1. science
2. mathematics
3. geometry

Physics and Nanotechnology
Probably the Best Education in the World
Jakob Rosenkrantz de Lasson
September 12 2013
3
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1.5
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My Background
Grew up in Odense
1/5
My Background
Grew up in Odense
B.Sc. at DTU from 2007
1/5
My Background
Grew up in Odense
B.Sc. at DTU from 2007
B.Sc. thesis in 2010
1/5
My Background
Grew up in Odense
B.Sc. at DTU from 2007
B.Sc. thesis in 2010
M.Sc. at DTU from 2010 (Honors Program)
Exchange at UMD
1/5
My Background
Grew up in Odense
M.Sc. at DTU from 2010 (Honors Program)
Exchange at UMD
B.Sc. at DTU from 2007
B.Sc. thesis in 2010
Summer school in Grenoble (2011)
1/5
My Background
Grew up in Odense
M.Sc. at DTU from 2010 (Honors Program)
Exchange at UMD
B.Sc. at DTU from 2007
Summer school in Grenoble (2011)
B.Sc. thesis in 2010
M.Sc. thesis in 2012
1/5
My Background
Grew up in Odense
M.Sc. at DTU from 2010 (Honors Program)
Exchange at UMD
B.Sc. at DTU from 2007
Summer school in Grenoble (2011)
B.Sc. thesis in 2010
M.Sc. thesis in 2012
...Ph.D. student at DTU Fotonik from October 2012
1/5
My Background
Grew up in Odense
M.Sc. at DTU from 2010 (Honors Program)
Exchange at UMD
B.Sc. at DTU from 2007
Summer school in Grenoble (2011)
B.Sc. thesis in 2010
M.Sc. thesis in 2012
...Ph.D. student at DTU Fotonik from October 2012
Go abroad with your studies!
1/5
My M.Sc. Education
Courses:
I Methods of Mathematical Physics
(UMD)
I Introduction to Quantum Mechanics
I (UMD)
I Continuum Mechanics (UMD)
I Nanophotonics (DTU)
I TEMO (DTU)
I Summer school (Grenoble)
I Statistical Physics (DTU)
I Transport in Nanostructures (DTU)
2/5
My M.Sc. Education
Courses:
I Methods of Mathematical Physics
(UMD)
I Introduction to Quantum Mechanics
I (UMD)
I Continuum Mechanics (UMD)
Projects:
I ”Modeling of Spontaneous Emission
Rate in Micropillars Using an Open
Geometry Formalism”
I Nanophotonics (DTU)
I TEMO (DTU)
I Summer school (Grenoble)
I Statistical Physics (DTU)
I Transport in Nanostructures (DTU)
I ”Volume Integral Equations and the
Electromagnetic Green’s Tensor”
I ”Electromagnetic Scattering in
Micro- and Nanostructured
Materials”
2/5
My M.Sc. Education
Courses:
I Methods of Mathematical Physics
(UMD)
I Introduction to Quantum Mechanics
I (UMD)
I Continuum Mechanics (UMD)
I Nanophotonics (DTU)
I TEMO (DTU)
I Summer school (Grenoble)
I Statistical Physics (DTU)
I Transport in Nanostructures (DTU)
Projects:
I ”Modeling of Spontaneous Emission
Rate in Micropillars Using an Open
Geometry Formalism”
Rosenkrantz de Lasson et al.
Vol. 29, No. 7 / July 2012 / J. Opt. Soc. Am. A
1237
Modeling of cavities using the analytic modal method
and an open geometry formalism
Jakob Rosenkrantz de Lasson,† Thomas Christensen,† Jesper Mørk, and Niels Gregersen*
DTU Fotonik, Department of Photonics Engineering, Technical University of Denmark, Ørsteds Plads,
Building 343, DK-2800 Kongens Lyngby, Denmark
*Corresponding author: ngre@fotonik.dtu.dk
Received September 27, 2011; revised March 12, 2012; accepted March 12, 2012;
posted March 15, 2012 (Doc. ID 155363); published June 6, 2012
We present an eigenmode expansion technique for calculating the properties of a dipole emitter inside a micropillar. We consider a solution domain of infinite extent, implying no outer boundary conditions for the electric
field, and expand the field on analytic eigenmodes. In contrast to finite-sized simulation domains, this avoids the
issue of parasitic reflections from artificial boundaries. We compute the Purcell factor in a two-dimensional
micropillar and explore two discretization techniques for the continuous radiation modes. Specifically, an equidistant and a nonequidistant discretization are employed, and while both converge, only the nonequidistant discretization exhibits uniform convergence. These results demonstrate that the method leads to more accurate
results than existing simulation techniques and constitutes a promising basis for further work. © 2012 Optical
Society of America
OCIS codes: 000.3860, 050.1755, 230.5750, 230.7370, 290.0290.
