Solver and analysis
- FDM
Calculate the waveguide modes using the finite difference method. It automatically runs
EM_mesh
as needed (generatingx
,y
,x_edge
,y_edge
,permittivity
, andpermeability
). After solving the mode, the effective index (effective_index
), mode propagation loss (loss_dB_per_m
), and field components (Fx
,Fy
,Ex
,Ey
,Ez
,Hx
,Hy
,Hz
,Sx
,Sy
,Sz
) are available, where the fields are normalized to the equation below.\[\frac{1}{2} \mathrm{Re} \iint \left( \vec E \times \vec H^* \right) \! \cdot \! \hat{z} \, \mathrm{d}x \, \mathrm{d}y = 1 \, \mathrm{W}\]It also calculates the TE fraction of each mode (
TE_fraction
) with the following equation, and it saves the indices of the TE and TM modes (TE_indices
andTM_indices
).\[\mathrm{{TE_fraction}} = \frac{\iint \left| \vec E_\mathrm{x} \right|^2 \, \mathrm{d}x \, \mathrm{d}y}{\iint \left| \vec E_\mathrm{x} \right|^2 + \left| \vec E_\mathrm{y} \right|^2 \, \mathrm{d}x \, \mathrm{d}y}\]- Parameters:
simulation_name (str) – simulation name, default: ‘emode’
- confinement
Calculate confinement factor of specified shape.
- Parameters:
shape_list – name (from
shape
) or list of names of shapes to include in confinement or ‘all’ for all shapes, default: ‘all’mode_list (str or list) – desired modes to calculate confinement, ‘all’, ‘TE’, ‘TM’, or a list of the desired mode indices, default: ‘all’
vertices (list (Nx2)) – list of vertices that define a closed polygon, specifying this parameter will override the
shape_list
input, default: Nonesimulation_name (str) – simulation name, default: ‘emode’
- effective_area
Calculate the effective areas for all modes. After running this function, an array called
effective_area
will become available andreport
will display the effective areas.\[A_\mathrm{eff} = \frac{\left( \iint \left| \vec E \right|^2 \, \mathrm{d}x \, \mathrm{d}y \right)^2}{\iint \left| \vec E \right|^4 \, \mathrm{d}x \, \mathrm{d}y}\]- Parameters:
simulation_name (str) – simulation name, default: ‘emode’
- group_index
Calculate the group index for all modes. First,
group_index
runsFDM
(if not already run), then it runsFDM
a second time with 0.01 % longer wavelength to calculate the group index. After running this function, an array calledgroup_index
will become available andreport
will display the group index.- Parameters:
simulation_name (str) – simulation name, default: ‘emode’
- report
Display a simulation report table with information about each mode: mode number; effective index; TE fraction; loss (dB/m); confinement factors (if calculated); effective areas (if calculated).
- Parameters:
save (bool) – whether to save the table to a file or not, default: False
file_name (str) – name of the file to save, default: ‘mode_report’
file_type (str) – file type to save, ‘txt’, ‘latex’, or ‘csv’, default: ‘txt’
simulation_name (str) – simulation name, default: ‘emode’
- label
Adds a label to the data from the current mode set. It can be used to run different simulations and compare the outputs. Also, it is used in conjunction with
calc_overlap
.- Parameters:
label (str) – label added to current mode set, default: ‘0’
simulation_name (str) – simulation name, default: ‘emode’
- overlap
Calculate overlap integral between two modes. The result is saved as
overlap
.Coldren, Larry A., Scott W. Corzine, and Milan L. Mashanovitch, ‘’Diode lasers and photonic integrated circuits,’’ John Wiley & Sons, 2012.
\[\mathrm{overlap} = \frac{4 n_\mathrm{eff,1} n_\mathrm{eff,2}}{(n_\mathrm{eff,1} + n_\mathrm{eff,2})^2} \frac{\left| \iint \vec E_2^* \cdot \vec E_1 \, \mathrm{d}x \, \mathrm{d}y \right|^2}{\iint \left| \vec E_1 \right|^2 \, \mathrm{d}x \, \mathrm{d}y \, \iint \left| \vec E_2 \right|^2 \, \mathrm{d}x \, \mathrm{d}y}\]- Parameters:
label_a (str) – label of first mode set, or a blank string for the current mode set, default: ‘’
mode_a (int) – mode number from the first mode set, default: 0
simulation_name_a (str) – simulation name for the first mode set, default: ‘emode’
label_b (str) – label of second mode set, or a blank string for the current mode set, default: ‘’
mode_b (int) – mode number from the second mode set, default: 0
simulation_name_b (str) – simulation name for the second mode set, default: ‘emode’
- scattering
Calculates the scattering loss from a specified shape and mode using the Volume Current Method [1]. Results are saved in the variables
shape_NAME_scattering_vertical_edges
(total loss from all vertical interfaces),shape_NAME_scattering_horizontal_edges
(total loss from all horizontal interfaces),shape_NAME_scattering_sum
(total scattering loss),shape_NAME_edges
(list of edge points for calculating scattering loss), andshape_NAME_scattering_all_edges
(scattering loss from corresponding edges).[1] T. Barwicz and H. A. Haus, “Three-dimensional analysis of scattering losses due to sidewall roughness in microphotonic waveguides,” J. Lightwave Technol. 23, 2719 (2005).
