Scalar Wave Approximation Research Articles

3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study

Reconstructing 3D refractive index profile of scatterers using optical microscopy measurements presents several challenges over the conventional microwave and RF domain measurement scenario. These include phaseless and polarization-insensitive measurements, small numerical aperture, as well as a Green’s function where spatial frequencies are integrated in a weighted manner such that far-field angular spectrum cannot be probed and high spatial frequencies that permit better resolution are weighed down. As a result of these factors, the non-linearity and the ill-posedness of the inverse problem are quite severe. These limitations have imposed that inverse scattering problems in the microscopy domain largely consider scalar wave approximations and neglect multiple scattering. Here, we present first inverse scattering results for optical microscopy setup where full-wave vectorial formulation and multiple scattering is incorporated. We present (a) how three popular inverse scattering solvers from microwave domain can be adapted for the present inverse problem, (b) the opportunities and challenges presented by each of these solvers, (c) a comparative insight into these solvers and contrast with the simpler Born approximation approach, and (d) potential routes to improve the performance of these solvers for the hard inverse problem of optical microscopy.

Engineering angle selectivity of extraordinary optical transmission and nonlocal spatial filtering

Plasmonic metasurfaces can provide rich opportunities for miniaturized analog optical computing, such as ultrathin spatial filtering and free-space wavefront differentiation. In this work, the extraordinary optical transmission (EOT), one of the most fascinating phenomena of plasmonics, is revisited and rigorously studied in terms of the angle selectivity of the transmission resonance. In particular, the fundamental mechanisms of angle-selective transmission in 1D plasmonic nanoslit metasurfaces are investigated. Based on temporal coupled mode theory and Fano resonances, it is elucidated that the angle selectivity is due to strong coupling between multiple resonance channels. Using the theory that explains the origin of angle selectivity, the basic design rules for nonlocal lowpass and bandpass spatial filters based on infinite periodic metasurface structures were determined and verified numerically. Furthermore, the effect of the finite size of the metasurface structures on the nonlocality of the EOT was investigated and formulated by both a full numerical calculation and an analytical scalar wave approximation based on the convolution theorem together with the optical transfer function obtained for the infinite periodic structures. It is expected that the formulation of angle-selective EOT will be fruitfully exploited for the development of ultrathin designer spatial filters required for coherent imaging processes in compact Fourier optics applications.

Factorization of Antenna Efficiency of Aperture-Type Antenna: Beam Coupling and Two Spillovers

Antenna efficiency is one of the most important figures of merit of a radio telescope for observations, especially at millimeter wavelengths or shorter wavelengths, even for a multibeam radio telescope. To analyze a system with a beam waveguide, a lossless antenna consisting of two apertures in series is considered in the frame of the scalar wave approximation. We found that the antenna efficiency can be evaluated with the field distribution over the second aperture, and the antenna efficiency is factorized into three factors: efficiencies of beam coupling, transmission spillover, and reception spillover. The factorization is applicable to general aperture-type antennas with beam waveguides and can relate the aperture efficiency to the pupil function. We numerically confirmed our factorization with an optical simulation. This evaluation enables us to manage the aberrations and is useful in the design of multibeam radio telescopes.

Reconfigurable Anticounterfeiting Coatings Enabled by Macroporous Shape Memory Polymers

Here, we report a new type of reconfigurable anticounterfeiting coating enabled by integrating the scientific principles of photonic crystal and shape memory polymer (SMP). The autonomous infusion of uncured oligomers in a polydimethylsiloxane (PDMS) stamp into a templated macroporous SMP photonic crystal coating, which was confirmed by quantitative X-ray photoelectron spectroscopy analysis, can program an iridescent pattern on the transparent SMP membrane with deformed macropores. By manipulation of the unconventional all-room-temperature shape memory effects exhibited by the shape memory copolymer comprising polyethylene glycol diacrylate and ethoxylated trimethylolpropane triacrylate, the iridescent pattern can be easily and instantaneously concealed and revealed by immersing in common household liquids (e.g., ethanol and water). Systematic experiments and theoretical simulations using scanning electron microscopy, atomic force microscopy, optical spectroscopy, scalar wave approximation modeling, and c...

