Controlling the phase evolution of few-cycle light pulses

Gigahertz semiconductor laser at a center wavelength of 2 µm in single and dual-comb operation

Dual-comb lasers are a new class of ultrafast lasers that enable fast, accurate and sensitive measurements without any mechanical delay lines. Here, we demonstrate a 2-µm laser called MIXSEL (Modelocked Integrated eXternal-cavity Surface Emitting Laser), based on an optically pumped passively modelocked semiconductor thin disk laser. Using III-V semiconductor molecular beam epitaxy, we achieve a center wavelength in the shortwave infrared (SWIR) range by integrating InGaSb quantum well gain and saturable absorber layers onto a highly reflective mirror. The cavity setup consists of a linear straight configuration with the semiconductor MIXSEL chip at one end and an output coupler a few centimeters away, resulting in an optical comb spacing between 1 and 10 GHz. This gigahertz pulse repetition rate is ideal for ambient pressure gas spectroscopy and dual-comb measurements without requiring additional stabilization. In single-comb operation, we generate 1.5-ps pulses with an average output power of 28 mW, a pulse repetition rate of 4 GHz at a center wavelength of 2.035 µm. For dual-comb operation, we spatially multiplex the cavity using an inverted bisprism operated in transmission, achieving an adjustable pulse repetition rate difference estimated up to 4.4 MHz. The resulting heterodyne beat reveals a low-noise down-converted microwave frequency comb, facilitating coherent averaging.

Carrier-envelope phase on-chip scanner and control of laser beams

The carrier-envelope phase (CEP) is an important property of few-cycle laser pulses, allowing for light field control of electronic processes during laser-matter interactions. Thus, the measurement and control of CEP is essential for applications of few-cycle lasers. Currently, there is no robust method for measuring the non-trivial spatial CEP distribution of few-cycle laser pulses. Here, we demonstrate a compact on-chip, ambient-air, CEP scanning probe with 0.1 µm3 resolution based on optical driving of CEP-sensitive ultrafast currents in a metal-dielectric heterostructure. We successfully apply the probe to obtain a 3D map of spatial changes of CEP in the vicinity of an oscillator beam focus with pulses as weak as 1 nJ. We also demonstrate CEP control in the focal volume with a spatial light modulator so that arbitrary spatial CEP sculpting could be realized.

Coherently averaged dual-comb spectroscopy with a low-noise and high-power free-running gigahertz dual-comb laser

We present a new type of dual optical frequency comb source capable of scaling applications to high measurement speeds while combining high average power, ultra-low noise operation, and a compact setup. Our approach is based on a diode-pumped solid-state laser cavity which includes an intracavity biprism operated at Brewster angle to generate two spatially-separated modes with highly correlated properties. The 15-cm-long cavity uses an Yb:CALGO crystal and a semiconductor saturable absorber mirror as an end mirror to generate more than 3 W average power per comb, below 80 fs pulse duration, a repetition rate of 1.03 GHz, and a continuously tunable repetition rate difference up to 27 kHz. We carefully investigate the coherence properties of the dual-comb by a series of heterodyne measurements, revealing several important features: (1) ultra-low jitter on the uncorrelated part of the timing noise; (2) the radio frequency comb lines of the interferograms are fully resolved in free-running operation; (3) we validate that through a simple measurement of the interferograms we can determine the fluctuations of the phase of all the radio frequency comb lines; (4) this phase information is used in a post-processing routine to perform coherently averaged dual-comb spectroscopy of acetylene (C₂H₂) over long timescales. Our results represent a powerful and general approach to dual-comb applications by combining low noise and high power operation directly from a highly compact laser oscillator.

Free-running Yb:KYW dual-comb oscillator in a MOPA architecture

Single-cavity dual-combs comprise a rapidly emerging technology platform suitable for a wide range of applications like optical ranging, equivalent time sampling, and spectroscopy. However, it remains a challenging task to develop a dual-comb system that exhibits low relative frequency fluctuations to allow for comb line resolved measurements, while simultaneously offering high average power and short pulse durations. Here we combine a passively cooled and compact dual-comb solid-state oscillator with a pair of core-pumped Yb-fiber-based amplifiers in a master-oscillator power-amplifier (MOPA) architecture. The Yb:KYW oscillator operates at 250 MHz and uses polarization multiplexing for dual-comb generation. To the best of our knowledge, this is the first demonstration of a single-cavity dual-comb based on this gain material. As the pulse timing characteristics inherent to the oscillator are preserved in the amplification process, the proposed hybrid approach leverages the benefit of both the ultra-low noise solid-state laser and the advantages inherent to fiber amplifier systems such as straight-forward power scaling. The amplifier is optimized for minimal pulse broadening while still providing significant amplification and spectral broadening. We obtain around 1 W of power per output beam with pulses then compressed down to sub-90 fs using a simple grating compressor, while no pre-chirping or other dispersion management is needed. The full-width half-maximum (FWHM) of the radio-frequency comb teeth is 700 Hz for a measurement duration of 100 ms, which is much less than the typical repetition rate difference, making this passively stable source well-suited for indefinite coherent signal averaging via computational phase tracking.

