Dispersive estimates for the Schrödinger equation

In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We focus particularly on the five and seven dimensional cases. We prove that the solution operator precomposed with projection onto the absolutely continuous spectrum of $H=-\Delta+V$ satisfies the following estimate $\|e^{itH} P_{ac}(H)\|_{L^1\to L^\infty} \lesssim |t|^{-\frac{n}{2}}$ under certain conditions on the potential $V$. Specifically, we prove the dispersive estimate is satisfied with optimal assumptions on smoothness, that is $V\in C^{\frac{n-3}{2}}(\R^n)$ for $n=5,7$ assuming that zero is regular, $|V(x)|\lesssim \langle x\rangle^{-\beta}$ and $|\nabla^j V(x)|\lesssim \langle x\rangle^{-\alpha}$, $1\leq j\leq \frac{n-3}{2}$ for some $\beta>\frac{3n+5}{2}$ and $\alpha>3,8$ in dimensions five and seven respectively. We also show that for the five dimensional result one only needs that $|V(x)|\lesssim \langle x\rangle^{-4-}$ in addition to the assumptions on the derivative and regularity of the potential. This more than cuts in half the required decay rate in the first chapter. Finally we consider a problem involving the non-linear Schr\"{o}dinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, \begin{align*} iu_t+d(t) u_{xx}+|u|^2 u=0. \end{align*} We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in $x$ and in the Fourier transform of $x$.

Direct Write Fabrication of Waveguides and Interconnects for Optical Printed Wiring Boards

Current copper based circuit technology is becoming a limiting factor in high speed data transfer applications as processors are improving at a faster rate than are developments to increase on board data transfer. One solution is to utilize optical waveguide technology to overcome these bandwidth and loss restrictions. The use of this technology virtually eliminates the heat and cross-talk loss seen in copper circuitry, while also operating at a higher bandwidth. Transitioning current fabrication techniques from small scale laboratory environments to large scale manufacturing presents significant challenges. Optical-to-electrical connections and out-of-plane coupling are significant hurdles in the advancement of optical interconnects. The main goals of this research are the development of direct write material deposition and patterning tools for the fabrication of waveguide systems on large substrates, and the development of out-of-plane coupler components compatible with standard fiber optic cabling. Combining these elements with standard printed circuit boards allows for the fabrication of fully functional optical-electrical-printed-wiring-boards (OEPWBs). A direct dispense tool was designed, assembled, and characterized for the repeatable dispensing of blanket waveguide layers over a range of thicknesses (25-225 µm), eliminating waste material and affording the ability to utilize large substrates. This tool was used to directly dispense multimode waveguide cores which required no UV definition or development. These cores had circular cross sections and were comparable in optical performance to lithographically fabricated square waveguides. Laser direct writing is a non-contact process that allows for the dynamic UV patterning of waveguide material on large substrates, eliminating the need for high resolution masks. A laser direct write tool was designed, assembled, and characterized for direct write patterning waveguides that were comparable in quality to those produced using standard lithographic practices (0.047 dB/cm loss for laser written waveguides compared to 0.043 dB/cm for lithographic waveguides). Straight waveguides, and waveguide turns were patterned at multimode and single mode sizes, and the process was characterized and documented. Support structures such as angled reflectors and vertical posts were produced, showing the versatility of the laser direct write tool. Commercially available components were implanted into the optical layer for out-of-plane routing of the optical signals. These devices featured spherical lenses on the input and output sides of a total internal reflection (TIR) mirror, as well as alignment pins compatible with standard MT design. Fully functional OEPWBs were fabricated featuring input and output out-of-plane optical signal routing with total optical losses not exceeding 10 dB. These prototypes survived thermal cycling (-40°C to 85°C) and humidity exposure (95±4% humidity), showing minimal degradation in optical performance. Operational failure occurred after environmental aging life testing at 110°C for 216 hours.

Design for placement of modified optodes to non-invasively map cerebral function

By using near infrared spectroscopy (NIRS) and by modifying the current Somanetics® optodes being used with the INVOS oximeter, the modified optodes are made to be fairly functional not only across the forehead, but across the hairy regions of the scalp as well. A major problem arises in the positioning of these optodes on the patients scalp and holding them in place while recording data. Another problem arises in the inconsistent repeatability of the trends displayed in the recorded data. A method was developed to facilitate the easy placement of these optodes on the patients scalp keeping in mind thepatient's comfort. The sensitivity of the optodes, too, was improved by incorporating better refined techniques for manufacturing the fiber optic brushes and fixing the same to the optode transmitting and receiving windows. The modified and improved optodes, in the single as well as in the multiplexed modes, were subjected to various tests on different areas of the brain to determine their efficiency and functionality.

ICN Insider, November-December 2016

The ICN, a state agency, is the country’s premier fiber-optic Network, committed to continued enhancement of distance learning and providing Iowans with convenient, equal access to education, government, and healthcare. This newsletter is produced monthly by the ICN of all the programs and activities of this department.

