Numerical analysis of plasmon-resonance absorption in bisinusoidal metal gratings

We numerically investigate plasmon-resonance absorption of incident light energy by a bisinusoidal metal grating, i.e., one whose surface profile is sinusoidally corrugated in two orthogonal directions with a common period. Employing Yasuura's modal expansion method, we solve the problem of plane-wave diffraction by the grating and evaluate the absorption, which is observed as dips in diffraction efficiency curves. We examine the field distribution and energy flow in detail at the angles of incidence at which the absorption occurs. We show that the absorption is caused by coupling of the TM component of an evanescent order with surface plasmons. A phase-matching condition is used in the prediction of the incident angle at which the absorption occurs. This, together with the field profile in the presence of the resonance absorption, explains the mechanism of the absorption. We then illustrate interesting features of the absorption: enhancement of polarization conversion between the incident light and the reflected light and simultaneous excitation of two plasmon waves in directions that are symmetric with respect to the plane of incidence.     

The Diffraction Efficiency of Double-grating Holographic Fan-out Elements

Abstract

An analytical expression is derived for the diffraction efficiency of a holographic fan-out element containing two superimposed gratings separated by a small angle. In addition to the usual zero and first orders an infinite set of the significant spurious waves is considered. In deriving the expression all these spurious waves are assumed to satisfy the Bragg condition exactly. The results are compared with a direct numerical solution and give very good agreement for angles up to 1°. Furthermore the analysis provides useful information for angles up to 5°. An analogy is drawn with a hybrid hologram consisting of a thick ‘carrier’ grating and a thin ‘modulation’ grating. Using this model the diffraction efficiencies can be calculated using the standard grating formulae. For fan-out applications the spurious waves around the first orders are considered the most important. From this analysis it can be seen that they can be made negligibly small but at the cost of a reduction in total diffraction efficiency.     

Transmittance analysis of diffraction phase grating

In order to accurately analyze and design the transmittance characteristic of a diffraction phase grating, the validity of both the scalar diffraction theory and the effective medium theory is quantitatively evaluated by the comparison of diffraction efficiencies predicted from both simplified theories to exact results calculated by the rigorous vector electromagnetic theory. The effect of surface profile parameters, including the normalized period, the normalized depth, and the fill factor for the precision of the simplified methods is determined at normal incidence. It is found that, in general, when the normalized period is more than four wavelengths of the incident light, the scalar diffraction theory is useful to estimate the transmittance of the phase grating. When the fill factor approaches 0.5, the error of the scalar method is minimized, and the scalar theory is accurate even at the grating period of two wavelengths. The transmittance characteristic as a function of the normalized period is strongly influenced by the grating duty cycle, but the diffraction performance on the normalized depth is independent of the fill factor of the grating. Additionally, the effective medium theory is accurate for evaluating the diffraction efficiency within an error of less than around 1% when no higher-order diffraction waves appear and only the zero-order waves exist. The precision of the effective medium theory for calculating transmittance properties as a function of the normalized period, the normalized groove depth, and the polarization state of incident light is insensitive to the fill factor of the phase grating.     

Diffraction of a one-dimensional phase grating in the deep Fresnel field

We analyze theoretically the diffraction of phase gratings in the deep Fresnel field on the basis of the theory of scalar diffraction and Green's theorem and present the general formula for the diffraction intensity of a one-dimensional sinusoidal phase grating. The numerical calculations show that in the deep Fresnel region the diffraction distribution can be described by designating three characteristic regions that are influenced by the parameters of the grating. The microlensing effect of the interface of the phase grating provides the corresponding explanation. Moreover, according to the viewpoint that the diffraction intensity distribution is the result of the interference of the diffraction orders of the grating, we find that the diffraction patterns, depending on the carved depth of the phase grating, are determined by the contributing diffraction orders, their relative power, and the quasi-Talbot effect of the phase grating, which results from the second meeting of the diffraction orders carrying most of the power of the total field, as in the case of the amplitude grating.     

Aberrations of diffracted wave fields: distortion

Near-field diffraction patterns are merely aberrated Fraunhofer diffraction patterns. These aberrations, inherent to the diffraction process, provide insight and understanding into wide-angle diffraction phenomena. Nonparaxial patterns of diffracted orders produced by a laser beam passing through a grating and projected upon a plane screen exhibit severe distortion (W311). This distortion is an artifact of the configuration chosen to observe diffraction patterns. Grating behavior expressed in terms of the direction cosines of the propagation vectors of the incident and diffracted orders exhibits no distortion. Use of a simple direction cosine diagram provides an elegant way to deal with nonparaxial diffraction patterns, particularly when large obliquely incident beams produce conical diffraction.     