Retrieving the saddle-splay elastic constant K24 of nematic liquid crystals from an algebraic approach.

The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant K24. However, the usual methods to retrieve the latter involve adjusting of computational parameters through visual comparisons between the experimental light interference pattern or a (2) H-NMR spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant K24. Considering an escaped-radial disclination inside a capillary tube with radius R0 of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle [Formula: see text] . Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius R0, the measurement of [Formula: see text] from the interference experiments involving two different radii allows us to algebraically retrieve K24. Our method allowed us to give the first reported estimation of K24 for the lyotropic chromonic liquid crystal Sunset Yellow FCF: K 24 = 2.1 pN.

Rapid electrostatics-assisted layer-by-layer assembly of near-infrared-active colloidal photonic crystals

Here we report a rapid and scalable bottom-up technique for layer-by-layer (LBL) assembling near-infrared-active colloidal photonic crystals consisting of large (⩾1μm) silica microspheres. By combining a new electrostatics-assisted colloidal transferring approach with spontaneous colloidal crystallization at an air/water interface, we have demonstrated that the crystal transfer speed of traditional Langmuir-Blodgett-based colloidal assembly technologies can be enhanced by nearly 2 orders of magnitude. Importantly, the crystalline quality of the resultant photonic crystals is not compromised by this rapid colloidal assembly approach. They exhibit thickness-dependent near-infrared stop bands and well-defined Fabry-Perot fringes in the specular transmission and reflection spectra, which match well with the theoretical calculations using a scalar-wave approximation model and Fabry-Perot analysis. This simple yet scalable bottom-up technology can significantly improve the throughput in assembling large-area, multilayer colloidal crystals, which are of great technological importance in a variety of optical and non-optical applications ranging from all-optical integrated circuits to tissue engineering.

Analysis Of Waveguide Whose Guiding Region Filled With Dielectric Material Bounded By Two Equiangular Spirals Separating It From Two Dielectric Cladding Regions

We Make an analytical study of a waveguide whose guiding cross-section is bounded by two equiangular spirals in which core and cladding regions are filled with different dielectric materials having refractive index n1 and n2 where n1>n2. The characteristic equation is derived under the scalar wave approximation for weak guidance. Dispersion curves and cutoff curve are also shown and interpreted. Unlike the planar waveguide, a nonzero cutoff is deduced which may be attributed to the curvature of the boundaries and the flare.

Impact of wave polarization on long-range intensity correlations in a disordered medium.

We present a theory of long-range intensity correlations in phase-coherent transport of polarized light through a disordered medium. Diagrammatic calculations of the intensity correlation function are performed beyond the scalar wave approximation. The correlations between the cross-polarized fields are shown to result in the dependence of mesoscopic intensity fluctuations on the polarization of the incident light. The intensity correlation function is represented as a sum of the contributions from the scalar mode and the basic modes of circular and linear polarization. The calculations, as applied to media with large scattering inhomogeneities, are carried out for diffusive transport and for small-angle multiple scattering of light. Each polarization contribution to the variance of relative transmission fluctuations is shown not to be a self-averaging quantity and tends to a nonvanishing value as the sample thickness increases. This value is proportional to the length of polarization decay in the medium and can be measured by varying the initial polarization of light.

Scattering of near normal incidence SH waves by sinusoidal and rough surfaces in 3-D: comparison to the scalar wave approximation.

