Analytical solution of the direct problem of ellipsometry for some profiles of optical constants of inhomogeneous layers

Differential equations that describe the reflection of polarized light from an optically inhomogeneous medium are considered. In the approximation of small variations of the refractive index, analytical expressions for the reflection coefficients are obtained for both types of polarization for the exponential and harmonic profiles of the optical constants. The accuracy of the obtained expressions is estimated by numerical simulation. It is found that analytical formulas describe well the behavior of the ellipsometric parameters of periodic structures based on Hg_1–xCd_xTe with a sinusoidal profile of the refractive index.     

Formation of holographic transmission and reflecting gratings in photopolymers under light-induced absorption

The formation of holographic transmission and reflection gratings is examined taking into consideration photoinduced absorption in photopolymer materials. The holographic gratings are assumed to be formed by light beams with arbitrary amplitude profiles. The problem is solved analytically in the zero-and first-harmonic approximation of the monomer concentration and refractive index with allowance for the interference-pattern contrast, an arbitrary degree of photopolymerization nonlinearity, and the dependence of the diffusion coefficient on the degree of polymerization. The effect of beam-amplitude profiles and light-induced absorption on the spatial profiles of holographic gratings is studied using numerical simulation. The effect of light-induced absorption on the diffraction characteristics of holographic gratings is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–89, October, 2006.     

Pulse record of holographic transmission and reflection diffraction gratings in absorbent photopolymers. 1. Theoretical analysis

In the present paper, the process of formation of holographic diffraction gratings (HDG) in photopolymer materials in transmission and reflection geometry of record by an optical pulse train with duration comparable with characteristic times of the polymerization and diffusion processes is investigated with allowance for light-induced absorption. A solution of the problem of forming HDG with 2D spatially non-uniform amplitude profiles by light beams is derived in the approximation of zero and first harmonics of the monomer concentration and refractive index. 3D spatial distributions of the HDG amplitude profiles are presented in an analytical form of recursion relations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 58–65, January, 2007.     

Influence of refractive profile shape on the distribution of modal attenuation in planar structures with absorption cover

The paper illustrates the influence of refractive profile shape in a sensor planar structure on the distribution of modal attenuation. Depending on the shape of refractive profile, the dependence of modes attenuation on their order can be an increasing function, decreasing function or non-monotonic one. The problem is discussed basing on the example of parabolic, exponential, Gaussian and linear profiles of refractive index. For the linear refractive profile, we present the influence of the gradient of waveguide’s refractive index and the influence of the thickness and refractive index of sensitive layer on the distribution of modal attenuation. Theoretical predictions are experimentally verified for two different refractive profiles. Theoretical predictions are excellent agreement with experimental results.     

Measuring method for the refractive index profile of optical glass fibres

A new method for measuring the refractive index profile of optical glass fibres is described. This simply monitors the reflection of a focused laser beam from a polished fibre end face. Detailed tests on the accuracy and resolution of the method are described and the index profiles of several fibres are given as an example of its feasibility.     

Synthesis of broadband interference filters: II. Suppression of high reflection bands of the fourth,fifth, and sixth orders

The spectral properties of multilayer interference systems formed by multiple replication of the symmetric ternary period ABCBA are investigated. The problem of synthesis of structures with suppression of adjacent bands of high reflection of the fourth, fifth, and sixth orders among their spectral characteristics is solved. It is shown that there are only six variants of selection of the optical thicknesses of layers in a period. When the high reflection bands of the fourth, fifth, and sixth orders are suppressed, the high reflection band of the first order remains in only four cases. The values of refractive indices of layers for which the problem hasa solution are found. The refractive indices of layers in all six cases are described by different relations determining the dependence of the refractive index of one of the components on arbitrarily selected refractive indices of the other two components.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

Effective refractive index for determining ray propagation in an absorbing dielectric particle

The ray-tracing technique can be employed to simulate the scattering of light by a dielectric particle whose characteristic dimension is much larger than the incident wavelength. When a scattering particle is absorptive, a localized electromagnetic wave refracted into the scatterer is inhomogeneous, which requires the use of an effective refractive index to determine the propagation direction of the refracted ray. The effective refractive index for the first-order reflection–refraction event (i.e., the case for the ray-transmission from air into a particle) has been previously derived by the authors. In this study, we further develop recurrence formulae for the effective refractive indices associated with higher-order reflection–refraction events when the ray-transmission is from a particle to air. It is shown from the new formulae that effective refractive indices in this case depend upon ray history. Numerical results indicate that the real and imaginary parts of the effective refractive index are larger and smaller, respectively, than the real and imaginary parts of the inherent complex refractive index of an absorbing particle. Furthermore, if the particle faces associated with two sequential internal reflections are parallel to each other, the corresponding effective refractive indices are the same.     

