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## Preamble

In this section, we will show modeling of several optical elements using WOLFSIM. We hope that these examples give you an idea of how to use WOLFSIM in a more practical sense.

- Binary Phase Grating
- Gradient-index AR Coating
- Twisted-nematic Liquid Crystal Cell
- Polarization Grating

## Example 1: Binary Phase Grating

We model a binary grating with rectangular grooves. Grating parameters of the binary grating are given by the average index `n`_{o}=1.5, the index modulation Δ*n*=0.2, the grating period Λ=8μ*m*, and the thickness *d*=2μ*m*. The fill-factor (FF) is 0.5. Note that the constrast of refractive indices in the grating is 2Δ*n*.

For our FDTD simulation, we use a Gaussian pulse as an input source centered at λ_{0}=0.8μ*m*. The incoming area where the source is excited is filled with air and the outgoing media is filled with dielectric media (*n*=1.7). The structure can be implemented using WOLFSIM-GUI as follows:

## Example 2: Gradient-index AR Coating

We model a dielectric slab with anti-reflecction (AR) coatings to evaluate the performance of AR layers. The index profile of AR layers is defined as: `n`(`t`)=n_{1}+(n_{2}-n_{1})(10`t`^{3}-15`t`^{4}+6`t`^{5}),where n_{1} and n_{2} are refrative indices of the incoming and outgoing media, respectively, and `t` is the position within [0,`d`] (`d` is the thickness of AR layers).

For our FDTD simulation, we use a Gaussian pulse as an input source centered at λ_{0}=0.8μ*m*. Two AR layers are integrated with a 2μ*m*-slab of dielectric media with the refractive index *n*=1.5 at both air-slab interfaces. The thickness of both AR layers is set to d=0.8μm. The structure can be implemented using WOLFSIM-GUI as follows:

## Example 3: Twisted-nematic Liquid Crystal Cell

The next example is a 90^{o}-twisted nematic liquid crystal (TN LC) cell. The twisted nematic structure can be implemented as a stack of stratified structures of uniaxially anisotropic media with variation of the optical axis along the thickness. The cell thickness is *d*=2μ*m* and LC material parameters are the ordinary index *n*_{o}=1.4 and the birefringence Δ*n*=0.2.

Again, we use a Gaussian pulse as an input source centered at λ_{0}=0.8μ*m*. To minimize the effect of the Fresnel losses at air-LC boundaries, gradient-index AR layers are added at both interfaces. The thickness of both AR layers is set to *d*=0.8μ*m*. Simulation parameters can be set in the "Input.txt" file:

The polar angle is an angle out of the yz-plane and the azimuth angle is measured from z-axis when the optical axis is projected onto the yz-plane. Note that the optical axis is initially the z-axis (*n*_{z}=*n*_{e} if the polar and azimuth angles are 0).

## Example 4: Polarization Grating

The last example is modeling of a special anisotropic grating, known as the circular polarization grating (PG). Unlike conventional phase gratings, a circular PG can have only three diffracted orders (0- and ±1-orders) and the maximum efficiency can reach ideally ~100% when Δ*nd*=λ/2. More details of circular PGs can be found in Ref.[1].

Grating parameters are the grating pitch Λ=8μ*m*, the birefringence Δ*n*=0.2, and the thickness *d*=4μ*m*. A Gaussian pulse is used as an input source centered at λ_{0}=0.8μ*m*. To minimize the effect of the Fresnel losses at air-LC boundaries, gradient-index AR layers are added at both interfaces. The thickness of both AR layers is set to *d*=0.8μ*m*. The structure can be implemented using WOLFSIM-GUI as follows:

## References

[1] C. Oh and M. J. Escuti, "Time-domain analysis of periodic anisotropic media at oblique incidence: anefficient FDTD implementation," Opt. Express 14, pp. 11870-11884 (2006). Link