# Creating Materials

In this section, you will learn how to:

- Add materials to your EMPro project
- Define materials and apply them to geometric objects

Once objects are created and situated correctly in the simulation space, material definitions must be added or else the project *will not* be considered valid. The electrical and magnetic materials available within EMPro are detailed in this section.

The *Material Editor* window is the main interface used to define materials to be applied to objects in a simulation. The series of tabbed windows within the editor are used to define a material based on its constitutive parameters. After adding materials to the project, simply drag-and-drop the material in the *Project Tree* onto the desired geometry to apply it to that object.

The following section describes the options under each tab within the *Material Editor*.

## Adding a New Material

To add a new material, right-click **Definitions: Materials** branch of the *Project Tree* and select *New Material Definition*, as seen in the following illustration. A *Material* object will be added to this branch. Depending on the project preferences, the *Material Editor* window will appear automatically. If not, simply double-click on this object to bring up the editor. Similarly, double-click on any existing *Material* icon to edit an existing material within the *Material Editor*.

For more information about project preference definitions, refer to Application Preferences.

###### Adding a New Material Definition to the project

Once the *Material Editor* window is open, type in the name of the new material in the *Name* dialog box. Define the *Type* of material as *Physical* or *Freespace*. *Freespace* is the most basic material definition. Every other type of material is included within the *Physical* definition, in which case the *Electric* and *Magnetic* types should be assigned in their respective drop-down lists below.

There are five electrical and magnetic material types available in EMPro.

- Freespace
- Perfect Conductor
- Isotropic
- Diagonally Anisotropic
- Anisotropic (Electric only)

Although frequency-independent materials require the least memory during FDTD simulations, there are some cases in which frequency-independent materials are not appropriate. Frequency-dependent or dispersive materials should be used in these instances. Some common examples of frequency-dependent materials are high water content materials such as human tissues, and metals excited at optical frequencies. EMPro has the capability of simulating electric and magnetic Debye and Drude materials such as plasmas, Lorentz materials, and anisotropic magnetic ferrites, as well as frequency-independent anisotropic dielectrics and nonlinear diagonally anisotropic dielectrics. These additional sub-types are specified within the *Isotropic*, *Diagonally Anisotropic* and *Anisotropic* definitions.

The following sections will detail the various types of materials.

### Freespace

*Freespace* is the most basic material. By default, the EMPro problem domain is initialized to free space. This material sets relative permittivity and permeability to one, and conductivities to zero.

The following figure shows the *Material Editor* when the *Freespace* material is defined. Notice that no *Electric* or *Magnetic* tab is available, since both are defined as *Freespace* material.

###### Defining a Freespace material

### Perfect Conductors

A *Perfect Conductor* has infinite conductivity and all fields found within it are zero. It has the same settings as the *Freespace* material, as seen in the figure above. It should typically be used as an approximation when a good conductor is needed in an electromagnetic calculation and losses aren't important. Attempting to include the effects of a good conductor (rather than perfect conductor) may be difficult since the wavelength inside the good conductor will become very small, requiring extremely small FDTD cells to provide adequate sampling of the field values inside the material. This can, however, be overcome by checking the *Surface Conductivity* box in the *Edit Material* dialog box.

Note

You can read more about the *Surface Conductivity* box in the Complex Permittivity, Loss Tangent and Surface Conductivity Correction Overview section.

### Electric Materials

#### Isotropic Materials

EMPro includes several *Isotropic* materials:

- Nondispersive
- Debye/Drude
- Djordjevic
- Lorentz
- Sampled (FDTD only)
- Nonlinear (FDTD only)

The next figure shows the *Material Editor* when an *Isotropic* material is defined. Note that only the *Electric* tab is available since *Magnetic* is defined as *Freespace*. If you define *Magnetic* as another type, a *Magnetic* tab would be available as well.

###### Defining an Electric Material

#### Nondispersive

Nondispersive material properties do not vary with frequency. The continuous-time expressions of Maxwell equations for linear, isotropic, and nondispersive materials that will be discretized in EMPro are:

and

where:

represents the electric permittivity,

represents the electric conductivity,

represents the magnetic permeability, and

represents the magnetic conductivity.

###### Defining a Nondispersive material

#### Debye/Drude

For a *Debye/Drude* material, the electrical *Conductivity* ( ) in , Infinite Frequency Relative Permittivity ( ), *Number Of Poles*, *Static Relative Permittivity* ( ), and *Relaxation Time* ( ) in seconds must be specified. For a *Debye* material, must equal zero. A non-zero conductivity value results in a *Drude* material.

