The role of angular momentum in the construction of electromagnetic multipolar fields

Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic fields, the multipolar solutions do not share a standard derivation or notation. As a result, expressions originating from different derivations can be difficult to compare. Some of the derivations of the multipolar solutions do not explicitly show their relation to the angular momentum operators, thus hiding important properties of these solutions. In this article, the relation between two of the most common derivations of this set of solutions is explicitly shown and their relation to the angular momentum operators is exposed.Comment: 13 pages, 2 figure

Frequency and duration of vigorous physical activity bouts are associated with adolescent boys’ bone mineral status: A cross-sectional study

Purpose: Vigorous physical activity (VPA) has been proven to promote osteogenesis in adolescents; however the specifics of the optimal pattern of frequency and duration of VPA are unknown. The main goal of the present study was to analyze the associations of different length of VPA bouts with bone health. Methods: 180 healthy male adolescents (11–13 years) had their bone mineral content and density assessed by dual-energy X-ray absorptiometry scans at the whole body, femoral neck (FN) and lumbar spine and their physical activity measured by an accelerometer during one week. Results: VPA was the intensity with the strongest associations with bone mineral parameters especially at the FN. Subjects whose longest VPA bout was 5 min or above had higher FN bone mineral density (BMD) than those who did not complete any 5-min bout and these differences were greater with participants who reached 15 consecutive minutes of VPA (>15': 0.977 ± 0.020 g/cm2; 5'-15': 0.907 ± 0.009 g/cm2; <5': 0.876 ± 0.009 g/cm2; all p < 0.05). When comparing the relevance of VPA bouts and volume of physical activity, the group with low volume and having a VPA bout had better FN BMD compared to the group with high volume but no VPA bout. Additionally, the group with both high volume and VPA bout showed better FN BMD than the rest of the groups. Conclusions: VPA may be the most effective activity intensity to improve bone mineral density and content of adolescent boys, with greater benefits if VPA periods either long or frequent

The supporting role of the teres major muscle, an additional component in glenohumeral stability? An anatomical and radiological study

Muscle coordination plays an important role in glenohumeral stability. The rotator cuff and the long head of the biceps are considered the primary dynamic stabilizers muscles. However, the fact that a subgroup of patients with a massive tear in the rotator cuff were able to keep a normal function, should make us question this traditional view. We hypothesize that the teres major which is also a monoarticular scapulohumeral muscle, although it is not part of the conjoined tendon of the rotator cuff, can play a role in glenohumeral stability by a direct support of the humeral head generated by the particular posteroanterior location of this muscle under the humeral head and which, as far as we know, has not been written up previously. This particular effect could appear while the arm is being lifted and the humeral head could be leaning on against the teres major muscle belly underneath it. An anatomical a radiological study was carried out to substantiate our hypothesis. Two cadaver specimens were used for the anatomical study. Frist body was studied through conventional dissection. The second body was analysed through sectional anatomy. Then a radiological study was carried out using magnetic resonance imaging in a healthy male volunteer. Both anatomically and radiologically, the anteroinferior surface of the humeral head was showed firmly resting against the muscle belly of the teres major, to the point of misshaping it from 110 degrees of arm elevation with external rotation. The specific contribution of this effect to the glenohumeral stability needs to be confirmed by further studies and can help us to prevent the high incidence of glenohumeral dislocations

Vigorous physical activity patterns affect bone growth during early puberty in boys

