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.     

Frequency-stabilized Yb:fiber comb with a tapered single-mode fiber

We demonstrate a stable Yb:fiber frequency comb with supercontinuum generation by using a specially designed tapered single-mode fiber, in which a spectrum spanning from 500 nm to 1500 nm is produced. The carrier-envelope offset signal of the Yb:fiber comb is measured with a signal-to-noise ratio of more than 40 dB and a linewidth narrower than120 k Hz. The repetition rate and carrier-envelope offset signals are simultaneously phase locked to a microwave reference frequency.     

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.     

Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO

We excite ZnO samples with two-cycle optical pulses directly from a mode-locked oscillator with average powers of several tens of milliwatts. The emitted light reveals peaks at the carrier-envelope offset frequency f(?) and at 2f(?) in the radio-frequency spectra. These peaks can still be detected in layers as thin as 350 nm-a step toward determining the carrier-envelope offset phase itself.     

Carrier-wave Rabi flopping: role of the carrier-envelope phase

Recently, a dependence of Rabi flopping on the carrier-envelope phase of the exciting laser pulses was predicted theoretically [Phys. Rev. Lett. 89, 127401 (2002)] for excitation of a thin semiconductor film with intense few-cycle pulses. Here, we report corresponding experiments on 50-100-nm thin GaAs films excited with 5-fs pulses. We find a dependence on the carrier-envelope phase arising from the interference of sidebands from the fundamental or the third-harmonic Mollow triplet, respectively, with surface second-harmonic generation.     

Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation

The shortest pulses periodically emitted directly from a mode-locked Ti:sapphire laser are approaching the two-optical-cycle range. In this region, the phase of the optical carrier with respect to the pulse envelope becomes important in nonlinear optical processes such as high-harmonic generation. Because there are no locking mechanisms between envelope and carrier inside a laser, their relative phase offset experiences random fluctuations. Here, we propose several novel methods to measure and to stabilize this carrier-envelope offset (CEO) phase with sub-femtosecond uncertainty. The stabilization methods are an important prerequisite for attosecond pulse generation schemes. Short and highly periodic pulses of a two-cycle laser correspond to an extremely wide frequency comb of equally spaced lines, which can be used for absolute frequency measurements. Using the proposed phase-measurement methods, it will be possible to phase-coherently link any unknown optical frequency within the comb spectrum to a primary microwave standard. Experimental studies using a sub-6-fs Ti:sapphire laser suggesting the feasibility of carrier-envelope phase control are presented. Received: 19 August 1999 / Published online: 8 September 1999     

Carrier-envelope offset dynamics of mode-locked lasers

We investigate coupling mechanisms between the amplitude and the carrier-envelope offset phase in mode-locked lasers. We find that nonlinear beam steering in combination with the intracavity prism compressor is the predominant mechanism that causes amplitude-to-phase conversion in our laser. A second mechanism, induced by self-steepening, is also identified. These mechanisms are important for stabilizing the carrier-envelope offset phase and also explain the extremely low pulse-to-pulse energy fluctuations observed in some lasers with carrier-envelope lock. The coupling mechanisms described have important implications for applications of few-cycle optical pulses.     

Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors

We demonstrate quantum interference control of injected photocurrents in a semiconductor using the phase stabilized pulse train from a mode-locked Ti:sapphire laser. Measurement of the comb offset frequency via this technique results in a signal-to-noise ratio of 40 dB (10 Hz resolution bandwidth), enabling solid-state detection of carrier-envelope phase shifts of a Ti:sapphire oscillator.     

High-power Yb-fiber comb with feed-forward control of nonlinear-polarization-rotation mode-locking and large-mode-area fiber amplification

We report on a simple scheme to precisely control carrier-envelope phase of a nonlinear-polarization-rotation mode-locked self-started Yb-fiber laser system with an average output power of ～7 W and a pulse width of 130 fs. The offset frequency was locked to the repetition rate of ～64.5 MHz with a relative linewidth of ～1.4 MHz by using a self-referenced feed-forward scheme based on an acousto-optic frequency shifter. The phase noise and timing jitter were calculated to be 370 mrad and 120 as, respectively.     

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.     

Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared

A phase-locked frequency comb in the near infrared is demonstrated with a mode-locked, erbium-doped, fiber laser whose output is amplified and spectrally broadened in dispersion-flattened, highly nonlinear optical fiber to span from 1100 to >2200 nm. The supercontinuum output comprises a frequency comb with a spacing set by the laser repetition rate and an offset by the carrier-envelope offset frequency, which is detected with the standard f-to-2f heterodyne technique. The comb spacing and offset frequency are phase locked to a stable rf signal with a fiber stretcher in the laser cavity and by control of the pump laser power, respectively. This infrared comb permits frequency metrology experiments in the near infrared in a compact, fiber-laser-based system.     

