SALMON Tutorial, Osaka Univ,, 2019

How to Use SALMON
Multiscale Simulation
Exercise-4-2

Mitsuharu UEMOTO
Center for Computational Sciences, University of Tsukuba
Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
http://salmon-tddft.jp/1Light Propagation in Solid State Material
Light irradiation into the solid material,+++

E(t) : Applied Electric Field
P(t) : Induced Polarization
Nature,. 432, pp. 9–12, (2004).

---Incident EM field

E(t)

P(t)

Weak intensity light• Light propagation in the solid media → Maxwell’s wave equation.

r ⇥ r ⇥ A(r, t)

Opt. Express, 15, 12 (2007)" @2A(r, t) =022c @t• Dielectric response to applied field → Linear Response

P=•(1)

E = ("1)/4⇡ · E

Strong intensity light

Optical Nonlinearity Induced by Intense Field
Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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SALMON Tutorial, Osaka Univ,, 20192

Light Propagation in Solid State Material
Induced current density in matter

J(t) =e X1m
⌦b,kZ

⌦

Re u?b,k (r, t)⇣⌘2ei~r + ~k + A(t) ub,k (r, t) dr + JNLc• “Constitution Relation” of Electromagnetics:(Current density can be described as the functional of the EM field)

J =J[A(t)]Light propagation in the mediaCouple• Governing equation of EM field (Maxwell’s wave eq.)

r⇥r⇥A

1 @
A=
2
2
c @t

4⇡
J
c

Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
http://salmon-tddft.jp/SALMON Tutorial, Osaka Univ,, 20193

Multiscale Maxwell-TDDFT method• A multiscale method treats light propagations in solid media,
combining the macroscopic Maxwell equation and microscopic electron dynamics.
Macroscopic system (EM field)

Microscopic system (Electron dynamics)x ⇠ 0.05 nmx ⇠ 10 nm

Solve Maxwell’s Eq. in Macroscopic grid:1 @ 2 A 4⇡r⇥r⇥A+ 2 2 = Jc @tc
FDTD-based EM calculation:J(tti ) ! A(t)Solve TD-KS Eq. in Microscopic GridÊunk = Ĥ(k)unk

RT-TDDFT calculation:A(tti ) ! J(t)Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
http://salmon-tddft.jp/SALMON Tutorial, Osaka Univ,, 20194Exercise• Short laser pulse propagation in a thin film silicon with a thickness L:

SiComputation Condition• Matter:• Silicon: R=123, K=43, dt=0.16 [au] (~3.8 [as])• Thickness L=80 [nm] (~1.5x104 [au])• Laser Pulse• Central Frequency: 1.55 [eV]• Intensity: I=1012 [W/cm2]• Pulse Length: T=10.6 [fs]Results• Matter Current Density• Electromagnetic Field Profile• Energy Absorption

Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
http://salmon-tddft.jp/SALMON Tutorial, Osaka Univ,, 20195Exercise• Computation Model:
Incident pulse

Nxvac_L

Si layerNxvac_R

Si layer

HX_m

NX_m

• Nxvac_L/R: Lower / upper-bound of computation domain• NX_m: Upper bound of the matter region• HX_m: Grid spacing

Thickness = NX_m * HX_m = 80 [nm]Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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Job Submission•Enter your working directory and submit the job script:$ cd ~/work/exercise4-2_ms$ sbatch job.sh•Parallelization scheme of the job (Hybrid MPI and OpenMP execution):

8 TDDFT cells
4 MPI procs.
(2 cells/MPI proc.)

10 OpenMP threads/MPI proc.

2 Computation nodes(2 MPI procs/node)
Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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Input File$ less Si_multiscale.inp
LIST1: Si_multiscale.inp&calculation
calc_mode = 'GS_RT’
use_ms_maxwell = 'y’/&controlsysname = 'Si’/…
•“use_ms_maxwell”
Enable the multiscale calculation mode
Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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Input File
LIST: Si_multiscale.inp&emfield
ae_shape1 = 'Acos2’
rlaser_int_wcm2_1 = 1d12
pulse_tw1 = 441.195136248d0
omega1 = 0.05696145187d0
epdir_re1 = 0.,0.,1.
/•••“pulse_tw1”
Incident pulse length: 441 [au] (~ 10.6 [fs])“rlaser_int_wcm2_1”
Intensity of the incident pulse: 1012 [W/cm2]”omega1”
Central frequency of the incident pulse: 0.056.. [au] (~ 1.55 [eV])Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
http://salmon-tddft.jp/
SALMON Tutorial, Osaka Univ,, 20199Input File
LIST: Si_multiscale.inp&multiscale
fdtddim = '1D’
twod_shape = 'periodic’
NX_m = 8
HX_m = 188.97
NXvacL_m = -500
NXvacR_m = +500/•••

NX_m: Number of the macroscopic grid points; 8 [macro-points]
HX_m: Grid spacing; 188.97 [au/cell] = 10 [nm/cell]
NXVac(L|R)_m: Upper/lower bound of computation domain;-500 ~ +500 [cell] = -5000 ~ +5000 [nm]Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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Output Files•(xxxxxx: Timestep)
multiscale/RT_Ac/Si_Ac_xxxxxx.data• Electromagnetic field and energy distributions at each timesteps
ColumnDetail

1,2,3

IX,IY,IZ

Index coordinates of macroscopic grid

4,5,6Acx, Acy, Acz

Vector potential

7,8,9

Ex, Ey, Ez

Electric field

10,11,12Bx, By, Bz

Magnetic field

13,14,15

Jmx, Jmy, Jmz

Matter current density

16E_exExcitation energy

1718E_abs
E_emAbsorbed energy
Total EM energy

Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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SALMON Tutorial, Osaka Univ,, 201911

Ez Field Plotting (GNUPLOT)
LIST: Operation to visualize E_z distribution:$ gnuplot> plot “multiscale/RT_Ac/Si_Ac_003000.data” us 1:9 w l

Example: Ez field profile at Timestep=3000 (t=11.6 [fs]).
Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
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Output Files•(xxxxxx: Macro-point index)
multiscale/Mxxxxx/Si_Ac_M.data• Current densities and vector potential at each macro-points

ColumnDetail

1

Time

2,3,4

Acx, Acy, Acz

Vector potential at xxxxxx-th macro-point

5,6,7Jmx, Jmy, Jmz

Matter current density$ gnuplot> plot “multiscale/M000004/Si_Ac_M.data” us 1:7 w l
Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience
http://salmon-tddft.jp/SALMON Tutorial, Osaka Univ,, 201913