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.     

Fabrication of gradient refractive index ball lenses using the method of combination of ion exchanging and sagging

Based on the Fick’s diffusion equations, the distribution function of refractive index of a gradient refractive index ball lens (GRIN ball lens/GBL) is derived. Lithium containing silicate glass is fabricated and GRIN ball lenses (GBLs) which diameters are from 0.3 mm to 3.0 mm are made by the method of combination of Ion exchanging and sagging in sodium nitrate. Refractive index profiles of these GBLs are measured by interferometer, and the performances such as effective focal length (EFL), back focal length (BFL) and numerical aperture (NA) between GBLs and homogeneous ball lenses (HBLs) are compared. Results show that the distribution of the index of refraction is parabolic curve and its Δn is about 0.0002, the performances of the former are super to the latter.     

Refractive index of standard oils as a function of wavelength and temperature

The refractive indices (n) of eight standard oils from Physikalisch Technische Bundesanstalt, Germany were determined with an accuracy of ±1×10⁻⁴ by using Abbe Refractometer. The measurements were performed at temperature 20°C in the spectral range 0.4–0.7 μm. The experimental data were fitted to the simple Cauchy dispersion formula and the results were found to be consistent within the limits of experimental error. In all cases, the refractive index decreased monotonically with increasing wavelength. The refractive indices (n) of these oils have been measured as a function of the temperature t (20°C up to 50°C) at λ=0.589 μm and were found to have linear temperature dependencies. The refractive indices of the studied oils and the uncertainty in their values are calculated at λ=0.589. The Lorentz–Lorenz (L–L) formula has been tested and it was found to be valid with a maximum deviation of 0.4% and was used to calculate the molecular polarizability θ.     

On the refractive index for neutrons

The commonly used result for the neutron refractive index does not include effects due to binding of the nuclei or multiple scattering. We show how these effects can be incorporated in the theory of coherent neutron scattering and present an expression for the refractive index, which adds to the familiar result correction terms quadratic in the scattering length. Examples discussed in more detail include a calculation of the refractive indexn for H₂ gas. Corrections to 1 —n are of the order 10^–3. Results from our theory, which takes into account the actual dynamics of the scatterers, can differ substantially from those of the static approximation, in which the nuclei are held at fixed positions in space.     

Measurements of the refractive indices and refractive index increment of a synthetic PMMA solutions at 488 nm

We describe a Mach–Zehnder interferometer (MZI) method for measuring the refractive index (RI) of polymethyl-methacrylate (PMMA) solution in both acetone and methyl-ethyl-ketone (MEK). The measurements are made as a function of concentration values 4, 8, 12, 16 and 20 g/l at a wavelength of 488 nm with a high degree of accuracy tends to 1.4×10⁻⁵. The refractive index increments (RIIs) dn/dc of PMMA in both investigated solvents are determined too. In addition, the RIIs Δn as a function of concentration and the RIIs at zero concentration (dn/dc)_c=0 are determined for both solvents accurately. The PMMA solutions in acetone and MEK solvents are chosen for laser light scattering investigations.     

Modified Michelson interferometer for probing refractive index of birefringent crystal CSBN50

Based on the modified Michelson interferometer and phase analysis method, a high-accuracy method for probing the refractive index (RI) of transparent medium is proposed. The validated test was performed on a birefringent crystal CSBN50 with the estimated accuracy being up to 10⁻⁴. The ordinary and extraordinary refractive indices of CSBN50 at 632.8 nm are determined as n₀=2.32853±0.00016 and n_e=2.27664±0.00016, respectively.     

Calculation of the carrier-induced refractive index change in InSb

We report a theoretical model for an estimate of carrier-induced changes in the refractive index of InSb at room temperature. The dispersion of n within the photon-energy interval of 0.12–0.24 eV is investigated for nonequilibrium carrier concentrations of 10¹⁵–10¹⁸ cm^–3. An analysis of the influence of the initial carrier density on n is performed. The obtained results can help to develop InSb opto-electronic devices.     

