Home/Products/Ansys Lumerical/Lumerical FDTD/STACK

ANSYS LUMERICAL / FDTD

Lumerical STACK: designing multilayer reflectance and transmittance

Obtains the reflectance and transmittance of a flat multilayer stack by the transfer matrix method. Even with many layers the calculation finishes instantly, so layer thicknesses can be optimized interactively.

Request a demo Request a quote

Transfer matrix methodMultilayer stacksThin-film design

Schematic of a STACK analysis handling emission inside a multilayer stack, showing the angular distribution of light radiated by a dipole source within a layer and its extraction in the far field

Overview Where it fits Application Inputs and outputs Workflow Related solvers FAQ

Overview

For a flat layer structure, nothing is faster

If the layers are flat and laterally uniform, the fields can be treated analytically in each layer. The transfer matrix method uses that property, obtaining the whole response simply by multiplying the matrices for each layer together.

There is no numerical approximation, and the cost only scales with the number of layers. When designing antireflection coatings, mirrors and bandpass filters, a thickness sweep finishes instantly even with tens of layers.

It cannot be used for structures with a lateral pattern. Those need RCWA or FDTD.

STACK as a method: principles, assumptions and limits →

Dipole orientation in a flat multilayer structure, showing the vertically polarized and in-plane polarized components against the layer stack and each axis

What STACK gives you

What being able to assume a flat layer structure achieves

Analytic solution

No numerical error to worry about, and no convergence check needed.

Instant

Even tens of layers compute in an instant.

Angle and polarization

The response can be obtained directly for each angle of incidence and polarization.

STACK solver analysis example, showing a dipole source inside a layer of a multilayer cylindrical structure alongside the far-field distribution of the light it radiates

Where it fits

Where it fits, and where it does not

For some problems another method solves faster and more accurately. The following is a guide to choosing.

Use STACK when

the layers are flat and laterally uniform
you are designing an antireflection coating or a mirror
you are settling the layer stack of a bandpass filter
you are studying the vertical layer stack of a waveguide
you need to evaluate the dependence on angle of incidence

Consider another method

There is a lateral pattern → RCWA(periodic structures)
Arbitrary geometry → FDTD
Waveguide modes → MODE

STACK compared with FDTD on the same structure. Where the layers are flat and laterally uniform, the two agree.

Typical applications

Where it is used

Reflectance spectrum of a dielectric multilayer stack, showing the wavelength dependence of P- and S-polarized reflectance at 30 degrees incidence

Optical thin films

Antireflection coatings and dielectric multilayer mirrors

$Layer stack of a dielectric multilayer, showing the refractive index of each layer at 550 nm and the groups of layers responsible for the blue, green and red reflection bands$

Color filters and wavelength-selective filters

Wavelength selection by a multilayer stack, reflection and transmission characteristics, and design evaluation of color filters

Layer stack of a circular polarizer, showing the rotation of circular polarization in the upper cover layer, the transmission axes (white arrows) and field directions (red arrows) of the two polarizing layers, and the incident and emerging light through the stack

Antireflection coatings and polarizing films

Suppressing ambient reflection with circular polarizers and multilayer stacks

Vertical cavities

DBR mirror design for VCSELs

Inputs and outputs

What you provide, and what you get

For a given layer stack and illumination conditions, it returns reflectance, transmittance and the fields within the layers.

INPUT

What you need to prepare

Layer stack	The material and thickness of each layer
Material	Wavelength-dependent complex refractive index
Excitation conditions	Wavelength range, angle of incidence, polarization
Substrate	The media on the incident and exit sides

STACK

Transfer matrix method

OUTPUT

What you get

Spectrum	Wavelength dependence of reflectance, transmittance and absorptance
Phase	Phase on reflection and transmission
Angular dependence	Response against angle of incidence
Distribution within layers	Electric field intensity within each layer

Analysis workflow

How it works in practice

Because it is an analytic calculation, convergence is not a concern. What matters instead is judging whether the structure can be approximated as a plane-layered stack at all. Step 01 is where most of your time should go.

Define the layer stack

List the thickness and material (or refractive index) of each layer.

Set the wavelength or frequency

This setting is shared by every analysis that follows.

Choose the analysis type and illumination conditions

Choose between RT (plane-wave reflection and transmission), Field (field distribution within the layers), Dipole (dipole emission within a layer) and Purcell (Purcell factor), then set the angle of incidence or the dipole position.

Compute

This is an analytic calculation by the transfer matrix method. No mesh and no convergence run are required.

Evaluate the results

Extract Rs, Rp, Ts and Tp, the fields within the layers, the far-field radiation pattern and the Purcell factor. Where the structure varies laterally, switch to FDTD or another method.

Related solvers

Related solvers, and how to choose between them

There is no fixed order. Choose according to what you need to check. FDTD and RCWA are solvers included in the same Lumerical FDTD product as STACK, so you can move between them without an additional purchase.

If this applies	Use this	Reason
There is a periodic lateral pattern	RCWA	Diffraction efficiency of a periodic structure needs a dedicated method
It includes arbitrary geometry	FDTD	Structures where flatness does not hold are solved in the time domain
Find the modes of a waveguide	MODE	Used for mode analysis once the layer stack is settled
Designing the substrate beneath a meta-atom	Photonica Metalens	Once the substrate layers are designed, move on to generating the meta-atom library

Frequently asked questions

Questions we are often asked about STACK

Questions we are often asked before adoption.

How many layers can it handle?

There is no practical limit. The cost simply scales with the number of layers, and even tens of layers finish instantly.

Can it handle absorbing materials?

Yes. Specify a complex refractive index.

Can it optimize layer thicknesses?

Yes, although STACK on its own has no dedicated thickness-optimization feature. You compute spectra with a script such as stackrt and search for thicknesses close to the target spectrum using parameter sweeps or optiSLang.

How do I choose between this and RCWA?

STACK if the structure is laterally uniform, RCWA if there is a periodic pattern. RCWA can handle flat layers too, but STACK is simpler and faster.

Japanese-language support and training

We can advise on everything from simulation setup to judging whether a result is sound. Hands-on training is also available.

Support →

Training →

Helpful to know before we talk

Target wavelengths and materials
Device structure and approximate dimensions
The characteristics you want to evaluate, and your target values
Whether you already have simulation data or measurements
Your expected schedule

You do not need to share everything. Whatever you are able to tell us is enough.

Try it on the structure you actually need to solve

The demo uses a structure close to your own. We can also give you an idea of the computational scale and the time it takes.

Request a demo Back to Products