Simultaneous visual detection of pulse chirp and temporal asymmetry in ultrashort laser pulses using analysis of unbalanced interferometric correlation envelope (ICE) functions

A simple method that uses envelope functions of unbalanced interferometric (auto/cross) correlation signals has been presented for simultaneous visual detection of pulse chirp and asymmetry, without direction-of-time ambiguity in ultrashort laser pulses. The ambiguity issues of unbalanced interferometric correlation envelope (ICE) difference signals have been studied. It is found that unbalanced ICE difference signals are visually different corresponding to practically indistinguishable unbalanced interferometric autocorrelation (IAC) signals for a distinct symmetric–asymmetric pulse pair with identical intensity autocorrelation and power spectra. The theoretical analysis of ICE signals is supported by experimental unbalanced IAC signals obtained using 200 fs laser pulses from a cw mode-locked Nd:phosphate laser oscillator. PACS 42.65.Re; 42.50.Hz; 07.60.Ly     

The effect of errors and detector noise on sensitive detection of chirp and pulse asymmetry of ultrashort laser pulses from interferometric autocorrelation signals

We have studied the effect of various types of systematic and non-systematic errors on unbalanced spectrally modified interferometric autocorrelation signals for detection of pulse chirp and asymmetry of ultrashort laser pulses. The effect of systematic errors arising due to limited number of data points per fringe, scan rate etc, and non-systematic errors due to phase noise, additive noise, multiplicative noise and quantization of interferometric autocorrelation (IAC) signals is illustrated using a linearly chirped asymmetric laser pulse. It is seen that the spectrally modified IAC signals based on difference of normalized envelope functions corresponding to different frequencies are not much sensitive to various noises, permitting their use for sensitive detection of pulse chirp and asymmetry. The analysis is supported by experimentally recorded IAC signals under different conditions.     

Angular chirp and tilted light pulses in CPA lasers

We investigate analytically and experimentally various aspects of the angular chirp of ultrashort laser pulses. This type of chirp is easily produced by slight misalignment of standard pulse stretcher and/or compressor setups. Angular chirp leads to tilted pulse fronts in the near field and to a strong reduction of intensity in the focus. The effect is rather difficult to observe with standard diagnostic techniques. We present a method that is based on interferometric field autocorrelation and allows us to measure the angular chirp reliably. Suggestions on how to avoid this effect are outlined as well.     

频域标定飞秒脉冲干涉自相关迹及钛宝石振荡器实时啁啾监测

采用频域处理的方法首次在频域标定飞秒激光脉冲干涉自相关迹的时间扫描.计算被测脉冲的均方根宽度和啁啾参数，并以此为依据在实验中优化钛宝石振荡器的调节从而获得接近变换极限的115fs脉冲.该方法只涉及到数值积分和快速傅里叶变换，在实验中完全可以用于实时监测振荡器的运行情况. 关键词： 频域标定 钛宝石振荡器 飞秒脉冲 干涉自相关迹     

Femtosecond Kerr-lens autocorrelation

An autocorrelation measurement of femtosecond laser pulse duration using the Kerr-lens mechanism is demonstrated. This technique can also be used as a sensitive and absolutely calibratable method for measuring ultrafast optical nonlinearities. A method that uses an electronic spectral-filtering scheme is proposed for determining the frequency chirp of pulses by interferometric autocorrelation.     

测量飞秒激光脉冲啁啾的方法

介绍了一种能够直接检测飞秒脉冲啁啾大小的方法。采用共轴结构的迈克尔逊干涉自相关二次谐波检测系统对自制碰撞脉冲锁模循环染料激光器输出的最窄脉冲宽度约为200fs的脉冲进行了测量。测得的飞秒脉冲自相关二次谐波曲线表明：实测曲线的下包络两翼明显隆起,包络外形很不整齐,对称性较差,说明光脉冲含有啁啾。通过比较干涉测量曲线和理论曲线的形状与面积的大小,可以直观地反映出光脉冲所含啁啾的大小。实验结果分析表明,利用满足光相关检测所需精度的光学元件和满足光相关探测基本条件的实验装置,能测得含有相位及啁啾信息的快干涉项信号,是一种能够直观检测光脉冲所含啁啾大小的可行方法。     

考虑不同脉冲形状时群速失配效应在二次谐波自相关法中的影响

本文讨论了在考虑不同脉冲形状时群速失配效应对二次谐波自相关法测量超短光脉冲宽度的影响.结果表明了脉冲形状不同时,群速失配效应对干涉自相关法和强度自相关法的影响不同.     

群速失配在二次谐波自相关法中的影响:Ⅰ类及Ⅱ类相位匹配

本文详细讨论了二次谐波自相关法测量超短光脉冲宽度时群速失配对测量的影响,发现群速失配对于干涉自相关法和Ⅱ类相位匹配强度自相关法测量影响显着,而对Ⅰ类相位匹配强度自相关法测量影响很小。     

单模光纤正常色散区零色散波长附近的啁啾演变特性

利用傅里叶变换法,首次推出了单模光纤正常色散区中二阶、三阶色散共同决定群速度色散效应时,所致啁啾的解析表达式.利用数位解法,模拟了零色散波长附近群速度色散效应和自相位调制效应共同导致的啁啾演变过程.计算结果表明:啁啾为非线性的,且有极值,因而导致脉冲形状的畸变.     

