Diffraction properties of ultrashort pulsed beams with arbitrary temporal profiles by a reflection volume holographic grating

The diffraction properties of reflection volume holographic gratings are studied when the gratings are illuminated by an ultrashort beam with arbitrary temporal profiles. The modified Kogelnik's theory of coupled waves is used. Simple analytical expressions for spectral and temporal distribution of the transmitted and diffracted are obtained. The dependences of the diffraction bandwidth, the Bragg selectivity bandwidth and the total diffraction efficiency of the reflection volume grating on the temporal profiles of the input ultrashort pulse are investigated. Study shows that the bandwidth of the reflection volume holographic gratings varies with the grating parameters more slowly than the transmitting volume holographic gratings. For three different temporal profiles, numerical results about diffraction properties of the reflection volume holographic gratings are given and compared with the transmitting volume holographic gratings.     

Diffraction properties of multi-layer volume holographic gratings under an ultrashort pulsed beam with arbitrary temporal profiles

The diffraction properties of a system of multi-layer volume holographic gratings under an ultrashort pulsed beam with arbitrary temporal profiles are investigated using the multi-layer coupled wave theory. The dependence of the pulse profiles of the diffracted beams, diffraction bandwidth and the total diffraction efficiency of the multi-layer system on the temporal profiles of the input ultrashort pulse are investigated. The calculated results indicate that the temporal shape of the input pulsed beams is an important factor in the analysis of the propagation characteristics. The analysis of this paper will be valuable for the applications of pulse shaping, processing and filter.     

Diffraction of an ultrashort pulsed beam with arbitrary polarization state from a volume holographic grating in LiNbO3 crystals

Based on a modified coupled wave theory of Kogelnik, we have studied the diffraction of an ultrashort pulsed beam with an arbitrary polarization state from a volume holographic grating in photorefractive LiNbO₃ crystals. The results indicate that the diffracted intensity distributions in the spectral and temporal domains and the diffraction efficiency of the grating are both changed by the polarization state and spectral bandwidth of the input pulsed beam. A method is given of choosing the grating parameters and input conditions to obtain a large variation range of the spectral bandwidth of the diffracted pulsed beam with an appropriate diffraction efficiency. Our study presents a possibility of using a volume holographic grating recorded in anisotropic materials to shape a broadband ultrashort pulsed beam by modulating its polarization state.     

Anisotropic Bragg diffraction of finite-sized volume holographic grating in photorefractive crystals

Anisotropic diffraction of uniform plane wave by finite-sized volume holographic grating in photorefractive crystals is considered. It is found that the anisotropic diffraction can take place when some special conditions are satisfied. The diffracted image is obtained in experiment for the anisotropic Bragg diffraction in Fe:LiNbO₃ crystals. A coupled wave analysis is presented to study the properties of anisotropic diffraction. An analytical integral solution for the amplitudes of the diffracted beams is submitted. A trade off between high diffraction efficiency and the deterioration of reconstruction fidelity is analyzed. Numerical evaluations also show that the finite-sized anisotropic volume grating exhibits strong angular and wavelength selectivity. All the results are useful for the optimizing design of VHOE based on finite-sized volume grating structures.     

Temporal diffraction characteristics of transmitted multilayer volume holographic grating illuminated by an ultrashort pulse

Based on the coupled wave theory of Kogelnik and Fourier optics, the time-domain diffraction characteristics of tramsmitted multilayer volume holographic grating (MVHG) under an ultrashort pulse readout are investigated. It is shown that the temporal diffraction characteristics depend not only on the numbers of the grating layers, but also on the thicknesses of the grating layers and buffer layers, grating period and the refractive index modulation. Furthermore, using group velocity dispersion we give explanation on the time-delay of diffraction pulse with respect to the center of the readout pulse. Results of our discussion may find applications in optical communications, pulse shaping and processing.     

超短脉冲激光光束在一维反射型体全息光栅中的衍射

基于Kogelnik的耦合波理论,研究了在色散效应的影响下,超短脉冲激光光束在反射型体全息光栅中衍射的性质.研究给出了衍射光及透射光在频谱域及时间域的振幅及强度分布、光栅的光谱宽度及衍射效率随光栅参量及入射条件的变化.数值研究的结果表明,在光栅记录介质色散效应的影响下,衍射光束的光谱宽度减小,脉冲展宽,衍射效率降低.通过适当的选取光栅参量及入射条件,可以控制衍射和透射光束的频谱和时间强度分布,得到满意的衍射和透射光束的带宽和波形,从而可以将其应用于脉冲整形等技术中.     

