Nonuniform Index Research Articles

Laser Self-Focusing and Nonlinear Absorption in Expanding Clusters

An intense short-pulse laser, propagating through a clustered gas, converts the clusters into hot plasma balls on subpicosecond time scale. The polarizability of a ball scales as (omegape 2/3 - omega2)-2, where omegape is the plasma frequency inside it and omega is the laser frequency. Initially, omegape 2/3 > omega2; however, as the clusters expand under hydrodynamic pressure, decreases, causing resonant enhancement in permittivity, first near the laser axis and later away from it. The nonuniform refractive index profile thus created leads to self-focusing of the laser. It also leads to enhanced absorption in its neighborhood that counters the self-focusing effect substantially.

Spectral characteristics and bend response of Bragg gratings inscribed in all-solid bandgap fibers

In this paper, we investigate the spectral characteristics and bend response of fiber Bragg gratings (FBGs) in all-solid photonic bandgap fibers (PBGFs). We inscribe FBGs within the secondary bandgap by ultraviolet (UV) side illumination and observe the couplings to backward core mode, guided LP(01) and LP(11) supermodes and radiative LP(02) supermodes. The mechanisms of these resonant couplings in the FBG are described in detail. We demonstrate that only those supermodes with certain phase relationships and symmetric mode field profiles are responsible for the supermode resonances. When the fiber grating is bent, the guided supermode resonances become chirped as a result of the strain gradient over the fiber cross section. Meanwhile, the core resonance is enhanced, due to more energy of the core mode distributed in the cladding rods. The bend response is direction dependant owing to the nonuniform UV-induced average index raises and index modulation over the high-index rod lattice. .

Critical coagulation concentration for a suspension of cation-absorptive biocolloids

Critical coagulation concentration (CCC) of a biocolloidal suspension is investigated theoretically by taking into account the influences of cationic absorption in particulate membrane phase, variation in dielectric constant, size of charged species and nonuniform distribution of fixed membrane groups. Here, an increase in both valence and effective radius of the original functional group (OFG) via absorption of electrolyte cation(s) is especially considered. The simulated results indicate that stronger membrane electricity yields a larger electrostatic repulsion and a higher potential energy, which generates a higher CCC. A lower CCC can be resulted from a larger (1) cation-functional group complex (CFGC) for a fixed difference between the radius of CFGC and that of OFG, Δ, (2) number of OFG(s) involved in the formation of a CFGC, (3) Δ for a positively charged CFGC, (4) dielectric constant of main membrane phase, in general, (5) membrane thickness for a constant amount of space-average functional groups, and (6) effective radius of anions. CCC decreases with the following parameters: (1) Δ for a negatively charged CFGC, (2) equilibrium constant of the reaction of cationic absorption, (3) nonuniform feature index of fixed groups, and (4) effective radius of cations.

Electrophoresis of a Biocolloid Covered with a Cation-Absorptive Membrane

The electrophoretic behavior of a biocolloid covered with a charged membrane is theoretically analyzed in the present study. Here, the influences of nonuniformly distributed fixed groups, absorption of cations by fixed original functional groups, variation in dielectric constant in the electrophoretic system, and ionic sizes are considered. The results of numerical simulation suggest that a larger absolute value of the electrophoric mobility of biocolloids could be generated by larger membrane electricity. The absolute value of the electrophoric mobility for the nonlinear distribution of the fixed groups is larger than that for the linear distribution of the fixed groups. The absolute value of the electrophoric mobility increases with (1) the concentration of total fixed groups, (2) the cation-absorption equilibrium constant, (3) the nonuniform feature index for functional-groups distribution, (4) the dielectric constants of the inner uncharged membrane zone for only mobile cationic charge and for both mobile cationic and anionic charge, and (5) the effective size of the cations. An increase in the absolute value of the electrophoric mobility can also be resulted from a decrease in the following parameters: (1) the friction coefficient of the biocolloidal membrane phase, (2) the membrane thickness, (3) the dielectric constant of space for all charge and of outer uncharged membrane zone, (4) the effective sizes of anions and fixed groups, and (5) the number of cations and the fixed original functional groups involved in the formation of a cation-functional group complex.

Description of readout processes during strong beam coupling.

We show, using the symmetry properties of the coupled-wave equations for the transmission and reflection geometries, that any readout characteristic of dynamic spatially nonuniform index gratings in photorefractive crystals can be explicitly expressed through the characteristics of the recording light beams. This approach is applied to describe the impact of beam coupling on the diffraction efficiency of dynamic gratings and on the output intensities of the light beams at instantaneous input phase changes (light grating translation). Further implications of this general approach are discussed.

Biological glass fibers: correlation between optical and structural properties.