Performance evaluation of N × 40 Gbps CS-RZ and DCS-RZ modulated signals transmitted over single mode fiber based on non-ideal LiNbO<Subscript>3</Subscript> Mach-Zehnder modulators

We investigate the transmission performance of N × 40 Gbps carrier-suppressed return-to-zero (CS-RZ) and duobinary CS-RZ (DCS-RZ) modulated wavelength division multiplexed (WDM) signals over the standard single-mode fiber (SSMF) based on non-ideal Mach-Zehnder (MZ) modulators through numerical simulations. In addition to that, the impact on receiver margin related to the residual chirp due to an asymmetry ratio of modulators as well as the effect of the applied chirp of modulators has been studied. As the asymmetry ratio of modulators is increased, dispersion penalties are increased asymmetrically at around the zero dispersion wavelength for the CS-RZ format. The DCS-RZ modulation format has a symmetric behavior due to different characteristics of the residual chirp of modulators. The receiver margin for the DCS-RZ modulation format is larger than the CS-RZ modulation format above the asymmetry ratio of 0.82 of modulators (extinction ratio of 20 dB) with the optimal Δλ_DCF. By controlling the negative/positive applied chirp of the first/second modulator, dispersion penalties can be reduced for both the CS-RZ and DCS-RZ formats. In the DCS-RZ format compared to the CS-RZ format, the effect of the applied chirp of the first modulator is more dominant than that of the second modulator. The simulation results show that the receiver margin is limited by the asymmetry ratio of modulators as well as a deviated wavelength from the zero dispersion wavelength of dispersion compensating fibers (DCF) in order to be fully post-compensated. Dispersion penalties can be reduced with appropriate chirp parameters of two non-ideal modulators.     

Retrieving the Amplitude and Phase Parameters of an Ultrashort Wave Packet by Autocorrelation Methods

Based on an analysis of the signal of an interferometric intensity autocorrelator, we demonstrate theoretically and experimentally a simple technique for retrieving the temporal distributions of the amplitude and phase of an ultrashort light pulse. Assuming that a phase-modulated wave packet has a Gaussian envelope, we derive an analytical expression for the autocorrelator signal in the cases of linear- and quadratic-chirp optical pulses. The experimental and theoretical results are in excellent agreement. In particular, we show that a linear chirp (quadratic phase modulation) can be measured with a good experimental accuracy of no worse than 10%. This yields the possibility of measuring the parameter k₂, which describes the dispersion characteristics of a medium in the second order of the dispersion theory, with the same accuracy. Measuring a quadratic chirp by the proposed method is possible only if such a chirp is sufficiently large.     

Autocorrelation measurements of free-electron laser radiation using a two-photon QWIP

The two-photon QWIP comprises three equidistant subbands, namely two bound states localized in the quantum well and an extended state in the continuum. This device is very promising for quadratic autocorrelation measurements of pulsed mid-infrared lasers due to its resonantly enhanced optical nonlinearity and sub-ps time resolution. We report on interferometric autocorrelation measurements of ps optical pulses from a free-electron laser (FEL). The intense FEL radiation further allows us to study the saturation properties of two-photon QWIPs at liquid nitrogen temperature and their detection properties at 300 K. The device is well suited for standard diagnostics of the FEL pulse shape via interferometric autocorrelation.     

Stimulated Raman spectroscopy using chirped pulses

We present a detailed theoretical and experimental characterization of a new methodology for stimulated Raman spectroscopy using two duplicates of a chirped, broadband laser pulse. Because of the linear variation of laser frequency with time (‘chirp’), when the pulses are delayed relative to one another, there exists a narrow bandwidth, instantaneous frequency difference between them, which, when resonant with a Raman‐active vibration in the sample, generates stimulated Raman gain in one pulse and inverse Raman loss in the other. This method has previously been used for coherent Raman imaging and termed ‘spectral focusing’. Here, gain and loss signals are spectrally resolved, and the spectrally integrated signals are used to determine the spectral resolution of the measured Raman spectrum. Material dispersion is used to generate a range of pulse durations, and it is shown that there is only a small change in the magnitude of the signal and the spectral resolution as the pulse is stretched from 800 to 1800 fs in duration. A quantitative theory of the technique is developed, which reproduces both the magnitude and linewidth of the experimental signals when third‐order dispersion and phase‐matching efficiency are included. The theoretical calculations show that both spectral resolution and signal magnitude are severely hampered by the third‐order dispersion in the laser pulse, and hence, a minimal amount of chirp produces the most signal with only a slight loss of spectral resolution. Copyright © 2014 John Wiley & Sons, Ltd.     

Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime

We report on the direct observation of the phase locking of the attosecond pulse train (APT) via interferometric autocorrelation in the extreme ultraviolet region. APT is formed with Fourier synthesis of high-order harmonic fields of a femtosecond laser pulse. Time-of-flight mass spectra of N+, resulting from the Coulomb explosion of N2 absorbing two photons of APT, efficiently yield correlated signals of APT. The measured autocorrelation trace exhibits that the duration of the pulse should be only 1.3 periods of the extreme ultraviolet carrier frequency. A few interference fringes within the short pulse duration clearly show two types of symmetry, which ensure the phase locking between pulses in APT.     

Conclusive evidence of an attosecond pulse train observed with the mode-resolved autocorrelation technique

We report on the direct observation of an attosecond pulse train with a mode-resolved autocorrelation technique. The chirp among the three harmonic fields is specified by analyzing two-photon above-threshold ionization spectra of electrons, resulting in a pulse duration that should be shorter than 450 as, which is, to our knowledge, the first determination of the chirp in the attosecond pulse train with an autocorrelation technique. These results will open the way to full characterization of an attosecond pulse train with its envelope.     

The feasibility of pulse compression by nonlinear effective bandwidth extension

Chirp-encoded excitation has been utilized for increased signal-to-noise ratio (SNR) in both linear and harmonic imaging. In either case, it is necessary to isolate the relevant frequency band to avoid artifacts. In contrast, the present study isolates and then combines the fundamental and the higher harmonics, treating them as a single, extended bandwidth. Pulse-inverted sum and difference signals are first used to isolate even and odd harmonics. Matched filters specific to the source geometry and the transmit signal are then separately applied to each harmonic band. Verification experiments are performed using up to the third harmonic resulting from an underwater chirp excitation. Analysis of signal peaks after scattering from a series of steel and nylon wires indicates increased compression using the extended bandwidth, as compared to well-established methods for fundamental and second harmonic chirp compression. Using third harmonic bands, a mean pulse width of 56% relative to fundamental compression and 48% relative to second harmonic compression was observed. Further optimization of the compression by altering the transmission indicated 17% additional reduction in the pulse width and a 47% increase in peak-to-sidelobe ratio. Overall, results establish the feasibility of extended bandwidth signal compression for simultaneously increasing SNR and signal resolution.     

Short-time fractional Fourier methods for the time-frequency representation of chirp signals

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.     

Pulse compression technique for simultaneous HIFU surgery and ultrasonic imaging: a preliminary study

In an ultrasound image-guided High Intensity Focused Ultrasound (HIFU) surgery, reflected HIFU waves received by an imaging transducer should be suppressed for real-time simultaneous imaging and therapy. In this paper, we investigate the feasibility of pulse compression scheme combined with notch filtering in order to minimize these HIFU interference signals. A chirp signal modulated by the Dolph-Chebyshev window with 3-9 MHz frequency sweep range is used for B-mode imaging and 4 MHz continuous wave is used for HIFU. The second order infinite impulse response notch filters are employed to suppress reflected HIFU waves whose center frequencies are 4 MHz and 8 MHz. The prototype integrated HIFU/imaging transducer that composed of three rectangular elements with a spherically con-focused aperture was fabricated. The center element has the ability to transmit and receive 6 MHz imaging signals and two outer elements are only used for transmitting 4 MHz continuous HIFU wave. When the chirp signal and 4 MHz HIFU wave are simultaneously transmitted to the target, the reflected chirp signals mixed with 4 MHz and 8 MHz HIFU waves are detected by the imaging transducer. After the application of notch filtering with pulse compression process, HIFU interference waves in this mixed signal are significantly reduced while maintaining original imaging signal. In the single scanline test using a strong reflector, the amplitude of the reflected HIFU wave is reduced to −45 dB. In vitro test, with a sliced porcine muscle shows that the speckle pattern of the restored B-mode image is close to that of the original image. These preliminary results demonstrate the potential for the pulse compression scheme with notch filtering to achieve real-time ultrasound image-guided HIFU surgery.     

Temporal characterization of short-pulse third-harmonic generation in an atomic gas by a transmission-grating Michelson interferometer

By use of a transmission-grating-based Michelson interferometer, second-order interferometric as well as intensity autocorrelation traces of the third harmonic of a Ti:sapphire 50-fs laser beam produced in Ar have been measured. The duration of the harmonic is found to be that expected from lowest-order perturbation theory. At this wavelength, the performance of the interferometer with respect to pulse-front distortion and dispersion is found to be satisfactory. This result is a first step toward the use of the interferometer for the temporal characterization of higher harmonics or harmonic superposition forming attosecond pulse trains.     

Ionization of atoms by chirped attosecond pulses

We investigate the ionization dynamics of atoms by chirped attosecond pulses using the strong field approximation method. The pulse parameters are carefully chosen in the regime where the strong field approximation method is valid. We analyse the effects of the chirp of attosecond pulses on the energy distributions and the corresponding left-right asymmetry of the ionized electrons. For a single chirped attosecond pulse, the ionized electrons can be redistributed and the left-right asymmetry shows oscillations because of the introduction of the chirp. For time-delayed double attosecond pulses at different intensities with the weaker one chirped, exchanging the order of the two pulses shows a relative shift of the energy spectra, which can be explained by the different effective time delays of different frequency components because of the chirp.