Design of few-mode fibers with M-modes and low differential mode delay

In this paper, we investigate the design of few-mode fibers (FMFs) guiding 2 to 12 linearly polarized (LP) modes with low differential mode delay (DMD) over the C-band, suitable for long-haul transmission. Two different types of refractive index profile have been considered: a graded-core with a cladding trench (GCCT) profile and a multi-step-index (MSI) profile. The profiles parameters are optimized in order to achieve: the lowest possible DMD and macro-bend losses (MBL) lower than the ITU-T standard recommendation. The optimization results show that the MSI profiles present lower DMD than the minimum achieved with a GCCT profile. Moreover, it is shown that the optimum DMD and the MBL scale with the number of modes for both profiles. The optimum DMD obtained for 12 LP modes is lower than 3 ps/km using a GCCT profile and lower than 2.5 ps/km using a MSI profile. The optimization results reveal that the most preponderant parameter of the GCCT profile is the refractive index relative difference at the core center, Δnco. Reducing Δn co, the DMD is reduced at the expense of increasing the MBL. Regarding the MSI profiles, it is shown that 64 steps are required to obtain a DMD improvement considering 12 LP modes. Finally, the impact of the fabrication margins on the optimum DMD is analyzed. The probability of having a manufactured FMF with 12 LP modes and DMD lower than 12 ps/km is approximately 68% using a GCCT profile and 16% using a MSI profile. © 2013 IEEE.

Design of few-mode fibers with arbitrary and flattened differential mode delay

This letter proposes the use of a refractive index profile with a graded core and a cladding trench for the design of few-mode fibers, aiming an arbitrary differential mode delay (DMD) flattened over the C+ L band. By optimizing the core grading exponent and the dimensioning of the trench, a deviation lower than 0.01 ps/km from a target DMD is observed over the investigated wavelength range. Additionally, it is found that the dimensioning of the trench is almost independent of the target DMD, thereby enabling the use of a simple design rule that guarantees a maximum DMD deviation of 1.8 ps/km for a DMD target between-200 and 200 ps/km. © 2012 IEEE.

Furnace chemical vapor deposition (FCVD) method for special optical fibers fabrication

The features of the Furnace Chemical Vapor Deposition (FCVD) method of manufacturing preforms for special optical fibers are considered. It is shown that misalignment of substrate silica tube and furnace hole axes has a negative effect on the quality of fabricated preforms, leading to angular and radial asymmetry of the refractive index profile. Ways of getting rid of this and other disadvantages of the FCVD method are described. Some advantages of the FCVD method over the MCVD method are shown. It was demonstrated that the FCVD method, despite some drawbacks, allows to manufacture high-quality fiber preforms with good symmetry of the refractive index profile, and thus it is promising for fabrication of dispersion, dispersion varying and active fibers. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

Planar refractive microlens arrays in indium phosphide and quartz substrates

Large-area concave refractive microlens arrays, or concave template structures, and then the non-refractive-index-gradient type of planar refractive microlens arrays in InP and quartz substrates, are fabricated utilizing the method consisting of conventional UV photolithography, thermal shaping of concave photoresist microlenses, etching with an argon ion beam of large diameter, and filling or growing optical medium structures onto the curved surfaces of preshaped concave templates. Several key conditions for fabricating concave and also planar microlenses are discussed in detail. The concave structures obtained are characterized by scanning electron microscope and surface profile measurements. The far-field optical characteristics of quartz/ZrO2 planar refractive microlens arrays have been acquired experimentally. (c) 2008 Society of Photo-Optical Instrumentation Engineers.

Holographic recording in [Sb(Po-3)(3)](n)-Sb2O3 glassy films by photoinduced volume and refraction index changes

Glassy films of 0.2[Sb(PO3)(3)]-0,8Sb(2)O(3) with 0.8 mum-thickness were deposited on quartz substrates by electron beam evaporation. A contraction in the film thickness (photoinduced decrease in volume) and photobleaching effect associated with a decrease of up to 25% in the index of refraction has been observed in the films after irradiation near the bandgap (3.89 eV), using the 350.7 nm (3.54 eV) Kr+ ion laser line with 2.5 W/cm(2) for 30 min. A loss of 30% in the phosphorus concentration was measured by wavelength dispersive X-ray microanalysis in the film after laser irradiation with 5.0 W/cm(2) for 1.0 h. These photoinduced changes in the samples are dependent on the power density and intensity profile of the laser beam. Using a Lloyd's mirror setup for continuous wave holography it was possible to record holographic gratings with period from 500 nm up to 20 mum and depth profile of similar to50 nm in the films after laser irradiation with 5.0 W/cm(2) for 1 h. Real-time diffraction efficiency measurements have shown that ultraviolet irradiation induces first a refractive index grating formation, and after this, the photocon traction effect takes place generating an irreversible relief grating. Diffraction efficiency up to 10% was achieved for the recorded gratings. 3D-refraction index measurements and atomic force microscopy images are presented. (C) 2004 Elsevier B.V. All rights reserved.

