Ultra-low-loss on-chip zero-index materials


A refractive index of zero induces a wave vector with zero amplitude and undefined direction. Therefore, light propagating inside a zero-index medium does not accumulate any spatial phase advance, resulting in perfect spatial coherence. Such coherence brings several potential applications, including arbitrarily shaped waveguides, phase-mismatch-free nonlinear propagation, large-area single-mode lasers, and extended super radiance. A promising platform to achieve these applications is an integrated Dirac-cone material that features an impedance-matched zero index. However, although this platform eliminates ohmic losses via its purely dielectric structure, it still entails out-of-plane radiation loss (about 1 dB/μm), restricting the applications to a small scale.

Previous research by Professor Shanhui Fan’s research group at Stanford University report the design of a low-loss Dirac-cone zero-index material based on symmetry-protected bound states in the continuum (BICs). However, this Dirac cone is consisted of high-order modes, thus it is challenging to homogenize the photonic crystal slab as a bulk zero-index medium. In a new paper published in Light Science & Applications, a team of scientists, led by Professor Yang Li from the Department of Precision Instrument at Tsinghua University in China, Professor Eric Mazur from the John A. Paulson School of Engineering and Applied Sciences at Harvard University, the US, Professor Weiguo Chu from Nanofabrication Laboratory at the National Center for Nanoscience and Technology, China, and co-workers achieved a zero-index design based on a purely dielectric photonic crystal slab (PhC slab). This design supports an accidental Dirac-cone degeneracy of an electric monopole mode and a magnetic dipole mode at the center of the Brillouin zone. Such low-order mode-based design can be better treated as a homogeneous zero-index medium.

Their design consists of a square array of silicon pillars embedded in silicon dioxide background matrix, featuring an easy fabrication using standard planar processes. To reduce the radiation loss, they model the top and bottom interfaces of a zero-index PhC slab as two partially reflective mirrors to form a Fabry-Pérot (FP) cavity. Then, they adjust the thickness of this FP cavity to induce destructive interference of upward (downward) radiations in the far field. Inside each pillar, there are axially propagating mode(s) with dipole symmetry showing a round-trip phase of an integer multiple of 2π, therefore becoming resonance-trapped modes. The monopole mode does not radiate in the out-of-plane direction because of its intrinsic mode symmetry.

Their design exhibits an in-plane propagation loss as low as 0.15 dB/mm at the zero-index wavelength. Furthermore, the refractive index is near zero (|neff| < 0.1) over a bandwidth of 4.9%. On-chip BIC Dirac-cone zero-index PhC slabs provide an infinite coherence length with low propagation loss. This opens the door to applications of large-area zero-index materials in linear and nonlinear optics as well as lasers. For examples, electromagnetic energy tunneling through a zero-index waveguide with an arbitrary shape, nonlinear light generation without phase mismatch over a long interaction length, and lasing over a large area in a single mode.

The significance of the study is that it can serve as an on-chip lab to explore fundamental quantum optics such as efficient generation of entangled photon pairs and collective emission of many emitters. Particularly, because the spatial distribution of Ez in each silicon pillar oscillates between a monopole mode and a dipole mode as time elapses, all the quantum emitters within the pillars will experience the same spatial phase in the monopole half cycle. This significantly alleviates the challenge of precise positioning of quantum emitters in a photonic cavity.

Ultra-low-loss on-chip zero-index materials - Advances in Engineering
FIGURE: a, Zero-index PhC slab without BICs. A photonic dipole mode forming the zero index results in out-of-plane radiation, dramatically increasing the propagation loss of the material. b, Zero-index PhC slab with a BIC. At a particular height, all the upward/downward out-of-plane radiation destructively interferes. Credit: Tian Dong, Jiujiu Liang, Philip Camayd-Muñoz, Yueyang Liu, Haoning Tang, Shota Kita, Peipei Chen, Xiaojun Wu, Weiguo Chu, Eric Mazur, and Yang Li
Ultra-low-loss on-chip zero-index materials - Advances in Engineering
FIGURE: a, Three-dimensional schematic of a zero-index PhC slab and its unit cell, consisting of silicon pillars embedded in silicon dioxide. b, Parameter sweep for design of a BIC zero-index PhC slab. Quality factor of the dipole mode (colour map) and degeneracy of monopole and dipole modes at the centre of the Brillouin zone (white line) as a function of pillar radius and height. The red dot indicates the degeneracy of a monopole mode and a high-Q dipole mode. c, Three-dimensional dispersion surfaces showing the Dirac-cone dispersion corresponding to the optimized parameters at the red dot in (b). d, Effective index and propagation loss of the PhC slab. When the real part of the effective index crosses zero, the loss curve reaches its valley (~0.15 dB/mm), indicating an ultra-low-loss zero index. Credit: Tian Dong, Jiujiu Liang, Philip Camayd-Muñoz, Yueyang Liu, Haoning Tang, Shota Kita, Peipei Chen, Xiaojun Wu, Weiguo Chu, Eric Mazur, and Yang Li

About the author

Eric Mazur

Balkanski Professor of Physics and Applied Physics at Harvard University

Eric Mazur’s research group uses ultra-short laser pulses to study ultrafast dynamics in physical systems and to create extreme non-equilibrium conditions in matter. For instance, ultrashort laser pulses provide a direct view of the ultrafast carrier and lattice dynamics in photo excited solids. A better understanding of electron behavior in solids is important for both microelectronics and micromachining applications. Mazur’s group also uses these short laser pulses to coherently control the lattice dynamics in solids on the femtosecond time scale.

The high intensity of ultrashort laser pulses can also be used to micromachine waveguides and other photonic structures inside transparent materials. Such structures can be used to fabricate highly integrated photonic devices. Mazur’s group currently studies the physical processes that take place during micromachining and is developing an array of active and passive photonic devices. By tightly focusing these laser pulses inside biological samples, the group recently developed a nanosurgery technique that allows the micro manipulation of subcellular organelles inside living cells and small organisms.

Mazur’s group also discovered a modified form of silicon obtained by focusing femtosecond laser pulses on the surface of a silicon wafer in the presence of a sulfur containing gas. The optoelectronic properties of the resulting microstructured surface provide interesting physics and open the door to new applications.

About the author

Prof. Li received B.S. degree in telecommunication engineering (2006) and M.S. degree in electromagnetic field and microwave technology (2008) from Huazhong University of Science and Technology, China, and Ph.D. degree in Electrical Engineering (2012) from Iowa State University. From 2013 to 2018, Prof. Li was a Postdoctoral Fellow of Mazur group at Harvard University. Prof. Li received the IEEE Antennas and Propagation Society Doctoral Research Award and was nominated for the R.W.P. King Award. Prof. Li was a Co-PI of several NSF and Samsung grants.

Research interest: On-chip metamaterials, lithium-niobate electro-optic devices, inverse design of photonic devices and systems.


Tian Dong, Jiujiu Liang, Sarah Camayd-Muñoz, Yueyang Liu, Haoning Tang, Shota Kita, Peipei Chen, Xiaojun Wu, Weiguo Chu, Eric Mazur & Yang Li. Ultra-low-loss on-chip zero-index materials. Light: Science & Applications volume 10, Article number: 10 (2021) 

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