Carrier Envelope Research Articles

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

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

Four-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi-Pasta-Ulam-Tsingou recurrence.

Modulation instability, breather formation, and the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena are studied in this article. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schrödinger equations. The Darboux transformation is used to calculate a class of breathers where the carrier envelope depends on the transverse coordinate of the Schrödinger equations. A "cascading mechanism" is utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. Unequal initial conditions for the two waveguides produce symmetry breaking, with "eye-shaped" breathers in one waveguide and "four-petal" modes in the other. An analytical formula for the time or distance of breather formation for a two-waveguide system is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed. For applications to temporal optical waveguides, the present formulation can predict the distance along a weakly birefringent fiber needed to observe FPUT.

New method of unipolar THz pulse generation in photo-ionised xenon plasma

We propose a new method for producing terahertz (THz) pulses with a high degree of unipolarity. This idea is based on the nonuniform amplification of seed THz one-cycle carrier envelope phase pulses in nonequilibrium xenon plasma. The significant impact of the propagated pulse on the evolution of plasma leads to a strong decrease in the gain coefficient within the duration of the one-cycle pulse. As a result, the leading edge of the pulse is amplified while the trailing tail of opposite polarity is absorbed; this effect leads to the formation of unipolarity. These results are obtained by the self-consistent solution of the second-order wave equation and kinetic Boltzmann equation for the electron velocity distribution function relaxation.

Schwinger pair production in inhomogeneous electric fields with symmetrical frequency chirp

Pair production in inhomogeneous electric fields with symmetrical frequency chirp is studied numerically using the Dirac-Heisenberg-Wigner formalism. We investigate high- and low-frequency modes and consider two carrier envelope phases. Momentum spectrum is sensitive to chirp causing different interference effect for different spatial scales as well as the carrier phase of the external field. The reduced particle number is in general enhanced with increasing chirp. The effect of spatial scale of the field on the reduced particle number is also examined. It is found that it is enhanced at small spatial scale but is almost unchangeable at large spatial scales for the considered field parameters. On the other hand, at small spatial scale, the reduced particle number is enhanced by one or two orders when chirp is applied with the exception of cosine low-frequency field which is only a few times larger. Moreover it is found that the reduced particle number is further increased by symmetrical chirp at about two times by comparing to the usual asymmetrical chirp in high frequency field.

Broadband mid-infrared molecular spectroscopy based on passive coherent optical–optical modulated frequency combs

Mid-infrared dual-comb spectroscopy is of great interest owing to the strong spectroscopic features of trace gases, biological molecules, and solid matter with higher resolution, accuracy, and acquisition speed. However, the prerequisite of achieving high coherence of optical sources with the use of bulk sophisticated control systems prevents their widespread use in field applications. Here we generate a highly mutually coherent dual mid-infrared comb spectrometer based on the optical–optical modulation of a continuous-wave (CW) interband or quantum cascade laser. Mutual coherence was passively achieved without post-data processes or active carrier envelope phase-locking processes. The center wavelength of the generated mid-infrared frequency combs can be flexibly tuned by adjusting the wavelength of the CW seeds. The parallel detection of multiple molecular species, including C 2 H 2 , CH 4 , H 2 CO , H 2 S , COS, and H 2 O , was achieved. This technique provides a stable and robust dual-comb spectrometer that will find nonlaboratory applications including open-path atmospheric gas sensing, industrial process monitoring, and combustion.

Nanoantenna design for enhanced carrier–envelope-phase sensitivity

Optical-field emission from nanostructured solids such as subwavelength nanoantennas can be leveraged to create sub-femtosecond, petahertz-scale electronics for optical-field detection. One application of particular interest is the detection of an incident optical pulse’s carrier–envelope phase (CEP). Such CEP detection requires few-cycle, broadband optical excitation where the resonant properties of the nanoantenna can strongly alter the response of the near field in time. Little quantitative investigation has been performed to understand how the geometry and resonant properties of the antennas should be tuned to enhance the CEP sensitivity and signal-to-noise ratio. Here we examine how the geometry and resonance frequency of planar plasmonic nanoantennas can be engineered to enhance the emitted CEP-sensitive photocurrent when driven by a few-cycle optical pulse. We find that with the simple addition of curved sidewalls leading to the apex, and proper tuning of the resonance wavelength, the net CEP-sensitive current per nanoantenna can be improved by 5 − 10 × , and the signal-to-noise-ratio by 50 − 100 × relative to simple triangular antennas operated on resonance. Our findings will inform the next generation of nanoantenna designs for emerging applications in ultrafast photoelectron metrology and petahertz electronics.

