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Guide

Implementation

Supports 1d (Ez, Hy), 2d TE (Hz, Ex, Ey), 2d TM (Ez, Hx, Hy), and 3d. Length and time are in units of wavelength and period. This normalization allows usage of relative permitivity and permeability in equations . Fields including electric, magnetic and current density are simply bundled as a vector of vectors of arrays . Boundary conditions pad the field arrays . PML paddings are multilayered, while All other boundaries add single layers. Paddings are stateful and permanent, increasing the size of field and geometry arrays. Finite differencing happens every update update and are coordinated to implictly implement a staggered Yee's grid .

Sources

We support plane waves and custom (eg modal) sources . A source has a time signal and a spatial profile . Both can be complex valued in which case the real component is taken from product of the two. Set excited current fields and their spatial profiles as keywords . A profile can be constant , a spatial function , or an array . In the case of array, it'll get resized automatically to fit the source 's spatial extent (spanning from lower bounds lb to upper bounds ub).

If a source has fewer nonzero dimensions (from ub - lb) than the simulation domain, its signal will get normalized along its singleton dimensions. For example, all planar sources in 3d will get scaled up by a factor of 1/dx. This way, discretisation would not affect radiated power.

Main.Luminescent.PlaneWave — Type
function PlaneWave(f, dims; fields...)

Constructs plane wave source

Args

  • f: time function
  • dims: eg -1 for wave coming from -x face
  • fields: which fields to excite & their scaling constants (typically a current source, eg Jz=1)
source
Main.Luminescent.Source — Type
function Source(f, c, lb, ub, label=""; fields...)
function Source(f, c, L, label=""; fields...)

Constructs custom source. Can be used to specify uniform or modal sources

Args

  • f: time function
  • c: origin or center of source
  • lb: lower bounds wrt to c
  • ub: upper bounds wrt to c
  • L: source dimensions in [wavelengths]
  • fields: which fields to excite & their scaling constants (typically a current source, eg Jz=1)
source

Boundaries

Unspecified boundaries default to PML

Main.Luminescent.PML — Type

function PML(dims, d=0.25f0, σ=20.0f0)

Constructs perfectly matched layers (PML aka ABC, RBC) boundary of depth `d` wavelengths 
Doesn't need to be explictly declared as all unspecified boundaries default to PML
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Monitors

Main.Luminescent.Monitor — Function
function Monitor(c, L; normal=nothing, label="")
function Monitor(c, lb, ub; normal=nothing, label="")

Constructs monitor which can span a point, line, surface, volume or point cloud monitoring fields or power.

Args

  • c: origin or center of monitor

  • L: physical dimensions of monitor

  • lb: lower bounds wrt to c

  • ub: upper bounds wrt to c

  • normal: flux monitor direction (eg normal to flux surface)

source
Main.Luminescent.field — Function
function field(u, k)
function field(u, k, m)

queries field, optionally at monitor instance m

Args

  • u: state
  • k: symbol or str of Ex, Ey, Ez, Hx, Hy, Hz, |E|, |E|2, |H|, |H|2
  • m
source

Physics

Main.Luminescent.update! — Function
function update!(u, p, t, field_boundvals, source_instances)
function update!(u1, u, p, t, field_boundvals, source_instances)

Updates fields for 3d. Please use update instead of update! when doing AD. Mutating update! Writes new fields either onto old fields or into buffer arrays u1

source
Main.Luminescent.update — Function
function update(u, p, t, field_boundvals, source_instances)

Updates fields for 3d in a manner amenable to AD. See also Mutating update!

source

GPU support

Simply use Flux.gpu to move simulation variables to GPU. This turns Arrays into CUDA arrays which get processed on GPU for both forward and backpropagation passes

Automatic differentiation adjoints

Compatible with Zygote.jl and Flux.jl. Please use update instead of update! when doing AD. See inverse design examples

Generative inverse design

Please contact us for latest scripts. We wrote Jello.jl, an innovative neural model to generate length scale controlled, efficiently paramaterized geometry .

Comparison with other FDTD software

Our focus is on inverse design and topology optimization using adjoints from automatic differentiation. We love a streamlined API backed by a clear, concise and extensible codebase. Attention is paid to speed and malloc but that's not our main concern. Meep is the most popular open source FDTD package owing to its maturity and comprehensive features. It supports AD in certain cases using custom adjoints which we avoid in our package in favor of more flexibility . There are numerous commercial software eg Ansys Lumerical, Comsol and various EDA or SI software. TMK none of them supports AD for inverse design