🔬 optics

Planar Scale Invariant Waveguides and Resonators with Uniform Air Confined Modes

This paper presents a planar metamaterial waveguide and resonator on a silicon-on-insulator platform that utilizes sub-wavelength gratings to achieve scale-invariant, uniform air-confined light modes with high quality factors, offering a robust and CMOS-compatible solution for enhanced light-matter interaction applications.

Original authors: Mohammad Enjavi, Amin Khavasi, Ashkan Zandi, Saeed Javadizadeh, Reza Marzban, Devin K Brown, Ali Adibi

Published 2026-02-04

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CC BY 4.0

Original authors: Mohammad Enjavi, Amin Khavasi, Ashkan Zandi, Saeed Javadizadeh, Reza Marzban, Devin K Brown, Ali Adibi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to guide a beam of light through a tiny, invisible hallway. Usually, when light travels through a material like silicon, it gets squeezed into a tight, concentrated beam in the middle, like water rushing through a narrow pipe. This is great for some things, but if you want to use that light to interact with something floating in the air (like a gas or a virus), the light is mostly stuck inside the silicon, barely touching the air.

The researchers in this paper built a special kind of "light hallway" that solves this problem. Here is how they did it, using simple analogies:

1. The "Magic Air Hallway"

Think of a standard light guide as a solid brick wall. The light bounces around inside the brick. The researchers wanted the light to travel mostly through the air gap between two walls, not inside the walls themselves.

To do this, they built a structure on a silicon chip that looks like two solid silicon walls with a gap in the middle. But instead of leaving the gap empty or just filling it with air, they filled it with a Sub-Wavelength Grating (SWG).

The Analogy: Imagine the gap is filled with a very fine, invisible mesh or a "forest" of tiny silicon pillars. To the light, which is too small to see the individual pillars, this mesh looks like a solid, uniform material. This trick allows the light to feel like it's traveling through a consistent medium, even though it's actually weaving through a pattern of silicon and air.

2. The "Stretchy Rubber Band" (Scale Invariance)

The most impressive feature of their design is something they call "scale invariance."

The Analogy: Imagine a normal rubber band. If you stretch it, it gets thinner and the tension changes. If you cut it shorter, the way it vibrates changes completely.
Their Innovation: The researchers made a "magic rubber band" (their waveguide) that doesn't change its behavior when you stretch or shrink it. Whether the air gap is very narrow or very wide, the light travels through it exactly the same way. The "speed" of the light (effective index) stays constant, and the shape of the light beam stays the same. This is rare and very useful because it means they can make the device bigger or smaller without having to redesign the whole thing.

3. The "Evenly Spread Crowd" (Uniform Field)

In a normal light guide, the light is like a crowd of people all huddled in one tight circle in the middle of a room. If you try to interact with them, you can only reach the people in the center.

Their Innovation: In their new design, the light spreads out evenly across the entire air gap, like a crowd of people standing shoulder-to-shoulder filling the whole room.
Why it matters: Because the light is spread out evenly, there are no "hot spots" (super bright spots that can burn things). This allows the device to handle much more power without breaking. It also means the light interacts with everything in the air gap equally, which is perfect for sensing.

4. The "Race Track" (The Resonator)

To prove this works, they built a "racetrack" loop using this special hallway.

The Result: They sent light around this loop and found that it could bounce around thousands of times before fading away. They measured a "Quality Factor" (Q) of about 40,000.
The Analogy: Think of a swing. A high Q means the swing keeps going for a long time with very little push. A Q of 40,000 is like a swing that barely slows down at all. This is a very high number for a device where the light is mostly in the air.

5. Built to Last (Robustness)

One worry with tiny chips is that if you make a tiny mistake while building them (like a wall being slightly too thick or too thin), the whole thing stops working.

The Finding: The researchers tested their design against "imperfections." They found that even if the silicon layer was slightly too thick or the walls were slightly the wrong width, the light still behaved perfectly. It's like a car that drives smoothly even if the road is a little bumpy.

Summary

The team created a new type of light guide on a standard computer chip (SOI platform) that:

Keeps light trapped in the air instead of the silicon.
Works the same way regardless of how wide the gap is (scale-invariant).
Spreads the light out evenly so it doesn't burn the material (high power handling).
Is tough enough to survive small manufacturing errors.
Achieves a very high performance level (Q ~ 40,000) while doing all this.

They claim this makes it an excellent tool for things that need light to interact with matter, such as sensing (detecting gases or chemicals), quantum photonics, and nonlinear optics, all while being compatible with the standard factories that make computer chips today.