Principal frequency of an ultrashort laser pulse

We introduce an alternative definition of the main frequency of an ultrashort laser pulse, the principal frequency $\omega_P$. This parameter is complementary to the most accepted and widely used carrier frequency $\omega_0$. Given the fact that these ultrashort pulses, also known as transients, have a temporal width comprising only few cycles of the carrier wave, corresponding to a spectral bandwidth $\Delta\omega$ covering several octaves, $\omega_P$ describes, in a more precise way, the dynamics driven by these sources. We present examples where, for instance, $\omega_P$ is able to correctly predict the high-order harmonic cutoff independently of the carrier envelope phase. This is confirmed by solving the time-dependent Schr\"odinger equation in reduced dimensions, supplemented with the time-analysis of the quantum spectra, where it is possible to observe how the sub-cycle electron dynamics is better described using $\omega_P$. The concept of $\omega_P$, however, can be applied to a large variety of scenarios, not only within the strong field physics domain.

Exploration of electron vortices in the photoionization of diatomic molecules in intense laser fields

Based on the approach within the single-electron approximation (SEA) frame, we numerically solve the two-dimensional (2D) time-dependent Schrdinger equation of N2 molecules under co-rotating and counter-rotating circularly polarized attosecond pulses. The vortex structure appears in counter-rotating circularly laser fields rather than the co-rotating case. The calculated vortex structures corresponding to the photoionization are found to be sensitive to the time delays T d of the two pulses, laser ellipticities and carrier envelope phases (CEPs). As the ellipticity increases to 1, the momentum distribution rotates and a vortex structure appears, and the interference is proved to play an important role in momentum distribution. The vortex structures also rotate clockwisely as the relative CEPs increase. The arms of the vortex structure become longer and thinner with the increasing T d . All these phenomena can be well understood by the attosecond perturbation ionization theory and the interference effect. Our findings clarify the applicability of the SEA model of diatomic molecules in attosecond extreme-ultraviolet fields.

Signatures of the Carrier Envelope Phase in Nonlinear Thomson Scattering

High-energy radiation can be generated by colliding a relativistic electron bunch with a high-intensity laser pulse—a process known as Thomson scattering. In the nonlinear regime the emitted radiation contains harmonics. For a laser pulse whose length is comparable to its wavelength, the carrier envelope phase changes the behavior of the motion of the electron and therefore the radiation spectrum. Here we show theoretically and numerically the dependency of the spectrum on the intensity of the laser and the carrier envelope phase. Additionally, we also discuss what experimental parameters are required to measure the effects for a beamed pulse.

Broadband Terahertz Wave Generation from Monolayer Graphene Driven by Few-Cycle Laser PulseSupported by the National Natural Science Foundation of China (Grant Nos. 11764038, 11864037, 11765018, and 91850209).

We theoretically investigate the characteristics of terahertz (THz) radiation from monolayer graphene exposed to normal incident few-cycle laser pulses, by numerically solving the extended semiconductor Bloch equations. Our simulations show that the THz spectra in low frequency regions are highly dependent on the carrier envelope phase (CEP) of driving laser pulses. Using an optimal CEP of few-cycle laser pulses, we can obtain broadband strong THz waves, due to the symmetry breaking of the laser-graphene system. Our results also show that the strength of the THz spectra depend on both the intensity and central wavelength of the laser pulses. The intensity dependence of the THz wave can be described by the excitation rate of graphene, while wavelength dependence can be traced back to the band velocity and the population of graphene. We find that a near single-cycle THz pulse can be obtained from graphene driven by a mid-infrared laser pulse.

Coupled nuclear and electron dynamics in the vicinity of a conical intersection.

Ultrafast optical techniques allow us to study ultrafast molecular dynamics involving both nuclear and electronic motion. To support interpretation, theoretical approaches are needed that can describe both the nuclear and electron dynamics. Hence, we revisit and expand our ansatz for the coupled description of the nuclear and electron dynamics in molecular systems (NEMol). In this purely quantum mechanical ansatz, the quantum-dynamical description of the nuclear motion is combined with the calculation of the electron dynamics in the eigenfunction basis. The NEMol ansatz is applied to simulate the coupled dynamics of the molecule NO2 in the vicinity of a conical intersection (CoIn) with a special focus on the coherent electron dynamics induced by the non-adiabatic coupling. Furthermore, we aim to control the dynamics of the system when passing the CoIn. The control scheme relies on the carrier envelope phase of a few-cycle IR pulse. The laser pulse influences both the movement of the nuclei and the electrons during the population transfer through the CoIn.