2D tunable graded index prism beam steering device based on nematic liquid crystals

Liquid crystal devices are being used in many non-display applications in order to construct small devices controlled by low voltage electronics without mechanical components. In this work, we present a novel liquid crystal device for laser beam steering. In this device the orientation of the liquid crystal molecules can be controlled. A change in the liquid crystal orientation results in a change of the refractive index. When a laser beam passes through the device, the beam will be deviated (Fig.1) and the device works a prism. The main difference between this device and a prism is that in the device the orientation profile of the liquid crystal molecules can be modified so that the laser beam can be deviated a required angle: the device is tuneable.

Chemical composition of volcanic glasses from bottom sediments of the Transpacific profile

Lithofacial types of sediments formed in certain geographic and physical-chemical conditions of the Pacific Ocean are distinguished and characterized. It is shown that the regular change of bottom sediment types forming a genetic series from the coast to the pelagic zone clearly demonstrates a leading role of biogenic-terrigenous sedimentation in their formation. In the pelagic zone of the ocean erosion of islands and seamounts, basalt volcanism of anticlinal uplifts, as well as exhalative contribution play some role in addition to the main source of terrigenous and pyroclastic material from continents. These sources do not change, but only complicate terrigenous sedimentation in the studied area of the ocean.

Dynamics of pattern writing and erasure in photorefractive lithium niobate for data storage applications

The present rate of technological advance continues to place significant demands on data storage devices. The sheer amount of digital data being generated each year along with consumer expectations, fuels these demands. At present, most digital data is stored magnetically, in the form of hard disk drives or on magnetic tape. The increase in areal density (AD) of magnetic hard disk drives over the past 50 years has been of the order of 100 million times, and current devices are storing data at ADs of the order of hundreds of gigabits per square inch. However, it has been known for some time that the progress in this form of data storage is approaching fundamental limits. The main limitation relates to the lower size limit that an individual bit can have for stable storage. Various techniques for overcoming these fundamental limits are currently the focus of considerable research effort. Most attempt to improve current data storage methods, or modify these slightly for higher density storage. Alternatively, three dimensional optical data storage is a promising field for the information storage needs of the future, offering very high density, high speed memory. There are two ways in which data may be recorded in a three dimensional optical medium; either bit-by-bit (similar in principle to an optical disc medium such as CD or DVD) or by using pages of bit data. Bit-by-bit techniques for three dimensional storage offer high density but are inherently slow due to the serial nature of data access. Page-based techniques, where a two-dimensional page of data bits is written in one write operation, can offer significantly higher data rates, due to their parallel nature. Holographic Data Storage (HDS) is one such page-oriented optical memory technique. This field of research has been active for several decades, but with few commercial products presently available. Another page-oriented optical memory technique involves recording pages of data as phase masks in a photorefractive medium. A photorefractive material is one by which the refractive index can be modified by light of the appropriate wavelength and intensity, and this property can be used to store information in these materials. In phase mask storage, two dimensional pages of data are recorded into a photorefractive crystal, as refractive index changes in the medium. A low-intensity readout beam propagating through the medium will have its intensity profile modified by these refractive index changes and a CCD camera can be used to monitor the readout beam, and thus read the stored data. The main aim of this research was to investigate data storage using phase masks in the photorefractive crystal, lithium niobate (LiNbO3). Firstly the experimental methods for storing the two dimensional pages of data (a set of vertical stripes of varying lengths) in the medium are presented. The laser beam used for writing, whose intensity profile is modified by an amplitudemask which contains a pattern of the information to be stored, illuminates the lithium niobate crystal and the photorefractive effect causes the patterns to be stored as refractive index changes in the medium. These patterns are read out non-destructively using a low intensity probe beam and a CCD camera. A common complication of information storage in photorefractive crystals is the issue of destructive readout. This is a problem particularly for holographic data storage, where the readout beam should be at the same wavelength as the beam used for writing. Since the charge carriers in the medium are still sensitive to the read light field, the readout beam erases the stored information. A method to avoid this is by using thermal fixing. Here the photorefractive medium is heated to temperatures above 150�C; this process forms an ionic grating in the medium. This ionic grating is insensitive to the readout beam and therefore the information is not erased during readout. A non-contact method for determining temperature change in a lithium niobate crystal is presented in this thesis. The temperature-dependent birefringent properties of the medium cause intensity oscillations to be observed for a beam propagating through the medium during a change in temperature. It is shown that each oscillation corresponds to a particular temperature change, and by counting the number of oscillations observed, the temperature change of the medium can be deduced. The presented technique for measuring temperature change could easily be applied to a situation where thermal fixing of data in a photorefractive medium is required. Furthermore, by using an expanded beam and monitoring the intensity oscillations over a wide region, it is shown that the temperature in various locations of the crystal can be monitored simultaneously. This technique could be used to deduce temperature gradients in the medium. It is shown that the three dimensional nature of the recording medium causes interesting degradation effects to occur when the patterns are written for a longer-than-optimal time. This degradation results in the splitting of the vertical stripes in the data pattern, and for long writing exposure times this process can result in the complete deterioration of the information in the medium. It is shown in that simply by using incoherent illumination, the original pattern can be recovered from the degraded state. The reason for the recovery is that the refractive index changes causing the degradation are of a smaller magnitude since they are induced by the write field components scattered from the written structures. During incoherent erasure, the lower magnitude refractive index changes are neutralised first, allowing the original pattern to be recovered. The degradation process is shown to be reversed during the recovery process, and a simple relationship is found relating the time at which particular features appear during degradation and recovery. A further outcome of this work is that the minimum stripe width of 30 ìm is required for accurate storage and recovery of the information in the medium, any size smaller than this results in incomplete recovery. The degradation and recovery process could be applied to an application in image scrambling or cryptography for optical information storage. A two dimensional numerical model based on the finite-difference beam propagation method (FD-BPM) is presented and used to gain insight into the pattern storage process. The model shows that the degradation of the patterns is due to the complicated path taken by the write beam as it propagates through the crystal, and in particular the scattering of this beam from the induced refractive index structures in the medium. The model indicates that the highest quality pattern storage would be achieved with a thin 0.5 mm medium; however this type of medium would also remove the degradation property of the patterns and the subsequent recovery process. To overcome the simplistic treatment of the refractive index change in the FD-BPM model, a fully three dimensional photorefractive model developed by Devaux is presented. This model shows significant insight into the pattern storage, particularly for the degradation and recovery process, and confirms the theory that the recovery of the degraded patterns is possible since the refractive index changes responsible for the degradation are of a smaller magnitude. Finally, detailed analysis of the pattern formation and degradation dynamics for periodic patterns of various periodicities is presented. It is shown that stripe widths in the write beam of greater than 150 ìm result in the formation of different types of refractive index changes, compared with the stripes of smaller widths. As a result, it is shown that the pattern storage method discussed in this thesis has an upper feature size limit of 150 ìm, for accurate and reliable pattern storage.

