Imaging with partially coherent light: elementary-field approach

Breakdown of Temporal Coherence in Photon Condensates

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counterexamples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This Letter establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power.

Generation of non-uniformly correlated sources with controllable beam profile by devising its statistics in the spatial frequency domain

We introduce an efficient approach to simultaneously tailor the spatial profile and the degree of coherence (DOC) of partially coherent light by devising its statistical properties in the spatial frequency domain. The relationship between the beam profile and the DOC in the source plane and the correlation function and power spectrum in the spatial frequency domain is analyzed in detail. This approach enables us to generate partially coherent sources with spatially uniform or non-uniform coherence states, and the source profiles are controlled. The condition for switching two coherence states is given through two theoretical examples. Furthermore, we validate our approach in experiment through generating two kinds of spatially non-uniform correlated sources with controllable beam profiles. The experimental results agree well with our theoretical analysis.

Simulating random optical fields: tutorial

Numerous applications-including optical communications, directed energy, remote sensing, and optical tweezing-utilize the principles of statistical optics and optical coherence theory. Simulation of these phenomena is, therefore, critical in the design of new technologies for these and other such applications. For this reason, this tutorial describes how to generate random electromagnetic field instances or realizations consistent with a given or desired cross-spectral density matrix for use in wave optics simulations. This tutorial assumes that the reader has knowledge of the fundamental principles of statistical optics and optical coherence theory. An extensive reference list is provided where the necessary background information can be found. We begin this tutorial with a brief summary of the coherent-mode representation and the superposition rule of stochastic electromagnetic fields as these foundational ideas form the basis of all known synthesis techniques. We then present optical field expressions that apply these concepts before discussing proper sampling and discretization. We finally compare and contrast coherent-mode- and superposition-rule-based synthesis approaches, discussing the pros and cons of each. As an example, we simulate the synthesis and propagation of an electromagnetic partially coherent field from the literature. We compare simulated or sample statistics to theory to verify that we have successfully produced the desired field and are capturing its propagation behaviors. All computer programs, including detailed explanations of the source code, are provided with this tutorial. We conclude with a brief summary.

Pseudo-modal expansions for generating random electromagnetic beams

We derive two pseudo-modal expansions that provide insight into the structure of stationary electromagnetic sources and can be used for their physical realization and in computer simulations. Both expansions are derived from the vectorial version of Bochner's theorem of functional analysis. The first expansion employs the incoherent superposition of two completely polarized fields, while the second is based on the incoherent sum of three polarized fields. We generate, in simulation, two random electromagnetic beams from the literature using both expansions and compare the results to theory to validate our work. The primary utility of this research is twofold: in optical simulations involving partially coherent, partially polarized light beams and in the design/validation of new random electromagnetic sources.

Evolution of Spatiotemporal Intensity of Partially Coherent Pulsed Beams with Spatial Cosine-Gaussian and Temporal Laguerre–Gaussian Correlations in Still, Pure Water

A new family of partially coherent pulsed beams with spatial cosine-Gaussian and temporal Laguerre–Gaussian correlations, named spatial cosine-Gaussian and temporal Laguerre–Gaussian correlated Schell-model (SCTLGSM) pulsed beams, is introduced. An analytic propagation formula is derived for the SCTLGSM pulsed beam through the spatiotemporal ABCD optical system characterizing a continuous dispersive medium. As an example, the evolution of spatiotemporal intensity of the SCTLGSM pulsed beam in a still, pure water column is then investigated. It is found that the SCTLGSM pulsed beams simultaneously exhibit spatiotemporal self-splitting and self-focusing phenomena, which can be attributed to the special spatial/temporal coherence structures and the presence of pulse chirper in the source plane. The physical interpretation of the obtained phenomena is given. The results obtained in this paper will be of interest in underwater optical technologies, e.g., directed energy and communications.

Genuine-field modeling of partially coherent X-ray imaging systems

A genuine representation of the cross-spectral density function as a superposition of mutually uncorrelated, spatially localized modes is applied to model the propagation of spatially partially coherent light beams in X-ray optical systems. Numerical illustrations based on mode propagation with VirtualLab software are presented for imaging systems with ideal and non-ideal grazing-incidence mirrors.

Measuring source width and transverse coherence length using Fresnel diffraction from a phase step

Measurement of the source size and specifying its effect on the spatial coherence of propagating light are important for characterizing distant sources such as stars, and imaging with partially coherent light. The common method for measuring spatial coherence is Young's two-pinhole experiment. For characterizing spatial coherence along a line, one needs to change the location of the pinholes over a large number of pairs of points. But it requires many measurements, which takes significant time. In this paper, we use Fresnel diffraction from a step in reflection to measure the source width and transverse coherence length. It is shown theoretically and experimentally that these quantities are determined by specifying the location of minimum visibility on the diffraction pattern. We utilize a sodium vapor lamp with a variable slit in front of it as an extended one-dimensional incoherent light source. The measurements are made through recording only one diffraction pattern formed by the step. The study is applicable in 2D, and one can characterize weak starlight using highly sensitive equipment.

Effect of partial coherence on dimensional measurement sensitivity for DUV scatterfield imaging microscopy

Optical scatterfield imaging microscopy technique which has the capability of controlling scattered fields in the imaging mode is useful for quantitative nanoscale dimensional metrology that yields precise characterization of nanoscale features for semiconductor device manufacturing process control. To increase the sensitivity in the metrology using this method, it is required to optimize illumination and collection optics that enhance scatterfield signals from the nanoscale targets. Partial coherence of the optical imaging system is used not only for enhancing image quality in the traditional microscopy or lithography but also for increasing the sensitivity of the scatterfield imaging microscopy. This paper presents an empirical investigation of the effect of partial coherence on measurement sensitivity using a deep ultraviolet scatterfield imaging microscope platform that uses a 193 nm excimer laser as a source and a conjugate back focal plane as a unit for controlling partial coherence. Dimensional measurement sensitivity is assessed through analyzing scatterfield images measured at the edge area of periodic multiline structures with nominal linewidths ranging 44-80 nm on a Molybdenum Silicide (MoSi) photomask. Intensities scattered from the targets under the illuminations with various partial coherence factors and two orthogonal polarizations are assessed with respect to sensitivity coefficient. The optimization of partial coherence factor for the target dimension is discussed through the sensitivity coefficient maps.

Spatial-Temporal Self-Focusing of Partially Coherent Pulsed Beams in Dispersive Medium

Partially coherent pulsed beams have many applications in pulse shaping, fiber optics, ghost imaging, etc. In this paper, a novel class of partially coherent pulsed (PCP) sources with circular spatial coherence distribution and sinc temporal coherence distribution is introduced. The analytic formula for the spatial-temporal intensity of pulsed beams generated by this kind of source in dispersive media is derived. The evolution behavior of spatial-temporal intensity of the pulsed beams in water and air is investigated, respectively. It is found that the pulsed beams exhibit spatial-temporal self-focusing behavior upon propagation. Furthermore, a physical interpretation of the spatial-temporal self-focusing phenomenon is given. This is a phenomenon of optical nonlinearity, which may have potential application in laser micromachining and laser filamentation.