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We demonstrate a high-flux and low transverse temperature atomic beam of ytterbium by applying two-dimensional cooling using the ${}^1\mathrm{S}_0\text{-}{}^3\mathrm{P}_1$ intercombination transition to the cold atomic beam produced by the dipolar-allowed ${}^1\mathrm{S}_0\text{-}{}^1\mathrm{P}_1$ transition. The optimized transverse temperature of $11 \pm 9\,\mathrm{\mu K}$ and an atomic flux of $(7.5 \pm 1.0) \times 10^8\,\mathrm{atoms/s}$ are obtained for the atomic beam whose longitudinal velocity is $30\,\mathrm{m/s}$. The transverse temperature is maintained below $23\,\mathrm{\mu K}$, while the flux is above $6.5 \times 10^8\,\mathrm{atoms/s}$ in the longitudinal velocity range of $22 - 30\,\mathrm{m/s}$. We also discuss the feasibility of further narrowing the transverse momentum width to less than the recoil momentum using the momentum-selective optical transition between the ground state and the long-lived metastable state. The transverse momentum width of our atomic beam, which is narrower than 5.7 times the recoil momentum, is a good starting point for the proposed method., Comment: 7 pages, 6 figures

In order to design a five-port grating with good uniformity, a single-groove reflective beam splitter with an incident wavelength of 1550 nm is designed. The incident structure is under normal incidence. We get better optimized parameters by rigorous coupled waves. The five diffraction order efficiencies of the grating are each close to 20%. The optimized data shows that grating structure has high efficiency and high tolerance, which will have good application value in the field of beam splitter. Furthermore, by investigating the coupling overlap integration and field distribution, the mechanism can be well explained for such a grating.

We demonstrated a linear-cavity fiber laser using a fiber Bragg grating (FBG) fabricated by femtosecond laser and a Sagnac loop as cavity mirrors. The temperature sensing response of the fiber laser was characterized by placing the FBG in a high-temperature environment. The stability of the fiber laser at high temperature was improved after the FBG was annealed at 1100 °C. The fiber laser can work stably as a temperature sensor at 1000 °C and its temperature sensing sensitivity is approximately 15.9 pm/°C from 300 °C to 1000 °C.

Radio frequency (RF) electromagnetic radiation over range of 30 ∼ 800 MHz from laser induced breakdown of air are investigated. The RF radiation, under different laser energies, laser polarization directions and detect position are measured. It is found that a much stronger RF signals emitted from air plasma was observed at moderate laser pulse energy in our case. The measured RF signal of air plasma is found to depend on laser polarization direction and pulse energy, and the spatial distribution of RF radiation is anisotropy. Underlying physics responsible for laser parameter-dependent RF emission, rich in emission lines and anisotropy of spatial distribution of RF emission of the laser induced air plasma are discussed.

Radial smoothing scheme based on the optical Kerr effect can add periodical spherical wavefront modulation to the laser beam and make the speckles within the focal spot in far field sweep periodically in radial direction, which improves the illumination uniformity of the laser beam on target in inertial confinement fusion facilities. In order to analyze the smoothing performance of radial smoothing scheme in a laser quad, the corresponding theoretical model was established and the temporal characteristic parameters of the pump laser were further analyzed and optimized. The results show that the fluctuation of the smoothing performance with time can slow down by appropriately adjusting the delay time between the laser beam and pump laser pulses in a laser quad. Furthermore, the different sweep period of the incoherent beams can be obtained by altering the pulse duration of pump laser pulses in a laser quad. Consequently, the group velocity of intensity envelope becomes faster with the increase of the frequency difference between incoherent beams. What’ more, a better smoothing performance can be achieved by applying the appropriate spatial deflection between the laser beam and pump laser pulses in a laser quad, and the deflection angle of the pump laser in a laser quad was further optimized to improve the illumination uniformity on target significantly. Radial smoothing with obliquely incident pump laser can add a spherical wavefront to the laser beam, and further makes the speckles redistribute rapidly both in radial and transverse directions. With appropriate incident direction and angle, RS can achieve a much better final smoothing performance than 2D-SSD.

