用SHG-FROG方法测量超短光脉冲的振幅和相位

介绍了二次谐波振荡频率分辨光学快门(SHGFROG)测量超短脉冲的实验系统和二维相位恢复算法,这种方法可以实现对超短脉冲振幅和相位的完全测量.利用矩阵方法数值模拟了几种常见超短脉冲的SHGFROG迹线,并用主元素广义投影算法(PCGPA)从这些无噪音的SHGFROG迹线中恢复了脉冲的振幅和相位,误差接近收敛的标准.研究结果表明,这种测量方法结构简单,算法可靠,是测量超短脉冲的理想方法之一.     

Evolving FROGS: phase retrieval from frequency-resolved optical gating measurements by use of genetic algorithms

We present a new technique based on genetic algorithms for retrieving the electric field and the phase of ultrashort pulses from frequency-resolved optical gating (FROG) traces. We have successfully applied a very basic genetic algorithm to the two most common beam geometries: polarization gate and second-harmonic generation (SHG). In the case of SHG FROG, the genetic algorithm returns a lower error than the standard iterative composite algorithm.     

Coherent artifact in modern pulse measurements

We simulate multishot intensity-and-phase measurements of unstable trains of complex ultrashort pulses using second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) and spectral-phase interferometry for direct electric-field reconstruction (SPIDER). Both techniques fail to see the pulse structure. But FROG yields the correct average pulse duration and suggests the instability by exhibiting significant disagreement between measured and retrieved traces. SPIDER retrieves the correct average spectral phase but significantly underestimates the average pulse duration. In short, SPIDER measures only the coherent artifact. An analytical calculation confirms this last fact.     

Convergence test for inversion of frequency-resolved optical gating spectrograms

We describe a new and simple method to aid in the analysis of retrieved pulses from inverted frequency-resolved optical gating (FROG) traces. The analysis can separate noise from distortion and shows that distortion is more deleterious to the retrieved pulse than is pure noise. The analysis relies on the fact that FROG traces can be constructed from a single outer product of two vectors, whereas distortion and noise require the sum of a series of outer products.     

Practical issues in ultra-short-pulse measurements with ‘GRENOUILLE’

We examine the characteristics and limitations of GRENOUILLE, a simple and compact implementation of the second-harmonic-generation (SHG) frequency-resolved-optical-gating (FROG) technique. We show that it can be made to operate effectively over a relatively wide range of pulse lengths and wavelengths. We also describe procedures for its design and calibration, and we discuss the use of arbitrary nonlinear SHG crystals. PACS 42.65.-k; 42.65.ReAn erratum to this article can be found at     

Pulse‐shape instabilities and their measurement

Multi‐shot pulse‐shape measurements of trains of ultrashort pulses with unstable pulse shapes are studied. Measurement techniques considered include spectral‐phase interferometry for direct electric‐field reconstruction (SPIDER), second harmonic generation frequency‐resolved optical gating (FROG), polarization gate FROG, and cross‐correlation FROG. An analytical calculation and simulations show that SPIDER cannot see unstable pulse‐shape components and only measures the coherent artifact. Further, the presence of this instability cannot be distinguished from benign misalignment effects in SPIDER. FROG methods yield a better, although necessarily rough, estimate of the pulse shape and also indicate instability by exhibiting disagreement between measured and retrieved traces. Only good agreement between measured and retrieved FROG traces or 100% SPIDER fringe visibility guarantees a stable pulse train.     

Sensing and compensation of femtosecond waveform distortion induced by all-order polarization mode dispersion at selected polarization states

We demonstrate full characterization of femtosecond pulse distortion induced by all-order polarization mode dispersion (PMD) at selected polarization states via second-harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements at an average power of under 28 nW. By applying the inverse of the measured spectral phase via a programmable pulse shaper, we compress the distorted pulses from more than 3 ps to nearly bandwidth-limited durations of less than 500 fs. Our results show that SHG FROG measurements performed by using fiber-pigtailed aperiodically poled lithium niobate waveguides can serve as a robust and sensitive tool for characterization of PMD-induced spectral phase.     

