Determination of refractive index profiles of gradient optical waveguides by ellipsometry

Ag⁺-Na⁺ and K⁺-Na⁺ ion-exchanged optical waveguides in soda-lime glass are characterised by ellipsometry. Refractive index profiles of the waveguides are calculated from ellipsometric multiple angle of incidence data using the Newton-Kantorovitch type iterative procedure and compared with those reconstructed by inverse WKB method. It is demonstrated that such continuous profiles with relatively small index gradient (of the order of 0.1 and 0.01), extending to few micrometers in depth, can be determined by ellipsometric measurements. A good agreement is found between results obtained by ellipsometry and by the inverse WKB method at depths above 500–600 nm, while there is a difference in the subsurface region, where ellipsometry is more sensitive to the quality of the surface. The profiles obtained by the two methods are consistent if the surface thin layer is etched.     

Generation of stable self-similar wave packets in inhomogeneous optical waveguides with a traveling refractive index wave

The specific features of the dynamics of wave packets in inhomogeneous optical waveguides with a traveling refractive index wave and a parabolic dependence of the refractive index on the transverse coordinates of the waveguide have been investigated. It has been shown that stable self-similar pulses of short (picoand subpicosecond) duration with a high total pulse energy and a large mode area can be generated in the corresponding waveguides. It has also been demonstrated that the self-similar regime of propagation of durationpreserving wave packets can be achieved, in particular, with the normal dispersion of the active optical waveguide used in the work.     

棱镜耦合法测波导衬底折射率

本文对棱镜耦合法测波导衬底折射率进行了实验研究,在两种入射情况下,对石英玻璃、CaF_2、LiF衬底及C-813-8胶块进行了折射率测量,并得到有益的实验结果.     

Inverse method for the reconstruction of refractive index profile and power management in gradient index optical waveguides

Accurate semi-analytical technique is developed for reconstructing refractive index profiles of optical waveguide by near-field pattern. The approach is shown to be effective for the synthesis of single-mode waveguides. Optimising profiles of planar waveguides for managing power distribution of propagating waves is demonstrated.     

A three-dimensional refractive index model for simulation of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed with using the so-called “split”-operator method, when the influence of the propagation medium’s refractive index inhomogeneities is accounted for only within a system of infinitely narrow layers (phase screens) where phase is distorted. Commonly, under certain assumptions, such phase screens are considered as mutually statistically uncorrelated. However, in several important applications including laser target tracking, remote sensing, and atmospheric imaging, accurate optical field propagation modeling assumes upper limitations on interscreen spacing. The latter situation can be observed, for instance, in the presence of large-scale turbulent inhomogeneities or in deep turbulence conditions, where interscreen distances become comparable with turbulence outer scale and, hence, corresponding phase screens cannot be statistically uncorrelated. In this paper, we discuss correlated phase screens. The statistical characteristics of screens are calculated based on a representation of turbulent fluctuations of three-dimensional (3D) refractive index random field as a set of sequentially correlated 3D layers displaced in the wave propagation direction. The statistical characteristics of refractive index fluctuations are described in terms of the von Karman power spectrum density. In the representation of these 3D layers by corresponding phase screens, the geometrical optics approximation is used.     

Fabrication of gradient refractive index ball lenses

The theoretical model of the Maxwell fish eye sphere lens has long been regarded as an absolute optical instrument without practical application since it was proposed. But the study on the theory of Maxwell fish eye micro-spherical lens shows that at certain condition it has fine image formation ability and coupling efficiency. Based on the Fick's diffusion equations, the distribution function of refractive index of gradient refractive index (GRIN) ball lenses is derived. Lithium-containing silicate glass is fabricated and GRIN ball lenses whose diameters are from 0.3 to 3.0 mm are made by ion exchange and the sagging method in sodium nitrate. Radial refractive index profiles of these GRIN ball lens are measured by interferometer. Results show that the distribution of the index of refraction is a parabolic curve and in concordance with the computational consequence and its Δn is 0.0002.     

