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
Dec 17, 2015
Calculations and Simulations of an Infrared Prism Spectrometer for Ultra-Fast Bunch Length
Diagnosis at LCLS
Julie CassSULI Program 2011
SLAC National Accelerator CenterAdvisor Josef Frisch
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Overview of Spectrometer Optics
• 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
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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
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rfθ f
⎛
⎝ ⎜
⎞
⎠ ⎟=
1 0−1f 1
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟riθ i
⎛
⎝ ⎜
⎞
⎠ ⎟
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rfθ f
⎛
⎝ ⎜
⎞
⎠ ⎟=
1 d
0 1
⎛
⎝ ⎜
⎞
⎠ ⎟riθ i
⎛
⎝ ⎜
⎞
⎠ ⎟
Free space propagation Passage through a lens of focal length f
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Gaussian Ray Transfer Matrix Analysis• 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 curvaturew – beam widthk – normalization constant for second component of beam vector
• MATLAB code calculates and graphs beam waists
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Optical Element Number*
*including free spaces of step size 100um
Log
of B
eam
Wid
th
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ZEMAX Simulation• 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)
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ZEMAX: Adding Mirror Tilts
• 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
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ZEMAX: Detector Tilt
• 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”
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Results and Analysis
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Results: Beam Size at First OAP Focus
• 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
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Results: Beam Size at Detector Surface• 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
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Updated Detector Tilt
• 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
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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
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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
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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