile, the intriguing pulse characteristics such as low repetition rate difference, qualified relative stability and unique wavelength/polarization multiplexing are experimentally obtained, showing the high potential to promote the wide applicability and performance improvement of multiple-comb metrology such as dual/triple-comb frequency measurement.

Seeding with a harmonic optical klystron resonator configuration in a high repetition rate free electron laser

The generation of highly coherent radiation in a high repetition rate free electron laser driven by a superconducting linear accelerator has become a topic of growing interest. External seeding schemes like high-gain harmonic generation (HGHG) and echo-enabled harmonic generation are proven to be able to generate coherent radiation in the extreme ultraviolet and x-ray range. However, the repetition rate of current laser systems with sufficient power to modulate the electron beam is limited to the kilohertz range. Recently, to achieve seeding at a high repetition rate, an optical resonator scheme has been introduced to recirculate the radiation in the modulator to seed the electron bunches. In this paper, two harmonic optical klystron resonator configurations either starting with a seed laser or starting from shot noise are studied. With the harmonic optical klystron as the seeding source, the efficiency of harmonic radiation generation at a comparatively high harmonic can be significantly enhanced when compared with a standard single-stage HGHG. Simulation results show that highly coherent, stable, and high repetition rate pulses in the water window range could be generated by the proposed seeding schemes. Some practical considerations including beam energy chirp effects and the power density effects on mirrors are discussed.

Passive repetition-rate stabilization for a mode-locked fiber laser by electro-optic modulation.

We report a passive stabilization of the repetition rate for a mode-locked fiber laser by using an electro-optic modulator in a phase-biased nonlinear amplifying loop mirror. The underlying mechanism, in contrast to active feedback operations, lies in the cross-phase modulation between electrical and optical pulses within an electro-optic crystal. The resulting spectral shift can automatically compensate for the cavity-length drift via the group velocity dispersion. Consequently, the artificial actuator enables a capture range up to 2.3 mm, much longer than that achieved by index changes of the modulator. A robust and tight locking for the repetition rate is then realized with a standard deviation as low as 9 μHz with a 1-s sample time over 11 hours, corresponding to a fractional instability of 4.3 × 10-13. Furthermore, a dynamic optical sampling by repetition-rate tuning has been manifested with a fast refresh rate at 100 kHz and a broad scanning range over 305 ps. The demonstrated passive servo action may provide a simple yet effective way to stabilize the repetition rate with high precision, large bandwidth, and wide tunability.

Optical high repetition rate stabilization based an all-polarization-maintaining figure-of-nine Er-fiber laser

Optical frequency comb (OFC) based on mode-locked fiber lasers has abstracted extensive interest in the field of laser ranging and precision spectroscopy with its extremely high time–frequency accuracy. Therefore, the repetition rate stabilization plays a notably key role in OFC. Mechanical motion is generally used to change the geometric length of the laser cavity to stabilize the repetition rate. However, this method has some disadvantages such as high feedback voltage and mechanical disturbance caused by the characteristics of the piezoelectric ceramic transducer (PZT). To overcome these problems, the refractive index of the gain fiber can be regulated via controlling the pump power, thereby optically stabilizing the repetition rate. In this study, we reported the optical repetition rate stabilization via regulating the nonlinear refractive index of Er-fiber in an all-polarization-maintaining (PM) figure-of-nine laser cavity. The repetition rate reached 80.1 MHz and was stabilized for more than 1 h. The standard deviation (SD) was 178 μHz within 1-s gate time. As far as we know, in terms of optical repetition rate stabilization, the mode-locked Er-fiber laser achieved the highest repetition rate.