I ”Volume Integral Equations and the
Electromagnetic Green’s Tensor”
I ”Electromagnetic Scattering in
Micro- and Nanostructured
Materials”
1. INTRODUCTION
eigenmodes can be determined using Fourier analysis or by
direct analytic determination of the eigenmodes. In a homoQuantum emitters embedded in optical microcavities, such as
geneous medium, the eigenmodes are indeed plane waves,
photonic crystals and micropillars, constitute an important
but in more advanced structures, such as the micropillar to
platform for exploring a range of interesting physical phenombe considered in this article, the complete set of eigenmodes
ena as well as realizing quantum information devices. This
includes a finite number of guided modes and a continuum of
includes a broad range of interesting features, including
radiation modes.
enhanced light–matter interactions, quantum entanglement,
A common issue for most of the suggested simulation techand single-photon emission [1]. The latter is intimately related
niques is that practical implementation enforces a finite-sized
to the Purcell effect that describes the enhancement or inhibisolution domain. In its simplest form, this implies the contion of the spontaneous emission rate (SER) of an emitter
straint that the field must vanish at the boundaries of the
when positioned inside an optical cavity [2]. Enhancement
solution domain, which inevitably produces parasitic reflecof the SER is vital in the development of efficient and reliable
tions at these metal-like boundaries [8]. As a means to reduce
single-photon sources in the scope of quantum information
these effects, absorbing boundaries, the so-called perfectly
-DNRE5RVHQNUDQW]GH/DVVRQ3KLOLS7U¡VW.ULVWHQVHQDQG-HVSHU0¡UN
technology
[3].
matched layers (PMLs), were introduced [9]. The use of anaTo obtain
the desired functionality in such devices, ac1996
J. Opt. Soc. Am. B / Vol. 30, No. 7 / July 2013
Lasson et al.
lytic eigenmodes in combination with PML wasdeinvestigated
curate numerical modeling of the electromagnetic field is cruby Bienstman and Baets [7,8], and numerically stable results
&LWDWLRQ$,3&RQI3URFGRL
cial. Numerical methods based on spatial discretization such
using this technique were demonstrated [10]. However, the
9LHZRQOLQHKWWSG[GRLRUJ
as finite-difference
time-domain (FDTD) [4] and the finite eleuse of PMLs requires a set of parameters to be determined
ment method (FEM) [5] are popular; however, the necessity of
9LHZ7DEOHRI&RQWHQWVKWWSSURFHHGLQJVDLSRUJGEWGEWMVS".(<
$3&3&69ROXPH
,VVXH
that define the boundary
region, and convergence
of theelecdiscretizing the entire computational domain leads to huge
tric field upon adjustment of these parameters, toward that of
memory 3XEOLVKHGE\WKH$PHULFDQ,QVWLWXWHRI3K\VLFV
requirements for realistic device geometries. On the
an open geometry, is not guaranteed [11]. Thus, even PML
other hand, modal methods such as the Fourier modal method
does not fully eliminate the parasitic perturbations of the
[6] and eigenmode expansion technique (EET) [7] are less
fields [12], and this inherent deficiency of finite-sized simulamemory 5HODWHG$UWLFOHV
demanding, and in addition the approaches themtion domains motivates the introduction of an open geometry
selves provide
a better insight into governing physical
8OWUDVPDOOUDGLDOSRODUL]HUDUUD\EDVHGRQSDWWHUQHGSODVPRQLFQDQRVOLWV
of infinite extent.