A technique for nonlinear refractive index measurement of a single trapped nanoparticle is investigated using Shack–Hartmann sensor. In this technique, trapping laser is used as a probe beam and an interacting green laser is illuminated as a pumping beam. Optical path difference and effective height of particle is measured with dual wavelength unwrapping technique. Using the absorption relation, we obtain the profile of nonlinear refractive index. Also, the results prove the quadric relation of the nonlinear refractive index to the nonlinear absorption. This result may have an enormous effect in investigating and characterization of nonlinear refractive index of Nano and Micro-sized particles. Also, measuring the thermal profile of the trapping site after illuminating the high power trapping laser leads to measuring the gradient intensity that could have an important role in nonconservative forces measurements. Another advantage is in having the effective thickness of particle which is important while geometry of the particle is crucial for determining trap stiffness. This measurement may lead to adaptive trap shape control and potential well measurement.

Laser waveform control in high-order harmonic generation (HHG) has been investigated and discussed by using the two-color chirp gating technology. It is found that the multiple-acceleration-recombination process in HHG can be found in a specific ‘W’ waveform structure. Moreover, by changing the chirp forms as well as laser parameters, the multiple-acceleration-recombination process in the ‘W’ waveform structure can be controlled, which leads to the remarkable improvements of harmonic cutoff and harmonic yield. Consequently, a water window spectral continuum with a bandwidth of 488 eV and with an intensity enhancement of 10 times can be obtained. Further, by the Fourier transformation of some selected harmonics on this spectral continuum, three single attosecond pulses (SAPs) with the pulse durations of 38 as can be produced. With the introduction of inhomogeneous effect of the laser field, the HHG spectra with a larger harmonic cutoff and a broader spectral continuum can be obtained. Consequently, by the Fourier transformation of some selected harmonics on the spectral continuum, a number of water window SAPs with the pulse durations of 36 as can be obtained.

Using the metallic nano-antennas we can enhance the intensity of a laser pulse to prepare it for high-order harmonic generation. Plasmonic resonances in the metal surfaces cause a non-homogeneous enhancement of the incoming laser field. In this article behavior of the generated high-order harmonics and attosecond pulses with respect to the location of a helium ion in the non-homogeneous field is investigated. It is cleared that the broader supercontinuum can be observed for the case when the ion target located around the center of non-homogeneity which leads to more intense and shorter attosecond pulses.

We succeeded in developing a broadband-frequency-variable laser comb with a mode spacing of 12.5 GHz in the near-infrared region. We found that the spectrum of optical pump pulses can be frequency shifted over the mode spacing frequency by a single-sideband (SSB) optical modulator involving the amplitude and phase. Optical heterodyne measurement showed that the frequency shift of the optical pump pulses was precisely consistent with the modulation frequency applied to the SSB modulator with an accuracy of 20 kHz. The pump pulses were amplified and compressed to enhance the peak intensity. Finally, the frequency-shifted pump pulses launched into highly nonlinear fibers and generated a frequency-shifted laser comb. The precise frequency shift of pump pulses induced a simultaneous frequency shift of all modes of the laser comb. As a result, we succeeded in fast frequency sweeping of the laser comb over a full spectral range of 1080 to 1750 nm. This full-wavelength tuning implies that laser light of arbitrary and accurate wavelength can be obtained over the comb bandwidth.

We theoretically investigate the high-order harmonic generation (HHG) of H 2 + molecule in the counter-rotating two-color circularly polarized laser pulse by numerically solving the two-dimensional (2D) time-dependent Schrodinger equation (TDSE). The results show that the even harmonics are suppressed with the fundamental laser wavelength 800 nm for the ratio of the second laser frequency and the fundamental laser frequency 3 or 5. In order to investigate the contributions of the HHG from two nuclei, the HHG is separated into two parts, which is originated from nucleus 1 and nucleus 2. The underlying physical mechanism of enhancing and suppressing high-order harmonic generation is illustrated by the interference effect of the HHG spectra originating from two nuclei. Meanwhile, the difference of the HHG spectra is investigated with the fundamental laser wavelength 1600 nm and 2400 nm.

