Simulation of near-field plasmonic interactions
with a local approximation order DGTD method
Results.DGTDPloc History
Hide minor edits - Show changes to output
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%center% Modulus of '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method. Field values have been scaled to [0 , 10]
to:
%center% Modulus of '''E''' field map in the bowtie antenna at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method. Field values have been scaled to [0 , 10]
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(:cellnr align='center':) %width=400px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie_dt1.png
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Several strategies can be considered to address this performance issue. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually combine both ''h''- and ''p''- adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
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Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
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%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
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As a second application, we consider the computation of the extinction cross section of a metallic bowtie nanoantenna. These structures are actively studied for the very strong field enhancement they provide between the tips of the two triangular nanoparticles, which is known to be inversely proportionnal to the size of the gap. Hence, bowtie nanoantennas are good candidates for surface-enhanced Raman spectroscopy (SERS) applications. Recent advances in lithography techniques allowed the creation of structures with gaps as small as 3 nm, while the typical size of the full structure can get close to 200 nm. Additionally, realistic geometries of such antennas include small roundings at the edges and tips, whose typical size is between a few to a few tens of nanometers. In the present case, we consider a pair of 10 nm thick, equilateral prisms of edge length 100 nm, with a spacing gap of 3 nm. The rounding radius is 2 nm, and is uniform for all edges and tips. The material considered is gold, described by a Drude model.
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As a second application, we consider the computation of the extinction cross section of a metallic bowtie nanoantenna. These structures are actively studied for the very strong field enhancement they provide between the tips of the two triangular nanoparticles, which is known to be inversely proportionnal to the size of the gap. Hence, bowtie nanoantennas are good candidates for surface-enhanced Raman spectroscopy (SERS) applications. Recent advances in lithography techniques allowed the creation of structures with gaps as small as 3 nm, while the typical size of the full structure can get close to 200 nm. Additionally, realistic geometries of such antennas include small roundings at the edges and tips, whose typical size is between a few to a few tens of nanometers. In the present case, we consider a pair of 10 nm thick, equilateral prisms of edge length 100 nm, with a spacing gap of 3 nm. The rounding radius is 2 nm, and is uniform for all edges and tips. The material considered is gold, described by a Drude model.
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%lfloat text-align=center width=350px% http://www-sop.inria.fr/nachos/pics/result/p_loc/bowtie3.png | Mesh setup for a bowtie nanoantenna. The gray cells correspond to the nanoantenna, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is close to 275.
to:
%lfloat text-align=center width=350px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie3.png | Mesh setup for a bowtie nanoantenna. The gray cells correspond to the nanoantenna, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is close to 275.
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%lfloat text-align=center width=350px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie3.png |
Mesh setup for a bowtie nanoantenna. The gray cells correspond to the nanoantenna, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is close to 275.
Mesh setup for a bowtie nanoantenna. The gray cells correspond to the nanoantenna, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is close to 275.
to:
%lfloat text-align=center width=350px% http://www-sop.inria.fr/nachos/pics/result/p_loc/bowtie3.png | Mesh setup for a bowtie nanoantenna. The gray cells correspond to the nanoantenna, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is close to 275.
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As a second application, we consider the computation of the extinction cross section of a metallic bowtie nanoantenna. These structures are actively studied for the very strong field enhancement they provide between the tips of the two triangular nanoparticles, which is known to be inversely proportionnal to the size of the gap. Hence, bowtie nanoantennas are good candidates for surface-enhanced Raman spectroscopy (SERS) applications. Recent advances in lithography techniques allowed the creation of structures with gaps as small as 3 nm, while the typical size of the full structure can get close to 200 nm. Additionally, realistic geometries of such antennas include small roundings at the edges and tips, whose typical size is between a few to a few tens of nanometers. In the present case, we consider a pair of 10 nm thick, equilateral prisms of edge length 100 nm, with a spacing gap of 3 nm. The rounding radius is 2 nm, and is uniform for all edges and tips. The material considered is gold, described by a Drude model.
