Refractive index variation in compression molding of precision glass optical components

Compression molding of glass optical components is a high volume near net-shape precision fabrication method. In a compression molding process, a variation of the refractive index occurs along the radial direction of the glass component due to thermal treatment. The variation of refractive index is an important parameter that can affect the performance of optical lenses, especially lenses used for high precision optical systems. Refractive index variations in molded glass lenses under different cooling conditions were investigated using both an experimental approach and a numerical simulation. Specifically, refractive index variations inside molded glass lenses were evaluated by measuring optical wavefront variations with a Shack-Hartmann sensor system. The measured refractive index variations of the molded glass lenses were compared with the numerical simulation as a validation of the modeling approach.     

Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab

The formulation for the extinction and scattering cross sections of closely spaced parallel infinite cylinders in a dielectric medium of finite thickness is presented. We consider the general case of dissimilar refractive indices for the half-spaces on both sides of the slab, and the diameter and refractive index of each cylinder can be different. The formulation accounts for the coherent scattering between the cylinders and scattering of the multiply reflected internal waves inside the slab. Discontinuity in the refractive index across the dielectric slab interfaces results in boundary reflections that modify the angular distribution of the scattered intensity in both forward and backward directions. The extinction cross section, which is derived by a formal application of the optical theorem, is shown to consist of both a forward and a backward component. The general solution is applied to obtain the formulas for the cases of cylinders in front of a reflecting plane, cylinders inside a semi-infinite dielectric medium, and cylinders in free space.     

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.     

Tunable electro-optic Microlens array. II. Cylindrical geometry

Although the concept of an artificial compound eye has been discussed in the literature, its optical arrangement has never been widely adopted for optical design. A design is presented for a tunable gradient-index microlens array, believed to be new, induced electro-optically inside a cylindrical shell. The transparent electrodes on the both sides of the shell are positioned such that the electrodes on the opposite side compensate the phase delay from the electrodes on the front side for a normally incident plane wave, thus suppressing the intrinsic electrode diffraction for the device without applied voltage. The original technique of the electric field calculation was developed to analyze the induced refractive index inside the shell for two types of electro-optic (EO) ceramics: with linear and with quadratic EO effects. For the linear effect it was shown that for given EO coefficients, electric field strength and intrinsic refractive index, the electrode number should exceed a certain amount to make the focal distance less than the cylinder radius. The quadratic effect provides higher sensitivity to the type of the diffracted wave polarization. It was shown how the quadratic coefficient ratio R(12)/R(11) affects the focal-length difference between TE and TM light polarization.     

Slot optical waveguide usage in forming passive optical devices

We have reviewed the work on SOI slot optical waveguides followed by our work. In a slot waveguide structure, light can be confined in a low index slot guarded by high index slabs. Slot structures are being used in forming complex structures; such as ring resonator circuits. The increased round trip in ring resonator circuits signifies the importance of dispersion calculations. We did analytical and numerical investigations of slot structures' dispersion characteristics. Our dispersion tuned slot structures can help in reducing the dispersion effects on optical signal, which will in turn improve the efficiency of light-on-chip circuits. Since the advent of slot optical waveguides, SOI based slot optical waveguides have been under consideration. It has been found that glass based slot optical waveguide structures with relatively low refractive index contrast ratio can also play an important role in forming complex nano-size optical devices. We made use of power confined inside low index slot regions for a double slot structure. Opto-mechanical sensors have been proposed based upon: (a) variation in power confined inside low index slot region due to the movement of central high index slab under the action of external force (temperature, pressure, humidity, etc). vide Chinese Patent No. ZL 200710176770.1, 2007 (b) variation in power confined inside low refractive index slot regions due to movement of both slots under the action of external force (temperature, pressure, humidity, etc).     

Evolution of graded refractive index in squid lenses.