mechanisms
of interest. In this article, we formulate and de$SSO3K\V/HWW
The open geometry has been treated by expansion of the
monstrate
the application of the EET to a geometry without
eigenmodes on a Fourier–Bessel basis [13]. On the other hand,
/RFDOL]HGVXUIDFHSODVPRQUHVRQDQFHVLQKLJKO\GRSHGVHPLFRQGXFWRUVQDQRVWUXFWXUHV
outer boundary
conditions,
the so-called
open de
geometry
thatJesper expansions
Jakob
Rosenkrantz
Lasson,*
Mørk, and on
Philip
Trøst Kristensen
$SSO3K\V/HWW
analytical
eigenmodes are applied in [14],
is commonly
encountered in optics.
where
an openofgeometry
radiation
a waveguide
into
DTU Fotonik, Department of Photonics Engineering, Technical
University
Denmark,with
Ørsteds
Plads,from
Building
343,
3RODUL]DWLRQGHSHQGDQWVFDWWHULQJDVDWRROWRUHWULHYHWKHEXULHGSKDVHLQIRUPDWLRQRIVXUIDFHSODVPRQSRODULWRQV
In modal
methods, or rigorous coupled-wave Kongens
analysis,Lyngby
the DK-2800,
free space
is treated. There, an integral equation for the field
Denmark
$SSO3K\V/HWW
electromagnetic fields are expanded on a complete
and ortho-author:atjakob@jakobrdl.dk
*Corresponding
the interface between the waveguide and free space is
&RQWUROODEOHSODVPRQLFDQWHQQDVZLWKXOWUDQDUURZEDQGZLGWKEDVHGRQVLOYHUQDQRIODJV
normal set
of basis functions. The set of basis functions can be
derived and solved by a perturbative approach. First- and
$SSO3K\V/HWW
chosen as
the set of eigenmodes supported by the optical ensolutions
presented, but the approximate
Received March 12, 2013; revised Aprilsecond-order
23, 2013; accepted
April are
24, 2013;
vironment
under consideration, giving
riseMay
to the
5HVRQDQWSODVPRQLFHIIHFWVLQSHULRGLFJUDSKHQHDQWLGRWDUUD\V
solution
procedure
posted
21,EET.
2013 These
(Doc. ID 186855);
published
June in
27,practice
2013 limits the index contrasts that
0XOWLSOHVFDWWHULQJIRUPDOLVPEH\RQGWKHTXDVLVWDWLFDSSUR[LPDWLRQ
$QDO\]LQJUHVRQDQFHVLQSODVPRQLFFKDLQV
Three-dimensional integral equation approach to light
scattering, extinction cross sections, local density
of states, and quasi-normal modes
$SSO3K\V/HWW
We present a numerical formalism for solving the Lippmann–Schwinger equation for the electric field in three
dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background
1084-7529/12/071237-10$15.00/0
© of
2012
Optical scatterers
Society of in
America
media, and we develop
it in detail for the specific case
spherical
a homogeneous background
important quantities may readily be calculated with
the formalism. These quantities include the extinction cross section, the total Green’s tensor, the projected local
$GGLWLRQDOLQIRUPDWLRQRQ$,3&RQI3URF
medium. In addition, we show how several physically
-RXUQDO+RPHSDJHKWWSSURFHHGLQJVDLSRUJ
density of states, and the Purcell factor as well as the quasi-normal modes of leaky resonators with the associated
resonance frequencies and quality factors. We demonstrate the calculations for the well-known plasmonic dimer
-RXUQDO,QIRUPDWLRQKWWSSURFHHGLQJVDLSRUJDERXWDERXWBWKHBSURFHHGLQJV
consisting of two silver nanoparticles and thus illustrate the versatility of the formalism for use in modeling of
advanced nanophotonic devices. © 2013 Optical Society of America
7RSGRZQORDGVKWWSSURFHHGLQJVDLSRUJGEWPRVWBGRZQORDGHGMVS".(<
$3&3&6
2/5
My M.Sc. Education
Courses:
I Methods of Mathematical Physics
(UMD)
I Introduction to Quantum Mechanics
I (UMD)
I Continuum Mechanics (UMD)
I Nanophotonics (DTU)
I TEMO (DTU)
I Summer school (Grenoble)
I Statistical Physics (DTU)
I Transport in Nanostructures (DTU)
Projects:
I ”Modeling of Spontaneous Emission
Rate in Micropillars Using an Open
Geometry Formalism”
Rosenkrantz de Lasson et al.
