751 lines
12 KiB
Plaintext
751 lines
12 KiB
Plaintext
#LyX 2.0 created this file. For more info see http://www.lyx.org/
|
|
\lyxformat 413
|
|
\begin_document
|
|
\begin_header
|
|
\textclass revtex4
|
|
\options pra,superscriptaddress,twocolumn,notitlepage
|
|
\use_default_options false
|
|
\maintain_unincluded_children false
|
|
\language english
|
|
\language_package default
|
|
\inputencoding auto
|
|
\fontencoding global
|
|
\font_roman default
|
|
\font_sans default
|
|
\font_typewriter default
|
|
\font_default_family default
|
|
\use_non_tex_fonts true
|
|
\font_sc false
|
|
\font_osf false
|
|
\font_sf_scale 100
|
|
\font_tt_scale 100
|
|
|
|
\graphics default
|
|
\default_output_format pdf4
|
|
\output_sync 0
|
|
\bibtex_command bibtex
|
|
\index_command default
|
|
\paperfontsize default
|
|
\spacing single
|
|
\use_hyperref false
|
|
\papersize a4paper
|
|
\use_geometry false
|
|
\use_amsmath 1
|
|
\use_esint 1
|
|
\use_mhchem 1
|
|
\use_mathdots 1
|
|
\cite_engine basic
|
|
\use_bibtopic false
|
|
\use_indices false
|
|
\paperorientation portrait
|
|
\suppress_date false
|
|
\use_refstyle 1
|
|
\index Index
|
|
\shortcut idx
|
|
\color #008000
|
|
\end_index
|
|
\secnumdepth 3
|
|
\tocdepth 3
|
|
\paragraph_separation indent
|
|
\paragraph_indentation default
|
|
\quotes_language english
|
|
\papercolumns 1
|
|
\papersides 1
|
|
\paperpagestyle default
|
|
\tracking_changes false
|
|
\output_changes false
|
|
\html_math_output 0
|
|
\html_css_as_file 0
|
|
\html_be_strict false
|
|
\end_header
|
|
|
|
\begin_body
|
|
|
|
\begin_layout Standard
|
|
|
|
\lang finnish
|
|
\begin_inset FormulaMacro
|
|
\newcommand{\ket}[1]{\left|#1\right\rangle }
|
|
\end_inset
|
|
|
|
|
|
\begin_inset FormulaMacro
|
|
\newcommand{\bra}[1]{\left\langle #1\right|}
|
|
\end_inset
|
|
|
|
|
|
\lang english
|
|
|
|
\begin_inset FormulaMacro
|
|
\newcommand{\vect}[1]{\mathbf{\boldsymbol{#1}}}
|
|
{\boldsymbol{\mathbf{#1}}}
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Title
|
|
Technical notes on quantum electromagnetic multiple scattering
|
|
\end_layout
|
|
|
|
\begin_layout Author
|
|
Marek Nečada
|
|
\end_layout
|
|
|
|
\begin_layout Affiliation
|
|
COMP Centre of Excellence, Department of Applied Physics, Aalto University,
|
|
P.O.
|
|
Box 15100, Fi-00076 Aalto, Finland
|
|
\end_layout
|
|
|
|
\begin_layout Date
|
|
\begin_inset ERT
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
|
|
\backslash
|
|
today
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Abstract
|
|
...
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Theory of quantum electromagnetic multiple scattering
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Incoherent pumping
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Cf.
|
|
Wubs
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "wubs_multiple-scattering_2004"
|
|
|
|
\end_inset
|
|
|
|
, Delga
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "delga_quantum_2014,delga_theory_2014"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
General initial states
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Look at
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "landau_computational_2015"
|
|
|
|
\end_inset
|
|
|
|
for an inspiration for solving the LS equation with an arbitrary initial
|
|
state.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Computing classical Green's functions
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Boundary element method
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
T-Matrix method
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
T-Matrix resummation (multiple scatterers)
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
BEM→TM
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Cf.
|
|
SCUFF-TMATRIX (
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "sub:SCUFF-TMATRIX"
|
|
|
|
\end_inset
|
|
|
|
)
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Available software
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
SCUFF-EM
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "reid_scuff-em_2015"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
|
|
\family typewriter
|
|
SCUFF-TMATRIX
|
|
\family default
|
|
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sub:SCUFF-TMATRIX"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
|
|
\family typewriter
|
|
SCUFF-SCATTER
|
|
\family default
|
|
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sub:SCUFF-SCATTER"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Caveats
|
|
\end_layout
|
|
|
|
\begin_layout Description
|
|
Units.