A lens with a graded refractive index is required for vision in aquatic animals with camera-type eyes. This optical design entails a radial gradient of protein density, with low density in external layers and high density in internal layers. To maintain the optical stability of the eye, different material properties are required for proteins in different regions of the lens. In low-density regions of the lens where slight protein aggregation causes significant light scattering, aggregation must be minimized. Squid lens S-crystallin proteins are evolutionarily derived from the glutathione S-transferase protein family. We used biochemistry, optical modelling and phylogenetics to study the evolution and material properties of S-crystallins. S-crystallins are differentially expressed in a radial gradient, suggesting a role in refractive index. This gradient in S-crystallin expression is correlated with their evolutionary history and biochemistry. S-crystallins have been under positive selection. This selection appears to have resulted in stabilization of derived S-crystallins via mutations in the dimer interface and extended electrostatic fields. These derived S-crystallins probably cause the glassy organization and stability of low refractive index lens layers. Our work elucidates the molecular and evolutionary mechanisms underlying the production and maintenance of camera-like optics in squid lenses.     

Highly engineered mesoporous structures for optical processing

Arranging periodic, or quasi-periodic, regions of differing refractive index in one, two, or three dimensions can form a unique class of mesoporous structures. These structures are generally known as photonic crystals, or photonic quasicrystals, and they are the optical analogue of semiconducting materials. Whereas a semiconductor's band structure arises from the interaction of electron or hole waves with an arrangement of ion cores, the photonic crystal band structure results from the interaction of light waves with an arrangement of regions of differing refractive index.What makes photonic crystals highly attractive to the optical engineer is that we can actually place the regions of differing refractive index in a pattern specifically tailored to produce a given optical function, such as an extremely high dispersion, for example. That is, we can define the geometrical arrangement of the dielectric foam to provide us with the form of band structure we require for our optical functionality.In this paper, the optical properties and applications of these highly engineered mesoporous dielectrics will be discussed.     

Laguerre-Gauss and Bessel-Gauss beams in uniaxial crystals

A simple correspondence between the paraxial propagation formulas along the optical axis of a uniaxial crystal and inside an isotropic medium is found in the case of beams with linearly polarized circularly symmetric boundary distributions. The electric fields of the ordinary and the extraordinary beams are related to the corresponding expressions in a medium with refractive index n(o) and n(e)2/n(o), where n(o) and n(e) are the ordinary and the extraordinary refractive indexes, respectively. Closed-form expressions for Laguerre-Gauss and Bessel-Gauss beams propagating through an anisotropic crystal are given.     

Propagation properties of flat-topped beams in a turbulent atmosphere

Based on the extended Huygens–Fresnel principle and the quadratic approximation for phase structure function, the analytical formulas for the average irradiance of the phase-locked and the non-phase-locked radial modified flat-topped array beams in turbulence have been derived. The propagation properties of radial modified flat-topped array beams have been investigated. It is found that the irradiance distributions of the radial flat-topped array beams propagating in turbulence are different from those in free space. The propagation properties depend on the refractive index structure constant, the beam order and the array radius. The power in the bucket (PIB) for the array beams increases with the decrease of the array radius for a given propagation distance. For a certain bucket radius, there exhibits a PIB maximum upon propagation. The optimal propagation distance becomes shorter along with the increasing refractive index structure constant, and the PIB maximum increases with bucket radius.     

Radiative transfer in the atmosphere-ocean system: the finite-element method

The finite-element method has been applied to solving the radiative-transfer equation in a layered medium with a change in the refractive index, such as the atmosphere-ocean system. The physical processes that are included in the algorithm are multiple scattering, bottom-boundary bidirectional reflectivity, and refraction and reflection at the interface between the media with different refractive properties. The incident radiation is a parallel flux on the top boundary that is characteristic of illumination of the atmosphere by the Sun in the UV, visible, and near-IR regions of the electromagnetic spectrum. The necessary changes, compared with the case of a uniformly refracting layered medium, are described. An energy-conservation test has been performed on the model. The algorithm has also been validated through comparison with an equivalent backward Monte Carlo code and with data taken from the literature, and optimal agreement was shown. The results show that the model allows energy conservation independently of the adopted phase function, the number of grid points, and the relative refractive index. The radiative-transfer model can be applied to any other layered system with a change in the refractive index. The fortran code for this algorithm is documented and is available for applications.     

Effect of refractive index on the measurement of optical properties in turbid media

Continuous-wave measurement-based methods offer a rapid cost-effective way to determine optical properties in turbid media. This method requires a measure of the refractive index of the medium, which is often unknown a priori. Whereas previous studies have reported that the refractive index has little impact on the measurement of optical properties, here we show a significant effect of refractive indices on measurements, using both simulations and experiments. In addition we propose a noniterative method to determine the refractive index of the medium. This method can also provide an optimal initial guess of the optical properties for the standard iterative method for determining optical properties in turbid media. Our method is confirmed by simulations and experiments with latex spheres and Intralipid suspensions.     

