Real Structures on Root Stacks and Parabolic Connections

Let $D$ be a reduced effective strict normal crossing divisor on a smooth complex variety $X$, and let $\mathfrak{X}_D$ be an associated root stack over $\mathbb C$. Suppose that $X$ admits an anti-holomorphic involution (real structure) that keeps $D$ invariant. We show that the root stack $\mathfrak{X}_D$ naturally admits a real structure compatible with $X$. We also establish an equivalence of categories between the category of real logarithmic connections on this root stack and the category of real parabolic connections on $X$.Comment: 27 pages, accepted for publication in Geometriae Dedicat

Surface Micromachined Widely Tunable VCSEL and OAM-Filter for Optical Data Transmission

The implication of wavelength division multiplexed passive optical network (WDM PON) is becoming more evident as the traffic demands of the mobile network operators keep increasing. It offers a cost-efficient solution to handle the bandwidth and latency requirements of the mobile fronthaul. The key component of such a WDM-PON system is a centralized wavelength-controlled tunable laser. The biggest challenge up to now is the lack of low-cost wideband 1550 nm tunable lasers with 10 Gbit/s transmission capacity. In the first part of this work, a widely-tunable microelectromechanical system vertical-cavity surface-emitting laser (MEMS VCSEL) is developed. The cost-efficient, directly-modulated laser can be utilized for 10Gbit/s transmission over relevant reach. It also offers simplicity for wideband autonomous tuning. The device is suitable for applications including hot backup and fixed wavelength laser replacement for inventory reduction. Within the framework of this work, a PECVD-deposited MEMS distributed Bragg reflector (DBR) mirror is surface-micromachined on top of a short-cavity active VCSEL structure. The MEMS-DBR consisting of SiNx/SiOy dielectric materials has a very high reflectivity with wide stopband. Wavelength tuning is realized by the electrothermal actuation of the MEMS electrode. The fabrication steps of the MEMS aiming for large volume production is discussed in detail. A comprehensive static and dynamic characterizations of MEMS VCSEL including far-field, linewidth, polarization behavior, modulation capacity and relative intensity noise is presented. The effect of the temperature change on its tuning behavior as well as on the static and dynamic performance is investigated. The obtained wavelength tuning range of more than 100 nm covers the complete telecom C-band (1530–1565 nm) and part of L-band (1565–1625 nm). A small-signal amplitude modulation bandwidth of up to 8.35GHz is demonstrated for the center emission wavelength around 1550 nm. This enables to implement a directly-modulated MEMS VCSEL based back-to-back link at 10Gbit/s data transmission for 76 nm tuning range. Also, quasi error-free 10Gbit/s transmission over 40 km standard single-mode fiber for a tuning range of more than 60 nm validates its potential for the above mentioned novel WDM-PON system. Apart from optical communication, the scope of this tunable source is investigated in applications such as dispersion spectroscopy and tunable terahertz (THz) signal generation. Experimental validation of multi-species dispersion spectroscopy using MEMS VCSEL is presented for the first time in this work, where concurrent detection of acetylene (C2H2), hydrogen cyanide (HCN), and carbon monoxide (CO) is demonstrated. The second part of the work constitutes demonstration and experimental validation of a novel optical component called MEMS orbital angular momentum (OAM) filter. The filter consists of a micro-sized spiral phase plate (SPP) which is integrated to the MEMS-DBR of a Fabry-Perot optical filter by means of direct laser writing. The onchip devices are suitable for distinguishing different OAM modes for a broad tuning range around 1550 nm emission and considered as a compact, robust and cost-effective solution for simultaneous OAM- and WDM optical communications. The utilization of the OAM modes as an additional orthogonal basis of information carriers in both free space and optical fiber communication systems potentially enhances the transmission capacity tremendously. Four devices with OAM orders of 0 (i.e., no SPP on MEMS), 1, 2 and 3 have been investigated. They are capable of generating/receiving the OAM beam of corresponding order over a continuous tuning range of more than 30 nm, for which the designed SPPs work with high mode purity. The system performance is evaluated by multiplexing two wavelength- and two OAM channels. Error-free free-space transmission at 10Gbit/s suggests that OAM-filters functioning over a wide wavelength range could be employed as an additional degree of freedom for increasing the capacity of free-space communication to a great extent

Analyzing the Efficacy of an LLM-Only Approach for Image-based Document Question Answering

Recent document question answering models consist of two key components: the vision encoder, which captures layout and visual elements in images, and a Large Language Model (LLM) that helps contextualize questions to the image and supplements them with external world knowledge to generate accurate answers. However, the relative contributions of the vision encoder and the language model in these tasks remain unclear. This is especially interesting given the effectiveness of instruction-tuned LLMs, which exhibit remarkable adaptability to new tasks. To this end, we explore the following aspects in this work: (1) The efficacy of an LLM-only approach on document question answering tasks (2) strategies for serializing textual information within document images and feeding it directly to an instruction-tuned LLM, thus bypassing the need for an explicit vision encoder (3) thorough quantitative analysis on the feasibility of such an approach. Our comprehensive analysis encompasses six diverse benchmark datasets, utilizing LLMs of varying scales. Our findings reveal that a strategy exclusively reliant on the LLM yields results that are on par with or closely approach state-of-the-art performance across a range of datasets. We posit that this evaluation framework will serve as a guiding resource for selecting appropriate datasets for future research endeavors that emphasize the fundamental importance of layout and image content information