Dual-comb optical parametric oscillator in the mid-infrared based on a single free-running cavity

We demonstrate a free-running single-cavity dual-comb optical parametric oscillator (OPO) pumped by a single-cavity dual-comb solid-state laser. The OPO ring cavity contains a single periodically-poled MgO-doped LiNbO₃ (PPLN) crystal. Each idler beam has more than 245-mW average power at 3550 nm and 3579 nm center wavelengths (bandwidth 130 nm). The signal beams are simultaneously outcoupled with more than 220 mW per beam at 1499 nm and 1496 nm center wavelength. The nominal repetition rate is 80 MHz, while the repetition rate difference is tunable and set to 34 Hz. To evaluate the feasibility of using this type of source for dual-comb applications, we characterize the noise and coherence properties of the OPO signal beams. We find ultra-low relative intensity noise (RIN) below -158 dBc/Hz at offset frequencies above 1 MHz. A heterodyne beat note measurement with a continuous wave (cw) laser is performed to determine the linewidth of a radio-frequency (RF) comb line. We find a full-width half-maximum (FWHM) linewidth of around 400 Hz. Moreover, the interferometric measurement between the two signal beams reveals a surprising property: the center of the corresponding RF spectrum is always near zero frequency, even when tuning the pump repetition rate difference or the OPO cavity length. We explain this effect theoretically and discuss its implications for generating stable low-noise idler combs suitable for high-sensitivity mid-infrared dual-comb spectroscopy (DCS).

Carrier-envelope offset frequency dynamics of a 10-GHz modelocked laser based on cascaded quadratic nonlinearities

Cascaded quadratic nonlinearities from phase-mismatched second-harmonic generation build the foundation for robust soliton modelocking in straight-cavity laser configurations by providing a tunable and self-defocusing nonlinearity. The frequency dependence of the loss-related part of the corresponding nonlinear response function causes a power-dependent self-frequency shift (SFS). In this paper, we develop a simple analytical model for the SFS-induced changes on the carrier-envelope offset frequency (f_CEO) and experimentally investigate the static and dynamic f_CEO dependence on pump power. We find good agreement with the measured dependence of f_CEO on laser output power, showing a broad f_CEO tuning capability from zero up to the pulse repetition rate. Moreover, we stabilize the relative intensity noise to the -157 dBc/Hz level leading to a tenfold reduction in f_CEO-linewidth.

Gain-switched semiconductor lasers with pulsed excitation and optical injection for dual-comb spectroscopy

In this work we demonstrate the capability of two gain-switched optically injected semiconductor lasers to perform high-resolution dual-comb spectroscopy. The use of low duty cycle pulse trains to gain switch the lasers, combined with optical injection, allows us to obtain flat-topped optical frequency combs with 350 optical lines (within 10 dB) spaced by 100 MHz. These frequency combs significantly improve the spectral resolution reported so far on dual-comb spectroscopy with gain-switched laser diodes. We evaluate the performance of our system by measuring the transmission profile of an absorption line of H¹³CN at the C-band, analyzing the attainable signal-to-noise ratio for a range of averaging times.

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.

Characterizing the carrier-envelope phase stability of mid-infrared laser pulses by high harmonic generation in solids

We present a novel approach for measuring the carrier-envelope phase (CEP) stability of a laser source by employing the process of high harmonic generation (HHG) in solids. HHG in solids driven by few-cycle pulses is very sensitive to the waveform of the driving pulse, therefore enabling to track the shot-to-shot CEP fluctuations of a laser source. This strategy is particularly practical for pulses at long central wavelength up to the mid-infrared spectral range where usual techniques used in the visible or near-infrared regions are challenging to transpose. We experimentally demonstrate this novel tool by measuring the CEP fluctuations of a mid-infrared laser source centered at 9.5~μm.

Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification

A simple and compact straight-cavity laser oscillator incorporating a cascaded quadratic nonlinear crystal and a semiconductor saturable absorber mirror (SESAM) can deliver stable femtosecond modelocking at high pulse repetition rates >10 GHz. In this paper, we experimentally investigate the influence of intracavity dispersion, pump brightness, and cavity design on modelocking with high repetition rates, and use the resulting insights to demonstrate a 10.4-GHz straight-cavity SESAM-modelocked Yb:CALGO laser delivering 108-fs pulses with 812 mW of average output power. This result represents a record-level performance for diode-pumped femtosecond oscillators with repetition rates above 10 GHz. Using the oscillator output without any optical amplification, we demonstrate coherent octave-spanning supercontinuum generation (SCG) in a silicon nitride waveguide. Subsequent f-to-2f interferometry with a periodically poled lithium niobate waveguide enables the detection of a strong carrier-envelope offset (CEO) beat note with a 33-dB signal-to-noise ratio.

Frequency noise correlation between the offset frequency and the mode spacing in a mid-infrared quantum cascade laser frequency comb

The generation of frequency combs in the mid-infrared (MIR) spectral range by quantum cascade lasers (QCLs) has the potential for revolutionizing dual-comb multi-heterodyne spectroscopy in the molecular fingerprint region. However, in contrast to frequency combs based on passively mode-locked ultrafast lasers, their operation relies on a completely different mechanism resulting from a four-wave mixing process occurring in the semiconductor gain medium that locks the modes together. As a result, these lasers do not emit pulses and no direct self-referencing of a QCL comb spectrum has been achieved so far. Here, we present a detailed frequency noise characterization of a MIR QCL frequency comb operating at a wavelength of 8 µm with a mode spacing of ∼7.4 GHz. Using a beat measurement with a narrow-linewidth single-mode QCL in combination with a dedicated electrical scheme, we measured the frequency noise properties of an optical mode of the QCL comb, and indirectly of its offset frequency for the first time, without detecting it by the standard approach of nonlinear interferometry applied to ultrafast mode-locked lasers. In addition, we also separately measured the noise of the comb mode spacing extracted electrically from the QCL. We observed a strong anti-correlation between the frequency fluctuations of the offset frequency and mode spacing, leading to optical modes with a linewidth slightly below 1 MHz in the free-running QCL comb (at 1-s integration time), which is narrower than the individual contributions of the offset frequency and mode spacing that are at least 2 MHz each.

Controlling Electron Dynamics with Carrier-Envelope Phases of a Laser Pulse

A theoretical study on the ionization dynamics of carbon atom irradiated with a few-cycle, intense laser field is performed within a quasiclassical model to get mechanistic insights into an earlier reported carrier-envelope phase dependency of ionization probabilities of an atom [ Phys. Rev. Lett. 2013, 110, 083602]. The carrier-envelope phase of the laser pulse is found to govern the overall dynamics, reflecting its importance in controlling electronic motion. To understand the origin of this effect, individual trajectories were analyzed at a particular laser intensity. We found that a variation in the carrier-envelope phase affects the angle of ejection of the electrons and subsequently the attainment of the desired final state.

Tightly locked optical frequency comb from a semiconductor disk laser

Ultrafast semiconductor disk lasers (SDLs) passively modelocked using semiconductor saturable absorbers mirrors (SESAMs) generate optical frequency combs (OFCs) with gigahertz line spacings - a regime where solid-state and fiber lasers struggle with geometrical and Q-switching limitations. We stabilized both the frequency comb spacing and the offset without any additional external optical amplification or pulse compression. The overall noise performance is competitive with other gigahertz OFCs. A SESAM-modelocked vertical external-cavity surface-emitting laser (VECSEL) at a center wavelength around 1 µm generates 122-fs pulses with 160 mW average output power and we only needed 17-pJ pulse energy coupled into a silicon nitride (Si₃N₄) waveguide for supercontinuum generation (SCG) and OFC offset stabilization.

An unstabilized femtosecond semiconductor laser for dual-comb spectroscopy of acetylene

Dual-comb systems based on two optical frequency combs of slightly different line spacing emerge as powerful tools in spectroscopy and interferometry. Semiconductor lasers have a high impact in continuous-wave tunable laser spectroscopy. Here we demonstrate the first dual-comb interferometer based on a single femtosecond semiconductor laser: a dual-comb modelocked optically pumped external-cavity surface-emitting laser (MIXSEL) ideally suited for a 1 to 10 GHz comb spacing. At a center wavelength of 1.03 µm (9709 cm^-1) we measured acetylene gas transmittance with a resolution of 2.7 GHz in 100 ms with residual errors of less than 3% using thousand comb lines without aliasing effects.

