Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser

A frequency comb spanning more than one octave has been achieved by injecting the second-harmonic generation (780 nm) of a mode-locked fiber laser (1.56 microm) into a photonic crystal fiber. We propose and realize a novel interferometric scheme for observing the carrier-envelope offset frequency of the frequency comb. Frequency noise has been observed on the measured carrier-envelope offset frequency, which has been confirmed to be generated in the photonic crystal fiber by comparing the measured beat frequencies between cw lasers and frequency combs before and after the photonic crystal fiber. The mode-locked fiber laser is considered to be an important candidate for the light source used in realizing a compact optical frequency measurement system including applications in the telecommunication bands.     

Carrier-envelope phase fluctuations of amplified femtosecond pulses: characterization with a simple spatial interference setup

We demonstrate a direct and versatile scheme to determine the carrier-envelope phase fluctuations of tunable ultrashort optical pulses. The spatial interferogram between the high frequency components and the parametrically amplified and frequency doubled low frequency components of an octave broad white light continuum is measured for every single pulse. It directly reveals the carrier-envelope phase fluctuations of the pump pulses from the regenerative amplifier, as well as of the white light and the tunable pulses generated from it. PACS 42.25.Kb; 42.65.Yj; 42.65.Re     

Noise performance of a feed-forward scheme for carrier-envelope phase stabilization

The noise performance of a feed-forward scheme for carrier-envelope phase stabilization is discussed. This scheme uses an acousto-optic frequency shifter to directly correct for fluctuations of the carrier-envelope phase in a pulse train emitted by a mode-locked laser without manipulating the intracavity dispersion. Generation of zero-offset frequency combs is demonstrated. Furthermore, it is shown that pump laser noise has only a minor effect on the achievable performance. Limited only by the travel time of the acoustic wave in the shifter, pump laser noise can be corrected up to near-megahertz frequencies, which yields superior noise performance compared to traditional feedback operation. Residual phase jitters down to 45 mrad are experimentally verified.     

Single-shot measurement of carrier-envelope phase changes by spectral interferometry

We demonstrated single-shot measurements of spectral interference between a white-light continuum generated in a hollow-fiber and its second harmonic. The interference has information on the carrier-envelope phase of an input pulse to the fiber and the time delay of the blue wing of the continuum. By analyzing the observed spectral interference, we estimated shot-by-shot changes of the carrier-envelope phase. This method is useful for determining the carrier-envelope phase changes of a low-repetition-rate, high-intensity laser.     

Phase stabilization of an octave-spanning Ti:sapphire laser

We obtain direct stabilization of the carrier-envelope phase for a standard x-folded geometry, octave-spanning, Ti:sapphire laser. The in-loop accumulated carrier-envelope phase error is 0.175 rad (1.65 mHz to 102 kHz). Intracavity continuum generation, which is responsible for the octave bandwidth, is characterized through measurement of the beam parameters.     

A linear optical method for measuring the carrier-envelope phase drift

The carrier-envelope offset frequency of a laser oscillator is determined from the visibility of spectrally resolved fringes in a combined two-path multiple-path interferometer. At maximum visibility the pulses have zero carrier-envelope phase drift, while the visibility becomes zero for uncorrelated pulses. The method is widely independent of bandwidth and pulse energy. The effects of carrier-envelope offset phase noise, finite detection time, and dispersion are also discussed. M. G?rbe and C. Grebing have equally contributed to this paper.     

Agile linear interferometric method for carrier-envelope phase drift measurement

A bandwidth-independent and linear interferometric method for the measurement of the carrier-envelope phase drift of ultrashort pulse trains is demonstrated. The pulses are temporally overlapped in a resonant multiple-beam interferometer. From the position of the spectral interference pattern, the relative carrier-envelope phase between two subsequent oscillator pulses is obtained at data acquisition rates up to 200 Hz. Cross calibration has been performed by f-to-2f interferometry in two independent experiments. The optical length of the interferometer has been actively stabilized, leading to a phase jitter of 117 mrad (rms). These results indicate a reduced noise and quicker data acquisition in comparison with previous linear methods for measuring the carrier-envelope phase drift.     

