Snell's law dictates the phenomenon of light refraction at the interface between two media. Here, we demonstrate arbitrary programming of light refraction through an engineered material where the direction of the output wave can be set independently for different directions of the input wave, covering arbitrarily selected permutations of light refraction between the input and output apertures. Formed by a set of cascaded transmissive layers with optimized phase profiles, this refractive function generator (RFG) spans only a few tens of wavelengths in the axial direction. In addition to monochrome RFG designs, we also report wavelength-multiplexed refractive functions, where a distinct refractive function is implemented at each wavelength through the same engineered material volume, i.e., the permutation of light refraction is switched from one desired function to another function by changing the illumination wavelength. As experimental proofs of concept, we demonstrate permutation and negative refractive functions at the terahertz part of the spectrum using 3D-printed materials. Arbitrary programming of refractive functions enables new design capabilities for optical materials, devices and systems.
Deconvolution phase microscopy enables high-contrast visualization of transparent samples through reconstructions of their transmitted phases or refractive indexes. Herein, we propose a method to extend 2D deconvolution phase microscopy to thick 3D samples. The refractive index distribution of a sample can be obtained at a specific axial plane by measuring only four intensity images obtained under optimized illumination patterns. Also, the optical phase delay of a sample can be measured using different illumination patterns.
Results from the calculation of the basic characteristics of the photonic crystal fiber with two rings of holes are presented by the approach which takes into account the exact distribution of the refractive index over the cross section of the photonic crystal fiber. Formulae are theoretically derived for the calculation of holes with arbitrary shapes by dividing the material within them into rotated at different angles rectangles. Keywords: photonic crystal fibre, Galerkin method, a set of sine functions, local coordinate systems.
Exact analytical results (in terms of Bessel functions) for the bandgaps, reflectance, and transmittance of one-dimensional photonic crystals with a sawtooth refractive index profile on the period are derived for the first time. This extends a group of exactly solvable models of periodic refractive indices. The asymptotic approximations of the above exact results have been also obtained.
Probability density functions for photon propagation in a binary (isotropic-Poisson) statistical mixture with unmatched positives/negatives refractive indexes
The set of realizable refractive indices as a function of frequency is considered. For passive media we give bounds for the refractive index variation in a finite bandwidth. Special attention is given to the loss and index variation in the case of left-handed materials.
Humidity and C_n^2 data collected from the Chesapeake Bay area during the 2003/2004 period have been analyzed. We demonstrate that there is an unequivocal correlation between the data during the same time periods, in the absence of solar insolation. This correlation manifests itself as an inverse relationship. We suggest that C_n^2 in the infrared region is also function of humidity, in addition to temperature and pressure.
A method to engineer the refractive indices of functional materials (TiO2, ZnO, SnO2, SiO2), by nanostructuring in the deep sub-wavelength regime (<20nm), is presented. Block-copolymer templating combined with a wet processing route is used to realize 3D functional nanostructures with continuously adjustable refractive indices from 1.17 to 2.2. Wet processing accessed refractive index engineering can be applied to address a variety of realizability concerns in attaining design specified refractive index values and refractive index gradients in 1D, 2D, and 3D that arise as the results of optica…
Accurate distance measurement in 3D confocal microscopy is important for quantitative analysis, volume visualization and image restoration. However, axial distances can be distorted by both the point spread function and by a refractive-index mismatch between the sample and immersion liquid, which are difficult to separate. Additionally, accurate calibration of the axial distances in confocal microscopy remains cumbersome, although several high-end methods exist. In this paper we present two methods to calibrate axial distances in 3D confocal microscopy that are both accurate and easily impleme…
We have presented a new general function photonic crystals (GFPCs), which refractive index is a function of space position. Based on Fermat principle, we achieve the motion equations of light in one-dimensional general function photonic crystals, and calculate its transfer matrix. In this paper, we choose the line refractive index function for two mediums $A$ and $B$, and obtain new results: (1) when the line function of refractive indexes is up or down, the transmissivity can be far larger or smaller than 1. (2) when the refractive indexes function increase or decrease at the direction of inc…
Conventional transparent materials at optical frequencies have refractive index values (n) greater than unity -- most commonly between about 1 and 4. This paper explores optical phenomena made possible by using materials with refractive indices less than unity. We focus primarily on fused silica (SiO2), a polar dielectric with strong phonon resonances in the mid infrared that result in a spectral region in which n < 1 with modest optical loss. Using this ubiquitous easy-to-deposit material, we demonstrate infrared-frequency external reflection, frustrated external reflection, and direct coupli…
