# FDE solver - Simulation object

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- BACKGROUND INDEX: The refractive index of the surrounding, background medium in the simulation region.
- SOLVER TYPE: Can choose either a 1D or 2D mode solver.

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- X, Y, Z: The center position of the simulation region
- X MIN, X MAX: X min, X max position
- Y MIN, Y MAX: Y min, Y max position
- Z MIN, Z MAX: Z min, Z max position
- X SPAN, Y SPAN, Z SPAN: X, Y, Z span of the simulation region

Note: The availability is based on the SOLVER TYPE |

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A uniform mesh is applied to the entire simulation volume, regardless of any material properties. If a mesh override region is used in conjunction, the simulation region may become non-uniformly meshed.

### Mesh definition

There are two options: NUMBER OF MESH CELLS or MAXIMUM MESH STEP

### Number of mesh cells

- DX, DY, DZ: Maximum mesh step

### Maximum mesh step

- MESH CELLS X, MESH CELLS Y, MESH CELLS Z: Number of mesh cells without a mesh override region
- ACTUAL NUMBER OF MESH CELLS USED: The actual number of mesh cells with a mesh override region

### Minimum mesh step settings

- MIN MESH STEP: Sets the minimum mesh step for the entire solver region including the mesh override regions.

### Mesh grading

- grading factor: Determines the maximum rate at which the mesh can be modified. For example, if dx(i+1) = a*dx(i), then 1/(GRADING FACTOR) <= a <= GRADING FACTOR. The grading factor should be between 1 and 2. The default setting is sqrt(2).

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The boundary conditions that are supported by FDTD/MODE Solutions are listed below.

Perfectly matched layer (PML)1 boundaries absorb electromagnetic waves incident upon them. They essentially model open (or reflectionless) boundaries. In FDTD and varFDTD simulation regions, the user can directly specify all the parameters that control their absorption properties including the number of layers. To facilitate the selection of PML parameters, a number of profiles (or predefined sets of parameters) are available under the boundary conditions tab. In most simulation scenarios, the user only needs to choose one of the predefined profiles and fine tune the number of layers. PML boundaries perform best when the surrounding structures extend completely through the boundary condition region. This will be the default behavior of structures whether or not they were drawn to end inside or outside the PML region.

1 J. P. Berenger, Perfectly Matched Layer (PML) for Computational Electromagnetics. Morgan & Claypool Publishers, 2007.

Metal boundary conditions are used to specify boundaries that behave as a Perfect Electric Conductor (PEC). The component of the electric field parallel to a metal (PEC) boundary is zero; the component of the magnetic field H perpendicular to a metal (PEC) boundary is also zero. Metal boundaries are perfectly reflecting, allowing no energy to escape the simulation volume along that boundary. In the FDE solver, metal BC is the default setting .

Perfect Magnetic Conductor (PMC) boundary conditions are the magnetic equivalent of the metal (PEC) boundaries. The component of the magnetic field H parallel to a PMC boundary is zero; the component of the electric field perpendicular to a PMC boundary is also zero.

Periodic BC should be used when both the structures and EM fields are periodic. Periodic boundary conditions can be used in one or more directions (i.e. only in the x direction) to simulate a structure which is periodic in one direction but not necessarily other directions.

Bloch BC should be used when the structures and the EM fields are periodic, but a phase shift exists between each period. Bloch boundary conditions are used in FDTD and propagator simulations predominantly for the following two simulations:

- Launching a plane wave at an angle to a periodic structure – in this situation, accurate reflection and transmission data can be measured at a single frequency point for a given simulation.
- Calculating the bandstructure of a periodic object – in this situation, a broadband pulse is injected via a dipole source into a periodic structure.

Note: if you choose BFAST plane wave source , the Bloch BCs will be automatically overridden and use its built_in boundary conditions.

