Beams generated by Gaussian quasi-homogeneous sources

Long-range spatial coherence can be induced in incoherent thermal emitters by embedding a periodic grating within a material supporting propagating polaritons or dielectric modes. However, only a single spatially coherent mode is supported by purely periodic thermal emitters. While various designs have been proposed for the purpose of allowing arbitrary emission profiles, the limitations associated with the partial spatial coherence of thermal emitters are not known. Here, we explore superstructure gratings (SSGs) to control the spatial and spectral properties of thermal emitters. SSGs have long-range periodicity but employ a unit cell that provides multiple Bragg vectors to interact with light. These Bragg vectors allow simultaneous launching of polaritons with different frequencies/wavevectors in a single grating, manifesting as additional spatial and spectral modes in the thermal emission profile. However, SSGs still have a well-defined period, which allows us to assess the role that finite spatial coherence plays in thermal emitters. We find that the spatial coherence length defines the maximum possible SSG period that can be used. This provides a fundamental limit on the degree of spatial coherence that can be induced in a thermal emitter and has broader implications for the use of techniques such as inverse design for structure optimization.

The degree of spatial coherence, as basic characteristics of the radiation, becomes an important guide to evaluate the performance of X-rays from newly introduced advanced light sources including the X-ray free electron laser (XFEL). Often the modification of the X-ray wavefronts to fulfill various applications is necessary, but also there is the need to preserve its coherence property. However, experimental investigation directly comparing the coherence property of focused X-ray radiations with the unmodified ones has not been available. We have performed Young's double-slit experiments by recording diffraction patterns both from slit apertures for unfocused XFEL radiation and from pairs of Au nanoparticles for one-micron focused XFEL radiations. The results confirm that the degree of spatial coherence is preserved for well-built K-B focusing mirrors.

Spatial coherences of SR beam at visible light region were measured both /spl sigma/ and /spl pi/-polarized components at Photon Factory. A wave-front division type polarized interferometer was designed and constructed for this experiment. Interferograms were observed clearly in the vertical direction. /spl pi/ phase difference of the interference fringe was observed between interferograms corresponding to /spl sigma/ and /spl pi/-polarized components. Degree of spatial coherence was measured and by means of the van Citterut-Zernike's theorem, a vertical beam profile was obtained by the Fourier transform of the degree of spatial coherence.

The spatial coherence function |Γ(s)| of ruby laser pulses has been measured by self-diffraction at a laser-induced grating depending on the distances between two points in the beam profile. The spatial coherence of the laser beam was changed by operating the laser in the fundamental transverse mode, in a transverse multimode and by applying different pump powers. The degree of spatial coherence was experimentally found to be a Gaussian, as described by the Collett-Wolf model. The new method for measuring the spatial coherence function |Γ(s)| is described and possible improvements are discussed.

The coherence properties of white light emission of a tungsten incandescent lamp additionally excited with laser radiation are investigated. The degree of spatial coherence is determined from measurements of the contrast of interference fringe patterns obtained for a tungsten bulb as the light source. It is demonstrated that the degree of spatial coherence of an incandescent lamp is increased by additional excitation of the filament with focused laser radiation. Furthermore, the degree of spatial coherence can be adjusted by selecting the voltage applied to the filament. Such light sources can find applications in imaging techniques where precise control of spatial coherence of illumination is required.

The propagation of radiation from a source embedded in an inhomogeneous refractive medium is studied, using both mode-analysis and ray-tracing methods. Scaling laws for excitation strengths of the modes, the degree of spatial coherence, and the shift of the spectral line are derived.

Spatial coherence is an impactful source parameter in many applications ranging from atomic and molecular physics to metrology or imaging. In lensless imaging, for example, it can strongly affect the image formation, especially when the source exhibits shot-to-shot variations. Single-shot characterization of the spatial coherence length of a source is thus crucial. However, current techniques require either parallel intensity measurements or the use of several masks. Based on the method proposed by González et al. [J. Opt. Soc. Am. A28, 1107 (2011)JOAOD60740-323210.1364/JOSAA.28.001107], we designed a specific arrangement of a two-dimensional non-redundant array of apertures, which allows, through its far field interference pattern, for a single-shot measurement of the spatial coherence, while being robust against beam-pointing instabilities. The strategic configuration of the pinholes allows us to disentangle the degree of spatial coherence from the intensity distribution, thus removing the need for parallel measurement of the beam intensity. An experimental validation is performed using a high-harmonic source. A statistical study in different regimes shows the robustness of the method.

