Approximate master equations for the spatial public goods game.

The spatial public goods game has been used to examine factors that promote cooperation. Owing to the complexity of the dynamics of this game, previous studies on this model neglected analytical approaches and relied entirely on numerical calculations using the Monte Carlo (MC) simulations. In this paper, we present the approximate master equations (AMEs) for this model. We report that the results obtained by the AMEs are mostly qualitatively consistent with those obtained by the MC simulations. Furthermore, we show that it is possible to obtain phase boundaries analytically in certain parameter regions. In the region where the noise in strategy decisions is very large, the phase boundary can be obtained analytically by considering perturbations from the steady state of the voter model. In the noiseless region, discontinuous phase transitions occur because of the characteristics of the function that represents strategy updating. Our approach is useful for clarifying the details of the mechanisms that promote cooperation and can be easily applied to other group interaction models.

Spectral-broadness simulation of a Littman/Metcalf external cavity diode laser with a dynamic-curvature end mirror.

We propose a dynamic-spectral-broadness Littman/Metcalf external cavity diode laser, which replaces the flat end mirror of the external cavity with a curved one with a tunable radius of curvature (RoC). The concept was verified via simulation; first, the frequency selectivity of the cavity was calculated for each RoC using Gaussian-beam optics combined with ray tracing, and second, laser oscillation and amplified spontaneous-emission (ASE) spectra were obtained using the transmission-line laser model. The simulation revealed a tuning range with spectral broadness: 250 kHz for single-mode operation, 1.2-47 GHz for multi-mode operation, and 50 GHz-3.9 THz for ASE.

Multi-focusing surface-emitting lasers.

Complete control of a beam pattern requires not only projecting a two-dimensional (2D) pattern but also focusing on a three-dimensional (3D) point cloud, which is typically achieved utilizing holography under the framework of diffraction. We previously reported direct focusing from on-chip size surface-emitting lasers that utilize a holographically modulated photonic crystal cavity based on 3D holography. However, this demonstration was of the simplest 3D hologram with a single point and single focal length, and the more typical 3D hologram with multiple points and multiple focal lengths has not yet been examined. Toward direct generation of a 3D hologram from the on-chip size surface-emitting laser, we here examined a simple 3D hologram featuring two different focal lengths with a single off-axis point in each to reveal the fundamental physics. Two types of holography, one based on superimposition and the other on random tiling, successfully demonstrated the desired focusing profiles. However, both types caused a spot noise beam in the far field plane due to interference between focusing beams with different focal lengths, especially in the case of the superimposing method. We also found that the 3D hologram based on the superimposing method consisted of higher order beams including the original hologram due to the manner of the holography. Secondly, we demonstrated a typical 3D hologram with multiple points and focal lengths and successfully showed the desired focusing profiles by both methods. We believe our findings will bring innovation to mobile optical systems and pave the way to developing compact optical systems in areas such as material processing, micro fluidics, optical tweezers, and endoscopy.

On-chip size, low-noise fringe pattern projector offering highly accurate 3D measurement.

Fringe pattern projectors are quite useful for highly accurate three-dimensional (3D) measurement when a projector or LED array is used for illumination. We have fabricated a 0.2 mm × 0.2 mm structured light source, which was an on-chip size surface-emitting laser that utilized a holographically modulated two-dimensional (2D) photonic crystal (PC). This will make possible an extremely compact 3D measurement system that will positively impact mobile systems. However, the fringe pattern tends to cause speckle-like noise that leads to severe positional error in 3D measurement. Here we present a simple approach to projecting a low-noise fringe pattern from our surface-emitting lasers by using a one-dimensional (1D) focusing hologram. This method improves the flatness of the fringe pattern by around four times.

Contact metalens for high-resolution optical microscope in semiconductor failure analysis.

