Multiple-beam Interference Method Research Articles

The Effect of Molecular Orientation in Disperse Red-1 Film on Its Refractive Index

The refractive index of materials is an important physical quantity in the design of various photonic devices. For thin-film based devices, the fabrication method should be compatible with existing processes in microelectronic fabrication and allow for controlling the refractive index. In this research, the material used is a polar Disperse Red 1 (DR1) molecule. The film fabrication was carried out using the physical vapor deposition method which had been equipped with an electric poling installation. The poling of the electric field during the deposition process was applied perpendicular to the substrate. The thickness measurement and the refractive index of the films were carried out using a reflectometer where the light was incident perpendicular to the substrate. The refractive index was determined by the multiple beam interference method. As a result, it was found that the application of an electric field causes a change in the orientation of the molecules, which were initially parallel to the substrate to become perpendicular. Increasing the field strength further reduces the number of molecules parallel to the substrate. This correlates with a decrease in the refractive index of the film.

Fabry–Perot etalon solved by an amplitude and phase approach

The amplitude and phase method is successfully applied to analytically solve a dielectric Fabry–Perot etalon of arbitrary thickness. The transmittivity of the system as a function of wavelength obtained in this way is shown to be equivalent to the results given by the conventional matrix theory or the multiple beam interference method. An asset of the amplitude and phase formalism is that in addition to describing the overall behaviour of the system, the wave properties are displayed as the field propagates through the optical system.

Synthesis of new wide nematic diaryl-diacetylenes containing thiophene-based heteromonocyclic and heterobicyclic structures, and their birefringence properties

New monocyclic and bicyclic thiophene-based diaryl-diacetylene liquid crystal (LC) materials were synthesised and demonstrated to exhibit wide enantiotropic nematic phases. One thiophenyl-benzene derivative, in particular, displayed a stable nematic phase across a temperature range of over 100°C. The birefringence properties of the compounds were measured using a multiple-beam interference (MBI) method, with the highest value found to be for the same thiophenyl-benzene molecule (Δn = 0.57, 550 nm) at 10°C above the crystal-to-nematic transition temperature. Furthermore, the effects of the cyclic structure on the mesomorphic behaviours, transition temperatures, and birefringence properties were investigated in detail from both experimental and theoretical viewpoints.

Large extraordinary refractive index in highly birefringent nematic liquid crystals of dinaphthyldiacetylene-based materials

The extraordinary and ordinary refractive indices in highly birefringent dinaphthyldiacetylene-based nematic liquid crystals with different alkoxy tails were accurately measured by the multiple-beam interference method. The high birefringence in the nematic liquid crystals was attributed to the high value of the extraordinary refractive index, ne. The value of ne increased from 1.8 to 2.1 as the number of carbon atoms in the alkoxy tail decreased from 12 to 3, whereas the ordinary index, no, remained at approximately 1.6.

Analytic method of studying defect mode of 1D doped phononic crystal

For the analytic study of the defect mode of 1D doped phononic crystal, the multiple-beam interference method and Bloh theorem are adopted, the analytical formula of defect mode is derived and the defect mode of 1D doped phononic crystal is studied. The varition law of defect mode is obtained. The method in freed from the weaknewes of other methods that cannot carry on the analysis of defect mode. The method is valid and accurate method of studying the defect mode of 1D doped phononic crystal.

Determining the optical properties of highly oriented fibres using a multiple-beam technique

Mathematical formulae are modified for the shape of multiple-beam Fizeau fringes in transmission to determine the mean refractive indices and birefringence of highly oriented fibres. These modified mathematical formulae are applied with the multiple-beam interference method to determine the optical anisotropy of polypropylene fibre with a draw ratio of 3.5. The refractive indices and birefringence results are compared with those obtained using the conventional method and are found to be in good agreement. The new method is also applied for (poly(ethylene 2,6-naphthalene-dicarboxylate), 1000 denier/248 filaments, PEN-Q50M4 (PEN) and poly(ethylene terephthalate) 1000 denier/250 filaments, PET-BHT, highly oriented yarn, Teijin, Japan (PET)) highly oriented fibres. Illustrations are given through microinterferograms.

Corrections To And Comments On "Dynamic Behavior Of Re Ection Optical Bistability In A Nonlinear Fiber Ring Resonator"

In the above paper on a transient analysis based on the multiplebeam interference method [1], some errors have been discovered. In this note, we detail corrections and discuss the validity of the multiple-beam interference method by comparison with another numerical method. Initially, we correct the mistakes in the analysis. The problem lies in the calculation of the total nonlinear phase shift of the partial wave entering the ring resonator at time t m R and leaving it at time t after the mth circulation. In the text, the nonlinear phase change suffered during each circulation was calculated using the intracavity field at the exit (port 3, see Fig. 1(a) of the above paper) of the ring resonator. The integration of the last circulation (corresponding to time interval from t R to t) was carelessly omitted. As a corrected formula becomes implicit, i.e., the phase change suffered during the last circulation is expressed in terms of the output field, itself to be determined, this formulation is not advantageous. A more adequate procedure is to use the intracavity field at the input (port 4) of the resonator, in which case the output field is computed by using previously determined values. In such a formulation, Eq. (10) on p. 1538 should be replaced by