Vol. 29, No. 7 / July 2012 / J. Opt. Soc. Am. A
1237
Modeling of cavities using the analytic modal method
and an open geometry formalism
Jakob Rosenkrantz de Lasson,† Thomas Christensen,† Jesper Mørk, and Niels Gregersen*
DTU Fotonik, Department of Photonics Engineering, Technical University of Denmark, Ørsteds Plads,
Building 343, DK-2800 Kongens Lyngby, Denmark
*Corresponding author: ngre@fotonik.dtu.dk
Received September 27, 2011; revised March 12, 2012; accepted March 12, 2012;
posted March 15, 2012 (Doc. ID 155363); published June 6, 2012
We present an eigenmode expansion technique for calculating the properties of a dipole emitter inside a micropillar. We consider a solution domain of infinite extent, implying no outer boundary conditions for the electric
field, and expand the field on analytic eigenmodes. In contrast to finite-sized simulation domains, this avoids the
issue of parasitic reflections from artificial boundaries. We compute the Purcell factor in a two-dimensional
micropillar and explore two discretization techniques for the continuous radiation modes. Specifically, an equidistant and a nonequidistant discretization are employed, and while both converge, only the nonequidistant discretization exhibits uniform convergence. These results demonstrate that the method leads to more accurate
results than existing simulation techniques and constitutes a promising basis for further work. © 2012 Optical
Society of America
OCIS codes: 000.3860, 050.1755, 230.5750, 230.7370, 290.0290.
I ”Volume Integral Equations and the
Electromagnetic Green’s Tensor”
I ”Electromagnetic Scattering in
Micro- and Nanostructured
Materials”
1. INTRODUCTION
eigenmodes can be determined using Fourier analysis or by
direct analytic determination of the eigenmodes. In a homoQuantum emitters embedded in optical microcavities, such as
geneous medium, the eigenmodes are indeed plane waves,
photonic crystals and micropillars, constitute an important
but in more advanced structures, such as the micropillar to
platform for exploring a range of interesting physical phenombe considered in this article, the complete set of eigenmodes
ena as well as realizing quantum information devices. This
includes a finite number of guided modes and a continuum of
includes a broad range of interesting features, including
radiation modes.
enhanced light–matter interactions, quantum entanglement,
A common issue for most of the suggested simulation techand single-photon emission [1]. The latter is intimately related
niques is that practical implementation enforces a finite-sized
to the Purcell effect that describes the enhancement or inhibisolution domain. In its simplest form, this implies the contion of the spontaneous emission rate (SER) of an emitter
straint that the field must vanish at the boundaries of the
when positioned inside an optical cavity [2]. Enhancement
solution domain, which inevitably produces parasitic reflecof the SER is vital in the development of efficient and reliable
tions at these metal-like boundaries [8]. As a means to reduce
single-photon sources in the scope of quantum information
these effects, absorbing boundaries, the so-called perfectly
-DNRE5RVHQNUDQW]GH/DVVRQ3KLOLS7U¡VW.ULVWHQVHQDQG-HVSHU0¡UN
technology
[3].
matched layers (PMLs), were introduced [9]. The use of anaTo obtain
the desired functionality in such devices, ac1996
J. Opt. Soc. Am. B / Vol. 30, No. 7 / July 2013
Lasson et al.
