Second-order grazing-angle scattering in uniform wide holographic gratings

Grazing-angle scattering (GAS) is a type of Bragg scattering in slanted wide periodic gratings. It occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates at a grazing angle to the grating boundaries. Previous research has been concerned only with first-order GAS, which has been shown to be a highly unusual type of scattering characterised by a strong resonant increase of amplitudes of the scattered and incident waves in the grating. In this paper, a rigorous numerical study of second-order GAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong resonances in the grating, which is strongly different from that for first-order GAS, is predicted, described, and discussed. Physical interpretations of the predicted results are presented. In particular, a special new type of eigenmodes in a slanted wide periodic grating with large amplitude is predicted. These eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed. Received: 16 September 2002 / Revised version: 4 November 2002 / Published online: 22 January 2003 RID="*" ID="*"Corresponding author. Fax: +61-7/3864-9079, E-mail: d.pile@osa.org     

Frequency response of second-order extremely asymmetrical scattering in wide uniform holographic gratings

Second-order extremely asymmetrical scattering (EAS) and grazing-angle scattering (GAS) are types of Bragg scattering in slanted wide periodic gratings. They occur when the second diffracted order satisfies the Bragg condition and has a wavevector parallel (for EAS) and almost parallel (for GAS) to the grating boundaries. In this paper, for the first time, a rigorous numerical study of the frequency responses of second-order EAS and GAS is presented for bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong optical resonances in the side-lobe structure of these frequency responses is predicted. A relationship between these resonances and the previously predicted GAS resonances (at zero detunings of the Bragg condition) is established and analysed. A special new type of eigenmodes in slanted wide periodic gratings with strong frequency detunings are predicted in the case of second-order EAS and GAS. The eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed. PACS 42.25Fx; 42.79Dj; 42.40Eq     

Extremely asymmetrical scattering in gratings with weak dissipation: some physical analogies

A detailed analysis of new effects related to extremely asymmetrical scattering (EAS) of bulk and guided weakly dissipating electromagnetic waves in oblique periodic gratings is presented. A very important role of the previously determined critical grating width is demonstrated for EAS in dissipative gratings. Incident and scattered wave amplitudes inside and outside the grating are analysed as functions of dissipation coefficient, grating width, grating amplitude, etc. Strong differences in the patterns of scattering in gratings that are narrower and wider than the critical width are demonstrated and discussed. Deep analogies between EAS and other resonant optical effects, such as attenuated total reflection, Fabry–Pérot interferometry, etc. are revealed and discussed. A physical interpretation of the obtained results is presented. Received: 19 February 2002 / Revised version: 28 June 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +61-7/3864-9079, E-mail: d.gramotnev@qut.edu.au     

Double-resonant extremely asymmetrical scattering of electromagnetic waves in non-uniform periodic arrays

A new type of Bragg scattering – double-resonant extremely asymmetrical scattering (DEAS) of optical waves in oblique, non-uniform, periodic Bragg arrays is analysed theoretically and numerically. Steady-state DEAS is demonstrated to occur in the extremely asymmetrical geometry where the scattered wave propagates parallel to the front array boundary. The non-uniform array is represented by two joint uniform, strip-like, periodic arrays with different phases (and amplitudes) of the grating. DEAS is characterised by a unique combination of two simultaneous resonances with respect to frequency and phase variation at the interface between the joint arrays. As a result, a strong resonant increase in the scattered wave amplitude compared with the amplitude of the incident wave is predicted and investigated theoretically. The amplitude of the incident wave inside the array is also shown to increase resonantly in the middle of the array where the step-like variation in the phase of the grating takes place. The effect of different widths of the joint arrays, and magnitudes of the grating amplitudes on DEAS is analysed. Physical explanations of this type of scattering, based on the diffractional divergence of the scattered wave from one of the joint arrays into another, are presented.     

Boundary effects in the diffraction of light by volume gratings: II. Phase transmission gratings

The two-wave approximation of the method of characteristics modes is used to analyze theoretically the diffraction of light by volume phase transmission gratings for arbitrary proportions between the average refractive index of the grating and the refractive indices of the ambient media. Simple expressions are derived for calculating the amplitudes of the diffracted waves in the case where the angle of incidence of the primary wave coincides with the Bragg angle. The roles of the front and back boundaries of the grating are discussed separately, and a new method for separating the contribution of the boundary diffraction, which is due to the periodic inhomogeneity of the grating boundaries, is proposed. The experimental possibility of selecting partial Bloch waves in the measurements of the diffraction efficiency of gratings that have high reflection coefficients of both boundaries is demonstrated.     

