Inhomogeneous Refractive Index Research Articles

Laser beam distortions caused by a shock wave near the turret of a supersonic aircraft

We present results of calculations of the mean intensity of a beam which passes in the beginning of the path through a shock wave which is formed during a supersonic air flow around the turret and propagates further in a homogeneous medium. It is shown that the spatial inhomogeneity of the air refractive index in the region of a shock wave can lead to strong anisotropic distortions of a beam intersecting the wave; the distortions result in focusing and defragmentation of the beam at comparatively short distances from the turret and rapid degradation of the beam in the process of its further propagation.

Blind deconvolution of 3D fluorescence microscopy using depth-variant asymmetric PSF

The 3D wide-field fluorescence microscopy suffers from depth-variant asymmetric blur. The depth-variance and axial asymmetry are due to refractive index mismatch between the immersion and the specimen layer. The radial asymmetry is due to lens imperfections and local refractive index inhomogeneities in the specimen. To obtain the PSF that has these characteristics, there were PSF premeasurement trials. However, they are useless since imaging conditions such as camera position and refractive index of the specimen are changed between the premeasurement and actual imaging. In this article, we focus on removing unknown depth-variant asymmetric blur in such an optical system under the assumption of refractive index homogeneities in the specimen. We propose finding few parameters in the mathematical PSF model from observed images in which the PSF model has a depth-variant asymmetric shape. After generating an initial PSF from the analysis of intensities in the observed image, the parameters are estimated based on a maximum likelihood estimator. Using the estimated PSF, we implement an accelerated GEM algorithm for image deconvolution. Deconvolution result shows the superiority of our algorithm in terms of accuracy, which quantitatively evaluated by FWHM, relative contrast, standard deviation values of intensity peaks and FWHM. Microsc. Res. Tech. 79:480-494, 2016. © 2016 Wiley Periodicals, Inc.

Optical properties of large germanium monocrystals

Optical characteristics of germanium monocrystals with a diameter of 150 and 200 mm grown by the Czochralski and directional crystallization methods were studied. We measured spectral transmittance of the monocrystals in the wavelength range of 2.3–25.0 μm, directional transmission and light scattering in the 2.4–3.0 μm range, and noninhomogeneity of the refractive index of monocrystals by the interference technique at 3.39 μm. The measurements were performed on antimony-doped germanium monocrystals with a diameter of 200 mm and thickness of 15 mm (grown by the directional crystallization method) and 18 mm thick (grown by the Czochralski method). Measurements were also performed on a germanium monocrystal with a diameter of 150 mm and thickness of 15 mm grown by the Czochralski method without adding a ligand. The measurement results revealed different optical quality of monocrystals, expressed in the nature and amount of refractive index inhomogeneity, which imposes restrictions on the use of blanks.

Retrieval of refractive index fields in two-dimensional gradient-index elements from external deflectometry data.

In a previous work, we presented a numerical method for retrieving inhomogeneous refractive index fields in rectangular gradient-index elements from boundary positions and internal boundary slopes associated with a set of interrogating probe beams that transit the medium. The present work extends this method to external boundary beam slopes without knowledge of the refractive index along the surface of the optical element, requiring minimal additional information (outside of beam position and slope data) such as a single known index point inside the medium. The inverse problem is cast as a linear algebraic system describing the deflection of probe beams inside the optical material, and an iterative inversion algorithm is used to generate an index field that produces the boundary value data. By incorporating Snell's law into the system equation through surface values derived from tentative reconstructions of the refractive index, we show in simulation that a series of inversion cycles applied to the system equation accurately recovers the index profile used to generate the test data.

折射率非均匀性对激光陀螺背向散射的影响分析

折射率非均匀性对激光陀螺背向散射的影响分析

TRACK--A new method for the evaluation of low-level extinction coefficient in optical films.