Effect of pulse duration on generation of attosecond pulse with coherent wake emission* *Project supported by the National Natural Science Foundation of China (Grant Nos. 91950203, 11874374, and 61690223) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB16).

High-order harmonics and attosecond pulse generation with coherent wake emission are theoretically investigated for the effect of pulse duration and carrier envelope phase (CEP) of few-cycle laser pulse. We find that short pulse duration will cause the negative chirp for the high harmonics. When the laser pulse is shortened to a few cycles, the influence of the laser CEP on the chirp of the harmonics will also become more prominent.

Sub-cycle valleytronics: control of valley polarization using few-cycle linearly polarized pulses

So far, it has been assumed that selective excitation of a desired valley in the Brillouin zone of a hexagonal two-dimensional material has to rely on using circularly polarized fields. We theoretically demonstrate a way to control the valley excitation in hexagonal 2D materials on a few-femtosecond timescale using a few-cycle, linearly polarized pulse with controlled carrier–envelope phase. The valley polarization is mapped onto the strength of the perpendicular harmonic signal of a weak, linearly polarized pulse, which allows to read this information all-optically without destroying the valley state and without relying on the Berry curvature, making our approach potentially applicable to inversion-symmetric materials. We show applicability of this method to hexagonal boron nitride and M o S 2 .

Laser Wakefield Driven Generation of Isolated Carrier-Envelope-Phase Tunable Intense Subcycle Pulses

Sources of intense, ultrashort electromagnetic pulses enable applications such as attosecond pulse generation, control of electron motion in solids, and the observation of reaction dynamics at the electronic level. For such applications, both high intensity and carrier-envelope-phase (CEP) tunability are beneficial, yet hard to obtain with current methods. In this Letter, we present a new scheme for generation of isolated CEP tunable intense subcycle pulses with central frequencies that range from the midinfrared to the ultraviolet. It utilizes an intense laser pulse that drives a wake in a plasma, copropagating with a long-wavelength seed pulse. The moving electron density spike of the wake amplifies the seed and forms a subcycle pulse. Controlling the CEP of the seed pulse or the delay between driver and seed leads to CEP tunability, while frequency tunability can be achieved by adjusting the laser and plasma parameters. Our 2D and 3D particle-in-cell simulations predict laser-to-subcycle-pulse conversion efficiencies up to 1%, resulting in relativistically intense subcycle pulses.

Electron-positron pair creation induced by two sequential short pulses

The computational quantum field theory (CQFT) is applied to study the dependence of the total EPP number on the time interval under the spatially localized double cosine-Gaussian pulse and the alternating-sign double-Gaussian pulse. The total EPP number damply oscillates with the time interval, and the oscillation frequency is about the energy gap ($2m{c}^{2}$) for all of the scenarios. This characteristic oscillation of the total EPP number is consistent with a formula, which is related to the amplitude mode in the BCS superconductors. Besides, we find that the Ramsey interference effect is not responsible for the characteristic oscillation by studying the double-Gaussian pulse with the same sign. Finally, when the favorable time interval is applied, the EPP number is much larger than the sum of the EPP number obtained in two single pulses. The favorable time interval mainly depends on the pulse duration and the carrier envelope phase (the quantity in cosine-Gaussian pulse).

Polarization control of the high-order harmonics generated from molecules by the carrier envelope phase of few-cycle laser field

Polarization state of high-order harmonic generation from molecules with few-cycle circularly polarized laser field is investigated. It is found that by controlling the carrier envelope phase (CEP) of the few-cycle driving field, the high-order harmonics with arbitrary polarization state ranging from nearly left circular polarization through linear polarization to nearly right circular polarization can be generated. Moreover, the degree of circular polarization (DCP) of the harmonics changes periodically with the CEP of the driving field. The corresponding period depends on the molecular symmetry. Our results provide a method to control the harmonic polarization with the CEP of few-cycle circularly polarized laser field, which will benefit the generation of isolated attosecond pulses with tunable polarization.

Molecular orientation induced by H+ collision and modulated with combined fields

We take H++CO as a prototype to analyze the effect of ion or proton collision on molecular orientation modulated by a two-color shaped pulse combined with the time-delayed terahertz (THz) pulse. Through examining the effect of ion collision on the molecular orientation, we found that when the impact parameter and collisional velocity have weak inverse influences on the maximal orientation degree, the appropriate two-color and THz field intensity employed can improve the molecular orientation degree. The carrier envelope phase and frequency of the THz laser pulse as well as the temperature also have certain influence on the collision-induced molecular orientation.