All-Fiber Spectroscope with Second-Order Fiber Bragg Grating for Rotational Raman Lidar

Owing to the second-order fiber Bragg grating possessing narrower reflectivity bandwidth than first-order, an all-fiber spectroscopic filter with several second-order fiber Bragg gratings and optical fiber couplers in the visible region is designed to extract interest rotational Raman spectra. Considering the inference fringe visibility of inscribing fiber Bragg grating and the fiber core index dispersion effect, numerical simulations are made by the improved mathematical model based on an exponential photorefractive dynamic, and its simulative results show better agreement with the experimental data. We propose an all-fiber spectroscopic configuration, which could balance lidar sensitivity against signal-to-noise ratio for optimizing remote sensing performance by fiber Bragg gratings serially. Simulative results show that the thumb principle for fabricating second-order fiber Bragg grating is the increasing gratings length, and that this all-fiber spectroscope can achieve >70 dB suppression to elastic scattering and efficiently extract the rotational Raman signal for profiling atmospheric temperature.     

Diffraction efficiency of sequentially stored gratings in reflection volume holograms

On the basis of the theory of coupled waves the amplitudes of the first-order diffracted waves and the diffraction efficiency is calculated for sequentially superposed phase gratings stored in dielectric reflection holograms. The investigations are restricted to the case of a fixed reference wave during recording and Bragg-angle incidence.By analogy to the transmission volume grating the coupling effects which appear between incident beams and diffracted waves give the possibility of building up beam-couplers and -splitters with certain coupling parameters determined by the recording process. Moreover, reflection gratings allow a favourable combination between coupling and reflecting properties and avoid the diffraction efficiency oscillations that are characteristic of transmission gratings. The performance of the reconstruction process with several waves simultaneously allows the tuning of the intensities of diffracted waves with dependence on amplitude or phase differences between incident beams.     

Measuring Stokes parameters by means of a polarization grating

Ordinary gratings act on the amplitude and (or) the phase of a wave front. Polarization gratings produce instead a periodic modulation of the state of polarization. A simple grating of the latter type is constituted by a linear polarizer whose orientation varies periodically along a line. It is shown that, for a generic polarization state of the incident field, such a grating gives rise to first-order diffracted beams with counterrotating circular polarizations. It is also shown that such a grating can be used for measuring the Stokes parameters of a light beam in an achromatic manner. Several extensions are briefly discussed.     

Grazing-angle scattering of electromagnetic waves in periodic Bragg arrays

A new powerful approximate approach for the theoretical analysis of Bragg scattering in oblique strip-like periodic arrays with the scattered wave propagating almost parallel to the array boundaries – grazing-angle scattering (GAS) – is introduced and justified. This approach is based on allowance for the diffractional divergence of the scattered wave by means of the parabolic equation of diffraction and Fourier analysis. The divergence is demonstrated to be an intrinsic physical cause of GAS. Detailed theoretical analysis of steady-state GAS is carried out for bulk and guided optical modes. It is demonstrated that the most interesting feature of GAS in arrays of width that is greater than a critical width is a unique combination of two strong simultaneous resonances with respect to frequency and angle of scattering. In such wide arrays, GAS is demonstrated to be not only unusually sensitive to angle of scattering, but also to small variations of array width and grating amplitude. Entire concentration of the resonantly strong scattered wave inside the array is shown to be possible. A relationship between GAS, conventional Bragg scattering, and extremely asymmetrical scattering (i.e. where the scattered wave propagates parallel to the array boundaries) is analysed. Applicability conditions for the used approximations and obtained results are derived and discussed.     

Grazing-angle scattering of waves in infinitely wide periodic gratings

The approximate method of analysis of grazing-angle scattering (GAS), based on allowance for the diffractional divergence of the scattered wave, is justified and extended to GAS in infinitely wide, slanted, periodic gratings. The analysis has revealed an unusual and strong dependence of the pattern of GAS on small variations of mean structural parameters at the grating boundary. Several times increase of already resonantly large scattered wave amplitudes can be achieved in this case. Sharp resonance-like maximums on the angular dependence of the scattered wave amplitude are predicted inside the grating. The theory is extended to the case of GAS of optical modes guided by a slab with a semi-infinite periodic groove array. Physical interpretation of the obtained results is presented.     

Modelling of strongly nonlinear sinusoidal Bragg gratings by the Method of Single Expression

The one-dimensional problem of plane EM wave interaction with strongly nonlinear sinusoidal Bragg gratings is exactly solved using the new Method of Single Expression (MSE). The basic point of the method is the presentation of the electrical field in the modulated medium (Bragg grating) in the form of a single expression, contrary to the traditional counter-propagating waves approach. The spectral characteristics of linear Bragg gratings of different length are presented. The influence of loss or gain on the spectral characteristics of Bragg gratings is considered. The electrical field amplitude distributions along a grating at the wavelengths corresponding to the minima and maxima of reflectivity in the vicinity of the Bragg resonance are illustrated. Bistable and multistable dependences of reflectivity on the incident electrical field amplitude are obtained for negative and positive nonlinearities.     