10 GHz regeneratively mode-locked thulium fiber laser with a stabilized repetition rate.

GHz pulsed thulium-doped fiber laser with stabilized repetition rate can enable a wide range of applications. By employing regenerative mode-locking and cavity stabilization technique, we have for the first time demonstrated a 10 GHz polarization-maintaining thulium-doped fiber laser, which has a long-term repetition-rate stabilization and picosecond timing-jitter. In our experiment, a RF circuitry is designed to extract the 10 GHz longitudinal clock signal so that stable regenerative mode-locking is achieved. A piezo actuator-based phase-lock-loop is used to lock the regeneratively mode-locked pulses to a local reference synthesizer. The regeneratively mode-locked pulses with picosecond pulse width exhibit a high super-mode suppression ratio of 60 dB. In addition, the repetition rate of the laser shows good long-term stability with a variation of 8 Hz in 8 hours, corresponding to a cavity free spectral range fluctuation of less than 16 mHz. Meanwhile, the Allan deviation of the stabilized 10 GHz regeneratively mode-locked pulses is measured to be as low as 2 × 10-12 over 1000 s average time, which is only limited by the stability of the reference synthesizer. Such an ultra-stable 10 GHz pulsed thulium fiber laser may find potential application in 2 µm optical communication, material processing and spectroscopy.

Towards a space-qualified Kerr-lens mode-locked laser.

We report a 1.5-GHz Kerr-lens mode-locked (KLM) Yb:Y2O3 ring laser constructed by directly bonding the cavity components onto an aluminum baseplate. Stable unidirectional operation with an output power ≥10mW was obtained for pump-diode currents of 300-500 mA, corresponding to a total electrical power consumption of 1.5 W. After repetition rate stabilization, a comparison with a conventionally constructed identical laser showed a 50% reduction in phase noise. In free-running operation the bonded laser showed superior passive repetition rate stability. The bonding process follows an already proven integration approach in space-borne instrumentation, mapping a development pathway for KLM lasers in aerospace applications.

Realization of carrier envelope phase control in an erbium-doped all-fiber comb via an intracavity electrical polarization controller.

We present an erbium-doped all-fiber comb that is realized via intracavity piezoelectric mechanical responses by inserting an electrical polarization controller (EPC) for carrier envelope phase offset (fceo) control and sticking a piezoelectric transducer (PZT) for repetition rate (fr) stabilization. With only three components inside the oscillator, it facilitates an all-fiber comb system with high integration and robustness. Besides fceo control, smart, recoverable, and precise searching of mode-locked states can also be achieved by finely tuning the EPC driving voltages. The fceo signal can be tightly phase-locked due to the 20 kHz 3 dB bandwidth of the EPC device. Compared with the traditional pump feedback mode, the EPC approach exhibits a larger and flatter gain in the near-zero-dispersion zone of the fiber comb, corresponding to less EPC induced intracavity fluctuations. It is also a benefit for reducing cross regulation between fr and fceo in long-term stabilization of the comb.

All-optical repetition rate stabilization methods for ultrafast Yb-based SESAM mode-locked fiber oscillator

We demonstrate optical to radio frequency (RF) locking technique using all-fiber phase shifter. Phase shift at 1030 nm was achieved by pumping Er-doped fiber incorporated in the resonator. Pump induced refractive index change was fast enough to stabilize optical pulse repetition rate of ultrafast Yb-doped fiber oscillator and achieve sub-200 fs timing jitter. We also investigate the source of phase noise in soliton fiber oscillators and provide guidelines how to further reduce timing jitter.

High-precision passive stabilization of repetition rate for a mode-locked fiber laser based on optical pulse injection

We have proposed and implemented a novel scheme to obtain high-precision repetition rate stabilization for a polarization-maintaining mode-locked fiber laser. The essential technique lies in the periodic injection of electronically modulated optical pulses into a nonlinear amplifying loop mirror within the laser resonator. Thanks to the nonlinear cross-phase modulation effect, the injected pulses referenced to an external clock serves as a stable and precise timing trigger for an effective intensity modulator. Consequently, synchronous mode-locking can be initiated to output ultrafast pulses with a passively stabilized repetition rate. The capture range of the locking system reaches to a record of 1 mm, which enables a long-term stable operation over 15 hours without the need of temperature stabilization and vibration isolation. Meanwhile, the achieved standard deviation is as low as 100 μHz with a 1-s sample time, corresponding to a fluctuation instability of 5.0×10-12. Additionally, the repetition rate stabilization performance based on the passive synchronization has been systematically investigated by varying the average power, central wavelength and pulse duration of the optical injection.

