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Credit: by Yang Li, C. T. Chan and Eric Mazur
In a medium with a refractive index of zero n = 0, the effective wavelength becomes infinite, λ = 2πc/ωn→∞, and the spatial phase distribution of a propagating wave becomes uniform over the entire medium, overcoming many limitations imposed by the short spatial wavelength in the optical regime.
But how do we achieve “zero index”? Scientists have designed a special metamaterial (DCZIM) that shows this unique property. In a new paper published in Light: Science & Applications, Associate Professor Yang Li from Tsinghua University, Professor C.T. Chan from Hong Kong University of Science and Technology, and Professor Eric Mazur from Harvard University provided an overview of the photonic DCZIMs.
Dirac-like cone dispersion is formed by an accidental 3-fold degeneracy of two linear bands with conical dispersion and a quadratic dispersive band (which is flat near k = 0) at the center of the Brillouin zone. The group velocities of the two linear dispersive bands change signs at their crossing point. From an effective medium point of view, the change in sign of group velocity implies that the effective refractive index changes sign at the Dirac point, which in turn means that the effective refractive index is zero at the Dirac-point frequency.
“Our review focuses on the fundamental physics of DCZIMs, comparison of DCZIM with zero-index materials based on volume plasmons, fishnet metamaterials and doped ENZ media, classification of DCZIMs, demonstration of optical DCZIMs, and promising potential applications of DCZIMs.” said Yang.
Fundamental physics and design
At the center of the photonic bandstructure of a square lattice of 2D dielectric pillars, a photonic Dirac-like cone is induced by the accidental degeneracy of an electric monopole mode, a transverse magnetic dipole mode, and a longitudinal magnetic dipole mode. For a TM-polarized Dirac-like cone with an electric field polarized along the pillar axis, only the electric monopole mode and the transverse magnetic dipole mode can be excited. These two modes induce zero permittivity and permeability, respectively, thus achieving an impedance-matched zero refractive index. (Figure 2.)
Advantages
Compared with spatially continuous zero index provided by volume plasmons, and zero indices achieved by fishnet metamaterial and photonic doping, DCZIMs can be realized via purely dielectric structures, avoiding ohmic losses. Such a feature enables fabricating photonic DCZIMs in the form of zero-index waveguiding structures using standard planar processes in silicon-on-insulator (SOI) wafers.
“These zero-index waveguiding structures facilitate the interactions between light and a zero-index medium over a large area in arbitrary shapes on a photonic chip. Hence, DCZIMs can serve as a scalable and flexible on-chip platform for exploring the rich physics and potential applications of zero index.” the scientists added.
Applications
“We believe that by fully leveraging DCZIMs’ unique electromagnetic property—the infinite effective spatial wavelength, there are promising potential applications of DCZIMs in electromagnetic waveguides, free-space wave manipulation, metrology, nonlinear optics, lasers and quantum optics.” (Figure 3.)
For example, in electromagnetic waveguides, DCZIMs can be used to achieve super-coupling. In free-space wave manipulation, we can achieve leaky-wave antennas for continuous beam scanning through broadside by varying the operating frequency. Besides, we can measure the displacement of the reflector by observing the intensity of the field within the metamaterial, providing a resolution better than a quarter of the free-space wavelength without using super-resolution imaging techniques.
DCZIMs can also be used in nonlinear optics for phase matching and nonlinear enhancement. In lasers, we can dramatically increase the mode spacings and eliminate the in-plane feedback, enabling larger-area single-mode Photonic Crystal Surface Emitting Lasers (PCSELs) with higher output power. Additionally, by taking advantage of the infinite spatial wavelength and perfect spatial coherence of zero-index metamaterials, we can overcome several limitations in quantum optics.
Summary and outlook
The scientists forecast that DCZIMs have the unique feature of using only dielectric structures compared with other mechanisms. Such a feature enables fabricating photonic DCZIMs in the form of zero-index waveguiding structures using standard planar processes in SOI wafers.
These zero-index waveguiding structures facilitate the interactions between light and zero-index medium over a large area in arbitrary shapes on a photonic chip. Based on these zero-index waveguiding structures, the interaction length of phase mismatching-free nonlinear signal generation can be increased from sub-free-space wavelength scale to almost 10 free-space wavelengths, integrated zero-index waveguides with arbitrary shapes may be realized, larger-area single-mode PCSELs with higher output power might be achieved, and extended superradiance may be realized for many emitters over a large spatial extent. Hence, DCZIMs can serve as a scalable and flexible on-chip platform for exploring the rich physics and potential applications of zero index.
“DCZIMs also have some limitations compared with other mechanisms for realizing a near-zero refractive index.” the scientists admitted. “The macroscopic zero index provided by DCZIMs can only replace the continuous zero index provided by volume plasmons for certain light-matter interactions.”
“And it is more challenging to fabricate DCZIMs in the out-of-plane configuration for applications in free-space optics. Moreover, DCZIMs consist of periodic structures, limiting their flexibility in forming an arbitrarily-shaped geometry. Hence, we should choose the mechanism to achieve a near-zero refractive index according to the particular application.”
So far, most potential applications of DCZIMs are only predicted by theoretical results, while a few are demonstrated through proof-of-concept experiments. To further develop those potential applications and even achieve performance beyond the state of the arts, such as zero-index waveguides whose overall performance is better than that of silicon waveguides, we envision “customized” DCZIMs designed to satisfy the particular requirements of certain applications.
Journal
Light Science & Applications