After a long-term research, the birefringence-Zeeman dual-frequency (BZDF) laser has entered the practical stage, and the BZDF laser interferometer has more powerful displacement and size measurement functions, especially the near-zero nonlinearity. This paper theoretically analyzes the mechanism of the near-zero nonlinear error, including theoretical simulation and experimental measurements. The measurement results show that the nonlinear error of the BZDF laser interferometer is only 0.3 nm, which is one order of magnitude smaller than that of traditional Zeeman dual-frequency (ZDF) laser interferometer. It has broad application prospects in the field of ultra-precision metrology.

Electromagnetically induced holographic imaging using strongly interacting Rydberg atoms is investigated via electromagnetically induced grating (EIG). We consider two schemes, i.e., by direct detection of holographic imaging pattern, known as electromagnetically induced classical holographic imaging (EICHI), and by employing entangled photon pairs for imaging which is called as electromagnetically induced quantum holographic imaging (EIQHI). Both schemes are employed to obtain 1D and 2D holographic imaging. In EICHI and EIQHI, amplitude and phase information of EIG can be imaged with controllable image variation in size. It is noticed that holographic imaging is influenced by van der Waals (vdW) effect present in Rydberg atoms.

The coherence of cold atom trapped and cooled by the partially coherent light (PCL) is investigated experimentally through Rabi oscillations. We control the degree of the spatial coherence of the laser beams by the modulation of electro-optic crystal. The experimental results show that the cold atoms captured by the different coherent degree of light have little different coherence properties and almost the same capacity of resisting disturbance, which indicates that the coherence of cold atom is affected weakly by the coherence of cooling field.

We report the regularity of experimental evolution of Rydberg six-wave mixing (SWM) spatial images that were effectively controlled by adjusting various probe field parameters. Due to the high-order nonlinear Rydberg process, evolution of the spatial defocusing and splitting was observed by changing the detuning, polarization, and power of the probe field. Modulated spatial images obtained in a Rydberg nonlinear medium were found to be related to the refractive index. This study clarifies the spatial transmission rules for Rydberg SWM, which can be used to study the light field modulation of space imaging of a Rydberg atom ensemble and can provide evidence for the design of advanced materials.

We report on the observation of magnetically assisted narrow band probe beam amplification in Zeeman degenerate closed two-level system associated with cold cesium atoms. In the experiment the closed cesium D 2 hyperfine transition F g = 3 → F e = 2 is coherently excited by a probe and an orthogonally polarized coupling beam in the presence of a transverse dc magnetic field. Single pass gain of 80% is observed for moderate values of the magnetic field and coupling beam power. The gain mechanism can be understood in terms of population transfer between the different Zeeman ground-state levels induced by the external magnetic field. We have developed a simple theoretical model using a simpler atomic transition F g = 1 → F e = 0 , which accounts reasonably for the main experimentally observed results.

Self-focusing of cw laser beam in a rubidium atomic vapor was studied. The beam radius and power at the entrance of a rubidium vapor cell were variable parameters. A steep grow of the self-focusing threshold power for the small beam radius ( ≤ 30 μ m) was observed. Our experimental data are in a qualitative agreement with the recently published theoretical results obtained for a conventional non-resonant gas. Additional experiments in the resonance and transparent non-resonant media are suggested in order to check and extend our measurements.

This paper proposes a numerical simulation of an optical frequency comb scheme at 1550 nm based on a dual-frequency laser pump in the AlGaAs-on-insulator waveguide. Optical frequency comb with a 5 dB spectral bandwidth of approximately 125 nm is obtained within a 0.08-m normal-dispersion AlGaAs waveguide based on pulse compression, self-phase modulation, and optical wave breaking. The influences of power difference and frequency spacing of the dual-frequency lasers on the optical frequency comb are investigated along with the improvements in comb flatness due to pulse shaping.

This paper proposes a theoretical scheme to synthesize white laser source based on the cascaded sum frequency generation (CSFG) model with stimulated Raman adiabatic passage (STIRAP). In the CSFG model, the signal laser, intermediate laser and output laser correspond to red, green and blue (RGB) lasers respectively. The results show that in general the red laser is completely converted to the blue laser, and there is no apparent intermediate green laser. Moreover, under the counterintuitive order, the pump parameters have a wider adjustment range of system conversion efficiency than the coupling delay parameters. We synthesize the white laser source through the following steps. First, we change the pump intensity to roughly adjust the conversion efficiency of the system, and then vary the coupling delay parameters to fine-tune RGB lasers output power ratio. Compared with the scheme based on frequency conversion with Stark-chirped rapid adiabatic passage to synthesize white laser source, the RGB lasers output of the new scheme can achieve better stability. The results of the investigation can provide a theoretical foundation for the research of novel optical devices.