Generation of 100-MeV Attosecond Electron Bunches with Terawatt Few-Cycle Laser Pulses

Laser-wakefield acceleration has been demonstrated to be a promising technique for compact electron accelerators. However, it is still challenging to achieve high-quality 100-MeV electron bunches of subfemtosecond duration with current techniques. Here, we present and numerically demonstrate an efficient scheme to produce such high-energy tunable ultrashort electron bunches, which is achieved by the use of a nonlinear wakefield driven by a terawatt few-cycle laser pulse in a tailored plasma channel. With the driving laser pulse energy of 25 mJ only, the resulting electron bunch can reach 101 MeV with 7.8-pC charge, approximately 4 mrad divergence, approximately 3% energy spread, energy efficiency above 3%, and a duration of hundreds of attoseconds. As such laser pulses may be obtained with a kilohertz repetition rate and high stability, our scheme could be interesting for ultrafast science and accelerator community.

Brillouin-Kerr Soliton Frequency Combs in an Optical Microresonator.

By generating a Brillouin laser in an optical microresonator, we realize a soliton Kerr microcomb through exciting the Kerr frequency comb using the generated Brillouin laser in the same cavity. The intracavity Brillouin laser pumping scheme enables us to access the soliton states with a blue-detuned input pump. Because of the ultranarrow linewidth and the low-noise properties of the generated Brillouin laser, the observed soliton microcomb exhibits narrow-linewidth comb lines and stable repetition rate. Also, we demonstrate a low-noise microwave signal with phase noise of -49 dBc/Hz at 10Hz, -130 dBc/Hz at 10kHz, and -149 dBc/Hz at 1MHz offsets for a 10.43GHz carrier with only a free-running input pump. The easy operation of the Brillouin-Kerr soliton microcomb with excellent performance makes our scheme promising for practical applications.

Program-controlled single soliton microcomb source

Soliton microcombs (SMCs) are spontaneously formed in a coherently pumped high-quality microresonator, which provides a new tool for use as an on-chip frequency comb for applications of high-precision metrology and spectroscopy. However, generation of SMCs seriously relies on advanced experimental techniques from professional scientists. Here, we experimentally demonstrate a program-controlled single SMC source where the intracavity thermal effect is timely balanced using an auxiliary laser during single SMC generation. The microcomb power is adopted as the criteria for microcomb states discrimination and a forward and backward thermal tuning technique is employed for the deterministic single SMC generation. Further, based on a closed-loop control system, the repetition rate stability of the SMC source improved more than 20 times and the pump frequency can be continuously tuned by simply changing the operation temperature. The reliability of the SMC source is verified by consecutive 200 generation trials and maintaining over 10 h. We believe the proposed SMC source will have significant promising influences in future SMC-based application development.

Compact 50 W All-Solid-State Picosecond Laser System at 1 kHz

Compact, stable, high-power and high repetition rate picosecond laser systems are excellent sources for optical parametric chirped pulse amplification systems and laser satellite ranging systems. Compared with the traditional complex high-power amplifier, this article reports a compact high-power picosecond laser system at a repetition rate of 1 kHz based on Nd:YAG bulk crystal. The thermal lens effect limits the regenerative amplifier to directly output higher energy. For this reason, multi-stage traveling-wave amplifiers are usually used to gradually increase the laser pulse energy. So as to achieve a compact structure, a regenerative amplifier that can output higher power at 1 kHz is designed in the laser system. The regenerative amplifier can output the power of 6.5 W at the pump power of 41.5 W; the beam quality of M2 factor was about 1.3. A more flexible thermal depolarization compensation structure is applied in the side-pumped amplifier, which can effectively compensate for thermal lens effect and thermal depolarization at different pump powers. Finally, the laser pulse can achieve an output power higher than 50 W at 1 kHz after passing through an end-pumped traveling-wave amplifier and a side-pumped traveling wave amplifier.

Femtosecond dual-comb Yb:CaF2 laser from a single free-running polarization-multiplexed cavity for optical sampling applications.

