Spatial chirp and angular dispersion of a laser crystal for a four-mirror cavity Kerr-lens mode-locked laser

We describe oscillating loops in a laser cavity and optical paths in a laser crystal of different wavelength rays for a four-mirror cavity Kerr-lens mode-locked laser. The relation between different wavelength ray paths and laser resonator parameters is deduced. The analytical expressions of second- and third-order dispersion including angular dispersion of the crystal are presented. The variations of group-delay dispersion (GDD) and third-order dispersion (TOD) with cavity parameters are calculated exactly. The calculation shows that GDD and TOD increase rapidly when the spacing between two folding mirrors approaches the boundary of a cavity stability zone. The rapid dispersion increase influences the mode-locked pulse width and the mode-locked stability.     

Ray-tracing model for stretcher dispersion calculation

We propose a ray-tracing model that provides a clear physical picture and simple formulas for grating pair stretcher dispersion calculations. With this model we can easily demonstrate why and to what extent the stretcher and compressor are opposite quantitatively without using a Fourier transform. The dispersion calculation shows that the spherical aberration in the stretcher decreases fourth-order dispersion compared with an aberration-free stretcher. In a chirped pulse amplification system, this fourth order can help to reduce residual fourth-order dispersion. The effect of the finite beam size and the misalignment are also considered.     

Compact cross-dispersion device based on a prism and a plane transmission grating

This paper presents a cross-dispersion prism-grating device using a plane transmission grating attached directly to a prism, which is different from traditional cross-dispersion grating-prism systems that are based on the reflection grating. Unlike conventional direct-vision grism or constant-dispersion grism in which both the prism and grating have the same dispersion direction, for this device the dispersion directions of the prism and grating are different. The analytical expressions for the cross-dispersion of this device are derived in detail and the formulas of the footprint of the dispersed spectra are given. The numerical results and ray-tracing simulations by ZEMAX are shown. The device provides a compact, small-sized and broadband cross-dispersion device used for the medium resolution spectrometer.     

Origin and effect of high-order dispersion in ultrashort pulse multiphoton microscopy in the 10 fs regime

Short pulses can induce high nonlinear excitation, and thus they should be favorable for use in multiphoton microscopy. However, the large spectral dispersion can easily destroy the advantages of the ultrashort pulse if there is no compensation. The group delay dispersion (GDD), third-order dispersion, and their effects on the intensity and bandwidth of second-harmonic generation (SHG) signal were analyzed. We found that the prism pair used for compensating the GDD of the two-photon microscope actually introduces significant negative high-order dispersion (HOD), which dramatically narrowed down the two-photon absorption probability for ultrashort pulses. We also investigated the SHG signal after GDD and HOD compensation for different pulse durations. Without HOD compensation, the SHG efficiency dropped significantly for a pulse duration below 20 fs. We experimentally compared the SHG and two-photon excited fluorescence (TPEF) signal intensity for 11 fs versus 50 fs pulses, a pulse duration close to that commonly used in conventional multiphoton microscopy. The result suggested that after adaptive phase compensation, the 11fs pulse can yield a 3.2- to 6.0-fold TPEF intensity and a 5.1-fold SHG intensity, compared to 50 fs pulses.     

Optically anisotropic crystalline grisms for astronomical spectrographs

We show that a crystalline LiNbO(3) grism and a hybrid grism made of a LiNbO(3) transmission grating and a ZnS prism can be new and powerful dispersing elements with refractive indices high enough to realize high spectral resolution for visible to near-infrared astronomical spectrographs with transmission optics. We describe the basic principle and the limitation to minimizing the spectral separation that is due to the inherent birefringence of such an optically anisotropic crystal used for grisms.     

Measurement of group delay dispersion of high numerical aperture objective lenses using two-photon excited fluorescence

We determined the group-delay dispersion (GDD) of five microscope objectives by measuring the second-order autocorrelation at the focal points of the objectives with two-photon excited fluorescence as the power square sensor. We found that typical microscope lens systems introduce significant GDD (2000-6500 fs(2)). The third-order dispersion determined for these objectives limits the minimum obtainable pulse width at the focal point of an objective to 20-30 fs if not compensated. No significant chromatic aberration or higher-order dispersion effects were found for any of the optical components measured within the wavelength range of 700-780 nm and for pulse widths greater than 50-60 fs.     

