Investigations on Nonlinear and Radiative Properties of Certain Photonic Materials

International School of Photonics, Cochin University of Science & Technology

Studies of nonlinear absorption and aggregation in aqueous solutions of rhodamine 6G using a transient thermal lens technique

Dual-beam transient thermal lens studies were carried out in aqueous solutions of rhodamine 6G using 532 nm pulses from a frequency-doubled Nd:YAG laser. The analysis of the observed data showed that the thermal lens method can effectively be utilized to study the nonlinear absorption and aggregation which are taking place in a dye medium.

Photoacoustic signal saturation and optical limiting in C70-toluene solution

Pulsed photoacoustic studies in solutions of C70 in toluene are made using the 532-nm radiation from a frequency-doubled Nd:YAG laser. It is found that contrary to expectation, there is no photoacoustic (PA) signal enhancement in the power-limiting range of laser fluences. Instead, the PA signal tends to saturate during optical power-limiting phenomenon. This could be due to the enhanced optical absorption from the photoexcited state and hence the depletion of the ground-state population. PA measurements also ruled out the possibility of multiphoton absorption in the C70 solution. We demonstrate that the nonlinear absorption leading to optical limiting is mainly due to reverse saturable absorption.

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

A Study of Photoacoustic Effects and Optical Limiting in the Solution of C60 in Toluene

Pulsed photoacoustic studies in solution of C60 in toluene have been made using the 532 nm radiation from a frequency doubled Nd:YAG laser. Though C60 is found to exhibit the phenomenon of optical limiting, the results on photoacoustic measurements do not give any indication of multiphoton transitions as suggested in some of the earlier works. Results of photoacoustic measurements show that excited state absorption is the dominant process responsible for optical limiting while phenomena like nonlinear scattering may contribute to a lesser extent.

Permutation Entropy Based Analysis of Complex Signals for Characterising Change in System Dynamics

Timely detection of sudden change in dynamics that adversely affect the performance of systems and quality of products has great scientific relevance. This work focuses on effective detection of dynamical changes of real time signals from mechanical as well as biological systems using a fast and robust technique of permutation entropy (PE). The results are used in detecting chatter onset in machine turning and identifying vocal disorders from speech signal.Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. Here we propose the use of permutation entropy (PE), to detect the dynamical changes in two non linear processes, turning under mechanical system and speech under biological system.Effectiveness of PE in detecting the change in dynamics in turning process from the time series generated with samples of audio and current signals is studied. Experiments are carried out on a lathe machine for sudden increase in depth of cut and continuous increase in depth of cut on mild steel work pieces keeping the speed and feed rate constant. The results are applied to detect chatter onset in machining. These results are verified using frequency spectra of the signals and the non linear measure, normalized coarse-grained information rate (NCIR).PE analysis is carried out to investigate the variation in surface texture caused by chatter on the machined work piece. Statistical parameter from the optical grey level intensity histogram of laser speckle pattern recorded using a charge coupled device (CCD) camera is used to generate the time series required for PE analysis. Standard optical roughness parameter is used to confirm the results.Application of PE in identifying the vocal disorders is studied from speech signal recorded using microphone. Here analysis is carried out using speech signals of subjects with different pathological conditions and normal subjects, and the results are used for identifying vocal disorders. Standard linear technique of FFT is used to substantiate thc results.The results of PE analysis in all three cases clearly indicate that this complexity measure is sensitive to change in regularity of a signal and hence can suitably be used for detection of dynamical changes in real world systems. This work establishes the application of the simple, inexpensive and fast algorithm of PE for the benefit of advanced manufacturing process as well as clinical diagnosis in vocal disorders.

Computationally Efficient Bootstrap Prediction Intervals for Returns and Volatilities in ARCH and GARCH Processes

We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.

