# Material Models

## Material Models Introduction

One of the main advantages of the FDTD approach is the lack of approximations for the propagating field—light is modeled in its full richness and complexity. The other significant advantage is the great variety of materials that can be consistently modeled within the FDTD context. In this sub-section we make a brief review of some…

## Constant Dielectrics

Constant dielectric material is expressed by a complex refractive index value ( ) or relative permittivity value (εr). Here, n is the refractive index indicating the phase velocity informaiton in the medium, while K is called the extinction coefficient, which indicates the amount of absorption loss when the electromagnetic wave propagates through the material. Note that…

## Lossy Dielectrics

Before proceeding with a more detailed description it should be emphasized that the fact that in the time domain all the fields (Hx, Ey, Hz) are real quantities. Thus, accounting for loss is possible only through a non-zero conductivity σ of the medium: where Here we have assumed that and corresponds to time-to-frequency domain Fourier transform.…

## Lorentz-Drude Model

By Lorentz dispersion materials, we mean materials for which the frequency dependence of the dielectric permittivity can be described by a sum of multiple resonance Lorentzian functions: where ω0m are the resonant frequencies Gm is related to the oscillator strengths Γm is the damping coefficient ε∞ is the permittivity at infinite frequency X0 is the…

## Nonlinear Material

In general, the nonlinear behavior is due to the dependence of the polarization P(t) on the applied electric field, E(t). Assuming an isotropic dispersive material, Maxwell’s equations are: where PL represents the linear polarization, in general  is the dispersive polarization which is controlled by Lorentz model in Equation 20 and denotes the nonlinear polarization. The nonlinear…

## Dispersive 2nd-Order Nonlinear Material

In this model, the electrical displacement D is where εL is the linear relative permittivity and X(2) is the second order isotropic susceptibility. They are the real values. In order to simulate second order nonlinear effect, you should input two parameters: the linear relative permittivity  εL and the second order isotropic susceptibility X(2).

## Dispersive 3rd-Order Nonlinear Material

Like the second-order nonlinearity, OptiFDTD takes third-order susceptibility to calculate the nonlinear polarization where εL is the linear relative permittivity and χ(3) is the third order isotropic susceptibility.

## Dispersive Kerr Effect

If the time scale over which the medium changed is greater than the pulse width, we should take into account the effects of the finite response time of the medium. Followed by Prof. Richard W. Ziolkowski ‘s work -, OptiFDTD treats the nonlinear effect with a finite response time as well as an instantaneous manner…

## Dispersive Raman Effect

Raman model allows another way to simulate the nonlinear phenomenon where the nonlinear susceptibility was modeled by a second-order derivative equation which is related to the resonant wavelength and the response time where εL is the linear relative permittivity XNL is the nonlinear susceptibility τ is the response time εR is Raman model permittivity ωR…

## Nonlinearity Simulation

To observe nonlinear effects in common used materials, a high-intensity light source is required. You should pay special attention to the input wave amplitude and/or the power level; each model with different parameters may need different input power or amplitude. If the input power is too low, you may not observe the nonlinear phenomenon. If the power is too…