FDTD Solutions training - Lumerical Inc. | Innovative … · · 2015-08-25FDTD Solutions chooses the simplest dispersive model that can create the correct permittivity ... The analytic

Material Modeling

FDTD Solutions

© 2012 Lumerical Solutions, Inc.

Outline

Dispersive materials in a time domain method

Available material models

: How to choose the correct model

Anisotropic materials

Tips

: Getting better material fits

: Understanding the mesh order

: Nonlinear simulations


Dispersive materials in the time domain

Well-known frequency domain relationship

FDTD is a time domain technique: relationship?

)()()( ED

t

tdtttEtEttD

0

)()()()()(


Material models

Common models

• Dielectric

• PEC (Perfect Electrical Conductor)

• Sampled Material

Nonlinear & Advanced

• Chi2

• Chi2/Chi3

• Kerr nonlinear

• Paramagnetic

• Custom plug-in

These models are implemented via the custom material plug-in framework.

FDTD Solutions supports the following models

Other linear models

• Analytic

• (n,k) Dielectric

• Conductive

• Plasma

• Debye

• Lorentz

• Sellmeier


Material models

Dielectric Material There is no dependence on frequency! Restriction

: n >= 1

This model is used when selecting “<Object defined dielectric>” for the material property of a structure.

constant)( 2 nr


Material models

PEC (Perfect Electrical Conductor)

: Equivalent to a conductor with

0E


Material models – Sampled material

Sampled Material There is experimental (or theoretical, or user’s own) data

for (n,k) as a function of wavelength : From built-in material database : From your own data

FDTD Solutions automatically fits the data over the wavelength range of your sources : Multi-coefficient model : You choose

• The number of coefficients • The fit tolerance

: More coefficients takes more time and memory


Example GaAs, 12 coefficients

Material models – Fitting sampled data

GaAs, 200-800nm



Fitting your (proprietary) data

: Example, representative data of color filters

Red filter



Fitting your (proprietary) data

: Example, representative data of color filters

Blue filter



Metals are not necessarily simple plasma materials

Chromium


Material models – Fitting tips Check the imaginary data to avoid “fake” gain

A fixed wavelength range for fitting can be specified

Imaginary part of permittivity can be overweighted or underweighted


Material models – Default materials

Built in material data with auto-fitting

NOTE:

Default material

properties cannot

be modified (but

copies can).


Sampled data material – Si example

Simple tests: FDTD vs theory for a 50 nm thick span of Si

: Analytic result for R and T can be easily calculated




: multi-coefficient auto-fit to Si




: Calculate the theoretical curve from the fit

: Average difference = 0.001

: Max difference = 0.008


Sampled data material – Si example Simple tests: FDTD vs theory for a 50 nm thick span of Si

: Calculate the theoretical curve from the original material data

: Average difference = 0.0023

: Max difference = 0.031

: Results come from one simulation



Compare Lorentz model with multi-coefficient model

Lorentz model Multi-coefficient model


Material models – More linear models (n,k) Dielectric FDTD Solutions chooses the simplest dispersive model that can create the

correct permittivity (real and imaginary) at the center frequency of your simulation : Perfect for single wavelength simulations

At other frequencies, the value of (n,k) will be different : In reality, physical materials with loss are also dispersive

• More accurate broadband results can be obtained using actual material data and a Sampled Material

: Use the Materials Explorer to see the difference between target (n,k) and actual (n,k) for broadband simulations


Material models – More linear models

Analytic : The analytic material model allows the user to enter an equation

for the real and imaginary part of the permittivity or refractive index which can depend on a set of variables.

: A common use example for the analytic material model is for materials such as AlxGa1-xAs where the refractive index is a function of x. The analytic material makes it easy to change x in between simulations.



Conductive f

ir

2

)(0

Debye

f

ic

cdebye

r

2

)(

Plasma (Drude)

f

i c

p

r

2

)(

2

Lorentz

f

i

lorentzr

2

2)(

2

0

2

0

2

0



Sellmeier

: fs is center frequency of the sources in your simulation : The resulting material is not dispersive! : Should be used for single wavelength simulations only : Typically used in MODE Solutions to calculate fiber dispersion

s

s

s

s

s

s

s

s

f

c

C

B

C

B

C

BAconstn

3

2

2

3

2

2

2

2

1

2

2

11

2


Material models – Nonlinear models

Kerr Chi3

)()()(2

)3()1( tEtEtP o

Chi2*

)()()( )2()1( tEtEtP iioi

Chi2/Chi3 *

)()()()(2)3()2()1( tEtEtEtP iiioi

Nonlinear Chi models (instantaneous)

* Implemented with material plug-in framework



)()(

)()(

0

0

tHtB

tEtD

r

r

Paramagnetic *

* Implemented with material plug-in framework

Multi-level multi-electron *

Coming soon…



Create your own!