Long-term frequency-stabilized optical frequency comb based on a turnkey Ti:sapphire mode-locked laser

We report a long-term frequency-stabilized optical frequency comb at 530–1100 nm based on a turnkey Ti:sapphire mode-locked laser. With the help of a digital controller, turnkey operation is realized for the Ti:sapphire mode-locked laser. Under optimized design of the laser cavity, the laser can be mode-locked over a month, limited by the observation time. The combination of a fast piezo and a slow one inside the Ti:sapphire mode-locked laser allows us to adjust the cavity length with moderate bandwidth and tuning range, enabling robust locking of the repetition rate (fr) to a hydrogen maser. By combining a fast analog feedback to pump current and a slow digital feedback to an intracavity wedge and the pump power of the Ti:sapphire mode-locked laser, the carrier envelope offset frequency (fceo) of the comb is stabilized. We extend the continuous frequency-stabilized time of the Ti:sapphire optical frequency comb to five days. The residual jitters of fr and fceo are 0.08 mHz and 2.5 mHz at 1 s averaging time, respectively, satisfying many applications demanding accuracy and short operation time for optical frequency combs.

Effect of spin–orbit coupling on strong field ionization simulated with time-dependent configuration interaction

Time-dependent configuration interaction with a complex absorbing potential has been used to simulate strong field ionization by intense laser fields. Because spin-orbit coupling changes the energies of the ground and excited states, it can affect the strong field ionization rate for molecules containing heavy atoms. Configuration interaction with single excitations (CIS) has been employed for strong field ionization of closed shell systems. Single and double excitation configuration interaction with ionization (CISD-IP) has been used to treat ionization of degenerate states of cations on an equal footing. The CISD-IP wavefunction consists of ionizing single (one hole) and double (two hole/one particle) excitations from the neutral atom. Spin-orbit coupling has been implemented using an effective one electron spin-orbit coupling operator. The effective nuclear charge in the spin-orbit coupling operator has been optimized for Ar+, Kr+, Xe+, HX+ (X = Cl, Br, and I). Spin-orbit effects on angular dependence of the strong field ionization have been studied for HX and HX+. The effects of spin-orbit coupling are largest for ionization from the π orbitals of HX+. In a static field, oscillations are seen between the 2Π3/2 and 2Π1/2 states of HX+. For ionization of HX+ by a two cycle circularly polarized pulse, a single peak is seen when the maximum in the carrier envelope is perpendicular to the molecular axis and two peaks are seen when it is parallel to the axis. This is the result of the greater ionization rate for the π orbitals than for the σ orbitals.

Influence of electro-optic modulator on Er-doped fiber femtosecond laser

Narrow-linewidth femtosecond optical frequency comb plays an important role in the fields, such as optical clock comparison, time frequency transfer, ultrastable microwave generation, absolute distance measurement, high precision spectroscopy, etc. Due to the influence of the lifetime of the upper energy level in the gain medium, the linewidth of Er-fiber combs is generally on the order of several hundred kilohertz. In order to narrow the linewidth of comb teeth, an effective method is to insert a fast response electro-optic modulator (EOM) into the laser cavity, so that the servo bandwidth of fiber comb is extended to several hundred kilohertz, which provides a feedback mechanism for fast servo locking. Among them, a high quality femtosecond laser is the core. Based on this, the influence of the EOM on the parameters of Er-fiber femtosecond laser is studied in this paper. By calculating the refractive index, group velocity dispersion, and phase delay of the electro-optic crystal, the influence of the introduction of the EOM on the laser performance is analyzed. A LiNbO<sub>3</sub> (LN) crystal with a length of 3 mm and <i>x</i>-cut is selected as the EOM and inserted into the laser cavity. The influence of the applied voltage of the EOM on the repetition rate and carrier envelope offset frequency of the laser are obtained experimentally. When the voltage on the LN crystal changes from -200 to 200 V, the adjustment of repetition rate is 60 Hz and the carrier envelope offset frequency is 25 MHz. Then the two parameters are phase locked through the EOM. Furthermore, by phase locking the beat note between the fiber comb and a narrow-linewidth continue wavelength laser at 1542 nm, it is verified that the introduction of the EOM can expand the servo bandwidth of the laser to more than 236 kHz, which provides a technical basis for establishing narrow linewidth femtosecond optical frequency combs. The following work will verify the performance of comb line, that is, when the comb is locked to a narrow-linewidth laser (such as 1542 nm), the performance of comb line at wavelength (such as 698, 729 nm, and so on) of distant place will be analyzed in detail.