Comment on 'Exact solution of resonant modes in a rectangular resonator'

We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation

Airy-Gauss beams and their transformation by paraxial optical systems

We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The model of the AiG beam describes in a more realistic way the propagation of the Airy wave packets because AiG beams carry finite power, retain the nondiffracting propagation properties within a finite propagation distance, and can be realized experimentally to a very good approximation

Elliptical beams

A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others

Normalization of the Mathieu-Gauss optical beams

A series scheme is discussed for the determination of the normalization constants of the even and odd Mathieu-Gauss (MG) optical beams. We apply a suitable expansion in terms of Bessel-Gauss (BG) beams and also answer the question of how many BG beams should be used to synthesize a MG beam within a tolerance. The structure of the normalization factors ensures that MG beams will always be normalized independently of the particular normalization adopted for the Mathieu functions. In this scheme, the normalization constants are expressed as rapidly convergent series that can be calculated to an arbitrary precision

Human Long Telomeres and Epigenetic Marks

We have read with interest the article “Telomere length regulates TERRA levels through increased trimethylation of telomeric H3K9 and HP1α” by Arnoult and colleagues [1]. This study focuses on human telomeric chromatin structure using different techniques like Chromatin Immunoprecipitation (ChIP), cytolocalization or RT-qPCR. However, it has been performed without taking into consideration the presence of Interstitial Telomeric Sequences (ITSs) in the human genome. Some of the conclusions of the article are undoubtedly clear but there are others that might be explained in alternative ways, considering the existence of ITSs. Following, we mention some comments that arise from this interesting article

Assessing the Epigenetic Status of Human Telomeres

The epigenetic modifications of human telomeres play a relevant role in telomere functions and cell proliferation. Therefore, their study is becoming an issue of major interest. These epigenetic modifications are usually analyzed by microscopy or by chromatin immunoprecipitation (ChIP). However, these analyses could be challenged by subtelomeres and/or interstitial telomeric sequences (ITSs). Whereas telomeres and subtelomeres cannot be differentiated by microscopy techniques, telomeres and ITSs might not be differentiated in ChIP analyses. In addition, ChIP analyses of telomeres should be properly controlled. Hence, studies focusing on the epigenetic features of human telomeres have to be carefully designed and interpreted. Here, we present a comprehensive discussion on how subtelomeres and ITSs might influence studies of human telomere epigenetics. We specially focus on the influence of ITSs and some experimental aspects of the ChIP technique on ChIP analyses. In addition, we propose a specific pipeline to accurately perform these studies. This pipeline is very simple and can be applied to a wide variety of cells, including cancer cells. Since the epigenetic status of telomeres could influence cancer cells proliferation, this pipeline might help design precise epigenetic treatments for specific cancer types.Spanish Agency of ResearchEuropean Fund for Regional Development European Union BIO2016-78955-

DNA methylation at tobacco telomeric sequences

Majerová et al. (Plant Mol Biol, 2011) have recently reported that a considerable fraction of cytosines at tobacco telomeres is methylated. Although the data presented in this report indicate that tobacco telomeric sequences undergo certain levels of DNA methylation, it is not clear whether the methylated sequences are at telomeres, at internal chromosomal loci or at both

Happy Objects and Bloom Spaces: Investigating the Potential of Rupi Kaur\u27s Poetry

In response to the movement of what is considered and labeled as “Instagram poetry,” poet and critic Rebecca Watts argues that to consider “artless” poetry as “poetry” we are denigrating the artform. This project centers around Watts’ claim that “the reader is dead” due to their encounter with such poetry. This project acts as a conversation that seeks to understand why certain forms of art are considered a “threat” to those who engage with them, as well as to their respective fields. Using affect theory (specifically the theory of the happy object) we can begin to understand why we gravitate towards certain objects, and how those objects act as a “bloom space” – a site of “becoming.” By framing a book of Instagram poetry (like Rupi Kaur’s milk and honey) as a happy object, or an object capable of orienting bodies towards certain possibilities, we can talk against hierarchical notions of art and literature that lead to these distinctions between “high” and “low” art

Higher-order moments and overlaps of Cartesian beams

We introduce a closed-form expression for the overlap between two different Cartesian beams. In the course of obtaining this expression, we establish a linear relation between the overlap of circular beams with azimuthal symmetry and the overlap of Cartesian beams such that the knowledge of the former allows the latter to be calculated very easily. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of Cartesian beams, and therefore of all their relevant special cases, including the standard, elegant, and generalized Hermite–Gaussian beams, cosh-Gaussian beams, Lorentz beams, and Airy beams, among others