Ultrafast electrooptic dual-comb interferometry

The femtosecond laser frequency comb has enabled the 21st century revolution in optical synthesis and metrology. A particularly compelling technique that relies on the broadband coherence of two laser frequency combs is dual-comb interferometry. This method is rapidly advancing the field of optical spectroscopy and empowering new applications, from nonlinear microscopy to laser ranging. Up to now, most dual-comb interferometers were based on modelocked lasers, whose repetition rates have restricted the measurement speed to ~ kHz. Here we demonstrate a novel dual-comb interferometer that is based on electrooptic frequency comb technology and measures consecutive complex spectra at a record-high refresh rate of 25 MHz. These results pave the way for novel scientific and metrology applications of frequency comb generators beyond the realm of molecular spectroscopy, where the measurement of ultrabroadband waveforms is of paramount relevance

Electro-optic dual-comb interferometry over 40-nm bandwidth

Dual-comb interferometry is a measurement technique that uses two laser frequency combs to retrieve complex spectra in a line-by-line basis. This technique can be implemented with electro-optic frequency combs, offering intrinsic mutual coherence, high acquisition speed and flexible repetition-rate operation. A challenge with the operation of this kind of frequency comb in dual-comb interferometry is its limited optical bandwidth. Here, we use coherent spectral broadening and demonstrate electro-optic dual-comb interferometry over the entire telecommunications C band (200 lines covering ~ 40 nm, measured within 10 microseconds at 100 signal-to-noise ratio per spectral line). These results offer new prospects for electro-optic dual-comb interferometry as a suitable technology for high-speed broadband metrology, for example in optical coherence tomography or coherent Raman microscopy

A Closer Look at the Racial Disparity Rates in Michigan Schools

Racial disparity in disciplinary actions has long been an issue in American public education. The United States Department of Education has collected data on this for over 35 years. Wright, Weekes and Mcglaughlin (2000) claim “research evidence indicates that those who are at disproportionate risk of exclusion are African-Caribbean boys of both primary and secondary schooling age”. With a closer focus on Michigan public schools, national research will also support data collected on racial disciplinary disparity rates by the American Civil Liberties Union of Michigan. In addition, contributing factors and issues associated with unfair disciplinary sanctions on minorities will be examined to determine their effect on multi-cultural education. Published data on disciplinary disparity rates for the state of Michigan have been available since 1996. Table 1.a. represents the suspension rates by race/ethnicity in the state of Michigan for 1990. From this, it is clear that students of Afro-Caribbean descent were getting hit the hardest. The disciplinary rate of these students surpassed their enrollment population for the participating, surveyed school districts. The document suggests that poverty has a strong correlation with disciplinary rates during this time period (1990-1995). Since then, other possible contributing factors have surfaced and raised issues in direct relation to educational inequality and justice. For example, the zero-tolerance policy, which will be discussed, is very controversial, due to harsh sanctions on minor offenses and the opportunity for mistreatment due to teacher biases. Language barriers and communications issues in relation to a culturally diverse classroom can also become problematic, as demonstrated in table 1.a. Table 1.b presents rates in disciplinary disparities by providing student population and suspensions rates by race/ethnicity. This chart will be analyzed independently of the other, due to it being a smaller sample compared to the surveyed schools from 1990. In this district, the Ann-Arbor Public Schools, every minority group except Asians has a disciplinary rate that surpasses its student enrollment rate for the district. According to the U.S. Census Bureau (2000), 74.7% of the Ann Arbor population is considered White; the other 25% consists of African-Americans, Hispanics and Asians. With that in mind, the probability of a controlled factor causing the incline in disciplinary rates among minorities is likely. Since both the city and school district are predominantly white, there is a question as to why the minority disciplinary rate surpasses the enrollment rate and has for nearly twenty years. Possible explanations for this continuing trend will be presented, using a national perspective in the form of data and relevant research

Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the unstable solitary waves which belong to the frontier between expanding and collapsing solutions and to provide an oscillating solitonic structure, some sort of breather-type solution. We obtain precise conditions on the control parameters to achieve the stabilization and compare our results with accurate numerical simulations of the nonlinear Schrodinger equation. Because of the application of these ideas to matter waves these solutions are some sort of matter breathers

Optical Frequency Comb Noise Characterization Using Machine Learning

A novel tool, based on Bayesian filtering framework and expectation maximization algorithm, is numerically and experimentally demonstrated for accurate frequency comb noise characterization. The tool is statistically optimum in a mean-square-error-sense, works at wide range of SNRs and offers more accurate noise estimation compared to conventional methods

An eMath Teacher TOOL for ACTIVE LEARNING FLEURY'S ALGORITHM

An eMathTeacher [Sánchez-Torrubia 2007a] is an eLearning on line self assessment tool that help students to active learning math algorithms by themselves, correcting their mistakes and providing them with clues to find the right solution. The tool presented in this paper is an example of this new concept on Computer Aided Instruction (CAI) resources and has been implemented as a Java applet and designed as an auxiliary instrument for both classroom teaching and individual practicing of Fleury’s algorithm. This tool, included within a set of eMathTeacher tools, has been designed as educational complement of Graph Algorithm active learning for first course students. Its characteristics of visualization, simplicity and interactivity, make this tutorial a great value pedagogical instrument

Electro optic combs rise above the noise

Electro-optic modulation of light can have a precision equivalent to one optical-field cycl