Self-pumped phase-conjugate interferometer with a photorefractive iron-doped lithium-niobate crystal

A single object wave is amplitude divided by a beam splitter into two waves of equal intensity that are made to interfere at the back surface of an iron-doped lithium-niobate crystal so that the normal to the back surface is the angular bisector of the input waves. The interference results in the formation of a phase grating (Bragg grating) in the volume of the crystal. These waves are diffracted at the Bragg grating on both the front focal plane and the back focal plane of the crystal. The wave diffracted in the back focal plane from the Bragg grating and counterpropagating to the incident wave is observed to be the phase conjugate of the input object wave. The wave diffracted in the front focal plane of the Bragg grating is incorporated into the design of an interferometer to measure a specific in-plane displacement of the object wave. It is theoretically evaluated and experimentally demonstrated that interferometers such as those that incorporate conjugate-wave pairs are highly sensitive.     

A computational inverse diffraction grating problem

Consider the diffraction of a time-harmonic plane wave incident on a perfectly reflecting periodic surface. A continuation method on the wavenumber is developed for the inverse diffraction grating problem, which reconstructs the grating profile from measured reflected waves a constant distance away from the structure. Numerical examples are presented to show the validity and efficiency of the proposed method.     

Diffraction Anomalies and Backscattering Resonance from an Echelette Grating

The solution to the problem of diffraction of parallel and perpendicularly polarized waves from an echelette grating is discussed with special emphasis on diffraction anomalies. Two new kinds of anomalies are described. The first kind occurs when the phase change of the incident wave over the groove is equal to a multiple of π, while the second kind occurs when this phase change is equal to an odd multiple of π /2. The first kind can coincide with a double Rayleigh anomaly, which for a perpendicularly polarized wave then results in an amplified anomaly. If, additionally, one of the grazing orders in the double Rayleigh anomaly is +1, a resonant-type anomaly results. This resonance anomaly could be utilized in a laser cavity or for the purpose of spectral or spatial filtering.     

Observation of self-diffraction effect in acid blue 7 dye soaked gelatin films

Abstract

Permanent self-diffraction gratings are formed in red sensitive Acid blue 7 dye soaked gelatin films under illumination of an interference pattern by two linearly polarized beams from a He-Ne laser at 632.8 nm. Growth of the self-diffraction grating is monitored by measuring intensities of various diffraction orders. Systematic studies are carried out to investigate the influence of various parameters involved in diffraction efficiency of the grating such as time of exposure, concentration of dye in the gelatin-coated plate, intensity of interfering beams and intensity ratio of interfering beams. Efficient gratings with ten diffracted orders are formed. Several interesting observations are made by blocking one of the writing beams and an attempt is made to analyse these results.     

Simple measuring technique for the diffraction efficiency of slanted volume gratings at various wavelengths

To measure diffraction efficiencies of gratings as a function of wavelength, it is necessary to have quasi-monochromatic light sources of various wavelengths. We propose a method to measure the wavelength dependence of the grating diffraction efficiency by using a quasi-monochromatic light source. This method of estimating the real diffraction characteristics of the gratings for various wavelengths is very useful and simple. First the diffraction efficiency of the grating as a function of various incident-beam angles of monochromatic light is measured, then, using these data, we can obtain the diffraction efficiencies for various wavelengths of the same incident angle of light by virtue of a mathematical-conversion method. The mathematical-conversion results for two laminated differently slanted angle gratings of the same volume grating period are in good agreement with the experimental ones.     

High transmission efficiency for surface plasmon resonance by use of a dielectric grating

The efficiency of the transmission of surface plasmon waves by use of a dielectric diffraction grating is discussed. The Kretschmann device allows us to obtain a surface plasmon resonance that consists of an absorption peak in the reflection spectrum. When surface plasmon resonance occurs, the TM-polarization mode of the incident electromagnetic wave is neither transmitted nor reflected. The procedure to transform an 4bsorption peak into a transmission peak is described. Transmittivity of 68% is obtained for a simple structure that consists of a thin-film layer of Ag coated on a volume diffraction grating and embedded between two dielectric media. The results presented herein were obtained by numerical simulations that were carried out by use of an algorithm based on the rigorous coupled-wave theory.     

Analysis and simulations of two-wave mixing in photopolymer holographic recording media

Abstract

The process of two-wave mixing in photopolymer recording materials was investigated theoretically. The diffraction grating already forms during exposition and it may influence the original interference field distribution through diffraction of waves on the refractive index modulation. In order to show this, Kogelnik's coupled wave theory was extended to demonstrate the possibility of energy transfer from one recording wave to the other. The energy transfer and the intensity distribution during the recording process were systematically analysed depending on the boundary conditions. As a next step, the first harmonic model of the transmission grating recording, based on a simple material model, was implemented and solved. The ratio of the input intensities was found to be a crucial parameter and thus extensive simulations for various ratios of intensities were carried out. Modelling implies that the interference field and the refractive index grating just coincide for equal intensities. For intensities differing from unity they do not overlap themselves during the recording process. It has also turned out that the diffraction efficiency of the recorded grating drops against the case where the effects of two-wave mixing are not considered. The results of our analysis and simulation help give a better understanding of the physics of the recording process and proper adjustment of recording parameters in such applications as optical holography and holographic memories.     

