Calculations and Simulations of an Infrared Prism Spectrometer for Ultra- Fast Bunch Length...

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