We develop a rigorous methodology named TRACK based on the collection of multi-angle spectrophotometric transmission and reflection data in order to assess the extinction coefficient of quasi-transparent optical films. The accuracy of extinction coefficient values obtained by this method is not affected by sample non-idealities (thickness non-uniformity, refractive index inhomogeneities, anisotropy, interfaces, etc.) and therefore a simple two-layer (substrate/film) optical model can be used. The method requires the acquisition of transmission and reflection data at two angles of incidence: 10° and 65° in p polarization. Data acquired at 10° provide information about the film thickness and the refractive index, while data collected at 65° are used for absorption evaluation and extinction coefficient computation. We test this method on three types of samples: (i) a CR-39 plastic substrate coated with a thick protective coating; (ii) the same substrate coated with a thin TiO(2) film; (iii) and a thick Si(3)N(4) film deposited on Gorilla glass that presents thickness non-uniformity and refractive index gradient non-idealities. We also compare absorption and extinction coefficient values obtained at 410 and 550 nm by both TRACK and Laser Induced Deflection techniques in the case of a 1 micron thick TiO(2) coating. Both methods display consistent extinction coefficient values in the 10(-4) and 10(-5) ranges at 410 and 550 nm, respectively, which proves the validity of the methodology and provides an estimate of its accuracy limit.

Nonautonomous Vortex Beams in an Isotropic Inhomogeneous Refractive-Index Waveguide

We demonstrate nonautonomous vortex beams in an isotropic inhomogeneous refractive-index waveguide with self-focusing nonlinearity. The results show that the nonautonomous vortex beams can self-similarly evolve during a short-term propagation when a delicate balance is obtained between the diffraction, nonlinearity, and gain, although these vortices are approximate. We are concerned with some special but interesting situations, and discuss the changes of the height, width, energy, and central position of the vortices with the increase of propagation distance. In addition, we are also interested in the azimuthal modulational instability of the system, and compare our predictions for the modulational instability growth rates to the numerical results.

Absolute thickness metrology with submicrometer accuracy using a low-coherence distance measuring interferometer.

Absolute physical thickness across the sample aperture is critical in determining the index of a refraction profile from the optical path length profile for gradient index (GRIN) materials, which have a designed inhomogeneous refractive index. Motivated by this application, instrumentation was established to measure the absolute thickness of samples with nominally plane-parallel surfaces up to 50mm thick. The current system is capable of measuring absolute thickness with 120nm (1σ) repeatability and submicrometer expanded measurement uncertainty. Beside GRIN materials, this method is also capable of measuring other inhomogeneous and opaque materials.

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.

Characterization of spark-generated N-waves in air using an optical schlieren method.

Accurate measurement of high-amplitude, broadband shock pulses in air is an important part of laboratory-scale experiments in atmospheric acoustics. Although various methods have been developed, specific drawbacks still exist and need to be addressed. Here, a schlieren optical method was used to reconstruct the pressure signatures of nonlinear spherically diverging short acoustic pulses generated using an electric spark source (2.5 kPa, 33 μs at 10 cm from the source) in homogeneous air. A high-speed camera was used to capture light rays deflected by refractive index inhomogeneities, caused by the acoustic wave. Pressure waveforms were reconstructed from the light intensity patterns in the recorded images using an Abel-type inversion method. Absolute pressure levels were determined by analyzing at different propagation distances the duration of the compression phase of pulses, which changed due to nonlinear propagation effects. Numerical modeling base on the generalized Burgers equation was used to evaluate the smearing of the waveform caused by finite exposure time of the high-speed camera and corresponding limitations in resolution of the schlieren technique. The proposed method allows the study of the evolution of spark-generated shock waves in air starting from the very short distances from the spark, 30 mm, up to 600 mm.

How schlieren affects beam transmissometers and LISST-Deep: an example from the stratified Danube River delta, NW Black Sea

The term ‘schlieren’ describes angular deflection of a light ray when it passes through a fluid region characterized by refractive index inhomogeneities. These inhomogeneities in the marine environment are generally caused by density variations, i.e. salinity and temperature anomalies. The influence of schlieren on transmissometers and the in situ particle sizer LISST-Deep of Sequoia Scientific are examined in the Danube delta during October 2007. A seasonal pycnocline driven mainly by an intense temperature gradient was identified as a major hydrological feature. It was associated with high buoyancy frequency values and minor changes of the refractive index of seawater. Measurements of two 25-cm path-length transmissometers (660 nm and 470 nm) showed distinguishable peaks at the pycnocline. LISST also uses a 5-cm transmissometer (670 nm), which proved to be very sensitive in both cases. This is mainly due to its very small acceptance angle, which enables enhanced light scattering outside the lens, thus increasing beam attenuation. Subsequently, LISST falsely predicts abundance of large particles within the pycnoclines. A buoyancy frequency N of 0.01 s-1 is the new proposed threshold for schlieren occurrence.