The continuous downscaling of electronic devices requires higher-resolution optical microscopic images for semiconductor failure analysis (FA). However, a part of the diffracted light from the measuring pattern in the silicon (Si) substrate cannot be collected due to the total internal reflection (TIR) at the interface between the Si substrate and air. We propose a metalens suitable for FA that improves resolution of optical microscopic images by collecting beyond the critical angle of TIR at the interface. For the proof of concept, we integrated the fabricated metalens into the optical setup of FA and acquired optical microscopic images of FA that clearly show improved resolution.

Scanless volumetric imaging by selective access multifocal multiphoton microscopy.

Simultaneous, high-resolution imaging across a large number of synaptic and dendritic sites is critical for understanding how neurons receive and integrate signals. Yet, functional imaging that targets a large number of submicrometer-sized synaptic and dendritic locations poses significant technical challenges. We demonstrate a new parallelized approach to address such questions, increasing the signal-to-noise ratio by an order of magnitude compared to previous approaches. This selective access multifocal multiphoton microscopy uses a spatial light modulator to generate multifocal excitation in three dimensions (3D) and a Gaussian-Laguerre phase plate to simultaneously detect fluorescence from these spots throughout the volume. We test the performance of this system by simultaneously recording Ca2+ dynamics from cultured neurons at 98-118 locations distributed throughout a 3D volume. This is the first demonstration of 3D imaging in a "single shot" and permits synchronized monitoring of signal propagation across multiple different dendrites.

Removal of surface-normal spot beam from on-chip 2D beam pattern projecting lasers.

Static arbitrary two-dimensional beam patterns have been demonstrated using on-chip size "integrable spatial-phase-modulating surface-emitting lasers," which use the band edge mode of a two-dimensional photonic crystal as an in-plane resonator, while the spatial phase of the lightwaves of the band edge mode are simultaneously modulated in a holographic manner by a local positional shift of holes from their lattice points. Meanwhile, the beam patterns include a spot beam in the surface-normal direction (0th-order beam), which corresponds to components of vertical diffraction of the band edge modes without spatial phase modulation. A promising method, used to remove the 0th-order beam, uses a structure that prohibits the vertical diffraction of band edge modes. For this purpose, we set the period of the virtual photonic crystal structure from the conventional Γ2 band edge to the Μ1 band edge, where vertical diffraction is prohibited. Moreover, the additional spatial phase modulation that cancels the in-plane component of the wavevectors of the lightwaves of the band edge modes at the Μ1 band edge are also imposed to output the beam patterns vertically. As a result, we successfully demonstrated two-dimensional beam patterns without a spot beam in the surface-normal direction.

Principle of beam generation in on-chip 2D beam pattern projecting lasers.

Integrable spatial-phase-modulating surface-emitting lasers, which utilize the band edge mode of two-dimensional photonic-crystals as resonators, project static arbitrary two-dimensional beam patterns from on-chip size. In this device, holes shifting from the lattice point of a two-dimensional photonic crystal provide spatial phase modulation to light waves, which form standing waves in the resonator. Thus far, the origin of the beam patterns has not been studied, especially the formation of subsidiary beam patterns against the designed beam pattern. In this work, we clarify the origin of beam patterns in two types of spatial phase modulating method, which impose in-plane shifting of holes according to circular and linear shift methods. Based on a theoretical study of spatial phase modulation, we reveal that the circular shift method provides a symmetric beam pattern, while the linear shift method causes an asymmetric beam pattern. Consequently, we demonstrated the asymmetric two-dimensional beam pattern by the linear shift method for the first time.

Single-Shot Optical Anisotropy Imaging with Quantitative Polarization Interference Microscopy.

Optical anisotropy measurement is essential for material characterization and biological imaging. In order to achieve single-shot mapping of the birefringence parameters of anisotropic samples, a novel polarized light imaging concept is proposed, namely quantitative polarization interference microscopy (QPIM). QPIM can be realized through designing a compact polarization-resolved interference microscopy system that captures interferograms bearing sample's linear birefringence information. To extract the retardance and the orientation angle maps from a single-shot measurement, a mathematical model for QPIM is further developed. The QPIM system is validated by measuring a calibrated quarter-wave plate, whose fast-axis orientation angle and retardance are determined with great accuracies. The single-shot nature of QPIM further allows to measure the transient dynamics of birefringence changes in material containing anisotropic structures. This application is demonstrated by capturing transient retardance changes in a custom-designed parallel-aligned nematic liquid crystal-based device.

