Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method

In certain species of moths and butterflies iridescent colours arise from subwavelength diffractive structures. The optical properties of such a structure depend strongly on wavelength, incidence angle and state of polarization of illuminating radiation and on the viewing angle. Such structures can be analyzed only by solving Maxwell's equations, but since analytical solutions exist for only a few simple, highly symmetric structures numerical methods must be employed. We investigated the optical properties of butterfly wings in two dimensions by simulating a scale structure using a high accuracy version of nonstandard finite-difference time-domain algorithm. The simulated structure is a computer-generated model of a certain quasi-periodic arrangement of tree-like structures observed in the transmission electron micrograph (TEM) image of a transverse cross-section of a single scale from Morpho butterfly wings. We assumed that the structure is made of a slightly lossy dielectric material. We checked the accuracy and validity of our approach, by computing scattered field intensities due to an infinite cylinder and compared the results with analytical calculations using Mie theory. Next we deduced the wavelength dependence of a real refractive index and an absorption coefficient for the ground scales on the wings of Morpho sulkowskyi butterfly by computing the reflectivity and transmissivity spectrum of a scale at normal incidence, and comparing with experimental measurements. Finally, we calculated the tristimulus values and corresponding colour coordinates for various viewing directions from the scale's far-field reflectivity and transmissivity spectra to characterize its colour rendering abilities.     

One dimensional photonic band gap material as an omnidirectional reflector

In this article, the reflection properties in one-dimensional dielectric-dielectric photonic band gap (PBG) structure have been studied. We have used SiO₂ as material of low refractive index and Te as a high refractive index material. Reflectivity of proposed PBG structure is plotted as a function of wavelength and angle of incidence and omni-directional PBGs are computed theoretically. To obtain reflectance, we used transfer matrix method for solving Maxwell’s equations for electromagnetic wave in PBG structures. For a large range of frequency, the PBG structure is found to exhibit omni-directional reflection which can be exploited in devices such as optical resonators, mirrors, etc.     

Soft X‐ray refractive index by reconciling total electron yield with specular reflection: experimental determination of the optical constants of graphite

The complex refractive index of many materials is poorly known in the soft X‐ray range across absorption edges. This is due to saturation effects that occur there in total‐electron‐yield and fluorescence‐yield spectroscopy and that are strongest at resonance energies. Aiming to obtain reliable optical constants, a procedure that reconciles electron‐yield measurements and reflection spectroscopy by correcting these saturation effects is presented. The procedure takes into account the energy‐ and polarization‐dependence of the photon penetration depth as well as the creation efficiency for secondary electrons and their escape length. From corrected electron‐yield spectra the absorption constants and the imaginary parts of the refractive index of the material are determined. The real parts of the index are subsequently obtained through a Kramers–Kronig transformation. These preliminary optical constants are refined by simulating reflection spectra and adapting them, so that measured reflection spectra are reproduced best. The efficacy of the new procedure is demonstrated for graphite. The optical constants that have been determined for linearly polarized synchrotron light incident with p‐ and s‐geometry provide a detailed and reliable representation of the complex refractive index of the material near π‐ and σ‐resonances. They are also suitable for allotropes of graphite such as graphene.     

梨花粉红外波段复折射率测定与分析

花粉是生物气溶胶重要的组成部分,复折射率是研究花粉光学特性以及探测、识别生物气溶胶成分的重要参数。采用压片法对梨花粉2.5~15 μm波段的反射光谱进行了测量,利用Krames-Kronig(K-K)关系计算了复折射率,并就傅里叶红外光谱仪测试压片的入射角和复折射率长波长、短波长区外推两方面对结果作了误差分析。结果表明,测试时18°入射角以及长波长、短波长区外推对梨花粉复折射率的计算结果影响不大,利用反射光谱计算花粉复折射率的方法是可行的。计算得到的复折射率谱对梨花粉光学特性的研究以及生物气溶胶成分的探测、识别有一定的参考价值。     

Wavelength Tuning Characteristics of a Vertival Cavity Surface Emitting Laser Diode with an External Short Cavity

The characteristics of a wavelength tunable vertical cavity surface emitting laser diode (VCSEL) with an external short cavity are analyzed, in which the oscillation wavelength can be changed over several tens of nanometers with a nearly constant optical power by slightly altering the external cavity length. Analysis is based on rate equations for the optical power and carrier density, taking the effect of carrier-induced refractive index change into consideration, together with the study of behaviors of a complex resonator. The reflection coefficient r₂ of a laser facet facing the external mirror is shown to affect notably the characteristics of wavelength tuning, optical power and carrier density for a change of the external cavity length. It is also noticed that the wavelength change for this length becomes slower with relatively larger r₂ due to an increasing contribution of the effect of carrier-induced refractive index change, within the optical gain spectrum of the laser diode.     

