The Pursuit of Mathematical Truths: A Rich and Meaningful Aesthetic Experience of Inquiry

Given a Deweyan philosophy of mathematics, education, and of the nature of experience, the pursuit of mathematical truths can be classified as rich and meaningful aesthetic experiences that are ends in themselves. My argument is that mathematical experiences of inquiry can have a meaningful impact on an individual that is of similar effect on an individual as a work of art, such as a painting, or a novel, or a piece of music. The nature of mathematical inquiry is to expand an individual’s conscious experience of themselves, their relation to other people, and their relation to the world at large. Discipline: Philosophy Faculty Mentor: Dr. Alain Beauclai

The Pursuit of Mathematical Truths: A Rich and Meaningful Aesthetic Experience of Inquiry as an End in Itself

Given a Deweyan philosophy of mathematics, education, and of the nature of experience, the pursuit of mathematical truths can be classified as rich and meaningful aesthetic experiences that are ends in themselves. My argument is that mathematical experiences of inquiry can have a meaningful impact on an individual that is of similar effect on an individual as a work of art, such as a painting, or a novel, or a piece of music. The nature of mathematical inquiry is to expand an individual’s conscious experience of themselves, their relation to other people, and their relation to the world at large

Electroplated Ni mask for plasma etching of submicron-sized features in LiNbO3

International audienceWe here report on the fabrication of electroplated nickel (Ni) masks for dry etching of sub-micron patterns in lithium niobate (LiNbO3). This process allows obtaining 350-nm thick Ni masks defining high air filling fraction holey arrays (e.g. openings of 1800 nm in diameter with inter-hole spacing of 300 nm, or 330 nm diameter holes spaced by 440 nm). The mask profile is perfectly vertical (angle ≈ 90°). The obtained metallic masks are used to realise photonic and phononic crystals. High aspect ratio and dense arrays of holey patterns were defined and transferred into LiNbO3 through RIE (Reactive Ionic Etching) in sulphur hexafluoride (SF6) chemistry. Nanometric holes exhibiting sidewall slope angles of the order of 60° have in this way been etched in LiNbO3. The LiNbO3/Ni selectivity is close to 6 and the etch rate around 6 nm/min

Optical characterization of ultra-short Bragg grating on lithium niobate ridge waveguide

International audienceIn this Letter, we report a technique to etch giant aspect ratio nanostructures in lithium niobate. An 8 μm long Bragg grating on a Ti:LiNbO3 ridge waveguide was fabricated by combining optical-grade dicing and focused ion beam milling. The reflectivity was evaluated using an optical coherence tomography system: it is measured to be 53% for the TM wave and 47% for the TE wave. We study by 2D-FDTD the modeled behavior of the electromagnetic field when an angle exists between two consecutive sidewalls of the grating in order to understand the difference between ideal Bragg grating and experimental samples. These simulations allow us to optimize the parameters in order to increase the reflection of the grating up to 80%

Lithium Niobate Optical Waveguides and Microwaveguides

Lithium niobate has attracted much attention since the 1970s due to its capacity to modify the light by means of an electric control. In this chapter, we review the evolution of electro-optical (EO) lithium niobate waveguides throughout the years, from Ti-indiffused waveguides to photonic crystals. The race toward ever smaller EO components with ever-lower optical losses and power consumption has stimulated numerous studies, the challenge consisting of strongly confining the light while preserving low losses. We show how waveguides have evolved toward ridges or thin film-based microguides to increase the EO efficiency and reduce the driving voltage. In particular, a focus is made on an easy-to-implement technique using a circular precision saw to produce thin ridge waveguides or suspended membranes with low losses

LiNbO3 acousto-optical and electro-optical micromodulators

We report on acousto-optical (AO) and electro-optical (EO) LiNbO3 modulators with an active length of only 11 µm. The miniature devices are based on photonic crystal (PhC) structures that are controlled by an external effect (DC electric field or Surface Acoustic Waves). Two processes are presented for realizing the PhCs despite the resistance of the material to etching. The first method is based on direct FIB writing and can yield the fabrication of holes with depth of 32 m and diameter of 12 m or less. The second method consists in FIB patterning of a mask which is deposited on the substrate. This process is followed by proton exchange (PE) and reactive ion etching (RIE). Thus, structures with a diameter of 400 nm and an aspect ratio of 3:1 have been fabricated. The methods have been applied to the fabrication of EO and AO micromodulators showing a driving voltage of 13,5 V and a driving electric power of 20 mW respectively. These developments open the way to dense integration of dynamic optical functionalities

Parrot beak‐inspired metamaterials with friction and interlocking mechanisms 3D/4D printed in micro and macro scales for supreme energy absorption/dissipation

Energy absorption and dissipation features of mechanical metamaterials have widespread applications in everyday life, ranging from absorbing shock impacts to mechanical vibrations. This article proposes novel bioinspired friction-based mechanical metamaterials with a zero Poisson's ratio behavior inspired from parrot's beaks and manufactured additively. The mechanical performances of the corresponding metamaterials are studied at both macro and micro scales by experiments and finite element analysis (FEA). An excellent agreement is observed between the FEA and both microscopic and macroscopic scale experiments, showing the accuracy of the developed digital tool. Performances are compared to traditional triangular lattice metamaterials. Both experimental tests and FEA results demonstrate the following advantages: 1) absorbing and dissipating energy per unit of mass (SEA) at large compressive strains without global buckling; 2) bistable deformation patterns including friction-based and interlocking mechanisms; 3) reversible deformation patterns after unloading; 4) shape recovery behavior after a heating–cooling process; and 5) the higher elastic modulus of micro metamaterials compared with their macro counterparts. This is the first demonstration of a bioinspired friction-based design of 3D-printed mechanical metamaterials that feature absorbing/dissipating energy, stability, and reversibility properties to cater to a wide range of sustainable meta-cylinders in micro and macro scales