Interferometric determination of refraction and dispersion of a birefringent material: numerical procedure

Air, liquid and solid sample interferometric gaps of the same thickness and simultaneously enclosed in a wedge interferometer are used to produce fringes of equal chromatic order. A mica sample of dimensions 2×5 mm² and an immersion liquid of the same refractive index are used. A single shot interferogram containing fringes in the three gaps is sufficient to deduce the needed experimental data. Locations of fringe maxima are introduced in a numerical procedure to retrieve the sample and liquid refractive indices across the visible spectrum. The numerical procedure is based on a simple dispersion function of wavelength and wavenumber. A modified two-term Sellmeier dispersion formula has been used for fitting the experimental data and deducing the needed dispersion parameters.     

Interferometric determination of refraction and dispersion of a birefringent material: non-numerical procedure

Fringes of equal chromatic order are produced in air, immersion liquid and mica sample interferometric gaps. The three gaps are of the same thickness and simultaneously enclosed in a wedge interferometer. A single-shot interferogram contains fringes in the three gaps is sufficient to deduce the needed experimental data. A non-numerical procedure is used for determining the refractive indices of the immersion liquid and mica sample across the visible spectrum. There is no need for any numerical fitting stage nor for the application of any theoretical model concerning the dispersion behavior of the sample under test. A modified two-term Sellmeier dispersion formula has been used for fitting the experimental data and deducing the needed dispersion parameters.     

Application of multiple-beam white-light fringes for measuring the refraction and dispersion of mica

Multiple-beam white-light interference fringes are applied to measure the two refractive indices of a mica sample and their dispersion across the visible spectrum. In addition, the mica birefringence and its dispersion are measured. A mica sample of dimensions 2 × 5 mm² and an immersion liquid of nearly the same refractive index are used. Only a single shot interferogram is needed to measure all the aforementioned parameters. Cauchy's and a modified single-term Sellmeier dispersion formula are used for fitting the experimental data and extracting the parameters required.     

各向异性介质的平行平板干涉

提出了各向异性介质平行平板干涉中的相位差计算方法.证明了e光干涉产生的条纹为严格的椭圆曲线,椭圆长短轴的比值等于o光主折射率与e光主折射率之比,而与晶体厚度、干涉级等参数无关.拍摄了实验干涉图,并用最小二乘法对干涉条纹进行椭圆曲线拟合,结果与理论完全一致.本文提出的方法可用于晶体主折射率比值的精确简便测量.     

High precision refractometry based on Fresnel diffraction from phase plates

When a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic parallel beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The visibility of the diffraction fringes varies periodically with changes in incident angle. The visibility period depends on the plate thickness and the refractive indices of the plate and the surrounding medium. Plotting the phase change versus incident angle or counting the visibility repetition in an incident-angle interval provides, for a given plate thickness, the refractive index of the plate very accurately. It is shown here that the refractive index of a plate can be determined without knowing the plate thickness. Therefore, the technique can be utilized for measuring plate thickness with high precision. In addition, by installing a plate with known refractive index in a rectangular cell filled with a liquid and following the described procedures, the refractive index of the liquid is obtained. The technique is applied to measure the refractive indices of a glass slide, distilled water, and ethanol. The potential and merits of the technique are also discussed.     

Slightly dispersive white-light spectral interferometry to measure distances and displacements

A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.     

有机材料在各种波长的折射率计算

使用Vogel方法和介质的色散关系,计算有机化合物在各波长的折射率n(λ).用Vogel方法把化合物分子分解成碎片,加和得到化合物在某几个波长的折射率.假设化合物在所计算的波长范围内为正常色散关系,使用Voyel方法得到的两个折射率,通过Cauchy公式得到色散曲线,从而得到各波长的折射率n(λ).通过对有机化合物芪盐和高分子材料聚苯乙烯的各波长折射率进行计算,并与材料在某一特定波长的实际折射率对比,证明了计算结果比较准确.并对双折射液晶材料的折射率计算进行了探索.     