Nonlinear refractive index in erbium-doped optical amplifiers

Nonlinear effects in erbium-doped fibre amplifiers are analysed by a numerical approach based on the combined use of the finite element method and the Runge-Kutta algorithm. In particular, the variation of the refractive index due to the perturbation in the gain coefficient is evaluated through the nonlinear Kramers-Kronig relations. For the first time the nonlinear coefficients of the polynomial expansion of the refractive index variation have been calculated. Several kinds of perturbation, produced by signal and pump intensity, by amplifier length and by dopant concentration have been considered to investigate the refractive index change behaviour. The use of the finite element method allows the local evaluation of the pump and signal intensities without introducing any simplifying hypothesis on the electromagnetic field distribution.     

Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy

The intrinsic aberrations of high-NA gradient refractive index (GRIN) lenses limit their image quality as well as field of view. Here we used a pupil-segmentation-based adaptive optical approach to correct the inherent aberrations in a two-photon fluorescence endoscope utilizing a 0.8 NA GRIN lens. By correcting the field-dependent aberrations, we recovered diffraction-limited performance across a large imaging field. The consequent improvements in imaging signal and resolution allowed us to detect fine structures that were otherwise invisible inside mouse brain slices.     

折射率渐变透镜的数值设计

传统折射率渐变透镜的设计要求初级馈源天线具有稳定的相位中心,这就限制了透镜的应用范围。为拓宽透镜的应用范围,提出了一种折射率渐变透镜的数值设计方法,通过对馈源天线的极化电场离散采样获得相位信息,并据此设计透镜,随后用金属短线结构的新型人工电磁材料来实现这种透镜。这种设计方法简单灵活,对馈源天线没有限制。以经典矩形贴片天线为例,比较了贴片天线和透镜天线的回波损耗和远场方向图,结果表明运用这种方法设计的透镜使贴片天线的增益提高了2 dB,口径效率从62%提高到了99%。     

Electromagnetic wave propagation from a point source in air through a medium with a negative refractive index

Refraction of an electromagnetic wave from a point source to a medium with a negative refractive index is considered. An electric Hertz dipole that is located in air and directed parallel to a plane interface is considered as the point source. It is rigorously shown that the electromagnetic radiation propagated from the dipole into the medium with the negative refractive index is focused within a certain region in this medium. The sizes of the focusing region are determined. As a result, it is pointed out that the diffraction limit cannot be overcome by using homogeneous materials with negative refractive indices.     

Measurement of gradient refractive index profile of crystalline lens of fisheye in vivo using optical coherence tomography

We report the use of optical coherence tomography (OCT) for noninvasive measurement of the refractive index profile of a crystalline lens of a fisheye. The approach exploits the fact that OCT provides a direct measurement of the optical path of the light traveled through the medium. The gradient refractive index profile for the crystalline lens was retrieved by iterative fitting of the optical path calculated by the ray tracing method with that experimentally measured using OCT. The estimated error in refractive index is approximately 1%. The measured gradient refractive index and Matthiessen’s ratio (ratio of focal length to lens radius) are in good agreement with the previously reported values. PACS 42.62.Be; 42.30.-d; 42.30.Wb; 07.60.Vg     

Resolving the wave vector in negative refractive index media

We address the general issue of resolving the wave vector in complex electromagnetic media including negative refractive media. This requires us to make a physical choice of the sign of a square root imposed merely by conditions of causality. By considering the analytic behavior of the wave vector in the complex plane, it is shown that there are a total of eight physically distinct cases in the four quadrants of two Riemann sheets.     

折射率梯度表面机理的研究

本文构建了一种折射率梯度表面,并利用几何光学法对其物理机理作了研究,发现这种折射率梯度表面可以实现入射波到正常反射波,异常反射波,以及介质波的转换.当入射点介质折射率大于某一阈值时,异常反射波束方向角正弦值与入射波束方向角正弦值存在线性关系,意味着平行入射的波经介质后将平行出射到空气;而当折射率梯度常数大于某一阈值时,任何方向入射的波在透射到介质后,将发生全反射,被束缚在介质中.总而言之,通过调节结构参数,可以实现对波束方向与强度的人工调控,从而提供了一种人工可控的全介质梯度表面的工程实现思路.     

