Double grating systems with one steel tape grating

Steel tape gratings are used in different metrology applications. As the period of these gratings was large (around 100μm,), its analytical study has been performed, up to date, using a geometrical approach. Nowadays, steel tape gratings can be manufactured with lower periods, around 20-40 μm, and diffractive effects must be taken into account. Also, due to the roughness of the surface, statistical techniques need to be considered to analyze their behavior. In this work, an analysis of the pseudo-imaging formation in a double grating system including one steel tape grating is performed. In particular Moiré and Lau configurations are analyzed. We have found that roughness significantly affects to Moiré configuration. However, its effect is negligible in Lau configuration. Generalized grating imaging configuration is also studied in depth. It is shown that roughness does not affect to the contrast of pseudoimages, but it modifies their depth of focus.     

Talbot effect in metallic gratings under Gaussian illumination

Metallic gratings can be found in applications such as optical metrology. Due to their fabrication process, the surface presents a certain roughness. In this work, the effect of roughness on Talbot effect has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used in order to determine the intensity distribution in the near field. Contrast of the self-images is obtained and it is found that it decreases in terms of the distance between the grating and the observation plane. When the autocorrelation function of roughness presents a Gaussian behaviour, the diffracted beams are still Gaussian although some of their properties change. For example, the width of the diffracted beams increases with respect to the case of the standard chrome on glass gratings. On the other hand, the power of each diffracted beam is independent on the roughness properties of the surface.     

Sensitivity enhancement of surface plasmon resonance sensor using continuous film metallic gratings

A surface plasmon resonance (SPR) sensor based on continuous film metallic gratings is numerically investigated for enhance sensitivity. The results calculated by rigorous coupled-wave analysis (RCWA) present that interplays between localized surface plasmons and surface plasmons polaritons contribute to sensitivity enhancement. The sensitivity enhancement factor (SEF), which represents the influence of metallic grating, increased as the grating period decreased. In addition, several reflection dips can be achieved as the period of metallic grating increased. By double-dips method, the sensitivity SPR sensor based on continuous film grating-based is improved into 153.23°/RIU, which is more sensitive than conventional thin film-based SPR sensor in the same condition. The SPR sensor based on continuous film metallic gratings exhibits good linearity.     

Heterodyne polarimetry for mapping defects in lithography masks

A new optical technique based on the heterodyne polarimetry is developed for fast inspection of uniformity of lithography masks in semiconductor industry. Sub-wavelength periodical structure of a sample acts as a wire-grid polarizer, making both the amplitude and phase of the reflected laser beam dependent on geometrical dimensions and optical properties of the mask pattern. The heterodyne technology based on the cross-polarized two-frequency Zeeman laser is used to simultaneously measure the amplitude and the phase of the reflected laser beam. A two-dimensional map of spatial variations can be obtained via point-by-point scanning of the sample. The technique is applicable not only to exact periodical structures like diffraction gratings, but also to double-periodical patterns consisting of large number of periodically distributed small areas of sub-wavelength gratings. Theoretical background, simulation, and experimental results are presented.     

Diffraction gratings of isotropic negative-phase velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric-magnetic half-spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive- or the negative-phase velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings — the Rayleigh-hypothesis method, a perturbative approach, and the C formalism — are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half-space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.     

Design, Fabrication and Test of a Soft X-Ray Even-Order Transmission Grating

Most transmission gratings in the x-ray region work with their first orders and dispersion is limited by the line density achievable with current fabrication technology. We present a novel design of a two-dimensional x-ray transmission grating. The grating works with higher dispersion using its second orders, and the influence from first and third orders can be suppressed. A grating according to the novel design is fabricated and its diffraction performance is tested in comparison with a traditional x-ray transmission grating with the same line density. The novel grating could be especially useful when high dispersion is desired while the fabrication of high-density gratings becomes more difficult.     

Improvement of plasmonic field-matter interaction by subwavelength dielectric gratings

We experimentally and theoretically investigate that detection sensitivity in surface plasmon resonance (SPR) biosensors can be significantly enhanced by employing subwavelength dielectric gratings deposited on a gold film. The enhancement originates from an improvement of field-matter interaction: enhanced evanescent field intensity at the binding region and increased surface reaction area. Using a large-area SiO₂ grating array fabricated by nanoimprint lithography, experimental sensor performance measured by parylene film coating shows that the SPR substrates combined with a dielectric grating provide a notable sensitivity improvement compared to a conventional bare gold film. We also demonstrate that plasmon field can be more confined and enhanced at the dielectric gratings with a larger width. The proposed SPR structure could potentially be useful in a variety of plasmonic applications including high-sensitivity biosensors.     