Dynamic behavior of reflection optical bistability in a nonlinear fiber ring resonator

We present an analysis of the dynamic behavior of a nonlinear fiber ring resonator when an optical pulse with an arbitrary shape envelope is incident into it through a fiber directional coupler. The transient analysis is based on the extension of a well-known multiple-beam interference method to non-linear transmission problems. The steady-state analyses reported so far predict that the ring resonator exhibits reflection optical bistability in the input-output characteristics under appropriate conditions. But, our transient analysis shows that a nearly periodical oscillation of the transmitted power always takes place at a suitable initial detuning when the resonator has no loss or a small loss. It seems that the present instability is caused by the repetition of accumulation and release of the power in the ring resonator. We can obtain a bistable hysteresis loop by introducing a loss to the directional coupler. The dynamic behavior of bistability in a nonlinear fiber ring resonator with coupler loss is then investigated. It is found that a remarkable undershoot and overshoot occur in the switch-off curve and switch-on curve, respectively.

Determination of optical constants and average thickness of inhomogeneous-rough thin films using spectral dependence of optical transmittance

The thickness variation, surface roughness, variation in refractive index, and illumination wavelength bandwidth strongly influence the optical transmittance of thin films. The consequences of linear and Gaussian distributions of the change in phase of radiation traversing a thin film on the spectral characteristics of optical transmittance are presented. A new method of determining the spectral dependences of the real part of the refractive index and absorption coefficient as well as thickness and standard deviation of its value is proposed for examinations of transmittance of thin films on thick substrates. This method takes into account the Gaussian distribution of the change in phase of radiation over the illuminated sample area. Its usefulness in investigations of the optical properties of a-Si:H is shown in comparison with the standard methods. The novel method gives film thickness more compatible with the result obtained using the multiple-beam interference method. The obtained values of optical parameters allow better fitting of the spectral characteristics of transmittance with the theoretical curve.

Lippmann–Bragg broadband holographic mirrors

Lippmann–Bragg broadband volume holographic mirrors, with chirp normal to the surface, represent an entirely new class of grating. These gratings are presented and analyzed theoretically by using a combination of the multiple-beam interference method and Kogelnik’s local solution for uniform gratings. Particularly noteworthy is the new grating’s combination of a very high Bragg diffraction efficiency (>99.5%) with a large tunable bandwidth (from 5 to >300 nm).

Der einfluss von strukturunregelmässigkeiten beim zusammenwachsen zweier aufdampfschichten auf das schichtdickenmessverfahren mit hilfe von vielstrahl-interferenzen

By means of thickness measurements of vacuum-deposited thin Ag layers with island structure it was shown that the thickness measuring method of multiple beam interference results in much higher errors than it was supposed earlier. The uncertainties in measuring are caused by the fact that the reflecting layer used in performing the measurements does not grow in exactly the same way on the test layer as it does on the free substrate layer close by. The following data affect the amount of correction between the measured thickness and the mean geometrical thickness of the test layer: the mean roughnesses of the reflecting surfaces, cavities between the test layer and the reflecting layer, and gaps in the reflecting surfaces of the sample. The sources of error are best avoided by ultra-high-vacuum evaporation of the reflecting layer immediately after the evaporation of the test layer and by avoiding too high condensation temperatures. This procedure, however, highly limits the applicability of the multiple beam interference method.

A specimen holder for film thickness measurement

The measurement of film thickness by the multiple-beam interference method requires a device for adjusting the separation between the film and a semi-reflecting mirror. This note describes a robust specimen holder for this purpose which is easy to use, is little affected by vibration, and can be adjusted to within one wavelength of light.

Phase Changes on Reflection from Evaporated Chromium Films

Measurements have been made by multiple beam interference methods using Fizeau fringes and fringes of equal chromatic order to obtain the variation of phase change on reflection as a function of film thickness for chromium films deposited by evaporation on glass substrates. The results do not agree closely with theoretical curves but this has been shown to be due to the inhomogeneity of the chromium films and the deviations from theory have been explained in terms of a structural model based on independent evidence. The experimental curve has been used to explain anomalies which have been reported previously in measurements of the thickness of silver films by multiple beam interference methods when chromium is used as the reflecting overlayer.