High-Speed Semiconductor Lasers based on Low-Dimensional Active Materials for Optical Telecommunication

The scope of this work is the fundamental growth, tailoring and characterization of self-organized indium arsenide quantum dots (QDs) and their exploitation as active region for diode lasers emitting in the 1.55 µm range. This wavelength regime is especially interesting for long-haul telecommunications as optical fibers made from silica glass have the lowest optical absorption. Molecular Beam Epitaxy is utilized as fabrication technique for the quantum dots and laser structures. The results presented in this thesis depict the first experimental work for which this reactor was used at the University of Kassel. Most research in the field of self-organized quantum dots has been conducted in the InAs/GaAs material system. It can be seen as the model system of self-organized quantum dots, but is not suitable for the targeted emission wavelength. Light emission from this system at 1.55 µm is hard to accomplish. To stay as close as possible to existing processing technology, the In(AlGa)As/InP (100) material system is deployed. Depending on the epitaxial growth technique and growth parameters this system has the drawback of producing a wide range of nano species besides quantum dots. Best known are the elongated quantum dashes (QDash). Such structures are preferentially formed, if InAs is deposited on InP. This is related to the low lattice-mismatch of 3.2 %, which is less than half of the value in the InAs/GaAs system. The task of creating round-shaped and uniform QDs is rendered more complex considering exchange effects of arsenic and phosphorus as well as anisotropic effects on the surface that do not need to be dealt with in the InAs/GaAs case. While QDash structures haven been studied fundamentally as well as in laser structures, they do not represent the theoretical ideal case of a zero-dimensional material. Creating round-shaped quantum dots on the InP(100) substrate remains a challenging task. Details of the self-organization process are still unknown and the formation of the QDs is not fully understood yet. In the course of the experimental work a novel growth concept was discovered and analyzed that eases the fabrication of QDs. It is based on different crystal growth and ad-atom diffusion processes under supply of different modifications of the arsenic atmosphere in the MBE reactor. The reactor is equipped with special valved cracking effusion cells for arsenic and phosphorus. It represents an all-solid source configuration that does not rely on toxic gas supply. The cracking effusion cell are able to create different species of arsenic and phosphorus. This constitutes the basis of the growth concept. With this method round-shaped QD ensembles with superior optical properties and record-low photoluminescence linewidth were achieved. By systematically varying the growth parameters and working out a detailed analysis of the experimental data a range of parameter values, for which the formation of QDs is favored, was found. A qualitative explanation of the formation characteristics based on the surface migration of In ad-atoms is developed. Such tailored QDs are finally implemented as active region in a self-designed diode laser structure. A basic characterization of the static and temperature-dependent properties was carried out. The QD lasers exceed a reference quantum well laser in terms of inversion conditions and temperature-dependent characteristics. Pulsed output powers of several hundred milli watt were measured at room temperature. In particular, the lasers feature a high modal gain that even allowed cw-emission at room temperature of a processed ridge wave guide device as short as 340 µm with output powers of 17 mW. Modulation experiments performed at the Israel Institute of Technology (Technion) showed a complex behavior of the QDs in the laser cavity. Despite the fact that the laser structure is not fully optimized for a high-speed device, data transmission capabilities of 15 Gb/s combined with low noise were achieved. To the best of the author`s knowledge, this renders the lasers the fastest QD devices operating at 1.55 µm. The thesis starts with an introductory chapter that pronounces the advantages of optical fiber communication in general. Chapter 2 will introduce the fundamental knowledge that is necessary to understand the importance of the active region`s dimensions for the performance of a diode laser. The novel growth concept and its experimental analysis are presented in chapter 3. Chapter 4 finally contains the work on diode lasers.

