Wavefront propagation through synchrotron radiation beamlines (PHASE)
Depending on the electron beam emittance and the wavelength the synchrotron radiation of third generation machines may have a high degree of coherence. Fourth generation light sources are explicitly designed for the production of coherent radiation. Ray tracing codes are not the appropriate tool to describe the effects of coherent radiation. Two methods can be used for the propagation of coherent beams.
- Fourier Optics
- Propagation based on the stationary phase approximation
The code PHASE which has been developed over the last years for BESSY II and other light sources includes both propagation techniques. Since the simulation principles are different the actual problem defines the choice of the simulation strategy.
PHASE is a versatile tool for the optical design of synchrotron radiation beamlines. It is based on analytic expressions for nonlinear transformation of beam coordinates across optical elements. The optical elements are described with 70x70 matrices and a complete beamline is represented by the product of the individual matrices. The code offers various modes of operation:
- ray tracing (geometric optics)
- propagation of electric field distributions for a fixed wavelength (physical optics)
- propagation of time dependent field distributions (physical optics)
- automated optimization of beamline parameters
The code can be used either with a Motif based user interface or in a batch mode. Recently, an IDL interface has been developed to provide more flexibility to the user.
- Fourth order optical aberration and phase-space transformation for reflection and diffraction optics - J. Bahrdt, Appl Opt. 34, 114 (1995)
- Beamline optimization and phase space transformation - J. Bahrdt, U. Flechsig and F. Senf, Rev. Sci. Instrum. 66, 2719 (1995)
- Wave-front propagation: design code for synchrotron radiation beam lines - J. Bahrdt, Appl Opt 36, 4367 (1997)
- Wave front propagation in synchrotron radiation beamlines - J. Bahrdt, U. Flechsig, published in "Gratings and grating monochromators for synchrotron radiation", Proc. of SPIE, Vol. 3150 pp158-170, San Diego, Ca, USA, 1997
- Tracking of Wavefronts – J. Bahrdt, Proc. of the FEL 2005 conference, Stanford, Ca, USA, http://accelconf.web.cern.ch/AccelConf/f05/PAPERS/FROB003.PDF
- Wavefront tracking within the stationary phase approximation- J. Bahrdt, PRST AB, 10, 060701 (2207). http://prst-ab.aps.org/abstract/PRSTAB/v10/i6/e060701
- PHASE, a Universal Software Package for the Propagation of Time-Dependent Coherent Light Pulses along Grazing Incidence Optics, Proc. of SPIE Vol. 81410E pp1-10, San Diego, Ca, USA, 2011
Fig. 1: PHASE output for a ray tracing run of. The focus of hard edged source using a toroidal grating with variable line density grating is plotted. The parameters of the VLS grating have been optimized automatically with PHASE.
Fig. 2: PHASE output for a physical optics run. Intensity distribution from an undulator focused in 5:1 demagnification by a toroidal mirror, with a 0.4mm slit in the 'source' plane (M. Bowler, private communication).