Search

Quantitative analysis methods based on the usage of a scanning electron microscope (SEM), such as energy dispersive x-ray spectroscopy, often require specimens to have a flat surface oriented normal to the electron beam. In-situ procedures for putting microscopic flat surfaces into this orientation generally rely on stereoscopic methods that measure the change in surface vector projections when the surface is tilted by some known angle. Although these methods have been used in the past, there is no detailed statistical analysis of the uncertainties involved in such methods, which leaves an uncertainty in how precisely a specimen can be oriented. Here, we present a first principles derivation of a specimen orientation method and apply our method to a flat sample to demonstrate it. Unlike previous works, we develop a computer vision program using the Scale Invariant Feature Transform to automate and expedite the process of making measurements on our SEM images, thus enabling a detailed statistical analysis of the method with a large sample size. We find that our specimen orientation method is able to orient flat surfaces with high precision and can further provide insight into errors involved in the standard SEM rotation and tilt operations., 8 pages, 5 figures

This paper reports the results of preparing alloy nanoparticles by mechanical grinding followed by filtration to sort the particles according to size. Although the long-term goal of this work is to prepare icosahedral quasicrystalline nanoparticles, the alloy used in this study is of Al65Cu25Fe15 composition and multi phases, under the assumption that the established procedure is applicable to future quasicrystalline nanoparticle fabrication. The obtained particle size and elemental information were investigated using scanning electron microscopy and energy dispersive x-ray spectroscopy. Problems with filter fragment fall-out and salt contamination were encountered and procedures to address the problems have been suggested and tested. The study is successful in obtaining alloy particles with reduced sizes.

Background Regional cortical thickness (rCTh) among cognitively normal (CN) adults (rCThCN) varies greatly between brain regions, as does the vulnerability to neurodegeneration. Objective The goal of this study was to: 1) rank order rCThCN for various brain regions, and 2) explore their vulnerability to neurodegeneration in Alzheimer's disease (AD) within these brain regions. Methods The relationship between rCTh among the CN group (rCThCN) and the percent difference in CTh (% CThDiff) in each region between the CN group and AD patients was examined. Pearson correlation analysis was performed accounting for amyloid-β (Aβ) protein and APOE genotype using 210 age, gender, and APOE matched CN (n = 105, age range: 56-90) and AD (n = 105, age range: 56-90) ADNI participants. Results Strong positive correlations were observed between rCThCN and % CThDiff accounting for Aβ deposition and APOE status. Regions, such as the entorhinal cortex, which had the greatest CTh in the CN state, were also the regions which had the greatest % CThDiff. Conclusions Regions with the greatest CTh at the CN stage are found to aggregate in disease prone regions of AD, namely in the medial temporal lobe, including the temporal pole, ERC, parahippocampal gyrus, fusiform and the middle and inferior temporal gyrus. Although rCTh has been found to vary considerably across the different regions of the brain, our results indicate that regions with the greatest CTh at the CN stage are actually regions which have been found to be most vulnerable to neurodegeneration in AD.

Background: Accumulating evidence indicates that the failure to recover from the effects of proactive semantic interference [frPSI] represents an early cognitive manifestation of preclinical Alzheimer's disease. A limitation of this novel paradigm has been a singular focus on the number of targets correctly recalled, without examining co-occurring semantic intrusions [SI] that may highlight specific breakdowns in memory. Objectives: We focused on SI and their relationship to amyloid load and regional cortical thickness among persons with amnestic mild cognitive impairment (aMCI). Methods: Thirty-three elders diagnosed with aMCI underwent F-18 florbetaben amyloid PET scanning with MRI scans of the brain. We measured the correlation of SI elicited on cued recall trials of the Loewenstein-Acevedo Scales for Semantic Interference and Learning [LASSI-L] with mean cortical amyloid load and regional cortical thickness in AD prone regions. Results: SI on measures sensitive to frPSI was related to greater total amyloid load and lower overall cortical thickness [CTh]. In particular, SI were highly associated with reduced CTh in the left entorhinal cortex [r=-.71; p Conclusion. Semantic intrusions on measures susceptible to frPSI related to greater brain amyloid load and lower cortical thickness. These findings further support the hypothesis that frPSI, as expressed by the percentage of intrusions, may be a cognitive marker of initial neurodegeneration and may serve as an early and distinguishing test for preclinical AD that may be used in primary care or clinical trial settings.