Full-field measurement of surface reflectivity using a microscopy for refractive index profiling of GRIN lenses

This paper outlines an improved technique for profiling the refractive index of Graded-index (GRIN) lenses based on the measurements obtained from a reflectivity image. Reflective cross-sectional image of the GRIN lens were compared with a reflectance reference target under illumination at small incidence angles to obtain the full-field refractive index distribution of the GRIN lens quickly and easily.     

Design and optimisation of high-brightness 980 nm laser diodes with distributed phase correction

Designs for 980 nm Al _x Ga_1–x As/In_0.2Ga_0.8As/GaAs high-power, high-brightness semiconductor lasers/amplifiers with distributed phase correction and short-cavity lengths (i.e. cavity lengths 560–1040 m) are presented. The proposed lasers/amplifiers employ a single mode feed waveguide coupled to a power amplifier with a laterally graded effective refractive index (GRIN) profile to control the lateral mode shape and phase. The lateral index of the power amplifier has a hyperbolic secant (HYSEC) profile, which can be approximately realised by tailoring the effective refractive index of the amplifier using a series of discrete etches. The epitaxial and structure designs of the laterally discretised GRIN lasers/amplifiers are presented. Finally, a method for improving the effective refractive index discretisation is described.     

Broad band antireflection coating on zinc sulphide simultaneously effective in SWIR, MWIR and LWIR regions

In recent years multi-spectral imagery is steadily growing popularity. Multi-channel imaging which includes short-wave infrared (SWIR), mid-wave infrared (MWIR) and long-wave infrared (LWIR) systems are useful for threat detection, tracking, thermal signature detection and terrain analysis. In this paper, a broad band antireflection coating on ZnS substrate, simultaneously effective in SWIR, MWIR and LWIR is reported. The coating design approach was evolved using gradient index concept, where refractive index varies gradually from incident media to the ZnS (n = 2.2) substrate. The gradient index profile depicted by 4th degree polynomial n(t) = −0.45t⁴ + 1.9t³ − 2.7t² + 1.9t + 1,where n(t) is the refractive index at the distance t from ambient, and t is the thickness in micron. The profile is best approximated by eight discrete step index layers, whose first layer is thorium fluoride (n = 1.42; lowest index stable material available). Other seven layers are replaced by two equivalent layer system of real materials thorium fluoride and zinc sulphide. Final 15 layers design is deposited by e-beam evaporation. The maximum layer thickness was restricted around 0.7 μm to overcome the stress problem in the film. This 15 layers coating has shown average transmission 95% in 0.9–10.5 μm spectral band having peak 99% at 9 μm.     

The temperature dependence of the refractive index of an aqueous suspension of polystyrene microspheres

We report an experimental measurement, based on an interferometric technique, for the determination of the temperature dependence of the refractive index n _L of a liquid suspension of dielectric spheres in the thermal range 20–52° C. In this range we have measured values of n _L /T of order of magnitude 10^–4° C^–1. The observed values are compared with those obtained for water.     

Nonlinear optical responses of Sudan IV doped liquid crystal by z-scan and moiré deflectometry techniques

The nonlinear optical properties of a nematic liquid crystal doped with an azo dye were investigated. The magnitude and the sign of the third-order nonlinear refractive index, n₂, were measured using both single-beam z-scan and moiré deflectometry techniques. The measurements were performed at 532 nm using a Nd:Yag CW laser. The positive sign showed that sample which was studied possess a self-focusing optical nonlinearity. Rather close agreement was found between the values for n₂ obtained by z-scan and by moiré deflectometry. The nonlinear refractive index was found to be in the order of 10^− 6 (cm²/W) and the nonlinear absorption coefficient to be β = 0.171 (cm/W).     

Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials

We represent an ultrafast beam-deflection method as a simple and powerful tool for the time-resolved measurement of induced changes of the refractive index in the order of n=10^–5. The method is applied for measuring the changes of components of the refractive index parallel and perpendicular to the pump-pulse polarization on a femtosecond time scale. Fused silica and CS₂ are used as samples for demonstrating our method.     