lytic eigenmodes in combination with PML wasdeinvestigated
curate numerical modeling of the electromagnetic field is cruby Bienstman and Baets [7,8], and numerically stable results
&LWDWLRQ$,3&RQI3URFGRL
cial. Numerical methods based on spatial discretization such
using this technique were demonstrated [10]. However, the
9LHZRQOLQHKWWSG[GRLRUJ
as finite-difference
time-domain (FDTD) [4] and the finite eleuse of PMLs requires a set of parameters to be determined
ment method (FEM) [5] are popular; however, the necessity of
9LHZ7DEOHRI&RQWHQWVKWWSSURFHHGLQJVDLSRUJGEWGEWMVS".(<
$3&3&69ROXPH
,VVXH
that define the boundary
region, and convergence
of theelecdiscretizing the entire computational domain leads to huge
tric field upon adjustment of these parameters, toward that of
memory 3XEOLVKHGE\WKH$PHULFDQ,QVWLWXWHRI3K\VLFV
requirements for realistic device geometries. On the
an open geometry, is not guaranteed [11]. Thus, even PML
other hand, modal methods such as the Fourier modal method
does not fully eliminate the parasitic perturbations of the
[6] and eigenmode expansion technique (EET) [7] are less
fields [12], and this inherent deficiency of finite-sized simulamemory 5HODWHG$UWLFOHV
demanding, and in addition the approaches themtion domains motivates the introduction of an open geometry
selves provide
a better insight into governing physical
8OWUDVPDOOUDGLDOSRODUL]HUDUUD\EDVHGRQSDWWHUQHGSODVPRQLFQDQRVOLWV
of infinite extent.
mechanisms
of interest. In this article, we formulate and de$SSO3K\V/HWW
The open geometry has been treated by expansion of the
monstrate
the application of the EET to a geometry without
eigenmodes on a Fourier–Bessel basis [13]. On the other hand,
/RFDOL]HGVXUIDFHSODVPRQUHVRQDQFHVLQKLJKO\GRSHGVHPLFRQGXFWRUVQDQRVWUXFWXUHV
outer boundary
conditions,
the so-called
open de
geometry
thatJesper expansions
Jakob
Rosenkrantz
Lasson,*
Mørk, and on
Philip
Trøst Kristensen
$SSO3K\V/HWW
analytical
eigenmodes are applied in [14],
is commonly
encountered in optics.
where
an openofgeometry
radiation
a waveguide
into
DTU Fotonik, Department of Photonics Engineering, Technical
University
Denmark,with
Ørsteds
Plads,from
Building
343,
3RODUL]DWLRQGHSHQGDQWVFDWWHULQJDVDWRROWRUHWULHYHWKHEXULHGSKDVHLQIRUPDWLRQRIVXUIDFHSODVPRQSRODULWRQV
In modal
methods, or rigorous coupled-wave Kongens
analysis,Lyngby
the DK-2800,
free space
is treated. There, an integral equation for the field
Denmark
$SSO3K\V/HWW
electromagnetic fields are expanded on a complete
and ortho-author:atjakob@jakobrdl.dk
*Corresponding
the interface between the waveguide and free space is
&RQWUROODEOHSODVPRQLFDQWHQQDVZLWKXOWUDQDUURZEDQGZLGWKEDVHGRQVLOYHUQDQRIODJV
normal set
of basis functions. The set of basis functions can be
derived and solved by a perturbative approach. First- and
$SSO3K\V/HWW
chosen as
the set of eigenmodes supported by the optical ensolutions
presented, but the approximate
Received March 12, 2013; revised Aprilsecond-order
23, 2013; accepted
April are
24, 2013;
vironment
under consideration, giving
riseMay
to the
5HVRQDQWSODVPRQLFHIIHFWVLQSHULRGLFJUDSKHQHDQWLGRWDUUD\V
solution
procedure
posted
21,EET.
2013 These
(Doc. ID 186855);
published
June in
27,practice
2013 limits the index contrasts that
0XOWLSOHVFDWWHULQJIRUPDOLVPEH\RQGWKHTXDVLVWDWLFDSSUR[LPDWLRQ
$QDO\]LQJUHVRQDQFHVLQSODVPRQLFFKDLQV
Special courses and M.Sc. project:
Chance to do research and
possibly publish an article.