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%center% E'_y_' field map in the nanolens device at t=10 fs
to:
%center% E'_y_' field map in the nanolens device at t=10 fs. Field values have been scaled to [-15 , 15]
Added lines 51-54:
As a second application, we consider the computation of the extinction cross section of a metallic bowtie nanoantenna. These structures are actively studied for the very strong field enhancement they provide between the tips of the two triangular nanoparticles, which is known to be inversely proportionnal to the size of the gap. Hence, bowtie nanoantennas are good candidates for surface-enhanced Raman spectroscopy (SERS) applications. Recent advances in lithography techniques allowed the creation of structures with gaps as small as 3 nm, while the typical size of the full structure can get close to 200 nm. Additionally, realistic geometries of such antennas include small roundings at the edges and tips, whose typical size is between a few to a few tens of nanometers. In the present case, we consider a pair of 10 nm thick, equilateral prisms of edge length 100 nm, with a spacing gap of 3 nm. The rounding radius is 2 nm, and is uniform for all edges and tips. The material considered is gold, described by a Drude model.
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%center% Modulus of '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method. Field values have been scaled to [0 , 10]
to:
%center% Modulus of '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method. Field values have been scaled to [0 , 10]
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(:table border='0' width='100%' align='center' cellspacing='1px':)
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%center% ''' Left figure''' : polynomial order repartition for the bowtie antenna mesh with respect to time-step for the P'_1_'P'_3_' case. '''Right figure''' : extinction cross section of the bowtie nanoantenna obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 2 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.0
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%center% ''' Left figure''' : polynomial order repartition for the bowtie antenna mesh with respect to time-step for the P'_1_'P'_3_' case. '''Right figure''' : extinction cross section of the bowtie nanoantenna obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 2 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.0
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%center% Modulus of '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method. Field values have been scaled to [0 , 10]
(:cellnr align='center':) %width=400px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie_range.png
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%center% Modulus of '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method. Field values have been scaled to [0 , 10]
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%center% '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method
(:cell align='center':) %width=380px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie_visu_P1P3_top.png
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%center% '''E''' field map in the nanolens device at t=12.3 fs, obtained with a DGTD-P'_1_'P'_3_' method
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%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie3.png |
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%lfloat text-align=center width=350px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie3.png |
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%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/bowtie_mesh.png |
Mesh setup for a bowtie nanoantenna. The gray cells correspond to the nanoantenna, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is close to 275.
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%center% ''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case
%center% '''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
to:
%center% ''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. '''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
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%center% ''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. The red elements correspond to P'_1_' approximation, the green ones to P'_2_', and the gray ones to P'_3_'
to:
%center% ''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case
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''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. The red elements correspond to P'_1_' approximation, the green ones to P'_2_', and the gray ones to P'_3_'.
'''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
'''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
to:
%center% ''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. The red elements correspond to P'_1_' approximation, the green ones to P'_2_', and the gray ones to P'_3_'
%center% '''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
%center% '''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
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''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. The red elements correspond to
P'_1_' approximation, the green ones to P'_2_', and the gray ones to P'_3_'.
P'_1_'
to:
''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. The red elements correspond to P'_1_' approximation, the green ones to P'_2_', and the gray ones to P'_3_'.
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''' Left figure''' : polynomial order repartition for the nanolens mesh with respect to time-step for the P'_1_'P'_3_' case. The red elements correspond to
P'_1_' approximation, the green ones to P'_2_', and the gray ones to P'_3_'.