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 61 MHz. 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.

Multi-branch fiber comb with relative frequency uncertainty at 10-20 using fiber noise difference cancellation

In multi-branch combs, the comb outputs from the branches suffer from different fiber noises, which often limit the uncertainty of the combs referring a highly-stable optical frequency. To overcome this limitation, we introduced fiber noise difference cancellation to multi-branch fiber combs. We detected and phase-locked the beat notes between the branch outputs and a common 1542 nm continuous wave laser. A piezo-electric transducer-based fiber stretcher was installed in each branch except for the branch used as the cancellation reference. We fabricated two quasi-identical combs with this mechanism and confirmed the relative frequency uncertainty by comparing them. The cancellation improved the frequency uncertainty to a low level of 10^-20 at a 100000-s averaging time.

Localized solutions of Lugiato-Lefever equations with focused pump

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Carrier-envelope offset stabilization of a GHz repetition rate femtosecond laser using opto-optical modulation of a SESAM

We demonstrate, to the best of our knowledge, the first carrier-envelope offset (CEO) frequency stabilization of a GHz femtosecond laser based on opto-optical modulation (OOM) of a semiconductor saturable absorber mirror (SESAM). The 1.05-GHz laser is based on a Yb:CALGO gain crystal and emits sub-100-fs pulses with 2.1-W average power at a center wavelength of 1055 nm. The SESAM plays two key roles: it starts and stabilizes the mode-locking operation and is simultaneously used as an actuator to control the CEO frequency. This second functionality is implemented by pumping the SESAM with a continuous-wave 980-nm laser diode in order to slightly modify its nonlinear reflectivity. We use the standard f-to-2f method for detection of the CEO frequency, which is stabilized by applying a feedback signal to the current of the SESAM pump diode. We compare the SESAM-OOM stabilization with the traditional method of gain modulation via control of the pump power of the Yb:CALGO gain crystal. While the bandwidth for gain modulation is intrinsically limited to ∼250  kHz by the laser cavity dynamics, we show that the OOM provides a feedback bandwidth above 500 kHz. Hence, we were able to obtain a residual integrated phase noise of 430 mrad for the stabilized CEO beat, which represents an improvement of more than 30% compared to gain modulation stabilization.

Full stabilization and characterization of an optical frequency comb from a diode-pumped solid-state laser with GHz repetition rate

We demonstrate the first self-referenced full stabilization of a diode-pumped solid-state laser (DPSSL) frequency comb with a GHz repetition rate. The Yb:CALGO DPSSL delivers an average output power of up to 2.1 W with a typical pulse duration of 96 fs and a center wavelength of 1055 nm. A carrier-envelope offset (CEO) beat with a signal-to-noise ratio of 40 dB (in 10-kHz resolution bandwidth) is detected after supercontinuum generation and f-to-2f interferometry directly from the output of the oscillator, without any external amplification or pulse compression. The repetition rate is stabilized to a reference synthesizer with a residual integrated timing jitter of 249 fs [10 Hz - 1 MHz] and a relative frequency stability of 10^-12/s. The CEO frequency is phase-locked to an external reference via pump current feedback using home-built modulation electronics. It achieves a loop bandwidth of ~150 kHz, which results in a tight CEO lock with a residual integrated phase noise of 680 mrad [1 Hz - 1 MHz]. We present a detailed characterization of the GHz frequency comb that combines a noise analysis of the repetition rate f_rep, of the CEO frequency f_CEO, and of an optical comb line at 1030 nm obtained from a virtual beat with a narrow-linewidth laser at 1557 nm using a transfer oscillator. An optical comb linewidth of about 800 kHz is assessed at 1-s observation time, for which the dominant noise sources of f_rep and f_CEO are identified.

A III-V-on-Si ultra-dense comb laser

Optical frequency combs emerge as a promising technology that enables highly sensitive, near-real-time spectroscopy with a high resolution. The currently available comb generators are mostly based on bulky and high-cost femtosecond lasers for dense comb generation (line spacing in the range of 100 MHz to 1 GHz). However, their integrated and low-cost counterparts, which are integrated semiconductor mode-locked lasers, are limited by their large comb spacing, small number of lines and broad optical linewidth. In this study, we report a demonstration of a III-V-on-Si comb laser that can function as a compact, low-cost frequency comb generator after frequency stabilization. The use of low-loss passive silicon waveguides enables the integration of a long laser cavity, which enables the laser to be locked in the passive mode at a record-low 1 GHz repetition rate. The 12-nm 10-dB output optical spectrum and the notably small optical mode spacing results in a dense optical comb that consists of over 1400 equally spaced optical lines. The sub-kHz 10-dB radio frequency linewidth and the narrow longitudinal mode linewidth (<400 kHz) indicate notably stable mode-locking. Such integrated dense comb lasers are very promising, for example, for high-resolution and real-time spectroscopy applications.