Monolithic CEO-stabilization scheme-based frequency comb from an octave-spanning laser

We demonstrate a carrier-envelope phase-stabilized octave-spanning oscillator based on the monolithic scheme. A wide output spectrum extending from 480 nm to 1050 nm was generated directly from an all-chirped mirror Ti:sapphire laser. After several improvements, the carrier-envelope offset(CEO) beat frequency accessed nearly 60 d B under a resolution of 100 k Hz. Using a feedback system with 50-k Hz bandwidth, we compressed the residual phase noise to 55 mrad(integrated from 1 Hz to 1 MHz) for the stabilized CEO, corresponding to 23-as timing jitter at the central wavelength of790 nm. This is, to the best of our knowledge, the smallest timing jitter achieved among the existing octave-spanning laser based frequency combs.     

Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers

We link the output spectra of a Ti:sapphire and a Cr:forsterite femtosecond laser phase coherently to form a continuous frequency comb with a wavelength coverage of 0.57-1.45 microm at power levels of 1 nW to 40 microW per frequency mode. To achieve this, the laser repetition rates and the carrier-envelope offset frequencies are phase locked to each other. The coherence time between the individual components of the two combs is 40 micros. The timing jitter between the lasers is 20 fs. The combined frequency comb is self-referenced for access to its overall offset frequency. We report the first demonstration to our knowledge of an extremely broadband and continuous, high-powered and phase-coherent frequency comb from two femtosecond lasers with different gain media.     

Demonstration of a HeNe/CH4-based optical molecular clock

We implement a simple optical clock based on the F2(2) [P(7), v3] optical transition in methane. A single femtosecond laser's frequency comb undergoes difference frequency generation to provide an IR comb at 3.39 microm with a null carrier-envelope offset. This IR comb provides a phase-coherent link between the 88-THz optical reference and the rf repetition rate. Comparison of the repetition rate signal with a second femtosecond comb stabilized to molecular iodine shows an instability of 1.2 x 10(-13) at 1 s, limited by microwave detection of the repetition rates. The single-sideband phase noise of the microwave signal, normalized to a carrier frequency of 1 GHz, is below -93 dBc/Hz at 1-Hz offset.     

Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation

A balanced cross correlator, the optical equivalent of a balanced microwave phase detector, is demonstrated. Its use in synchronizing an octave-spanning Ti:sapphire laser and a 30-fs Cr:forsterite laser yields 300-attosecond timing jitter measured from 10 mHz to 2.3 MHz. The spectral overlap between the two lasers is strong enough to permit direct detection of the difference in carrier-envelope offset frequency between the two lasers.     

Frequency metrology with a turnkey all-fiber system

The repetition rate and carrier-envelope phase offset frequencies of a turnkey, all-fiber-based continuum generator were phase locked to a hydrogen maser. The frequency of the hydrogen maser was calibrated with a highly stable cesium atomic clock, and therefore a fully phase-locked optical frequency comb with well-defined absolute frequencies was obtained. In contrast with the commonly used Ti:sapphire-laser-based systems, we have accomplished a fully turnkey system with no user-adjustable parts. To evaluate the performance of this novel system, we performed absolute frequency measurements in the telecommunications region and at 1064 nm and compared them with our traditional Ti:sapphire-based comb.     

Intensity-related dynamics of femtosecond frequency combs

We have performed systematic studies of intensity-related dynamics of the pulse repetition and carrier-envelope offset frequencies in mode-locked Ti:sapphire lasers. We compared the results far two laser systems that have different intracavity dispersion-compensation schemes. We found that the carrier-envelope phase noise and its dynamic response depend critically on the mode-locking conditions. An intensity-related shift of the laser spectrum was found to be instrumental in interpretations.     

Scattering of a few-cycle laser pulse by a single relativistic electron

The scattering of a single relativistic electron with few-cycle plane wave laser pulse with intensity of about $I=1.38\times 10^{14}\,\text{ W/cm }^{2}$ is theoretically and numerically analyzed in the linear regime, and the radiated energy spectra of electron shows that zeptosecond X-ray pulses can be supported. The influences of the initial carrier-envelope phase offset $\varphi _0$ of the incident few-cycle laser pulses are studied, and the results demonstrate that a single zeptosecond pulse can be produced from scattering by using a single-cycle laser pulse with fixed initial carrier-envelope phase offset $\varphi _0 =\pi /2$ . It is discovered that the influence of the initial carrier-envelope phase $\varphi _0$ on the spectrum of the radiation is apparent for low and high frequency of the spectrum, but there is no influence of the central part of the spectrum.     

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.     

All-passive phase locking of a compact Er:fiber laser system

A passively phase-locked laser source based on compact femtosecond Er:fiber technology is introduced. The carrier-envelope offset frequency is set to zero via difference frequency generation between a soliton at a wavelength of 2?μm and a dispersive wave at 860?nm generated in the same highly nonlinear fiber. This process results in a broadband output centered at 1.55?μm. Subsequently, the 40?MHz pulse train seeds a second Er:fiber amplifier, which boosts the pulse energy up to 8?nJ at a duration of 125?fs. Excellent phase stability is demonstrated via f-to-2f spectral interferometry.