Technical Summary: Planar Scale-Invariant Waveguides and Resonators with Uniform Air-Confined Modes

Problem Statement
Resonance-based integrated photonic structures are critical for light-matter interaction applications such as sensing, atom-photon coupling, and nonlinear optics. However, existing designs face significant limitations. High-index material confinement often restricts interaction efficiency because analytes or atomic vapors interact only with the evanescent tail of the optical mode. Conversely, structures designed to confine light in low-index regions (e.g., air or water) often suffer from low quality factors ( $Q$ ) or non-uniform field distributions. Specifically, slot resonators offer air confinement but typically exhibit very low $Q$ factors in large structures, while sub-wavelength grating (SWG) based structures often display non-uniform mode patterns that reduce interaction efficiency. Furthermore, previous scale-invariant designs have been limited by non-planar geometries or multi-material cores, complicating fabrication and integration with standard CMOS processes. There is a demonstrated need for resonators that combine high $Q$ factors, large interaction volumes, uniform field confinement in air, and compatibility with planar fabrication.

Methodology
The authors propose a planar metamaterial-based waveguide and resonator design implemented on a standard silicon-on-insulator (SOI) platform (220 nm Si layer). The core innovation involves embedding a sub-wavelength grating (SWG) region between two silicon ridges.

Design Principle: The structure consists of two Si ridges of width $w$ separated by an SWG region of width $d$ and period $\Lambda$ . The SWG period is engineered such that its effective index matches that of a solid Si waveguide of width $2w$ . This condition ensures that the effective index of the guided mode remains constant regardless of the separation $d$ , thereby achieving scale invariance in the lateral direction.
Simulation: Theoretical design and verification were conducted using 3D finite-difference time-domain (FDTD) simulations (Lumerical) with Bloch boundary conditions to analyze band structures and field profiles.
Fabrication: Devices were fabricated using electron-beam lithography (EBL) and inductively coupled plasma reactive-ion etching (ICP-RIE) on a 220-nm SOI platform. Hydrogen silsesquioxane (HSQ) resist was used for patterning.
Characterization:
- Waveguides: Unbalanced Mach–Zehnder interferometers (MZIs) were used to extract the effective and group indices by analyzing transmission spectra.
- Resonators: Racetrack resonators were fabricated and coupled to the scale-invariant waveguides. Transmission spectra were measured using a tunable laser and high-speed spectrum analyzer to determine loaded and intrinsic $Q$ factors.
- Robustness Analysis: Statistical simulations were performed to assess sensitivity to fabrication imperfections, including variations in Si layer thickness and lithographic deviations in ridge width ( $w$ ).

Key Contributions

Planar Scale-Invariant Waveguide: The authors demonstrate a waveguide that maintains a nearly constant effective index and a uniform field distribution across varying widths while confining light primarily in the air region. This is achieved using a single-material (Si) SOI platform, avoiding the multi-material complexities of previous scale-invariant designs.
Uniform Field Profile: The design supports a "flat-top" optical mode in the air region. Simulations indicate that the maximum field intensity in the scale-invariant waveguide is reduced by a factor of 2.17 compared to a conventional rectangular waveguide of the same total width and power, theoretically enabling higher power handling.
High-Q Air-Confined Resonator: The authors successfully translated the waveguide concept into a racetrack resonator. They report an intrinsic quality factor ( $Q$ ) of approximately 40,000 for a resonator with strong light confinement in air, which they state is the largest value reported to date for such resonators.
Fabrication Robustness: The study demonstrates that the scale-invariant properties are robust against typical fabrication imperfections, including Si thickness variations of up to $\pm10\%$ and lithographic width deviations of $\sim15$ nm.

Experimental Results

Scale Invariance Verification: MZI measurements confirmed that the effective index remains nearly constant as the total waveguide width ( $2w + d$ ) varies. Experimental data (red dots in Fig. 2d) aligned closely with 3D FDTD simulations (blue line), contrasting sharply with the varying indices of conventional Si ridge or pure SWG waveguides of equivalent width.
Bandwidth: The uniform field profile was maintained across a 200 nm wavelength range (1450 nm to 1650 nm), with less than $\pm6\%$ deviation in intensity, representing a large operational bandwidth for scale-invariant SOI waveguides.
Resonator Performance: A critically coupled racetrack resonator with a 290 nm coupling gap exhibited a loaded $Q$ of 20,000. This corresponds to an intrinsic $Q$ of $\sim40,000$ and a waveguide loss of $\approx1.5$ dB/mm.
Group Index: Measurements indicated a group index between 3.2 and 3.8, confirming the absence of slow-light behavior.

Significance and Claims
The paper claims to present the first demonstration of scale-invariant resonators with high field confinement in air and reasonably high $Q$ factors on a standard SOI platform. The significance of this work lies in its ability to provide large interaction regions with uniform light intensity, which is advantageous for light-matter interaction applications such as sensing, quantum photonics, and nonlinear optics. The uniform field distribution eliminates "hot spots," offering improved power handling and robustness against fabrication imperfections. By utilizing a planar, single-material design compatible with CMOS processes, the authors position this technology as a promising platform for integrated photonics that overcomes the trade-offs between mode volume, quality factor, and fabrication complexity found in previous approaches.