|
|
|
|
\family typewriter
|
|
SCUFF-SCATTER
|
|
\family default
|
|
's Angular frequencies specified using the
|
|
\family typewriter
|
|
--Omega
|
|
\family default
|
|
or
|
|
\family typewriter
|
|
--OmegaFile
|
|
\family default
|
|
arguments are interpreted in units of
|
|
\begin_inset Formula $c/1\,\mathrm{μm}=3\cdot10^{14}\,\mathrm{rad/s}$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Foot
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\family typewriter
|
|
\begin_inset CommandInset href
|
|
LatexCommand href
|
|
name "http://homerreid.dyndns.org/scuff-EM/scuff-scatter/scuffScatterExamples.shtml"
|
|
target "http://homerreid.dyndns.org/scuff-EM/scuff-scatter/scuffScatterExamples.shtml"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
.
|
|
|
|
\emph on
|
|
TODO what are the output units?
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
MSTM
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "mackowski_mstm_2013"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
The incident field is a gaussian beam or a plane wave in the vanilla code
|
|
(no multipole radiation as input!).
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
The bulk of the useful code is in the
|
|
\family typewriter
|
|
mstm-modules-v3.0.f90
|
|
\family default
|
|
file.
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
For solving the interaction equations
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
after "(14)"
|
|
key "mackowski_mstm_2013"
|
|
|
|
\end_inset
|
|
|
|
, the BCGM (biconjugate gradient method) is used.
|
|
(According to Wikipedia, this method is numerically unstable but has a
|
|
stabilized version (stabilized BCGM).)
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
According to the manual
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
after "2.3"
|
|
key "mackowski_mstm_2013"
|
|
|
|
\end_inset
|
|
|
|
, they use some method (rotational-axial translation decomposition of the
|
|
translation operation), which
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
reduces the operation from an
|
|
\begin_inset Formula $L_{S}^{4}$
|
|
\end_inset
|
|
|
|
process to
|
|
\begin_inset Formula $L_{S}^{3}$
|
|
\end_inset
|
|
|
|
process where
|
|
\begin_inset Formula $L_{S}$
|
|
\end_inset
|
|
|
|
is the truncation order of the expansion
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
(more details can probably be found at
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
after "around (68)"
|
|
key "mackowski_calculation_1996"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
|
|
\end_layout
|
|
|
|
\begin_deeper
|
|
\begin_layout Itemize
|
|
|
|
\emph on
|
|
Not sure if this holds also for nonspherical particles, I should either
|
|
read carefully
|
|
\emph default
|
|
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "mackowski_calculation_1996"
|
|
|
|
\end_inset
|
|
|
|
|
|
\emph on
|
|
or look into
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "mishchenko_electromagnetic_2003"
|
|
|
|
\end_inset
|
|
|
|
which is also cited in the manual.
|
|
\end_layout
|
|
|
|
\end_deeper
|
|
\begin_layout Itemize
|
|
By default spheres, it is possible to add own T-Matrix coefficients instead.
|
|
|
|
\end_layout
|
|
|
|
\begin_deeper
|
|
\begin_layout Itemize
|
|
|
|
\emph on
|
|
Is it then possible to insert a T-Matrix of an arbitrary shape, or is it
|
|
somehow limited to
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
spherical-like
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
particles?
|
|
\end_layout
|
|
|
|
\end_deeper
|
|
\begin_layout Itemize
|
|
Why the heck are the T-matrix options listed in the
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
Options for random orientation calculations
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
?
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Code integration
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Testing and reproduction of foreign results
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Delga PRL
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "delga_quantum_2014"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Parameters
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Surrounding lossless dielectric
|
|
\series bold
|
|
medium
|
|
\series default
|
|
with permittivity
|
|
\begin_inset Formula $\epsilon_{d}=2.13$
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
QEs:
|
|
\series default
|
|
dipole moment
|
|
\begin_inset Formula $\mu=0.19\, e\cdot\mathrm{nm}=9.12\,\mathrm{D}$
|
|
\end_inset
|
|
|
|
, count
|
|
\begin_inset Formula $N\in\left\{ 1,50,100,200\right\} $
|
|
\end_inset
|
|
|
|
, radial orientation,
|
|
\begin_inset Formula $h=1\,\mathrm{nm}$
|
|
\end_inset
|
|
|
|
above the sphere (except for Fig.
