Formation Of Interference Patterns Research Articles

Интерферометр для контроля выпуклых гиперболических поверхностей малого диаметра

We used Fourier transforms to perform a theoretical analysis of how the process of interference pattern formation in a laboratory-scale Fizeau laser interferometer is affected by the error in the working wave front. The interferometer is designed to monitor convex hyperbolic surfaces characterised by small diameters and low aperture angles. We indicate their application scope. The interferometer consists of a laser illuminator, a microlens, a beam splitter, that is, a thin plane-parallel plate with a semitransparent coating on its front surface, and a screen. A thin translucent plate located perpendicular to the line connecting the geometric foci of the hyperbolic surface acts as a separator and a reference simultaneously. The paper provides the main equations describing the wave aberration of the working branch and the position of optical elements in the interferometer design. We present an example of computing aberration in the working branch of the interferometer. This calculation reveals that aberrations in the thin plane-parallel plate can be discarded at low aperture angles. The interferometer forms a high-precision optical surface map, that is, interference band distortion caused by the interferometer error does not exceed 0.1 of the distortion caused by the error inherent to the surface being monitored. The interferometer provides highly accurate measurement of hyperbolic surfaces while featuring an obviously simple design

A Moir\xe9 interference pattern formation of magnetic nanoparticles by rotational magnetic field controlled interfacial self-assembly

‘Magic-angled’ structure currently attracts increasing attention from condensed matter physics due to its amazing performance in superconductivity of graphene. The similar pattern formation of nanoparticles will bring about novel physics in nanoscale that causes the next generation nanodevices. However, it remains a challenging task to acquire such patterns by self-assembly process. In this article, we reported a Moiré interference pattern formation of magnetic nanoparticles regulated by a rotational magnetic field. The colloidal concentration, the strength, and the frequency of magnetic field were found to affect the pattern formation. The mechanism lied in a two-step process. First, the magnetic nanoparticles formed bilayers of superlattice driven by hydrophobic interaction of interfacial self-assembly. Then, the bilayers of superlattice yielded asynchronous rotational displacement resulting from the magnetic force so that the Moiré interference pattern of nanoparticles formed. This fabrication methodology based on the field-controlled self-assembly provided a novel and simple means to get ‘magic angled’ structures in nanoscale that will enrich the physical understanding of nanotechnology.

A Novel Method for Measurement of the Refractive Indices of Transparent Solid Media Using Laser Interferometry

The refractive index is a number that governs how light changes its direction of propagation as it enters one material medium from another. This phenomenon is known as refraction and the angles of incidence and refraction of light, referred to the normal to the interface of the two media at the point of incidence, are related by Snell’s law. The refractive index (RI) depends on the color (or wavelength λ) of light. Tables of values of refractive indices for various media and wavelengths of light, with respect to vacuum, are readily available. The refractive index of a material can be measured by many methods, for example, by using a spectrometer in conjunction with a prism made of the experimental substance. An important class of methods of measuring RI involves the formation of interference patterns. Interferometric measurements are concerned with the study of separation between bright fringes (or dark fringes) resulting from the superposition of light waves, originating from a single source and propagating along paths of different optical lengths (refractive index multiplied by geometric path length). Researchers have exploited (nearly) monochromatic light from laser sources to enhance precision in measuring refractive index by applying interferometric techniques.

Interference patterns produced by an evaporating droplet on a horizontal surface

We study dynamical Newton-ring like fringes created by interfering Fresnel reflections of an evaporating sessile liquid droplet, which acts as a miniature convex lens. We show that conventional thin-film interference theory cannot be applied to explain the physical phenomenon. Because of the large thickness and curvature of the liquid droplet, the geometrical light paths of the reflected beams become very complicated and can no longer be considered approximately collimated. This results in interference fringes of concentric circles with different directional motion depending on the observation plane. The change in the interference pattern as a function of time is demonstrated by both simulation and experiment. This investigation allows us to fully understand the formation of interference patterns of an optical system having arbitrary thickness and curvature. In addition, by analyzing the high-contrast dynamic rings, we demonstrate nanoscale sensitivity to surface height changes of an evaporating water drop.

