FREE SPACE PROPAGATION AND NORMAL INCIDENCE OPTICS

The design of beamlines for VUV and X-ray FEL facilities requires a detailed knowledge of the coherent radiation source. Time dependent simulations with FEL codes like GENESIS provide the electric field distribution at the end of the FEL which represents the complete information. Ray tracing codes used to transform the light from the source to the sample are generally based on geometrical optics and do not include directly the coherent properties of the FEL radiation. On the other hand Fourier optic techniques are usually applied to the propagation across normal incidence optics. We present an algorithm based on physical optics which permits the propagation of wavefronts across grazing incidence optics including interference effects, diffraction, polarization variation and pulse lengthening. Examples are given for the proposed BESSY Soft X-Ray FEL and a 3 generation storage ring beamline. INTRODUCTION The next generation of synchrotron radiation facilities is based on FEL sources. The radiation properties are superior to those of storage rings in many aspects. The peak brightness overcomes the numbers of third generation machines by 10 orders of magnitude; the pulse length is in the fs-regime; the light is transversely coherent (SASE [1], [2], [3] and HGHG [4]) and longitudinally coherent (HGHG). The photon beam quality depends strongly on the parameters of the electron gun, the linac and the FEL undulators. Extensive start-to-end simulations have been performed at various laboratories to estimate the radiation properties at the end of the last undulator module including tolerances. Table 1: Comparison of geometrical and physical optic codes. geometrical optic physical optic total intensity yes yes brightness yes yes field amplitudes no yes diffraction limited source no yes diffraction effects of beamline indirect yes polarization modulation in beamline no yes time structure indirect yes The user of an FEL facility will be interested in the beam quality at the experiment. Consequently, the startto-end simulations have to be extended to include also the beamline. Ray tracing codes used in the past are generally based on geometrical optics. These codes can not simulate directly the important coherent properties of the FEL radiation. In this paper we will present the physical optics code PHASE which has been written over the last years at BESSY. Table 1 shows the advantages of physical optics codes with respect to geometrical optics codes. In the next section the propagation of radiation in normal incidence geometries is described. Then, a matrix formalism is presented which permits the propagation through grazing incidence optics. The simulation of the time dependence which has recently been added to the code will be explained in more detail. Next, a few details to the code PHASE are discussed and finally, examples for various aspects of the radiation propagation are presented. FREE SPACE PROPAGATION AND NORMAL INCIDENCE OPTICS Figure 1: Principle layout of a normal incidence optic. For monochromatic waves the electric field distribution in a plane perpendicular to the direction of propagation completely defines the properties of the radiation (Huygens’ construction). The wavefront can be propagated by a direct integration of the equation of Fresnel and Kirchhof (eq.1) which is, however, time comsuming. dz dy r r e y z E y z E r r k i ⋅ ⋅ − = ∫ ∫ ∞