Tomographic retrieval of the polarization state of an ultrafast laser pulse

We introduce a self-referenced method for determining the complete polarization state of an ultrafast pulse field. The algorithm is based on any well-established technique that measures both the intensity and phase of a single polarization, such as frequency-resolved optical gating (FROG). We demonstrate the retrieval of nontrivial fields generated using a polarization-amplitude-phase ultrafast pulse shaper using four standard FROG measurements.     

频率分辨光学开关法行迹相位还原的时频分析

将小波变换分析光谱相位相干原理应用于频率分辨光学开关(FROG)行迹图的时间-频率分析，不需要传统的迭代算法，从对FROG行迹的脊的分析中，直接得到超短脉冲的相位.对于FROG行迹的脊变化平缓的脉冲得到了精确的相位. 关键词： 超短脉冲 相位重建     

Complete pulse characterization at 1.5 mum by cross-phase modulation in optical fibers

Cross-phase modulation in optical fibers has been used for complete characterization of ultrashort pulses by a modified frequency-resolved optical gating (FROG) measurement technique. This technique has been used for characterization of picosecond pulses at 1.5mum with energy as low as 24 pJ, and the results are in excellent agreement with second-harmonic generation (SHG)-FROG characterization. The use of an optical waveguide gives measurement sensitivity comparable with that of SHG-FROG but without any temporal ambiguity in the retrieved pulse.     

Milliwatt-peak-power pulse characterization at 1.55 microm by wavelength-conversion frequency-resolved optical gating

A novel wavelength-conversion configuration based on four-wave mixing in an optical fiber has been used to generate a frequency-resolved optical gating (FROG) trace identical to that obtained from second-harmonic generation (SHG). The use of an optical fiber waveguide permits enhanced measurement sensitivity compared with that of conventional SHG-FROG and has been used for complete characterization of 1-mW peak-power picosecond pulses at 1.55 microm from an unamplified semiconductor laser diode gain switched at 10 GHz.     

Feedback-controlled femtosecond pulse shaping

We describe the experimental implementation of feedback-optimized femtosecond laser pulse shaping. A frequency-domain phase shaper is combined with different pulse characterization methods and appropriate optimization algorithms to compensate for any phase deviation. In particular, bandwidth-limited, amplified laser pulses are achieved by maximizing the second-harmonic generation (SHG) of the shaped laser pulses with the aid of an evolutionary algorithm. Real-time measurement of the absolute phases is achieved with spectral interferometry where the reference pulse is characterized by FROG, the so-called TADPOLE method. Using the complete electric field as feedback, arbitrary laser pulse shapes can be optimally generated in two different ways. First, a local convergence algorithm can be used to apply reliable and accurate spectral chirps. Second, an evolutionary algorithm can be employed to reach specific temporal profiles.     

VVA triangle graph ambiguities in four and N dimensions

We demonstrate that ambiguities arising from (i) arbitrariness in the internal momentum variable in four-dimensional Feynman integrals, (ii) arbitrariness in the location of γ₅ within γ-matrix traces under dimensional regularization, and (iii) arbitrariness associated with which vertex occurs first in γ-matrix traces under dimensional reduction all lead to equivalent relations between vector-current and axial-vector-current divergences in the absence of externally imposed vector-current constraints. We find, however, that further ambiguities, associated with the projection of less-than-four-dimensional momenta on four-dimensional γ-matrices, occur within regularization by dimensional reduction.     

Generation of double pulses in-line by using reflective Dammann gratings

Doubled femtosecond laser pulses in-line are needed in the collinear pump-probe technique, collinear second harmonic generation frequency-resolved optical gating (SHG FROG) and the spectral phase interferometry for direct electric-field reconstruction (SPIDER), etc. Normally, it is generated by using a Michelson's structure. In this paper, we proposed a novel structure with two-layered reflective Dammann gratings and the reflective mirrors to generate doubled femtosecond laser pulses in line without transmission optical elements. Angular dispersion and spectral spatial walk-off are both compensated. In addition, this structure can also compress the positive chirped pulse, which cannot be realized with a Michelson's structure. By adopting triangular grating and blazed gratings, the efficiency of the system would in principle be increased as the Michelson's scheme. Experiments demonstrated that this method should be an alternative approach for generation of the double compressed pulses of femtosecond laser for practical applications.     

