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.     

Interferometric determination of refraction and dispersion of human blood-serum, saliva, sweat and urine

Multiple-beam interference fringes of equal chromatic order are produced in air and liquid sample interferometric gaps. The two gaps are of the same thickness and simultaneously enclosed in a wedge interferometer. A single shot interferogram containing fringes in the two gaps is sufficient to deduce the needed experimental data. Locations of the fringe maxima, in the two gaps, are introduced in a non-numerical procedure for determining the gap thickness and the liquid-phase refractive indices across the visible spectrum. The method has been used for measuring the phase refractive indices of human blood-serum, saliva, sweat, urine and water liquids. A third-order polynomial dispersion relation is applied for fitting the measured phase indices. Group refractive indices have been derived and fitted to the same dispersion formula.     

Interferometric determination of the refractive indices and birefringence of some highly oriented fibres

Variable wavelength interferometric technique (VAWI) is a direct method for determining the refractive indices and birefringence of highly oriented fibres. This method uses the polarizing interference Pluta microscope with a monochromatic light from wedge interference filter that provides a continuously variable wavelength. The standard calibration process of the Pluta polarizing interference microscope is carried out and a calibration graph is obtained. The refractive indices and birefringence of PEN, CONEX and TECHNORA were measured over the visible range of the spectrum and the constants for the Cauchy's dispersion formula were determined. The oscillation and dispersion energies were calculated from the measurements of the refractive index.     

Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber

Spectral interference of white-light beams propagating through a tandem configuration of birefringent crystal and sensing birefringent fiber is analyzed theoretically and experimentally. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer taking into account the dispersion of birefringence in the crystal and in the fiber. Two types of spectral interferograms are modeled knowing dispersion characteristics of the sensing fiber and using a quartz crystal of the positive or a calcite crystal of the negative birefringence. The theoretical analysis is accompanied by two experiments employing a highly birefringent fiber and a birefringent quartz crystal of two suitable thicknesses. Within both experiments the spectral interference fringes are resolved in accordance with the theory with phases dependent on the fiber length.     

Modified Michelson interferometer for probing refractive index of birefringent crystal CSBN50

Based on the modified Michelson interferometer and phase analysis method, a high-accuracy method for probing the refractive index (RI) of transparent medium is proposed. The validated test was performed on a birefringent crystal CSBN50 with the estimated accuracy being up to 10⁻⁴. The ordinary and extraordinary refractive indices of CSBN50 at 632.8 nm are determined as n₀=2.32853±0.00016 and n_e=2.27664±0.00016, respectively.     

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.     

A theoretical result on dispersion in a photonic crystal

A theoretical result on the type of dispersion of a photonic crystal is derived by using the fact that the refractive index of the crystal is a periodic function of wavelength whose period is the atomic lattice spacing of the crystal as well as by using Rolle's theorem of differential calculus.     

A high-precision optical metrology system for determining the thickness of birefringent wave plates

This study develops a non-destructive measurement system for determining the thickness and refractive indices of birefringent optical wave plates. Compared to previous methods presented in the literature, the proposed metrology system provides the ability to measure the thickness of the birefringent optical plate in high-precision. The results show that for a commercially available birefringent optical wave plate with refractive indices of n_e=1.5518, n₀=1.5427 and a thickness of 452.1428 μm, the experimentally determined value for the error in the wave plate thickness measurement is just 0.046 μm. The measurement resolution of the proposed system exceeds that of the interferometer hardware itself. The proposed method provides a simple yet highly accurate means of measuring the principal optical parameters of birefringent glass wave plates.     

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.     

Interferometric studies on the influence of temperature on the optical and dispersion parameters of GRIN optical fibre

Opto-thermal device attached to automate Fizeau interferometer is used to investigate the influence of temperature on opto-thermal properties of multimode graded-index (GRIN) optical fibre in the range from 27 to 54 °C. The effect of temperature on the refractive index profile of fibre is studied. The optical parameters and the opto-thermal coefficient of this fibre are determined. Also the variation of oscillation and dispersion energies, zero dispersion wavelengths, coupling efficiency, normalised frequency, number of propagation modes with the temperature and the material dispersion with the wavelength at different temperatures are calculated. Microinterferograms are given for illustration.     

Refractive index and material dispersion in relativistic electron optics

The refractive index and material dispersion associated with relativistic motion of electrons are calculated. Moreover, the wavelength dependence of refractive index is compared with the Sellmeier model for the index of refraction of lightwaves.     

Interferometric method to measure and test the optical homogeneity of transparent materials

The main idea of the method is to eliminate physically the influence of errors of glass sample plane surfaces on the wavefront transmitting through the sample. This makes it possible to reveal the “pure” optical inhomogeneity of the material independently of the errors of flat surfaces of a glass sample made in the form of a plane-parallel plate or a wedge of the small refractive angle. A basic optical layout of the laser interferometer explaining the capabilities of the practical application of the method is presented.     