Attosecond physics at the nanoscale

Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond  =  1 as  =  10^-18 s), which is comparable with the optical field. For comparison, the revolution of an electron on a 1s orbital of a hydrogen atom is  ∼152 as. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with nanometric precision. Although nano-engineering is a vast and well-established research field on its own, the merger with intense laser physics is relatively recent. In this report on progress we present a comprehensive experimental and theoretical overview of physics that takes place when short and intense laser pulses interact with nanosystems, such as metallic and dielectric nanostructures. In particular we elucidate how the spatially inhomogeneous laser induced fields at a nanometer scale modify the laser-driven electron dynamics. Consequently, this has important impact on pivotal processes such as above-threshold ionization and high-order harmonic generation. The deep understanding of the coupled dynamics between these spatially inhomogeneous fields and matter configures a promising way to new avenues of research and applications. Thanks to the maturity that attosecond physics has reached, together with the tremendous advance in material engineering and manipulation techniques, the age of atto-nanophysics has begun, but it is in the initial stage. We present thus some of the open questions, challenges and prospects for experimental confirmation of theoretical predictions, as well as experiments aimed at characterizing the induced fields and the unique electron dynamics initiated by them with high temporal and spatial resolution.

Phase locking of a mode-locked titanium-sapphire laser-based optical frequency comb to a reference laser using a fast piezoelectric actuator

We phase lock an octave-spanning optical frequency comb, generated using a mode-locked titanium-sapphire laser and a photonic-crystal fiber, to a continuous-wave laser line-narrowed to a reference cavity. To phase lock the pulse-repetition frequency, the cavity length of the mode-locked laser is controlled by using a fast piezoelectric-actuated mirror of a servo bandwidth up to 80 kHz. The residual phase noise is 0.35 rad, and 89% of the power is concentrated to the carrier. To apply the system to optical frequency-ratio measurements and to evaluate the phase locking, a simultaneous frequency measurement of the beat between the other mode of the comb and another laser line-narrowed to a different resonance of the common reference cavity is demonstrated.

Bottle microresonator broadband and low-repetition-rate frequency comb generator

We propose a new type of broadband and low repetition rate (RR) frequency comb generator that has the shape of an elongated and nanoscale-shallow optical bottle microresonator created at the surface of an optical fiber. The free spectral range (FSR) of the broadband azimuthal eigenfrequency series of this resonator is the exact multiple of the FSR of the dense and narrowband axial series. The effective radius variation of the microresonator is close to a parabola with a nanoscale height that is greater or equal to λ/2πn₀. (Here λ is the characteristic radiation wavelength and n₀ is the refractive index of the microresonator material.) Overall, the microresonator possesses a broadband, small FSR and accurately equidistant spectrum convenient for the generation of a broadband and low RR optical frequency comb. It is shown that this comb can be generated by pumping with a cw laser, with a radiation frequency that matches a single axial eigenfrequency of the microresonator or, alternatively, by pumping with a mode-locked laser, which generates a narrowband low RR comb matching a series of equidistant axial eigenfrequencies situated between adjacent azimuthal eigenfrequencies.

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.

Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking

The carrier envelope phase (CEP) is a crucial parameter for a few-cycle laser pulse since it substantially determines the laser waveform. Stepping forward from infrared to extreme ultraviolet (EUV) pulses, we propose a strategy to directly characterize the CEP of an isolated attosecond pulse (IAP) by numerically simulating the tunneling ionization of a hydrogen atom in a combined IAP and phase-stabilized circularly polarized IR laser pulse. The fine modulations of the combined laser fields, due to the variation of the CEP of the IAP, are exponentially enlarged onto the distinct time-dependent tunneling ionization rate. Electrons released at different time with distinct tunneling ionization rates are angularly streaked to different directions. By measuring the resulting photoelectron momentum distribution, the CEP of the IAP can be retrieved. The characterization of the CEP of an IAP will open the possibility of capturing sub-EUV-cycle dynamics.