Note

This is discussed in detail in Chapter 8 of the Kunz and Leubbers text [1].

###### Defining a Debye/Drude material

These parameters cannot be set arbitrarily or instability can occur in FDTD simulations. One constraint is that the FDTD timestep must be small enough to accurately calculate the transient behavior of the material. If the timestep is 3% of the relaxation time or smaller, the time variation of the material parameters should be sufficiently resolved. Typically, the timestep is a very small fraction of the relaxation time. In order to be clear about the signs in the following discussion, note that we are using the engineering time variation of:

and we are defining the complex permittivity as:

For the FDTD calculation to be stable, the imaginary (loss) part ( ) of the complex permittivity, including the effect of the conductivity term, must be positive for all frequencies from zero frequency to infinite frequency. This condition results in a passive material. If is negative, then the material has gain and FDTD simulations will become unstable as the field amplitudes grow.

Note

See equation 8.29 of the Kunz and Leubbers text [1].

For a *Debye* material ( ), stability is assured by setting to a larger value than . In order to have realistic behavior at high frequencies, should be no less than one and should not be much larger than one. Thus the condition for strictly *Debye* material to be stable for FDTD simulations is:

>

= 0

If the conductivity is not zero, then the material has *Drude* behavior. There are different conditions that can be satisfied for the imaginary part of the complex permittivity to be positive so that FDTD simulations produce stable results. If the static permittivity is greater than the infinite frequency permittivity then the conductivity can have any positive value. This results in the simplest set of conditions for a stable *Drude* Material:

>

These conditions are, however, too restrictive to specify general *Drude* materials. The more general *Drude* conditions are:

If( ),

then:

otherwise:0

where is the *Freespace Permittivity* of 8.854e-12 !img227.png!.

Note

More general conditions for *Drude* materials can be determined from the discussion in Chapter 8, Section 3 the Kunz and Leubbers text [1].

#### Djordjevic

A *Djordjevic* material is implemented in a number of substrate models to fulfill the causality requirement. The Djordjevic material ensures causality by using the following formula to describe the complex permittivity as a function of frequency:

(2)

where * f_{L}* and

*are the model parameters*

**f**_{H}

is the permittivity value when frequency approaches infinity and *a* is a constant factor. These two parameters are calculated by EMPro from *Er*, *TanD*, *FreqForEpsrTanD*, *LowFreqForTanD*, and *HighFreqForTanD*, which are substrate model parameters entered by the user. *FreqForEpsrTanD* is the frequency at which for given *Er* and *TanD* the equations (1) and (2) are equivalent. Specifically,

(3)

In other words, *FreqForEpsrTanD* represents the frequency at which *Er* and *TanD* have been measured, given the fact that the permittivity is frequency dependent in the physical world.

Below is an example illustrating the permittivity profile and how it is related to substrate model parameters. The horizontal axis in both plots is frequency (Hz).

###### Graph Shows Real Part of Permittivity

###### Solid Plot Shows Imaginary Part of Permittivity. Dashed Plot Shows TanD.

The corresponding parameters are:

Er = 4.6

TanD = 0.03

FreqForEpsrTanD = 1 GHz

HighFreqForTanD = 1 THz

LowFreqForTanD = 1 kHz

#### Lorentz

Stability in *Lorentz* materials for FDTD simulations should be obtained as long as *Conductivity* and the FDTD timestep is 3% of the relaxation time or less. The limits on the material parameters are:

> 0

> 0

###### Defining a Lorentz material

#### Sampled

This material enables you to enter multiple relative permittivities and conductivities at one time. It will behave like a nondispersive material when the calculation engine is called and the *Wideband* *Eval Frequency* dictates what parameters to use.

Note

This is not a dispersive material and will not automatically be converted to one.

###### Defining a Sampled material

#### Nonlinear

The relative permittivity of a nonlinear isotropic dielectric material satisfies:

Where:

is relative permittivity

E is instantaneous cell edge E-field

is static (low ) relative permittivity

is infinite relative permittivity

is the E magnitude above which the material becomes non-linear

is a scaling term

, and are coefficients

Note

Nonlinear materials are not supported in FEM simulations.

###### Defining a Nonlinear material

#### Diagonally Anisotropic

The definitions for a *Diagonally Anisotropic* are equivalent to those corresponding definitions detailed for *Isotropic* materials, except the definitions in each of the principle directions are independently specified.