In this paper, we experimentally demonstrated wavelength-tunable cylindrical vector beams of very narrow spectral linewidth at ∼ 1 μ m with an authentic all-fiber structure for the first time to the best of our knowledge. An ytterbium-doped fiber laser was utilized to initiate the continuous-wave single-longitudinal-mode laser emission, and an off-set splice spot together with a few-mode fiber Bragg grating were used as the mode converter as well as mode selecting output coupler. By adjusting the built-in polarization controllers, radially and azimuthally polarized CVB outputs were both obtained. The central wavelength was at 1053.4 nm with a tuning range of 1.1 nm with thermal control, and two fiber Mach–Zehnder interferometers were cascaded to achieve a 20-dB linewidth of 14.7 kHz.

We present an observation of competition effect among multiple quantum paths in a Raman-type Mach-Zehnder atom interferometer. By measuring the contrast of interference fringes, the competition effect among multiple interference paths is experimentally investigated. Due to the phase competition, the contrast periodically oscillates when modulating either the phase or the interrogation time between Raman pulses. The multiple quantum paths form because of the imperfect population transfer efficiency in stimulated Raman transitions, and are verified by modulating the duration of Raman pulses. The contrast could be optimized by suppressing the phase competition., 6 pages, 5 figures

The study proposes enhancement in self-compression of the laser pulse with relativistic nonlinearity in a plasma. It is presented that, a low-intensity laser pulse can tune the pulse duration and peak intensity of the high-intensity laser pulse. The coupled modified nonlinear Schrodinger equations (MNLS) have been established for both laser pulses in plasma. The enhancement in compression of the high-intensity laser pulse is solved by numerical methods. The nonlinearity of plasma, self-phase modulation (SPM), and group velocity dispersion (GVD) compress the laser pulse to the extremely short duration high peak intensity laser pulse. As a result, it is observed that the compression of the high-intensity laser pulse is highly sensitive to the combined intensity of both laser pulses, plasma density and even a small walkoff between two pulses can affect the high-intensity laser pulse compression.

We perform a sub-Doppler spectroscopy of the D 2 line of 87Rb atoms in a vapor cell using a mode-locked 1 GHz femtosecond laser and a cw diode laser. The experiment explores the high resolution of the frequency comb and the possibility of the atoms interacting with more than one mode of the comb. We probe several velocity groups or a selective group of atoms using a velocity-selective and a repetition rate spectroscopy, in a co-propagating configuration of the beams. By detecting the diode transmission we can distinguish the resonances associated with the hyperfine structure of the 5 P 3 ∕ 2 level and follow the competition of the optical pumping processes, in the regime that the two beams have approximately the same intensities. The results are well described in the frequency domain picture, using rate equations for a four level system interacting with three cw lasers.

Using the two-dimensional classical ensemble method, we investigate the nonsequential double-ionization (NSDI) processes of Ar atom by few-cycle linearly polarized laser field. We demonstrate that the recollision-induced excitation with subsequent ionization (RESI) and the recollision-induced ionization (RII) channels can be effectively controlled by laser intensities. Moreover, the carrier-envelope-phases (CEPs) play a key role in controlling RESI and RII mechanism. The correlated electron momentum distribution is demonstrated for the RII and RESI channels at different CEPs and intensities.

In this article, enhance of optical trapping efficiency by the nonlinear optical tweezers is investigated. The expressions described the longitudinal and transverse optical trapping efficiencies are theoretically derived. The influence of average laser power on the optical trapping efficiency is observed and discussed in comparison with that of linear optical tweezers. Remarkably, the optical trapping efficiency of nonlinear optical tweezers can be enhanced by using average laser power, and get several times higher than that of the linear optical ones having the same configuration.