Complete characterization of a self-mode-locked ti:sapphire laser in the vicinity of zero group-delay dispersion by frequency-resolved optical gating

The intensity and the phase of ultrashort pulses from a self-mode-locked Ti:sapphire laser operating in the vicinity of zero group-delay dispersion (GDD) have been completely characterized by the technique of frequency-resolved optical gating (FROG). For small values of negative GDD, the appearance of a dispersive wave in the pulse spectrum is manifested in the measured FROG trace, and pulse retrieval directly shows its association with a broad leading-edge pedestal. For positive GDD, we confirm previous experimental observations of picosecond pulses with large positive chirp and report a new operating regime in which the output pulses are of picosecond duration but are intensity modulated at 20 THz. The physical origin of this modulation is discussed by analogy with similar effects observed during pulse propagation in optical fibers, and the experimental results are compared with a model of intracavity four-wave mixing about the cavity zero GDD wavelength.     

超短孤子脉冲在色散缓变光纤中的时间抖动

通过微扰理论分析了超短孤子在色散缓变光纤(DDF)中传输的时间抖动。结果发现三阶色散和拉曼散射分别影响了孤子的位置和频率,是决定时间抖动大小的重要因素。在光纤的拉曼系数一定的情况下,选择不同的三阶色散参数,系统的时间抖动存在一个最小值。当DDF的三阶色散参数为接近零的一个负值的时候,系统时间抖动最小,这个负值与拉曼系数和传输距离有关,其绝对值随传输距离的增大而增大。在采用色散缓变光纤进行超短孤子传输的系统设计中应该重点考虑三阶色散的影响,当DDF的三阶色散参数较大的时候,必须对系统的三阶色散进行补偿,使时间抖动达到最小,能够极大地增加了孤子的传输距离。     

Grating coupler dispersion compensation with a surface-relief reflection grating

Experimental results are presented that show that diffraction off a surface-relief reflection grating can be used to extend the FWHM input coupling efficiency versus the coupled-light wavelength of a grating coupler from 0.7 to 17 nm. Use of a surface-relief reflection grating allows high diffraction efficiency over a wide wavelength range. Dispersion-matching calculations are included that illustrate that for certain output coupling applications the FWHM can be extended to 33 am. Analysis shows that for inputcoupling applications the lateral beam shift resulting from angular dispersion may be the limiting factor for wavelength compensation.     

Optimal dispersion precompensation by pulse chirping

For the procedure of dispersion precompensation in fibers by prechirping, we found that there is a maximum distance over which a pulse initially compressed by prechirping can return to its original width. The distance constraint comes in the form of a mathematical relationship involving the distance, dispersion, initial pulse width, and peak power, implying that the restriction governs all the fiber parameters. Simple closed-form approximations for the constraint and for the corresponding required prechirp are derived on the basis of a variational approach. The validity of the analytical formulas is confirmed by split-step Fourier numerical simulation.     

Dispersion properties of grating-based rapid scanning optical delay lines

The signal expression measured by an OCT system is derived, which reveals the possibility of tissue dispersion compensation by introducing the required amount of dispersion in the reference arm and may be implemented by incorporating the grating- based rapid scanning optical delay (RSOD) lines in the reference arm of OCT. The more accurate expressions for the group-delay dispersion (GDD) and the second-order GDD are derived for the grating-based RSOD lines. A comparison of our results with previous ones is done, which shows that when only the GDD is of concern, the previously reported results are accurate. However, when it becomes necessary to take the effect of the second-order GDD into account, the more accurate formula must be used. The obtained results may be of great importance for maximizing the imaging properties of OCT in tissue imaging.     

Chirped-cavity dispersion-compensation filter design

A new basic structure of a dispersive-compensation filter, called a chirped-cavity dispersion-compensator (CCDC) filter, was designed to offer the advantages of small ripples in both reflectance and group-delay dispersion (GDD). This filter provides a high dispersion compensation, like the Gires-Tournois interferometer (GTI) filter, and a wide working bandwidth, like the chirped mirror (CM). The structure of the CCDC is a cavity-type Fabry-Perot filter with a spacer layer (2 mH or 2 mL) and a chirped high reflector. The CCDC filter can provide a negative GDD of -50 fs2 over a bandwidth of 56 THz with half the optical thickness of the CM or the GTI.     

Hook method: improvement and simplification of the experimental setup

The conventional experimental setup used to measure anomalous dispersion by the hook method has been modified by replacing the spectrograph by a single grating in combination with a camera. The grating is used for diffraction angles close to pi/2 rad, and the focal distance for projection of the hook spectrum is 4 m. The high dispersion thus obtained (typically 200 mm/nm) considerably facilitates the use of the hook method for diagnostic purposes. Further, it is demonstrated that, for such large diffraction angles, a focusing element after diffraction at the grating can be avoided without losing too much sharpness in the hook spectrum.     

