Propagation of coherent light pulses with PHASE

Abstract

The current status of the software package PHASE for the propagation of coherent light pulses along a synchrotron radiation beamline is presented. PHASE is based on an asymptotic expansion of the Fresnel-Kirchhoff integral (stationary phase approximation) which is usually truncated at the 2 nd order. The limits of this approximation as well as possible extensions to higher orders are discussed. The accuracy is benchmarked against a direct integration of the Fresnel-Kirchhoff integral. Long range slope errors of optical elements can be included by means of 8 th order polynomials in the optical element coordinates w and l. Only recently, a method for the description of short range slope errors has been implemented. The accuracy of this method is evaluated and examples for realistic slope errors are given. PHASE can be run either from a built-in graphical user interface or from any script language. The latter method provides substantial flexibility. Optical elements including apertures can be combined. Complete wave packages can be propagated, as well. Fourier propagators are included in the package, thus, the user may choose between a variety of propagators. Several means to speed up the computation time were tested -among them are the parallelization in a multi core environment and the parallelization on a cluster.

Shaping Photon Beams with Undulators and Wigglers

“…Various codes have been developed for a beam propagation within physical optics (PO). Today, three methods are utilized: (i) drifts are handled with FFTs, and optical elements are implemented via phase screens and local GO algorithms (Chubar et al 2011); (ii) the Fresnel-Kirchhoff integral is evaluated analytically in the presence of an optical element utilizing the stationary-phase approximation (Bahrdt et al 2014); (iii) RAY tracing is combined with PO propagation for a realistic description of the diffracting effects such as slope errors, apertures, etc. (Shi et al 2014).…”

Numerical analysis of partially coherent radiation at soft x-ray beamline

“…We implement the local stationary phase approximation to simulate the MOI propagating through the reflecting mirrors [19][20][21]. In this approximation the local propagation of the electric field is assumed to be along the geometrical rays [2,20,22].…”

“…where  ( ) P Q is scalar function describing the transformation of coordinates for points in transverse wavefronts before and after the reflecting mirror, and ( , ) Q P Γ is the function describing the optical path between the two wavefronts [21]. The MOI at the reflecting plane can be expressed as …”

Physical optics simulations with Phase for SwissFEL beamlines

“…While the SPA method is intuitively relative easy to understand, the serious mathematical treatment is rather complex [1]. For details about the fundamental principles of PHASE see for instance [2,3], for a recent summary of PHASE features [4]. There are other beam propagation methods for instance the finite-difference technique [5] or Fourier optics FO implemented for instance in SRW [6] and partly also implemented within PHASE .…”