Wavelength dependent propagation in optical multimode fibers

Under various assumptions concerning the wavelength dependence of the refractive index of a fiber whose radial dependence is not an “a priori” known function of r, a method is described to obtain a closed form expression for the flight time of a ray in a multimode fiber. Consequently, the refractive index n(r) is shown to be the solution of a differential equation. Thus, for these selected profiles, we avoid the problem of the high precision required in the calculation of the flight time of a ray, a problem that arises frequently if the impulse response is to be reconstructed from a large number of rays, and transpose it to the determination of a single function of r, namely the refractive index.     

基于传输矩阵法讨论光疏介质表面的全反射

探究了光在光密介质与超薄光疏介质界面处的全反射,通过在光密介质中嵌入一光疏介质薄层,利用传输矩阵法,定量地分析了入射角度以及光疏介质的厚度对反射率的影响.数值模拟结果表明,当光疏介质的厚度小于约一个波长时,即使入射角大于全反射的临界角,反射率也不一定会达到1,也就是说,光学隧道效应将会出现.     

基于SM-NCF反射光谱辨识的液体折射率监测方法

针对分子生物学与环境监测领域高灵敏度特异性检测需求,提出一种基于反射光谱特征辨识的单端反射式光纤折射率传感器模型,并给出了这种基于多模干涉原理的单模光纤-无芯光纤(Single mode fiber-No core fiber, SM-NCF)串接结构传感机理及其理论模型。无芯光纤实质上是一种结构特殊的多模光纤,在实际应用中无芯光纤结构本身作为纤芯,外界环境介质当作包层,构成光波导结构。这与普通多模光纤相比,不需要采用氢氟酸对多模光纤的包层进行化学腐蚀,不会降低光纤的机械性能,也不会破坏芯模传输条件,可以更好的实现对周围环境折射率的传感监测。当无芯光纤所处外界环境折射率发生改变时,其波导结构和包层有效折射率均会发生改变,从而引起传输光信号的纵向传播常数和模场分布也会随之发生改变,最终导致不同波长对应传输光功率的变化。上述效应反映在反射光谱上,即干涉波谷对应的谐振波长、波谷峰值强度以及半波宽度发生相应变化,通过辨识该反射光谱特征就可实现对外界环境折射率的测量。借助光束传播法(BPM),数值模拟得到无芯光纤长度分别为自映像距离和非自映像距离时的SM-NCF内部光场能量分布规律,并制作了无芯光纤长度分别为自映像距离和非自映像距离的SM-NCF光纤折射率传感探头,将作为传感区域的无芯光纤一端与标准单模光纤熔接,采用磁控溅射技术在无芯光纤另一端面镀上金膜,用以提升反射光谱强度。在此基础上,搭建了基于SM-NCF终端反射型的光纤折射率试验系统,并开展了相关实验研究。研究结果表明,当无芯光纤长度是15 mm(自映像距离)时,随着液体折射率从1.331 5依次增大至1.390 2,SM-NCF反射光谱逐渐向长波方向偏移,其反射峰谐振波长对应的折射率灵敏度约为197.57 nm·RIU-1,相关系数为0.93;反射峰值强度也呈现逐渐降低趋势,其折射率灵敏度约为-62.80 dB·RIU-1。当无芯光纤长度是20 mm(非自映像距离)时,随着液体折射率依次增大,SM-NCF反射光谱呈现明显双峰现象,且均逐渐向长波方向偏移,dip2谐振峰波长折射率灵敏度约为133 nm·RIU-1,相关系数为0.96;反射峰值强度也呈现逐渐降低趋势,其折射率灵敏度约为-31.66 dB·RIU-1。对比分析可知,不论是从反射峰谐振波长偏移的角度,还是从反射峰值强度的角度,自映像距离长度对应的 SM-NCF终端反射型光纤传感器均具有较高灵敏度。对于相同折射率液体环境,非自映像距离长度对应的SM-NCF反射光谱半波宽度与自映像距离长度相比,呈现显著变窄趋势。相对于SMS透射型传感结构,当传感区域长度相同时,SM-NCF反射型结构能够实现对光波信号的往返两次调节。这种终端反射型SM-NCF传感器改进了传统透射型折射率传感器不便与待测液体相接触的缺点,具有结构简单、易于制作、抗电磁干扰能力强以及便于远程遥测等优点,能够为后续生化与环保监测领域研究应用提供有益支持。     

Transformation of a Gaussian light beam reflected in the vicinity of the Brewster angle

Variations in the profile and shift of a Gaussian light beam upon reflection from a plane interface between a transparent dielectric and a medium with a complex refractive index are studied. The beam is assumed to be incident at angles close to the Brewster’s angle, where the effects of transformation of the beam profile are most substantial. Based on numerical analysis, the reflected beam profiles are obtained for different properties of the media, parameters of the incident beam, and positions of the plane of observation.     

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.     