Grating matrix method to describe a volume transmission diffraction grating

In this work we present a grating matrix method to describe the properties of volume transmission diffraction gratings. The grating matrix will be introduced by using Kogelnik’s coupled wave theory so that the amplitudes of the diffracted and transmitted orders can be obtained at any point of the grating by knowing the values at the input. The use of the grating matrix method will permit predicting the efficiency of the first reflected order which cannot be predicted by only using Kogelnik’s formulation. The results obtained by using this method will be compared to those obtained using the rigorous coupled wave theory and also by the results obtained correcting Kogelnik’s expressions for the transmission and diffraction efficiency to take into account Fresnel losses. As will be seen by using the grating matrix method we will be able to describe the interference pattern created by multiple diffracted waves due to reflections at the boundaries of the diffraction grating, which cannot be predicted using Kogelnik’s coupled wave theory.     

光纤光栅温度传感理论与实验

从光纤光栅温度传感模型出发，理论分析研究了光纤光栅的温度传感特性，推导了光纤光栅温度传感的一阶、二阶和有效线性灵敏度系数的解析式，计算了各灵敏度系数的理论值，实验得到了反射波长与温度的二次多项式，对比分析了理论与实验结果，讨论了石英的力学参数对光纤光栅温度传感特性的影响、反射波长与温度的线性及非线性的适用范围等问题. 关键词： 光纤光栅 光纤传感 温度传感     

Characterization of Fourier components in type I infrared ultrafast laser induced fiber Bragg gratings

Type I infrared ultrafast laser induced fiber Bragg gratings have been shown to exhibit higher-order resonances related to the Fourier components possessed by their nonsinusoidal index change profile. Using successive higher-order phase masks, we determine the Fourier components of type I-IR gratings in both hydrogen-loaded and unloaded fiber. Knowledge of the relative dc and ac components of a fiber Bragg grating is required for tailoring its spectral response.     

在局域响应的光折变晶体中的相干光放大

理论和实验表明，在由光生伏打电荷迁移为主的局域非线性响应的薄光折变晶体（LiNbO₃∶Fe）中实现弱信号光放大是可能的．光能流从抽运光向信号光不可逆转移的起因是两束入射光与背面反射光之间的四波作用形成互倾斜、彼此有一定空间相移的两组相位栅．当入射抽运光在非布喇格条件下读出由反射光和其衍射光所写入的新光栅时，弱信号便获得相干放大．对理论计算与实验结果进行了比较． 关键词：     

局域体全息光栅的衍射特性

基于三维耦合波理论，研究了两束有限宽度的任意偏振平面波干涉产生的局域体全息光栅的衍射问题。以单位均匀振幅的任意偏振平面波为例，给出了透射波和衍射波振幅的主分量和交叉分量的解析表达式，讨论了记录过程和再现过程中入射的参考光波的偏振角对透射波和衍射波振幅的影响。计算结果表明，记录过程中的偏振角越小，形成的光栅内的耦合越强，衍射效率越高，但光束质量越差；再现过程中不同的偏振角，由于入射波和衍射波的电矢量的不同方向的耦合强弱不同，透射波和衍射波振幅的主分量和交叉分量的振幅变化行为不同。     

Soret effect in forced Rayleigh scattering

In forced Rayleigh scattering of mixtures or suspensions the temperature gratings generate, by the Soret effect, concentration gratings that may be very important since they produce both a phase and an amplitude grating superimposed on the principal one. The experimental evidence of their influence was given by Thyagarajan and Lallemand using a mixture of carbondisulfide and ethanol. In this paper we study the temporal behaviour of the concentration grating versus the sample properties and its effect on the detected diffracted beam. Explicit expressions are given for the output intensity taking into account both the generated amplitude and phase gratings.     

Lineshape and polarization mode dispersion of waves diffracted by apodized and chirped fiber Bragg gratings in reflection

The amplitude and phase of a light wave propagating in an apodized and chirped Bragg grating is given by the superposition of two orthogonal coupled wave functions that are the solution of a non-linear Riccati equation. An analytical solution, in the form of an integral transform, that predicts the amplitude, phase, and intensity profile of the light diffracted by grating, in which the local Bragg wavelength is asymmetric, and the forward and counter propagating modes are non-degenerate is presented. For even apodization and odd chirp the lineshape has an asymmetrical Gaussian form the result of mixing of the real and imaginary components of the apodized grating wave function. The effect of chirping is to shift the resonance wavelength, increase the grating bandwidth and polarization mode dispersion. The dependence of linewidth and dispersion on parameters that alter apodization and chirp after fabrication, is also discussed.     

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.     

Beam splitting, combining, and cross coupling through multiple superimposed volume-index gratings

We investigate the diffraction properties of multiple-superimposed index gratings from a vector synthetic viewpoint using coupled wave analysis with Bragg and non-Bragg readout. The vector synthetic gratings consist of two volume-index gratings with different grating wave vectors, which can be obtained in photorefractive materials, in optical fibers or in Bragg cells with two driving acoustic waves. This structure can realize beam splitting, beam combining, and beam cross coupling, etc. Analytic expressions for the diffraction efficiency as well as the amplitude of the waves involved are obtained. The results are presented and discussed.