|
|
5 where variable), natural frequency
|
|
\begin_inset Formula $\Omega_{n}=\omega_{0}-i\gamma_{\mathrm{QE}}/2,$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Formula $\omega_{0}=$
|
|
\end_inset
|
|
|
|
varies,
|
|
\begin_inset Formula $\gamma_{\mathrm{QE}}=15\,\mathrm{meV}$
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
Sphere:
|
|
\end_layout
|
|
|
|
\begin_deeper
|
|
\begin_layout Itemize
|
|
radius
|
|
\begin_inset Formula $a=7\,\mathrm{nm}$
|
|
\end_inset
|
|
|
|
,
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Drude model
|
|
\begin_inset Formula $\epsilon_{m}(\omega)=\epsilon_{\infty}-\frac{\omega_{p}^{2}}{\omega\left(\omega+i\gamma_{p}\right)}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_deeper
|
|
\begin_layout Itemize
|
|
Drude parameters
|
|
\begin_inset Formula $\omega_{p}=9\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
,
|
|
\begin_inset Formula $\epsilon_{\infty}=4.6$
|
|
\end_inset
|
|
|
|
,
|
|
\begin_inset Formula $\gamma_{p}=0.1\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_deeper
|
|
\begin_layout Itemize
|
|
background permittivity
|
|
\begin_inset Formula $\epsilon_{d}(\omega)=2.13$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
(approximate?; not really a parameter) LSP resonances
|
|
\begin_inset Formula $\omega_{l}=\omega_{p}/\sqrt{\epsilon_{\infty}+\left(1+1/l\right)\epsilon_{d}}$
|
|
\end_inset
|
|
|
|
; particularly,
|
|
\begin_inset Formula $\omega_{1}\approx3.0236\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
,
|
|
\begin_inset Formula $\omega_{2}\approx3.2236\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
,
|
|
\begin_inset Formula $\omega_{3}\approx3.30\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
,
|
|
\begin_inset Formula $\omega_{4}\approx3.34\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
,
|
|
\begin_inset Formula $\omega_{5}\approx3.364\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Formula $\omega_{\infty}\approx3.4692\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_deeper
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
Detector:
|
|
\series default
|
|
|
|
\end_layout
|
|
|
|
\begin_deeper
|
|
\begin_layout Itemize
|
|
Far field:
|
|
\begin_inset Formula $1\,\mathrm{\mu m}$
|
|
\end_inset
|
|
|
|
away from the center of the nanoparticle along the
|
|
\begin_inset Formula $y$
|
|
\end_inset
|
|
|
|
axis (Fig.
|
|
3).
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Near field: position not specified in the paper; but in Fig.
|
|
4(b) there are
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
polarization spectra
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
instead of
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
light spectra
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
(eq.
|
|
4) in Fig.
|
|
4(a).
|
|
Does this mean that they are evaluated somewhere in/on the sphere? Or in
|
|
the particle? The latter is likely, as it is given by
|
|
\begin_inset Formula $P_{n}\left(\omega\right)=\left\langle \sigma_{n}^{+}\left(-\omega\right)\sigma_{n}^{-}(\omega)\right\rangle $
|
|
\end_inset
|
|
|
|
(cf.
|
|
the column below Fig.
|
|
3).
|
|
\end_layout
|
|
|
|
\end_deeper
|
|
\begin_layout Subsubsection
|
|
Testing
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
In my
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
old
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
code, there no splitting observable around
|
|
\begin_inset Formula $\omega\approx\omega_{0}\approx\omega_{\infty}\approx3.46\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
.
|
|
This is perhaps because the couplings to the higher multipoles is miscalculated
|
|
(too small).
|
|
No splitting around the NP dipole (
|
|
\begin_inset Formula $\approx3,02\,\mathrm{eV}$
|
|
\end_inset
|
|
|
|
) should be OK for single QE in far field (cf.
|
|
Fig.
|
|
3).
|
|
And there are yet the
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
switched axes
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
...
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Delga JoO
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "delga_theory_2014"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Parameters
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
QEs:
|
|
\series default
|
|
dipole moment
|
|
\begin_inset Formula $\mu=0.38\, e\cdot\mathrm{nm}=18.24\,\mathrm{D}$
|
|
\end_inset
|
|
|
|
(double), otherwise the same parameters as in
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "delga_quantum_2014"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
Sphere:
|
|
\series default
|
|
as in
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "delga_quantum_2014"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
Detector:
|
|
\series default
|
|
not stated in the paper
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
|
|
\series bold
|
|
Numerics:
|
|
\series default
|
|
looking at the leftmost ball in Fig.
|
|
3, it seems that their SVW cutoff is around 12.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset bibtex
|
|
LatexCommand bibtex
|
|
bibfiles "dipdip"
|
|
options "apsrev"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|