四波混频实时光学检测

分析了利用掺铁铌酸锂晶体作介质的简并四波混频及其在干涉计量术中应用的原理,描述了被测透明样品的表面各光波及其干涉形成的透射条纹及反射条纹,利用光折变晶体的介电驰豫特性,求得透射条纹和反射条纹的对比度随时间变化的公式及各参数的相互关系。对由透射条纹及反射条纹计算被测透明物体样品折射率和厚度不均匀性的方法作了数学分析,提出一种新型四波混频实时测量透明物体的光学不均匀性的方法和实验光路,对相关参数对测量过程及测量结果的影响作了探讨,得到了平板玻璃样品的干涉条纹图像,计算出实验结果。     

Liquid refraction and dispersion measurements by multiple-beam white-light Newton's fringes

Multiple-beam white-light Newton's fringes in transmission are produced in a Newton's interferometer containing a liquid sample and followed with a grating spectrograph. An equation describing the shape of the formed interference fringes is derived. A simple procedure is introduced for analyzing the resulting interference fringes. This enables the determination of both: the liquid refractive index, the fringe order of interference and the thickness at the point of contact. Errors of the measured liquid refractive index are discussed. The method is used for measuring the refraction and dispersion of glycerin, dimethylformamide (DMF) and water across the visible spectrum. The method is a single-shot, static, material-economic and low-cost interferometric one.     

Group refractive index measurement by fringes of equal chromatic order

Fringes of equal chromatic order in transmission across a thin liquid or a thin solid sample inside a wedge interferometer, followed with a grating spectrograph, are produced. A single-shot interferogram of the air and sample regions is recorded. Locations of fringes maxima in the air region are fitted in a numerical procedure based on Cauchy's dispersion function. Then it is used for measuring the interferometric gap thickness. The order of interference in the sample region is represented by a third-order polynomial in the wavenumber for deducing the sample group refractive index. An error analysis of the measured group refractive index is given. The method is applied for measuring the group refractive index of water and mica samples across the visible spectrum. The method measures both the sample thickness and its group refractive index. It is static with no moving parts and suitable for thin liquid or solid samples without immersion liquids.     

基于反射和透射光谱的氢化非晶硅薄膜厚度及光学常量计算

采用紫外-可见透射光谱仪测量了对靶磁控溅射沉积法制备的氢化非晶硅（a-Si:H）薄膜的透射光谱和反射光谱.利用T/(1-R)方法来确定薄膜的吸收系数,进而得到薄膜的消光系数|通过拟合薄膜透射光谱干涉极大值和极小值的包络线来确定薄膜折射率和厚度的初始值,并利用干涉极值公式进一步优化薄膜的厚度值和折射率|利用柯西公式对得到的薄膜折射率进行拟合,给出了a-Si:H薄膜的色散关系曲线.为了验证该方法确定的薄膜厚度和光学常量的可靠性,将理论计算得到的透射光谱与实验数据进行了比较,结果显示两条曲线基本重合,可见这是确定a-Si:H薄膜厚度及光学常量的一种有效方法.     

New interferometric method for determining the refractive index of thin dielectric film,its thickness,the phase shift,and the order of interference

A new interferometric method is proposed, using white light fringes of equal chromatic order to determine simultaneously the following paramcters:

1. The refractive index of a thin dielectric film, and hence its dispersion.
2. The film thickness.
3. The correct value of the order of interference.
4. The phase shift occuring due to reflection at the dielectric/metal interface. In the present work, doubly silvered zinc sulphide (ZnS) thin dielectric film was used as an example in applying the proposed method.

     

Research technique of metamaterials with the controlled effective negative refractive index and their characteristics

A design of the two-beam hybrid microwave interferometer for measuring refractive indices of metamaterials is described. It is based on the branching of radiation using a waveguide directional coupler. Radiations of the interferometer waveguide arms are summed and the phase disbalance of the interferometer arms is counted on the waveguide measuring line. The frequency dispersion of the negative refractive indices of the metamaterial samples with a variable distance between its constituent plates is experimentally investigated. A possibility of controlling the refractive index of a metamaterial is demonstrated.     

