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     

Higher-order extremely asymmetrical scattering

Extremely asymmetrical scattering (EAS) is a type of Bragg scattering in periodic gratings, that occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates parallel to the grating boundaries. Previous studies were concerned only with first-order EAS that was shown to be a highly unusual type of scattering, characterised by a strong resonant increase of the scattered wave amplitude (i.e. the amplitude of the first diffracted order). In this paper, a rigorous numerical study of higher-order EAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings of various amplitudes and widths. In particular, it is demonstrated that typical scattered wave amplitudes in higher-order EAS are significantly smaller than those in first-order EAS, and display strongly different dependencies on grating width, grating amplitude, distance from the front grating boundary, etc. Similar to first-order EAS, second-order EAS is shown to be strongly sensitive to small variations of mean structural parameters at the grating boundaries. EAS in non-sinusoidal gratings is investigated in detail with special focus on the transition between first-order EAS and second-order EAS in such gratings. Tolerance of second-order EAS to the presence of the second grating harmonic is analysed. The effect of phase of the second grating harmonic on transitional EAS is investigated. Physical explanation of the predicted effects is presented.     

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.     

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.     

Frustration of Bragg reflection by cooperative dual-mode interference: a new mode of optical propagation

A new optical mode of propagation is described, which is the natural eigenmode (supermode) of a fiber (or any optical waveguide) with two cospatial periodic gratings. The mode frustrates the backward Bragg scattering from the grating by destructive interference of its two constituent submodes (which are eigenmodes of a uniform waveguide). It can be used in a new type of spatial mode conversion in optical guides.     

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.     

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.     

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 periodic arrays separated by a gap

Two strong simultaneous resonances of scattering – double-resonant extremely asymmetrical scattering (DEAS) – are predicted in two parallel, oblique, periodic Bragg arrays separated by a gap, when the scattered wave propagates parallel to the arrays. One of these resonances is with respect to frequency (which is common to all types of Bragg scattering), and another is with respect to phase variation between the arrays. The diffractional divergence of the scattered wave is shown to be the main physical reason for DEAS in the considered structure. Although the arrays are separated, they are shown to interact by means of the diffractional divergence of the scattered wave across the gap from one array into the other. It is also shown that increasing separation between the two arrays results in a broader and weaker resonance with respect to phase shift. The analysis is based on a recently developed new approach allowing for the diffractional divergence of the scattered wave inside and outside the arrays. Physical interpretations of the predicted features of DEAS in separated arrays are also presented. Applicability conditions for the developed theory are derived.     

Diffraction from angular multiplexing slanted volume hologram gratings

The diffraction characteristics of the volume holographic gratings made by multiexposures with angular multiplexing during its construction is investigated. Because of the reflection by the interface between the emulsion and the substrate or the air there is an extra unslanted periodic structure inside a slanted grating, it will affect properties of the slanted volume holographic gratings. When the angle between the surface of the substrate and the grating plane of the slanted grating is less than a certain value, an extra peak accompanying the main peak will appear in the diffraction spectrum. But, when the angle is larger than the certain value, one designed and expected main peak will disappeared while the extra peak is kept and observed. This phenomenon limits the capacity of the volume hologram for the application in wavelength-division multiplexing (WDM).     

Integration of optical pulses by resonant diffraction gratings

The possibility of integrating optical pulses by resonant diffraction gratings has been considered. It has been shown that a diffraction grating provides integration of the pulse envelope in the vicinity of quasiguided-mode resonances. The integration is performed with an exponential weight function, whose decay rate is deter-mined by the quality factor of the resonance. Metallic diffraction gratings for integration of picosecond pulses have been computed. The calculation of the grating eigenmodes with the use of the scattering-matrix method has shown that the integration is performed in the vicinity of the resonances corresponding to the excitation of surface plasmon polaritons at the grating boundary. According to the results of numerical simulation, the integration quality is quite high.     

Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses

We present volume Bragg gratings (VBGs) with a period of 1.075 μm inscribed in fused silica using a femtosecond laser and a phase mask. The femtosecond-inscribed VBGs can be used as reflecting elements with reflectivities of about 80% for a 1-mm-long grating. Due to the non-sinusoidal refractive-index shape, higher order Bragg resonances up to the 7th reflection order could be measured. Therefore, the Bragg gratings also reflect light in the visible-wavelength range.     

73-nm tuning of a double-clad Yb<Superscript>3+</Superscript>-doped fiber laser based on a hybrid array

We report on a wide wavelength tuning in a double-clad ytterbium-doped fiber laser. The laser cavity consists of an array of broadband high-reflection fiber Bragg gratings and a bulk grating as the output coupler and wavelength selection element. The proposed fiber laser configuration combines a low intracavity loss of the fiber Bragg grating mirrors with a wide wavelength tuning of the bulk gratings. We demonstrate a >70-nm wavelength tuning range, limited only by the available fiber Bragg gratings.     

Raman gap solitons

We show that an intense pump pulse, detuned far from the Bragg resonance of a nonlinear periodic structure, can excite a gap soliton at a wavelength within the band gap that corresponds to the Raman shift of the medium. This Raman gap soliton is a stable, long-lived, quasistationary excitation that exists within the grating even after the pump pulse has passed. We find both stationary solitons as well as slow Raman gap solitons with velocities as low as 1% of the speed of light. The predicted phenomena should be observable in fiber Bragg gratings and other nonlinear photonic band gap structures.     

Real-time observation of Bragg grating formation in As2S3 chalcogenide ridge waveguides

Real-time study of the formation of Bragg gratings in monolayer As₂S₃ ridge waveguides is presented. A transverse holographic method is used to record such gratings. The periodic photodarkening of the layer leads to the formation of a Bragg grating with resonant wavelength 1.55 μm. The experiment allowed to control in situ the grating parameters such as the reflectivity, the resonant wavelength (between 1500 and 1630 nm) and the bandpass at −3 dB.     

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.     

X-ray Bragg diffraction on periodic surface gratings

We report on the X-ray Bragg diffraction analysis of periodic surface gratings on (100) GaAs crystals. We show that the X-ray Bragg diffraction is a very powerful method to investigate ultrafine surface gratings and allow us to determine not only the grating period but, in particular, the width of the grooves and to characterize the quality of the sidewalls, which is not easily possible with optical methods. The X-ray diffraction on surface crystal gratings is analogue to the Fraunhofer diffraction of multiple slits or reflection gratings.     

Scattering of ultrashort electromagnetic pulses on metal clusters

We have calculated and analyzed the probability of ultrashort electromagnetic pulse (USP) scattering on small metal clusters in the frequency range of plasmon resonances during the field action. The main attention is devoted to dependence of the probability of scattering on the pulse duration for various detunings of the USP carrier frequency from the plasmon resonance frequency. Peculiarities of the USP scattering from plasmon resonances with various figures of merit are revealed.