WOLFSIM:Examples

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Contents 1 Navigation 2 Preamble 3 Example 1: Binary Phase Grating 4 Example 2: Gradient-index AR Coating 5 Example 3: Twisted-nematic Liquid Crystal Cell 6 Example 4: Polarization Grating 7 References

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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 Δn=0.2, the grating period Λ=8μm, and the thickness d=2μm. The fill-factor (FF) is 0.5. Note that the constrast of refractive indices in the grating is 2Δn.

For our FDTD simulation, we use a Gaussian pulse as an input source centered at λ₀=0.8μm. 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)=n₁+(n₂-n₁)(10t³-15t⁴+6t⁵),where n₁ and n₂ 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 λ₀=0.8μm. Two AR layers are integrated with a 2μm-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=2μm and LC material parameters are the ordinary index n_o=1.4 and the birefringence Δn=0.2.

Again, we use a Gaussian pulse as an input source centered at λ₀=0.8μm. 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=0.8μm. 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 Δnd=λ/2. More details of circular PGs can be found in Ref.[1].

Grating parameters are the grating pitch Λ=8μm, the birefringence Δn=0.2, and the thickness d=4μm. A Gaussian pulse is used as an input source centered at λ₀=0.8μm. 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=0.8μm. 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