Theoretical study of micro-structure fabrication by multi-beam laser interference lithography with different polarization combinations

In this study, we systematically and comprehensively investigated the influence of polarization angle on the fabrication of micro-structures by multi-beam laser interference lithography. Using theoretical analysis and simulation, we studied the effect of different polarization combinations, i.e. transverse electric (TE) and transverse magnetic (TM) polarization combinations, on the characteristics of the micro-structures fabricated by three-, four-, and six-beam laser interference lithography. We successfully obtained micro-structures with different periodic patterns such as honeycomb dots, quasi-elliptic dots, different square dots, and quasi-triangular dots. The simulation results illustrate that polarization affects the formation of interference patterns, pattern contrasts, and periods. The methods discussed herein are simple, low cost, and allow excellent control over structural parameters, and hence are useful for the micro-structure manufacturing industry.

Анализ интерферометра с микрозеркалом на светоделительном кубике

The control of the shape of the optical part surface by the interference method has become an integral part of the process of their shaping. With a precisely focused interferometer interferometry allows obtaining an interference pattern similar to a topographic map of the error profile of the wave surface under investigation. The interferometer must form a map of the optical surface with high accuracy --- the permissible distortion of the interference fringe caused by an interferometer error should not exceed 0.1 of the distortion value caused by an error on the examined surface. The dependence of the interference pattern formation on the errors in the arrangement of the interferometer components, i.e., defocusing, was theoretically analyzed using Fourier transforms. The analysis was performed for an interferometer containing a laser illuminator, a concave spherical mirror with a central hole, coaxial to the illuminator, and a beamsplitting element in the form of a cube-prism with a semitransparent hypotenuse face. On the first flat face of the cube-prism, a microspherical concave mirror is made with the center located on the optical axis of the interferometer. A method for calculating the defocusing of a controlled spherical mirror and the corresponding wave aberration of the working wavefront is presented. An example of calculating the design parameters of the interferometer and the permissible defocusing of the controlled spherical mirror is given

Demonstration of Interference Patterns by the Random Walk of Particles

Visualization of interference phenomena by Chladni patterns is treated. The formation of the pattern in the Young's double-slit experiment is described by a new model of driven random walk exhibited by particles bouncing on a vibrating surface. In the model the mean length of horizontal displacement is described deterministically by the wave amplitude. The presented example indicates that such formation of interference patterns can take place without any pilot-waves associated to particles. In spite od this, the pheomenon remeinds to formation of interference patterns observed at scattering of particles in quantum mechanics.

Mono-crystalline gold platelets: a high-quality platform for surface plasmon polaritons

Abstract We use mono-crystalline gold platelets with ultra-smooth surfaces and superior plasmonic properties to investigate the formation of interference patterns caused by surface plasmon polaritons (SPPs) with scattering-type scanning near-field microscopy at 521 and 633 nm. By applying a Fourier analysis approach, we can identify and separate several signal channels related to SPPs launched and scattered by the atomic force microscopy tip and the edges of the platelet. Especially at the excitation wavelength of 633 nm, we can isolate a region in the center of the platelets where we find only contributions of SPPs which are launched by the tip and reflected at the edges. These signatures are used to determine the SPP wavelength of λ SPP = 606 nm in good agreement with theoretical predictions. Furthermore, we were still able to measure SPP signals after 20 µm propagation, which demonstrates impressively the superior plasmonic quality of these mono-crystalline gold platelets.

The complex quantum potential and wave–particle duality

The equation of motion for a particle moving in complex space is obtained and then solved. The interaction between the real and imaginary components of motion can produce what can be regarded as a wave motion in real space. The formation of interference patterns and polarization of a matter wave can be accounted for by the particle’s motion in complex space. The deterministic particle view of a free particle can then be reconciled with its dual probabilistic wave picture but the formulation is entirely in complex space.