Al-Cu-Fe alloys are important due to reports that stable icosahedral quasicrystalline phase with composition in the vicinity of Al65Cu20Fe15 can be prepared. However, it has been widely reported that the as-prepared alloy, very often by arc-melting, is porous, consisting of particles with different morphologies. Among these, one type of particles of a spherical shape is considered as pure cubic β phase in previous reports. In this research, this spherical particle was studied using a Scanning Electron Microscope, Energy Dispersive X-ray Spectroscopy, Transmission Electron Microscope, and Electron Diffraction. It was found that the particles are not single phase, consisting of icosahedral quasicrystalline grains embedded inside single crystal matrix of τ phase. Additionally, there are places where the τ phase appears to have out-most layer enriched in Cu. The surface of the particles is faceted and the facets can be classified to three types according to their detailed structures. A close examination and analysis led to the conclusion that these three types are parallel to the atomic planes of {1 1 0}, {1 1 1}, and {1 0 0}, respectively. A model for the spherical particle formation is suggested and the reasons for the formation of facets are discussed. This report is valuable in clarifying some discrepancies in previous reports, and in understanding the phase development in an Al-Cu-Fe alloy system.

Background Both amyloid (Aβ) load and APOE4 allele are associated with neurodegenerative changes in Alzheimer's disease (AD) prone regions and with risk for cognitive impairment. Objective To evaluate the unique and independent contribution of APOE4 allele status (E4+∖E4-), Aβ status (Amy+∖Amy-), and combined APOE4 and Aβ status on regional cortical thickness (CoTh) and cognition among participants diagnosed as cognitively normal (CN, n = 251), early mild cognitive impairment (EMCI, n = 207), late mild cognitive impairment (LMCI, n = 196), and mild AD (n = 162) from the ADNI. Methods A series of two-way ANCOVAs with post-hoc Tukey HSD tests, controlling independently for Aβ and APOE4 status and age were examined. Results Among LMCI and AD participants, cortical thinning was widespread in association with Amy+ status, whereas in association with E4+ status only in the inferior temporal and medial orbito-frontal regions. Among CN and EMCI participants, E4+ status, but not Amy+ status, was independently associated with increased CoTh, especially in limbic regions [e.g., in the entorhinal cortex, CoTh was 0.123 mm greater (p = 0.002) among E4+ than E4-participants]. Among CN and EMCI, both E4+ and Amy+ status were independently associated with cognitive impairment, which was greatest among those with combined E4 + and Amy+ status. Conclusion Decreased CoTh is independently associated with Amy+ status in many brain regions, but with E4+ status in very restricted number of brain regions. Among CN and EMCI participants, E4 + status is associated with increased CoTh, in medial and inferior temporal regions, although cognitive impairment at this state is independently associated with Amy+ and E4 + status. These findings imply a unique pathophysiological mechanism for E4 + status in AD and its progression.

Icosahedral quasicrystals display irregular shape if it is embedded in bulk material. If it has free surface, it has well-defined facets, reflecting its unique 5-, 3-, and 2-fold rotational symmetries. In this study, an Al-Cu-Fe alloy with nominal composition of Al65Cu20Fe15 was prepared by arc melting and the microstructure was studied by using Scanning Electron Microscope, Energy Dispersive X-ray Spectroscopy, and Electron Back Scattering Diffraction (EBSD). On the surface of λ crystalline phase, an extra layer is found. EBSD from this layer revealed 5-, 3-, and 2-fold rotational symmetries, demonstrating the icosahedral quasicrystalline structure. Further, it has been found that the icosahedral quasicrystalline extra layer and the λ substrate have orientation relationship revealed by the coincidences of Kikuchi bands and poles on the EBSD patterns. This report is important to future studies regarding the formation of icosahedral quasicrystalline phase and thin film preparation related to icosahedral quasicrystalline phase.