Summary: This study aims to analyze the impact of participation in vigorous physical activity as it can promote a healthy bone development. Adolescents who increased their participation in vigorous physical activity showed higher improvements in bone parameters compared to those who did not, which highlights the relevance of vigorous physical activity engagement. Introduction: The main purpose of the study was to analyze the effects of different patterns of vigorous physical activity (VPA) on bone development. Methods: One-week accelerometry registers and dual-energy X-ray absorptiometry scans at the whole body, hip, and lumbar spine of 140 healthy male adolescents (11–13 years, at baseline) were performed twice with a 1-year interval between measurements. Four patterns of VPA evolution (“low–low, ” “low–high, ” “high–low, ” and “high–high”) and three patterns of bone growth (“optimal, ” “mean, ” and “reduced”) were defined according to the median participation in VPA and a cluster analysis of the longitudinal changes in BMC and BMD in all sites measured, respectively. Bone mineral parameters were adjusted for skeletal age and body weight prior to statistical comparison among groups. Results: Participants in the “low–high” group had greater adjusted BMD increases at both the femoral neck and lumbar spine when compared to the “low–low” group (estimated mean (95% CI) 0.066 (0.047–0.085) vs. 0.034 (0.021–0.047) g/cm2 and 0.074 (0.054–0.093) vs. 0.049 (0.035–0.062) g/cm2 respectively, both p &lt; 0.05). Femoral neck BMD adjusted increase was also different between the “high–high” and the “high–low” groups (0.053 (0.041–0.066) vs. 0.030 (0.011–0.049) g/cm2, p &lt; 0.05). Additionally, a higher percentage of “optimal” growth was found in the “low–high” group than in the “low–low” and “high–low” categories (36.3, 12.5 and 13.6% respectively, p &lt; 0.05). Conclusions: Engaging in VPA as well as maintaining high levels of VPA during puberty is associated with greater gains in bone mass, which can have an impact in future bone health

Tailoring multipolar Mie scattering with helicity and angular momentum

Linear scattering processes are usually described as a function of the parameters of the incident beam. The wavelength, the intensity distribution, the polarization or the phase are among them. Here, we discuss and experimentally demonstrate how the angular momentum and the helicity of light influence the light scattering of spherical particles. We measure the backscattering of a 4 μm diameter TiO2 single particle deposited on a glass substrate. The particle is probed at different wavelengths by different beams with total angular momenta ranging from −8 to +8 units. It is observed that the spectral behavior of the particle is highly dependent on the angular momentum and helicity of the incoming beam. While some of the properties of the scattered field can be described with a simple resonator model, the scattering of high angular momentum beams requires a deeper understanding of the multipolar modes induced in the sphere. We observe that tailoring these induced multipolar modes can cause a shift and a spectral narrowing of the peaks of the scattering spectrum. Furthermore, specific combinations of helicity and angular momentum for the excitation lead to differences in the conservation of helicity by the system, which has clear consequences on the scattering pattern

Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles.

In this work we theoretically and experimentally analyze the resonant behavior of individual 3 × 3 gold particle oligomers illuminated under normal and oblique incidence. While this structure hosts both dipolar and quadrupolar electric and magnetic delocalized modes, only dipolar electric and quadrupolar magnetic modes remain at normal incidence. These modes couple into a strongly asymmetric spectral response typical of a Fano-like resonance. In the basis of the coupled mode theory, an analytical representation of the optical extinction in terms of singular functions is used to identify the hybrid modes emerging from the electric and magnetic mode coupling and to interpret the asymmetric line profiles. Especially, we demonstrate that the characteristic Fano line shape results from the spectral interference of a broad hybrid mode with a sharp one. This structure presents a special feature in which the electric field intensity is confined on different lines of the oligomer depending on the illumination wavelength relative to the Fano dip. This Fano-type resonance is experimentally observed performing extinction cross section measurements on arrays of gold nano-disks. The vanishing of the Fano dip when increasing the incidence angle is also experimentally observed in accordance with numerical simulations

Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles

In this work we theoretically and experimentally analyze the resonant behavior of individual 3 × 3 gold particle oligomers illuminated under normal and oblique incidence. While this structure hosts both dipolar and quadrupolar electric and magnetic delocalized modes, only dipolar electric and quadrupolar magnetic modes remain at normal incidence. These modes couple into a strongly asymmetric spectral response typical of a Fano-like resonance. In the basis of the coupled mode theory, an analytical representation of the optical extinction in terms of singular functions is used to identify the hybrid modes emerging from the electric and magnetic mode coupling and to interpret the asymmetric line profiles. Especially, we demonstrate that the characteristic Fano line shape results from the spectral interference of a broad hybrid mode with a sharp one. This structure presents a special feature in which the electric field intensity is confined on different lines of the oligomer depending on the illumination wavelength relative to the Fano dip. This Fano-type resonance is experimentally observed performing extinction cross section measurements on arrays of gold nano-disks. The vanishing of the Fano dip when increasing the incidence angle is also experimentally observed in accordance with numerical simulations