Gigahertz frequency comb offset stabilization based on supercontinuum generation in silicon nitride waveguides

Silicon nitride (Si₃N₄) waveguides represent a novel photonic platform that is ideally suited for energy efficient and ultrabroadband nonlinear interactions from the visible to the mid-infrared. Chip-based supercontinuum generation in Si₃N₄ offers a path towards a fully-integrated and highly compact comb source for sensing and time-and-frequency metrology applications. We demonstrate the first successful frequency comb offset stabilization that utilizes a Si₃N₄ waveguide for octave-spanning supercontinuum generation and achieve the lowest integrated residual phase noise of any diode-pumped gigahertz laser comb to date. In addition, we perform a direct comparison to a standard silica photonic crystal fiber (PCF) using the same ultrafast solid-state laser oscillator operating at 1 µm. We identify the minimal role of Raman scattering in Si₃N₄ as a key benefit that allows to overcome the fundamental limitations of silica fibers set by Raman-induced self-frequency shift.

Direct generation of 12.5-GHz-spaced optical frequency comb with ultrabroad coverage in near-infrared region by cascaded fiber configuration

We generated a 12.5-GHz-spacing optical frequency comb that can be resolved over 100 THz, from 1040 to 1750 nm, without spectral mode filtering. To cover such a broad spectrum, we used electro-optic modulation of single frequency light and line-by-line pulse synthesis to produce a clear pulse train and subsequent spectral broadening in highly nonlinear fibers (HNLFs). We numerically and experimentally investigated a configuration of the HNLFs and find that a two-stage broadening through different HNLFs is required when using limited pulse energy at a high repetition rate. We designed and fabricated solid silica-based HNLFs with small zero-dispersion wavelengths to obtain strong spectral broadening, especially at the shorter wavelengths. The individual lines of the proposed frequency comb are resolvable with high contrast over the entire spectral range. The results described in this paper should lead to the development of multicarrier sources for wavelength-division-multiplexing communication and super-multi-point frequency calibration for spectrometers, especially in astrophysics.

Supercontinuum generation in a multi-plate medium

We analyze femtosecond supercontinuum generation in a distribution of thin solid plates to show that the distributed scheme inhibits processes leading to pulse breakup while allowing spectral expansion to proceed as desired. We introduce basic criteria for setting the plate thickness or initial laser intensity and the location of each plate in the laser beam path and confirm that under these conditions a fully-coherent and intense supercontinuum can be generated for input peak power of as much as two thousand times the critical power for self-focusing of the solid medium.

Dual-comb modelocked lasers: semiconductor saturable absorber mirror decouples noise stabilization

In this paper we present the stabilization of the pulse repetition rate of dual-comb lasers using an intracavity semiconductor saturable absorber mirror (SESAM) for passive modelocking and an intracavity birefringent crystal for polarization-duplexing to obtain simultaneous emission of two modelocked beams from the same linear cavity sharing all components. Initially surprising was the observation that the cavity length adjustments to stabilize one polarization did not significantly affect the pulse repetition rate of the other. We gained insight in the underlying physics using both a semiconductor and Nd:YAG laser gain material with the conclusion that the pulse arrival timing jitter of the two beams is decoupled by the uncorrelated time delay from the saturated SESAM and becomes locked with sufficient but not too much pulse overlap. Noise stabilization is in all cases still possible for both combs. The dual-comb modelocked laser is particularly interesting for the semiconductor laser enabling the integration of gain and absorber layers within one wafer (referred to as the modelocked integrated external-cavity surface emitting laser--MIXSEL).

Frequency comb offset dynamics of SESAM modelocked thin disk lasers

We present a detailed study of the carrier-envelope offset (CEO) frequency dynamics of SESAM modelocked thin disk lasers (TDLs) pumped by kW-class highly transverse multimode pump diodes with a typical M(2) value of 200-300, and give guidelines for future frequency stabilization of multi-100-W oscillators. We demonstrate CEO frequency detection with > 30 dB signal-to-noise ratio with a resolution bandwidth of 100 kHz from a SESAM modelocked Yb:YAG TDL delivering 140 W average output power with 748-fs pulses at 7-MHz pulse repetition rate. We compare with a low-power CEO frequency stabilized Yb:CALGO TDL delivering 2.1 W with 77-fs pulses at 65 MHz. For both lasers, we perform a complete noise characterization, measure the relevant transfer functions (TFs) and compare them to theoretical models. The measured TFs are used to determine the propagation of the pump noise step-by-step through the system components. From the noise propagation analysis, we identify the relative intensity noise (RIN) of the pump diode as the main contribution to the CEO frequency noise. The resulting noise levels are not excessive and do not prevent CEO frequency stabilization. More importantly, the laser cavity dynamics are shown to play an essential role in the CEO frequency dynamics. The cavity TFs of the two lasers are very different which explains why at this point a tight CEO frequency lock can be obtained with the Yb:CALGO TDL but not with the Yb:YAG TDL. For CEO stabilization laser cavities should exhibit high damping of the relaxation oscillations by nonlinear intra-cavity elements, for example by operating a SESAM in the roll-over regime. Therefore the optimum SESAM operation point is a trade-off between enough damping and avoiding multiple pulsing instabilities. Additional cavity components could be considered for supplementary damping independent of the SESAM operation point.

