C
alcul
ating strong-field, momentum-resolved photoelectron spectr
a (PES) from numeric
al solutions of the time-dependent Schrödinger equ
ation (TDSE) is
a very dem
anding t
ask due to the l
arge sp
ati
al excursions
and drifts of electrons in intense l
aser fields. The time-dependent surf
ace flux (t-SURFF) method for the c
alcul
ation of PES [T
ao
and
Scrinzi (2012)]
allows to keep the numeric
al grid much sm
aller th
an the sp
ace over which the w
avefunction would be spre
ad
at the end of the l
aser pulse. We present
an implement
ation of the t-SURFF method in the well est
ablished TDSE-solver
an class="smallcaps">Qpropan> [B
auer
and Kov
al (2006)].
an class="smallcaps">Qpropan> efficiently prop
ag
ates w
avefunctions for single-
active electron systems with spheric
ally symmetric binding potenti
als in cl
assic
al, line
arly (
along
an id="mmlsi29" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301801&_mathId=si29.gif&_user=111111111&_pii=S0010465516301801&_rdoc=1&_issn=00104655&md5=2b95d8935b19779c629ad7a661491c1d" title="Click to view the MathML source">zan>an class="mathContainer hidden">an class="mathCode">ath altimg="si29.gif" overflow="scroll">zath>an>an>an>) or elliptic
ally (in the
an id="mmlsi30" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301801&_mathId=si30.gif&_user=111111111&_pii=S0010465516301801&_rdoc=1&_issn=00104655&md5=7ee8d8a32504c3ad46cb220bca73fca1" title="Click to view the MathML source">xyan>an class="mathContainer hidden">an class="mathCode">ath altimg="si30.gif" overflow="scroll">xyath>an>an>an>-pl
ane) pol
arized l
aser fields in dipole
approxim
ation. Its combin
ation with t-SURFF m
akes the simul
ation of PES fe
asible in c
ases where it is just too expensive to keep the entire w
avefunction on the numeric
al grid, e.g., in the long-w
avelength or long-pulse regime.
absSec_2">Program summary
Program title: Qprop
Catalogue identifier: ADXB_v2_0
Program summary URL:an id="ir000010" class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/summaries/ADXB_v2_0.html">http://cpc.cs.qub.ac.uk/summaries/ADXB_v2_0.htmla>an>
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: GNU General Public License, version 3
No. of lines in distributed program, including test data, etc.: 12458
No. of bytes in distributed program, including test data, etc.: 86258
Distribution format: at.gz
Programming language: C++.
Computer: x86_64.
Operating system: Linux.
RAM: The memory requirements for calculating PES are determined by the maximum an id="mmlsi14" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301801&_mathId=si14.gif&_user=111111111&_pii=S0010465516301801&_rdoc=1&_issn=00104655&md5=da1dd11253d7f764d57a233b243670f0" title="Click to view the MathML source">ℓan>an class="mathContainer hidden">an class="mathCode">ath altimg="si14.gif" overflow="scroll">ℓath>an>an>an> in the spherical harmonics expansion of the wave function and the number of momentum (or energy) values for which the PES are to be calculated. The example with the largest memory demand (ass="boldFont">large-clubs) uses approximately 6GB of RAM. The size of the numerical representation of a wavefunction during propagation is modest for the examples included (53 MB for the ass="boldFont">large-club example).
Number of processors used: The evaluation of the PES can be distributed over up to an id="mmlsi32" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301801&_mathId=si32.gif&_user=111111111&_pii=S0010465516301801&_rdoc=1&_issn=00104655&md5=454e9659aaa68ce8ee8247a16e9c5214" title="Click to view the MathML source">Nkan>an class="mathContainer hidden">an class="mathCode">ath altimg="si32.gif" overflow="scroll">Nkath>an>an>an> MPI processes (an id="mmlsi32" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301801&_mathId=si32.gif&_user=111111111&_pii=S0010465516301801&_rdoc=1&_issn=00104655&md5=454e9659aaa68ce8ee8247a16e9c5214" title="Click to view the MathML source">Nkan>an class="mathContainer hidden">an class="mathCode">ath altimg="si32.gif" overflow="scroll">Nkath>an>an>an> is the number of momentum values).
Catalogue identifier of previous version: ADXB_v1_0
Journal reference of previous version: Comput. Phys. Comm. 174(2006)396
Classification: 2.5.
External routines: GNU Scientific Library, Open MPI (optional), BOOST (optional)
Does the new version supersede the previous version?: For TDDFT calculations the previous version should be used.
Nature of problem:
When atoms are ionized by intense laser fields electrons may escape with large momenta (especially when rescattering is involved). This translates to a rapidly spreading wavefunction in numerical simulations of these systems thus rendering the calculation of PES very costly for increasing wave lengths and peak intensities.
Solution method:
The TDSE is solved by propagating the wavefunction using a Crank–Nicolson propagator. The wavefunction is represented by an expansion in spherical harmonics. In order to reduce the requirements with respect to the grid size the t-SURFF method is used to calculate PES.
Reasons for new version:
Using the window operator method to calculate PES is increasingly costly with increasing ponderomotive energies and pulse durations. The new version of Qprop provides an implementation of the t-SURFF method which allows the use of much smaller numerical grids.
Summary of revisions:
An implementation of the t-SURFF method and examples for calculating PES are provided in the new release.
Restrictions:
The dipole approximation for the laser interaction has to be applicable. t-SURFF is only implemented for velocity gauge. Furthermore a finite cutoff for long range binding potentials has to be used in the implemented t-SURFF method.
Additional comments:
For additional information see an id="ir000015" class="interref" data-locatorType="url" data-locatorKey="http://www.qprop.de">www.qprop.dea>an>
Running time:
Depends strongly on the laser interaction studied. The examples given in this paper have run times from a few minutes to 12.5 hours.