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity being an arbitrary continuous function of the coordinate. We have shown that the problem of plane wave scattering by an inhomogeneous layer is reduced to a system of first order differential equations that contain the derivative of the refractive index or dielectric permittivity of the layer, which can be used, for example, when searching for an analytical sol…
Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on the concept of geodesic lens. The requirement is a continuous refractive index profile of dielectrics, which shows almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal tra…
Electrically-tunable optical properties in materials are desirable for many applications ranging from displays to lasing and optical communication. In most two-dimensional thin-films and other quantum confined materials, these constants have been measured accurately. However, the optical constants of single wall nanotubes (SWCNT) as a function of electrostatic tuning are yet to be measured due to lack of electronic purity and spatial homogeneity over large areas. Here, we measure the basic optical constants of ultrathin high-purity (>99%) semiconducting single wall carbon nanotube (s-SWCNT) fi…
We show that bulk rhenium diselenide, ReSe2 is characterized by record high value of the refractive index exceeding 5 in near-infrared frequency range. We use back focal plane reflection spectroscopy to extract the components of the ReSe2 permittivity tensor and reveal its extreme biaxial anisotropy. We also demonstrate the good agreement between the experimental data and the predictions of the density functional theory. The combination of the large refractive index and giant optical anisotropy makes ReSe2 a perspective material for all-dielectric nanophotonics in the near-infrared frequency r…
Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design: for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators, higher index directly leads to better devices with greater functionality. Although standard transparent materials have been limited to refractive indices smaller than 3 in the visible, recent metamaterials designs have achieved refractive indices above 5, accompanied by high losses, and near the phase transition of a ferroelectric perovskite a broadband index above 26 has been…
In this paper, We have presented a new general function photonic crystals (GFPCs), which refractive indexes are line functions of space position in two mediums $A$ and $B$, and obtain new results: (1) when the line function of refractive indexes is up or down, the transmissivity can be far larger or smaller than 1. (2) when the refractive indexes function increase or decrease along the direction of incident light, the light intensity should be magnified or weaken, which can be made optical magnifier or attenuator. (3) The GFPCs can be made optical diode when the light positive and negative inc…
Using the Cryogenic, High-Accuracy Refraction Measuring System (CHARMS) at NASA's Goddard Space Flight Center, we have measured the absolute refractive index of five specimens taken from a very large boule of Corning 7980 fused silica from temperatures ranging from 30 to 310 K at wavelengths from 0.4 to 2.6 microns with an absolute uncertainty of +/-1 x 10^-5. Statistical variations in derived values of the thermo-optic coefficient (dn/dT) are at the +/-2 x 10^-8/K level. Graphical and tabulated data for absolute refractive index, dispersion, and thermo-optic coefficient are presented for sele…
In order to enable high quality lens designs using calcium fluoride (CaF2) and Heraeus Infrasil 301 (Infrasil) for cryogenic operating temperatures, we have measured the absolute refractive index of these two materials as a function of both wavelength and temperature using the Cryogenic, High-Accuracy Refraction Measuring System (CHARMS) at NASA's Goddard Space Flight Center. For CaF2, we report absolute refractive index and thermo-optic coefficient (dn/dT) at temperatures ranging from 25 to 300 K at wavelengths from 0.4 to 5.6 microns, while for Infrasil, we cover temperatures ranging from 35…
In the paper, we present a new general function photonic crystals (GFPCs), which refractive index of medium is a arbitrary function of space position. Unlike conventional photonic crystals (PCs), which structure grow from two mediums $A$ and $B$, with different constant refractive indexes $n_{a}$ and $n_{b}$. Based on Fermat principle, we give the motion equations of light in one-dimensional GFPCs, and calculate its transfer matrix, which is different from the conventional PCs. We choose the linearity refractive index function for two mediums $A$ and $B$, and find the transmissivity of one-dim…
We demonstrate the capability of block-copolymer templating to tune the refractive indices of functional oxides over a broad range by structuring materials on the 20-1000 atoms scale, with simple one-pot synthesis. The presented method is then combined with genetic algorithm-based optimization to explore its application for anti-reflection coating design. Merging these techniques allows for the realization of a minimal two-layer anti-reflection stack for silicon with broadband reflectivity of just 3% from the nominal value of 38%, over a 120° angular span, validated by fabrication followed by …
We present in this paper a method to recover the refractive index profile of graded waveguide from the effective indices by cubic spline interpolation function. It is proved by numerical analysis of several typical index distributions that the refractive index profile can be reconstructed closely to its exact profile with the presented interpolation model. This method can reliably retrieve index profile of both more-mode (more than 4 guiding mode) and fewer-mode (2-4) waveguides.