Frequency comb offset detection using supercontinuum generation in silicon nitride waveguides

We present the first direct carrier-envelope-offset (CEO) frequency detection of a modelocked laser based on supercontinuum generation (SCG) in a CMOS-compatible silicon nitride (Si(3)N(4)) waveguide. With a coherent supercontinuum spanning more than 1.5 octaves from visible to beyond telecommunication wavelengths, we achieve self-referencing of SESAM modelocked diode-pumped Yb:CALGO lasers using standard f-to-2f interferometry. We directly obtain without amplification strong CEO beat signals for both a 100-MHz and 1-GHz pulse repetition rate laser. High signal-to-noise ratios (SNR) of > 25 dB and even > 30 dB have been generated with only 30 pJ and 36 pJ of coupled pulse energy from the megahertz and gigahertz laser respectively. We compare these results to self-referencing using a commercial photonic crystal fiber and find that the required peak power for CEO beat detection with a comparable SNR is lowered by more than an order of magnitude when using a Si(3)N(4) waveguide.

High-power multi-megahertz source of waveform-stabilized few-cycle light

Waveform-stabilized laser pulses have revolutionized the exploration of the electronic structure and dynamics of matter by serving as the technological basis for frequency-comb and attosecond spectroscopy. Their primary sources, mode-locked titanium-doped sapphire lasers and erbium/ytterbium-doped fibre lasers, deliver pulses with several nanojoules energy, which is insufficient for many important applications. Here we present the waveform-stabilized light source that is scalable to microjoule energy levels at the full (megahertz) repetition rate of the laser oscillator. A diode-pumped Kerr-lens-mode-locked Yb:YAG thin-disk laser combined with extracavity pulse compression yields waveform-stabilized few-cycle pulses (7.7 fs, 2.2 cycles) with a pulse energy of 0.15 μJ and an average power of 6 W. The demonstrated concept is scalable to pulse energies of several microjoules and near-gigawatt peak powers. The generation of attosecond pulses at the full repetition rate of the oscillator comes into reach. The presented system could serve as a primary source for frequency combs in the mid infrared and vacuum UV with unprecedented high power levels.

Frequency combs have revolutionized the study of electronic structures and dynamics of matter but currently used lasers systems are limited in terms of achievable pulse energies. Here, Pronin et al. demonstrate few cycle pulse emission from a thin-disk laser with 150 nJ pulse energy and 7.7 fs pulse duration.

Gigahertz frequency comb from a diode-pumped solid-state laser

We present the first stabilization of the frequency comb offset from a diode-pumped gigahertz solid-state laser oscillator. No additional external amplification and/or compression of the output pulses is required. The laser is reliably modelocked using a SESAM and is based on a diode-pumped Yb:CALGO gain crystal. It generates 1.7-W average output power and pulse durations as short as 64 fs at a pulse repetition rate of 1 GHz. We generate an octave-spanning supercontinuum in a highly nonlinear fiber and use the standard f-to-2f carrier-envelope offset (CEO) frequency f_CEO detection method. As a pump source, we use a reliable and cost-efficient commercial diode laser. Its multi-spatial-mode beam profile leads to a relatively broad frequency comb offset beat signal, which nevertheless can be phase-locked by feedback to its current. Using improved electronics, we reached a feedback-loop-bandwidth of up to 300 kHz. A combination of digital and analog electronics is used to achieve a tight phase-lock of f_CEO to an external microwave reference with a low in-loop residual integrated phase-noise of 744 mrad in an integration bandwidth of [1 Hz, 5 MHz]. An analysis of the laser noise and response functions is presented which gives detailed insights into the CEO stabilization of this frequency comb.