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''Right figure'': field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
to:
'''Right figure''' : field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
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Right figure: field enhancement in the vicinity of the smallest sphere of a self-similar nanolens} obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
to:
''Right figure'': field enhancement in the vicinity of the smallest sphere of a self-similar nanolens obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
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Right figure: field enhancement in the vicinity of the smallest sphere of a self-similar nanolens} obtained with DGTD-P'_1_', DGTD-P'_3_' and DGTD-P'_1_'P'_3_' methods. Less than 1 % of relative error is observed between DGTD-P'_3_' and DGTD-P'_1_'P'_3_' computations, for a speedup factor of 2.6
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(:cellnr align='center':) %width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1.png
(:cell align='center':) %width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P3.png
(:cell align='center':) %width=
to:
(:cellnr align='center':) %width=280px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1.png
(:cell align='center':) %width=280px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P3.png
(:cell align='center':) %width=280px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P3.png
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(:cellnr align='center':) %width=400px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1P3.png
to:
(:cellnr align='center':) %width=280px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1P3.png
Changed line 32 from:
%center%
to:
%center% E'_y_' field map in the nanolens device at t=10 fs
Changed lines 22-23 from:
(:cellnr align='center':) %width=400px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1.png
(:cellnr align='center':) DGTD method with affine elements
(:
to:
(:cellnr align='center':) %width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1.png
(:cell align='center':) %width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P3.png
(:cellnr align='center':) DGTD-P'_1_' method
(:cell align='center':) DGTD-P'_3_' method
(:tableend:)
(:table border='0' width='100%' align='center' cellspacing='1px':)
(:cell align='center':) %width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P3.png
(:cellnr align='center':) DGTD-P'_1_' method
(:cell align='center':) DGTD-P'_3_' method
(:tableend:)
(:table border='0' width='100%' align='center' cellspacing='1px':)
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(:cellnr align='center':) DGTD method with curvilinear elements
to:
(:cellnr align='center':) DGTD-P'_1_'P'_3_' method
Added lines 18-28:
(:linebreaks:)
(:table border='0' width='100%' align='center' cellspacing='1px':)
(:cellnr align='center':) %width=400px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1.png
(:cellnr align='center':) DGTD method with affine elements
(:cellnr align='center':) %width=400px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_visu_P1P3.png
(:cellnr align='center':) DGTD method with curvilinear elements
(:tableend:)
%center%
Changed lines 12-14 from:
%lfloat text-align=center width=300px http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png |
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.%
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png |
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
(:linebreaks:)
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
(:linebreaks:)
Changed lines 12-13 from:
%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png |
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.\\
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
%lfloat text-align=center width=300px http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png |
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.%
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.%
Changed line 13 from:
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.\\
Added lines 16-17:
To overcome the limitation of the diffraction limit, it is possible to exploit the focusing effect provided by coupled surface plasmons. A typical nanolens is composed of a chain of metallic nanoparticles (nanospheres being the most common) of decreasing size, aligned with the polarization direction of the incident field. When the nanospheres are of significantly different sizes, the local field enhancement of the first particle is not perturbed by the second one because of its small relative size. As a result, the locally enhanced field of the first particle acts as an incident field for the second particle, resulting in a second enhancement, and so on. Eventually, the strongest enhancement is obtained in the gap between the two smaller particles.
Changed lines 12-13 from:
to:
%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png |
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
(:linebreaks:)
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
(:linebreaks:)
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%lfloat text-align=right width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
%lfloat text-align=left width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
Changed line 13 from:
%lfloat text-align=center width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
%lfloat text-align=right width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
Changed line 13 from:
%lfloat text-align=center %width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
%lfloat text-align=center width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
Changed lines 12-16 from:
(:cellnr align='center':) %width=320px% http:
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
to:
%lfloat text-align=center %width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png | Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
Added lines 9-16:
(:linebreaks:)
(:table border='0' width='90%' align='center' cellspacing='1px':)
(:cellnr align='center':) %width=320px% http://www-sop.inria.fr/nachos/pics/results/p_loc/nanolens_mesh.png
(:tableend:)
Mesh setup for a metallic nanolens. The gray cells correspond to the metallic spheres, the blue cells to vacuum, while the red cells constitute the PML region. For this mesh, the ratio between the largest and the smallest edge length of the tetrahedral mesh is above 400.
