Shifted-elementary-mode representation for partially coherent vectorial fields

Modified angular spectrum algorithm for the propagation of partially coherent beams in optical systems

A modified angular spectrum algorithm is presented for the diffraction calculation of partially coherent beams propagating in optical systems. The proposed algorithm can directly calculate the cross-spectral density of partially coherent beams at each surface of the optical system and possesses much higher computational efficiency for low coherent beams compared with that of the common modal expansion methods. Then, a Gaussian-Schell model beam propagating in a double-lens array homogenizer system is introduced to carry out a numerical simulation. Results show that the proposed algorithm can obtain an identical intensity distribution as the selected modal expansion method but with a much higher speed, thus verifying its accuracy and high efficiency. However, it's worth noting that the proposed algorithm is only suitable to the optical systems in which the partially coherent beams and optical components have no coupling effects in the x and y directions and can be dealt with individually.

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.

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.

Experimental synthesis of partially coherent sources

A flexible pseudo-mode sampling superposition method for synthesizing partially coherent sources has been introduced that can be thought of as an approximate discrete representation of Gori's nonnegative definiteness criterion for designing spatial correlation functions. Importantly, without performing formidable mode analysis, this method enables us to develop a convenient and efficient experimental technology to customize partially coherent sources without sacrificing theoretical accuracy. As an example, we experimentally generate a new, to the best of our knowledge, class of nontrivial pseudo-Schell model sources recently proposed by de Sande et al. Our approach opens up a useful avenue for manipulating nontrivial partially coherent beams and promotes applications for optical tweezers and photolithography.

Temporal modes of stationary and pulsed quasistationary electromagnetic beams

We present a novel time-domain coherent-mode representation for random, stationary electromagnetic beams. We subsequently introduce random, quasistationary pulsed electromagnetic beams and develop an analogous (pseudo) mode decomposition for them as well. The former decomposition is valid provided the time window in which the field is considered is much longer than the coherence time, while the latter requires the field to vanish outside the window. For stationary beams, the theory is demonstrated by an example illustrating the role of polarization in the representation. In both cases, the data needed for the construction of the mode decomposition are straightforward to measure. The formalisms enable us to treat random vector-light beams in the time domain in terms of deterministic fields. We expect that the modal representations will find a wide range of applications in problems involving spatiotemporal propagation of temporally partially coherent light in optical systems.

Quasi-monochromatic modes of quasi-stationary, pulsed scalar optical fields

We investigate the temporal coherence of random, pulsed, quasi-stationary scalar light fields and introduce a new type of expansion for the mutual coherence function in terms of fully coherent frequency-shifted quasi-monochromatic modes of identical shape. The mode representation is valid provided the pulse length is shorter and the coherence time is much shorter than the width of the time window in which the field is considered. The construction of the expansion is particularly straightforward since information is required only on the average spectrum and the average temporal intensity. The method enables us to assess the coherence properties of quasi-stationary light by analyzing the behavior of deterministic quasi-monochromatic fields. The frequency-domain counterpart of the representation is also given. The method is illustrated by application to a pulsed free-electron laser source.

Modeling of light-emitting diode wavefronts for the optimization of transmission holograms

The objective of applying transmission holograms in automotive headlamp systems requires the adaptation of holograms to divergent and polychromatic light sources like light-emitting diodes (LEDs). In this paper, four different options to describe the scalar light waves emitted by a typical automotive LED are regarded. This includes a new approach to determine the LED's wavefront from interferometric measurements. Computer-generated holograms are designed considering the different LED approximations and recorded into a photopolymer. The holograms are reconstructed with the LED and the resulting images are analyzed to evaluate the quality of the wave descriptions. In this paper, we show that our presented new approach leads to better results in comparison to other wave descriptions. The enhancement is evaluated by the correlation between reconstructed and ideal images. In contrast to the next best approximation, a spherical wave, the correlation coefficient increased by 0.18% at 532 nm, 1.69% at 590 nm, and 0.75% at 620 nm.

Deterministic mode representation of random stationary media for scattering problems

Deterministic mode representation (DMR) is introduced for a three-dimensional random medium with a statistically stationary refractive index distribution. The DMR allows for the designing and fine tuning of novel random media by adjusting the weights of individual deterministic modes. To illustrate its usefulness, we have applied the decomposition to the problem of weak light scattering from a Gaussian Schell-model medium. In particular, we have shown how individual deterministic modes of the medium contribute to the scattered far-field spectral density distribution.

Imaging with partially coherent light: elementary-field approach

Numerical modeling of bright-field and dark-field imaging with spatially partially coherent light is considered. The illuminating field is expressed as a superposition of transversely shifted fully coherent elementary fields of identical form. Examples of imaging under variable coherence conditions demonstrate the computational feasibility of the model even when the coherence area of the illumination is in the wavelength scale.

Difference of two Gaussian Schell-model cross-spectral densities

We present a number of results relating to the difference of two Gaussian Schell-model cross-spectral densities (CSDs). They allow us to specify conditions under which such a difference represents itself in a valid CSD. In particular, a sufficient condition is derived for the non-negative definiteness of the resulting CSD, for any admissible choice of the involved parameters, while a necessary and sufficient condition is obtained for the case of CSDs endowed with the property of being shape-invariant upon propagation.

Difference of cross-spectral densities

Generally speaking, the difference between two cross-spectral densities (CSDs) does not represent a correlation function. We will furnish a sufficient condition so that such difference be a valid CSD. Using such a condition, we will show through some examples how new classes of CSDs can be generated.

Coherent-mode representation of partially polarized pulsed electromagnetic beams

Coherent-mode representation provides physical insight and computational simplification into the analysis of random optical signals. In this work, we present the coherent-mode decomposition for pulsed electromagnetic beam fields. We show that the mode decomposition can be done for any valid space-frequency or space-time coherence matrix representing nonstationary pulsed electric field, and moreover, the spectral and temporal modes are connected via a Fourier transform relation. The analysis also yields the coherent modes of electromagnetic time-domain signals in temporal optics. We present the overall degree of coherence as a measure of the average temporal or spectral and spatial coherence of the beam. Several illustrative examples are discussed analytically and numerically.

Spatial coherence of broad-area laser diodes

We model the spatial coherence of broad-area laser diodes (BALDs) by representing the mutual intensity as superpositions of individually fully coherent but mutually uncorrelated fields. Consideration of spectroscopic modal structure measurements and intensity-based mode recovery shows that the standard Mercer-type coherent-mode expansion can lead to unsatisfactory results for real BALDs. However, we show that a so-called shifted elementary-field method provides a sufficiently accurate tool for spatial coherence and propagation modeling even if the modal structure of the BALD is severely distorted.