High-contrast polarization control devices composed of sub-wavelength metal gratings - nanowire grid polarizers - are replacing bulk optical elements. Nanowire grid polarizers offer improved extinction ratio contrast, minimal absorption to address high brightness illumination, and compact form factors to facilitate mass manufacture and integration within small optical assemblies. However, nanowire grid polarizers are challenging components to design, especially if manufacturing imperfections are taken into account. In this application example, we show how FDTD can be used to maximize the contrast ratio of a nanowire grid polarizer at any angle, while maintaining high transmission.
We will calculate the contrast ratio of a nanowire grid polarizer made of a glass substrate (n=1.4) with an aluminium nanowire grating of linewidth W and thickness H. The source illuminates the top surface of the grating polarizer. We anticipate that the polarizer should block S-polarized light, i.e. when the electric field is polarized tangential to the grating lines as shown in the figure above.
In the first analysis, we will calculate the contrast ratio versus pitch for a 50% duty cycle grating with thickness of H=140nm and normal incidence light. The pitch will be varied between 40nm and 240nm (corresponding to a variation in linewidth of W=20nm to W=120nm). We will plot the results at 3 different wavelengths (λ=450nm, λ=550nm and λ=650nm).
In the second stage of the analysis, we will calculate calculate the contrast ratio at 550nm and a grating pitch of 140nm as a function of the duty cycle, again with light at normal incidence.
The third investigation involves illuminating the nanowire grid polarizer with non-normal incidence light. Efficiency of the previous structure (550nm wavelength, 140nm pitch) with a 50% duty cycle is measured at a 45 degree incidence angle. Field amplitude and phase plots are also generated.
Contrast ratio vs pitch
The results of the mwp_spectrum.lsf script are shown below. By sampling the contrast of the transmission for gratings with several different periods we can find the desired results. This result is in good agreement with the results obtained by Seh-Won Ahn et al..
Tip: Movie monitors
You can add a movie monitor to your simulation to view the time domain fields. To make the movies easier to interpret, increase the simulation size to include multiple periods of the device. In these simulations, we simulate 5 periods of the device.
Movies of P (left) and S (right) polarized simulations
Contrast ratio vs duty cycle
The script mwp_dutysweep.lsf performs a parameter sweep to calculate the contrast ratio versus grating duty cycle and plots three results: the contrast, the S transmission and the P transmission.
Contrast ratio of the aluminium nanowire grid polarizer as a function of the grating duty cycle. This plot apparently shows that the contrast ratio varies over 7 orders of magnitude and has a maximum at a duty cycle of 0.9. However, this curve is misleading because the large contrast ratios are in fact due to a small S transmission.
Transmission of S-polarized light for the aluminium nanowire grid polarizer as a function of the grating duty cycle. This S transmission is numerically simulated to be approximately 8e10^-5 for a duty cycle of 50% and decreases to 10^-10 for larger duty cycles. For manufactured devices, S transmissions on the order of 10^-3 are more realistic.
Transmission of P-polarized light for the aluminium nanowire grid polarizer as a function of the grating duty cycle. This curve shows that the transmission of P-polarized light decreases as the duty cycle increases. Based on these results, an aluminum grating with a duty cycle of 50% has a transmission of about 85%. With an s-polarized transmission of 8e10^-5 , an ideal 50% duty-cycle aluminum grating can achieve a contrast ratio of approximately 1e10^4.
The above results demonstrate that contrast ratios on the order of 1e10^4 can be obtained. However, such large contrast ratios are difficult to achieve in practice due to manufacturing imperfections.
Open mwp.fsp, and run mwp_45deg.lsf. The script will first modify the simulation parameters in the following way:
- The boundary conditions are changed from periodic to Bloch, which are required for non-normal incidence illumination.
- The source is rotated by 45 degrees
- The simulation volume along the Y-axis is increased to make the fields easier to visualize.
- The source polarization is set to P (or TE)
The electric field intensity is plotted for a cross-section through the nanowire grid polarizer. It's interesting to note that there is no interference pattern visible above the grating because the angle is exactly 45 deg. For other angles, an interference pattern would be observed.
The real part of Ex (left) and Ey (right) field components. The ripples in the region above the aluminum metal grating result from interference between the incoming light and that reflected from the top surface of the nanowire grid polarizer.
The phase of the Ex (left) and Ey (right) field components. The change in angle of the wavefront results from the higher refractive index of the silicon substrate relative to the air region above the aluminum grating nanowire grid polarizer.
The aluminum grating wiregrid polarizer has a TE transmission of approximately 85% for a normally-incident plane wave. The transmission is mostly unchanged for a 45 degree incidence.
Note: Multiple periods
Only one period has been simulated, but pictures spanning multiple periods can be generated by concatenating several copies of the data together, and adjusting the phase accordingly.
Ahn et al,. "Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography", Nanotechnology, 16, 1874–1877 (2005)