Changed line 8 from:
To overcome this limitation, several strategies can be considered. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually combine both ''h''- and ''p''- adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
to:
To overcome this limitation, several strategies can be considered. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually combine both ''h''- and ''p''- adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
Changed lines 8-9 from:
To overcome this limitation, several strategies can be considered. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually
combine both ''h'' and ''p''- adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
to:
To overcome this limitation, several strategies can be considered. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually combine both ''h''- and ''p''- adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
Changed line 9 from:
combine both ''h''- and ''p''-adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
to:
combine both ''h'' and ''p''- adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
Changed lines 6-15 from:
In most of the existing works on the development of high order DGTD
methods for the numerical modeling of light/matter interactions on the
nanoscale, the formulation of the method is derived assuming a uniform
distribution of the polynomial order to the cells of the underlying
mesh. However, in the case of a mesh showing large variations in cell
size, the time step imposed by the smallest cells can be a serious
hindrance when trying to exploit high approximation orders. Indeed, a
potentially large part of the CPU time is spent in the update of the
physical field inside small cells where high polynomial orders might
not be essential, while they are necessary in the larger cells.
nanoscale, the formulation of the method is derived assuming a uniform
mesh. However, in the case of a mesh showing large variations in cell
size, the time step imposed by the smallest cells can be a serious
to:
In most of the existing works on the development of high order DGTD methods for the numerical modeling of light/matter interactions on the nanoscale, the formulation of the method is derived assuming a uniform distribution of the polynomial order to the cells of the underlying mesh. However, in the case of a mesh showing large variations in cell size, the time step imposed by the smallest cells can be a serious hindrance when trying to exploit high approximation orders. Indeed, a potentially large part of the CPU time is spent in the update of the physical field inside small cells where high polynomial orders might not be essential, while they are necessary in the larger cells.
To overcome this limitation, several strategies can be considered. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually
combine both ''h''- and ''p''-adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
To overcome this limitation, several strategies can be considered. The strategy discussed here relies on the use of non-uniform distribution of the polynomial order in the framework of a global time step DGDT method. By imposing low orders in small cells and high orders in large cells, it is possible to significantly alleviate both the global number of degrees of freedom and the time step restriction with a minimal impact on the method accuracy. Strategies exploiting locally adaptive (LA) formulations usually
combine both ''h''- and ''p''-adaptivity in order to concentrate the computational effort in the areas of high field variations. Here, the adopted point of view is quite different: starting from a given mesh and an uniform distribution of the polynomial order ''k'', the LA strategy exploits all the polynomial orders ''p'', with ''p'' lesser or equal than ''k'' to obtain a solution of similar accuracy with a reduced computational cost.
Changed lines 4-15 from:
(:linebreaks:)
to:
(:linebreaks:)
In most of the existing works on the development of high order DGTD
methods for the numerical modeling of light/matter interactions on the
nanoscale, the formulation of the method is derived assuming a uniform
distribution of the polynomial order to the cells of the underlying
mesh. However, in the case of a mesh showing large variations in cell
size, the time step imposed by the smallest cells can be a serious
hindrance when trying to exploit high approximation orders. Indeed, a
potentially large part of the CPU time is spent in the update of the
physical field inside small cells where high polynomial orders might
not be essential, while they are necessary in the larger cells.
In most of the existing works on the development of high order DGTD
methods for the numerical modeling of light/matter interactions on the
nanoscale, the formulation of the method is derived assuming a uniform
distribution of the polynomial order to the cells of the underlying
mesh. However, in the case of a mesh showing large variations in cell
size, the time step imposed by the smallest cells can be a serious
hindrance when trying to exploit high approximation orders. Indeed, a
potentially large part of the CPU time is spent in the update of the
physical field inside small cells where high polynomial orders might
not be essential, while they are necessary in the larger cells.
Changed lines 1-2 from:
(:title Simulation of near-field plasmonic interactions\\
to:
(:title Simulation of near-field plasmonic interactions\\\
Added lines 1-4:
(:title Simulation of near-field plasmonic interactions\\
with a local approximation order DGTD method:)
(:linebreaks:)
with a local approximation order DGTD method:)
(:linebreaks:)