We experimentally study intracavity four-wave mixing (FWM) using Λ -type, three-level electromagnetically induced transparency (EIT) atoms confined in an optical ring cavity. The original dark-state peak disappears accompanying the generation of intracavity FWM when the coupling light is changed from traveling-wave to standing wave. Additionally, this FWM signal is on resonance with the optical cavity only when the coupling laser is detuned from the atomic resonance center, where the absorption is drastically reduced for both the probe and FWM fields. At last, we do theoretically analysis for the susceptibility of this composite atom–cavity system.

We report a low-cost laser thermal distortion all-time metrology system (LATAMS) to overcome the intrinsic limitations of conventional approaches. The LATAMS is especially useful for the thermal distortion measurement of the laser crystal in solid-state lasers, compared with other approaches. A LATAMS setup is constructed and embedded into an existing solid-state laser, consisting of displaying the fringe patterns and recording the changes processes. The LATAMS could provide high-precision real-time thermal distortion measurement throughout the whole process of the solid-state laser. The experimental results successfully demonstrated its capability in measuring the wavefront distortion of laser crystal.

Surface emitting distributed feedback (SE-DFB) semiconductor lasers with second-order grating have become one of research hotspots due to be in terms of high beam quality, narrow linewidth and so on. The diffraction and feedback of the second-order grating are utilized to achieve wavelength stabilization and surface emitting. In the paper, SE-DFB laser with asymmetric waveguide is designed, and the effect of waveguide structures on slope efficiency is discussed. The results show that the slope efficiency of SE-DFB laser with P-asymmetric waveguide is 1.04 W/A which enhances 0.12 W/A than the device with symmetric waveguide. It provides an idea for SE-DFB laser research.

We theoretically investigate single-photon coherent transport in a one-dimensional coupled-resonator waveguide coupled to two quantum emitters with dipole–dipole interactions. The numerical simulations demonstrate that the transmission spectrum of the photon depends on the two atoms dipole–dipole interactions and the photon–atom couplings. The dipole–dipole interactions may change the dip positions in the spectra and the coupling strength may broaden the frequency band width in the transmission spectrum. We further demonstrate that the typical transmission spectra split into two dips due to the dipole–dipole interactions. This phenomenon may be used to manufacture new quantum waveguide devices.

We introduced a compact V-shaped external Talbot cavity for phase locking of high power broad-area laser diodes. The length of compact cavity is ∼ 25 mm. Near diffraction-limit coherent addition of 10 broad-area laser diodes indicated that high quality phase locking was achieved. We measured the near-field emission mode of each individual broad-area laser diode with different feedback, such as a volume Bragg grating and a high reflection mirror. We found out that the best result of phase locking broad-area laser diodes was achieved by the compact V-shaped external Talbot cavity with volume Bragg grating feedback.

We study the optical nonreciprocal propagation in an optical molecule of two coupled cavities with one of them interacting with a two-level atomic ensemble. The effect of increasing the number of atoms on the optical isolation ratio of the system is studied. We demonstrate that the significant nonlinearity supplied by the coupling of the atomic ensemble with the cavity leads to the realization of greatly-enhanced optical nonreciprocity compared with the case of single atom.

An optical system was demonstrated that enables continuous control over the peak power level of ultrashort duration laser light. The optical characteristics of amplified and compressed femtosecond-duration light from a chirped-pulse amplification laser are shown to remain invariant and maintain high-fidelity using this system. When the peak power was varied by an order-of-magnitude, up to its maximum attainable value, the phase, spectral bandwidth, polarization state, and focusability of the light remained constant. This capability led to precise control of the focused laser intensity and enabled a correspondingly high level of control over the power of an all-laser-driven Thomson X-ray light source.

The measurement precision of frequency-modulated continuous-wave (FMCW) laser distance measurement should be proportional to the scanning range of the tunable laser. However, the commercial external cavity diode laser (ECDL) is not an ideal tunable laser source in practical applications. Due to the unavoidable mode hopping and scanning nonlinearity of the ECDL, the measurement precision of FMCW laser distance measurements can be substantially affected. Therefore, an FMCW laser ranging system with two auxiliary interferometers is proposed in this paper. Moreover, to eliminate the effects of ECDL, the frequency-sampling method and mode hopping influence suppression method are employed. Compared with a fringe counting interferometer, this FMCW laser ranging system has a measuring error of ± 20 μ m at the distance of 5.8 m.