Symmetric / Anti-SymmetricSymmetric/anti-symmetric boundary conditions are used when the user is interested in a problem that exhibits one or more planes of symmetry; both the structure and source must be symmetric. Symmetric boundaries are mirrors for the electric field, and anti-mirrors for the magnetic field. On the other hand, antisymmetric boundaries are anti-mirrors for the electric field, and mirrors for the magnetic field. Careful consideration must be given to whether symmetric or anti-symmetric boundary conditions are required, given the vector symmetry of the desired solution. For meaningful results, the sources used must have the same symmetry as the boundary conditions. Further information about symmetric and anti-symmetric boundary conditions can be found in Choosing between symmetric and anti-symmetric BCs .

ALLOW SYMMETRY ON ALL BOUNDARIES: Allows symmetric boundary conditions with periodic structures (this option is not available in the boundary condition tab of mode sources and mode expansion monitors).

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### Mesh Refinement:

Mesh refinement can give sub-cell accuracy for a simulation. See the Mesh refinement options page for more information.

### FIT MATERIALS WITH MULTI-COEFFICIENT MODEL

(For sampled material data) When MODE solves for modes, it uses material data that is obtained from a linear interpolation from the closest data points. This means that when a frequency sweep is run, the material data used can be discontinuous in time. This is especially problematic for properties such as dispersion which depends on a second derivative of the refractive index as a function of wavelength.

If you check this option, you can choose to fit two types of materials with a multi-coefficient model. Here are the options that are available when the checkbox is checked:

- Fit sampled materials : By default this is checked. Sampled material data will be fit with a smooth multi-coefficient material model.
- Fit analytic materials: Check this option to fit a multi-coefficient model to the analytic material data. The only reason to fit analytic models with a multi-coefficient model is to compare MODE results with FDTD. FDTD simulations must fit a multi-coefficient model to the analytic data in order to run simulations, but the multi-coefficient model may not be able to fit the analytic model perfectly.
- Wavelength min/max or center/span : Set bandwidth over which to apply the fit.

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### CALCULATE CHARACTERISTIC IMPEDANCE

By default, this option is disabled. When enabled, the Z0 characteristic impedance result will be calculated for each of the modes which are found using the specified integration region settings. For more information about the characteristic impedance calculation, see the Power and impedance section of the FDE analysis window.

When the CALCULATE CHARACTERISTIC IMPEDANCE box is checked, the following settings are available:

- INTEGRATION SHAPE: Options include circular, and rectangular.
- X1, X2, Y1, Y2 (or Z1, Z2) (valid for rectangular integration): defines the vertices of a rectangle over which the characteristic impedance Z0 is integrated
- CENTER X, CENTER Y (or CENTER Z), RADIUS (valid for circular integration): defines the center and radius of a circle over which the characteristic impedance is integrated

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WARNING: This tab includes options which should only be changed if you are quite familiar with the meshing algorithm and techniques used . |

### Mesh settings

- FORCE SYMMETRIC X, Y, Z MESH: This will force a symmetric mesh about the x, y or z axis. When this option is enabled, the meshing algorithm ONLY considers objects in the positive half of the simulation region. The mesh in the negative half is simply a copy of the positive half mesh. All physical structures and mesh override regions in the negative half will not be considered by the meshing algorithm. This option also forces a mesh point at the center of the simulation region. Forcing a symmetric mesh ensures that the mesh does not change when going from a simulation with symmetry to a simulation without symmetry.

### PML settings

- PML KAPPA: The normalized imaginary electric and magnetic conductivity used in the PML boundaries.
- PML SIGMA: The maximum normalized electric and magnetic conductivity used in the PML boundaries.
- PML LAYERS: The number of cells which are used for PML boundary conditions. Increasing this number will reduce the back-reflection arising from the PML boundaries but will also increase time and memory requirements for simulations. Defaults to a setting of 12.
- PML POLYNOMIAL: The polynomial power which determines how rapidly the electric and magnetic conductivity increases as radiation propagates at normal incidence into the PML. The default setting of 3 denotes a cubic increase of electric and magnetic conductivity with increasing depth into the PML.
- SET DEFAULTS: This button resets the parameters of the advanced settings tab to the default settings.

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