Enhanced Third-Harmonic Generation in Diamond Photonic Crystal Slabs via Doubly Resonant Quasi-Bound States in the Continuum

summary

Video file (mp4)

The gist

The gist: The authors propose and numerically demonstrate doubly resonant third-harmonic generation in a diamond photonic crystal (PhC) slab, in which the fundamental harmonic (FH) and the third

In short

Researchers engineered a diamond photonic crystal slab to achieve doubly resonant third-harmonic generation by simultaneously matching the fundamental and third harmonic modes within the same structure. By breaking symmetry using triangular holes, they enabled a previously forbidden nonlinear coupling, leading to high efficiency ($2.7 imes10^{-7}~ ext{W}^{-2}$) and establishing a scalable route for on-chip frequency conversion in all-diamond platforms.

Key concepts

Doubly Resonant THG
This technique involves making both the fundamental light (first harmonic) and the third harmonic light (third harmonic) oscillate strongly at the exact same time within a photonic crystal structure. This simultaneous resonance dramatically enhances how efficiently light is converted from one frequency to another, similar to tuning two musical notes perfectly together.
Quasi-BIC Mode
This refers to a mode that is nearly bound (trapped) within the material structure but not perfectly confined. In this study, the third harmonic mode acts as a quasi-BIC because its symmetry prevents it from radiating into free space, allowing it to be highly localized and coupled effectively with other modes.
Symmetry Breaking
The original design used circular holes, which preserved a high degree of symmetry that prevented the fundamental and third harmonic modes from interacting nonlinearly. By changing the hole shape to equilateral triangles, the symmetry was broken. This change is crucial because it allows a previously weak nonlinear coupling between the two modes to become strong enough for efficient conversion.
Figure of Merit (FOM)
The FOM is a mathematical metric used to guide the design process. In this study, it quantifies how good the proposed unit cell geometry and cavity structure are at achieving high third-harmonic generation efficiency. Optimizing this value helps researchers find the best physical dimensions for the diamond slab before expensive fabrication.

Terminology used across episodes

This episode discusses

The paper

Enhanced Third-Harmonic Generation in Diamond Photonic Crystal Slabs via Doubly Resonant Quasi-Bound States in the Continuum · Read on arXiv

Sangmin Ji, Satoshi Iwamoto, Hideki Gotoh

Research Institute for Semiconductor Engineering, Hiroshima University · Research Center for Advanced Science and Technology, The University of Tokyo

We propose and numerically demonstrate doubly resonant third-harmonic generation (THG) in a diamond photonic crystal (PhC) slab, in which the fundamental harmonic (FH) and the third harmonic (TH) modes are simultaneously resonant within the same membrane. A hexagonal-lattice slab with triangular air holes is designed so that a K-point band-edge FH mode and a Γ-point quasi-bound-state-in-the-continuum (quasi-BIC) TH mode satisfy the frequency-tripling condition 3ω 1 aboutω 3. Modifying the hole shape from circular to equilateral triangular breaks the in-plane symmetry that otherwise forces the nonlinear coupling to vanish, thereby converting a TH mode with negligible overlap into one with finite while simultaneously reducing the required slab thickness. Guided by a closed-form expression for THG efficiency derived from coupled-mode theory, we design the unit cell and a PhC heterostructure cavity. Three-dimensional simulations of the designed cavity yield a normalized THG efficiency η=2.7 times10-7 W-2 under moderate quality factors, which is projected to reach 0.034 W-2 at the fabrication-limited quality factor (Q = 200,000). Because the operating wavelength is set by the lattice constant, this design, combined with the ultra-wide transparency window of diamond, can map a single geometry across various fabricable wavelengths, spanning from telecommunication bands to color-center-resonant visible and deep-UV outputs. These results establish a robust route toward efficient, monolithic on-chip frequency conversion in an all-diamond platform for quantum and nonlinear photonics.

DOI: 10.1016/j.cap.2026.10.004

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: Today's paper: "Enhanced Third-Harmonic Generation in Diamond Photonic Crystal Slabs via Doubly Resonant Quasi-Bound States in the Continuum".

Mira: The gist: The authors propose and numerically demonstrate doubly resonant third-harmonic generation in a diamond photonic crystal (PhC) slab,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: To dive deeper into the paper "Enhanced Third-Harmonic Generation in Diamond Photonic Crystal Slabs via Doubly Resonant Quasi-Bound States in the Continuum," we need to understand exactly what they are proposing with this geometry.

Mira: Essentially, it boils down to them showing how they can get both fundamental and third harmonic modes resonating at the same time inside a diamond photonic crystal slab.

Lev: They achieved this by breaking the symmetry of the holes, which lets them create that nonlinear coupling that normally wouldn't happen in a centrosymmetric material like diamond.

Kai: That symmetry breaking is what makes it all work; it turns a weak interaction into something measurable and controllable within a realistic slab thickness.

Mira: They use coupled-mode theory to set up a figure of merit—that equation that tells you how good the design is—and they optimized it using material properties from single-crystal diamond.

Lev: So, what this means for us in terms of actual hardware is that we need high quality factors for both those resonant modes and a big nonlinear coupling coefficient to get a meaningful power conversion.

Kai: If we can manage those quality factors, this structure gives us a solid way to do on-chip frequency conversion using just diamond platforms.

Mira: It’s not just about one specific wavelength either; because the geometry is defined by the lattice constant, you can map this whole design across different wavelengths.

Lev: The real hurdle is that every time you want to apply this idea to a new nonlinear process or a different material, you have to redo all that optimization work.

Kai: So the big picture here is using symmetry breaking in diamond photonic crystals to enable efficient frequency tripling through simultaneous resonance of fundamental and third harmonic modes.

Mira: It sets up a general and scalable route toward monolithic frequency conversion in an all-diamond platform for quantum and nonlinear photonics.

Conclusion: Kai: So we're wrapping up our look at the paper "Enhanced Third-Harmonic Generation in Diamond Photonic Crystal Slabs via Doubly Resonant Quasi-Bound States in the Continuum."

Mira: It really boils down to them showing how they can get both fundamental and third harmonic modes resonating at the same time inside a diamond photonic crystal slab.

Lev: They achieved this by breaking the symmetry of the holes, which lets them create that nonlinear coupling that normally wouldn't happen.

Kai: That symmetry breaking is what makes it all work; it turns a weak interaction into something measurable and controllable within a realistic slab thickness.

Mira: They used coupled-mode theory to set up a figure of merit—that equation that tells you how good the design is—and they optimized it using material properties from single-crystal diamond.

Lev: So, what this means for us in terms of actual hardware is that we need high quality factors for both those resonant modes and a big nonlinear coupling coefficient to get a meaningful power conversion.

Kai: If we can manage those quality factors, this structure gives us a solid way to do on-chip frequency conversion using just diamond platforms.

Mira: It’s not just about one specific wavelength either; because the geometry is defined by the lattice constant, you can map this whole design across different wavelengths.

Lev: The real hurdle is that every time you want to apply this idea to a new nonlinear process or a different material, you have to redo all that optimization work.

Kai: So the big picture here is using symmetry breaking in diamond photonic crystals to enable efficient frequency tripling through simultaneous resonance of fundamental and third harmonic modes.

Mira: It sets up a general and scalable route toward monolithic frequency conversion in an all-diamond platform for quantum and nonlinear photonics.

Lev: And next, we need to see how this kind of integrated on-chip conversion stacks up against the error correction overhead we deal with in superconducting qubits.

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