Using a π phase-shifted fiber Bragg grating (PSFBG) as narrow band filtering component is an important method for narrow linewidth fiber lasers, which have lots of applications in fiber sensors, optical communication, coherent detection and combination. In this paper, we design and fabricate two π PSFBGs by π phase-shifted phase mask. A narrow linewidth 1.5 μ m Er-doped fiber ring laser employing one of the two π PSFBGs is set up, and the characteristics of the laser power and spectrum are investigated experimentally. A maximum laser power about 2.22 W at 1549.5 nm with linewidth ∼ 1 GHz is achieved, and the maximum slope efficiency is 35.8%. To the best of our knowledge, it is the highest power for GHz-level C-band fiber lasers. Further, high-efficient, high-power, single-longitudinal-mode fiber lasers could be achieved by optimizing the π PSFBG and the structure of the cavity.

In the two-particle approximation, we consider the mechanism for the formation of an ordered arrangement of transparent spherical particles of small size in a concentration grating excited by the gradient force of counter-propagating Gaussian laser beams. This mechanism is due to the joint action of the transverse gradient force and the Coulomb force arising as a result of dipole-dipole interactions between particles., 3 pages, 2 figures

An axial pulsed external magnetic field (EMF), instead of continuous one, has been applied on the operation of a CuBr laser with small-bore tube. A double synchronize triggering system has been designed and used for the laser pumping and simultaneously applying a magnetic field pulses up to 1100 Gauss. By applying an EMF along the tube axis, the laser output power has been decreased. Through adjusting the delay timing between triggers of magnetic field and laser discharge circuits, the laser output power can be changed, continuously. The maximum decrease of the laser output power has been obviously observed at a delay time of 120 ns between triggers.

We report a Kerr lens mode-locked thin-disk ring laser oscillator with an output power of 22 W and a pulse duration of 711 fs. A repetition rate of 120.7 MHz is the highest ever obtained from a thin-disk ring laser oscillator, to the best of our knowledge. This work is expected to open up another route in dual-frequency-comb spectroscopy using a single ring laser source.

Photoelectron holography in strong field tunneling ionization has subatomic spatial and attosecond temporal resolutions and thus it is a promising method to probe the attosecond electronic dynamics in atoms and molecules. The proof-of-concept studies have been performed in atoms and diatomic molecules. Here, we illustrate the application of the strong-field photoelectron holography in probing the attosecond electron dynamics in more complex system. As a demonstrated, by solving the time-dependent Schrodinger equation, we shown that the ultrafast charge migration in the triatomic molecule H 3 could be retrieved from the holographic fringes in the photoelectron momentum distribution. Our study indicates that the concept of photoelectron holography can be extended to probe the attosecond electron dynamics in more complex molecules which is of essential significance for the newly emerging attosecond chemistry.

We propose a scheme for generating two continuously tunable laser wavelengths with picometer linewidths using only one solid-state laser gain medium, two end mirrors, one output coupler, and one grating in a double Littman resonator. Each laser wavelength emission can be tuned independently while maintaining the very narrow linewidth. We demonstrate our scheme in the ultraviolet region by simulating the ultraviolet laser emission from a cerium-doped lithium calcium aluminum fluoride crystal, where we obtained a linewidth of about 2 pm and continuous tunability in the wavelength range from 278 nm to 315 nm. This wavelength region has important applications in monitoring the concentration of sulfur dioxide and ozone in the atmosphere using differential absorption lidar, which require two closely spaced wavelengths with linewidths of 100 pm or less. The proposed scheme can be extended to other wavelength regions using an appropriate laser gain medium, enabling other applications requiring a tunable dual wavelength and narrow linewidth laser.

We investigate the features of electron returning trajectories in recollision-induced nonsequential double ionization by intense circularly polarized laser pulses within a classical ensemble model. We find typical two-dimensional returning trajectories of the first ionized electron that can be decomposed into local circular motion driven by the laser field and overall elliptical motion due to the Coulombic attraction of the parent ion. Such trajectories burst within a narrow time window of less than two laser cycles and end periodically with kinetic energies around the instantaneous ponderomotive energy after many laser cycles, which is very different from the well-known simple one-dimensional returning trajectories in the case of linear laser polarization.