Optical constants for Ge30− x Se70Ag x (0 ≤ x ≤ 30 at%) thin films based only on their reflectance spectra

In this paper, different homogenous compositions of Ge_{30? x} Se₇₀Ag _x (0?≤?x?≤?30 at%) thin films were prepared by thermal evaporation. Reflection spectra, R(λ), for the films were measured in the wavelength range 400–2500?nm. A straightforward analysis proposed by Minkov [J. Phys. D: Appl. Phys. 22 (1989) p.1157], based on the maxima and minima of the reflection spectra, allows us to derive the real and imaginary parts of the complex index of refraction and the film thickness of the studied films. Increasing Ag content at the expense of Ge atoms is found to affect the refractive index and the extinction coefficient of the films. The dispersion of the refractive index is discussed in terms of the single-oscillator Wemple–DiDomenico model. Optical absorption measurements were used to obtain the fundamental absorption edge as a function of composition. With increasing Ag content, the refractive index increases while the optical band gap decreases. The compositional dependence of the optical band gap for the Ge_{30? x} Se₇₀Ag _x (0?≤?x?≤?30) thin films is discussed in terms of the chemical bond approach.     

Polarisation properties of comet NEAT C/2001 Q4

Comets exhibit high (up to 25 %) amount of optical polarization when they are observed through ground based or space telescopes. These polarizations are caused due to the scattering of cometary dust. The observed linear polarisation of comets is generally a function of the wavelength of incident light (λ), the scattering angle (θ), the geometrical shape and size of the particle and the composition of dust particles in terms of the complex values of the refractive index. The scattering properties of cometary dust will help to know the nature of cometary dust. In the present work, the observed linear polarization data of Comet NEAT are studied through simulations using Ballistic Particle-Cluster Aggregate (BPCA) and Ballistic Cluster-Cluster Aggregate (BCCA). Using Superposition T-matrix code, the best-fitting values of complex refractive indices are calculated which can well fit the observed polarization data of Comet NEAT C/2001 Q4. The best fitting values of complex refractive indices coming out from the present analysis correspond to mixture of both silicates and organics.     

High-negative effective refractive index of silver nanoparticles system in nanocomposite films

We have proved on the basis of the experimental optical reflection and transmission spectra of the nanocomposite film of poly(methyl methacrylate) with silver nanoparticles that (PMMA + Ag) nanocomposite films have quasi-zero refractive indices in the optical wavelength range. We show that to achieve quasi-zero values of the complex index of refraction of composite materials is necessary to achieve high-negative effective refractive index in the system of spherical silver nanoparticles.     

Plasmonic enhancement of linear birefringence and linear dichroism in anisotropic optical metamaterials

The resonant behavior of linear birefringence and linear dichroism spectra is found in anisotropic optical metamaterials made of noble metal thin films with stripes and rectangular hole nanoapertures forming one- or two-dimensional subwavelength gratings. Differences in effective refractive index and extinction coefficient for linearly polarized eigenstates are increased in spectral range of resonances of local and surface plasmon-polaritons at the normal incidence and reach the values of Δn ≃ 2.5 and Δκ ≃ 2.75, respectively.     

Determination of the refractive index and thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity

Linearly polarized light incident on a transparent film coating a transparent substrate remains linearly polarized after reflection only at a set of discrete angles of incidence φ_m (m integer). Measurement of these angles of incidence for zero reflection-induced ellipticity (ZRIE) allows simple, direct and explicit determination of the refractive index and thickness of the film, independent of the substrate refractive index. The latter can be separately and easily determined from the azimuths of the incident and reflected linear vibrations at one of the angles of incidence φ_m or, alternatively, from the angle of refraction of light into the substrate using Snell's law. The proposed technique requires that the thickness of the film exceed one-fourth the wavelength of light in the medium of the film, and that it does not fall in a “higher-order” thickness gap when the ratio of the refractive index of the film to that of the ambient is greater than $\text{2}\text{√3}$.     