The challenge of accurately simulating how incident scalar waves interact with rough boundaries has made it an important area of research within many scientific disciplines. Conventional methods, which in the majority of cases focus only on scattering in two dimensions, often suffer from long simulation times or reduced accuracy, neglecting phenomena such as multiple scattering and surface self-shadowing. A simulation based on the scalar wave distributed point source method (DPSM) is presented as an alternative which is computationally more efficient than fully meshed numerical methods while obtaining greater accuracy than approximate analytical techniques. Comparison is made to simulated results obtained using the finite element method for a sinusoidally periodic surface where scattering only occurs in two dimensions, showing very good agreement (<0.2 dB). In addition to two-dimensional scattering, comparison to experimental results is also carried out for scattering in three dimensions when the surface has a Gaussian roughness distribution. Results indicate that for two-dimensional scattering and for rough surfaces with a correlation length equal to the incident wavelength (λ) and a root mean square height less than 0.2λ, the scalar wave approximation predicts reflected pulse shape change and envelope amplitudes generally to within 1 dB. Comparison between transducers within a three-element array also illustrate the sensitivity pulse amplitude can have to sensor position above a rough surface, differing by as much as 17 dB with a positional change of just 1.25λ.

Real-Time Synchronous CCD Camera Observation and Reflectance Measurement of Evaporation-Induced Polystyrene Colloidal Self-Assembly

A new monitoring technique, which combines real-time in-situ CCD camera observation and reflectance spectra measurement, has been developed to study the growing and drying processes of evaporation-induced self-assembly (EISA). Evolutions of the reflectance spectrum and CCD camera images both reveal that the entire process of polystyrene (PS) EISA contains three stages: crack-initiation stage (T1), crack-propagation stage (T2), and crack-remained stage (T3). A new phenomenon, the red-shift of stop-band, is observed when the crack begins to propagate in the monitored window of CCD camera. Deformation of colloidal spheres, which mainly results in the increase of volume fraction of spheres, is applied to explain the phenomenon. Moreover, the modified scalar wave approximation (SWA) is utilized to analyze the reflectance spectra, and the fitting results are in good agreement with the evolution of CCD camera images. This new monitoring technique and the analysis method provide a good way to get insight into the growing and drying processes of PS colloidal self-assembly, especially the crack propagation.

基于标量波近似方法模拟三维光子晶体光学特性

基于标量波近似方法模拟三维光子晶体光学特性

Optical studies of random disorder of colloidal photonic crystals and its evolution in evaporation induced self-assembly

Self-assembled photonic structures have been under theoretical and experimental study for decades, whereas previous theories on optical properties were mainly concerned with perfect structure or some certain limited kinds of disordered photonic crystals (PCs), making them unsuitable for characterizing the real self-assembled PCs. In order to improve our understanding of the mechanism of self-assembly and provide more crucial clues to further grow perfect crystals, we extended previous widely used scalar wave approximation (SWA), making it be able to characterize long-range disorder (β) and short-range disorder (α) in PCs synthetically in a simple and effective way. Excellent agreement with in situ observed reflectance of evaporation induced self-assembled colloidal photonic crystals (CPCs) was obtained, demonstrating that the introduction of the parameters α and β in SWA can successfully characterize the disorder in self-assembled CPCs. Furthermore, extended SWA was further used to study the disorder formation in self-assembly, and it was found that during growing stage both β and α drop down, whereas in drying stage β stays nearly unchanged while α increases significantly. It turned out that the growing stage of self-assembly is a stage when the structure transforms from disordered to ordered one, and growth induced disorder mainly arises in drying stage. The results obtained provide an insight into the growth mechanisms of self-assembly and theoretical basis for characterizing optical properties of disordered PCs.

Porosity tuning of the optical properties of mesoporous silica planar defect in macroporous silica opal

Periodic mesoporous silica films were embedded between photonic crystals to form defect-based monolithic structures capable of post-growth tuning. Tetramethyl orthosilicate was infiltrated into monolithic structures in order to form silica layers in their void spaces, resulting in changes to the optical spectra. With the increase in the number of infiltration cycles, the optical signatures of the defect-based monolithic structures red-shift, caused mainly by the increase in the effective index of refraction of the entire structure. Furthermore, the red-shift of the optical signatures in monolithic structures deviates when compared to the net-effect of infiltration on stand-alone structures of periodic mesoporous silica films and photonic crystals. Simulations based on scalar wave approximation corroborate the results obtained by ellipsometry, UV-VIS spectroscopy, scanning electron microscopy, and x-ray diffraction experiments.