Perturbation theory for the refractive index mismatch between the inclusion and the surrounding tissues

Abstract

Tissue refractive index is one optical contrast mechanism with diagnostic potential, it is very important to investigate the effect of the refractive index mismatch on light propagation through diffusive regions. Here, we present a new analytical solution of perturbation theory for the refractive index mismatch between the small spherical inclusion and the surrounding tissues. The solution has been used to implement fitting procedures in order to obtain the optical properties of a heterogeneous sphere in semi-infinite medium from measurements of diffuse reflectance. Finally, perturbation theory has been validated by comparisons with the results of Monte Carlo simulation. The new perturbation theory would provide a basis for allowing early disease diagnosis and automatic screening.     

Optical distortion evaluation of an aerodynamically heated window using the interfacial fluid thickness concept

The interfacial fluid thickness (IFT) concept was used to develop a harmonic-mean refractive index gradient magnitude threshold to retrieve the high refractive index gradient regions of an aerodynamically heated window. The retrieved high-gradient regions were used to reconstruct the refractive index field of the window. The numerical three-dimensional optical distortion evaluation was conducted for both the reconstructed and the original refractive index fields of the window using the ray-tracing program based on a recursive algorithm. Wave aberration results show that the methodology based on the IFT concept reduces the refractive index information required to capture the essential optical distortion of the window. The method can also be used for numerically evaluating the optical distortion of the window.     

Surface plasmon resonance sensor using an optical fiber with an inverted graded-index profile

A new optical fiber sensor based on surface plasmon resonance is described. It uses an optical fiber with an inverted graded-index profile. A theoretical analysis of the optical propagation when a point light source was used and a computation of the optical power transmitted by the fiber were performed. Experiments were carried out to measure changes of the transmitted power caused by refractive-index variations of the surrounding dielectric medium. Both the simulation and experiments have shown that the sensor exhibits high sensitivity for changes of the surrounding medium in a refractive index range from 1.33 to 1.39.     

Effects of refractive index on near-infrared tomography of the breast

Near infrared (NIR) optical tomography is an imaging technique in which internal images of optical properties are reconstructed with the boundary measurements of light propagation through the medium. Recent advances in instrumentation and theory have led to the use of this method for the detection and characterization of tumors within the female breast tissue. Most image reconstruction approaches have used the diffusion approximation and have assumed that the refractive index of the breast is constant, with a bulk value of approximately 1.4. We have applied a previously reported modified diffusion approximation, in which the refractive index for different tissues can be modeled. The model was used to generate NIR data from a realistic breast geometry containing a localized anomaly. Using this simulated data, we have reconstructed optical images, both with and without correct knowledge of the refractive-index distribution to show that the modified diffusion approximation can accurately recover the anomaly given a priori knowledge of refractive index. But using a reconstruction algorithm without the use of correct a priori information regarding the refractive-index distribution is shown as recovering the anomaly but with a degraded quality, depending on the degree of refractive index mismatch. The results suggest that provided the refractive index of breast tissue is approximately 1.3-1.4, their exclusion will have minimal effect on the reconstructed images.     

Kramers-Kronig analysis of molecular evanescent-wave absorption spectra obtained by multimode step-index optical fibers

Spectral distortions that arise in evanescent-wave absorption spectra obtained with multimode step-index optical fibers are analyzed both theoretically and experimentally. Theoretical analysis is performed by the application of Kramers-Kronig relations to the real and the imaginary parts of the complex refractive index of an absorbing external medium. It is demonstrated that even when the extinction coefficient of the external medium is small, anomalous dispersion of that medium in the vicinity of an absorption band must be considered. Deviations from Beer's law, band distortions, and shifts in peak position are quantified theoretically as a function of the refractive index and the extinction coefficient of the external medium; the effect of bandwidth for both Lorentzian and Gaussian bands is also evaluated. Numerical simulations are performed for two types of sensing sections in commonly used plastic-clad silica optical fibers. These sensors include an unclad fiber in contact with a lower-index absorbing liquid and a fiber with the original cladding modified with an absorbing species. The numerical results compare favorably with those found experimentally with these types of sensing sections.     