The aims of this study were to evaluate the effects of gastric sleeve surgery on diabetes remission in db/db mice as well as to determine the underlying mechanisms. Thirty spontaneously obese, diabetic mice (C57BL/Ksj-db/db) were randomly divided into three groups: sleeve gastrectomy group, sham-operated group, and control db/db group. Ten db/m lean mice were used as nondiabetic littermate controls. All mice were sacrificed on day 28. The fasting plasma glucose, serum insulin, lipid profile, and oral glucose tolerance were measured pre- and postoperatively. Inflammatory cytokines (TNF-α and IL-6), endoplasmic reticulum (ER) stress–related markers (GRP78, PERK, IRE-1, and ATF6), and glucose transporter 4 (GLUT4) in the adipose tissue were assayed. Sleeve gastrectomy significantly reduced the body weight and food intake in the db/db mice. This surgery improved glucose and lipid metabolism, as manifested by the decrease in the fasting plasma glucose level and partial restoration of lipid abnormalities. Also, the surgery improved glucose tolerance and alleviated insulin resistance in db/db mice. Sleeve gastrectomy surgery induced downregulation of the inflammatory adipocytokines TNF-α and IL-6; suppressed expression of the ER stress–related markers GRP78, PERK, IRE-1, and ATF-6; and increased the expression and distribution of GLUT4 in adipose tissue of db/db mice. The improvement in glucose tolerance following sleeve gastrectomy is associated with alleviation of insulin resistance, reduction of inflammatory adipocytokine levels, and suppression of ER stress. Further studies are needed to assess whether these effects have a causal role.

Alzheimer's disease (AD) is the most prevalent neurodegenerative disease that is progressive and can be characterized mostly by neuronal atrophy, amyloid deposition, accompanied by cognition, behavioral and psychological deficits. In the recent decade, a variety of machine learning algorithms have been explored and used for AD diagnosis, focusing on its subtle prodromal stage of mild cognitive impairment (MCI) to assess essential features that characterize its early manifestation and to plan for early treatment. However, diagnosis of early MCI (EMCI) remains most challenging as it is extremely difficult to delineate from cognitively normal controls (CN), and as a consequence, most of the classification algorithms for these two groups are mixed with low classification accuracy results. In this study, a machine learning approach based on deep neural network (DNN) has been proposed in order to detect AD in its early stage using multimodal imaging, combining magnetic resonance imaging (MRI), positron emission tomography (PET) and standard neuropsychological test scores. The proposed approach makes use of the optimization method of Adam to update the learning weights in order to improve its accuracy. The algorithm is able to classify cognitively normal control group from EMCI with an unprecedented accuracy of 84.0%. Although the focus here is distinguishing the two groups of CN and EMCI for early diagnosis and treatment planning, this study also shows how the proposed deep learning algorithm can be extended for multiclass classification involving CN and all the stages of EMCI, late MCI (LMCI) and AD.

Background Using multiple modalities of biomarkers, several machine leaning-based approaches have been proposed to characterize patterns of structural, functional and metabolic differences discernible from multimodal neuroimaging data for Alzheimer’s disease (AD). Current investigations report several studies using binary classification often augmented with local feature selection methods, while fewer other studies address the challenging problem of multiclass classification. New method To assess the merits of each of these research directions, this study introduces a supervised Gaussian discriminative component analysis (GDCA) algorithm, which can effectively delineate subtle changes of early mild cognitive impairment (EMCI) group in relation to the cognitively normal control (CN) group. Using 251 CN, 297 EMCI, 196 late MCI (LMCI), and 162 AD subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) and considering both structural and functional (metabolic) information from magnetic resonance imaging (MRI) and positron emission tomography (PET) modalities as input, the proposed method conducts a dimensionality reduction algorithm taking into consideration the interclass information to define an optimal eigenspace that maximizes the discriminability of selected eigenvectors. Results The proposed algorithm achieves an accuracy of 79.25 % for delineating EMCI from CN using 38.97 % of Gaussian discriminative components (i.e., dimensionality reduction). Moreover, for detecting the different stages of AD, a multiclass classification experiment attained an overall accuracy of 67.69 %, and more notably, discriminates MCI and AD groups from the CN group with an accuracy of 75.28 % using 48.90 % of the Gaussian discriminative components. Comparison with existing method(s) The classification results of the proposed GDCA method outperform the more recently published state-of-the-art methods in AD-related multiclass classification tasks, and seems to be the most stable and reliable in terms of relating the most relevant features to the optimal classification performance. Conclusion The proposed GDCA model with its high prospects for multiclass classification has a high potential for deployment as a computer aided clinical diagnosis system for AD.