Effect of laser beam conditioning on fabrication of clean micro-channel on stainless steel 316L using second harmonic of Q-switched Nd:YAG laser

Laser micromachining of metals for fabrication of micro-channels generate ridge formation along the edges accompanied by ripples along the channel bed. The ridge formation is due to the formation of interference pattern formed by back reflections from the beam splitter and other optical components involved before focusing on the work piece. This problem can be curtailed by using a suitable aperture or Iris diaphragm so as to cut the unwanted portion of the laser beam before illuminating the sample. This paper reports an experimental investigation on minimizing this problem by conditioning the laser beam using an Iris diaphragm and using optimum process parameters. In this work, systematic experiments have been carried out using the second harmonic of a Q-switched Nd:YAG laser to fabricate micro-channels. Initial experiments revealed that formation of ridges along the sides of micro-channel can easily be minimized with the help of Iris diaphragm. Further it is noted that a clean micro-channel of depth 43.39µm, width up to 64.49µm and of good surface quality with average surface roughness (Ra) value of 370nm can be machined on stainless steel (SS) 316L by employing optimum process condition: laser beam energy of 30mJ/pulse, 11 number of laser scans and scan speed of 169.54µm/s with an opening of 4mm diameter of Iris diaphragm in the path of the laser beam.

Artificial gravity effect on spin-polarized exciton-polaritons

The pseudospin dynamics of long-living exciton-polaritons in a wedged 2D cavity has been studied theoretically accounting for the external magnetic field effect. The cavity width variation plays the role of the artificial gravitational force acting on a massive particle: exciton-polariton. A semi-classical model of the spin-polarization dynamics of ballistically propagating exciton-polaritons has been developed. It has been shown that for the specific choice of the magnetic field magnitude and the initial polariton wave vector the polariton polarization vector tends to an attractor on the Poincaré sphere. Based on this effect, the switching of the polariton polarization in the ballistic regime has been demonstrated. The self-interference of the polariton field emitted by a point-like source has been shown to induce the formation of interference patterns.

ZnO coated Fabry-Perot interferometric optical fiber for detection of gasoline blend vapors: Refractive index and fringe visibility manipulation studies

ZnO nanoparticles-coated Fabry-Perot interferometer based optical fiber sensor is demonstrated to detect different gasoline blend concentrations in ethanol. Different gasoline blends (with ethanol varying from 0% (E0) to 100% (E100)) have been subjected to the sensor to observe the change in refractive index of the material that leads to the wavelength shift and fringe visibility change of the interference spectrum. The sensor shows the remarkable response with different gasoline blend mixtures within the time span of 0–60s in terms of wavelength and Intensity (power) shift. The maximum wavelength shift of 12.1nm is observed for E0 mixture and least of 3nm for E100 in 60s, respectively. A fast response time and recovery time of 5s and 9s, respectively, are obtained for E0 mixture. The results are related to the formation of interference pattern due the ZnO-mediated-Fabry-Perot cavity, changes in refractive index with the change in external gaseous environment, changes in fringe visibility of the spectrum and the interaction of oxygen vacancies on ZnO surface with the gasoline moieties. The rates of sensing and recovery times are related to the Reid vapor pressures of ethanol and gasoline. Hence a dual scale of sensing, both in terms of wavelength shift (refractive index) and intensity shift (fringe visibility) has been proposed for gasoline blend sensing.

Elastoplasmonic interaction in metal-insulator-metal localized surface plasmon systems

We investigate theoretically and numerically the coupling between elastic and localized surface plasmon modes in a system of gold nanocylinders separated from a thin gold film by a dielectric spacer of few nanometers thickness. That system supports plasmon modes confined in between the bottom of the nanocylinder and the top of the gold film, which arise from the formation of interference patterns by short-wavelength metal-insulator-metal propagating plasmon. First we present the plasmonic properties of the system though computer-simulated extinction spectra and field maps associated to the different optical modes. Next a simple analytical model is introduced, which allows to correctly reproduce the shape and wavelengths of the plasmon modes. This model is used to investigate the efficiency of the coupling between an elastic deformation and the plasmonic modes. In the last part of the paper, we present the full numerical simulations of the phononic properties of the system, and then compute the acousto-plasmonic coupling between the different plasmon modes and five acoustic modes of very different shape. The efficiency of the coupling is assessed first by evaluating the modulation of the resonance wavelength, which allows comparison with the analytical model, and finally in term of time-modulation of the transmission spectra on the full visible range, computed for realistic values of the deformation of the nanoparticle.

Studying the optical second-order interference pattern formation process with classical light in the photon counting regime.