#### Anisotropic

Frequency-independent *Anisotropic* materials are defined in EMPro by the relative permittivity, , and *Conductivity*, , tensors.

###### Defining an Anisotropic material

The parameters below *Conductivity* represent the terms of and the parameters below Permittivity (Infinite Frequency) represent the terms of as follows:

The conductivity and permittivity for frequency-independent anisotropic dielectric materials are represented by and , unlike the equations for linear, non-dispersive, frequency-dependent, isotropic materials. These are used in the time-domain FDTD update equations in place of and :

#### Complex Permittivity

The value of complex permittivity may need to be calculated for some materials. The real part of the complex permittivity may be used for the relative permittivity. The conductivity can be calculated from the imaginary part of the complex permittivity by multiplying by a desired output frequency value (in radian frequency), as shown by:

#### Loss Tangent

The loss tangent can be entered directly into EMPro when it is known, typically for good dielectrics. The FDTD engine can then calculate the conductivity as a function of frequency using:

#### Surface Conductivity Correction

The fields inside a good conductor decay exponentially with a decay rate given by the skin depth. In order to get accurate results for the fields inside a good conductor, it would be neccessary to generate a mesh that has a cell size that is smaller than the skin depth. At high frequencies, this would require very small cells and is thus computationally expensive. Both the FDTD and FEM simulators offer a choice to approximate the fields inside good conductors to reduce this expense. These choices are controlled by the *Surface Conductivity Correction* box. By default, the *Surface Conductivity Correction* box is not selected.

In FDTD simulations, the default behavior is to model the fields inside conductors. This gives the proper loss modeling at low frequencies, but underestimates the losses at high frequencies unless the FDTD grid creates small cell sizes along the inside surface of good conductors. An accurate accounting of the high frequency losses can be obtained by checking the *Surface Conductivity Correction* box and specifying a nominal frequency about which the calculated losses will be most accurate.

In FEM simulations, the default behavior is to **not** model the fields inside conductors. Instead, an approximate surface impedance model is used on the surface of conductors. This gives the correct loss modeling at high frequencies. It also gives the correct DC losses for conductors with a uniform cross section. Slightly more accurate DC and low frequency losses for structures of varying cross section can be obtained by checking the *Surface Conductivity Correction* box. However, this can significantly degrade the accuracy of the high frequency losses from FEM simulations.

The *Evaluation Frequency* parameter that appears with the *Surface Conductivity Correction* box selected is ignored for FEM simulations.

### Magnetic Materials

EMPro also includes several types of magnetic materials. Many of these materials are simply the magnetic counterpart to the dielectrics described in Electric Materials. All restrictions noted in the *Electric Materials* section apply to their magnetic counterparts.

The figure below shows the *Material Editor* when a Magnetic *Isotropic* material is defined. Note that only the *Magnetic* tab is available since *Electric* is defined as *Freespace*. If *Electric* was defined as another type, a *Electric* tab would be available as well.

###### Defining a Magnetic material

#### Isotropic

#### Nondispersive

See Nondispersive in the *Electric Materials* section.

#### Debye/Drude.

See Debye/Drude in the *Electric Materials* section.

#### Magnetized Ferrites

The first parameter related to magnetized ferrites is the *Applied Field*, ( ). Enter its value in units of . This number will be used to calculate the Larmor precession frequency ( ),

where is the gyromagnetic ratio ( ).

Next, enter the *Internal Magnetization* ( ) in units of . This number is used to calculate the saturation frequency ( ), .

Then, use the *Damping Coefficient* to account for damping in the ferrite or of any absorption of power due to the ferrite. Finally, enter the direction of the biasing field using the spherical direction fields THETA and PHI.

Note

Note

Ferrite materials are not supported in FEM simulations.

###### Defining an Magnetized Ferrite material

#### Sampled

See Sampled in the *Electric Materials* section.

#### Nonlinear

See Nonlinear in the *Electric Materials* section.

#### Diagonally Anisotropic

See Diagonally Anisotropic in the *Electric Materials* section.

## Appearance

Use the *Appearance* tab to assign the aesthetic properties of each defined material. Colors and other properties can be assigned to the faces, edges, and vertices of objects that contain the material so that they can be easily distinguished from other materials in the project.

## Physical Parameters

The *Physical Parameters* tab governs the definitions most commonly associated with biological tissue. These definitions are thus necessary when performing biological calculations. These values are computed automatically for tissues in Agilent Technologies high fidelity meshes.