A better understanding of the optical properties of random photonic structures is beneficial for many applications, such as random lasing, optical imaging and photovoltaics. Here we investigated the light transmission properties of disordered photonic structures in which the high refractive index layers are aggregated in clusters. We sorted the size of the clusters from a power law distribution tuning the exponent a of the distribution function. The sorted high refractive layer clusters are randomly distributed within the low refractive index layers. We studied the total light transmission, wi…
Silicon and germanium are perhaps the two most well-understood semiconductor materials in the context of solid state device technologies and more recently micromachining and nanotechnology. Meanwhile, these two materials are also important in the field of infrared lens design. Optical instruments designed for the wavelength range where these two materials are transmissive achieve best performance when cooled to cryogenic temperatures to enhance signal from the scene over instrument background radiation. In order to enable high quality lens designs using silicon and germanium at cryogenic tempe…
Polymeric materials are prized for their formability, low density, and functional versatility. However, the refractive indices of common polymers fall in a relatively narrow range between 1.4 and 1.6. Here, we demonstrate that loading commercially-available polymers with large concentrations of a plant-based pigment can effectively enhance their refractive index.For polystyrene loaded with 67w/w\% $β$-carotene, we achieve a peak value of 2.2 near the absorption edge at $531~\mathrm{nm}$, while maintaining values above 1.75 across longer wavelengths of the visible spectrum. Despite high pigment…
Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect witho…
We have theoretically investigated a general function photonic crystals (GFPCs) with defect layer, and choose the line refractive index function for two mediums $A$ and $B$, and analyze the effect of defect layer's position, refractive indexes and period numbers on the transmission intensity and the electric field distribution. We obtain some new characters that are different from the conventional PCs, which should be helpful in the design of photonic crystals.
Light's internal reflectivity near a critical angle is very sensitive to the angle of incidence and the optical properties of the external medium near the interface. Novel applications in biology and medicine of subcritical internal reflection are being pursued. In many practical situations the refractive index of the external medium may vary with respect to its bulk value due to different physical phenomena at surfaces. Thus, there is a pressing need to understand the effects of a refractive-index gradient at a surface for near-critical-angle reflection. In this work we investigate theoretica…
Refractive Index, Its Chromatic Dispersion, and Thermal Coefficients of Four Less Common Glycols
Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Laser and Fibre Optics Centre, Department of Physics, School of Physical Sciences, College of Agriculture and Natural Sciences, University of Cape Coast（开普海岸大学农业与科学学院物理学院激光与光纤中心）
Hyperbolic phonon polaritons (HPhPs) are generated when infrared photons couple to polar optic phonons in anisotropic media, confining long-wavelength light to nanoscale volumes. However, to realize the full potential of HPhPs for infrared optics, it is crucial to understand propagation and loss mechanisms on substrates suitable for applications from waveguiding to infrared sensing. In this paper, we employ scattering-type scanning near-field optical microscopy (s-SNOM) and nano-Fourier transform infrared (FTIR) spectroscopy, in concert with analytical and numerical calculations, to elucidate …
Methods for fast and accurate material properties estimate with terahertz time-domain spectroscopy in transmission and reflection with optically thick materials
A detailed analytical inspection of light scattering by a particle with high refractive index m+iκand small dissipative constant κis presented. We have shown that there is a dramatic difference in the behavior of the electromagnetic field within the particle (inner problem) and the scattered field outside it (outer problem). With an increase in m at fix values of the other parameters, the field within the particle asymptotically converges to a periodic function of m. The electric and magnetic type Mie resonances of different orders overlap substantially. It may lead to a giant concentration of…
All known optical materials have an index of refraction of order unity. Despite the tremendous implications that an ultrahigh index could have for optical technologies, little research has been done on why the refractive index of materials is universally small, and whether this observation is fundamental. Here, we investigate the index of an ordered arrangement of atoms, as a function of atomic density. At dilute densities, this problem falls into the realm of quantum optics, where atoms do not interact with one another except via the scattering of light. On the other hand, when the lattice co…
In the paper, we present a new kind of function photonic crystals, which refractive index is a function of space position. Unlike conventional PCs, which structure grow from two materials, A and B, with different dielectric constants $ε_{A}$ and $ε_{B}$. By Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we study the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals. By choosing various refra…