Three-dimensional integral equation approach to light
scattering, extinction cross sections, local density
of states, and quasi-normal modes
$SSO3K\V/HWW
We present a numerical formalism for solving the Lippmann–Schwinger equation for the electric field in three
dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background
1084-7529/12/071237-10$15.00/0
© of
2012
Optical scatterers
Society of in
America
media, and we develop
it in detail for the specific case
spherical
a homogeneous background
important quantities may readily be calculated with
the formalism. These quantities include the extinction cross section, the total Green’s tensor, the projected local
$GGLWLRQDOLQIRUPDWLRQRQ$,3&RQI3URF
medium. In addition, we show how several physically
-RXUQDO+RPHSDJHKWWSSURFHHGLQJVDLSRUJ
density of states, and the Purcell factor as well as the quasi-normal modes of leaky resonators with the associated
resonance frequencies and quality factors. We demonstrate the calculations for the well-known plasmonic dimer
-RXUQDO,QIRUPDWLRQKWWSSURFHHGLQJVDLSRUJDERXWDERXWBWKHBSURFHHGLQJV
consisting of two silver nanoparticles and thus illustrate the versatility of the formalism for use in modeling of
advanced nanophotonic devices. © 2013 Optical Society of America
7RSGRZQORDGVKWWSSURFHHGLQJVDLSRUJGEWPRVWBGRZQORDGHGMVS".(<
$3&3&6
2/5
My Teaching Assistant Jobs
Courses:
I Advanced Engineering Mathematics
1 (01005)
I Introduction to Numerical
Algorithms (02601)
I Introductory Programming with
Matlab (02631)
I Partial Differential Equations –
Applied Mathematics (01246)
I Thermodynamics and Statistical
Physics (10034)
I Nanophotonics (34051)
3/5
My Teaching Assistant Jobs
Courses:
I Advanced Engineering Mathematics
1 (01005)
I Introduction to Numerical
Algorithms (02601)
I Introductory Programming with
Matlab (02631)
I Partial Differential Equations –
Applied Mathematics (01246)
I Thermodynamics and Statistical
Physics (10034)
I Nanophotonics (34051)
Projects:
I ”Semiconductor Quantum Dots”
I ”Single-Photon Sources for
Quantum Information Processing”
I ”Optical Simulations of Structured
Materials”
3/5
My Teaching Assistant Jobs
Courses:
I Advanced Engineering Mathematics
1 (01005)
I Introduction to Numerical
Algorithms (02601)
I Introductory Programming with
Matlab (02631)
I Partial Differential Equations –
Applied Mathematics (01246)
I Thermodynamics and Statistical
Physics (10034)
I Nanophotonics (34051)
Projects:
I ”Semiconductor Quantum Dots”
I ”Single-Photon Sources for
Quantum Information Processing”
I ”Optical Simulations of Structured
Materials”
Teaching assistant jobs: Optimal
way of reviewing courses and
understanding curricula even
better.
3/5
My Teaching Assistant Jobs
Courses:
I Advanced Engineering Mathematics
1 (01005)
I Introduction to Numerical
Algorithms (02601)
I Introductory Programming with
Matlab (02631)
I Partial Differential Equations –
Applied Mathematics (01246)
I Thermodynamics and Statistical
Physics (10034)
I Nanophotonics (34051)
Projects:
I ”Semiconductor Quantum Dots”
I ”Single-Photon Sources for
Quantum Information Processing”
I ”Optical Simulations of Structured
Materials”
Teaching assistant jobs: Optimal
way of reviewing courses and
understanding curricula even
better.
And to earn money ^
¨
3/5
What Does a Physicist Do?
4/5
What Does a Physicist Do?
4/5
What Does a Physicist Do?
Physicists develop mathematical models to predict and analyze
complex phenomena.
4/5
What Does a Physicist Do?
Physicists develop mathematical models to predict and analyze
complex phenomena. And understand the limitations of the models.
4/5
More Information
I
Visit my homepage at www.jakobrdl.dk
5/5
More Information
I
Visit my homepage at www.jakobrdl.dk
I
Visit my blog at www.ing.dk/blogs/dtu-indefra
5/5
More Information
I
Visit my homepage at www.jakobrdl.dk
I
Visit my blog at www.ing.dk/blogs/dtu-indefra
I
Visit www.fotonik.dtu.dk/nanotheory
5/5
More Information
I
Visit my homepage at www.jakobrdl.dk
I
Visit my blog at www.ing.dk/blogs/dtu-indefra
I
Visit www.fotonik.dtu.dk/nanotheory
I
Send me an e-mail at jrdl@fotonik.dtu.dk
5/5
More Information
I
Visit my homepage at www.jakobrdl.dk
I
Visit my blog at www.ing.dk/blogs/dtu-indefra
I
Visit www.fotonik.dtu.dk/nanotheory
I
Send me an e-mail at jrdl@fotonik.dtu.dk
...Thank you for your attention! Any questions?
5/5