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Efficient topology estimation for large scale optical mapping

Large scale image mosaicing methods are in great demand among scientists who study different aspects of the seabed, and have been fostered by impressive advances in the capabilities of underwater robots in gathering optical data from the seafloor. Cost and weight constraints mean that lowcost Remotely operated vehicles (ROVs) usually have a very limited number of sensors. When a low-cost robot carries out a seafloor survey using a down-looking camera, it usually follows a predetermined trajectory that provides several non time-consecutive overlapping image pairs. Finding these pairs (a process known as topology estimation) is indispensable to obtaining globally consistent mosaics and accurate trajectory estimates, which are necessary for a global view of the surveyed area, especially when optical sensors are the only data source. This thesis presents a set of consistent methods aimed at creating large area image mosaics from optical data obtained during surveys with low-cost underwater vehicles. First, a global alignment method developed within a Feature-based image mosaicing (FIM) framework, where nonlinear minimisation is substituted by two linear steps, is discussed. Then, a simple four-point mosaic rectifying method is proposed to reduce distortions that might occur due to lens distortions, error accumulation and the difficulties of optical imaging in an underwater medium. The topology estimation problem is addressed by means of an augmented state and extended Kalman filter combined framework, aimed at minimising the total number of matching attempts and simultaneously obtaining the best possible trajectory. Potential image pairs are predicted by taking into account the uncertainty in the trajectory. The contribution of matching an image pair is investigated using information theory principles. Lastly, a different solution to the topology estimation problem is proposed in a bundle adjustment framework. Innovative aspects include the use of fast image similarity criterion combined with a Minimum spanning tree (MST) solution, to obtain a tentative topology. This topology is improved by attempting image matching with the pairs for which there is the most overlap evidence. Unlike previous approaches for large-area mosaicing, our framework is able to deal naturally with cases where time-consecutive images cannot be matched successfully, such as completely unordered sets. Finally, the efficiency of the proposed methods is discussed and a comparison made with other state-of-the-art approaches, using a series of challenging datasets in underwater scenarios

Development of chemical separation processes for the treatment and monitoring of metallic cations and oxoanions in polluted waters

The chemical contamination of natural waters is a global problem with a worldwide impact. Considering the relevance of this problem, this thesis is intended, on one hand, to develop different separation/preconcentration techniques based on membranes ability to permeate anions for the transport of toxic oxyanions of chromium(VI) and arsenic contained in aqueous matrices. In particular, we have investigated supported liquid membranes and polymer inclusion membranes, both of which contain the commercial quaternary ammonium salt Aliquat 336 as a carrier, as well as commercial anion exchange membranes. On the other hand, we have focused on the development of chemical sensors to facilitate the monitoring of several metals from different aqueous matrices. Thus, a selective optical sensor for Cr(VI) based on polymeric membranes containing Aliquat 336 as an ionophore has been designed. Additionally, mercury-based screen-printed electrodes have been evaluated for for cadmium, lead, copper and zinc detection.

Processes influencing ozone levels in Alaskan forest fire plumes during long-range transport over the North Atlantic

A case of long-range transport of a biomass burning plume from Alaska to Europe is analyzed using a Lagrangian approach. This plume was sampled several times in the free troposphere over North America, the North Atlantic and Europe by three different aircraft during the IGAC Lagrangian 2K4 experiment which was part of the ICARTT/ITOP measurement intensive in summer 2004. Measurements in the plume showed enhanced values of CO, VOCs and NOy, mainly in form of PAN. Observed O3 levels increased by 17 ppbv over 5 days. A photochemical trajectory model, CiTTyCAT, was used to examine processes responsible for the chemical evolution of the plume. The model was initialized with upwind data and compared with downwind measurements. The influence of high aerosol loading on photolysis rates in the plume was investigated using in situ aerosol measurements in the plume and lidar retrievals of optical depth as input into a photolysis code (Fast-J), run in the model. Significant impacts on photochemistry are found with a decrease of 18% in O3 production and 24% in O3 destruction over 5 days when including aerosols. The plume is found to be chemically active with large O3 increases attributed primarily to PAN decomposition during descent of the plume toward Europe. The predicted O3 changes are very dependent on temperature changes during transport and also on water vapor levels in the lower troposphere which can lead to O3 destruction. Simulation of mixing/dilution was necessary to reproduce observed pollutant levels in the plume. Mixing was simulated using background concentrations from measurements in air masses in close proximity to the plume, and mixing timescales (averaging 6.25 days) were derived from CO changes. Observed and simulated O3/CO correlations in the plume were also compared in order to evaluate the photochemistry in the model. Observed slopes change from negative to positive over 5 days. This change, which can be attributed largely to photochemistry, is well reproduced by multiple model runs even if slope values are slightly underestimated suggesting a small underestimation in modeled photochemical O3 production. The possible impact of this biomass burning plume on O3 levels in the European boundary layer was also examined by running the model for a further 5 days and comparing with data collected at surface sites, such as Jungfraujoch, which showed small O3 increases and elevated CO levels. The model predicts significant changes in O3 over the entire 10 day period due to photochemistry but the signal is largely lost because of the effects of dilution. However, measurements in several other BB plumes over Europe show that O3 impact of Alaskan fires can be potentially significant over Europe.

