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Document No.:
00000123
Edition:
A
Process:
CAL
No. of pages:
9
Test-Cases
Test-Cases for TP14_048 Performance Software Beam Propagation Method (BPM)
Position
Prepared
Name
Signature
Date
Applied Physicist
Michael Morrissey
12.1.2015
Technical Director
Bruno Le Garrec
12.1.2015
Approved
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Contents
1
Justification for Test-Cases ........................................................................................ 3
2
Preliminary Information ............................................................................................... 4
2.1 Essential Parameters .......................................................................................... 4
2.2 Test-Case Documentation .................................................................................. 4
3
Test Cases .................................................................................................................... 6
3.1 Test-Case 1: Broad Bandwidth – short pulse duration .................................. 6
3.2 Test-Case 2: Focal spot using low f-number optics........................................ 6
3.3 Test-Case 3: An Ultra-short pulse with a Broad Bandwidth coming to
a focal spot using low f-number optics.............................................................. 7
3.4 Test-Case 4: Simulation Resolution .................................................................. 7
3.5 Test-Case 5: Self-Focusing ................................................................................ 7
4
Conclusion .................................................................................................................... 9
5
Reference...................................................................................................................... 9
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JUSTIFICATION FOR TEST-CASES
Many technical requirements are presented in the technical query document of the tender in
question [1] where the software developers are required to comment on their ability to simulate,
or their potential to develop the knowledge to simulate, under specified conditions. Here in the
test-case document, it is proposed that these cases and conditions are investigated further using
the developer’s software so that both the limitations and abilities of the current software are
understood and quantified.
Two crucial requirements of the beam propagation method (BPM) software are the
simulation the spatio-temporal properties of ultra-short pulses (i) with very short pulse durations
(<20 fs) which subsequently results in a broad spectral profile and (ii) in the non-paraxial regime
where large focusing angles are created by low f-number optics. The software developer will
thus simulate these conditions and present their results. In addition the software developer shall
also provide a test case where both cases are combined and occur simultaneously. Therefore the
third test-case shall be (iii) the simulation of the spatio-temporal properties of an ultrashort pulse
which has a broad bandwidth and is focused to a spot using a low f-number optical component.
We are also interested in knowing (iv) the achievable resolution and (v) the simulation of nonlinear optical phenomena.
Section 3 gives details of the actual test cases where the developer’s software must
provide examples of their ability to simulate ELI-Beamlines specified cases. Therefore, as part of
the tender we request the software developer to simulate these cases using their currentlyavailable softwares.
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2.1
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PRELIMINARY INFORMATION
Essential Parameters
The final BPM software shall provide results in a 7-dimensional solution as is illustrated in
figure 1. It is crucial for ELI-Beamlines to be able to simulate the intensity profile as well as the
wavefront profile as the beam propagates through the optical system. Both these parameter
require two 2-D arrays from which typical parameters such as the peak intensity, total power,
beam profile, phase, tilt etc. as well as any deformations and aberrations. In addition to the
spatial properties of the beam, the spectral and temporal parameters also need to be determined.
From the simulation of these properties, parameters such as pulse energy, pulse duration, spectral
phase and bandwidth can be determined in 1-D. All these properties need to be determined as the
beam propagates through the optical system and there is an addition 1-D pseudo axis. The
complete solution is therefore a 7-D solution.
Figure 1: Simulation parameters for test-cases
2.2
Test-Case Documentation
The following are some guidelines to aid in the documentation of each test-case:

Description: A concise but clear description of the simulations shall be provided in order
to allow us to have a complete understanding of what processes are taking place.
Graphical illustrations and screen shots may be used to aid in the description in the
system.

Reference: Where specified and/or is possible, test-case results shall be compared to
peer-review published results. Referenced publications and literature can be provided on
request.
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Basic Operation: In addition to the repetition of referenced results where specified, the
software developer shall simulate the essential parameters described in section 2.1 where
appropriate.

Initial Parameter: A variety of initial parameter shall be used to infer the scope of the
software. In particular, which ever parameter/effect is being investigated a large varying
range of this parameter shall be used.

Mathematical Model: Where appropriate the software developer shall comment on which
models and techniques are being applied to simulate the physical system.