- Parameters:
shape (str) – name of the shape for calculating the interfacial scattering
mode_list – mode number, list of mode numbers, or ‘all’, default: ‘all’
correlation_length (float or list) – interfacial roughness correlation length, a single value is applied to all interfaces, a list of 2 applies the first value to all vertical interfaces and the second value to all horizontal interfaces, a list the length of edges applies each value to the corresponding edge, default: [100,80]
roughness_rms (float or list) – interfacial roughness standard deviation in nm rms, a single value is applied to all interfaces, a list of 2 applies the first value to all vertical interfaces and the second value to all horizontal interfaces, a list the length of edges applies each value to the corresponding edge, default: [5,0.5]
num_slices (int or str) – number of slices to analyze at the interfacial boundary, must be greater than 0, an automatic function scales the number of slices to have at least 1 per 5 nm, default: ‘auto’
slice_op (str) – operation to apply on interfacial slices to find the field value at the interface, either ‘max’ or ‘mean’, default: ‘max’
simulation_name (str) – simulation name for the second mode set, default: ‘emode’
- plot
Interactive plot for the fields (if available), refractive index, and shapes, or saving a plot. Colorbars are in V/nm for the electric fields, A/nm for the magnetic fields, and W/nm for the Poynting vectors.
- Parameters:
component (str) – field component or index, ‘Ex/y/z’; ‘Hx/y/z’; ‘Sx/y/z’; ‘Index’; ‘Shapes’, default: ‘Ex’
plot_function (str) – plotting function, ‘real’; ‘imag’; ‘abs’; ‘abs^2’; ‘log’, default: ‘real’
mode (int) – mode number, default: 0
aspect_ratio (str or float) – the height:width aspect ratio, ‘norm’ uses the normal aspect ratio of 0.707, ‘real’ uses the real aspect ratio defined by the simulation window, or a float specifies the aspect ratio, default: ‘norm’
index_outline (bool) – setting index outline, default: True
text_display (bool) – setting text display, default: True
mesh_display (bool) – setting mesh display, default: False
window_display (bool) – setting window display, default: False
legend (bool) – setting inclusion of a legend on the index and shape plots, default: True
file_name (str) – if specified, forces the function to save a file with the given parameters and will not display the interactive plot, default: False
file_type (str) – file type for saving a plot, ‘pdf’ or ‘png’, default: ‘pdf’
simulation_name (str) – simulation name, default: ‘emode’
- material_explorer
Interactive material explorer to plot the refractive indices of all available materials. The default wavelength range in the plot corresponds to the recommended range from the material reference listed below the plot. If wavelengths are specified outside this range, the model will be plotted with a dashed line instead of a solid line. User defined materials are also available.
- Parameters:
simulation_name (str) – simulation name, default: ‘emode’
- refractive_index
Returns the refractive index from a material name (retrieved from the internal reference list) or from a custom refractive index value. Optionally, the material’s reference (or citation) may be returned.
- Parameters:
material (str or float) – material name or refractive index value; for AlGaAs, the fraction of Al relative to Ga is included in the material name separated by a comma, for example: “AlGaAs, 0.2” for a Al_{0.2}Ga_{0.8}As.
wavelength (float) – [nm] wavelength, default: 1550
reference (bool) – additionally return the citation for the material, default: False
- Returns:
[n_xx, n_yy, n_zz] or ([n_xx, n_yy, n_zz], reference)
- permeability
Returns the relative permeability from a material name (retrieved from the internal reference list) or from a custom permeability value. Optionally, the material’s reference (or citation) may be returned.
- Parameters:
material (str or float) – material name or refractive index value
wavelength (float) – [nm] wavelength, default: 1550
reference (bool) – additionally return the citation for the material, default: False
- Returns:
[permeability_xx, permeability_yy, permeability_zz] or ([permeability_xx, permeability_yy, permeability_zz], reference)
- mesh
Generalized mesh tool for arbitrary shapes on a rectangular grid. This is called internally by
FDM
if it has not already been called by the user. Generates vertices for each shape (shape_name_vertices
), the actual refractive index for each shape (shape_NAME_refractive_index_value
), arrays to define the edges (x_edge
,y_edge
) and center points (x
,y
) of the mesh grid, and the relative permittivity and permeability matrices (permittivity
andpermeability
).- Parameters:
simulation_name (str) – simulation name, default: ‘emode’