Spectral decomposition at a complex laser polarization configuration

We study the role of laser polarization in the diamagnetic spectrum for the transition from the ground state to the highly excited Rydberg states through a single photon absorption. For simplicity, one usually polarizes the irradiation laser to the selected main quantum axis, which is along the applied external electric or magnetic field. The transition selection rule is simply expressed as Am = O, which corresponds to the π transition. When the polarization is circularly polarized around the main axis, the σ＋ or σ- transition occurs, corresponding to the selection rule of △m = 1 or △m = - 1, respectively. A slightly more complex case is that the laser is linearly polarized perpendicular to the main axis. The numerical calculation shows that we can decompose the transition into the sum of σ＋ and σ- transitions, it is noted as the σ transition. For the more complex case in which the laser is linearly polarized with an arbitrary angle with respect to the main axis, we have to decompose the polarization into one along the main axis and the other one perpendicular to the main axis. They correspond to π and σ transitions, respectively. We demonstrate that these transitions in the diamagnetic spectrum and the above spectral decomposition well explain the experimentally observed spectra.

Laser Polarization Orientations in(e,2e)Reactions in Atoms

Second-order Born calculations are performed to investigate the triple differential cross sections of coplanar asymmetric laser-assisted （e, 2e） collisions for hydrogen and helium targets. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing the Volkov solutions in both the initial and final channels. Detailed calculations of the scattering amplitudes are performed using the Sturmian basis expansion. The state of the ejected electron is described by a Coulomb-Volkov wave function. Two geometries are investigated in which the laser polarization vector is either parallel to the incident momentum of the projectile or parallel to the momentum transfer. Our numerical results show that, in the low energy range, these two laser polarization orientations give the same shape and the same order of magnitude of laser-assisted ionization cross sections of helium and hydrogen targets.

Relationship measurement between ac-Stark shift of^40Ca^+clock transition and laser polarization direction

Ac-Stark shift of atom levels is caused by an ac-electromagnetic field. As an electromagnetic wave, laser light does induce ac-Stark shift. It is proved experimentally that if the light is linearly polarized, the dynamic polarizability changes with polarization direction. The polarization direction of the linearly-polarized laser is tuned by 720°, and the ac-Stark shifts of the 4S1/2,m=±1/2→3D5/2,m=±1/2 clock transitions in ^40Ca^＋ are measured in steps of 10°. The frequency shifts change with laser polarization in a periodical manner and have values opposite to each other.

Internal collision double ionization of molecules driven by co-rotating two-color circularly polarized laser pulses

The double ionization process of molecules driven by co-rotating two-color circularly polarized fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that a considerable part of the sequential double ionization(DI) events of molecules occur through internal collision double ionization(ICD), and the ICD recollision mechanism is significantly different from that in non-sequential double ionization(NSDI). By analyzing the results of internuclear distances R = 5 a.u. and 2 a.u., these two recollision mechanisms are studied in depth. It is found that the dynamic behaviors of the recollision mechanisms of NSDI and ICD are similar. For NSDI, the motion range of electrons after the ionization is relatively large, and the electrons will return to the core after a period of time. In the ICD process,electrons will rotate around the parent ion before ionization, and the distance of the electron motion is relatively small. After a period of time, the electrons will come back to the core and collide with another electron. Furthermore, the molecular internuclear distance has a significant effect on the electron dynamic behavior of the two ionization mechanisms. This study will help to understand the multi-electron ionization process of complex systems.

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

The multielectron dissociative ionization dynamics of N2 molecule in intense femtosecond laser fields with arbitrary polarization

The field-ionization Coulomb explosion model is extended to investigate the multielectron dissociative ionization process of N2 molecule irradiated by an intense femtosecond laser field with an arbitrary polarization. The ionization process of N2 molecule is found to be optimal at the critical internuclear distance Rc=7a.u., which is independent of the laser polarization state, the molecular explosion channel and the angle between the molecular axis and the direction of laser electric field. The kinetic energies of the ion fragments are identical in the cases of linear and circular polarizations at the same incident laser intensity. However, the probability of electron ionization is very sensitive to the above three parameters. At the critical distance Rc=7a.u. the angular dependence of the threshold intensity for the over-the-barrier ionization leads to the geometric alignment of molecules in the case of linear polarization. The threshold intensity in the case of circular polarization is apparently higher than that in the case of linear polarization, which can well explain the significant decrease of ionization in the case of circular polarization. The numerical calculations are compared with the experimental measurements.

Low-repetition-rate, all-polarization-maintaining Yb-doped fiber laser mode-locked by a semiconductor saturable absorber

A low-repetition-rate, all-polarization-maintaining（PM）-fiber sub-nanosecond oscillator is presented, which is simple and low-cost, composed of standard components. The ring cavity is elongated by 114-m-long standard PM fiber, and passively mode-locked by a fiber pigtailed semiconductor saturable absorber. Linearly polarized pulses with 1.66 MHz repetition rate and 22 dB polarization extinction ratio are generated at a wavelength of 1030 nm, which is determined by an intracavity filter. In addition, to demonstrate that the oscillator is a good seed for high energy pulse generation, an all-fiber master oscillator power amplifier is built and amplified pulses with energy about 2 μJ are obtained.

