利用泽尼克系数求取衍射光栅的分辨本领

光栅分辨本领检测设备的焦距通常达几米甚至十几米,采用直接测量法难度大、成本高,利用衍射波前间接求取光栅分辨本领是解决该问题的有效途径之一。在光栅光谱成像傅里叶变换理论基础上,建立了利用泽尼克多项式拟合系数求解衍射光栅分辨本领的归一化模型,揭示了光栅衍射波前与分辨本领的求取关系,提出了依据泽尼克多项式拟合系数求取衍射光栅分辨本领的新方法。根据该方法实测了一块衍射光栅的分辨本领,并与直接测量法进行对比测试。结果表明该方法误差小于4.42%,降低了分辨本领的测试难度,是衍射光栅分辨本领求取的有效手段,应用于ZYGO干涉仪等仪器中,通过简单的波前测试即可得到定量的衍射光栅分辨本领指标。     

波前相位编码体光栅选择性衍射的理论分析

阐述了波前相位复用技术记录和再现体全息光栅的原理;运用波耦合理论,从衍射波的一阶微分方程推导出多重体光栅对随机波前相位的选择性衍射;构造了一个复随机过程函数,并利用其相关函数得到了随机波前相位编码体光栅实现无串扰再现的充分必要条件;给出了理论上分析多重体光栅对随机波前相位选择性衍射的一种方法.     

Long-period fiber gratings fabricated with a CO2 laser beam and phase mask

A new holographic technique is proposed for fabricating long-period fiber gratings (LPGs) using a CO₂-laser and a phase mask. A CO₂ laser operating at 10.6 μm is incident normally on the phase mask and the diffracted interfering beams imprint a thermally induced periodic modulation into the cladding of the fiber placed behind the mask. Preliminary results of this technique are presented and discussed. An unusual self-tapered fiber LPG (STFLPG) is also presented.     

Spectral characterization of fiber gratings with high resolution

We demonstrate a high-resolution technique to measure the optical magnitude and phase responses of fiber gratings. The technique employs single-sideband modulation of an optical source and has spectral resolution in the hertz regime. The technique is demonstrated by measurement of the phase ripples of unapodized and apodized chirped gratings as well as the transmission spectrum of a pi-phase-shifted grating. Although it is demonstrated on fiber gratings, the technique is applicable to any optical device.     

The influence of the polarization effect in Talbot self-imaging of high-density gratings

The Talbot self-imaging of high-density gratings with different period at half Talbot distance for different polarization is analyzed with the finite-difference time-domain (FDTD) method. The numerical results indicate that the Talbot self-imaging of high-density gratings is obviously different for different polarization when the period d of the grating between 2λ and 3λ, which is verified through experimental results with the scanning near-field optical microscopy (SNOM) technique. Furthermore, the Fourier spectrum (far field) generated by the gratings is also given with the rigorous coupled-wave method, which is in agreement with the near field.     

Power penalty of cascaded Bragg gratings in the presence of PMD and PDL

Considering the presence of birefringence in Bragg gratings, the spectral polarization mode dispersion (PMD) and polarization dependent loss (PDL) induced power penalty of eye opening is examined for a network with cascaded Bragg gratings. It is shown that when the birefringence in the grating is less than 10⁻⁵, the induced power penalty is less than 0.1 dB for a network with up to 30 cascaded Bragg gratings. However, when the grating birefringence is on the order of 10⁻⁴, the induced power penalty can be as high as 5.6 dB for a network with 14 cascaded Bragg gratings.     

A high-resolution spatial heterodyning interference spectrometer

A novel spectrometer which has a resolution of 0.013 nm with high throughput is described. The system uses a Michelson interferometer in which the mirrors have been replaced with Littrow-mounted diffraction gratings. First-order diffracted beams returning from the gratings interfere at the interferometer output to produce a spatial interferogram which is heterodyned about an optical frequency determined by the setting angles of the gratings. The heterodyning process leads to increased resolution, but limits the free-spectral range of the instrument to, in our case, about 3 nm. This is sufficient for characterizing narrow-band sources such as laser diodes. We present the theory of operation of the instrument and some sample spectra obtained from a sodium vapor lamp, a HeNe discharge, and a 670 nm diode laser.     

Study on measuring refractive index modulation of volume phase holographic gratings

In this paper, we present an approach to measure the refractive index modulation of volume phase holographic gratings (VPHG) by use of its angular selectivity, with the advantage of avoiding the diffraction efficiency errors induced by noise. Based on Kogelnik's coupled wave theory for volume holographic gratings, the wave vectors matching relationship for reflective VPHG at different readout wavelengths is deduced and the diffraction efficiency as a function of readout angle is also obtained. Then an all-fiber experimental system is designed to measure corresponding diffraction efficiency with different readout angles for VPHG recorded in dichromate gelatin. By seeking the Bragg angle where diffraction efficiency is maximum and the blank angle where diffraction efficiency drops to the minimum value, the refractive index modulation can be calculated. The experiment results proves the feasibility of the method.     