Fabrication of blazed gratings by area-coded effective medium structures

Area-coded effective medium structures (ACES) are a recently presented novel type of diffractive structure. Because of their higher stability compared to 2D binary blazed gratings, they have the potential of a broader use in micro-optics applications. The first fabrication with electron-beam lithography validate the theoretical model of blazed ACES. The measured diffraction efficiencies are in very good agreement with the values obtained from rigorous electromagnetic analysis.     

Total internal reflection diffraction grating in conical mounting

The main conditions and parameters for obtaining surface relief total internal reflection diffraction gratings in conical mounting are presented. Calculated and experimental investigations reveal that there are ranges of grating periods, incidence angles, diffraction angles and gratings depths for which such gratings could be obtained, both for TE and TM polarizations. With optimized grating parameters the diffraction efficiency of the total internal reflection diffraction gratings can be greater than 90%.     

Photonic nanojet modulation by elliptical microcylinders

The detailed analysis of localized photonic nanojets generated at the shadow side surfaces of dielectric elliptical microcylinder illuminated by a plane wave is reported. We have studied the distribution of the electric energy density within and in the vicinity outside an elliptical microcylinder by using finite-difference time-domain calculation with high resolution. The location of photonic nanojet depends on the radius ratio of the microcylinder. We have further analyzed the effect of the rotation angle of elliptical microcylinder upon the focal length of photonic nanojets. The horizontal and vertical shifts of photonic nanojet can be changed by rotating the rotation angle of elliptical microcylinder. The mechanisms of elliptical microcylinder may supply a new ultra-lens approach to distinguish nanoscale targets such as nanoparticles, optical gratings, and nanoscale surface roughness.     

Fabrication of planar gratings by direct ablation using an ultrashort pulse laser in a common optical path configuration

Planar gratings have wide applications and to date, many methods for the fabrication of gratings have been reported. Ultrashort pulse lasers have been used for the machining of gratings primarily because they allow direct ablation and the manufacturing of sub-wavelength structures. In this paper, we present a novel direct ablation technique for the fabrication of planar gratings which makes use of the interference of ultrashort pulses in a common optical path configuration. This technique of grating fabrication not only simplifies the optical setup, but also immunizes the system to extraneous and inherent vibrations, thus enabling the manufacturing of planar gratings of good edge acuity. We have successfully fabricated planar gratings on a copper substrate. Received: 6 November 2001 / Accepted: 4 March 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +65/77-904-674, E-mail: mvenkata@ntu.edu.sg     

Temperature-Insensitive Fibre-Optic Acceleration Sensor Based on Intensity-Referenced Fibre Bragg Gratings

A temperature-insensitive acceleration sensor using two fibre Bragg gratings （FBGs）, based on reflection spectrum intensity modulation and optical power detection, is proposed and demonstrated. A cantilever beam is used to generate acceleration-induced axial strain along two sensing gratings, which are glued on the two opposite surfaces of the beam. Because the two gratings operate within the linear spectral range of a light source, formed by a thermally-tunable extrinsic Fabry-Perot optical filter, the intensity difference of the two reflections from the gratings is proportional to the acceleration applied. This eliminates the need for sophisticated wavelength interrogation of the gratings, and it also endows the sensor with immunity to temperature variation. Compared with a commercial micromachined accelerometer, the sensor is proven to be capable of accurately detecting acceleration.     

Transport and photoinduced properties in highly Sr-deficient manganite films

We used the method of finite-difference time domain (FDTD) to study the characteristics of the patch antenna based on a novel periodic structure, and the theory of photonic crystal structure (also photonic band gap [PBG]) structure was introduced. The results obtained show that the surface waves propagating along the substrate surface can be suppressed by the periodic structure due to the influence of its forbidden band, and the energy of the electromagnetic waves is concentrated mainly in the substrate. As a result, the patch antenna based on the periodic structure has a wider bandwidth in comparison with the conventional patch antennae; and a higher gain is reached, so the patch antenna’s performance is improved. Due to such the advantages, the application of patch antennae can be extended in such fields as mobile communication, satellite communication, aviation, etc.     

Considerations to Rayleigh’s hypothesis

In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh’s approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh’s approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called “Rayleigh’s hypothesis” as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green’s function formulations of Huygens’ principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh’s hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann’s point of view and free of problems with Rayleigh’s hypothesis. But the obtained results show that Lippmann’s argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh’s hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach.     