梯度折射率球透镜的制备及其光线轨迹测试

自麦克斯韦鱼眼透镜理论模型提出后,长期以来学术界一直以为它只是一种绝对光学仪器,在实践中并没有应用的可能。但通过对麦克斯韦鱼眼微球透镜的理论研究表明,在一定条件下,它具有良好的成像性能和耦合效率。根据菲克定律推导出梯度折射率球透镜的折射率分布函数。并且熔制了含Li+硅酸盐玻璃和采用槽沉法以及Na+/Li+离子交换法制备直径为0.3—3.0mm的梯度折射率球透镜。通过干涉法测得了梯度折射率球透镜的折射率分布曲线,并研究了光线通过梯度折射率球透镜的轨迹。研究结果表明:在590℃,离子扩散系数为3.07×10-6mm2/s;所制备的梯度折射率球透镜的折射率分布是抛物线分布,并且和理论分析相吻合;梯度折射率球透镜的光线轨迹满足椭圆方程。     

Effect of crystalline lens surfaces and refractive index on image quality by model simulation analysis

The surfaces and refractive index of crystalline lens play an important role in the optical performance of human eye.On the basis of two eye models,which are widely applied at present,the effect of lens surfaces and its refractive index distribution on optical imaging is analyzed with the optical design software ZEMAX (Zemax Development Co.,San Diego,USA).The result shows that good image quality can be provided by the aspheric lens surfaces or (and) the gradient-index (GRIN) distribution.It has great potential in the design of intraocular lens (IOL).The eye models with an intraocular implantation are presented.     

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.     

Study of the structure and refractive parameters of diethylamine and triethylamine

The refractive index (n) and thermal coefficient of the refractive index (dn/dt) are measured at four wavelengths for the diethylamine and triethylamine. The measurements are carried out using the Bellingham+Stanley model 60/ED high-accuracy Abbe refractometer. The optical permittivity (ε) and its variation with temperature are calculated. Applying the Cauchy equation, the following refractive properties are obtained: the optical dispersion dn/dλ, the dielectric dispersion dε/dλ, the variation of -dn/dT, dε/dT, as a function of wavelength (λ), and Cauchy's constants against temperature. Additionally, molar refractivity versus temperature and wavelength are determined.     

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. , in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as  = _r + i_i and μ = μ_r + iμ_i. The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability _i > 0 and μ_i > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability _i < 0 and μ_i < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters _r, μ_r, _i, and μ_i, in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re{Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously  < 0 and μ < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for _r < 0, μ_r > 0, _i > 0, and μ_i > 0, the refractive index is negative n < 0 provided μ_i/_i > μ_r/_r.     

Design of a hybrid diffractive/refractive achromatized telecentric f·θ lens

The design of a hybrid diffractive/refractive achromatized telecentric f·θ lens with a field of view (FOV) 50° and an effective focal length of 750 mm is presented. The optical stop is placed at the front focal plane so that it is a telecentric system. The design is based on a traditional refractive counterpart, and the designed system consists of a hybrid diffractive/refractive lens and four refractive lenses. The designed f·θ lens shows a considerable reduction in weight with a simplified structure, and exhibits superior performance compared to the refractive system. It is emphasized that the designed f·θ lens can be applied to modern color scanning systems that operate in the visible wavelength range with high performance. It can also be applied to high-energy scanning systems. When applying the designed hybrid diffractive/refractive f·θ lens to the high-energy scanning system, a big laser operating in one longitudinal mode can be replaced by a small multi-mode laser, and the scanning system can be simplified greatly with the accuracy improved.     

Determination of the refractive index over a wide wavelength range through time-delay measurements of femtosecond pulses

We present a simple method to measure the refractive index dispersion over a broad wavelength range (0.6-1.6 μm). In a first step, the optical group indices are obtained by measuring the time-retardation of tunable 150 fs laser pulses within a sample relative to air. The refractive index dispersion is then calculated using a Sellmeier equation that describes the measured group index dispersion. We show that our experimental data agree with previously published results to within 2 × 10⁻⁴ for a 3 mm thick sample of fused silica and to within 3 × 10⁻³ for the index n₁ of a 2 mm thick crystal of the highly dispersive and anisotropic organic crystal 4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate (DAST).