The coherent-mode representation is a fundamental tool that helps us understand the processes of producing and propagating optical fields. In this work, such representation for self-imaging phenomena under partially coherent illumination is presented within the frame of partial coherence theory in the space-frequency domain. Additionally, it is shown that the well-known Talbot and Lau effects are particular cases included in this new formalism. When complete coherence of the field is considered, the general expression for coherent self-imaging of optical fields is obtained (Talbot effect for both linear and circular gratings are presented); on the other hand, when an incoherent superposition of an infinite number of modes are considered, the expression to describe the Lau effect is obtained.

High/ultra-precision motion measurements for precision translation stages are highly desired in modern manufacturing systems and instruments. In this work, we introduce a wide range three-axis grating encoder with nanometric resolution, which can measure the x -, y- and z -axial translational motions of a stage simultaneously. The grating encoder is composed of a reflective-type planar scale grating with a period of 8 μ m and an optical reading head. A planar reference grating, which is the same as the planar scale grating except the length and width, is employed in the optical reading head. The x - and y- directional ±1st order diffractive beams of the planar scale grating interfere with the corresponding diffractive beams of the planar reference grating, forming the measurement signals. The x - and y- directional ±1st order diffractive beams of the two planar gratings propagate against their original incident path, working as the autocollimatic diffractive beams. Therefore, the z -axial measurement range of the proposed grating encoder is greatly enhanced. The x - and y- axial measurement ranges depend on the size of the planar scale grating. To make the grating encoder more compact, a double grating beam-splitting (DGBS) unit and two diffractive optical elements (DOEs) are introduced. The experimental results indicate that the z -axial displacement resolution is as high as 4 nm with an electronic data division card of 80 segments developed by our lab.

We have investigated velocity selective spectral profile variations of probe beam transmittance at F g = 3 → F e = 2 , 3 , and 4 hyperfine manifolds of 85 Rb atoms along with coherence effects at the F g = 3 → F e = 4 transition with various coupling laser polarization configurations and a fixed probe polarization ( σ + ). Laser linewidth, atomic velocity distributions, frequency mixing of the coupling and probe laser beams between degenerate magnetic sublevels, and polarization variations of the coupling beam with the probe beam fixed at the F g = 3 → F e = 4 transition were used to simulate the line profiles. The calculated transmittance signals are in good agreement with observed signals for each coupling laser polarization configuration.

Combining the kinetic and fluid dynamic processes in static and flowing-gas diode-pumped alkali vapor lasers, a comprehensive physical model with three cyclically iterative algorithms for simulating the three-dimensional pump and laser intensities as well as temperature distribution in the vapor cell of side-pumped alkali vapor lasers is established. Comparison with measurement of a static side-pumped cesium vapor laser with a diffuse type hollow cylinder cavity, and with classical and modified models is made. Influences of flowed velocity and pump power on laser power are calculated and analyzed. The results have demonstrated that for high-power side-pumped alkali vapor lasers, it is necessary to take into account the three-dimensional distributions of pump energy, laser energy and temperature in the cell to simultaneously obtain the thermal features and output characteristics. Therefore, the model can deepen the understanding of the complete kinetic and fluid dynamic mechanisms of a side-pumped alkali vapor laser, and help with its further experimental design.

We theoretically propose a scheme for two-dimensional electromagnetically induced grating in a five-level atomic system interacting with two orthogonal standing-wave fields. In such atomic system, nonlinear absorption or refractivity can be significantly enhanced with nearly vanishing linear absorption under different resonant conditions. When applying two coupling fields with standing-wave pattern, absorption grating or phase grating, which efficiently diffracts a probe beam into high-order directions, can be formed in the media. The diffraction efficiencies of the gratings depend strongly on the interaction length, the intensities and detunings of the coupling fields. By investigating the third-order nonlinearity of the system, it is found that the spatial variations of amplitude and phase arise from the nonlinear modulation. The proposed gratings can be used as multi-channel beam splitter and have potential applications in optical information processing and optical networking.