In Situ Optical Microspectroscopy Monitoring of Binary Colloidal Crystal Growth Dynamics via Evaporation-Induced Cooperative Self-Assembly

Real-time monitoring of the binary colloidal crystal (bCC) growth via evaporation-induced cooperative self-assembly (EICSA) was studied by an in situ optical microspectroscopy technique. Evolution of the recorded reflectance spectra reveals that the whole growth process of bCCs via EICSA could be separated into three different stages corresponding to that of unary colloidal crystals because of the same evaporation model. We show the detailed cooperative self-assembly information, including the evolution of the number of layers and filling factors of different components of the growing bCCs using the scalar wave approximation method. Furthermore, when the size ratio and number ratio of the two colloids were varied, the real-time optical properties of the bCCs with various stoichiometric configurations were investigated systematically. This study would be valuable in furthering the current understanding of the bCC growth dynamics via EICSA and tailoring optical properties of hierarchical materials for applications in many fields.

Vapor detection enabled by self-assembled colloidal photonic crystals

Here we report the sensitive and reversible detection of vapors by using self-assembled colloidal photonic crystals. The condensation of various vapors in the interstitials of silica colloidal photonic crystals leads to red-shift and amplitude reduction of optical stop bands. A linear relationship between wavelength shift and vapor partial pressure has been observed for a variety of vapors including ethanol, water, and toluene. Importantly, the sensitivity of colloidal photonic crystal-based vapor detectors can be improved by nearly two orders of magnitude by using a new full-peak analysis technique that takes advantage of the manifest amplitude reduction of optical stop bands during vapor condensation. Optical simulation based on a scalar-wave approximation model shows that the predicted optical responses during vapor condensation in colloidal photonic crystals agree well with experimental results. The condensation of vapors between submicrometer-scale microspheres, a topic that has received little examination, has also been investigated by both experiments and theoretical calculations. Predictions based on a modified Kelvin equation match with the experiments for a wide range of vapor partial pressures.

Dynamic photoswitching of micropatterned lasing in colloidal crystals by the photochromic reaction

In this report, we successfully demonstrate the reversible photoswitching of micropatterned lasing in colloidal crystals (CCs) by the photochromic reaction. The CC-laser (CC-L) cavity proposed in this study consists of a photochromic light-emitting planar defect, containing both diarylethene and pyrromethene compounds, between a pair of CC films. Optical excitation of the CC-L cavity with a low threshold power gives rise to a single laser emission peak with a narrow spectral linewidth of 0.16 nm, which appears within the reflection wavelength range of CC films by the defect mode localized in the photonic band-gap (PBG). From a theoretical standpoint, such defect mode lasing is supported by numerical calculation on the basis of the scalar wave approximation (SWA) results of CC films. When the CC-L cavity is alternately irradiated with 313 nm and 530 nm light, the single laser emission peak is dynamically switched by the photochromic reaction of the diarylethene compound in the CC-L cavity. We can observe the high contrast micropatterned lasing images with a high resolution of only a few micrometers as the most interesting performance. Various micropatterned images of laser emission are reversibly erased and rewritten by alternating photoirradiation with 313 nm and 530 nm light through photomasks. We can envisage that unique photoswitchable lasers are realized by combining the photochromic light-emitting materials in various 1D-, 2D- and 3D-photonic crystal (PC) systems. This report provides new guidelines not only to realize the on-demand photocontrol of laser feedback effects by using photochromic compounds in a variety of PCs, but also to fabricate small-sized and high density all-optical photoswitching devices in next generation optoelectronics.