Biological systems have, through the course of time, evolved unique solutions for complex optical problems. These solutions are often achieved through a sophisticated control of fine structural features. Here we present a detailed study of the optical properties of basalia spicules from the glass sponge Euplectella aspergillum and reconcile them with structural characteristics. We show these biosilica fibers to have a distinctive layered design with specific compositional variations in the glass/organic composite and a corresponding nonuniform refractive index profile with a high-index core and a low-index cladding. The spicules can function as single-mode, few-mode, or multimode fibers, with spines serving as illumination points along the spicule shaft. The presence of a lens-like structure at the end of the fiber increases its light-collecting efficiency. Although free-space coupling experiments emphasize the similarity of these spicules to commercial optical fibers, the absence of any birefringence, the presence of technologically inaccessible dopants in the fibers, and their improved mechanical properties highlight the advantages of the low-temperature synthesis used by biology to construct these remarkable structures.

Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers

A perfect two-dimensional porous alumina photonic crystal with 500 nm interpore distance was fabricated on an area of 4 cm2 via imprint methods and subsequent electrochemical anodization. By comparing measured reflectivity with theory, the refractive indices in the oxide layers were determined. The results indicate that the porous alumina structure is composed of a duplex oxide layer: an inner oxide layer consisting of pure alumina oxide of 50 nm in thickness, and an outer oxide layer of a nonuniform refractive index. We suggest that the nonuniform refractive index of the outer oxide arises from an inhomogeneous distribution of anion species concentrated in the intermediate part of the outer oxide.

Error estimation of laser-Doppler anemometry measurements in fluids with spatial inhomogeneities of the refractive index

We report a combined experimental and theoretical investigation of the influence of spatial non-uniformities of the refractive index on the accuracy of laser Doppler anemometry (LDA) measurements in transparent fluids. One LDA beam is guided through heated air of a thermal boundary layer near a heated vertical flat plate. It is found that the hot air is deflecting the beam because of a modification of the refractive index n in the fluid. This deflection causes three effects: (1) spatial displacement of beam intersection, (2) waist mismatch in the measurement volume and (3) variation in interference fringe distance. With the help of a rotating disk calibration system the resulting displacement of the LDA measurement volume and the Doppler frequency variation is systematically studied at different temperatures. Using a simple model of beam propagation under the influence of well-defined temperature inhomogeneities, the displacement of measurement volume and change in Doppler frequency are calculated and are found to be in agreement with the experimental observations. The results provide a rational framework for an assessment of the accuracy of LDA data in arbitrary transparent fluids with non-uniform refractive index.

Photosensitivity and application with 157-nm F/sub 2/ laser radiation in planar lightwave circuits

Photosensitivity studies of germanosilica planar waveguides were carried out with short-wavelength 157-nm light from an F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> laser. More than a 5×10/sup -3/ refractive-index change was induced in a nonuniform index profile concentrated near the cladding-core interface and confirmed by an atomic force microscopy in 157-nm radiated fiber. This profile geometry narrows with the laser exposure to offer practical application in trimming phase errors and controlling birefringence in frequency domain modulators where a 1.7×10/sup -3/ effective index change and a 5×10/sup -4/ birefringence change were induced, respectively. The 157-nm photosensitivity response is more than 15 times stronger than that by a 248-nm KrF laser and more than twofold stronger than that by a 193-nm ArF laser.

An experimental examination of intensity fluctuations of a host droplet containing an inclusion

We report experimental data showing the dependence of the experimental intensity fluctuation amplitudes at a scattering angle of 90° of a liquid droplet with an inclusion. Despite efforts to match the refractive indices of host and inclusion, we could not make the amplitude vanish. This could be due to a non-uniform refractive index of the solid inclusion. Qualitative agreement is reached between experimental results and model simulations.

Improving the Spectral Efficiency of DWDM-DST Systems through Line Coding and Optimized FBGs

In this contribution we show that by using the dense wavelength division multiplexing (DWDM) and the dispersion supported transmission (DST) techniques, together with compressed bandwidth data formats and optimized fiber Bragg grating (FBG) filters, it is possible to implement optical fiber communication systems with very high spectral efficiencies and long fiber spans. This is achieved by using fiber gratings with a Gaussian apodization together with a non-uniform average index perturbation, acting simultaneously as optical demultiplexers and group velocity dispersion compensators. For a be 32 x 20 Gsymbol/s WDM-DST system, we demonstrate spectral efficiencies of 0.7 bit/s/Hz for the binary and duobinary data formats, at distances of 65 km and 100 km, respectively, over standard single-mode fiber. Using 4-level coding, 1.28 Tbit/s (32 x 40 Gbit/s) can be packed in approximately 10 nm of optical bandwidth, corresponding to a spectral efficiency of 1 bit/s/Hz, and transmitted over a fiber span with 45 km.

