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Metamaterials are artificially engineered structures that have unique properties not usually found in natural materials, such as negative refractive index. Conventional interferometry or ellipsometry is generally used for characterizing the optical properties of metamaterials. Here, we report an alternative optical vortex based interferometric approach for the characterization of the effective parameters of optical metamaterials by directly measuring the transmission and reflection phase shifts from metamaterials according to the rotation of vortex spiral interference pattern. The fishnet metamaterials possessing positive, zero and negative refractive indices are characterized with the vortex based interferometry to precisely determine the complex values of effective permittivity, permeability, and refractive index. Our results will pave the way for the advancement of new spectroscopic and interferometric techniques to characterize optical metamaterials, metasurfaces, and nanostructured thin films in general.
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Optical parameter extraction for metamaterials via robust effective and equivalent medium models
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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- Award ID(s):
- 1846239
- PAR ID:
- 10487717
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optical Materials Express
- Volume:
- 14
- Issue:
- 2
- ISSN:
- 2159-3930
- Format(s):
- Medium: X Size: Article No. 457
- Size(s):
- Article No. 457
- Sponsoring Org:
- National Science Foundation
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