Pressure crack-figures on diamond faces II. The dodecahedral and cubic faces

The study of pressure figures on diamond is extended to the cubic and dodecahedral faces. The formation of cracks on a sawn but unpolished dodecahedral (two-point) face is first studied. The loads required for the initiation of cracks, using a diamond ball, were between 7 and 24 Kg. Two different types of cubic face were available, one on a natural cubic boart stone, the other a polished approximation to a cube face secured by truncating an octahedral stone. The loads required to initiate cracks were of the order 20 to 30 Kg. All the cracks observed were specifically oriented in accordance with crystallographic expectations of easy cleavage directions. The cracks were accompanied by permanent surface distortions which were studied by multiple-beam interference methods. The permanent distortions broadly resemble those found in part I for octahedral faces. There is one important difference in that for both the cube faces studied, the surface level within the perimeter of the ring crack is appreciably depressed, being some 800 Å below the outer undisturbed level. This is considered to offer further evidence for the existence of plastic flow in diamond at room temperature. For the polished cube face studied observations could also be made on the accompanying internal cracking effects within the body of the crystal.

Interferometric Studies of the Growth of Stearic Acid Crystals and their Optical Properties

On the basal planes of stearic acid crystals, grown from solution, growth spirals observed by optical and phase contrast microscopic techniques are reported. These growth spirals are in accordance with the theory of Burton, Cabrera and Frank. For the measurement of spiral step-heights multiple-beam interference methods were used, including a modified multiple-beam interference method, which is described. The minimum step-height found was 46.3 ± 0.8 A, which agrees with the x-ray repeat unit. In addition, step-heights which were integral, as well as half integral, multiples of this unit were found. By interferometric methods the refractive index was found to be 1.42 ± 0.04 and for the two types of crystal rhomb observed the birefringence for directions of vibration parallel to the `a' and `b' axes was approximately 0.018 and 0.015 respectively for λ = 5461 A.

XXXVII. Interferometric studies of hardness test indentations: Investigations on tungsten carbide, steel, duraluminium and tin

Abstract Studies are made on the surface distortions which occur on metal surfaces which have received hardness test indentations from both diamond pyramid and diamond cone indenters. The surface contours are evaluated by multiple-beam interference methods. Experiments are reported for indentations over a wide range of hardness, the surfaces studied being those of sintered tungsten carbide, niekel-steel, duraluminium and tin. The distortions found in polycrystalline masses resemble one another but reveal secondary differences. On single erystallites of tin unsymmetrical patterns are found, with piling-up in two directions and sinking-in in directions at right angles to these. The effects are deternfined by the directions of the crystal axes. The concavity and convexity of the sides of the pyramid indentations axe discussed in relation to piling-up and sinking-in, and the influence of recovery is indicated.

Vibration Measurement by Interferometry

IN the experimental investigation of the problem of isolating very sensitive measuring instruments from the effects of building vibration, it has been found desirable to measure amplitudes of the order of 0.25 µ (10−5 in.). Optical interference methods have been investigated and used by Thomas and Warren1, Osterberg2, Cortez3, Kennedy4 and other workers. Multiple-beam interference methods, however, have not been applied by these workers. Tolansky and Bardsley5 have demonstrated the use of multiple-beam methods in studying vibration in quartz crystals. The use of multiple-beam interference techniques in conjunction with stroboscopic techniques offers a method of calibrating the most sensitive vibration detectors in terms of light waves to a high precision.

Interferometric Studies on the Vibration of Piezoelectric Plates

A description is given of the application of a number of multiple-beam interference methods to the study of the piezoelectric oscillations of some quartz crystals. The distribution of surface nodes and anti-nodes of motion and the amplitudes of oscillation are revealed by simple methods. By employing a stroboscopic illumination technique the phase relations between the various vibrating regions of the crystal suface are revealed. The nodal regions are shown to be at rest to within less than 50 A and the surface deformations are revealed to at least a similar order of accuracy. By a modified technique fringes are obtained through the crystal body and these reveal changes in the optical thickness. One crystal developed sharp surface discontinuities after being set into oscillation, indicating that crystallographic glide or slip had taken place. This is shown to be closely related to the familiar shattering of quartz crystals at excessive amplitudes of oscillation.

Interferometric Study of Slip Bands on Metal Crystals

WE have applied multiple-beam interference methods to the study of the displacements which may be expected to appear on the surfaces of metal crystal when strained, and this technique has revealed nove features. The principal advantages resulting from using this technique are fourfold: (i) the detailed contours of displacement steps are clearly revealed ; (ii) exact evaluation of displacements of even but a few angstrom units can be made ; (iii) owing to high sensitivity, the onset of the slip is shown at a very early stage ; (iv) slip with abnormally low loads can be detected.

Interferometric Examination

WE have applied multiple-beam interference methods to the study of abrasion test marks cut in diamond surfafces prepared for us by a new method due to P. Grodzinski (see above note). In this abrasion test the directional mechanical properties of the diamond are revealed by the sizes of the cuts produced in the various directions by (as near as possible) the same number of revolutions, under constant load, of a sharp grinding wheel charged with diamond dust. The accompanying illustrations are interferometric studies made on the cube top face of a truncated pyramid of a ‘glassy’ diamond, the same face, in fact, as that described in the preceding note by Grodzinski and Stern.