Results: Appropriate figures of merit and graphical illustrations shall be presented to
display the results as well as provide information of the ability of the software to simulate
the process.
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TEST CASES
Provided below are five test cases which the developer must simulate using their commercially
available software and provide appropriate results. These results shall be compared to the
referenced publications where possible. The test cases should be performed in a sequential
manner when possible i.e the parameters/results of one case follow through to the next case.
3.1
Test-Case 1: Broad Bandwidth – short pulse duration
The pulse duration of the expected beams in ELI-Beamlines varies from 150 fs down to ~15 fs.
However, we also wish to be able to simulate pulses of much shorter durations for reasons of
future research and development. We consider the limit of many standard techniques (e.g. splitstep-method) used to simulate such physical systems to be approximately 15 fs below which
these techniques provide very different results. Due to the lack of published literature available
on this topic, it is up to the software developer to provide a test-case which provides an adequate
technique to simulate the propagation of ultrashort pulses with pulse durations of 5, 10 and 15 fs.
The software developer shall provide comments on; the appropriateness of the simulation
technique; how sampling issues resulting from having a broad bandwidth are resolved; and on
the reliability of the results.
3.2
Test-Case 2: Focal spot using low f-number optics
It is vitally important that the ELI-Beamlines facility can both simulate and measure the optical
parameters in the vicinity of the focal spot. In ELI-Beamlines, the focal spot will be created with
the aid of an off-axis parabolic mirror with a low f-number (f-number < 1) to create large
intensities. In this case the paraxial approximation is not a valid simulation technique due to the
large angles created by the off-axis parabolic mirror. References [2-3] give a theoretical model
and numerical results for the simulation of electromagnetic waves by a parabolic mirror.
Reference [3] specifically simulates the intensity distribution in the focal and meridional planes
for various off-axis parabola parameters. The results are illustrated in figures 4-6. The software
developer shall repeat these simulations using their current software and compare the results.
Any discrepancies shall be commented upon as much as possible. If a parabolic mirror is not
available in the current version of the software developer’s software, a low f-number spherical
mirrors may be used.
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Test-Case 3: An Ultra-short pulse with a Broad Bandwidth coming to a focal spot
using low f-number optics
Test-cases 1 and 2 are of the most important for ELI-Beamlines regarding the simulation of the
laser system. Of course, when simulating the ELI-Beamlines laser setup, both of these cases
conditions will occur simultaneously. The software developer shall combine the parameters of
test-case 1 and 2 and thus simulate an ultrashort pulse with a broad bandwidth being focused to a
spot with the aid of a low f-number optical component.
3.4
Test-Case 4: Simulation Resolution
The largest beams in ELI-Beamlines are expected to be approximately 400 x 400 mm with a plane
wave which is flat in intensity and phase. Let’s assume a simulation area of 600 x 600 mm is
required to reproduce misalignment effects as well as all other effects that can be observed in the
physical system. If we require a spatial resolution of 50 µm, which is the expected resolution to
distinguish various beam deformation and aberrations, it is clear that a certain amount of
computational power will be required to perform these high resolution simulations in a timely
𝜆
manner. This resolution results in a spatial cut-off frequency of 16 mrad (𝜃 = 𝑝 =
0.8 𝜇𝑚
50 𝜇𝑚
=
16 𝑚𝑟𝑎𝑑). The software developer shall comment on the ability of their software to handle such
large data arrays as well as their limitations. The software developer shall also consider this beam
coming to a focus with the aid of a low f-number optical component as in test-case 2. The software
should be tested to resolve the details of the Airy disk for the above parameters in the diffraction
limited case. The software developer shall mentioned parameters such as; encircled energy, strehl
ratio, computational time, sampling techniques, data requirement etc. This resolution requirement
becomes even more crucial when calculating the phase profile which is foreseen to require much
more complexity and computational power. The software developer should also comment on the
feasibility of performing such phase computation to such a degree of accuracy.
3.5
Test-Case 5: Self-Focusing
In the technical query [1] it is mentioned that the non-linear simulations required for ELIBeamlines is limited to the Kerr effect. This phenomena leads to many effects, one of which is
self-focusing. Accurate simulation of this phenomena is crucial to ELI-Beamlines as it can result
in the catastrophic damage of optical components [5]. The position of non-linear self-focusing of
a Gaussian beam can be simulated using the Marburger and Dawes equation which can be found
in reference [5], equation 9 and can give classical theoretical predictions regarding the shift of
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the non-linear focus. The software developer shall perform simulations and use the resultant data
to compare to the theory as well as the results that are illustrated in figure 4 of this reference
where the shift in the non-linear focus is plotted as a function of the pulse power [5]. The
software developer shall also perform simulations to illustrate self-focusing whereby the beam
area is varied while the peak intensity is kept constant. Results should be compared to those
achieved in reference [4], Figure 1. Any discrepancies in the results should be commented upon.
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CONCLUSION
The software developer is encouraged to use these test-case requirements as a method to clearly
show the suitability and diversity of their software as well as the potential development of their
software to be use in the ELI-Beamlines facility as the main simulation software.
5
REFERENCE
[1] M. Morrissey, B. le Garrec, “Requirements for TP14_048 Performance Software: Beam
Propagation Method (BPM)”, Technical Query, ELI-BL-4510-TQ-00000123-F.
[2] P. Varga and P. Torok, “Focusing of electromagnetic waves by paraboloid mirrors. I.
Theory”, J. Opt. Soc. Am. A 17, 2081 (2000).
[3] P. Varga and P. Torok, “Focusing of electromagnetic waves by paraboloid mirrors. II.
Numerical results”, J. Opt. Soc. Am. A 17, 2090 (2000).
[4] H. Bercegol L. Lamaignère, B. Le Garrec, M. Loiseau, P. Volto, “ Self-focusing and rear
surface damage in a fused silica window at 1064 nm and 355 nm”, Proc. of SPIE Vol. 4932
(2003).
[5] A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and
damage in fused silica induced by tightly focused femtosecond laser pulse”, Phys. Rev. B
71, 125435 (2005)
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