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Methodology

The Anti-Reflective Properties of Subwavelength Structures on Lenses

Jared Nash | Dr. Shaul Hanany | Scott Cray

Sponsoring Institution: University of Minnesota School of Physics and Astronomy

Home Institution: Albion College

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Figure 5: Transmission predicted using HFSS FEA method (above)

Figure 1: Polarization of the cosmic microwave background radiation

Figure 2: Simplified visual representation of light as it propagates through a material (left)

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Figure 3: Side profile of SWS. Scale is on the order of microns (right)

  • As electromagnetic energy propagates through a given material, energy can be reflected, absorbed, or transmitted through the material

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  • Alumina’s high thermal conductivity and transmission spectrum make it an appealing low pass filter material for instruments operating at millimeter wavelengths[2]

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  • One of the challenges in using alumina as a filter material is its tendency to reflect light due to the materials high index of refraction n = 3.12[3]

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  • One technique of mitigating reflection is achieved by fabricating anti-reflective subwavelength structures on the surface of the alumina lens through laser ablation

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  • Ansys High Frequency Structure Simulator (HFSS) is a simulation tool which allows for the study of electromagnetic energy using finite element analysis (FEA)

  • The transfer matrix method (TMM) is a method is used in optics to analyze the propagation of electromagnetic waves through a medium.[4] Using TMM, simulations were coded which represented that of an alumina lens with infinite radius coupled with SWS anti-reflective coating (ARC).

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  • Using Ansys HFSS, a partial element (including SWS ARC) of the entire lens can be modeled (figure 4). Infinite periodic boundary conditions can then be applied to the partial element to represent an infinite lens with SWS. Results comparing the two methods can therefore be analyzed

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  • Transmission was predicted using Ansys HFSS of a subwavelength structure in the 0 THz to 1 THz frequency range

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  • HFSS modeling verifies anti-reflective properties of SWS, enabling the prediction of complex surfaces with SWS

[1] “Polarization of the Cosmic Microwave Background.” Jet Propulsion Laboratory: California Institute of Technology, 2021, www.jpl.nasa.gov/images/pia18916-polarization-of-the-cosmic-microwave-background.

[2]  Y. Inoue, T. Matsumura, M. Hazumi, A. T. Lee, T. Okamura, A. Suzuki, T. Tomaru, and H. Yamaguchi, “Cryogenic infrared filter made of alumina for use at millimeter wavelength,” Appl. Opt. 53, 1727–1733 (2014)

[3] J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millim. Waves 17, 1997–2034 (1996)

[4] Born, M; Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light. Oxford, Pergamon Press, 1964

Acknowledgements: Special thanks to Dr. Shaul Hanany, Scott Cray, and the University of Minnesota School of Physics and Astronomy for their support and guidance

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Results

Acknowledgements

Theory

Abstract

The Cosmic Microwave Background (CMB) radiation is the oldest detectable light in our universe, imprinted on the sky when the Universe was just 380,000 years old.[1] Produced during the creation of the universe, a fraction of this radiation is slightly polarized – vibrating in preferred directions. The study of this polarization gives physicists an insight into the distribution of energy and matter in the early universe. To study this polarization with precision, astronomers need sensitive equipment which allow the maximum amount of light to be collected during observation. As a result, numerous anti-reflective coating techniques have been developed, including laser ablated subwavelength structures (SWS). This poster will include the process for simulating and modeling the transmission of light through subwavelength structures on alumina lenses.

Figure 4: HFSS model of partial element of alumina lens with pyramid shaped SWS placed above and below the substrate

Figure 6: Transmission predicted by analytical TMM model (above)

Figure 7: Difference in predicted transmission between HFSS and TMM. Results agree to within 3%

School of Physics and Astronomy

This work was supported partially by the

Research Experiences for Undergraduates

(REU) Program of the

National Science Foundation

under Award Number

PHY-2049645