Background Diagnosis of early mild cognitive impairment (EMCI) as a prodromal stage of Alzheimer’s disease (AD) with its delineation from the cognitively normal (CN) group remains a challenging but essential step for the planning of early treatment. Although several studies have focused on the MCI diagnosis, this study introduces the early stage of MCI to assess more thoroughly the earliest signs of disease manifestation and progression. New method We used random forest feature selection model with a Gaussian-based algorithm to perform method evaluation. This integrated method serves to define multivariate normal distributions in order to classify different stages of AD, with the focus placed on detecting EMCI subjects in the most challenging classification of CN vs. EMCI. Results Using 896 participants classified into the four categories of CN, EMCI, late mild cognitive impairment (LMCI) and AD, the results show that the EMCI group can be delineated from the CN group with a relatively high accuracy of 78.8% and sensitivity of 81.3%. Comparison with existing method(s) The feature selection model and classifier are compared with some other prominent algorithms. Although higher accuracy has been achieved using the Gaussian process (GP) model (78.8%) over the SVM classifier (75.6%) for CN vs. EMCI classification, with 0.05 being the cutoff for significance, and based on student’s t-test, it was determined that the differences for accuracy, sensitivity, specificity between the GP method and support vector machine (SVM) are not statistically significant. Conclusion Addressing the challenging classification of CN vs. EMCI provides useful information to help clinicians and researchers determine essential measures that can help in the early detection of AD.

ObjectiveSemantic intrusion (SI) errors may highlight specific breakdowns in memory associated with preclinical Alzheimer disease (AD); however, there have been no investigations to determine whether SI errors occur with greater frequency in persons with amnestic mild cognitive impairment (aMCI) confirmed as amyloid positive (Amy+) vs those who have clinical symptoms of aMCI-AD with negative amyloid scans (suspected non-AD pathology [SNAP]) or persons who are diagnosed with other brain disorders affecting cognition.MethodsEighty-eight participants with aMCI underwent brain amyloid PET and MRI scans and were classified as early AD (Amy+), SNAP (Amy−), or other neurological/psychiatric diagnosis (Amy−). We focused on SI on the Loewenstein-Acevedo Scales for Semantic Interference and Learning (LASSI-L) targeting proactive semantic interference (PSI; old semantic learning interferes with new semantic learning), failure to recover from PSI after an additional learning trial (frPSI), and retroactive semantic interference (new semantic learning interferes with memory for old semantic learning).ResultsSIs on measures of PSI and frPSI distinguished between Amy+ AD and SNAP and other non-AD cases. PSI and frPSI intrusions evidenced moderately high associations with reduced volumes in the entorhinal cortex, superior temporal regions, and supramarginal gyrus. No such associations were observed in cases with SNAP.ConclusionsSIs on the LASSI-L related to PSI and frPSI uniquely differentiated Amy+ and Amy− participants with aMCI and likely reflect deficits with inhibition and source memory in preclinical AD not captured by traditional cognitive measures. This may represent a specific, noninvasive test successful at distinguishing cases with true AD from those with SNAP.

The hybrid optical bistable devices with electro-optical feedback have many potential important applications for controlling light by light or electricity, such as optical modulator, optical switch, optical logic, optical limiter, optical stabilizer, optical amplifer, optical oscillator and optical sensor. Some examples which have been done by us are shown in this paper.

Background: Deposition of beta amyloid protein (Aβ) is known to be an early event that is closely associated with the pathogenesis of Alzheimer's disease (AD), along with related downstream events such as neuronal loss, neurofibrillary tangles, cortical thinning and cognitive deficits. APOE e4 allele (E4) is also known to be associated with increased risk for AD. Objectives: The goal of this study is to examine the association of Aβ deposition to cortical thickness (CoTh), in healthy control (CN), early MCI (EMCI), late MCI (LMCI) and AD stages by controlling for E4 load, both in regional and hemispheric levels, and to interpret patterns of different brain regions based on their correlation performance among the four groups. Methods: We analyzed Amyloid PET Scan, Volumetric MRI (CoTh) data from participants in the ADNIGO/ADNI2 cohort whose APOE gene information are available. Statistical analysis includes Pearson partial correlations, Analysis of Covariance (ANCOVA) with post-hoc Tukey HSD. Complete-linkage hierarchical clustering analysis was further performed to group brain regions based on their significant correlation performance. Results: 25 out of 68 regions showed significant correlation of Aβ load and CoTh at least in one diagnostic group. Furthermore, 6 main clusters were recognized based on the performance patterns of those 25 regions across 4 diagnosis groups. Conclusion: Our major finding clustered the cortical regions into 2 general groups, positive correlation in CN or AD, and negative correlation in EMCI and/or LMCI, and 6 more specific groups were then recognized, confirming the interplay between of Aβ and CoTh in the different stages of the disease.