Phase-modulating lasers toward on-chip integration.

Controlling laser-beam patterns is indispensable in modern technology, where lasers are typically combined with phase-modulating elements such as diffractive optical elements or spatial light modulators. However, the combination of separate elements is not only a challenge for on-chip miniaturisation but also hinders their integration permitting the switchable control of individual modules. Here, we demonstrate the operation of phase-modulating lasers that emit arbitrarily configurable beam patterns without requiring any optical elements or scanning devices. We introduce a phase-modulating resonator in a semiconductor laser, which allows the concurrent realisation of lasing and phase modulation. The fabricated devices are on-chip-sized, making them suitable for integration. We believe this work will provide a breakthrough in various laser applications such as switchable illumination patterns for bio-medical applications, structured illuminations, and even real three-dimensional or highly realistic displays, which cannot be realised with simple combinations of conventional devices or elements.

Usefulness of brain natriuretic peptide for predicting left atrial appendage thrombus in patients with unanticoagulated nonvalvular persistent atrial fibrillation.

BACKGROUND: The CHADS2 scoring system is simple and widely accepted for predicting thromboembolism in patients with nonvalvular atrial fibrillation (NVAF). Although congestive heart failure (CHF) is a component of the CHADS2 score, the definition of CHF remains unclear. We previously reported that the presence of CHF was a strong predictor of left atrial appendage (LAA) thrombus. Therefore, the present study aimed to elucidate the relationship between LAA thrombus and the brain natriuretic peptide (BNP) level in patients with unanticoagulated NVAF. METHODS: The study included 524 consecutive patients with NVAF who had undergone transesophageal echocardiography to detect intracardiac thrombus before cardioversion between January 2006 and December 2008, at Hiroshima City Asa Hospital. The exclusion criteria were as follows: paroxysmal atrial fibrillation, unknown BNP levels, prothrombin time international normalized ratio ≥2.0, and hospitalization for systemic thromboembolism. RESULTS: Receiver operating characteristic analysis yielded optimal plasma BNP cut-off levels of 157.1 pg/mL (area under the curve, 0.91; p<0.01) and 251.2 pg/mL (area under the curve, 0.70; p<0.01) for identifying CHF and detecting LAA thrombus, respectively. Multivariate analyses demonstrated that a BNP level >251.2 pg/mL was an independent predictor of LAA thrombus (odds ratio, 3.51; 95% confidence interval, 1.08-10.7; p=0.046). CONCLUSIONS: In patients with unanticoagulated NVAF, a BNP level >251.2 pg/mL may be helpful for predicting the incidence of LAA thrombus and may be used as a surrogate marker of CHF. The BNP level is clinically useful for the risk stratification of systemic thromboembolism in patients with unanticoagulated NVAF.

Self-distortion compensation of spatial light modulator under temperature-varying conditions.

Conventional methods of compensating for self-distortion in liquid-crystal-on-silicon spatial light modulators (LCOS-SLM) are based on aberration correction, where the wavefront of the incident beam is modulated to compensate for aberrations caused by the imperfect optical flatness of the LCOS-SLM surface. However, the phase distribution of an LCOS-SLM varies with changes in ambient temperature and requires additional correction. We report a novel phase compensation method under temperature-varying conditions based on an orthonormal Legendre series expansion of the phase distribution. We investigated the temperature dependency by controlling the ambient temperature with an incubator and successfully corrected for self-distortion in a temperature range of 20 °C to 50 °C. Our approach has the potential to be adopted in tight-focusing applications which require wavefront modulation with very high accuracy.

Effects of dielectric planar interface on tight focusing coherent beam: direct comparison between observations and vectorial calculation of lateral focal patterns.