Self-induced thermal effects and modal competition in continuous-wave optical parametric oscillators

We present a model of quasi-phase-matched continuous-wave optical parametric oscillators that accounts for self-induced heating of the photorefractive crystal and modal interaction through pump depletion. The model allows the temperature and therefore the refractive index of the nonlinear medium to vary in the radial and longitudinal dimensions as a result of local absorption of the optical power. We consider the effect of this nonuniform index on single-mode and multimode operation. For a single signal–idler pair we observe thermal lensing, bulk tuning, and modal distortion. For multiple pairs of signal and idler we demonstrate and discuss other phenomena, including spatially dependent modal competition.

Explanation of the lens paradox.

The lens paradox is the phenomenon in which the curvature of the human eye lens increases (steepens) with age, yet most human eyes do not become more powerful as they get older. One explanation of this phenomenon resides in changes in the refractive index distribution of the lens of the eye. This study provides the first noninvasive measurements of refractive index distribution that support this explanation of the lens paradox. The lens of the human eye is a mass of densely packed cellular tissue filled with protein and contained within an elastic capsule. Unlike most man-made lenses, it has a nonuniform refractive index, such that the refractive index increases from the surface inwards to the center. This “gradient index” is an important contributor to the power of the lens. In fact, because of the gradient, the power of the lens is greater than it would be if the refractive index were constant and equal to the highest value inside the lens. The lens grows throughout life. New cells, shaped as long fibers, continually form and wrap around older cells without any of the cells being discarded. As part of this growth, the lens becomes thicker and its surfaces become more curved. It would therefore be expected that the lens, and hence the eye itself, should become more powerful and that there would be a trend towards eyes becoming myopic with age (Figs. 1a and b). However, the opposite occurs, with the majority of eyes changing in the opposite direction (hypermetropia) by an average of approximately 2 D between the ages of 30 and 60 years 8 (Fig. 1c). Brown coined the term “lens paradox” for this apparent contradiction. Because the power of the cornea at the front of the eye does not become weaker with age, 10 the most likely explanation for the lens paradox is an age-dependent change in the refractive index of the human lens. Confirmation of this has been limited by a paucity of experimental results for the refractive index distribution, particularly in a plane containing the optical axis of the lens. Attempts by a number of authors to explain the lens paradox have therefore relied on theoretical modeling of the refractive index distribution and of possible changes to the distribution with age. Suggested changes due to age include a reduced amplitude of refractive index variation through the lens, or a change in refractive index profile across the lens. In the former case, either the refractive index of the outer cortex could increase or the refractive index of the inner nucleus could decrease, while for the latter the gradient index profile could become flatter in the middle of the lens and then increase in steepness towards the edges. Theoretically, all of these are possible. It should be mentioned that another hypothesis that has been put forward to explain the lens paradox is that there is a decrease in eye length with age. This was based on analysis of biometric data from the late 1950s. However some more recent measurements do not support this theory, 13 although it is still considered to be a possibility. We have investigated the change in gradient index with age and its effect on lens power using magnetic resonance micro-imaging. A preliminary description of the method has been given previously and a similar technique has been applied to measure the refractive index gradient in fish eye lenses. The technique relies on the nuclear magnetic resonance transverse relaxation rate R2 1/T2 for water protons being linearly dependent on protein concentration. Human lenses were obtained from the Queensland and New South Wales Eye banks and stored at 34.5°C in artificial aqueous humor. The artificial aqueous humour (AAH) was made under sterile conditions using Auto-Pow minimum essential medium with Earl’s salts (MEME: ICN Biochemicals, Costa Mesa, CA), with the addition of HEPES (10 mm), glutamine (2 mm), penicillin (1000 g l ), streptomycin (1 mg l ) amphotericin (10 mg l ) and adjusted to a pH of 7.4. Some lenses were stripped of their capsule and homogenized by hand mixing with a stainless steel spatula. Homogenates of various concentrations were made and refractive index measured using an Abbe refractometer. Measurements of transverse relaxation rate R2 were made on a Bruker MSL200 NMR spectroscopy/micro-imaging system, using a standard Carr-Purcell/Meiboom-Gill pulse sequence 19 with a 180° pulse spacing of 4.2 ms. A plot of refractive index n as a function of R2 showed a strong linear correlation:

Some aspects of the optimal control of non-linear descriptor systems

The modification of the algorithms of the calculus of variations and Pontryagin's maximum principle required for them to be applicable to non-linear descriptor control systems is demonstrated. The classical calculus of variations is still applicable in optimization without constraints on the control, but when such constraints are imposed, the application of Pontryagin's maximum principle in its standard or extended form requires a distinction to be made between proper and non-proper descriptor systems. In the non-proper case, the solution depends on higher-order time derivatives of the control inputs. For the correct description of the problem and for Pontryagin's maximum principle to be applicable additional phase variables and corresponding integrator chains have to be introduced. The optimal control thus obtained becomes dynamic. To simplify the notation, the index of the algebraic equations of the constraints is assumed to be uniform. In principle, the results remain valid for a non-uniform index also, i.e. when different constraint equations have different indices and different components of the control occur with different maximum orders of the time derivatives. The results are somewhat complicated, particularly in the case of constrained optimization of non-proper systems.