Modified polarizing prism

We accomplish the production of linearly polarized light by modifying our earlier design of a non-deviating dispersion prism for three cases by setting, (i) the angle of incidence equal to the inverse of the cotangent of the refractive index (n), (ii) twice the angle of incidence equal to the angle of refraction plus the inverse of the cotangent of the refractive index (n), and (iii) the angle of incidence equal to the difference of twice the inverse of the cotangent of the refractive index (n), and the angle of refraction. Finally, we present a design for an achromatic polarizer using a penta prism. These designs and their salient features are discussed in the light of Cervantes’ review and other polarizers. Some possible applications are given.     

Comparison of resonances and spectral properties for microstructures incorporating singular layered metal dielectric subwavelength grating with different profiles

A multilayered structure incorporating a single metal-dielectric subwavelength grating is a structure with characteristic of polarization separation for visible light, enabling creating visible color aspect. Based on that, two specific structures separately with grating layers of rectangular and sinusoidal refractive index profiles are designed and their related resonant behaviors and spectral properties are compared respectively for s and p polarized incident lights. The impacts of structural parameters of the structures together with dielectric materials on their resonances and spectra in reflection are studied in detailed. Similarities of resonant behaviors, reflection spectra and variations in resonant locations and spectral profiles between both structures are also demonstrated for both polarizations, especially for s polarized light. Due to such similarities and convenience in fabrication, the structure with a sinusoidal grating can replace that with a rectangular grating in mass production for color-based various applications such as color security, image reproduction.     

Resonance optical spectroscopy of long-period quantum-well structures

Theory of specular light reflection from long-period quantum-well structures taking into account the exciton contribution to dielectric polarization has been developed for an arbitrary relation between the background refractive index in the well, n _a, and barrier-material refractive index nb. General expressions for the optical reflection and transmission coefficients for a structure with N equidistant quantum wells are derived with the use of the Green’s function and transfer matrix methods. Normal and oblique light reflectance spectra from II-VI-based heterostructures were found to reveal a bright interference pattern caused by the difference between n _a and n _b. A comparison of the theory with experiment has yielded the dispersion of n _a and n _b within a broad wavelength range and the parameters of the quasi-two-dimensional heavyhole exciton (e1-hh1), namely, the resonant frequency and the radiative and nonradiative damping rates. Reflectance spectra from resonant Bragg and quasi-Bragg structures with real exciton parameters are calculated, and the effect on these spectra of the refractive-index difference and the deviation from the Bragg condition is analyzed. Fiz. Tverd. Tela (St. Petersburg) 39, 2072–2078 (November 1997)     

Polarization and Color Separator Using Binary Phase Grating with Subwavelength Period

A data projector using three liquid crystal display panels has a complex optical system. The illuminating optics separate the beam from a light source into three primary colors and separate those into opposite polarizations using multi-layer films and prisms. A reflection grating with the period of subwavelength has high diffraction efficiency for p polarized light and high regularly reflectance for s polarized light. The diffraction angle of a grating largely depends on the wavelength, because a diffractive optical element (DOE) has large chromatic dispersion. The grating with the period of subwavelength can separate the unpolarized light into polarization components effectively using its polarization dependency and can separate white light into color components using its chromatic dispersion simultaneously. The grating makes the optical system simpler and smaller than those with conventional devices. In this paper the efficiency of polarization separation for the grating is calculated by a rigorous analytical method. Next, the condition for color separation is calculated by Snell#x0027;s law, and an optical system using a grating that performs polarization and color separation is proposed. Experimental results of the DOE fabricated are well matched with those of this simulation.     