Deflectometry for measuring inhomogeneous refractive index fields in two-dimensional gradient-index elements.

We present a numerical method for calculating inhomogeneous refractive index fields in rectangular gradient-index (GRIN) elements from measured boundary positions and slopes of a collection of rays that transit the medium. The inverse problem is reduced to a set of linear algebraic equations after approximating ray trajectories from the measured boundary values and is solved using a pseudo-inverse algorithm for sparse linear equations. The ray trajectories are subsequently corrected using an iterative ray trace procedure to ensure consistency in the solution. We demonstrate our method in simulation by reconstructing a hypothetical rectangular GRIN element on a 15×15 discrete grid using 800 interrogating rays, in which RMS refractive index errors less than 0.5% of the index range (n(max)-n(min)) are achieved. Furthermore, we identify three primary sources of error and assess the importance of data redundancy and system conditioning in the reconstruction process.

Active control of electromagnetic radiation through an enhanced thermo-optic effect.

The control of electromagnetic radiation in transformation optical metamaterials brings the development of vast variety of optical devices. Of a particular importance is the possibility to control the propagation of light with light. In this work, we use a structured planar cavity to enhance the thermo-optic effect in a transformation optical waveguide. In the process, a control laser produces apparent inhomogeneous refractive index change inside the waveguides. The trajectory of a second probe laser beam is then continuously tuned in the experiment. The experimental results agree well with the developed theory. The reported method can provide a new approach toward development of transformation optical devices where active all-optical control of the impinging light can be achieved.

3000 W direct-pumping all-fiber laser based on domestically produced fiber

In this paper we present an all-fiber directly pumped fiber laser in master oscillator power amplifier configuration based on domestically manufactured fibers. In the amplifier stage of the laser, the gain fibers adopt the 20/400 μm Yb-doped double cladding fibers manufactured separately by Wuhan Fiber Home Technologies Group and China Electronics Technology Group Corporation No. 46 Research Institute in two individual experiments. Via this homemade amplifier stage, the system achieves a 1080 nm fiber laser with output powers of 3050 W and 3092 W respectively with two types of fibers. When the gain fiber of the amplifier adopts the YDF manufactured by Wuhan Fiber Home Technologies Group, the corresponding extraction efficiency and the optical-to-optical efficiency reach 67.3% and 63.0% respectively. No residual pump laser is found in the spectrum of output laser, and the beam quality is measured to be M2<2. Similarly, when the gain fiber of the amplifier adopts the YDF manufactured by China Electronics Technology Group Corporation No. 46 Research Institute, the corresponding extraction efficiency and the optical-to-optical efficiency reach 68.2% and 63.9% respectively. To the best of our knowledge, this is the best result ever reported for directly pumped all-fiber laser. Meanwhile, as we use the domestically manufactured fiber as the gain fiber in the amplifier stage, the result verifies the usage of homemade active fibers in 3-kilowatt level fiber laser. By combining the results of the high power fiber laser, the low efficiency of domestic fiber laser in our experiment might be explained to be due to defects in fiber manufacturing process, the inhomogeneous refractive index of the core, structural flaw of the homemade fiber observed by the microscopic images of the cross section and the splicing fuse of homemade fibers. The main difficulty of these two experiments lies in the heat dissipation of the gain fiber in the amplifier stage. Also, due to the restriction of experimental condition, photodarkening test is unable to run for a longer period of time, which is the focus of our further work. Therefore, measures such as refining fiber manufacturing techniques, increasing pump power and optimizing the length of fiber are suggested to be taken in order to obtain a higher output power from homemade fiber laser.