Over the past few years, several approaches have been proposed to assist in the early diagnosis of Alzheimer's disease (AD) and its prodromal stage of mild cognitive impairment (MCI). For solving this high dimensional classification problem, the widely used algorithm remains to be Support Vector Machines (SVM). But due to the high variance of the data, the classification performance of SVM remains unsatisfactory, especially for delineating the MCI group from the cognitively normal control (CN) group. This study introduces a novel algorithm based on the Gaussian discriminant analysis (GDA) for a more effective and accurate classification performance. Subjects considered in this study included 190 CN, 305 MCI, and 133 AD subjects. Using 75% of the data as the training set with a tenfold cross validation, the proposed algorithm achieved an average accuracy of 94.17%, a sensitivity of 93.00%, and a specificity of 95.00% for discriminating AD from CN; and an average accuracy of 84.86%, a sensitivity of 84.78%, and a specificity of 85.00% for discriminating MCI from CN. Then a true test was implemented for the remaining 25% data, for discriminating specifically MCI from CN, resulting in an accuracy of 82.20%, a sensitivity of 83.10%, and a specificity of 80.85%. As revealed through the literature, these results involving the delineation of the MCI group from CN could be considered as the best classification performance obtained so far. This study also shows that by separating left and right hemispheres of the brain into two decision spaces, then combining the results of these two spaces, the classification performance can be improved significantly; an assertion proven in this study.

Neuroimaging is an important research platform that can be very useful for eliciting new understanding on the complicated pathogenesis between genetics and disease phenotypes. Due to the extremely high dimensionality of image and genetic data, and considering the potential joint effect of genetic variants, multivariate techniques have been examined to detect Alzheimers disease (AD) related genetic variants expressed through single-nucleotide polymorphisms (SNPs). However, the image features used in support of those methods are not immediately related to the disease, and the detected genetic markers may not be related to AD. In this study, we propose an ensemble model based framework for firstly extracting 50 region-based image features whose values are predicted by base learners trained on raw neuroimaging morphological variables. This task is followed by performing sparse Partial Least Squares regression (sPLS) method on the extracted 50 AD related image features and pre-selected 1508 SNPs to detect the significant SNPs associated with the extracted image features. Instead of modeling a direct link between genetic variants and disease label, we captured disease information indirectly.

This study introduces a novel Gaussian discriminant analysis (GDA)-based computer aided diagnosis (CAD) system using structural magnetic resonance imaging (MRI) data uniquely as input for screening different stages of Alzheimers disease (AD) involving its prodromal stage of mild cognitive impairment (MCI) in relation to the cognitive normal control group (CN). Taking advantage of multiple modalities of biomarkers, over the past few years, several machine learning-based CAD approaches have been proposed to address this high-dimensional classification problem. This study presents a novel GDA-based CAD system on the basis of a tenfold cross validation and a held-out test data set. Subjects considered in this study included 187 CN, 301 MCI, and 131 AD subjects from the Alzheimers Disease Neuroimaging Initiative (ADNI) database. In the tenfold cross validation, the proposed system achieved an average F1 score of 97.20%, accuracy of 96.00%, sensitivity of 99.14%, and specificity of 88.67% for discriminating together the MCI and AD groups from the CN group; and an average F1 score of 79.82%, accuracy of 87.43%, sensitivity of 79.09%, and specificity of 91.25% for discriminating AD from MCI. By testing on the held-out test data, for discriminating MCI and AD from CN, an accuracy of 93.28%, a sensitivity of 98.78%, and a specificity of 81.08% were obtained. These results also show that by separating left and right hemispheres of the brain into two decisional spaces, and then combining their outputs, the GDA-based CAD system demonstrates a high potential for clinical application.

Background The rise in incidence of Alzheimer's disease (AD) has led to efforts to advance early detection of the disease during its preclinical stages. To achieve this, the field needs to develop more sensitive cognitive tests that relate to biological markers of disease pathology. Failure to recover from proactive interference (frPSI) is one such cognitive marker that is associated with volumetric reductions in the hippocampus, precuneus, and other AD-prone regions, and to amyloid load in the brain. Objective The current study attempted to replicate and extend our previous findings that frPSI is a sensitive marker of early AD, and related to a unique pattern of volumetric loss in AD prone areas. Methods Three different memory measures were examined relative to volumetric loss and cortical thickness among 45 participants with amnestic mild cognitive impairment. Results frPSI was uniquely associated with reduced volumes in the hippocampus (r = 0.50) precuneus (r = 0.41), and other AD prone regions, replicating previous findings. Strong associations between frPSI and lower entorhinal cortex volumes and cortical thickness (r≥0.60) and precuneus (r = 0.50) were also observed. Conclusion Unique and strong associations between volumetric reductions and frPSI as observed by Loewenstein and colleagues were replicated. Together with cortical thickness findings, these results indicate that frPSI is worthy of further study as a sensitive and early cognitive marker of AD.