On dispersion relations of Rayleigh waves in a functionally graded piezoelectric material (FGPM) half-space

For propagation of Rayleigh surface waves in a transversely isotropic graded piezoelectric half-space with material properties varying continuously along depth direction, the Wentzel–Kramers–Brillouin (WKB) technique is employed for the asymptotic analytical derivations. The phase velocity equations for both the electrically open and shorted cases at the free surface are obtained. Influences of piezoelectric material parameters graded variations on Rayleigh wave dispersion relations, particles’ displacements magnitude and corresponding decay properties are discussed. Results obtained indicate that coupled Rayleigh waves can propagate at the surface of the graded piezoelectric half-space, and their dispersion relations and the particles displacements ellipticity at the free surface are dependent upon the graded variation tendency of the material parameters. By the Rayleigh surface waves phase velocities relative changing values combined with the relationship between the wave number and the material graded coefficient, a theoretical foundation can be provided for the graded material characterization by experimental measurement.     

Powerful FE approaches for Pochhammer's dispersion modelling

Simple and very effective finite element approaches for modelling of the dispersion of torsional, longitudinal and flexural waves propagated in infinite and elastic cylindrical bars (Pochhammer's problem) and hollow cylinders are presented. The approaches allow one to model given problems without using infinite elements and their usage is demonstrated by using dispersion curves, shapes of waves and tables of phase velocities. Comparison of finite element solutions (solved in one task from small‐sized models) with exact solutions shows an excellent agreement. The maximum relative differences among the 20 lowest FEM and analytical phase velocities was less than 0.000015%. The approaches and results hold also for cylinders with finite lengths, simply supported on both ends. Copyright © 2003 John Wiley & Sons, Ltd.     

A direct perturbation method investigation of the interplay between self-frequency shift and cross-phase modulation for solitons

The self-frequency shift of solitons, mainly observed in femtosecond pulses and arising from the Raman effect, can be counteracted by the cross-phase modulation (XPM) arising from collisions between pulses of different frequency. The same could be said for the time displacement that follows the frequency shift. The current work is an analytical approach to the interplay between the Raman self-frequency shift and XPM with third-order dispersion (TOD) effects taken into account. By using coupled NLS equations, the effect of XPM between two channels is considered for the cases of complete and incomplete collision. The analysis is based on the direct perturbation method and provides quantitative and qualitative insight of the spectral and temporal evolution of ultra short soliton pulses.     

Analytic study on soliton-effect pulse compression in dispersion-shifted fibers with symbolic computation

The soliton-effect pulse compression of ultrashort solitons in a dispersion-shifted fiber (DSF) is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion (TOD), self-steepening (SS) and stimulated Raman scattering (SRS). By using Hirota's bilinear method with a set of parametric conditions, the analytic one-, two- and three-soliton solutions of this model are obtained. According to those solutions, the higher-order soliton is shown to be compressed in the DSF for the pulse with width in the range of a few picoseconds or less. An appealing feature of the soliton-effect pulse compression is that, in contrast to the second-order soliton compression due to the combined effects of negative TOD and SRS, the third-order soliton can significantly enhance the soliton compression in the DSF with small values of the group-velocity dispersion (GVD) at the operating wavelength.     

Influence of nonlinear coupling of pulses on spatio-temporal compression

Abstract

Properties of a novel configuration of an optical (spatio-temporal) pulse compressor, that is based on a Kerr-type planar waveguide into which two pulses are simultaneously launched, are studied. It is assumed that the pulse which is the subject of the compression propagates in the anomalous dispersion regime, while the auxiliary pulse is in normal dispersion. The best parameters of the proposed compressor are obtained when duration of the auxiliary pulse is so large that this dispersion can be neglected, while energy of the second pulse is above the threshold of first-order soliton generation. It is observed that in such a configuration the compression occurs simultaneously with the generation of a soliton-like solution. It is argued that the proposed configuration with two simultaneously propagating pulses has advantages over the configuration with a single pulse, namely the maximal compression factor and the optimal length of the compressor is, respectively, more than 3 times larger and, at least, 10 times greater than the corresponding values of the compressor with a single pulse. It is also demonstrated that such a compressor can be considered as a universal device, since its operation depends only slightly on the initial parameters of the pulse subject to the compression.     

Grating triplet

A grating-pair device is useful for producing negative group velocity dispersion of temporal optical signals. When high dispersion is needed or large bandwidth is involved, higher-order dispersion terms become significant. The grating triplet is a new approach to create dispersion that can produce negative or positive group-velocity dispersion without higher-order dispersion terms.     

Femtosecond dispersion compensation with multilayer coatings: toward the optical octave

Dispersive multilayer coatings have found widespread use, particularly in the compensation of material dispersion in femtosecond oscillators and amplifiers. Other than prism or grating sequences, only chirped mirrors allow for the compensation of a much more general spectral dependence of the dispersion. The current state of the art in ultrabroadband mirror design for dispersion compensation is reviewed. Approaches to expand the utility of chirped-mirror coatings toward the coverage of an even-wider bandwidth beyond the optical octave are discussed.