Multiple-beam Interference Patterns Research Articles

Multiple-beam optical interferometry of anisotropic soft materials nanoconfined with the surface force apparatus.

Soft anisotropic materials that change their macroscopic properties in response to external stimuli such as light, electric field, or pressure are central to several new directions of technology, including optics, micro-mechanics, and bioengineering. Responsiveness is fundamentally connected to the anisotropic ordering of the material's building blocks at the nanometer scale. Here we propose the surface force apparatus as a powerful tool for investigating optically anisotropic materials at the nanometer scale using multiple-beam optical interference, allowing for simultaneous determination of film thickness, alignment, and chiral rotation of the optical axis. We present a method based on 4 × 4 matrices for calculating the exact transmission and reflection coefficients for light incident normal to a planar optical multilayer comprising an arbitrary number of chiral anisotropic layers with the helical axis normal to the layer. The multilayer can also include uniform birefringent media, optical adsorbing (e.g., metals) and isotropic materials. We introduce a technique to analyze and interpret the complex multiple-beam interference patterns arising from such multilayers and demonstrate it for the case of a twisted nematic liquid crystal confined to nanoscale thickness with the surface force apparatus. The analysis opens the prospect of studying the effect of strong confinement on the structure and response of a wide class of anisotropic materials.

A novel double‐image Fizeau system for accurate investigation of anisotropic polymer fibres

This paper introduces a double-image multiple-beam Fizeau fringes system. The introduced system can dynamically determine the variations of the refractive indices for both parallel and perpendicular polarization simultaneously. This is achieved by the simultaneous capturing of two multiple-beam interference patterns during the mechanical processing of isotactic polypropylene fibre. This parallel determination of the refractive indices of both polarization directions allowed us to determine the full-field distribution of the stress vector, S. To accomplish this, a mathematical model was deduced to calculate the components of the stress vector, S, i.e. parallel stress component, S₁, and perpendicular stress component, S₂. Double-image Fizeau fringes system and the deduced mathematical model were used to investigate the variation of the refractive index and stress components of the fibre during the stretching process and propagation of necked regions.

Reconstruction of refractive indices distribution in 3D using a single pattern of multiple-beam interference fringes for online investigation of necking phenomenon

A proposed model for reconstructing the refractive indices distribution in three dimensions is introduced. The reconstruction process requires a single multiple-beam interference pattern which facilitates online investigation of structural changes. In order to increase the accuracy of the measured refractive indices, fringe analysis was applied on the basis of the inverse interferogram principle proposed in this article. Verification of the modified technique was made using reconstructed noise-free interference patterns. The modified technique is helpful in studying the necking phenomenon observed during creep extension of polypropylene fibres. Refractive index distribution in 3D across the fibre was determined and the birefringence profile was calculated. Microinterferograms are given for illustration.

Multiple-beam interference with coaxial cable analogs of optical arrays

We study the interference properties of N coherent oscillators by using an equivalent radiofrequency coaxial cable electrical system consisting of N coaxial cables of different lengths, a 1×N splitter, and a N×1 coupler. The typical multiple-beam interference pattern is measured for several values of N as a function of the frequency. Unlike its optical counterpart, we have to consider the attenuation of the cables. The experimental curves agree well with theory and show the characteristics of multiple-beam interference. This approach represents an inexpensive way of experimentally investigating optical arrays.

Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography

We demonstrate an approach for easy fabrication of two-dimensional (2D) hexagonal and three-dimensional (3D) face-centered-cubic (fcc)-type photonic crystal (PhC) microstructures in a photosensitive polymer by applying a simple single refracting prism. This prism enables the splitting and recombining of a single incoming laser beam to form multiple-beam interference pattern simultaneously. Thus, antivibration equipment and complicated optical alignment system are not required, leading to a much more simple optical setup than previously reported laser holographic lithography techniques. Large-scale (over 1cm2) 2D hexagonal and 3D fcc-type PhCs have been produced. Reflection/transmission measurements performed on the fabricated 3D fcc-type PhC structures agree well with the corresponding band structure calculation.

Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask.

We compare the cladding patterns present in grating structures fabricated with an ultrafast laser and a phase mask with a cw beam interference model. We find that the observed patterns agree well with the model results for picosecond pulses; however, for femtosecond pulses, we show that the full bandwidth and the pulsed nature of the sources must be considered because the pattern can be affected by group-velocity walk-off. An interesting consequence of order walk-off is the possibility of pure two-beam interference generation with a phase mask in the femtosecond pulse regime.

Generation of a variable linear array of phase-coherent supercontinuum sources

We investigate the coherence properties of a linear array of white-light sources produced in bulk media by ultrashort laser pulses. The array is generated out of the spatial interference pattern between two laser pump pulses, so that the number of supercontinuum sources and their separations can be easily manipulated by varying the geometry of the laser beam interaction. We find that all the secondary white-light sources which arise from the generation of filaments in the optical medium are well phase-locked and are thus able to generate stable and high-visibility multiple-beam interference patterns in the far-field. Observations are compared to the results of a simple model which takes into account a clamping of the peak laser intensity inside the filaments and includes intensity-dependent phase shifts among the different sources.

Herschel’s interference demonstration

Early in the nineteenth century, W. Herschel introduced a striking demonstration of interference arising from many coherent rays. Today’s students can reproduce this demonstration and attain beautiful multiple-beam interference patterns.

Ultraresolution in optical imaging using spatiotemporal scanning.

Spatial information exceeding the passband of an imaging system can be captured by using the optics to generate a spatiotemporal multiple beam interference pattern that is scanned over the object, rather than using it to image the object directly. The modulation of the higher temporal harmonics of the signal resulting from collecting the scattered light represents a mapping in the time domain of higher spatial harmonics of the data. Upon reconstruction, the additional temporal degrees of freedom are mapped back in the spatial domain where they represent spatial frequencies exceeding the passband of the optics. The spatial resolution is thus not limited by the spatial passband, but rather by the temporal bandwidth of the detection system. Due to hardware limitations, experimental demonstration is provided only for a one-dimensional scan of Ronchi gratings with 50 and 200 lines per inch.

Partially coherent multiple-beam interference

The general formula for multiple-beam interference due to regular slit arrays illuminated with partially coherent quasi-monochromatic light is derived. The correlation functions chosen for partially coherent light assume Gaussian, sinc and besinc forms of correlation. The intensity distribution in the interference patterns is presented and discussed as a function of the spatial coherence condition. It is shown that spatial coherence of the illumination largely affects the features of multiple-beam interference patterns.

Phase Modulation of the First Beam in Reflected Multiple Beam Interference Fringes

A new method is given for evaluating the intensity in the multiple beam interference pattern in reflection based on considering the interfering beams as two vectors only and summing them diagrammatically. The method is applied to calculate the effect on the intensity distribution of modulating the phase of the first beam. The phase modulation is achieved by introducing a thin silver film of predetermined phase shift in transmission.