We analytically and numerically investigate the propagation dynamics of initially chirped symmetric Airy pulses in an optical fiber. The results show that the positive chirps act to promote the interference in generating a focal point on the propagation axis, while the negative chirps tend to suppress the focusing effect, as compared to conventional unchirped symmetric Airy pulses. The numerical results demonstrate that the linear propagation of chirped symmetric Airy pulses depend considerably on the chirp parameter and the primary lobe position. In the anomalous dispersion region, positively chirped symmetric Airy pulses first undergo an initial compression, and reach a foci due to the opposite acceleration, and then experience a lossy inversion transformation, and come to the opposite facing focal position. The impact of truncation coefficient and Kerr nonlinearity on the chirped symmetric Airy pulses propagation is also disclosed separately.

In this paper we investigate the ionization of O 2 molecule exposed to few-cycle pulses with different optical cycle numbers by calculating the photoelectron angular distributions (PADs) of O 2 molecule. In order to show the influence of the molecular electronic structure and the laser pulse on the PADs, we also calculate the PADs of H atom, which has an isotropic electronic distribution in its ground state. We find that for one-cycle laser pulse, the PADs of O 2 molecule are inversion asymmetric, and the PADs are not dependent on the photoelectron energy. For two-cycle and three-cycle laser pulses, although the PADs are still inversion asymmetric, the PADs have a certain dependence on the photoelectron energy. According to this phenomenon, we can control the emission directions of photoelectrons by choosing a fitted photoelectron energy. At same time, with a fitted photoelectron energy, by changing the carrier-envelope (CE) phase, the split position of the PADs of O 2 molecule can be controlled, and then can forecast the main emission direction of photoelectron. While for long pulse ( ten -cycle pulse) the dependence of PADs on the photoelectron energy nearly disappears, and the ionization behaviors extend to that in an infinitely monochromatic plane wave.

On the edge of bandgap in a fiber grating, narrow peaks of high transimittivity exist at frequencies where light interferes constructively in the forward direction. In the vicinity of these transmittivity peaks, light reflects back and forth numerous times across the periodic structure and experiences a large group delay. In order to generate the extremely slow light in fiber grating for applications, in this research, the common sense of formation mechanism of slow light in fiber grating was introduced. The means of producing and operating fiber grating was studied to support structural slow light with a group index that can be in principle as high as several thousand. The simulations proceeded by transfer matrix method in the paper were presented to elucidate how the fiber grating parameters effect group refractive index. The main parameters that need to be optimized include grating length, refractive index contrast, grating period, loss coefficient, chirp and apodization functions, those can influence fiber grating characteristics.

We measure the branching ratios from the y 8 P 9 / 2 excited state to six metastable states of europium through fluorescence spectroscopy of an atomic beam. The sum of the six branching ratios is estimated to be 1.05 ( 2 ) × 10 − 3 . This research provides us with insightful information to determine the feasibility of using the a 8 S 7 / 2 − y 8 P 9 / 2 transition in order to implement the Zeeman slowing for europium atoms in the ground state. Based on this result, we also propose a scheme for Zeeman slowing and magneto-optical trapping, using a specific metastable state which has a cyclic transition.

We present a theoretical study to investigate sub- and super-luminal light propagation in a rubidium atomic system consisting of a Rydberg state by using density matrix formalism. The analysis is performed in a 4-level vee+ladder system interacting with a weak probe, and strong control and switching fields. The dispersion and absorption profiles are shown for stationary atoms as well as for moving atoms by carrying out Doppler averaging at room temperature. We also present the group index variation with control Rabi frequency and observe that a transparent medium can be switched from sub- to super-luminal propagation in the presence of switching field. Finally, the transient response of the medium is discussed, which shows that the considered 4-level scheme has potential applications in absorptive optical switching., Comment: 12 pages, 6 figures

Attosecond-resolution molecular high-order harmonic generation (MHHG) and isolated attosecond pulse generation (IAP) from H2+ has been theoretically investigated through solving the Non-Bohn-Oppenheimer (NBO) time-dependent Schrodinger equation (TDSE). Results show that the harmonic spectra present the asymmetric distribution to the two H nuclei. Particularly, when the laser field is larger than zero (E(t)>0.0), the harmonic generation from the negative-H is higher than that from the positive-H; while when the laser field is smaller than zero (E(t)