Metamaterials are a unique type of material: their structural morphology significantly affects their inherent properties. Zero-index metamaterials (ZIMs) stand out among electromagnetic metamaterials, showcasing an exceptional ability to distribute uniform electromagnetic fields across arbitrary shapes.
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The phenomenon of zero refractive index, exhibited by ZIMs, has proven highly useful, especially in the fields of waveguiding and optics.
The Science Behind Zero-Index Metamaterials
When a medium changes its effective refractive index, transitioning from negative to positive, it is expected to demonstrate a zero refractive index at the frequency of the transition. According to a recent publication, Zero Index Metamaterials: Trends and Applications, such an occurrence is abnormal for natural materials but plausible for metamaterials. Factors such as negative refractive index or negative permeability, which are not recorded in general composites, are frequently observed in metamaterials.
Is Silicon Carbide a Natural Zero-Index Metamaterial?
Silicon carbide, classified as a polaritonic material, exhibits resonance in the mid-infrared spectrum, making it a natural zero-index metamaterial. It demonstrates a permittivity value of Re(ε) = −0.0009 (approximately 0) at 10.3 μm, remaining close to zero within the range of 10.0 μm to 10.5 μm.
This characteristic makes it a promising natural candidate for zero-index applications. However, a notable challenge arises from its substantial extinction coefficient, which leads to significant material loss. In addition to silicon carbide, other materials with near-zero properties in the optical spectrum include aluminum zinc oxide (AZO) and indium tin oxide (ITO). Similarly, the high extinction coefficient of these materials also restricts their performance.
Magnetically Tunable ZIMs: Essential for Future Applications
Traditional ZIM substances often experience significant ohmic losses due to their metallic components. ZIMs designed with all-dielectric photonic crystals exhibit zero ohmic loss, allowing the realization of ZIMs across large areas with arbitrary shapes.
While photonic-crystal-based ZIMs may not be the optimal solution for many applications, such as nonlinear optics, the absence of ohmic loss can significantly reduce power requirements, making them a popular choice.
Despite these advancements, most reported ZIMs are passive, possessing constant post-fabrication electromagnetic properties, limiting their applications in passive devices.
To address this limitation, ongoing research efforts are focused on implementing active ZIMs with tunable properties. Among these innovations, magnetically tunable ZIMs have emerged as a theoretical solution capable of exhibiting unique properties such as "Hall opacity" and "Hall transparency" under an applied magnetic field. However, experimental research on this concept did not commence until mid-2023.
A recent article published in Photonics Research explains the design of a magnetically tunable ZIM using yttrium iron garnet (YIG) pillars embedded between two copper-clad laminates, designed for operation in the microwave regime. The research team utilized a Dirac-like cone-based ZIM (DCZIM) featuring a square array of dielectric pillars.
Exploiting the Cotton–Mouton effect in the YIG pillars under applied magnetic fields, the researchers modified the symmetry and bandgap opening of the DCZIM, facilitating its operation for experimental testing. The device exhibited an effective refractive index near zero (|neff| < 0.1) across a bandwidth of 6.77 % without an applied magnetic field and 5.43 % (extinction ratio over 100 dB) with an applied magnetic field, comparable to commercial devices.
A shift to a single negative metaphase was observed at 9 GHz. This resulted in a change in the value of the effective index from 0 to 0.09i. Leveraging this property, a microwave switch was developed by manipulating the super-coupling effect, achieving an intrinsic loss reduction of 0.95 dB and a high extinction ratio of 30.63 dB at 9 GHz.
This innovative study introduces a novel approach to active ZIMs, particularly in the development of efficient active electromagnetic and non-reciprocal devices.
Development of Highly Efficient On-Chip ZIMs
Light propagating within a zero-index medium undergoes no spatial phase advance, leading to perfect spatial coherence. This coherence holds potential for groundbreaking applications in linear, nonlinear, and quantum optics. However, in traditional ZIMs, the associated zero-index modes often come with significant losses, resulting in short propagation lengths due to intrinsic ohmic losses.
To overcome this problem and significantly reduce losses, a team of researchers developed a low-loss zero-index Dirac-cone Photonic Crystal (PhC) slab by utilizing Bound States in the Continuum (BICs). The outcomes of this study were published in Light: Science & Applications.