Seasonal variations of the physical and optical characteristics of Saharan Dust: results from the Dust outflow and Deposition to the Ocean (DODO) experiment

North African dust is important for climate through its direct radiative effect on solar and terrestrial radiation and its role in the biogeochemical system. The Dust Outflow and Deposition to the Ocean project (DODO) aimed to characterize the physical and optical properties of airborne North African dust in two seasons and to use these observations to constrain model simulations, with the ultimate aim of being able to quantify the deposition of iron to the North Atlantic Ocean. The in situ properties of dust from airborne campaigns measured during February and August 2006, based at Dakar, Senegal, are presented here. Average values of the single scattering albedo (0.99, 0.98), mass specific extinction (0.85 m^2 g^-1 , 1.14 m^2 g^-1 ), asymmetry parameter (0.68, 0.68), and refractive index (1.53--0.0005i,1.53--0.0014i) for the accumulation mode were found to differ by varying degrees between the dry and wet season, respectively. It is hypothesized that these differences are due to different source regions and transport processes which also differ between the DODO campaigns. Elemental ratios of Ca/Al were found to differ between the dry and wet season (1.1 and 0.5, respectively). Differences in vertical profiles are found between seasons and between land and ocean locations and reflect the different dynamics of the seasons. Using measurements of the coarse mode size distribution and illustrative Mie calculations, the optical properties are found to be very sensitive to the presence and amount of coarse mode of mineral dust, and the importance of accurate measurements of the coarse mode of dust is highlighted.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Assessing the sources and magnitude of diurnal nitrate variability in the San Joaquin River (California) with an in-situ optical nitrate sensor and dual nitrate isotopes

We investigated diurnal nitrate (NO3-) concentration variability in the San Joaquin River using an in situ optical NO3- sensor and discrete sampling during a 5-day summer period characterized by high algal productivity. Dual NO3- isotopes (delta N-15(NO3) and delta O-18(NO3)) and dissolved oxygen isotopes (delta O-18(DO)) were measured over 2 days to assess NO3- sources and biogeochemical controls over diurnal time-scales. Concerted temporal patterns of dissolved oxygen (DO) concentrations and delta O-18(DO) were consistent with photosynthesis, respiration and atmospheric O-2 exchange, providing evidence of diurnal biological processes independent of river discharge. Surface water NO3- concentrations varied by up to 22% over a single diurnal cycle and up to 31% over the 5-day study, but did not reveal concerted diurnal patterns at a frequency comparable to DO concentrations. The decoupling of delta N-15(NO3) and delta O-18(NO3) isotopes suggests that algal assimilation and denitrification are not major processes controlling diurnal NO3- variability in the San Joaquin River during the study. The lack of a clear explanation for NO3- variability likely reflects a combination of riverine biological processes and time-varying physical transport of NO3- from upstream agricultural drains to the mainstem San Joaquin River. The application of an in situ optical NO3- sensor along with discrete samples provides a view into the fine temporal structure of hydrochemical data and may allow for greater accuracy in pollution assessment.