Scripted PolygonsΒΆ

Learning targets

  • Use scripting to create complicated polygons

  • Transparent boundary conditions in 3D

  • Inhomogeneous exterior domain: waveguides and layered media

This example describes a computational domain with transparent boundary conditions at all sides. In this case, waveguides are included some of which touch the boundary of the computational domain, and which are modeled to extend also to the exterior domain. Further, a substrate is included which also extends to the exterior domain.

The following figure shows an image of parts of the geometry and mesh:

_images/ex3d_scripted_polygons_mesh1.png

The input file layout.jcm is shown below, it is created using the Matlab script run_geometry.m together with the template file layout.ring_resonator.jcmt, also shown below.

Input Files

  • layout.jcm [ASCII]

     1
 2Layout3D {
 3  Name = "TutorialExample3D"
 4  UnitOfLength = 1e-06
 5  MeshOptions {
 6    MaximumSideLength = 4
 7    MinimumMeshAngle = 18
 8  }
 9  Extrusion {
10    Objects {
11      Polygon {
12        Name = "ComputationalDomain"
13        DomainId = 10
14        Priority = -1
15        Points = [-6.375 -7.625 ;7.175 -7.625 ;7.175 7.625 ;-6.375 7.625 ;]
16        Boundary {
17          Class = Transparent
18        }
19      }
20      Polygon {
21        Name = "Waveguide"
22        DomainId = 20
23        Priority = 1
24        MeshOptions {
25          MaximumSideLength = 0.45
26        }
27        Points = [5.550000 -7.625000 ;6.050000 -7.625000 ;6.050000 7.625000 ;5.550000 7.625000 ;]
28      }
29      Polygon {
30        Name = "Ring"
31        DomainId = 20
32        Priority = 1
33        MeshOptions {
34          MaximumSideLength = 0.45
35        }
36        Points = [5.244714 1.485540 ;5.202486 1.954725 ;5.118372 2.418235 ;4.993047 2.872339 ;4.827521 3.313381 ;4.623127 3.737810 ;4.381510 4.142209 ;4.104615 4.523321 ;3.794673 4.878079 ;3.454178 5.203625 ;3.085873 5.497339 ;2.692721 5.756856 ;2.277890 5.980087 ;1.844718 6.165233 ;1.396693 6.310805 ;0.937424 6.415630 ;0.470606 6.478865 ;0.000000 6.500000 ;-0.470606 6.478865 ;-0.937424 6.415630 ;-1.396693 6.310805 ;-1.844718 6.165233 ;-2.277890 5.980087 ;-2.692721 5.756856 ;-3.085873 5.497339 ;-3.454178 5.203625 ;-3.794673 4.878079 ;-4.104615 4.523321 ;-4.381510 4.142209 ;-4.623127 3.737810 ;-4.827521 3.313381 ;-4.993047 2.872339 ;-5.118372 2.418235 ;-5.202486 1.954725 ;-5.244714 1.485540 ;-5.244714 -1.485540 ;-5.202486 -1.954725 ;-5.118372 -2.418235 ;-4.993047 -2.872339 ;-4.827521 -3.313381 ;-4.623127 -3.737810 ;-4.381510 -4.142209 ;-4.104615 -4.523321 ;-3.794673 -4.878079 ;-3.454178 -5.203625 ;-3.085873 -5.497339 ;-2.692721 -5.756856 ;-2.277890 -5.980087 ;-1.844718 -6.165233 ;-1.396693 -6.310805 ;-0.937424 -6.415630 ;-0.470606 -6.478865 ;-0.000000 -6.500000 ;0.470606 -6.478865 ;0.937424 -6.415630 ;1.396693 -6.310805 ;1.844718 -6.165233 ;2.277890 -5.980087 ;2.692721 -5.756856 ;3.085873 -5.497339 ;3.454178 -5.203625 ;3.794673 -4.878079 ;4.104615 -4.523321 ;4.381510 -4.142209 ;4.623127 -3.737810 ;4.827521 -3.313381 ;4.993047 -2.872339 ;5.118372 -2.418235 ;5.202486 -1.954725 ;5.244714 -1.485540 ;]
37      }
38      Polygon {
39        Name = "Ring_Inner_Edge"
40        DomainId = 10
41        Priority = 2
42        MeshOptions {
43          MaximumSideLength = 4
44        }
45        Points = [4.745217 1.463108 ;4.707011 1.887608 ;4.630908 2.306974 ;4.517518 2.717831 ;4.367757 3.116869 ;4.182829 3.500876 ;3.964223 3.866761 ;3.713700 4.211577 ;3.433276 4.532548 ;3.125209 4.827089 ;2.791980 5.092831 ;2.436272 5.327632 ;2.060948 5.529602 ;1.669030 5.697116 ;1.263675 5.828824 ;0.848145 5.923666 ;0.425787 5.980878 ;0.000000 6.000000 ;-0.425787 5.980878 ;-0.848145 5.923666 ;-1.263675 5.828824 ;-1.669030 5.697116 ;-2.060948 5.529602 ;-2.436272 5.327632 ;-2.791980 5.092831 ;-3.125209 4.827089 ;-3.433276 4.532548 ;-3.713700 4.211577 ;-3.964223 3.866761 ;-4.182829 3.500876 ;-4.367757 3.116869 ;-4.517518 2.717831 ;-4.630908 2.306974 ;-4.707011 1.887608 ;-4.745217 1.463108 ;-4.745217 -1.463108 ;-4.707011 -1.887608 ;-4.630908 -2.306974 ;-4.517518 -2.717831 ;-4.367757 -3.116869 ;-4.182829 -3.500876 ;-3.964223 -3.866761 ;-3.713700 -4.211577 ;-3.433276 -4.532548 ;-3.125209 -4.827089 ;-2.791980 -5.092831 ;-2.436272 -5.327632 ;-2.060948 -5.529602 ;-1.669030 -5.697116 ;-1.263675 -5.828824 ;-0.848145 -5.923666 ;-0.425787 -5.980878 ;-0.000000 -6.000000 ;0.425787 -5.980878 ;0.848145 -5.923666 ;1.263675 -5.828824 ;1.669030 -5.697116 ;2.060948 -5.529602 ;2.436272 -5.327632 ;2.791980 -5.092831 ;3.125209 -4.827089 ;3.433276 -4.532548 ;3.713700 -4.211577 ;3.964223 -3.866761 ;4.182829 -3.500876 ;4.367757 -3.116869 ;4.517518 -2.717831 ;4.630908 -2.306974 ;4.707011 -1.887608 ;4.745217 -1.463108 ;]
46      }
47    }
48    MultiLayer {
49      LayerInterface {
50        BoundaryClass = Transparent
51      }
52      Layer {
53        Thickness = 0.225
54        DomainIdMapping = [10 1, 20 1]
55      }
56      LayerInterface {
57        GlobalZ = 0.0
58      }
59      Layer {
60        Thickness = 0.25
61        DomainIdMapping = [10 3, 20 2]
62      }
63      Layer {
64        Thickness = 0.225
65        DomainIdMapping = [10 3, 20 3]
66      }
67      LayerInterface {
68        BoundaryClass = Transparent
69      }
70    }
71  }
72  
73