Influence of polarization of laser beam on emission intensity of femtosecond laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy(LIBS)is an important technique which is widely used to analyze element composition.In order to improve the sensitivity of LIBS,much effort has been made to enhance the spectral intensity of LIBS by proposing a number of methods.In addition,we find that laser polarization has great influence on the emission intensity of femtosecond LIBS.By comparing the emission intensity of femtosecond LIBS in the circular polarization with that in the linear polarization,the spectral intensity in the case of circular polarization is stronger than that in the case of linear polarization.Moreover,this phenomenon is more obvious as laser energy increases.The polarization plays an important role in LIBS signal intensity.Based on the observation,the enhanced mechanism of the laser polarization for the spectral intensity is discussed in this paper,which will be helpful in spectral analysis and component analysis.

Polarization control of multi-photon absorption under intermediate femtosecond laser field

It has been shown that the femtosecond laser polarization modulation is a very simple and well-established method to control the multi-photon absorption process by the light-matter interaction. Previous studies mainly focused on the multi- photon absorption control in the weak field. In this paper, we further explore the polarization control behavior of multi- photon absorption process in the intermediate femtosecond laser field. In the weak femtosecond laser field, the second- order perturbation theory can well describe the non-resonant two-photon absorption process. However, the higher order nonlinear effect （e.g., four-photon absorption） can occur in the intermediate femtosecond laser field, and thus it is necessary to establish new theoretical model to describe the multi-photon absorption process, which includes the two-photon and four-photon transitions. Here, we construct a fourth-order perturbation theory to study the polarization control behavior of this multi-photon absorption under the intermediate femtosecond laser field excitation, and our theoretical results show that the two-photon and four-photon excitation pathways can induce a coherent interference, while the coherent interference is constructive or destructive that depends on the femtosecond laser center frequency. Moreover, the two-photon and four- photon transitions have the different polarization control efficiency, and the four-photon absorption can obtain the higher polarization control efficiency. Thus, the polarization control efficiency of the whole excitation process can be increased or decreased by properly designing the femtosecond laser field intensity and laser center frequency. These studies can provide a clear physical picture for understanding and controlling the multi-photon absorption process in the intermediate femtosecond laser field, and also can provide a theoretical guidance for the future experimental realization.

Effect of elliptical polarizations on nonsequential double ionization in two-color elliptically polarized laser fields

Using the classical ensemble model, we investigate the nonsequential double ionization（NSDI） of Ar and Mg in the two-color elliptically polarized laser pulse for different elliptical polarizations. Numerical results show that for Ar atoms the NSDI yield increases as the ellipticity increases, which is different from the case of Mg atoms. Moreover, the correlated behavior in the correlated electron momentum along the x direction and ion momentum distributions of Ar atoms are influenced by the ellipticity. By statistical analysis of different times, we can conclude that the ellipticity may be responsible for the NSDI processes. The correlated momenta distributions along the x direction at the recollision time are demonstrated and the results show that the travelling time and ellipticity can affect the emitted directions of both electrons.

Imprints of molecular orbitals using photoelectron angular distribution by strong laser pulses of circular polarization

We theoretically investigate the strong-field ionization of H＋2 molecules in four different electronic states by calculating photoelectron angular distributions in circularly polarized fields. We find that the structure of photoelectron angular distribution depends on the molecular orbital as well as the energy of the photoelectron. The location of main lobes changes with the symmetric property of the molecular orbital. Generally, for molecules with bonding electronic states, the photoelectron’s angular distribution shows a rotation of π/2 with respect to the molecular axis, while for molecules with antibonding electronic states, no rotation occurs. We use an interference scenario to interpret these phenomena. We also find that, due to the interference effect, a new pair of jets appears in the waist of the main lobes, and the main lobes or jets of the photoelectron’s angular distribution are split into two parts if the photoelectron energy is sufficiently high.

Correlation between the magic wavelengths and the polarization direction of the linearly polarized laser in the Ca^+ optical clock

The magic wavelengths for different Zeeman components are measured based on the ^40Ca^＋ optical clock. The dynamic dipole polarizability of a non-zero angular moment level has correlation with the polarization direction of the linearly polarized laser beam, and we show that the four hyperfine structure levels of 4S1/2,m=±1/2 and 3d5/2,m=±1/2 for ^40Ca^＋ have the same dynamic dipole polarizability at the magic wavelength and a certain polarization direction. In addition, the existence of a specific direction of polarization may provide a new idea for improving the precision of magic wavelength measurement in experiment.