Use of analyte-modulated modal power distribution in multimode optical fibers for simultaneous single-wavelength evanescent-wave refractometry and spectrometry

A new method is described for the simultaneous determination of absorbance and refractive index of a sample medium. The method is based on measurement of the analyte-modulated modal power distribution (MPD) in a multimode waveguide. In turn, the MPD is quantified by the far-field spatial pattern and intensity of light, i.e., the Fraunhofer diffraction pattern (registered on a CCD camera), that emerges from a multimode optical fiber. Operationally, light that is sent down the fiber interacts with the surrounding analyte-containing medium by means of the evanescent wave at the fiber boundary. The light flux in the propagating beam and the internal reflection angles within the fiber are both affected by optical absorption connected with the analyte and by the refractive index of the analyte-containing medium. In turn, these angles are reflected in the angular divergence of the beam as it leaves the fiber. As a result, the Fraunhofer diffraction pattern of that beam yields two parameters that can, together, be used to deduce refractive index and absorbance. This MPD based detection offers important advantages over traditional evanescent-wave detection strategies which rely on recording only the total transmitted optical power or its lost fraction. First, simultaneous determination of sample refractive index and absorbance is possible at a single probe wavelength. Second, the sensitivity of refractometric and absorption measurements can be controlled simply, either by adjusting the distance between the end face of the fiber and the CCD detector or by monitoring selected modal groups at the fiber output. As a demonstration of these capabilities, several weakly absorbing solutions were examined, with refractive indices in the range from 1.3330 to 1.4553 and with absorption coefficients in the range 0-16 cm-1. The new detection strategy is likely to be important in applications in which sample coloration varies and when it is necessary to compensate for variations in the refractive index of a sample.     

Design of omnidirectional high reflectors with quarter-wave dielectric stacks for optical telecommunication bands

A design for omnidirectional high reflectors with quarter-wave dielectric stacks in the optical telecommunication band that uses conventional optical thin-film design theory is described. The omnidirectional bandwidth is derived in units of wavelength and investigated as a function of its high- and low-refractive-index values in the near infrared. The results show that the high refractive index should be larger than 2.26 for an omnidirectional high reflector and that the low refractive index for maximum onmidirectional bandwidth should be approximately 1.5. It is shown that one can design broad-bandwidth omnidirectional high reflectors for S, C, and L bands for optical telecommunication simply by connecting the band edges of omnidirectional high reflectors.     

Scaling property of the diffusion equation for light in a turbid medium with varying refractive index

A spatially varying refractive index leads to the bending of photon paths in a medium, which complicates the Monte Carlo modeling of a photon random walk. We show that the process of photon diffusion in a turbid medium with varying refractive index and curved photon paths can be mapped to the diffusion process in a medium with straight photon paths and modified optical properties. Specifically, the diffusion coefficient, the absorption, and the refractive index of the second medium should differ from the corresponding properties of the first medium by the factor of the squared refractive index of the first medium. The specific intensity of light in the second medium will then be equal to the specific intensity in the first medium divided by the same factor, which also means that the photon density distributions in the two media will be identical. In a Monte Carlo simulation the scaling property suggests that two different algorithms can be used to obtain the photon density distribution, namely, the algorithm with curved photon paths and given optical properties and the algorithm with straight photon paths and modified optical properties.     

Complete algorithm for the calculation light patterns inside the ocular media

Realistic mathematical models are of great importance for studying the optical performance of the human eye. Light propagation algorithms provide robust methods to calculate field distributions inside a homogeneous medium, and thus they can be applied to the study of light patterns inside the anterior and posterior chambers of the eye. Dealing with real eyes implies using very short propagation distances together with highly refractive power surfaces. Thus, the general solutions of the field equation are used instead of paraxial Fresnel solutions. Conditions of application and sampling conditions of the method are clearly stated here. Numerical evaluation of the different refractive surfaces is also analysed. The main result is that a complete algorithm to obtain light patterns at any axial distance inside the eye is proposed. The method uses real corneal measures and axial distances together with crystalline models. Statistical results and individual predictions show the validity of the model. Application of the method is illustrated with the study of a bifocal intraocular lens.