FDTD Solutions - Material Modeling - Lumerical solutions - material... · Material Modeling FDTD...

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Material Modeling

FDTD Solutions

© 2011 Lumerical Solutions, Inc.

Outline

� Dispersive materials in a time domain method

� Material model review

: How to choose the correct model

� Anisotropic materials

� Advanced tips

: Getting better material fits

: Understanding the mesh order

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Dispersive materials in the time domain

� The fields in FDTD are real

: exception for Bloch boundaries

� Well-known frequency domain relationship

� FDTD is a time domain technique: relationship?

)()()( ωωεω EDrr

=

∫ ′′−′=∗=

t

tdtttEtEttD

0

)()()()()( εεrrr


Dispersive Materials

� FDTD Solutions supports the following models: Dielectric

: Sampled Material

: PEC (Perfect Electrical Conductor)

: Analytic

: (n,k) Dielectric

: Conductive

: Plasma

: Debye

: Lorentz

: Kerr nonlinear

: PDLC (Plasma – Debye – Lorentz – Conductive)

• Backwards compatibility mode only

: Sellmeier

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Dielectric Material� There is no dependence on frequency!

� Restriction: n >= 1

constant)(2 == nr ωε



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

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� Example GaAs, 12 coefficients

Multi-coefficient model

GaAs, 200-800nm


Auto-fitting of materials

� Fitting your (proprietary) data

: Example, representative data of color filters

Red filter

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� Fitting your (proprietary) data

: Example, representative data of color filters

Blue filter



� Metals are not necessarily simple plasma materials

Chromium

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Some tips for material fitting� 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



� Built in material data with auto-fitting

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Working in simulations

� 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

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: Calculate the theoretical curve from the fit

: Average difference = 0.001

: Max difference = 0.008


Working in simulations� 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

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� Compare Lorentz model with multi-coefficient model

Lorentz model Multi-coefficient model


Dispersive Materials(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

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PEC (Perfect Electrical Conductor)

: Equivalent to a conductor with

0=Er

∞→σ



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.

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Conductive

f

ir

⋅=

+= ∞

πω

ωε

σεωε

2

)(0



Debye

( )f

ic

cdebye

r

⋅=

−

⋅+= ∞

πω

ων

νεεωε

2

)(

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Plasma

( )f

i c

p

r

⋅=

+−= ∞

πω

ωνω

ωεωε

2

)(

2



Lorentz

( )f

i

lorentzr

⋅=

−−

⋅+= ∞

πω

ωωδω

ωεεωε

2

2)(

2

0

2

0

2

0

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PDLC (Plasma – Debye – Lorentz –Conductive): Combination of Plasma, Debye, Lorentz and Conductive models

: Backwards compatibility mode only • with FDTD Solutions 5.1 and before

: you cannot create one of these materials with FDTD 6.0 or above• For more these types of complex, dispersive materials, it is best to use Sampled Materials



Kerr nonlinear (instantaneous)

)()()(

)()()(

2)3(

2)3()1(

tEtEtD

tEtEtP

ro

o

rrr

rrr

+=

+=

χεε

χχε

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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

=

−+

−+

−+===

λ

λ

λ

λ

λ

λ

λε

3

2

2

3

2

2

2

2

1

2

2

1

1

2



Check your material models before running simulations!

Adjust number of coefficients and tolerance if necessary

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

Removing noise from data and correcting errors will improve the fit



Example Mie Scattering, gold sphere

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Example Mie Scattering

: mesh size 1 nm



� 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

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Anisotropic Materials

TOPICS

� Anisotropic materials

: introduction

: in FDTD Solutions

� Example



� Anisotropic materials have

� Where εij is a nine element tensor

=

333231

232221

131211

εεε

εεε

εεε

ε ij

jiji ED ε=

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� FDTD Solutions currently supports a diagonal permittivity tensor

=

z

y

x

ε

ε

ε

ε

00

00

00



� Set any material to anisotropic and you can enter values for each axis – or import data for each axis

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� Here’s how you enter it in the “index” field of any object


Index fieldnx ny nz

1.5 1.5 1.5 1.5

1.5;1.6 1.5 1.6 1.6

1.5;1.6;1.7 1.5 1.6 1.7

1.5+x/100;1.3;1.5+y/100 1.5+x/100 1.3 1.5+y/100



� Example: open the file anisotropy1.fsp

� n = 2;2;1.1

TE (Hz) TM (Ez)

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� What kind of anisotropy is available in FDTD Solutions?

� How do I define anisotropic materials?


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 imaginart part to get a better fit to imag(ε) 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 ε over the extended view range. If imag(ε)<0 your simulation will likely diverge.

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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!

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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


Questions and Answers…

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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

FDTD Solutions - Material Modeling - Lumerical solutions - material... · Material Modeling FDTD...

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