ICN Insider, January-February 2017

The ICN, a state agency, is the country’s premier fiber-optic Network, committed to continued enhancement of distance learning and providing Iowans with convenient, equal access to education, government, and healthcare. This newsletter is produced monthly by the ICN of all the programs and activities of this department.

The fingerprinting of the materials used in portuguese illuminated manuscripts: origin, production and specificities of the 16th century Anttiphonary paints from the Biblioteca Pública de Évora

This thesis focuses on the characterization of materials utilized within the illuminations of Codex 116c of Manizola, a large 16th century antiphonal housed in the Biblioteca Pública de Évora (BPE). Using various spectroscopic techniques (XRF, FTIR, Raman and SEM-EDS), a selection of illuminations were analyzed for pigment and binder identification. The manuscript was further analyzed using fiber optic reflectance spectroscopy (FORS), a non-invasive and portable analysis method ideal for use in illuminations. Using historical documentation and results gained from more extensive analysis of the manuscript, a collection of reference paint samples were created to be analyzed using this method. These samples serve as a reference not only to assist in the identification of pigments used within the manuscript, but also for future studies on similar materials allowing for a better understanding of manuscript production during the 16th century; RESUMO: O presente trabalho é dedicado à caracterização dos materiais utilizados na produção das iluminuras do Codex 116c da Manziola do espólio da Biblioteca Pública de Évora (BPE). Trata-se de um antifonário de grandes dimensões produzido no séc XVI que deverá ter pertencido à Livraria de São Bento de Cástris. A identificação dos materiais utilizados na produção das iluminuras pode ser feita através de análises científicas. No entanto, alguns dos componentes das tintas utilizadas, especialmente os pigmentos orgânicos (lacas) e algumas misturas, apresentam obstáculos à sua identificação por métodos não invasivos. Através de várias técnicas espectroscópicas (XRF, FTIR, Raman e SEM-EDS), foi analisado um conjunto representativo de iluminuras, de modo a identificar os pigmentos e os ligantes presentes nas tintas. O manuscrito foi também analisado por FORS, um método portátil e não invasivo, ideal para a análise de iluminuras. Com base em documentos históricos e nos resultados analíticos, foi criado um conjunto de amostras de referência para ser analisado com FORS. Com esta abordagem, pretende-se que estas amostras, especialmente as de lacas, sirvam de referência não só na identificação dos pigmentos no manuscrito como em estudos sobre materiais semelhantes, contribuindo para um conhecimento mais aprofundado sobre a produção de manuscritos no séc XVI.

Development and fabrication of an optimized thermo-electro-optic device using a Mach-Zehnder interferometer

The development and fabrication of a thermo-electro-optic sensor using a Mach-Zehnder interferometer and a resistive micro-heater placed in one of the device`s arms is presented. The Mach-Zehnder structure was fabricated on a single crystal silicon substrate using silicon oxynitride and amorphous hydrogenated silicon carbide films to form an anti-resonant reflective optical waveguide. The materials were deposited by Plasma enhanced chemical vapor deposition technique at low temperatures (similar to 320 degrees C). To optimize the heat transfer and increase the device response with current variation, part of the Mach-Zehnder sensor arm was suspended through front-side bulk micromachining of the silicon substrate in a KOH solution. With the temperature variation caused by the micro-heater, the refractive index of the core layer of the optical waveguide changes due to the thermo-optic effect. Since this variation occurs only in one of the Mach-Zehnder`s arm, a phase difference between the arms is produced, leading to electromagnetic interference. In this way, the current applied to the micro-resistor can control the device output optical power. Further, reactive ion etching technique was used in this work to define the device`s geometry, and a study of SF6 based etching rates on different composition of silicon oxynitride films is also presented. (C) 2007 Elsevier B.V. All rights reserved.

Evaluation of retinal nerve fiber layer thickness measurements using optical coherence tomography in patients with tobacco-alcohol-induced toxic optic neuropathy

Three patients with progressive visual loss, chronic alcoholism and tabagism were submitted to a complete neuro-ophthalmic examination and to retinal nerve fiber layer (RNFL) measurements using optical coherence tomography (OCT) scanning. Two patients showed marked RNFL loss in the temporal sector of the optic disc. However, a third patient presented RNFL measurements within or above normal limits, based on the Stratus-OCT normative database. Such findings may be due to possible RNFL edema similar to the one that may occur in the acute phase of toxic optic neuropathies. Stratus-OCT was able to detect RNFL loss in the papillomacular bundle of patients with tobacco-alcohol-induced toxic optic neuropathy. However, interpretation must be careful when OCT does not show abnormality in order to prevent diagnostic confusion, since overestimation of RNFL thickness measurements is possible in such cases.

Optic radiation fiber tracking using anteriorly angulated diffusion tensor imaging: a tested algorithm for quick application

Fiber tracking (FT) of the optic pathways (OPs) is difficult because there is no standard for the parameters of diffusion tensor imaging (DTI), placement of seed volumes, or interpreting the results.