Abstract. We have examined, for the first time, the spatial coherence of oceanic parameters, namely, the ocean surface wind and significant wave height (SWH), using near-instantaneous along-track sampling over vast oceanic tracks provided by Poseidon-2 Radar Altimeter onboard Jason-1. The spatial coherence length scales over the Arabian Sea and the Bay of Bengal regions, derived using Auto correlation analysis, display interesting characteristics in relation to onset and evolution of SW Monsoon over India. The estimated spatial coherence scales are found to be of the order of 100–500 km. Generally, SWH coherence lengths over Arabian Sea are observed to increase from June to July during good monsoon year (2012). This trend is not followed for the poor monsoon year (2002). Similar trend is observed for spatial coherence scales for wind speed. The temporal evolution of analyzed spatial coherence scales of winds and waves over Arabian Sea clearly brings out the distinction between a "good" (2012) and a "poor" (2002) monsoon year. The spatial coherence lengths of these parameters over the Bay of Bengal are found to be shorter and do not show any systematic relation to onset and evolution of SW monsoon. Anisotropy in coherence lengths is also analyzed by treating ascending and descending tracks separately. Generally, the descending tracks measurements show higher spatial coherence lengths than the ascending ones. Like the spatial coherence scales, the anisotropy of the coherence scales over the Arabian Sea also mimics the behaviour of the strength of SW Monsoon.

Recent researches on the foundation of radiometry [1,2] have made it possible to provide answers to a number of puzzling questions relating to radiation from sources of different states of coherence. In particular, a relationship between the coherence properties of a source and the directionality of the light that the source generates has been established [3,4] at least for a wide class of sources of practical interest, and the coherence properties of Lambertian sources have been clarified [5] to a large extent.

Based on the mathematical framework of the partially coherent Gaussian Schell model vortex (PCGSMV) beam and the Huygens-Fresnel integral, we conducted a study to analyze the intensity distribution and depth of focus (DOF) of the PCGSMV beam as it propagates through a classical axicon. Our numerical results indicate the influence of factors such as the beam width, spatial degree of coherence, topological charge, and axicon base angle on the intensity distribution and DOF. In addition, we investigated the relationship between the beam spot size and propagation distance, as well as the effects of the spatial degree of coherence and propagation distance on the intensity profile. Our findings highlight the importance of the intensity values along the DOF for various applications, including the optical trapping and manipulation of micro particles.

We analyze the z-scan experiment with anisotropic Gaussian Schell-model (AGSM) beams. The expression for the cross-spectral density of the AGSM beam passing through the lens and onto the nonlinear thin sample is derived. Based on the expression, we simulate the results of the z-scan experiment theoretically and analyze the effects of the e factor (e=w(0x)/w(0y)) and the spatial degree of coherence in the x and y orientations on the on-axis z-scan transmittance. It is found that DeltaTp(-v) becomes larger with an increment of the e factor and the spatial degree of coherence. So we can improve the sensitivity of the z-scan experiment by increasing the e factor and the spatial degree of coherence. The results are helpful for improving the sensitivity of the z-scan experiment.

Radiometric analysis of diffraction of quasi-homogenous optical fields

Classical nonlinear waves exhibit, as a general rule, an irreversible process of thermalization toward the Rayleigh–Jeans equilibrium distribution. On the other hand, several recent experiments revealed a remarkable effect of spatial organization of an optical beam that propagates through a graded-index multimode optical fiber (MMF), a phenomenon termed beam self-cleaning. Our aim here is to evidence the qualitative impact of disorder (weak random mode coupling) on the process of Rayleigh–Jeans thermalization by considering two different experimental configurations. In a first experiment, we launch speckle beams in a relatively long MMF. Our results report a clear and definite experimental demonstration of Rayleigh–Jeans thermalization through light propagation in MMFs, over a broad range of kinetic energy (i.e., degree of spatial coherence) of the injected speckle beam. In particular, the property of energy equipartition among the modes is clearly observed in the condensed regime. The experimental results also evidence the double turbulence cascade process: while the power flows toward the fundamental mode (inverse cascade), the energy flows toward the higher-order modes (direct cascade). In a 2nd experiment, a coherent laser beam is launched into a relatively short MMF length. It reveals an effect of beam cleaning driven by an incipient process of Rayleigh–Jeans thermalization. As discussed through numerical simulations, the fast process of Rayleigh–Jeans thermalization observed in the 1st experiment can be attributed due to a random phase dynamics among the modes, which is favored by the injection of a speckle beam and the increased impact of disorder in the long fiber system.

We present a mathematical model and its numerical implementation for the analysis of the interaction of spatially partially coherent electromagnetic fields with micro- and nanostructured objects. The model is based on the decomposition of the incident field into a set of fully coherent but mutually uncorrelated elementary field modes, and the use of the Fourier Modal Method (FMM) with the S-matrix propagation algorithm. We apply the model to studies of the excitation of surface plasmons in thin metallic slabs, nanowires, and resonant structures. We demonstrate, e.g., that the plasmon excitation efficiency is not essentially affected by the degree of spatial coherence. However, certain plasmon interference effects can be efficiently smoothed out by using illumination with reduced coherence.

ABSTRACTWe investigate the effect of primary illumination properties on partially coherent Bessel mode vortex beams. Based on the coherent mode representation, we show that a wide class of such vortices can be obtained by applying well-known apodization functions to the primary illumination. In particular, we find that the combined effect of apodization windows with high topological charges induces transitions of high intensity gradient from the vortex core to the outer vortex rim. The specific choice of apodization filters leads to a change on the spatial degree of coherence as a function of the topological charge. This suggests a synthesis procedure to generate partially coherent vortex beams where the intensity gradient can be shaped by changing the degree of coherence and the topological charge.