Optimization of the parallelogrammic grating diffraction efficiency for normally incident waves

The diffraction directivity of parallelogrammic gratings with second-order pitch is examined for a plane wave normally incident upon a corrugated waveguide structure. The three diffracted components are assumed to be in the form of guided waves, which permits a self-consistent calculation. The efficiencies of diffraction into the horizontal components are obtained. Also, the dependence of efficiency on grating thickness, waveguide thickness, grating pitch, and angle of inclination is determined. The approach provides a useful simulation tool for optimizing the design parameters for waveguide couplers with an orthogonal source.     

Four-level phase grating generated by combination of two binary gratings through coherent imaging

With the aim of steering as much incident light power in the +1 diffraction order as possible and suppressing the power in the -1 order, we generated an effective four-level grating by coherently imaging a 180 degrees binary-phase grating onto a 90 degrees phase grating. The periods of the gratings were well matched. The measured overall power fractions in the +1 and -1 orders were 54% and 2%, respectively.     

Analysis of the transmission characteristics of an internal reflection microstructure grating

The transmission characteristics of an internal reflection grating primarily integrated into light-emitting diodes are numerically calculated and optimized by using rigorous coupled-wave analysis (RCWA). The obvious polarization effect of the near field distribution is demonstrated. To easily analyze the transmittance performance of the internal reflection grating, simple methods involving scalar diffraction theory and effective medium theory are used. The validity of both methods is quantitatively evaluated by comparing the transmittance results obtained using the simple methods and RCWA. The limitation of both simple methods mainly depends on the grating structure parameters, such as the normalized period and normalized groove depth. Generally, when the dimensions of the normalized period is more than twofold wavelengths of incident light, the scalar treatment can be used to calculate precisely the transmittance of the optical element within 5% error. Also, the validity of the scalar theory is slightly influenced by the change in incident angle. The effective medium theory is accurate for evaluating the transmittance within 1% error when higher-order diffraction waves other than zeroth-order waves do not propagate.     

Calibration of an extreme-ultraviolet transmission grating spectrometer with synchrotron radiation

The responsivity of an extreme-ultraviolet transmission grating spectrometer with silicon photodiode detectors was measured with synchrotron radiation. The spectrometer was designed to record the absolute radiation flux in a wavelength bandpass centered at 30 nm. The transmission grating had a period of 200 nm and relatively high efficiencies in the +1 and the -1 diffraction orders that were dispersed on either side of the zero-order beam. Three photodiodes were positioned to measure the signals in the zero order and in the +1 and -1 orders. The photodiodes had aluminum overcoatings that passed the desired wavelength bandpass centered at 30 nm and attenuated higher-order radiation and wavelengths longer than approximately 80 nm. The spectrometer's responsivity, the ratio of the photodiode current to the incident radiation power, was determined as a function of the incident wavelength and the angle of the spectrometer with respect to the incident radiation beam. The spectrometer's responsivity was consistent with the product of the photodiode responsivity and the grating efficiency, both of which were separately measured while removed from the spectrometer.     

Nonparaxial scalar treatment of sinusoidal phase gratings

Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where lambda/d>0.1. It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

带有力反馈控制的三明治式微机械干涉加速度计

设计了一种静电力反馈控制的三明治式微机械干涉加速度计,加速度计由敏感芯片、半导体激光器、光电二极管以及相应的驱动电路和反馈控制电路组成.敏感芯片为玻璃-硅-玻璃3层结构,通过硅-玻璃键合体硅工艺制成.硅质量块由铝梁支撑,底部玻璃基片上有金属光栅和电极,通过在质量块和底部玻璃基片上的电极之间施加电压可以调节质量块与玻璃基片间的间隙.入射激光照射到敏感芯片上的光栅上,产生衍射光束,其光强随质量块与下玻璃的间距而变化.反馈控制电路通过测量衍射光强的变化来改变质量块与底电极之间的电压,使得质量块与底部玻璃基片的距离保持为入射光波长1/8的奇数倍,从而提高输出线性度,改善灵敏度,增大量程.     

Polarization properties of inversely twisted nematic liquid-crystal gratings

Based on the Jones matrix representation of twisted nematic liquid crystals (LC's), we have carried out a theoretical analysis of the polarization properties of inversely twisted nematic (ITN) LC gratings. Some interesting polarization behaviors are expected in the ITN LC grating. When a linearly polarized light parallel or perpendicular to the grating direction is incident on the ITN LC grating, the diffracted light in the 0th order is linearly polarized with the same polarization direction of incident light, while the diffracted light in high orders is linearly polarized perpendicular to that of incident light. Using a multirubbing alignment technique, we have practically prepared an ITN LC grating with ?45 degrees inversely twisted structures. The experimental investigations of the optical characteristics of the ITN LC grating demonstrate agreement with theoretical expectations.