Hilbert reconstruction of phase-shifted second-harmonic holographic images

New techniques are presented that make phase-shifting holography viable for second-harmonic generation (SHG) holography with weak object fields. We developed an intrinsic phase shift calibration of SHG holograms, an algorithm that extracts the reference and object intensity directly from a set of phase-shifted holographic data, and a more robust phase-shifting holography reconstruction algorithm based on π-shifted hologram pairs that permits self-calibration of the phase shift and recovery of the complex field through a Hilbert transform.     

Observation of chirped soliton dynamics at lambda = 1.55 microm in a single-mode optical fiber with frequency-resolved optical gating

We present an experimental observation of the dynamics of an initially chirped optical soliton at 1.55microm that is propagating through a single-mode optical fiber, using frequency-resolved optical gating (FROG). FROG permits observation of both the amplitude and the phase profiles of ultrashort pulses, providing complete information on the pulse evolution. The features that are detected, which include what is believed to be the first experimental observation of phase slips, are in quantitative agreement with numerical simulations that employ the nonlinear Schr?dinger equation.     

The second-harmonic generation in parabolic quantum dots in the presence of electric and magnetic fields

The second-harmonic generation (SHG) coefficient for parabolic quantum dots (QDs) subject to applied electric and magnetic fields is theoretically investigated, within the framework of the compact-density-matrix approach and an iterative method. Numerical results are presented for typical GaAs/AlGaAs parabolic QDs. These results show that the radius of QD and the magnitude of electric and magnetic fields have a great influence on the SHG coefficient. And the peak shifts to the aspect of high energy when considering the influence of electric and magnetic fields. Moreover, the SHG coefficient also depends sensitively on the relaxation rate of the spherical QD system.     

Polarization-insensitive ultralow-power second-harmonic generation frequency-resolved optical gating

We demonstrate polarization-insensitive ultralow-power second-harmonic generation frequency-resolved optical gating (FROG) measurements with a fiber-pigtailed, aperiodically poled lithium niobate waveguide. By scrambling the polarization much faster than the measurement integration time, we eliminate the impairment that frequency-independent random polarization fluctuations induce in FROG measurements. As a result we are able to retrieve intensity and phase profiles of few hundred femtosecond optical pulses with 50 MHz repetition rates at 5.2 nW coupled average power without control of the input polarization.     

Many-photon effects in inelastic light scattering

The usual approach to second harmonic generation (SHG) is based on low-order pertubation theory and neglects the changes in the electronic states that are induced by the exciting beam. To see whathappens in this approximation fails we propose a new formalism, based on the method of excitation amplitudes, to set up a theory of the SHG response and other inelastic light scattering phenomena. We develop the quantum theory in the dipole approximation and show that the inclusion of electron-photon coupling to all others leads to new features. Strong exciting fields produce a nonnegligible SHG response in highly polarisable centro-symmetric systems, and the emitted spectrum shows a dynamical Stark effect.     

Coherent control of the optical nonlinear and luminescence anisotropies in molecular thin films by multiphoton excitations

Photoinduced orientational distributions are implemented with one- and two-photon absorption interference in polymer films containing chromophores that exhibit luminescent and nonlinear properties. The odd- and even-order parameters of the final distribution are probed by simultaneous measurement of second-harmonic generation (SHG) and two-photon fluorescence (TPF). We show the possibility of engineering local SHG and TPF anisotropies by controlling the polarization states and intensities of the writing optical fields. Complex multipolar orders are modeled with an irreducible spherical tensor-based formalism jointly applied to the molecular polarizabilities and field tensors.