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

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

飞秒钛宝石放大激光脉冲的载波包络相位测量与控制

通过对重复频率为1 kHz的放大飞秒激光脉冲的光谱干涉实验,结合傅里叶变换进行了载波包络相位漂移的实验研究.在此基础上利用锁相环反馈控制技术实现了对载波包络相位的精密锁定,锁定后的激光脉冲稳态相位均方根误差小于80mrad,锁定时间超过3h.同时在理论上分析了光谱干涉测量放大激光脉冲载波包络相位的原理,给出了光谱干涉信号与载波包络相位的关系. 关键词： 飞秒钛宝石放大器 载波包络相位 光谱干涉 超连续     

Nonlinear effects on the carrier-envelope phase

Calculations, using the Maxwell equations, are presented of nonlinear effects on the carrier-envelope phase for pulse durations in the two-optical-cycle range for pulses propagating in sapphire. Initially, with increasing pulse intensity the carrier-envelope phase increases monotonically. However, at higher intensities there is a turnabout in the direction of the phase change and a large change in the phase that is caused by a warping of the envelope from strong nonlinear effects. The Kerr nonlinear response occurs on a time scale of approximately 1 fs and gives significantly different results from those obtained by assuming an instantaneous response.     

Self-stabilization of the carrier-envelope phase of an optical parametric amplifier verified with a photonic crystal fiber

Experimental verification is given for self-stabilization of the carrier-envelope phase (CEP) of idler pulses from a noncollinear optical parametric amplifier. The verification is performed by spectral interference (SI) between an octave-broadened supercontinuum (SC) and its second harmonic. This SC is generated by nonlinear propagation of the second harmonic of the idler through a photonic crystal fiber (PCF). Although the modulational instability causes the intensity and CEP fluctuation and the amplified spontaneous emission noise in PCF degrades the visibility of SI, the CEP is verified to be stabilized.     

Nonlinear optics with phase-controlled pulses in the sub-two-cycle regime.

Nonlinear optical effects due to the phase between carrier and envelope are observed with 5 fs pulses from a Kerr-lens mode-locked Ti:sapphire laser. These sub-two-cycle pulses with octave spanning spectra are the shortest pulses ever generated directly from a laser oscillator. Detection of the carrier-envelope phase slip is made possible by simply focusing the short pulses directly from the oscillator into a BBO crystal. As a further example of nonlinear optics with such short pulses, the interference between second- and third-harmonic components is also demonstrated.     

Carrier-envelope phase of ultrashort pulsed Laguerre-Gaussian beam

The carrier-envelope phase of the ultrashort pulsed Laguerre-Gaussian beam is studied.The order of Laguerre function affects seriously the variations of the carrier-envelope phase with the propagation distance increasing.The beam waist also affects the carrier-envelope phase in a few Rayleigh distances.The variation of the carrier-envelope phase is larger on the axis than on the beam periphery in propagation.     

Long-term carrier-envelope-phase stabilized fiber-bulk hybrid laser with millihertz linewidth and 50 W average power

Long-term carrier-envelope-phase stabilization was demonstrated in high-power large-modearea fiber chirped-pulse spectral fraction amplification at 1030 nm of a broadband femtosecond Ti:sapphire laser. The carrier enveloped phase was stably controlled with the maximum average power up to 50 W by pre-compensating the carrier-envelope phase changes in the high-power fiber amplifiers. The locked in loop and out of loop frequency fluctuation was measured to be 1.44 and 46 mHz within half an hour. The locked carrier-frequency exhibited an in loop and out of loop beat signal linewidth of 1.66 and 2.27 mHz, accordingly accumulated phase jitter was estimated to be 0.22 and 0.73 rad, respectively, with the integration range from 10 mHz to 100 kHz. The phase stabilization was measured to change little as the output power increased, confirming negligible amplitude-to-phase noise conversions in the linear high-power fiber chirped pulse amplification.     