The refractive index enhancement at Eg in narrow-gap semiconductors: comparison between the interband absorption edge and the oscillator model

A comparison is made between the refractive index enhancement near the M₀-type absorption edge in direct narrow-gap semiconductors and the dispersive structure of a Lorentz oscillator. Phenomenologically, both absorptive structures can be described by three parameters, and the analogy between both models concerning n(E) is discussed. Examples for the predicted dependencies are given. With increasing energy gap the n(E) enhancement becomes related to discrete excitonic bands rather than to free-to-free transitions, thereby undergoing a spectral shift from energies above gap to energies below gap.     

Design of Topas microstructured fiber with ultra-flattened chromatic dispersion and high birefringence

A microstructured polymer optical fiber (mPOF) with both ultra-flattened near-zero chromatic dispersion and high birefringence based on Topas cyclic olefin copolymer is designed. Three rings of uniform elliptical air holes are arranged in triangular lattice in the cladding and an extra small defected hole is introduced in the fiber core. Guided modes, dispersion, birefringence and mode confinement properties of the designed mPOF are investigated by using the full-vector finite element method. Dispersion values between ± 0.5 ps/km/nm over the wavelength 1.1-1.7 μm and high birefringence of the order of 10⁻³ are obtained for the optimized fiber structure. Low confinement losses and small effective mode area are obtained at the same time. The relatively simple architecture of the proposed Topas mPOF can be fabricated by our extrusion-stretching techniques.     

Determination of GR-IN optical fibre parameters from transverse interferograms considering the refraction of the incident ray by the fibre

The core–cladding refractive index difference Δn and the index gradient profile parameter of the graded index (GR-IN) optical fibre has been determined. The curve representing the real path, in the core region, due to refraction of the beam and the change in the exit wavefront are considered. Multiple-beam Fizeau fringes and two-beam interference Pluta polarizing microscope, are used for this investigation. A new method, based on a derived mathematical expression, is used with a prepared computer program to estimate the fringe shift inside GR-IN of the fibre core. The estimated and experimental values of the fringe shift, along the core radius, are used to obtain the refractive index profile of the optical fibre. A comparison between the new method and a previous model considering the refraction has been shown. Microinterferograms are given for illustrations.     

用光纤白光干涉技术测量晶体的弹光系数

运用折射率椭球分析晶体的弹光效应,给出了三方晶系沿光轴方向的应力与折射率的变化关系.针对晶体的各向异性和折射率随应力变化很小的因素,利用白光干涉技术空间分辨率高的特点,将白光干涉技术拓展到研究各向异性材料的光学性质. 并对测量群折射率的光纤迈克尔逊白光干涉技术进行了改进.采用光栅位移传感器和全保偏光纤提高反射扫描镜的位移准确度.通过测量石英晶体在不同外力下折射率的变化情况,确定了晶体的弹光系数. 石英晶体的弹光系数P33和P13分别为0.110和0.279,其准确度达到0.001.     

共振光的大折射率

揭示了在多能级原子介质中的一种新现象:利用原子相干可使共振光获得明显大于1的折射率.     

Computing Eigen value equation and modal dispersion characteristics of an elliptical Bragg waveguide

Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a new type of Bragg waveguide having elliptical core cross section with multilayered cladding is derived. The eigen equation is written in the form of Mathieu and the modified Mathieu functions and a dispersion relation is obtained for various modes supported by the proposed Bragg waveguide. The cutoff frequencies for several lower order even-odd modes have been calculated and their propagation characteristics are plotted. The results show that the dispersion curves are discontinuous and modes can exist only in particular wavelength bands. The effects of elliptical eccentricity on the mode cutoff values and mode transmission are addressed. Finally, the modal birefringence in the said waveguide is also estimated.     

Measurement of thickness of a thin film by means of laser interference at many incident angles

An optical method for directly measuring the thickness of a thin transparent film has been proposed by means of multi-wave laser interference at many incident angles, and confirmed experimentally by means of equipment made on an experimental basis. Two methods are available: one can be used when an index of refraction of the film, a wavelength λ, and two successive angles of incidence at which the sinusoidal light intensity has minimum values, are known (Method I), and another can be used without an index of film refraction when three successive angles of incidence and a wavelength are known (Method II). The smallest measurable thickness is 1.43λ for Method I, and 2.5λ for Method II. The largest measurable thickness is about 100λ for both methods. The measurement error by means of numerical calculation is Δh/h−1.01×10⁻², and that obtained experimentally with an angular resolution of incident light of 0.3° is Δh/h7×10⁻² for Method I. The refractive index can also be measured by means of Method II.