Eg: Negative index, gain saturation, complex Chi

Plugin to create your own polarization update

It will be added to any existing material update

Write a C++ method with inputs a, b, En-1

Solve the following equation for

Trivial example

b

a 0

nn P

E

a

b

n

nn

E

EP 0

http://docs.lumerical.com/en/fdtd/ref_matdb_user_defined_models.html

http://docs.lumerical.com/en/fdtd/ref_matdb_user_defined_models.html


Tips – Material Explorer

Check your material models before running simulations!

Particularly for Sampled data materials

Adjust number of coefficients and tolerance if necessary


Tips – Material Explorer

Beware of errors in the data, and using too many coefficients

Removing noise from data and correcting errors will improve the fit


Sampled data – Gold Mie example

Example Mie Scattering, gold sphere

A good test case because analytic solution exists


Sampled data – Gold Mie example

Example Mie Scattering

: mesh size 1 nm


Material models - Review

What built-in materials are available?

What material model should I use?

How do I define my own dispersive materials?

Cautions about divergence!! : Some models created by the Sampled Material auto-fit will

diverge. Can be fixed by • Reducing the “dt stability factor”

• Reducing “PML sigma” and increasing “PML Kappa” where materials intersect the PML boundary condition, or preventing materials from intersecting the PML

• See docs.lumerical.com/en/fdtd/user_guide_diverging_simulations.html for more details

http://docs.lumerical.com/en/fdtd/user_guide_diverging_simulations.html




Anisotropic Materials

TOPICS

Anisotropic materials

: introduction

: in FDTD Solutions

Example



Anisotropic materials have

Where ij is a nine element tensor

333231

232221

131211

ij

jiji ED



Diagonal permittivity tensor

: In the Material Database, set the Anisotropy field to Diagonal, then specify the three diagonal terms.

z

y

x

00

00

00



Full permittivity tensor : First, diagonalize the anisotropy (use the eig script command) and find

both the eigenvalues and the unitary transformation that makes the permittivity diagonal.

: Create a new material in the Material Database using the diagonalized permittivity tensor.

: Use the Matrix transform grid attribute feature to apply the unitary transformation

: Example: http://docs.lumerical.com/en/fdtd/anisotropy_faraday_effect.html

UU

z

y

x

00

00

00†

333231

232221

131211

http://docs.lumerical.com/en/fdtd/anisotropy_faraday_effect.html



Example: open the file anisotropy1.fsp

nxx = 2, nyy=2, nzz=1

Ex Ez



What kind of anisotropy is available in FDTD Solutions?

How do I define anisotropic materials?

Relevant examples

: Faraday effect

: Magneto-optical Kerr effect

: Liquid crystals

http://docs.lumerical.com/en/fdtd/anisotropy.html

http://docs.lumerical.com/en/fdtd/anisotropy.html


Advanced tips

Many fits with large numbers of coefficients will reduce numerical stability : Most issues can be resolved by carefully controlling the fit

: Sometimes the size of dt needs to be reduced by reducing the “dt stability factor”

• See http://docs.lumerical.com/en/fdtd/user_guide_diverging_simulations.html for more details

Tips

: Increase the weight of the imaginary part to get a better fit to imag() if the absorption is critical for your simulation

: You may want to lock material fits to a particular wavelength range

• The fit will not change as you change the source bandwidth

: Unchecking “improve stability” may get a better fit but there is more chance of divergence

: If you uncheck “make fit passive” plot over the extended view range. If imag()<0 your simulation will likely diverge.




Advanced tips

Tips

: If you combine results from several different bandwidth simulations, you may want to lock the simulation meshing algorithm to use a larger wavelength range that encompasses all the wavelengths you want to study

: This means that the FDTD mesh will not change as you change the source bandwidth


Advanced tips

What happens when materials overlap?

The mesh order determines the result

In this case, the order in the Objects Tree

determines the result.

This should be avoided since reordering

your objects will change the results!


Advanced tips

What happens at the interface where objects touch?

: Which material is used here?

When conformal meshing is on, it does not matter!

When conformal meshing is not used

: Set mesh order correctly for precise control

Silicon

Glass

•Set Silicon mesh order to 2

•Set Glass mesh order to 3

The interface point will be

Silicon!

Silicon

Glass


Advanced tips

Nonlinear simulations can be

substantially more complicated

to setup, analyze and to ensure

convergence, compared to a

similar linear simulation.

See the following link for a number of important tips related to

setting up nonlinear simulations

http://docs.lumerical.com/en/fdtd/nonlinear_tips.html

http://docs.lumerical.com/en/fdtd/nonlinear_tips.html


Questions and Answers…


Getting help

Technical Support

: Email: [email protected]

: Online help: docs.lumerical.com/en/fdtd/knowledge_base.html

• Many examples, user guide, full text search, getting started, reference guide, installation manuals

: Phone: +1-604-733-9006 and press 2 for support

Sales information: [email protected]

Find an authorized sales representative for your region:

: www.lumerical.com and select Contact Us

mailto:[email protected]

http://docs.lumerical.com/en/fdtd/knowledge_base.html



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FDTD Solutions training - Lumerical Inc. | Innovative … · · 2015-08-25FDTD Solutions chooses the simplest dispersive model that can create the correct permittivity ... The analytic