julie cass suli program 2011 slac national accelerator center advisor josef frisch
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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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3
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
€
rfθ f
⎛
⎝ ⎜
⎞
⎠ ⎟=
1 0−1f 1
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟riθ i
⎛ ⎝ ⎜
⎞ ⎠ ⎟
€
rfθ f
⎛
⎝ ⎜
⎞
⎠ ⎟=
1 d0 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
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