Real-time studies of evaporation-induced colloidal self-assembly by optical microspectroscopy

Real-time monitoring of the whole growth process of evaporation-induced colloidal self-assembly has been conducted using an optical microspectroscopy setup. Our observations suggest that the assembly process can be divided into three different growth stages as evidenced by the variations detected in the reflectance spectra. The thickness variation of the growing colloidal crystal was monitored by examining the Fabry-Perot fringes in the reflectance spectra. Furthermore, the scalar wave approximation was utilized to analyze the evolution of optical properties with growth. More detailed information, including the time dependence of number of layers and volume fraction of water, has been revealed by comparing the experimental and calculated reflectance spectra. The present work demonstrates that in situ real-time microspectroscopy is a promising technique for monitoring and investigating the dynamic process of colloidal self-assembly.

Large-Scale Colloidal Self-Assembly by Doctor Blade Coating

This article reports a simple, roll-to-roll compatible coating technology for producing 3D highly ordered colloidal crystal-polymer nanocomposites, colloidal crystals, and macroporous polymer membranes. A vertically beveled doctor blade is utilized to shear align silica microsphere-monomer suspensions to form large-area nanocomposites in a single step. The polymer matrix and the silica microspheres can be selectively removed to create colloidal crystals and self-standing macroporous polymer membranes. The thickness of the shear-aligned crystal is correlated with the viscosity of the colloidal suspension, and the coating speed and the correlations can be qualitatively explained by adapting the mechanisms developed for conventional doctor blade coating. We further demonstrate that the doctor blade coating speed can be significantly increased by using a dual-blade setup. The optical properties of the self-assembled structures are evaluated by normal-incidence reflection measurements, and the experimental results agree well with the theoretical predictions using Bragg's law and a scalar wave approximation model. We have also demonstrated that the templated macroporous polymers with interconnected voids and uniform interconnecting nanopores can be directly used as filtration membranes to achieve size-exclusive separation of particles.

Self-Cleaning Diffractive Macroporous Films by Doctor Blade Coating

Here we report a scalable bottom-up technology for creating three-dimensionally highly ordered macroporous polymer films with excellent water-repelling and optical diffractive properties. A simple doctor blade coating process is first utilized to create silica colloidal crystal-polymer nanocomposites. The close-packed silica spheres are selectively removed to fabricate flexible macroporous polymer films with crystalline arrays of voids which are interconnected through small nanopores. The size of the voids can be easily controlled by tuning the duration of an oxygen reactive-ion etching process prior to the removal of the templating silica spheres. After surface functionalization with fluorosilane, superhydrophobic surface with large apparent water contact angle and small sliding angle can be obtained. The water-repelling property can be quantitatively explained by adapting the Cassie's dewetting model. We further demonstrate that self-cleaning functionality can be achieved on superhydrophobic macroporous coatings by preventing bacterial contamination. The high crystalline quality of the macroporous polymers also enables strong optical diffraction from the periodic lattice. The optical properties are evaluated by normal-incidence reflectance measurements and theoretical calculation using a scalar-wave approximation model. A good agreement between theory and experiment has been obtained. The simultaneous achievement of controlled dewetting and strong optical diffraction by templated porous films could open new applications in self-cleaning diffractive optics.

Modal Analysis of a Doubly Clad Optical Waveguide Having a Cross-section of the Shape of a Lemniscate

In this paper, we choose a simple analytical method based on scalar wave approximation to study the modal behaviour of an unconventional doubly clad optical waveguide having a cross section of the shape of a lemniscate. We take the appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation we obtain numerical results in the form of dispersion curves and cutoff frequencies. An attempt has been made to estimate how the modal behaviour changes when a single cladded waveguide having a lemniscates of Bernoulli type core cross-section is changed to a waveguide having double cladded shape of a lemniscate. It is noted that the double cladded waveguide provides an additional degree of freedom to control the cutoff frequencies on our choice.