  • Matlab script run_geometry.m [ASCII]

     1% Interface for 3D ring resonator (stadium shape) geometry setup
 2
 3keys.uol = 1.0e-6; % Unit of Length (in m)
 4
 5% incoming waveguide
 6keys.wg_width = 0.5; % waveguide width
 7keys.wg_height = 0.25; % waveguide height 
 8
 9% resonator parameters
10keys.resonator_radius = 5.0; % ring resonator radius
11keys.resonator_wg_gap = 0.3; % gap between resonator and waveguide
12keys.resonator_coupling_length = 2.5;
13
14% meshing parameter
15keys.wg_segment_length = 0.45; % discretization segment length
16
17jcmwave_geo('.', keys, 'jcmt_pattern', 'ring_resonator', 'show', inf);

  • Layout template file layout.ring_resonator.jcmt [ASCII]

      1<?
  2keys.slc1 = 4; % background
  3keys.slc2 = keys.wg_segment_length; % waveguide
  4keys.offset_xy = keys.wg_segment_length*2.5;
  5keys.offset_z = keys.wg_segment_length/2;
  6
  7% coordinate positions from layout parameters
  8x1 = - keys.resonator_radius - keys.wg_width/2 - keys.offset_xy;
  9x2 = keys.resonator_radius + keys.wg_width/2 + keys.resonator_wg_gap;
 10x3 = x2 + keys.wg_width;
 11x4 = x3 + keys.offset_xy;
 12
 13y1 = -(keys.resonator_radius + keys.wg_width/2 + keys.offset_xy + keys.resonator_coupling_length/2);
 14y2 = -y1;
 15
 16keys.points_cd = [x1 y1; x4 y1; x4 y2; x1 y2];
 17keys.points_wg = [x2 y1; x3 y1; x3 y2; x2 y2];
 18
 19% define circles
 20n = ceil(2*pi*keys.resonator_radius/keys.wg_segment_length);
 21points_ring_outer = (keys.resonator_radius + keys.wg_width/2)*exp(1i*[0.5:n]*2*pi/n);
 22points_ring_inner = (keys.resonator_radius - keys.wg_width/2)*exp(1i*[0.5:n]*2*pi/n);
 23
 24% insert linear segments to the circles (making them 
 25points_ring_outer(1:end/2) = points_ring_outer(1:end/2) + keys.resonator_coupling_length*0.5i;
 26points_ring_inner(1:end/2) = points_ring_inner(1:end/2) + keys.resonator_coupling_length*0.5i;
 27points_ring_outer(end/2+1:end) = points_ring_outer(end/2+1:end) - keys.resonator_coupling_length*0.5i;
 28points_ring_inner(end/2+1:end) = points_ring_inner(end/2+1:end) - keys.resonator_coupling_length*0.5i;
 29
 30keys.points_ring_outer = [real(points_ring_outer); imag(points_ring_outer)].';
 31keys.points_ring_inner = [real(points_ring_inner); imag(points_ring_inner)].';
 32
 33?>
 34Layout3D {
 35  Name = "TutorialExample3D"
 36  UnitOfLength = %(uol)e
 37  MeshOptions { 
 38    MaximumSideLength = %(slc1)e
 39    MinimumMeshAngle = 18
 40  }
 41  BoundaryConditions {
 42    Boundary {
 43      Direction = All 
 44      Class = Transparent 
 45    }
 46  }
 47  Extrusion {
 48    Objects {
 49      Polygon { 
 50        Name = "ComputationalDomain" 
 51        DomainId = 10 
 52        Priority = -1 
 53        Points = %(points_cd)3f        
 54      }
 55      Polygon { 
 56        Name = "Waveguide" 
 57        DomainId = 20 
 58        Priority = 1
 59        MeshOptions {
 60          MaximumSideLength = %(slc2)e          
 61        }
 62        Points = %(points_wg)6f
 63      }
 64      Polygon { 
 65        Name = "Ring" 
 66        DomainId = 20 
 67        Priority = 1
 68        MeshOptions {
 69          MaximumSideLength = %(slc2)e          
 70        }
 71        Points = %(points_ring_outer)6f
 72      }
 73      Polygon { 
 74        Name = "Ring_Inner_Edge"
 75        DomainId = 10
 76        Priority = 2
 77        MeshOptions {
 78          MaximumSideLength = %(slc1)e          
 79        }
 80        Points = %(points_ring_inner)6f
 81      }
 82    }
 83    MultiLayer {
 84
 85      Layer { 
 86        Thickness = %(offset_z)e
 87        DomainIdMapping = [10 1, 20 1]
 88      }
 89      LayerInterface {
 90        GlobalZ = 0.0
 91      }
 92      Layer { 
 93        Thickness = %(wg_height)e
 94        DomainIdMapping = [10 3, 20 2]
 95      }
 96      Layer { 
 97        Thickness = %(offset_z)e
 98        DomainIdMapping = [10 3, 20 3]
 99      }
100    }
101  }
102}