Carrier-envelope Offset Phase Research Articles

Ultra-precise optical phase-locking approach for ultralow noise frequency comb generation

Optical frequency comb (OFC) with low phase noise enables more stringent metrology in classical and quantum systems. To eliminate phase noise, it is essential to extend the feedback bandwidth of the carrier-envelope phase and the repetition rate. Here, we present an approach to the construction of an ultralow-noise OFC. By exploiting different electro-optic modulators as fast actuators, this method can extend the feedback bandwidth to more than 150 kHz at the repetition rate phase locking and carrier-envelope offset phase locking We obtain a residual phase noise of 21.8 mrad (18.1 as) and 86.1 mrad (71.3 as) for the stabilised optical beat signal (fbeat) and carrier-envelope offset frequency (fceo), respectively. We validate this architecture by a measurement the relative linewidth between two combs, which reveals an in-loop beat fractional instability of less than 1.18 × 10−18 and an out-of-loop beat fractional instability of less than 2.31 × 10−15 at a 1-s averaging time. The out-of-loop beat phase noise is 145 mrad (120 as). These results indicate that the combination of Er-fiber laser technology and active feedback with a high bandwidth ensures coherent tracking of an optical reference with ultralow noise. The ultralow-noise OFC offers a universal tool for accurate, high-resolution optical spectroscopy.

A Femtosecond Pulse Train with a Selectable Carrier–Envelope Offset Phase

A method and a scheme of obtaining a femtosecond pulse train without frequency comb offset and selectable carrier–envelope offset phase are proposed.

Carrier-envelope offset frequency stabilization of a thin-disk laser oscillator operating in the strongly self-phase modulation broadened regime.

We demonstrate the carrier-envelope offset (CEO) frequency stabilization of a Kerr lens mode-locked Yb:Lu2O3 thin-disk laser oscillator operating in the strongly self-phase modulation (SPM) broadened regime. This novel approach allows overcoming the intrinsic gain bandwidth limit and is suited to support frequency combs from sub-100-fs pulse trains with very high output power. In this work, strong intra-oscillator SPM in the Kerr medium enables the optical spectrum of the oscillating pulse to exceed the bandwidth of the gain material Yb:Lu2O3 by a factor of two. This results in the direct generation of 50-fs pulses without the need for external pulse compression. The oscillator delivers an average power of 4.4 W at a repetition rate of 61MHz. We investigated the cavity dynamics in this regime by characterizing the transfer function of the laser output power for pump power modulation, both in continuous-wave and mode-locked operations. The cavity dynamics in mode-locked operation limit the CEO modulation bandwidth to ~10 kHz. This value is sufficient to achieve a tight phase-lock of the CEO beat via active feedback to the pump current and yields a residual in-loop integrated CEO phase noise of 197 mrad integrated from 1 Hz to 1 MHz.

Carrier envelope offset frequency detection and stabilization of a diode-pumped mode-locked Ti:sapphire laser.

We demonstrate the first diode-pumped Ti:sapphire laser frequency comb. It is pumped by two green laser diodes with a total pump power of 3 W. The Ti:sapphire laser generates 250 mW of average output power in 61-fs pulses at a repetition rate of 216 MHz. We generated an octave-spanning supercontinuum spectrum in a photonic-crystal fiber and detected the carrier envelope offset (CEO) frequency in a standard f-to-2f interferometer setup. We stabilized the CEO-frequency through direct current modulation of one of the green pump diodes with a feedback bandwidth of 55 kHz limited by the pump diode driver used in this experiment. We achieved a reduction of the CEO phase noise power spectral density by 140 dB at 1 Hz offset frequency. An advantage of diode pumping is the ability for high-bandwidth modulation of the pump power via direct current modulation. After this experiment, we studied the modulation capabilities and noise properties of green pump laser diodes with improved driver electronics. The current-to-output-power modulation transfer function shows a bandwidth larger than 1 MHz, which should be sufficient to fully exploit the modulation bandwidth of the Ti:sapphire gain for CEO stabilization in future experiments.

First investigation of the noise and modulation properties of the carrier-envelope offset in a modelocked semiconductor laser

We present the first characterization of the noise properties and modulation response of the carrier-envelope offset (CEO) frequency in a semiconductor modelocked laser. The CEO beat of an optically-pumped vertical external-cavity surface-emitting laser (VECSEL) at 1030 nm was characterized without standard f-to-2f interferometry. Instead, we used an appropriate combination of signals obtained from the modelocked oscillator and an auxiliary continuous-wave laser to extract information about the CEO signal. The estimated linewidth of the free-running CEO beat is approximately 1.5 MHz at 1-s observation time, and the feedback bandwidth to enable a tight CEO phase lock to be achieved in a future stabilization loop is in the order of 300 kHz. We also characterized the amplitude and phase of the pump current to CEO-frequency transfer function, which showed a 3-dB bandwidth of ∼300 kHz for the CEO frequency modulation. This fulfills the estimated required bandwidth and indicates that the first self-referenced phase-stabilization of a modelocked semiconductor laser should be feasible in the near future.