Profile measurement of a moving object using an improved projection grating phase-shifting profilometry

3-D profile measurement of a moving object using a novel phase-shifting technique is introduced. Digital gratings with two steps phase-shifting are projected periodically onto a measured object surface. The deformed fringe patterns are captured by a frame CCD camera within a short exposure time. By synchronizing the projector and the CCD camera accurately, there is an overlapping part which is the same part of the object among three neighbouring frames. The length of an overlapping part can be controlled as one third of a frame length. Hence the intensity values at the same surface point modulated by three neighbouring gratings can be obtained, and its phase value can be computed by an improved phase-extracting algorithm. The profile of a specimen is detected by the proposed method. Experimental results demonstrate that this method is effective for the profile measurement of a moving object.     

复合金属光栅模式分离与高性能气体传感器应用

为实现近红外波段表面等离子体共振(SPR)模式的分裂和移动, 同时提高光栅基SPR传感器的品质因数, 提出了一种由双金属光栅构成的新型复合结构光栅, 并研究了其气体传感特性. 运用有限时域差分算法对该结构进行了数值模拟, 发现由复合金属光栅激发的SPR出现模式分裂的现象. 通过增大双金属光栅阵列间的相对位移改变原结构的对称性, 导致复合金属光栅分裂的SPR模式朝相反方向移动. 当相对位移量进一步增大到双光栅合并成新的单一光栅时, 随光栅结构对称性的恢复, 分裂的两共振模式最后又重新合并为一个模式. 如果待测物的折射率为1.01≤n_a≤1.05, 当相对位移量为0时, 基于复合光栅结构气体传感器的折射率灵敏度为1207.5 nm/RIU, 且品质因数达到1290.7; 当相对位移量为100 nm时, 与双共振模式对应的折射率灵敏度分别为1205.0 nm/RIU和1210.0 nm/RIU, 品质因数分别为1295.4和762.3. 因此, 复合光栅SPR传感器具有超高品质因数的性能, 使得它在生物化学传感领域中有巨大的应用潜力.     

Ray picture of diffraction gratings

We elaborate on a geometrical picture of diffraction gratings. Exact paraxial propagation including coherence effects is obtained by allowing the geometrical rays to transport Wigner function instead of simply specific intensity. We apply this formalism to perfect and less than perfect gratings, illuminated by plane and Gaussian waves.     

Plasmon resonances in deep nanogrooves of reflective metal gratings

Metallic gratings with very deep and narrow grooves are fabricated and their reflection spectra are characterized, which explicitly show high-order standing-wave-like resonances of surface plasmons in the cavity of nanogrooves. The effect of in-plane surface plasmon resonance is also observed, which is shown to have only a minor role on the reflection of such gratings, unlike that for shallow gratings. Using numerical simulations, the cavity resonances and their effects on the reflection of the gratings are identified and further analyzed. As field is more enhanced in the nanogrooves under cavity resonance conditions, the enhancement is also found to be dependent on the grating period, i.e. the strongest enhancement takes place for higher-order resonance modes for smaller grating period. For gratings with shallower grooves, comparable enhancement of field is also achievable by proper design of the grating period. The study suggests that field enhancement can be realized at selective wavelengths in a wide spectrum range using cavity resonances in the deep nanogrooves of metal gratings, and the position for field-enhancement can be tuned by the depth and period of the gratings.     

Characteristics of light emission from surface plasmons based on rectangular silver gratings

We investigated the characteristics of transmitted light from propagating surface plasmons based on rectangular silver gratings. The results calculated by rigorous coupled-wave analysis presented that silver diffraction gratings can produce significant transmittance and conversion efficiency, comparable to the case of dielectric gratings. Especially, silver gratings optimized at a wide range of grating thickness and period may lead to an improved diffraction efficiency larger than 64%. Moreover, the effect of silver oxide layer on the transmittance was examined and a bimetallic structure with a thin gold coating was introduced to prevent an oxidation of silver substrates. As a practical sensor application, silver grating-based surface plasmon resonance (SPR) configuration showed an enhanced sensitivity associated with an increase of surface reaction area and strong excitations of local plasmon fields, outperforming a conventional thin-film-based SPR structure.     

光纤布喇格光栅沉降传感器

根据光纤布喇格光栅的光学传感原理,提出了一种基于悬臂梁及金属弹性膜片的光纤布喇格光栅沉降传感器结构,对其传感特性进行了实验研究.实验通过产生水的液位差来模拟地基沉降,分析结果显示,光纤布喇格光栅中心反射波长漂移对液位差呈现良好的线性关系,线性度高于0.999,灵敏度可达-2.11 pm/mm.通过改变悬臂梁厚度和有效长度,可以对传感器测量范围和灵敏度进行调整,以满足各种应用场合.综合实验结果,该传感器在桥梁、铁路地基等沉降监测方面具有重要意义.