Electronic control of nonlinear-polarization-rotation mode locking in Yb-doped fiber lasers

We demonstrate a convenient approach to precisely tune the polarization state of a nonlinear-polarization-rotation mode-locked Yb-doped fiber laser by using an electronic polarization controller. It is shown to benefit self-starting of mode-locking states, with precise tuning of the spectral profile, pulse width, and carrier-envelope offset frequency. The pulse width changed linearly by 0.78 ps in the time domain, and the carrier-envelope offset frequency shifted ~77.5 MHz in the frequency domain with a slight change of the driving voltage of 30.7 mV applied on the controller, corresponding to a polarization rotation of 0.0135π. This facilitated precise and automatic regeneration of a particular mode-locking state by setting an accurate voltage at the polarization controller with a programmed microprocessor control unit.

High-speed carrier-envelope phase drift detection of amplified laser pulses

An instrument for measuring carrier-envelope phase (CEP) drift of amplified femtosecond laser pulses at repetition rates up to the 100-kHz regime is presented. The device can be used for real-time pulse labeling and it could also enable single-loop CEP control of future high-repetition rate laser amplifiers. The scheme is demonstrated by measuring the CEP drift of a 1-kHz source.

Carrier-Envelope Phase stabilization of a 20 W, grating based, chirped-pulse amplified laser, using electro-optic effect in a LiNbO₃ crystal

Using an original CEP stabilization technique based on the linear electro-optical effect in a specific crystal, we achieved long term CEP stabilization of a 20 W, 1 kHz laser with residual noise as low as 440 mrad (rms). At 3 W, the CEP shot to shot noise is kept as low as 320 mrad (rms) over half an hour.

Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit

We demonstrate an essentially dispersion-free and diffraction-limited focusing of few-cycle laser pulses through all-reflective microscope objectives. By transmitting 6-fs-pulses from a Ti:sapphire oscillator through an all-reflective 0.5 NA objective, we reach a focus with a beam diameter of 1.0 µm, preserving the time structure of the pulses. The temporal and spatial pulse profile is recorded simultaneously using a novel tip-enhanced electron emission autocorrelator, indicating a focal volume of these pulses of only 1.8 µm3. We anticipate that the demonstrated technique is of considerable interest for inducing and probing optical nonlinearities of individual nanostructures.

Recent development and new ideas in the field of dispersive multilayer optics

A dispersive-mirror-based laser permits a dramatic simplification of high-power femtosecond and attosecond systems and affords promise for their further development toward shorter pulse durations, higher peak powers, and higher average powers with user-friendly systems. The result of the continuous development of dispersive mirrors permits pulse compression down to almost single cycle pulses of 3 fs duration. These design approaches together with the existing modern deposition technology pave the way for the manufacture of dielectric multilayer coatings able to compress pulses of tens of picoseconds duration down to a few femtoseconds.

Spatial distribution of carrier-envelope phase for femtosecond pulsed laser beam profile determined by asymmetric spectral interferometry

The spatial distribution of the carrier-envelope phase (CEP) for a femtosecond laser pulse from a regenerative amplifier was measured by a method based on the spectral interferometric technique. Our results show that the spatial distribution of the carrier-envelope phase from an ultrafast regenerative amplified laser is stable from pulse to pulse, but the difference between different locations within the laser profile is significant. In contrast, the CEP spatial distribution for the beam profile from the oscillator is homogenous within the experimental error. We attribute the observed spatial CEP distribution to the discrepancy between the dispersion of group velocity and phase velocity when the laser pulse passes through the dispersive optical elements, which can be corrected by a prism.

Controlling the carrier-envelope phase of Raman-generated periodic waveforms

We demonstrate control of the carrier-envelope phase of ultrashort periodic waveforms that are synthesized from a Raman-generated optical frequency comb. We generated the comb by adiabatically driving a molecular vibrational coherence with a beam at a fundamental frequency plus its second harmonic. Heterodyne measurements show that full interpulse phase locking of the comb components is realized. The results set the stage for the synthesis of periodic arbitrary waveforms in the femtosecond and subfemtosecond regimes with full control.

Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field

High-order harmonic generation in the presence of a strong terahertz field is investigated, and phase stabilization of the few-cycle laser pulses is extended to the extremely ultraviolet region. It is found that the strong terahertz field significantly breaks the symmetry between the consecutive half-cycle and greatly extends the harmonic cutoff, producing both odd and even harmonics which are covered with an extremely broad bandwidth and well locked in phase. These results can support the generation of few-cycle attosecond pulse trains with stabilized carrier-envelope phase from pulse to pulse, and also enables the generation of phase-stabilized pulse train with tunable wavelength.