Simulation of Intermediate State Absorption Enhancement in Rare-Earth Ions by Polarization Modulated Femtosecond Laser Field

We extend the third perturbation theory to study the polarization control behavior of the intermediate state absorption in Nd^（3＋）ions. The results show that coherent interference can occur between the single-photon and three-photon excitation pathways, and depends on the central frequency of the femtosecond laser field. Moreover,single-photon and three-photon absorptions have different polarization control efficiencies, and the relative weight of three-photon absorption in the whole excitation processes can increase with increasing the laser intensity.Therefore, the enhancement or suppression of the intermediate state absorption can be realized and manipulated by properly designing the intensity and central frequency of the polarization modulated femtosecond laser field.This research can not only enrich theoretical research methods for the up-conversion luminescence manipulation of rare-earth ions, but also can provide a clear physical picture for understanding and controlling multi-photon absorption in a multiple energy level system.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

Up-conversion luminescence polarization control in Er^(3+)-doped NaYF_4 nanocrystals

We propose a femtosecond laser polarization modulation scheme to control the up-conversion（UC） luminescence in Er^（3＋）-doped NaYF_4 nanocrystals dispersed in the silicate glass. We show that the UC luminescence can be suppressed when the laser polarization is changed from linear through elliptical to circular, and the higher repetition rate will yield the lower control efficiency. We theoretically analyze the physical control mechanism of the UC luminescence polarization modulation by considering on- and near-resonant two-photon absorption, energy transfer up-conversion, and excited state absorption, and show that the polarization control mainly comes from the contribution of near-resonant two-photon absorption. Furthermore, we propose a method to improve the polarization control efficiency of UC luminescence in rare-earth ions by applying a two-color femtosecond laser field.

Polarization and phase control of two-photon absorption in an isotropic molecular system

We theoretically and experimentally study the polarization and phase control of two-photon absorption in an isotropic molecular system. We theoretically show that the two-photon transition probability decreases when the laser polarization changes from linear through elliptical to circular, and the laser polarization does not affect the control efficiency of two-photon transition probability by shaping the spectral phase. These theoretical results are experimentally confirmed in coumarin 480. Furthermore, we propose that the combination of the laser polarization with the spectral phase modulation can further increase the control efficiency of the two-photon absorption.

A Single-Frequency Linearly Polarized Fiber Laser Using a Newly Developed Heavily Tm3+-Doped Germanate Glass Fiber at 1.95 μm

A compact linearly polarized, low-noise, narrow-linewidth, single-frequency fiber laser at 1950nm is demonstrated. This compact fiber laser is based on a 21-mm-long homemade Tm3＋-doped germanate glass fiber. Over 100-mW stable continuous-wave single transverse and longitudinal mode lasing at 195Ohm are achieved. The measured relative intensity noise is less than -135dB/Hz at frequencies over 5 MHz. The signal-to-noise ratio of the laser is larger than 72dB, and the laser linewidth is less than 6kHz, while the obtained linear polarization extinction ratio is higher than 22 dB.

External-cavity birefringence feedback effects of microchip Nd:YAG laser and its application in angle measurement

External-cavity birefringence feedback effects of the microchip Nd：YAG laser are presented. When a birefringence element is placed in the external feedback cavity of the laser, two orthogonally polarized laser beams with a phase difference are output. The phase difference is twice as large as the phase retardation in the external cavity along the two orthogonal directions. The variable extra-cavity birefringence, caused by rotation of the external-cavity birefringenee element, results in tunable phase difference between the two orthogonally polarized beams. This means that the roll angle information has been translated to phase difference of two output laser beams. A theoretical analysis based on the Fabry-Perot cavity equivalent model and refractive index ellipsoid is presented, which is in good agreement with the experimental results. This phenomenon has potential applications for roll angle measurement.

Electron correlations in nonsequential double ionization of argon atoms by elliptically polarized laser pulses

Using a classical ensemble model, we investigate the correlation behaviour of electrons originating from nonsequential double ionization （NSDI） of argon atoms by the elliptically polarized laser pulses. Because of the ellipticity, not only the first electron to return but also the later return of tunneled electrons contribute significantly to NSDI. We mainly discuss two kinds of events of NSDI originating from the first and the second return separately. For the NSDI resulting from the recollision of the first return, the correlated electron momentum spectrum along the long axis of the laser polarization plane reveals an obvious V-like shape, located at the first and third quadrant. However, for the NSDI resulting from the recollision of the second return, the momenta of two electrons are distributed in the four quadrants uniformly. By analysing the trajectories of these two kinds, we find that the recollision energy and the laser phase at recollision are different for the first and second returning trajectories, which are responsible for the difference in the correlated behavior of the final electron momentum.

High-order harmonic generation of N2molecule in two-color circularly polarized laser fields

The generation of high-order harmonics and the attosecond pulse of the N2 molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spectra is dramatically extended and a continuous harmonic spectrum with the bandwidth of 113 eV is obtained. When a static field is added to the x direction, the quantum path control is realized and a supercontinuum spectrum can be obtained, which is beneficial to obtain a shorter attosecond pulse. The underlying physical mechanism is well explained by the time-frequency analysis and the semi-classical three-step model with a finite initial transverse velocity. By superposing several orders of harmonics in the combination of two-color circularly polarized laser fields and a static field, an isolated attosecond pulse with a duration of 30 as can be generated.