偏振光谱BRDF建模与仿真

在偏振光条件下,物体的表面反射受到折射率、表面粗糙度、入射角等多种因素的影响。针对粗糙物体表面在不同波段光照下表现出不同的偏振反射特性,提出一种基于Kirchhof理论的偏振光谱BRDF模型。利用已知材质在不同波长下的复折射率,对其折射率和消光系数部分分别反演出的对应光谱模型,进而得到复折射率的光谱模型;同借鉴经典的表面粗糙度测量方法,结合菲涅耳反射公式,推导出表面粗糙度的光谱模型,将得到的复折射率和粗糙度光谱模型与BRDF模型相结合,推导出偏振光谱BRDF建模。模型分别在折射率随波长变化、粗糙度为常量,折射率、粗糙度均随波长变化以及原模型三种情况下进行仿真对比实验,并将所得到的数据与其他资料进行对比。其结果表明,该模型能够较为准确的反映物体表面的偏振反射特性,并且能够描述偏振度随波长变化趋势的光谱特征,能够为偏振遥感、物质分类等方面的应用提供可靠依据。     

Accuracy of ellipsometric monitoring during growth of semiconductor nanostructures

The determination accuracy of the parameters of multilayer structures during their in situ ellipsometric monitoring is analyzed. A qualitative criterion is proposed that makes it possible to evaluate the validity of replacement of the multilayer structure by a certain medium with effective optical constants. According to this criterion, this replacement is possible if the complex reflection coefficients R _{p, s} of the structure satisfy the relation (R _p /R _s + cos2φ)/(R _s + R _p cos2φ) = 1, where φ is the angle of incidence of light. It is shown that, for structures consisting of layers with a high refractive index, this condition is implemented with a high accuracy. This proves that, upon the successive solution of the ellipsometry problem for layers of this structure, errors are not accumulated. In particular, this inference can be applied to structures based on a cadmium-mercury-tellurium ternary compound.     

亚波长金属偏振分束光栅设计分析

结合有效介质理论和薄膜光学的抗反射设计方法,设计了基于0.65μm工作波长的亚波长金属偏振分束光栅,给出了光栅的优化设计参数,采用严格耦合波理论分析了光栅的偏振分束特性.结果表明,亚波长金属光栅对TE偏振表现为金属膜特性,具有高反射,对TM偏振表现为介质膜特性,具有高透射,在-30°<θ<30°的大入射角范围和0.47μm<λ<0.80μm的宽入射波谱内,该光栅的透射光和反射光均具有高偏振消光比和低插入损耗的特点. 关键词： 亚波长金属偏振分束光栅 有效介质理论 薄膜光学 严格耦合波理论     

Negative refraction and imaging beyond the diffraction limit by a two-dimensional left-handed metamaterial

We report our experimental results on two-dimensional left-handed metamaterials (LHM) exhibiting negative refraction and subwavelength imaging. Transmission and reflection spectra of LHM are studied and a left-handed transmission band is observed at the frequencies where both dielectric permittivity and magnetic permeability are negative. Impedance matching is verified both with the experiments and simulations. The two-dimensional LHM structure is verified to have a negative refractive index. We employed three different methods to observe negative refraction; refraction through prism-shaped LHM, beam shifting method, and phase shift experiments. We further demonstrated subwavelength imaging and resolution using LHM superlenses. The effect of thickness on the resolving power is investigated experimentally.     

基于耦合介质纳米线的深亚波长局域波导

提出了一种基于耦合介质纳米线的深亚波长局域波导,通过两根紧邻的高折射率介质纳米线的耦合,该波导可以将光场有效束缚在纳米线之间的低折射率纳米缝隙中. 计算模拟的结果表明,该波导的有效模场面积达到Λ²₀/200,比单根纳米线波导小一个数量级,这种深亚波长的模场束缚能力可以与表面等离激元混合波导相比拟. 计算模拟的结果还表明,纳米线可能带有的低折射率氧化膜、低折射率衬底的存在、以及纳米线间尺寸存在的一定差异对于该波导结构的实际应用都不会产生很大 关键词： 介质波导 亚波长局域 表面等离激元波导 纳米线     

Tuning of the photonic band gaps and the reflection spectra of a one-dimensional photonic crystal based on silicon and a liquid crystal

The reflection spectra and the photonic band gaps of a one-dimensional composite photonic crystal are calculated for different filling factors (the ratio of the thickness of a silicon layer to the lattice constant A). A change in the refractive index of the filler in a photonic crystal leads to the shift of both edges for certain side photonic bands. It is shown that, with a change in the refractive index from 1.49 to 1.69, the shift of the edges (the tuning effect) can reach the value A/λ = 0.04 for the main photonic band and 0.08 for a side band. An additional criterion for designing a photonic crystal is the estimation of the sharpness of the edges of photonic bands in the reflection spectra.