Application of a liquid crystal spatial light modulator on optical roughness measurements by a speckle correlation method using two refractive indices

A system of roughness measurements using a CCD camera and a liquid crystal spatial light modulator (LCSLM) has been developed. The scattered light patterns from the surface, which is covered by liquids with several different refractive indices, are acquired by the CCD camera and stored in a frame grabber in a computer. The superposition of two arbitrary patterns is calculated by the computer and displayed on the LCSLM. It is then illuminated by coherent light to produce interference fringes of equal inclination at infinity. The surface roughness can be determined through the relationship between the fringe visibility and the difference of refractive indices. The performance of this system is estimated by experiments.     

LFI法测量半透明油的折射率

LFI方法曾被用来测量大直径光纤的折射率.用一半盛油一半为空气的毛细管代替光纤,并用聚焦的条形光束照射毛细管,空气与油的干涉条纹同时产生.根据空气的条纹可以确定参数b,根据一组已知折射率的标准样品可确定另一参数c,同时可以建立标准液体最外条纹的偏折角与折射率的标准曲线.对于未知折射率的样品,一旦测量出其最外条纹的偏折角,从标准曲线上就可以读出其折射率.实测了一组半透明油的折射率,其结果与阿贝折射仪测量结果接近.     

Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum

A method has been proposed for determining the optical properties of a thin film layer on absorbing substrates. The film optical parameters such as thickness, refractive index, absorption coefficient, extinction coefficient and the optical energy gap of an absorbing film are retrieved from the interference fringes of the reflection spectrum at normal incidence. The envelopes of the maxima of the spectrum E_M and of the minima E_m are introduced in analytical forms to find the reflectance amplitudes at the interfaces and approximate values of the thin film refractive index. Then, the interference orders and film thickness are calculated to get accurate values of the needed optical parameters. There are no complex fitting procedures or assumed theoretical refractive index dispersion relations. The method is applied to calculate the optical properties of an epitaxial gallium nitride thin film on a silicon (1 1 1) substrate. Good agreement between our results and the published data are obtained.     

Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser

We describe a measurement method of refractive indices by way of spectrally resolved interferometry using a femtosecond pulse laser. The method is dispersion insensitive and requires no prior precise knowledge of the geometrical thickness of the specimen. Not only the group but also the phase refractive index can be determined over the wide spectral range covered by the optical comb of the femtosecond pulse laser in use.     

On the problem of calculating the optical film parameters from the measured transmission spectra

The procedure for calculating the dispersion of the refractive and absorption indices and thickness of an optical film, based on measurements of spectral dependence of the transmittance, is described. The film parameters are calculated using a solution of the approximation problem. The effect of the film model on the calculated values of the refractive and absorption indices is analyzed.     

石榴石外延膜色散关系的确定和膜厚的测量

本文提出了确定石榴石外延膜的色散关系和测量膜厚的一种方法。充分利用分光光度计获得的透射光谱,在波长大于2μm,因而膜和衬底的吸收及色散近于可忽略时,由透过率的极值计算得到相应波长下膜的折射率。按干涉条件计算并推定出所有干涉极值的干涉级数,进而算出各干涉极值波长下膜的折射率。最后用最小二乘法求得科希色散公式的系数,从而得到该膜的色散关系。利用此色散关系就可计算膜厚。 关键词：     

Transmission properties of asymmetric slab waveguides with left-handed materials

A new dielectric slab waveguide with a left-handed material (LHM) cover and substrate is proposed. The dispersion relations and normalized effective thickness of the asymmetric LHM slab waveguide are investigated, in view of the normalized parameters. A number of unusual properties are found, for example, the fundamental and first-order modes do not exist and higher-order modes have double degeneracy. The propagation modes are absent at the low normalized frequency, and the cutoff frequencies of some LHM slab waveguide modes decrease with increase in the asymmetry measure. Unlike traditional slab waveguides, the V –H curves of the LHM slab waveguides are in one-to-one correspondence. Both TE and TM modes are discussed; in addition, the dispersion relations and normalized effective thicknesses of the TM modes are discussed in detail, when the difference in refractive indices of the film and the substrate is small. The results show that the region of mode coexistence taking place near the cutoff frequency becomes narrower with increase in the difference in refractive indices of the film and the substrate. The influence of this difference on the normalized effective thickness curves is different, and becomes smaller and smaller with increase in the value of the asymmetry measure, if different values of the refractive indices are employed.