Determination of refractive index profiles in diffused optical waveguides

An improved method for the reconstruction of diffused waveguide index profiles from experimental mode spectra is proposed. The method uses a parabolic approximation between successive points. It is tested on the example of an exponential profile, and applied to the reconstruction of index profiles in Ag⁺ ion-exchanged waveguides from measured mode spectra. This method appears to work well also in the cases of very few mode wave-guides.     

An interferometric method for refractive index profiling of planar gradient index waveguides

In this paper, we present an interferometric method to determine the refractive index profile in graded-index planar waveguides. To begin, part of the soda-lime glass substrate surface was coated with aluminum and then was immersed in molten AgNO₃ to fabricate a planar waveguide on the uncoated part of the surface. After the ion exchange, the coating was removed. Then, the sample was polished obliquely along the boundary between the ion-exchanged and non-ion-exchanged regions, to form a wedge. Thereafter, it was placed inside a Mach–Zehnder interferometer. The fringe pattern was analyzed using the well-known Fourier method and the refractive index profile was determined. The sample preparation, data analysis and experimental results are presented.     

Large refractive index with vanishing absorption in optical fibers

We propose and demonstrate a novel scheme for realizing large refractive index with vanishing absorption in a three-level quantum system consisting of the energy levels of Er³⁺-doped ZrF₄–BaF₂–LaF₃–AlF₃–NaF (ZBLAN) optical fiber. It is found that the refractive index of the probe field can be controlled via the coherent coupling field and incoherent pumping field. The switching from negative refractive index to positive refractive index and manipulation of the value of the index of refraction while maintaining vanishing absorption of the probe field can be achieved via tuning the detuning of the coherent coupling field. Our scheme may provide some new possibility for technological applications in fiber communication.     

Multilayer graphene refractive index tuning by optical power

Graphene's optical absorption coefficient increases linearly with the number of layers making it more effective in the construction of optical tuning graphene-based devices. Refractive index(RI) is one of the important optical parameters of the graphene for accurately describing its optical characteristics and further applications. In view of the RI research of the multilayer graphene is lacking and existing measurement methods are complicated. Optical power tuning RI of multilayer graphene is investigated using a simple measurement and no temperature cross sensitivity all optical fiber sensing structure.Optical power tuning RI characteristics of multilayer graphene are studied by tuning the introducing broad band light power from 0.57 mW to 22.7 m W. Different thickness graphene coating shows different tuning efficiency. At 4.86-μm thickness,a 3.433-nm Bragg wavelength shift is obtained with 156.2-pm/mW wavelength versus optical power tuning sensitivity corresponding to 3.25×10~3 RI change and 0.154 URI/W(URI, unit of RI) RI optical power tuning efficiency.     

Experimental observation of wave chaos in a conventional optical resonator

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, macroscopic approach offers complete and easy control and allows unprecedented study of optical wave chaos.     

Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave

The conditions for the onset of modulation instability of wave packets in an optical waveguide in the presence of the traveling refractive index wave are investigated. An expression governing the growth rate of a small harmonic perturbation at the early development stage of the modulation instability is obtained. Based on numerical analysis, the behavior of the wave packet at the developed modulation instability stage is studied for different parameters of the waveguide and the refractive index wave.     

Ray delay in gradient waveguides with asymmetric transverse refractive index profiles

Former investigations of symmetric refractive index profiles in gradient waveguides are extended to include also asymmetric profile curves. The generalized delay expression is derived and illustrated by means of various examples. Possibilities of compensating symmetric by asymmetric components of the refractive index in the delay formula lead to a number of optimum profiles for low-dispersion transmission.The pulse broadening in a waveguide with a gradient profile being distributed in a ring-shaped form over its cross section, which is to serve as an example of a guide with an asymmetric profile, is assessed.