Anisotropic emission in quantum-beat spectroscopy of helium excited states

We present quantum-beat spectroscopy of excited states of helium atoms populated selectively with high-order-harmonic emission below the atomic ionization potential by means of low-pass filtering of the pump radiation. The created electron wave packet is ionized by few-cycle infrared (IR) pulses leading to characteristic peaks in the photoelectron yield, which beat with a frequency proportional to the energy gap between the states involved in the two-color photoionization process. Minimizing the direct ionization by the extreme ultraviolet (XUV) radiation, we can follow the evolution of the electron wave packet also in the region of temporal pump-probe overlap. A detailed time-frequency analysis of the quantum beats and direct comparison with the solution of the time-dependent Schr\odinger equation reveal the existence of quantum beats characterized by a final state of mixed parity. Finally, we show that by varying the carrier-envelope offset phase of the probe pulse, one can optically control the preferred direction of photoelectron emission and the contrast of such beats.

Trade-off between linewidth and slip rate in a mode-locked laser model.

We demonstrate a trade-off between linewidth and loss-of-lock rate in a mode-locked laser employing active feedback to control the carrier-envelope offset phase difference. In frequency metrology applications, the linewidth translates directly to uncertainty in the measured frequency, whereas the impact of lock loss and recovery on the measured frequency is less well understood. We reduce the dynamics to stochastic differential equations, specifically diffusion processes, and compare the linearized linewidth to the rate of lock loss determined by the mean time to exit, as calculated from large deviation theory.

Phase Stabilization of a Frequency Comb using Multipulse Quantum Interferometry

From the interaction between a frequency comb and an atomic qubit, we derive quantum protocols for the determination of the carrier-envelope offset phase, using the qubit coherence as a reference, and without the need of frequency doubling or an octave spanning comb. Compared with a trivial interference protocol, the multipulse protocol results in a polynomial enhancement of the sensitivity O(N-2) with the number N of laser pulses involved. We specialize the protocols using optical or hyperfine qubits, Λ schemes, and Raman transitions, and introduce methods where the reference is another phase-stable cw laser or frequency comb.

Titanium:sapphire laser oscillator delivering two-optical-cycle pulses

A titanium:sapphire laser oscillator has been built using commercially available ultra-broadband optics. It emits 1.3 nJ energy pulses, with 5.9 fs duration and a spectral bandwidth larger than oneoctave (>570-1200 nm). It is the first two-optical cycles pulse oscillator built in Spain and, given its characteristics, it will be possible to stabilize its carrier-envelope offset phase.

A time/frequency quantum analysis of the light generated by synchronously pumped optical parametric oscillators

We present in this paper a general model for determining the quantum properties of the light generated by a synchronously pumped optical parametric oscillator (SPOPO) operating below threshold. This model considers time and frequency on an equal footing, which allows us to find new quantum properties, related for example to the carrier envelope offset (CEO) phase, and to consider situations that are close to real experiments. We show that, in addition to multimode squeezing in the so-called ‘supermodes’, the system exhibits quadrature entanglement between frequency combs of opposite CEO phases. We have also determined the quantum properties of the individual pulses and their quantum correlations with the neighboring pulses. Finally, we determine the quantum Cramer–Rao limit for an ultra-short time delay measurement using a given number of pulses generated by the SPOPO.

Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 15-µm solid-state laser

We report the first full stabilization of an optical frequency comb generated from a femtosecond diode-pumped solid-state laser (DPSSL) operating in the 1.5-μm spectral region. The stability of the comb is characterized in free-running and in phase-locked operation by measuring the noise properties of the carrier-envelope offset (CEO) beat, of the repetition rate, and of a comb line at 1558 nm. The high Q-factor of the semiconductor saturable absorber mirror (SESAM)-modelocked 1.5-µm DPSSL results in a low-noise CEO-beat, for which a tight phase lock can be much more easily realized than for a fiber comb. Using a moderate feedback bandwidth of only 5.5 kHz, we achieved a residual integrated phase noise of 0.72 rad rms for the locked CEO, which is one of the smallest values reported for a frequency comb system operating in this spectral region. The fractional frequency stability of the CEO-beat is 20‑fold better than measured in a standard self-referenced commercial fiber comb system and contributes only 10(-15) to the optical carrier frequency instability at 1 s averaging time.

Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser

We report on quantum-limited noise performance of a mode-locked ytterbium all-fiber laser. The laser operates at a high normal net dispersion without dispersion compensation. We show that the naïve application of analytical models to such lasers leads to strongly underestimated timing jitter, whereas a numerical simulation is in reasonable agreement with measurements. The measured timing phase noise is found to be essentially limited by quantum noise influences and not by technical noise. Furthermore we show that the phase noise of different comb lines has a quasi-fix point at the center of the optical spectrum and that the jitter is translated into high carrier-envelope offset phase noise with a linewidth of around 3 MHz.

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.

Self-compression of optical laser pulses by filamentation

During the propagation of intense femtosecond laser pulses in a transparent medium, pulse shortening can occur without external guiding. Experimental evidence for this effect and a description of its physical origin are presented. Nearly single cycle pulses at 800 nm with an energy of 0.120 mJ can be obtained with excellent beam quality. Carrier envelope offset phase (CEP) stability is conserved or even improved after the nonlinear propagation stage. Prospects for further improvement are discussed.

Bandwidth-independent linear method for detection of the carrier-envelope offset phase

We propose and demonstrate a novel linear procedure for measurement of the carrier-envelope offset (CEO) phase of femtosecond oscillators. The technique is based on a Mach-Zehnder interferometer, a ring resonator, and a spectrograph. In this scheme, interference between subsequent pulses from a pulse train may frustrate the interference between identical pulses in the Mach-Zehnder, resulting in a modification of interference contrast depending on the CEO phase. We suggest spectrally and spatially resolved interferometry for robust detection of the fringe visibility. It is shown by numerical simulations and experimentally demonstrated that the visibility of such fringes uniquely depends on the CEO phase of the pulse train. Since the method relies only on linear interactions and does not require any nonlinear conversion, it allows characterizing the CEO frequency of mode-locked oscillators with virtually arbitrarily low bandwidth and power levels.

Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua

We demonstrate sub-millijoule-energy, sub-4 fs-duration near-infrared laser pulses with a controlled waveform comprised of approximately 1.5 optical cycles within the full-width at half-maximum (FWHM) of their temporal intensity profile. We further demonstrate the utility of these pulses for producing high-order harmonic continua of unprecedented bandwidth at photon energies around 100 eV. Ultra-broadband coherent continua extending from 90 eV to more than 130 eV with smooth spectral intensity distributions that exhibit dramatic, never-before-observed sensitivity to the carrier-envelope offset (CEO) phase of the driver laser pulse were generated. These results suggest the feasibility of sub-100-attosecond XUV pulse generation for attosecond spectroscopy in the 100 eV range, and of a simple yet highly sensitive on-line CEO phase detector with sub-50-ms response time.

Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors

Ultrashort pulse light-matter interactions in a semiconductor are investigated within the regime of resonant optical rectification. Using pulse envelope areas of around 1.5-3.5 pi, a single-shot dependence on carrier-envelope-offset phase (CEP) is demonstrated for 5 fs pulse durations. A characteristic phase map is predicted for several different frequency regimes using parameters for thin-film GaAs. We subsequently suggest a possible technique to extract the CEP, in both sign and amplitude, using a solid state detector.

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.

5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis

Intense 5.1 fs CEO (carrier envelope offset) phase stable pulses were generated through two-fold filamentation in a noble gas at atmospheric pressure. The preservation of the CEO phase during the filamentation process was investigated. We show that generating these short pulses using filaments is not detrimental for the CEO phase stabilization, and that the more than one octave-spanning spectrum intrinsically generated by the process is feasible, and offers certain benefits, for direct use in single shot f–2f spectral interferometry.

Circumvention of noise contributions in fiber laser based frequency combs

We investigate the performance of an Er:fiber laser based femtosecond frequency comb for precision metrological applications. Instead of an active stabilization of the comb, the fluctuations of the carrier-envelope offset phase, the repetition phase, and the phase of the beat from a comb line with an optical reference are synchronously detected. We show that these fluctuations can be effectively eliminated by exploiting their known correlation. In our experimental scheme, we utilize two identically constructed frequency combs for the measurement of the fluctuations, rejecting the influence of a shared optical reference. From measuring a white frequency noise level, we demonstrate that a fractional frequency instability better than 1.4 x 10(-14) for 1 s averaging time can be achieved in frequency metrology applications using the Er:fiber based frequency comb.