Long-term carrier-envelope phase stability from a grating-based, chirped pulse amplifier

We demonstrate a carrier-envelope phase (CEP) stabilized, chirped pulse laser amplifier that exhibits greatly improved intrinsic long-term CEP stability compared with that of other amplifiers. This system employs a grating-based stretcher and compressor and a cryogenically cooled laser amplifier. Single-shot carrier envelope phase noise measurements are also presented that avoid underestimation of this parameter caused by fringe averaging and represent a rigorously accurate upper limit on CEP noise.     

Optical phase noise and carrier-envelope offset noise of mode-locked lasers

The timing jitter, optical phase noise, and carrier-envelope offset (CEO) noise of passively mode-locked lasers are closely related. New key results concern analytical calculations of the quantum noise limits for optical phase noise and CEO noise. Earlier results for the optical phase noise of actively mode-locked lasers are generalized, particularly for application to passively mode-locked lasers. It is found, for example, that mode locking with slow absorbers can lead to optical linewidths far above the Schawlow–Townes limit. Furthermore, mode-locked lasers can at the same time have nearly quantum-limited timing jitter and a strong optical excess phase noise. A feedback timing stabilization via cavity length control can, depending on the situation, reduce or greatly increase the optical phase noise, while not affecting the CEO noise. Besides presenting such findings, the paper also tries to clarify some basic aspects of phase noise in mode-locked lasers. PACS 42.50.Lc; 42.60.Fc     

Long-term carrier-envelope phase coherence

The carrier-envelope phase of the pulse train emitted by a 10-fs mode-locked laser has been stabilized such that carrier-envelope phase coherence is maintained for at least 150 s (measurement limited). The phase coherence time was measured independently of the feedback loop.     

飞秒钛宝石光学频率梳的精密锁定

经相位锁定后的飞秒钛宝石光学频率梳已经广泛用于绝对光频的测量，这是光频标领域一个革命性的突破.在自建的90MHz飞秒钛宝石激光器的基础上首先采用光子晶体光纤将其光谱展宽到一个光倍频程，接着利用锁相环技术分别将重复频率和载波包络频移同时高精度地锁定到一台稳定度为6×10^－14的Cs钟上，进而得到了稳定度相同的飞秒光学频率梳.     

Stimulated Brillouin scattering-induced phase noise in an interferometric fiber sensing system

Stimulated Brillouin scattering-induced phase noise is harmful to interferometric fiber sensing systems. The localized fluctuating model is used to study the intensity noise caused by the stimulated Brillouin scattering in a single-mode fiber. The phase noise structure is analyzed for an interferometric fiber sensing system, and an unbalanced Michelson interferometer with an optical path difference of 1 m, as well as the phase-generated carrier technique, is used to measure the phase noise. It is found that the phase noise is small when the input power is below the stimulated Brillouin scattering threshold, increases dramatically at first and then gradually becomes flat when the input power is above the threshold, which is similar to the variation in relative intensity noise. It can be inferred that the increase in phase noise is mainly due to the broadening of the laser linewidth caused by stimulated Brillouin scattering, which is verified through linewidth measurements in the absence and presence of the stimulated Brillouin scattering.     

Stimulated Brillouin scattering-induced phase noise in an interferometric fiber sensing system

Stimulated Brillouin scattering-induced phase noise is harmful to interferometric fiber sensing systems.The localized fluctuating model is used to study the intensity noise caused by the stimulated Brillouin scattering in a single-mode fiber.The phase noise structure is analyzed for an interferometric fiber sensing system,and an unbalanced Michelson interferometer with an optical path difference of 1 m,as well as the phase-generated carrier technique,is used to measure the phase noise.It is found that the phase noise is small when the input power is below the stimulated Brillouin scattering threshold,increases dramatically at first and then gradually becomes flat when the input power is above the threshold,which is similar to the variation in relative intensity noise.It can be inferred that the increase in phase noise is mainly due to the broadening of the laser linewidth caused by stimulated Brillouin scattering,which is verified through linewidth measurements in the absence and presence of the stimulated Brillouin scattering.