Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons and Mirror Symmetry

We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles the variety of six-dimensional spin manifolds. We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. Therefore the mirror symmetry of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory perspective.Comment: v5; 49 pages, version to appear in Advances in High Energy Physic

In vivo Brillouin optical microscopy of the human eye

We report the first Brillouin measurement of the human eye in vivo. We constructed a Brillouin optical scanner safe for human use by employing continuous-wave laser light at 780 nm at a low power of 0.7 mW. With a single scan along the optic axis of the eye, the axial profile of Brillouin frequency shift was obtained with a pixel acquisition time of 0.4 s and axial resolution of about 60 μm, showing the depth-dependent biomechanical properties in the cornea and lens

Multistage VIPA etalons for high-extinction parallel Brillouin spectroscopy

We demonstrate a high-resolution high-extinction parallel spectrometer for Brillouin spectroscopy of turbid samples. Cascading multiple VIPA etalons in the cross-axis configuration allowed us to achieve a high extinction ratio of up to 80 dB with sub-GHz resolution. Using a three-stage VIPA, we obtained the Brillouin spectra from Intralipid solutions at concentrations up to 10%

Half-Wave Dipolar Metal-Semiconductor Laser

Nano-scale lasers harnessing metallic plasmons hold promise across physical sciences and industrial applications. Plasmons are categorized as surface plasmon polaritons (SPP) and localized surface plasmons (LSP). While SPP has gained popularity for nano-lasers by fitting a few cycles of SPP waves into resonators, achieving LSP lasing in single nanoparticles remains an elusive goal. Here, we highlight the equivalence of LSP and SPP within resonant systems and present lasers oscillating in the lowest-order LSP or, equivalently, half-cycle SPP. This diffraction-limited dipolar emitter is realized through strong coupling of plasmonic oscillation in gold and dielectric resonance in high-gain III-V semiconductor in the near infrared away from surface plasmon frequencies. The resulting single-mode stimulated emission peak exhibits linewidth Q factors over 50 at room temperature, with wide tunability spanning from 1190 to 1460 nm determined by resonator sizes ranging from 190 to 280 nm. A semiconductor laser model elucidates the temporal and spectral buildup dynamics under optical pumping. Notably, linewidth Q values surpassing 250 are attained from higher-order, isolated laser particles within live biological cells. These results offer fresh perspectives in nanophotonics and indicate promising opportunities for multiplexed biological applications

Feasibility of Reduced Lap-Spliced Length in Polyethylene Fiber-Reinforced Strain-Hardening Cementitious Composite

This research investigates the interfacial behavior between polyethylene (PE) fiber-reinforced strain-hardening cement composite (PE-SHCC) and reinforcing bars that are spliced in the tension region to determine feasibility of reduced lap-spliced length in PE-SHCC. Twenty test specimens were subjected to monotonic and cyclic tension loads. The variables include the replacement levels of an expansive admixture (0% and 10%), the compressive strength of the SHCC mixtures (40 MPa and 80 MPa), and the lap-spliced length in the tension region (40% and 60% of the splice length recommended by ACI 318). The PE-SHCC mixture contains polyethylene fiber to enhance the tensile strength, control the widths of the cracks, and increase the bond strength of the lap splice reinforcement and the calcium sulfo-aluminate- (CSA-) based expansive admixture to improve the tension-related performance in the lap splice zone. The results have led to the conclusion that SHCC mixtures can be used effectively to reduce the development length of lap splice reinforcement up to 60% of the splice length that is recommended by ACI 318. The addition of the calcium sulfo-aluminate-based expansive admixture in the SHCC mixtures improved the initial performance and mitigated the cracking behavior in the lap splice region

Cellular dye lasers : lasing thresholds and sensing in a planar resonator

This research was supported in part by the U.S. National Science Foundation (ECCS-1101947, ECCS-1505569) and National Institutes of Health (P41 EB015903). M.H. was supported in part by the Marie Curie International Outgoing Fellowship N° 627274 within the 7th European Community Framework Programme. M.C.G. was supported in part by the Starting Grant N° 640012 within the H2020 European Community Framework Programme.Biological cell lasers are promising novel building blocks of future biocompatible optical systems and offer new approaches to cellular sensing and cytometry in a microfluidic setting. Here, we demonstrate a simple method for providing optical gain by using a variety of standard fluorescent dyes. The dye gain medium can be located inside or outside a cell, or in both, which gives flexibility in experimental design and makes the method applicable to all cell types. Due to the higher refractive index of the cytoplasm compared to the surrounding medium, a cell acts as a convex lens in a planar Fabry-Perot cavity. Its effect on the stability of the laser cavity is analyzed and utilized to suppress lasing outside cells. The resonance modes depend on the shape and internal structure of the cell. As proof of concept, we show how the laser output modes are affected by the osmotic pressure.Publisher PDFPeer reviewe

In vivo Optical Coherence Elastography Reveals Spatial Variation and Anisotropy of Corneal Stiffness

Objective: The mechanical properties of corneal tissues play a crucial role in determining corneal shape and have significant implications in vision care. This study aimed to address the challenge of obtaining accurate in vivo data for the human cornea. Methods: We have developed a high-frequency optical coherence elastography (OCE) technique using shear-like antisymmetric (A0)-mode Lamb waves at frequencies above 10 kHz. Results: By incorporating an anisotropic, nonlinear constitutive model and utilizing the acoustoelastic theory, we gained quantitative insights into the influence of corneal tension on wave speeds and elastic moduli. Our study revealed significant spatial variations in the shear modulus of the corneal stroma on healthy subjects for the first time. The central cornea exhibited a shear modulus of 74 kPa, while the corneal periphery showed a decrease to 41 kPa. The limbus demonstrated an increased shear modulus exceeding 100 kPa. We obtained wave displacement profiles that are consistent with highly anisotropic corneal tissues. Conclusion: Our approach enabled precise measurement of corneal tissue elastic moduli in situ with high precision (< 7%) and high spatial resolution (< 1 mm). Significance: The high-frequency OCE technique holds promise for biomechanical evaluation in clinical settings, providing valuable information for refractive surgeries, degenerative disorder diagnoses, and intraocular pressure assessments