Analysis of photorefractive volume holographic lenses with different recording and read-out wavelengths

The photorefractive volume holographic lenses for converting a plane wave to a lateral-spread spherical wave with different recording and reconstructing wavelength has been studied. Using the coupled-wave theory, the half-analytical solutions for the amplitudes of the space harmonics of the field inside the transmission geometry are presented. The values of the off-Bragg parameter at the reconstructed process and the diffracted beam's amplitude distribution are analyzed. In addition, the dependences of diffraction properties on the focal length of recording spherical wave and on the geometrical dimensions of the grating are discussed. Furthermore, the focusing properties of this photorefractive holographic lens are analyzed.     

Propagation properties of ultrashort chirped pulsed Gaussian beams in the free space

Based on the Rayleigh diffraction integral and complex analytical signal representation, the free-space analytical propagation equation and its Fourier spectrum for ultrashort chirped pulsed Gaussian beams with constant diffraction length are derived. The effect of chirp parameter on the spatiotemporal and spectral properties is illustrated with analytical formulas and numerical calculation results. It is shown that the axial spectra of ultrashort chirped pulsed Gaussian beams become broadened with increasing chirp parameter. For single optical cycle, the transversal intensity distribution is affected by increasing chirp parameter, but almost not affected for several optical cycles. Moreover, the positive or negative sign of the chirp parameter has no effect on the spectral distribution and intensity distribution.     

超短脉冲贝塞尔-高斯光束在自由空间的传输特性

 使用复解析信号法研究了束宽与频率无关的超短脉冲贝塞尔-高斯光束在自由空间的传输特性。研究表明：在无衍射长度内,超短脉冲贝塞尔-高斯光束的横向光强分布几乎不变并集中在传输轴附近,轴上脉冲随传输距离增加而展宽。在无衍射长度外,横向光强分布显著扩展。随传输距离增加,轴上光谱蓝移先增加,达到极大值后逐渐减小,最后在远场趋于一渐近值。对单周期的超短脉冲贝塞尔-高斯光束的轴上光谱蓝移先增加,达到极大值0.50 fs^-1。然后逐渐减小,在远场蓝移趋于渐近值0.16 fs^-1。     

Temporal and spectral properties of ultrashort pulsed Laguerre-Gaussian beams in dispersive media

The temporal and spectral properties of ultrashort pulsed Laguerre-Gaussian (LG) beams propagating in dispersive media are studied both theoretically and numerically. It is shown that the on-axis pulse broadens with increasing propagation distance and the on-axis spectrum is blueshifted. For the off-axis spectrum the blueshifts decrease and then the spectrum becomes redshifted as the radial distance increases. The propagation of ultrashort pulsed LG beams in free space and of ultrashort pulsed Gaussian beams can be regarded as special cases of our results, and some interesting properties are discussed.     

Elimination of the spatial singularity of ultrashort pulsed beams in dispersive media

Under the condition that the propagation constant k in dispersive media should be larger than zero, a simple method is proposed to eliminate the spatial singularity of ultrashort pulsed beams propagating in dispersive media. Taking the pulsed Gaussian beam (PGB) as a typical example, the analytical propagation equation in the space–time domain is derived and the spatiotemporal propagation properties of PGBs in normal and anomalous dispersive media are discussed both analytically and numerically. The physical explanation of the results is presented.     

体全息光栅透镜的设计和应用

设计了一种新型的体全息光栅透镜, 在一块光学平板（体全息记录材料）内可以将输入光束产生横向传输并聚焦, 或对输入光点产生横传的准直. 它由一束平面波和一束球面波正交入射到光学平板上干涉形成的. 研究了该体全息透镜的光栅间距变化情况, 为设计和制备体全息光栅透镜及相关器件提供了理论依据. 基于两光束耦合波理论, 得到了该光栅透镜的耦合波方程, 近似计算了该透镜的衍射效率及其达到高衍射效率时透镜的最佳尺寸. 最后, 讨论了该透镜在集成光学等领域中的应用.     