Tunable liquid crystal-photonic crystal fiber interferometer

In this work, we present a novel interferometer based on liquid crystal and photonic crystal fiber technology. The objective of this project is the development of a tunable (switchable) modal (Mach-Zehnder) interferometer for optical communications or sensing.

Mach-Zehnder interferometer based on all-fiber multimode interference device for DPSK signal demodulation

Differential Phase Shift Keying (DPSK) modulation format has been shown as a robust solution for next-generation optical transmission systems. One key device enabling such systems is the delay interferometer, converting the signal phase information into intensity modulation to be detected by the photodiodes. Usually, Mach-Zehnder interferometer (MZI) is used for demodulating DPSK signals. In this paper, we developed an MZI which is based on all-fiber Multimode Interference (MI) structure: a multimode fiber (MMF) located between two single-mode fibers (SMF) without any transition zones. The standard MZI is not very stable since the two beams go through two different paths before they recombine. In our design the two arms of the MZI are in the same fiber, which will make it less temperature-sensitive than the standard MZI. Performance of such MZI will be analyzed from transmission spectrum. Finally such all-fiber MI-based MZI (MI-MZI) is used to demodulate 10 Gbps DPSK signals. The demodulated signals are analyzed from eye diagram and bit error rate (BER).

Corneal Biomechanics, Retinal Nerve Fiber Layer, and Optic Disc in Children

Purpose: To evaluate the possible associations between corneal biomechanical parameters, optic disc morphology, and retinal nerve fiber layer (RNFL) thickness in healthy white Spanish children. Methods: This cross-sectional study included 100 myopic children and 99 emmetropic children as a control group, ranging in age from 6 to 17 years. The Ocular Response Analyzer was used to measure corneal hysteresis (CH) and corneal resistance factor. The optic disc morphology and RNFL thickness were assessed using posterior segment optical coherence tomography (Cirrus HD-OCT). The axial length was measured using an IOLMaster, whereas the central corneal thickness was measured by anterior segment optical coherence tomography (Visante OCT). Results: The mean (±SD) age and spherical equivalent were 12.11 (±2.76) years and −3.32 (±2.32) diopters for the myopic group and 11.88 (±2.97) years and +0.34 (±0.41) diopters for the emmetropic group. In a multivariable mixed-model analysis in myopic children, the average RNFL thickness and rim area correlated positively with CH (p = 0.007 and p = 0.001, respectively), whereas the average cup-to-disc area ratio correlated negatively with CH (p = 0.01). We did not observe correlation between RNFL thickness and axial length (p = 0.05). Corneal resistance factor was only positively correlated with the rim area (p = 0.001). The central corneal thickness did not correlate with the optic nerve parameters or with RNFL thickness. These associations were not found in the emmetropic group (p > 0.05 for all). Conclusions: The corneal biomechanics characterized with the Ocular Response Analyzer system are correlated with the optic disc profile and RNFL thickness in myopic children. Low CH values may indicate a reduction in the viscous dampening properties of the cornea and the sclera, especially in myopic children.

Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80° tilted structures

For the first time to the authors' knowledge, fiber Bragg gratings (FBGs) with >80° tilted structures have been fabricated and characterized. Their performance in sensing temperature, strain, and the surrounding medium's refractive index was investigated. In comparison with normal FBGs and long-period gratings (LPGs), >80° tilted FBGs exhibit significantly higher refractive-index responsivity and lower thermal cross sensitivity. When the grating sensor was used to detect changes in refractive index, a responsivity as high as 340nm/refractive-index unit near an index of 1.33 was demonstrated, which is three times higher than that of conventional LPGs.

Implementation and characterization of liquid-level sensor based on a long-period fiber grating Mach-Zehnder interferometer

An optical liquid-level sensor (LLS) based on a long-period fiber grating (LPG) interferometer is proposed and experimentally demonstrated. Two identical 3-dB LPGs are fabricated to form an in-fiber Mach-Zehnder interferometer, and the fiber portion between two LPGs is exposed to the liquid as the sensing element. The sensitivity and measurement range of the sensors employing different orders of cladding modes are investigated both theoretically and experimentally. The experimental results show good linearity and large measurement range. One of the significant advantages of such a sensing structure is that the measurement level is not limited to the length of the LPG itself. Also, the measurement range and sensitivity of the proposed LLS can be readily tailored for a particular applications.

Acousto-optic effect in microstructured polymer fiber bragg gratings : simulation and experimental overview

A fine control of the microstructured polymer fiber Bragg grating spectrum properties, such as maximum reflected power and 3-dB bandwidth, through acousto-optic modulation is presented. For simulation purposes, the device is modelled as a single structure, comprising a silica horn and a fiber Bragg grating. For similar sized structures a good correlation between the numerical results and the experimental data is obtained, allowing the strain field to be completely characterized along the whole structure. It is also shown that the microstructured polymer fiber Bragg grating requires less effort from the piezoelectric actuator to produce modification in the grating spectrum when compared with a silica fiber Bragg grating. This technique has potential to be applied on tunable optical filters and tunable cavities for photonic applications.