Optical measurement of effective recombination lifetime in silicon epitaxial layers

In this letter we present a novel all-optical pump-probe technique for the measurement of effective recombination lifetime in silicon epitaxial layers. The procedure is based on the measurement of the variation of the attenuation coefficient due to optically injected free carriers of a planar dielectric waveguide defined by the epitaxial layer cladded between the substrate and the air. Perturbation theory is used to take into account nonuniform refractive index distribution due to nonzero surface recombination. The measurement technique is validated by both numerical simulation and experimental results.

Optical power transversely scattered from fiber Bragg gratings: far-field measurements and modeling

Far-field properties of the optical power scattered from type IIA Bragg gratings photowritten within high-N.A. germanosilicate fibers have been studied under various experimental conditions. Experiments were carried out in order to measure the angular distribution of the diffracted beam intensity. The optical power detected in the far field was shown to be scattered around a cone centered on the fiber axis. The azimuthal distribution of scattered optical power was nonuniform. A theoretical model, which takes into account the LP01-mode coupling to radiation modes for wavelengths well below the Bragg wavelength, properly fits the features of the observed pattern. This theoretical model assumes the existence of a nonuniform UV-induced refractive index change across a plane perpendicular to the fiber axis.

Modal analysis of optical fibers with symmetrically distributed nonuniform cores

This paper describes the modal analysis of optical fibers with symmetrically distributed multiple cores. Each core has an identical, axially symmetrical, and nonuniform refractive index profile. Group theoretical approach is applied to treat the symmetry of the waveguide structure. The point-matching method combined with the staircase-approximation method is used to take into account complex boundary conditions and complex refractive index distributions. The numerical computation based on this approach has been found to be very effective.

Moving through a mirage

We consider image motion in the visual field of an observer moving through a rigid environment under mirage conditions, in which light rays follow curved trajectories as a result of a nonuniform atmospheric refractive index. We show that, under these conditions, the translation motion field does not conform to the simple pattern observed in the absence of refraction; instead it depends on the transfer characteristic of the mirage. An interesting finding is that if the mirage has a transfer characteristic that folds, as occurs for example in the desert mirage, the motion field will, in general, be infinite at the fold point.

Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers

Heating effects on the light power vs. current characteristic of planar top-emitting vertical-cavity laser diodes are analyzed by thermal, optical and electrical modeling. The two-dimensional finite element thermal-electrical simulation considers the spatial current funneling in the top p-doped distributed Bragg reflector and a current density dependent resistivity of the hetero-barrier. Layered regions are described by anisotropic material parameters. Non-uniform refractive index temperature coefficients of the semiconductor materials are applied in the vertical optical modeling. The strongly inhomogeneous temperature distribution causes thermal increases of emission wavelength and reflectivity as well as decreases of threshold gain and external quantum efficiency with rising current. Finally, the calculated maximum light power is found to be decisively affected by the temperature coefficients of the refractive indices. >

Dissociation of highly excited triplet benzophenone into phenyl radicals and carbon monoxide: determination of the reaction quantum yield and the heat of reaction by time-resolved thermal lensing technique

The photodissociation path and quantum yield of benzophenone in the highly excited triplet (T n ) state were determined in benzene solution at room temperature using two-photon absorption (TPA) and time-resolved thermal lensing (TRTL) techniques. The TRTL signals measured were composed of fast and slow components: the fast one rose with a time constant less than the instrumental response time (≈ 100 ns), while the slower rose with a time constant of about 3 μs. The fractions of the fast and slow TRTL signals increased and decreased, respectively, with the laser power. The TRTL signals were quantitatively analyzed on the basis of the probe-light tracing in the nonuniform refractive index medium. The efficiency of thermal lensing (TRTL signal intensity/heat available to thermal lens) depends on the spatial profile of thermal distribution. Therefore, the TRTL signal due to TPA is more intense than that due to single photon absorption (SPA): TPA was about four times more sensitive in the TRTL signal than SPA under the experimental conditions employed. The TRTL signals were simulated using a kinetic model including the S 1←S 0 and T n ←T 1 absorptions of benzophenone and the subsequent dissociation of the T n molecule. The reaction quantum yield (Φ r) and the heat of reaction (Δ H) in benzene solution were determined to be 0.39 and 117 kcal mol −1, respectively, based on the experiment and simulation. The dissociation path open for benzophenone in the T n state was thus confirmed to be Ph 2CO→2Ph+CO.