We report direct observation of lateral focal patterns through an acrylic material to investigate the effects of aberrations caused by a planar dielectric interface. Numerical analyses based on vectorial Huygens-Fresnel diffraction theory were also performed to examine the behavior of three-dimensional point spread functions. Experimental and numerical results showed agreement of the behavior of the peak position in the focal patterns with changes in the interface position. Our approach has the potential to predict the effects of aberrations in confocal laser scanning microscopes and super-resolution applications.

Presentations of acute coronary syndrome related to coronary lesion morphologies as assessed by intravascular ultrasound and optical coherence tomography.

BACKGROUND: Pathologically, the lesions responsible for acute coronary syndrome (ACS) are ruptures of vulnerable plaques (and occasionally fibrous-cap erosions or calcified nodules) with a superimposed thrombosis. We aimed to clarify the clinical presentations related to the morphologies of coronary lesions of ACS using intravascular ultrasound (IVUS) and optical coherence tomography (OCT). METHODS AND RESULTS: Seventy-five culprit lesions of ACS patients were clearly assessed with IVUS and OCT. Patients were classified into two groups based on the presence or absence of a rupture of a culprit plaque as identified by OCT. Clinical characteristics and lesion morphologies were compared between the two groups. Waist circumference was significantly greater (p<0.02) and prevalence of the metabolic syndrome (MS) higher (p=0.0011) in the rupture group. The prevalence of prodromal angina was higher in patients without plaque ruptures (p<0.0001). Using multivariate analysis, the MS and prodromal angina were independent predictors of rupture of a culprit coronary plaque (odds ratio (OR): 27.30, p<0.003 and OR: 0.04, p=0.0004, respectively). Among the components of the MS, the prevalence of abdominal obesity was a significant independent predictor of rupture of a culprit plaque (OR: 4.24, p<0.02). CONCLUSIONS: There are two presentations related to the coronary lesion morphologies of ACS: we should understand these aspects of ACS.

High-quality generation of a multispot pattern using a spatial light modulator with adaptive feedback.

We propose and demonstrate high-quality generation of a uniform multispot pattern (MSP) by using a spatial light modulator with adaptive feedback. The method iteratively updates a computer generated hologram (CGH) using correction coefficients to improve the intensity distribution of the generated MSP in the optical system. Thanks to a simple method of determining the correction coefficients, the computational cost for optimizing the CGH is low, while maintaining high uniformity of the generated MSP. We demonstrate the generation of a 28×28 square-aligned MSP with high uniformity. Additionally, the proposed method could generate an MSP with a gradually varying intensity profile, as well as a uniform MSP consisting of more than 1000 spots arranged in an arbitrary pattern.

Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes.

We investigate optical singularities in coaxial superpositions of two Laguerre-Gaussian (LG) modes with a common beam waist from the viewpoints of a general formulation of phase structure, experimental generation of various superposition beams, and evaluation of the generated beams' fidelity. By applying a holographic phase-amplitude modulation scheme using a phase-modulation-type spatial light modulator, output fidelity beyond 0.960 was observed under several typical conditions. Additionally, an elliptic-type folded singularity, which provides a different class of phase structures from familiar helical singularities, was predicted and observed in a superposition involving two LG modes of both radially and azimuthally higher orders.

Formation of quaternary carbon center with a trifluoromethyl group using a Pd-catalyzed allylation reaction.

Synthesis of compounds with quaternary carbons is one of the most attractive reactions in the synthetic chemistry. However, there are only a few reports on synthesis of the compounds with a fluoroalkyl group at a quaternary carbon center. Recently, we reported the synthesis of alpha-trifluoromethylated ketones by the reaction of alpha,beta-unsaturated ketones with CF(3)-I using a Rh catalyst. When the alpha-trifluoromethylated ketones and allyl carbonates were treated with a Pd catalyst, the allylation reaction proceeded smoothly at the trifluoromethylated carbon to give the desired compounds with a trifluoromethylated quaternary carbon center in good to excellent yields.