SLAC National Accelerator Center Calculations and Simulations of an Infrared Prism Spectrometer for Ultra-Fast Bunch Length Diagnosis at LCLS Julie Cass SULI Program 2011 SLAC National Accelerator Center Advisor Josef Frisch

Overview of Spectrometer Optics 1 90° off-axis parabolic mirrors (OAP) HeNe laser at 632.816 nm (visible) to align optics Alignment complicated when infrared laser is used KRS-5 crystal acts as spectrometer prism, dispersing transition radiation

MATLAB Model: Ray Transfer Matrix Analysis 2 MATLAB Model: Ray Transfer Matrix Analysis MATLAB used to model beam size with ray transfer matrix analysis Ray transfer matrix: 2 x 2 matrices describing each optical element or free space propagated by beam Free space propagation Passage through a lens of focal length f

Gaussian Ray Transfer Matrix Analysis 3 Designed for modeling light rays of negligible waist size HeNe laser is Gaussian - generated a vector to represent the initial beam in terms of a complex beam parameter q R – radius of curvature w – beam width k – normalization constant for second component of beam vector MATLAB code calculates and graphs beam waists

Optical Element Number* 4 Log of Beam Width Optical Element Number* *including free spaces of step size 100um

ZEMAX Simulation 5 Study spectrometer resolution achievable: simulation using optics modeling software ZEMAX ZEMAX offers ray-tracing computations, following paths of perfect geometric rays as they are reflected and refracted Spot size analyzed at two points: (1) Focal point of first OAP (2) Detector surface (focal point of 3rd OAP)

ZEMAX: Adding Mirror Tilts 6 Mirror tilts in increments of 0.05° along optical, horizontal and vertical axes Angles adjusted until beam size similar to measured beam size reached, then compared with estimated misalignment error

ZEMAX: Detector Tilt Dispersion causes chromatic aberrations 7 Dispersion causes chromatic aberrations Detector tilt required New simulation to account for differences in design parameters C. Behrens et al., “Design of a Single-Shot Prism Spectrometer in the Near- and Mid-Infrared Wavelength Range for Ultra-Short Bunch Length Diagnostics”

Results and Analysis

Results: Beam Size at First OAP Focus 8 Measured: 172 um MATLAB: 65 um ZEMAX: Tilts of ~0.4° to change beam size at focus from 0 to 172um Consistent with human error in alignment

Results: Beam Size at Detector Surface 9 Measured: 280 um MATLAB: 38 um Much larger degree of error (~ 7x magnification) ZEMAX: 14 um Tilts of ~1.03° about horizontal/vertical axes needed to achieve measured size Tilts of ~1.07° about optical axis needed to achieve measured size This measurement is much more complicated

Updated Detector Tilt Detector tilt of 45° for optimal focusing 10 Detector tilt of 45° for optimal focusing All wavelengths will not fit on detector surface: range limited by this size rather than KRS-5 transmission 14mm

Conclusions Current alignment leaves significant aberrations 11 Conclusions Current alignment leaves significant aberrations Development of alignment procedures with greater precision Addition of lasers with a range of wavelengths Detector range limited by its size unless: Adjustments are made to current design

Acknowledgements Advisor: Joe Frisch ZEMAX advising : Alan Fischer 12 Acknowledgements Advisor: Joe Frisch ZEMAX advising : Alan Fischer Colleagues: Kiel Williams and Gilles Dongmo-Momo SULI Program Director: Steve Rock DOE and SLAC National Accelerator Laboratory for funding and direction of SULI Program

References [1] Y. Ding et al., “Measurements and Simulations of Ultralow Emittance and Ultrashort Electron Beams in the Linas Coherent Light Source”, PRL 102, 254801, 2009  [2] Linear Coherent Light Source http://lcls.slac.stanford.edu/ [3] K. Williams, “Optical Design of a Broadband Infrared Spectrometer for Bunch Length Measurement at the Linac Coherent Light Source,” SLAC National Accelerator Laboratory SULI Program 2011, Palo Alto, CA  [4] Pyreos Ltd, http://www.pyreos.com/ [5] G. Dongmo-Momo, “Calibration of the Heat Sensor for the Free Electron Laser Bunch Length Measurements,” SLAC National Accelerator Laboratory SULI Program, Palo Alto, CA 2011 [6] MATLAB 7.0.4, The MathWorks Inc. [7] Bahaa E. A. Saleh and Malvin Carl Teich (1991). Fundamentals of Photonics. New York: John Wiley & Sons. Section 1.4, pp. 26-36 [8] Gaussian Beams http://www.rp-photonics.com/ [9] Radiant ZEMAX LLC, http://www.zemax.com [10] C. Behrens et al., “Design of a Single-Shot Prism Spectrometer in the Near- and Mid-Infrared Wavelength Range for Ultra-Short Bunch Length Diagnostics”, DIPAC'11, Hamburg, Germany, 201