The researchers achieved this bound state through the destructive interference of out-of-plane radiation from dipole modes, which form the Dirac cone at the center of the Brillouin zone. The resulting BIC zero-index PhC slab demonstrated an impressively low in-plane propagation loss of 0.15 dB/mm at the zero-index wavelength.
The refractive index remained near zero (|neff | < 0.1) over a bandwidth of 4.9 %. This unique design approach allowed for BIC zero-index PhC slabs with a Dirac-cone dispersion, encompassing various modes in the multipole expansion, including monopole and dipole modes.
The on-chip BIC Dirac-cone zero index PhC slabs offer extensive applications with an infinite coherence length and low propagation loss. This introduces possibilities for utilizing large-area zero-index materials in both linear and nonlinear optics, as well as laser applications, including electromagnetic energy tunneling through a zero-index waveguide with an arbitrary shape. The distinctive design serves as an on-chip laboratory for investigating fundamental quantum optics, such as the efficient generation of entangled photon pairs and collective emission from multiple emitters.
Using Homogeneous ZIMs for High Directivity Antennas
ZIMs can sustain consistent electromagnetic field distributions across various frequencies. However, their application is hindered by their homogenization level, which is constrained to only 3 unit cells per free-space wavelength. This limitation has been attributed to low-permittivity inclusions (microwave relative permittivity εr approximately 12) and the background matrix (εr approximately 1).
According to a recent article published in eLight, a microwave DCZIM was developed by incorporating high-permittivity SrTiO3 ceramic (εr ≈ 294) pillars into a BaTiO3 (εr ≈ 25) background matrix. The lattice constant of the metamaterial was set to one-tenth of the free-space wavelength, ensuring compliance with the effective medium condition and achieving high homogeneity.
The results demonstrated a homogenization level of a/λ0 ≈ 0.1, surpassing the state-of-the-art ZIM more than three times. This advancement has the potential to improve the performance of various ZIM-based devices, including the compactness of ZIM-based waveguides with arbitrary shapes and the thickness of free-space cloaks.
To fully capitalize on the high homogeneity of DCZIM, the researchers created a high-directivity DCZIM-based antenna with a scalable aperture size range spanning from subwavelength dimensions to much larger scales.
The antenna achieved a directivity as high as 11.2 dB with an aperture size as small as 1.2λ0×1.2λ0. It also demonstrated high directivity across a range of aperture sizes, initiating from 0.5λ0×0.5λ0, approaching the fundamental limit of antenna directivity in a broad aperture size spectrum. The DCZIM-based antennas exhibited comparable directivities and superior scalability compared to traditional choices.
A review published in Applied Physics Letters offers an overview of the use of ZIM in classical and quantum applications. Interest in ZIMs has surged in recent years, connecting nanophotonics, electrical engineering, materials science, nanofabrication, and quantum physics.
These metamaterials play a crucial role in the domain of quantum optics and modern particle guiding. Wavelength expansion, facilitated by ZIMs, enhances long-range entanglement, enabling longer entanglement distances and robustness against inaccuracies in emitter positioning. Metamaterials also offer unprecedented control over trapping and guiding light waves in various platforms.
Due to their unique advantageous properties, ZIMs are becoming invaluable across a wide spectrum of fields.
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References and Further Reading
Liu, Y., et al. (2024). High-permittivity ceramics enabled highly homogeneous zero-index metamaterials for high-directivity antennas and beyond. eLight. doi.org/10.1186/s43593-023-00059-x
Shankhwar, N. Sinha, RK. (2021). Zero index metamaterials: Trends and applications. Springer. doi.org/10.1007/978-981-16-0189-7
Yang, Y., et. al. (2023). Magnetically tunable zero-index metamaterials. Photonics Research. doi.org/10.1364/PRJ.495638
Dong, T., et al. (2021). Ultra-low-loss on-chip zero-index materials. Light Sci. Appl. doi.org/10.1038/s41377-020-00436-y
Liberal, I., et al. (2022). Zero-index metamaterials for classical and quantum light. Applied Physics Letters. doi.org/10.1063/5.0102712
TranSpread. (2024). Zero-index metamaterials and the future. Available at: https://phys.org/news/2024-02-index-metamaterials-future.html (Accessed on 20 February, 2024).
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