External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range

We present two external-cavity diode lasers that utilize a volume holographic grating as the frequency selective feedback element. By using the grating at normal incidence, it is possible to design simple and compact external-cavity diode lasers that have sufficient tunability for molecular spectroscopy. The first design utilizes a long-cavity designed for narrow linewidth and good long-term stability. The laser operates near 635 nm and it has a PZT-controlled tuning range of 28 GHz and a 1-s linewidth of 900 kHz. The second design utilizes a grating attached very close to the laser diode, making the laser compact, robust and easy to operate. The short external-cavity laser operates near 658 nm and it has a linewidth of 30 MHz. Continuous and mode-hop free tuning range of 145 GHz can be obtained by using a simple temperature tuning method.     

变波长读出条件下光折变局域体全息光栅的衍射性质

利用二维耦合波理论,研究了用短波长记录全息光栅而用通讯波段内的长波长读出时,用于90°结构垂直读出平板型的光折变局域体全息光栅的衍射性质.讨论了局域体全息光栅的几何尺寸对其衍射效率及光栅布喇格选择性的影响.结果表明,随着光栅的纵向和横向尺寸的增加,光栅的衍射效率也逐渐增加.当光栅的纵向和横向尺寸发生改变但光栅的总面积不变时,光栅衍射效率保持不变.此外,随着光栅尺寸的增加光栅的布喇格选择性越好.在利用短波长记录全息光栅而用长波长读出的光学器件设计过程中,为了获得最佳的衍射效率及其布喇格选择特性,应当根据要求合理地设计光栅的几何尺寸.     

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change.     

啁啾超短脉冲光波照射下光栅Talbot效应的研究

应用傅里叶频谱分析法，给出了光栅在啁啾超短脉冲光波照射下菲涅耳衍射方程并分析了其Talbot效应. 数值计算表明，在Talbot距离处的衍射光强不仅与照射的超短脉冲光波的宽度有关，而且与脉冲光波的啁啾有关. 根据光栅在Talbot距离处衍射光强的变化，给出了一种检验超短脉冲光波是否含有啁啾的简单方法. 关键词： 光栅 菲涅耳衍射 Talbot效应 啁啾超短脉冲激光     

Diffraction patterns for a transmission volume hologram under Bragg mismatch

We have presented simulations and experiments for 2-dimensional diffraction distributions of a transmission volume hologram. We sample the input pattern with a few elementary points and calculate the diffraction of the corresponding elementary grating. The simulations can describe well the diffraction pattern obtained in the experiment and can be used to predict the tolerance for angular deviation of the reading beam. The tolerance for angular deviation depends on its direction. It is affected by the Bragg degeneracy. The simulation results provide a clear picture of the spatial tolerance for reading a transmission volume hologram.     

Propagation properties of ultrashort pulsed beams with constant waist width in free space

Based on the Rayleigh diffraction integral and complex analytical signal representation, the strict propagation expression and its Fourier spectrum for ultrashort pulsed Gaussian beams with constant waist width are derived, which have the general applicable advantage, because the paraxial approximation, pulsed envelope representation and far-field approximation are not invoked. The far-field and paraxial expressions are obtained as the special cases of our general results. Numerical calculation results are given to illustrate the spatiotemporal propagation properties of few- and single-cycle pulsed Gaussian beams with constant waist width. A comparison with the paraxial results and previous work is also made.     

反射型体全息光栅对超短脉冲激光光束衍射的性质

在光栅记录介质色散效应的影响下,拓展Kogelnik的耦合波理论研究了反射型体全息光栅对偏振方向垂直和平行于入射面的超短脉冲激光光束衍射的性质。结果表明对于记录在LiNbO3光折变晶体中的体全息光栅,在色散效应、光栅参量和入射条件的共同影响下,光栅对偏振方向垂直于入射面的超短脉冲激光光束衍射的光谱带宽大于对偏振方向平行于入射面的超短脉冲激光光束衍射的光谱带宽,在不考虑光栅介质色散效应的影响时,它们都变大。进一步给出了衍射光的光谱带宽及光栅的衍射效率随入射脉冲的光谱带宽与光栅的光谱带宽比值的变化情况。