The formation process of the second-order interference pattern is studied experimentally in the photon counting regime by superposing two independent single-mode continuous-wave lasers. Two-photon interference based on the superposition principle in Feynman's path integral theory is employed to interpret the experimental results. The second-order interference pattern of classical light can be formulated when, with high probability, there are only two photons in the interferometer at one time. The studies are helpful in understanding the second-order interference of classical light in the language of photons. The method and conclusions can be generalized to the third- and higher-order interference of light and interference of massive particles.

X-ray multilens interferometer based on Si refractive lenses.

We report a multilens X-ray interferometer consisting of six parallel arrays of planar compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. Overlapping such coherent beams produces an interference pattern demonstrating substantially strong longitudinal functional dependence. The interference fringe pattern produced by multilens interferometer was described by Talbot imaging formalism. Theoretical analysis of the interference pattern formation was carried out and corresponding computer simulations were performed. The proposed multilens interferometer was experimentally tested at ID06 ESRF beamline in the X-ray energy range from 10 to 30 keV. The experimentally recorded fractional Talbot images are in a good agreement with computer simulations.

Vortex interactions in the collision of Bose–Einstein condensates

We investigate the effects of vortex interaction on the formation of interference patterns in a coherent pair of two-dimensional Bose condensed clouds of ultra-cold atoms traveling in opposite directions subject to a harmonic trapping potential. We identify linear and nonlinear regimes in the dipole oscillations of the condensates according to the balance of internal and centre-of-mass energies of the clouds. Simulations of the collision of two clouds each containing a vortex with different winding number (charge) are carried out in these regimes in order to investigate the creation of varying interference patterns. The interaction between different vortex types can be clearly distinguished by those patterns.

Laser Interference Nanolithography with a 405nm Fiber Semiconductor Laser

This paper presents a method of laser interference nanolithography for the formation of interference patterns on the resist using a fiber semiconductor laser with a wavelength of 405nm. In the method, surface pattern structures are fabricated through the control of the incident angles of two interfering beams, the exposure dose of laser radiation and the development time. The angle adjustment becomes more convenient and the influence of environmental variations on the system has been reduced due to the use of fiber optic components. In the work, a feature size of down to 63nm and a pattern period of 215nm were achieved. The experimental results have shown that the method can be used for low cost micro and nano fabrication of periodical surface patterns with the features of low cost, simplicity and flexibility.

Effects of polarization on four-beam laser interference lithography

This paper demonstrates that polarization plays an important role in the formation of interference patterns, pattern contrasts, and periods in four-beam interference lithography. Three different polarization modes are presented to study the effects of polarization on four-beam laser interference based on theoretical analysis, simulations, and experiments. A four-beam laser interference system was set up to modify the silicon surface. It was found that the secondary periodicity or modulation was the result of the misaligned or unequal incident angles only in the case of the TE-TE-TM-TM mode. The resulting patterns have shown a good correspondence with the theoretical analysis and simulations.

Interference Pattern Formation between Bound Solitons and Radiation in Momentum Space: Possible Detection of Radiation from Bound Solitons with Bose–Einstein Condensate of Neutral Atoms

We propose an indirect method to observe radiation from an incomplete soliton with sufficiently large amplitude. We show that the radiation causes a notched structure on the envelope of the wave packet in the momentum space. The origin of this structure is a result of interference between the main body of oscillating solitons and the small radiation in the momentum space. We numerically integrate the nonlinear Schr\"odinger equation and perform Fourier transformation to confirm that the predicted structure really appears. We also show the simple model which reproduces the qualitative result. Experimental detection of the notched structure with Bose-Einstein condensation of neutral atoms is discussed and suitable parameters for this detection experiment are shown.

Extension of the Rotating Planar Waveguide Model to Formation of Interference Patterns in Optical Fibers

After the successful extension of the rotating planar waveguide model to Wave Optics, where a clear identification between the angular velocity of one hypothetical waveguide and the phase differences between two points on the path of one bounded mode was found, an application of the model to explain the interference theory is presented. We demonstrate that, for two bounded modes to create an interference pattern, a constrain to the relative parameters among both is imposed by the fiber optics. This result, not reported in the literature up to date, provides a new horizon to understand the interaction light-light when propagated within optical fibers.