Metastable icosahedral quasicrystalline nanoparticles precipitate in the initial crystallization processes of some selected zirconium and hafnium based metallic glasses. All such particles reported so far are embedded in residual glassy matrix. It is predicted that, if these are separated as free standing particles, they can be applied in a variety of fields. Breaking the suitably annealed metallic glasses to small pieces by mechanical approaches is considered to be the first step toward this goal. The result of such an attempt is reported here. Several previously reported metallic glasses such as Zr 70 Cu 27.5 Rh 2.5 and Hf 69.5 Al 7.5 Ni 11 Cu 12 have been abraded by using regular sandpapers and diamond papers, scraped with diamond scratchers, and sliced by using microtome. Thus obtained small pieces have been examined by Scanning Electron Microscope, Transmission Electron Microscope, and Energy Dispersive X-ray Spectroscopy. It has been revealed that the mechanical breaking processes cause an undesired phase transformation of the quasicrystalline nanoparticles to the crystalline phases. The reason for this undesired phase transformation was analyzed and the appropriate procedures to avoid this negative effect for future work were suggested.

In an effort to synthesize doped ZnO nanowires, SiOx nanowires were obtained accidently. In the experiment, mixed powders containing chemicals such as ZnO, graphite, Ga2O3, and In2O3 were placed in the center of a tube furnace, where the temperature was set to 1200 °C and the vacuum was approximately 27 Pa. Silicon wafers were placed around the vicinity of the furnace exit to collect the expected nanomaterials. After prolonged heating, grey layers were found on top of one wafer located inside the furnace. The layer showed no adhesion to the substrate. Characterization by using Scanning Electron Microscope (SEM), Transmission Electron Microscope (TEM), and Energy Dispersive X-ray Spectroscopy (EDS) revealed that this layer consisted of SiOx nanowires. Formation of Si-containing liquid drop and the subsequent growth of SiOx nanowires out of it are suggested as the growth mechanism.

This chapter studies the property of the nonlinear optical system with feedback—optical bistability. We will discuss firstly the basic conception of optical bistability; secondly, the working principles of typical optical bistable devices (OBD) including two kinds of all-optical OBDs: nonlinear F–P etalons filled with the saturable absorption material and optical Kerr material, and three kinds of electro-optical hybrid OBDs: electro-optical F–P etalon, electro-optical M–Z interferometer, and electro-optical polarization modulation; finally, the theoretical analysis of stability problems of optical bistability, including the stability condition of optical bistability system, and two kinds of optical instability: the optical pulsation in the double feedback system and the optical chaos in the feedback delayed system.

In this chapter, the first section gives the reviews of all-optical switch (AOS), including the significance, basic principle, classification method, application requirement, recent problem, and development direction.

This chapter studies the phenomenon of nonlinear interaction between the laser pulse and the propagation fiber. At first, we will deduce the nonlinear Schrodinger equation for describing the propagation of light pulse in the fiber. Under this foundation, we will analyze the two effects of dispersion and self-phase modulation how to affect the propagation of light pulse in the fiber and how to form the time optical soliton in both combined action.

In this chapter, firstly we will study light intensity induced medium refractive-index change phenomenon, i.e., optical Kerr effect. Mainly study on the self-phase modulation optical Kerr effect, the cross-phase modulation optical Kerr effect, and related light induced birefringence effect. Secondly, we will study the self-focusing effect induced by transverse strength inhomogeneous distribution of Gaussian beam, including steady-state and dynamic self-focusing, time and space self-phase modulation phenomena.

This chapter uses a reformed first-order frequency-domain wave equation for the isotopic medium to approximately describe the second-order nonlinear optics effects in the anisotropic medium. At first, the three-wave coupling equations are deduced, then based on these equations, several typical second-order nonlinear optics effects are studied: optical frequency doubling, sum frequency, difference frequency, and optical parameter amplification and parameter oscillation.

This chapter starting from the Maxwell’s equations deduces different forms of nonlinear wave equations for the light propagation in the isotropic and anisotropic nonlinear mediums, and in the time and frequency domains.