I型全息凹面光栅制作误差对光谱像的影响分析

通过对I型全息凹面光栅制作参量误差对光谱像的影响进行数值计算发现|1)两记录臂长的相对误差而不是绝对误差决定光谱像的展宽程度,即使绝对误差较大,只要两记录臂长的误差值相同,像宽也没有明显改变|2)由于I型光栅的记录臂一般较长,记录角度误差对像宽的影响不大,但会影响光栅的刻线密度,导致光谱成像位置的偏移|3)曲率半径误差对像宽的影响较大.通过数值模拟明确了I型全息凹面光栅制作的误差容许范围,找到了对光谱像宽度影响较大的误差来源,从而为此类光栅的制作提供理论指导,有助于制作出高质量光栅,降低罗兰圆光谱仪的调节难度.     

New reformulation of the Fourier modal method with spatial adaptive resolution for multilayered metallic strip grating

The parametric formulation of the combined boundary conditions method (CBCM) with spatial adaptive resolution is extended to multilayered structures of strip gratings. Furthermore, it is shown that it is not necessary to solve the eigenvalue problem in all the layers of these structures; leading to drastic reduction of the computational load.     

Modelling the diffraction of laser-cooled atoms from magnetic gratings

The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets. Received 13 June 2000 and Received in final form 15 December 2000     

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.     

Period interaction on diffraction efficiency of blazed transmission gratings

The period interaction on diffraction of the blazed transmission gratings is analyzed with a modified extended scalar theory. For one certain period, the lights reflected from the neighboring structures can be refracted by the grating facets and form two extra fields on the bottom facet of blazed transmission gratings. The effects of this period interaction versus several diffraction orders for a fixed fabrication error of blazed transmission gratings with intermediate structures are discussed for both TE and TM polarizations. The results have been compared with those obtained with finite-difference time-domain method.     

零像散宽波段平场全息凹面光栅的优化设计

平场全息凹面光栅的理想像面应为一平面,此时子午焦线与弧矢焦线均位于像面内且彼此重合,形成接近理想像点的光谱像。但子午焦线总是存在弯曲,只有弧矢焦线在满足一定条件的情况下可以成为直线。鉴于此,提出一种满足平场弧矢焦线条件的平场全息凹面光栅设计方法。利用光学设计软件ZEMAX研究了运用此方法设计的零像散光栅的成像特性,并与原有设计方法得到的结果进行比较。模拟结果显示,满足平场弧矢焦线条件的光栅能够达到与原有方法所设计光栅相当的光谱分辨率,而其全波段零像散特性使其拥有更加出色的弧矢方向聚焦性能,显著提高平场光谱仪的信噪比。     

Demonstration of two-point velocity measurement using diffraction grating elements for integrated multi-point differential laser Doppler velocimeter

We have proposed a configuration of an integrated multi-point differential laser Doppler velocimeter (LDV) using arrayed waveguide gratings (AWGs) as grating elements. This paper demonstrates two-point velocity measurement using the proposed configuration with diffraction grating elements. An experiment was conducted using a free-space optical setup with bulk diffraction gratings instead of AWGs. The experimental results indicate that velocities at different positions can be measured using the proposed configuration. The measured separation of the two measurement positions was about 20.5 mm, about 11% of the working distance.     

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the −1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems.     

Sub-wavelength imaging of photo-induced refractive index pattern in chalcogenide glass films

Mapping of refractive index patterns with sub-wavelength resolution is achieved using Near-field Scanning Optical Microscopy (NSOM) in reflection mode. Imaging of index pattern is performed on surface gratings photo-imprinted in As₂S₃ films. The NSOM is adapted with a near infrared laser which wavelength (785 nm) is chosen to be within the transparency window of the glass film therefore allowing consistent measure of reflected light. Quantitative measurements of photo-induced index changes can then be obtained from knowledge of the initial film index. Images of gratings with a period of 0.5 micron are easily collected therefore demonstrating sub-wavelength spatial resolution. The technique permits to concurrently obtain a topographic image and index image of the gratings thereby permitting to quantify the extent of photodarkening and photoexpansion simultaneously. It is shown that relief gratings tend to vanish in films aged in air for several months however the index gratings remain.     

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.     

High spectroscopic qualities in blazed ion-etched holographic gratings

Blazed ion-etched holographic gratings with a high absolute diffraction efficiency, good diffracted wavefront, high resolution, and low stray light have been produced. The performances were proved to be the same as, or superior to, commercially available blazed gratings produced by a ruling technique.     

High-power laser beam shaping by inseparable two-dimensional binary-phase gratings for surface modification of stamping dies

For surface modification of stamping dies, an inseparable two-dimensional binary-phase gratings is introduced to implement the wavefront transformation of high-power laser beams. The design and fabrication of the gratings are described in detail. Two-dimensional even sampling encoding scheme is adopted to overcome the limitations of conventional Dammann grating in the design of two-dimensional output patterns. High diffractive efficiency (>70%) can be achieved through the transformation of the Gaussian laser beam into several kinds of two-dimensional arrays in focal plan. The application of the binary-phase gratings in the laser surface modification of ductile iron is investigated, and the results show that the hardness and the wear resistance of the sample surface were improved significantly by using the binary-phase gratings.