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Metamaterials are complex structured mixed-material systems with tailored physical properties that have found applications in a variety of optical and electronic technologies. New methods for homogenizing the optical properties of metamaterials are of increasing importance, both to study their exotic properties and because the simulation of these complex structures is computationally expensive. We propose a method to extract a homogeneous refractive index and wave impedance for inhomogeneous materials. We examine effective medium models, where inhomogeneities are subwavelength, and equivalent models where features are larger. Homogenization is only physically justified in the former; however, it is still useful in the latter if only the reflection, transmission, and absorption are of interest. We introduce a resolution of the branching problem in the Nicolson-Ross-Weir method that involves starting from the branch of the complex logarithm beginning with the minimum absolute mean derivative and then enforcing continuity, and also determine an effective thickness. We demonstrate the proposed method on patterned PbS colloidal quantum dot films in the form of disks and birefringent gratings. We conclude that effective models are Kramers-Kronig compliant, whereas equivalent models may not be. This work illuminates the difference between the two types of models, allowing for better analysis and interpretation of the optical properties of complex metamaterials.
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Effective and Equivalent Refractive Index Models for Patterned Solar Cell Films via a Robust Homogenization Method
Solar cells containing complex geometric structures such as texturing, photonic crystals, and plasmonics are becoming increasingly popular, but this complexity also creates increased computational demand when designing these devices through costly full-wave simulations. Treating these complex geometries by modeling them as homogeneous slabs can greatly speed up these computations. To this end, we introduce a simple and robust method to solve the branching problem in the homogenization of metamaterials. We start from the branch of the complex logarithm in the Nicolson-Ross-Weir method with the minimum absolute mean derivative in the low frequency range and enforce continuity. This is followed by comparing the reflectance, transmittance, and absorptance of the original and homogenized slabs. We use our method to demonstrate accurate and fast optical simulations of patterned PbS colloidal quantum dot solar cell films. We also compare patterned solar cells homogenized via equivalent models (wavelength-scale features) and effective models (sub-wavelength-scale features), finding that for the latter, agreement is almost exact, whereas the former contains small errors due to the unphysical nature of the homogeneity assumption for that size regime. This method can greatly reduce computational cost and thus facilitate the design of optical structures for solar cell applications.
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- Award ID(s):
- 1846239
- PAR ID:
- 10517575
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-6654-6059-0
- Page Range / eLocation ID:
- 1 to 3
- Format(s):
- Medium: X
- Location:
- San Juan, PR, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/PVSC48320.2023.10360062