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.

Age-dependence of the average and equivalent refractive indices of the crystalline lens

Lens average and equivalent refractive indices are required for purposes such as lens thickness estimation and optical modeling. We modeled the refractive index gradient as a power function of the normalized distance from lens center. Average index along the lens axis was estimated by integration. Equivalent index was estimated by raytracing through a model eye to establish ocular refraction, and then backward raytracing to determine the constant refractive index yielding the same refraction. Assuming center and edge indices remained constant with age, at 1.415 and 1.37 respectively, average axial refractive index increased (1.408 to 1.411) and equivalent index decreased (1.425 to 1.420) with age increase from 20 to 70 years. These values agree well with experimental estimates based on different techniques, although the latter show considerable scatter. The simple model of index gradient gives reasonable estimates of average and equivalent lens indices, although refinements in modeling and measurements are required.

Refractive indices with Haag-Streit Lenstar biometer

Purpose: To estimate refractive indices used with the Lenstar biometer. Methods: Axial lengths of model eyes were determined using an IOLMaster biometer and a Lenstar; comparing these lengths gave an overall eye index for the Lenstar. Using the Lenstar Graphical User interface, we determined that boundaries between media could be manipulated so that there were opposite changes in optical pathlength on either side of the boundary and specified changes in distances determined the ratios of media indices. These ratios were combined with the overall eye index to estimate indices. Results: The IOLMaster and Lenstar produced axial length estimates to within ±0.01 mm. Estimations of group refractive indices were 1.340, 1.341, 1.415 and 1.354 for cornea, aqueous, lens and overall eye, respectively. The aqueous and lens indices, but not those for the cornea, are similar to schematic eye indices and reasonable lens indices. Conclusion: The Lenstar appears to use different refractive indices for different ocular media.

Refractive indices used by the Haag-Streit Lenstar to calculate axial biometric dimensions

PURPOSE To estimate refractive indices used by the Lenstar biometer to translate measured optical path lengths into geometrical path lengths within the eye. METHODS Axial lengths of model eyes were determined using the IOLMaster and Lenstar biometers; comparing those lengths gave an overall eye refractive index estimate for the Lenstar. Using the Lenstar Graphical User Interface, we noticed that boundaries between media could be manipulated and opposite changes in optical path lengths on either side of the boundary could be introduced. Those ratios were combined with the overall eye refractive index to estimate separate refractive indices. Furthermore, Haag-Streit provided us with a template to obtain 'air thicknesses' to compare with geometrical distances. RESULTS The axial length estimates obtained using the IOLMaster and the Lenstar agreed to within 0.01 mm. Estimates of group refractive indices used in the Lenstar were 1.340, 1.341, 1.415, and 1.354 for cornea, aqueous, lens, and overall eye, respectively. Those refractive indices did not match those of schematic eyes, but were close in the cases of aqueous and lens. Linear equations relating air thicknesses to geometrical thicknesses were consistent with our findings. CONCLUSION The Lenstar uses different refractive indices for different ocular media. Some of the refractive indices, such as that for the cornea, are not physiological; therefore, it is likely that the calibrations in the instrument correspond to instrument-specific corrections and are not the real optical path lengths.

Thermal Expansivities and Temperature Coefficients of Refractive Indices for Molten Salts

An empirical relation for temperature–independent molar polarization is suggested. When this relation was used, the thermal expansivity was estimated correctly from refractive index data.