Wavelength control of random polymer fiber laser based on adaptive disorder.

We demonstrate the realization of two different kinds of random polymer optical fiber lasers to control the random lasing wavelength by changing the disorder of polymer optical fibers (POFs). One is a long-range disorder POF based on copolymer refractive-index inhomogeneity, and the other is a short-range disorder POF based on polyhedral oligomeric silsesquioxanes scattering. By end pumped both disorder POFs, the coherent random lasing for both is observed. Meanwhile, the random lasing wavelength of the short-range disorder POF because of a small scattering mean-free path has been found to be blue shifted with respect to the long-range disorder POF, which will give a way to control the random lasing wavelength.

Effect of boundary on refractive index of PDMS

In this contribution we present some results of a study of a refractive index inhomogeneity near the boundary of polydimethylsiloxane (PDMS) samples. We have observed inhomogeneities of the refractive index at PDMS–glass, PDMS–brass, PDMS–Teflon, PDMS–polystyrene and PDMS–PDMS boundaries. The greatest changes of the refractive index were observed at the PDMS–PDMS boundary where an increase of the refractive index in a narrow region close to the boundary was observed. It gives the possibility for guiding light. The existence of such a waveguide was proved by the fact that the boundary also guided light when samples containing PDMS–PDMS boundaries had been bent.

Perspectives of mid-infrared optical coherence tomography for inspection and micrometrology of industrial ceramics.

Optical coherence tomography (OCT) is a promising tool for detecting micro channels, metal prints, defects and delaminations embedded in alumina and zirconia ceramic layers at hundreds of micrometers beneath surfaces. The effect of surface roughness and scattering of probing radiation within sample on OCT inspection is analyzed from the experimental and simulated OCT images of the ceramic samples with varying surface roughnesses and operating wavelengths. By Monte Carlo simulations of the OCT images in the mid-IR the optimal operating wavelength is found to be 4 µm for the alumina samples and 2 µm for the zirconia samples for achieving sufficient probing depth of about 1 mm. The effects of rough surfaces and dispersion on the detection of the embedded boundaries are discussed. Two types of image artefacts are found in OCT images due to multiple reflections between neighboring boundaries and inhomogeneity of refractive index.

Adaptive refinement and selection process through defect localization for reconstructing an inhomogeneous refraction index

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce the number of parameters used in reconstruction, while preserving accuracy. This is achieved through the use of geometrical information obtained from a previously developed defect localization method. The first enhancement consists of a preliminary selection of relevant parameters, while the second one is an adaptive refinement to enhance precision with a low number of parameters. Each of them is numerically illustrated.

The parametric doppler effect upon oblique radiation incidence in quartz glass

Frequency and reflection angle of probe radiation from a refractive-index inhomogeneity induced by an intense pumping pulse in quartz glass and moving with a relativistic velocity are calculated. Conditions under which the normal component of the wave vector of the reflected wave is directed to the opposite or to the same direction as the same component for the incident wave are determined. Comparison with the case of radiation reflection from a relativistic mirror in vacuum is performed. Conditions of the appearance of the Vavilov-Cherenkov radiation from a relativistic refractive-index inhomogeneity induced in the medium by an intense laser pulse are discussed.

Specially shaped negative lens produced in a lithium niobate crystal

The photorefractivity of iron-doped lithium niobate crystal is utilized for creating a negative lens-like structure. The refractive index inhomogeneity acting as a lens is formed due to illumination of the crystal by an optical field with Gaussian spatial distribution of intensity modified by a proper cylindrical lens. Blue line (488 nm) of an argon ion laser is used as a source of light for inducing the inhomogeneity within the crystal. Imaging properties of the photorefractive inhomogeneity are discussed in terms of wave and ray optics approaches and they are practically demonstrated by means of coherent light coming from a He–Ne laser (633 nm). Finally, the focal lengths of the “lens” are calculated using both the lens equation and the formula resulting from analysis of the phase curvature of the wave of light, which passed through the refractive index inhomogeneity.