1. 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

2. Overview of Spectrometer Optics1
90° off-axis parabolic mirrors (OAP)
HeNe laser at nm (visible) to align optics
Alignment complicated when infrared laser is used
KRS-5 crystal acts as spectrometer prism, dispersing transition radiation

3. MATLAB Model: Ray Transfer Matrix Analysis2
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

4. Gaussian Ray Transfer Matrix Analysis3
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

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

6. 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)

7. ZEMAX: Adding Mirror Tilts6
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

8. ZEMAX: Detector Tilt Dispersion causes chromatic aberrations7
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”

9. Results and Analysis

10. Results: Beam Size at First OAP Focus8
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

11. Results: Beam Size at Detector Surface9
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

12. Updated Detector Tilt Detector tilt of 45° for optimal focusing10
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

13. Conclusions Current alignment leaves significant aberrations11
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

14. Acknowledgements Advisor: Joe Frisch ZEMAX advising : Alan Fischer12
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

15. References
[1] Y. Ding et al., “Measurements and Simulations of Ultralow Emittance and Ultrashort Electron Beams in the Linas Coherent Light Source”, PRL 102, , 2009 
[2] Linear Coherent Light Source
[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,
[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
[8] Gaussian Beams
[9] Radiant ZEMAX LLC,
[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