Dual optical frequency combs are an appealing solution to many optical measurement techniques due to their high spectral and temporal resolution, high scanning speed, and lack of moving parts. However, industrial and field-deployable applications of such systems are limited due to a high-cost factor and intricacy in the experimental setups, which typically require a pair of locked femtosecond lasers. Here, we demonstrate a single oscillator which produces two mode-locked output beams with a stable repetition rate difference. We achieve this via inserting two 45°-cut birefringent crystals into the laser cavity, which introduces a repetition rate difference between the two polarization states of the cavity. To mode-lock both combs simultaneously, we use a semiconductor saturable absorber mirror (SESAM). We achieve two simultaneously operating combs at 1050 nm with 175-fs duration, 3.2-nJ pulses and an average power of 440 mW in each beam. The average repetition rate is 137 MHz, and we set the repetition rate difference to 1 kHz. This laser system, which is the first SESAM mode-locked femtosecond solid-state dual-comb source based on birefringent multiplexing, paves the way for portable and high-power femtosecond dual-combs with flexible repetition rate. To demonstrate the utility of the laser for applications, we perform asynchronous optical sampling (ASOPS) on semiconductor thin-film structures with the free-running laser system, revealing temporal dynamics from femtosecond to nanosecond time scales.

Photonic microwave generation in the X- and K-band using integrated soliton microcombs

Microwave photonic technologies, which upshift the carrier into the optical domain to facilitate the generation and processing of ultrawide-band electronic signals at vastly reduced fractional bandwidths, have the potential to achieve superior performance compared to conventional electronics for targeted functions. For microwave photonic applications such as filters, coherent radars, subnoise detection, optical communications and low-noise microwave generation, frequency combs are key building blocks. By virtue of soliton microcombs, frequency combs can now be built using CMOS compatible photonic integrated circuits, operated with low power and noise, and have already been employed in system-level demonstrations. Yet, currently developed photonic integrated microcombs all operate with repetition rates significantly beyond those that conventional electronics can detect and process, compounding their use in microwave photonics. Here we demonstrate integrated soliton microcombs operating in two widely employed microwave bands, X- and K-band. These devices can produce more than 300 comb lines within the 3-dB-bandwidth, and generate microwave signals featuring phase noise levels below 105 dBc/Hz (140 dBc/Hz) at 10 kHz (1 MHz) offset frequency, comparable to modern electronic microwave synthesizers. In addition, the soliton pulse stream can be injection-locked to a microwave signal, enabling actuator-free repetition rate stabilization, tuning and microwave spectral purification, at power levels compatible with silicon-based lasers (<150 mW). Our results establish photonic integrated soliton microcombs as viable integrated low-noise microwave synthesizers. Further, the low repetition rates are critical for future dense WDM channel generation schemes, and can significantly reduce the system complexity of photonic integrated frequency synthesizers and atomic clocks.

Q-switched and mode-locked erbium-doped fiber laser using gadolinium oxide as saturable absorber

Abstract Q-switched and mode-locked Erbium-doped fiber lasers (EDFLs) were demonstrated using gadolinium oxide (Gd2O3) as a saturable absorber. The Gd2O3 nano-powder was embedded into polyvinyl alcohol (PVA) film and integrated into the EDFL cavity to achieve both lasers. At first, a stable Q-switched laser was realized at a center wavelength of 1564.1 nm. The repetition rate increased from 78 to 90.74 kHz and the pulse width reduced from 5.68 to 4.68 µs as the pump power adjusted within 96.28 to 147.16 mW. The output power increased steadily from 19.3 to 26.4 mW as the pump power was raised from 96.28 to 147.16 mW. The slope efficiency of the output power was 14%. Later, a 100 m single mode fiber was incorporated into the similar laser cavity to generate a stable mode-locked laser at a threshold pump power of 96.28 mW with a central wavelength of 1561.5 nm. We observed a stable repetition rate of 1.907 MHz with a pulse width of 3.82 ps as the pump power raised from 96.28 to 147.16 mW. The peak power obtained from the mode-locked laser was tunable from 1.78 to 2.58 kW as the pump power was adjusted from minimum to the maximum. These results indicate the outstanding performance of Gd2O3 SA for both Q-switching and mode-locking applications. The lasers are useful for various applications including, micromachining of material, frequency comb-generation and remote sensing.