The refractive nonlinearities of InAs/GaAs quantum dots above-bandgap energy

The third-order optical nonlinear refractive properties of InAs/GaAs quantum dots grown by molecular beam epitaxy have been measured using the reflection Z-scan technique at above-bandgap energy. The nonlinear refractive index and nonlinear absorption index of the InAs/GaAs quantum dots were determined for wavelengths from 740 to 777 nm. The measured results are compared with the nonlinear refractive response of several typical III-V group semiconductor materials. The corresponding mechanisms responsible for the large nonlinear response are discussed.     

保偏微结构光纤啁啾光栅折射率传感特性分析

将有限元法和传输矩阵法相结合,系统地研究了保偏微结构光纤(PM-MOF)啁啾布拉格光栅的折射率传感特性。仿真研究了光纤空气孔中充入不同折射率被测物时啁啾光栅的反射谱,结果表明随着被测物折射率的增加,反射谱的面积出现明显变化,由此得到了光栅反射谱面积与被测物折射率的关系。分析了中心孔直径、啁啾系数、切趾函数等光栅结构参数对反射谱的影响。分析表明由于光纤两个方向的偏振模对温度、噪声等干扰响应相似,因此利用两个偏振模式反射谱的相对变化进行监测能够有效地降低干扰,提高传感器的稳定性;其次,由于反射谱面积正比于光强,这一方法将光栅的光谱解调转化为光强解调,简化了解调系统,便于现场实时测量。研究结果为保偏微结构光纤光栅在折射率传感器及其生物传感器方面的应用提供了理论依据。     

光波导技术同步测量棱镜及波导薄膜参数

依据全反射理论和棱镜耦合原理,实现了对棱镜折射率及波导薄膜材料折射率和厚度的同步测量。使用高准直半导体激光器激光入射到棱镜内部与波导膜的分界面上,逐步旋转棱镜或改变棱镜的入射角,得到棱镜耦合M线,曲线前面几组的波谷为波导模激发,在M线左侧收尾处有一个不完整波峰,其反射光强随入射角迅速衰减,为全反射时的临界点,由此可实现棱镜及波导薄膜参数的同步测量;用此法测量了棱镜耦合一体化平面波导棱镜的折射率和聚甲基丙烯酸甲酯(PMMA)聚合物波导薄膜的折射率和厚度。测量棱镜折射率精度为±1.9×10-4,波导薄膜折射率和厚度的精度分别为±6.2×10-4 μm和±1.6×10-2 μm。     

Transparent and UV-Reflective Photonic Films and Supraballs Composed of Hollow Silica Nanospheres

For an optically transparent, UV-reflective film, hollow silica nanospheres smaller than the visible wavelength (<λ_vis) are prepared and assembled into colloidal glasses, of which interstices are then backfilled with a polymer. The polymer refractive index is matched with the silica shell to minimize backscattering in the visible range, and the average distance between the hollow silica particles is adjusted by tuning the shell thickness to satisfy the interference resonance condition for a UV selective reflection. The resulting composite film shows a strong UV reflection as expected, but it is translucent in visible light due to non-negligible backscattering, which may be caused by large defects or fluctuation of the particle concentration. In order to avoid such backscattering, another polymer is introduced of which the refractive index is matched with the average refractive index of the hollow nanospheres. This allows an optically transparent film that selectively reflects the UV light. Furthermore, spherical aggregates of hollow silica nanospheres called “supraballs” are prepared and their average refractive index is matched with a solvent by adjusting the mixture ratio of water and ethylene glycol, which yields an optically transparent solution, selectively reflecting UV.     

The light wave flow effect in a plane-parallel layer with a quasi-zero refractive index under the action of bounded light beams

It is shown that external optical radiation in the 450–1200 nm range can be efficiently transformed under the action of bounded light beams to a surface wave that propagates along the external and internal boundaries of a plane-parallel layer with a quasi-zero refractive index. Reflection regimes with complex and real angles of refraction in the layer are considered. The layer with a quasi-zero refractive index in this boundary problem is located on a highly reflective metal substrate; it is shown that the uniform low reflection of light is achieved in the wavelength range under study.     

Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides

A generally applicable method to simulate the two-dimensional profiles of Ti-concentration and refractive index of Ti:LiNbO₃, waveguides is presented. The influence of the fabricational parameters on the refractive index profiles has been studied in detail. The model parameters are extracted from the available experimental data. The computed values of surface refractive index change agree closely with the experimental results. The model is also extended for coupled waveguides.     

Optimization of reflection spectra for phase-only sampled fiber Bragg gratings

In this paper, the reflection spectra of a phase-only sampled fiber Bragg grating is obtained by optimizing its phase profile. The standard simulated annealing method is improved for optimization, and superior phase profiles which contain as few segments as possible per sampling period are obtained for 8, 16 and 32 identical channels. As very well known, increased number of WDM channels results in higher grating length and refractive index modulation amplitude. It is observed that application of these phase profiles limits the increases in both of these parameters considerably.