AI 中文总结
研究通过双共振在金刚石光子晶体平板中实现三次谐波产生，利用耦合模理论设计结构，经模拟得到中等品质因数下的归一化效率，有望在特定品质因数下提升，为全金刚石平台的频率转换提供途径。
AI 中文摘要
我们提出并通过数值证明了金刚石光子晶体（PhC）平板中的双共振三次谐波产生（THG），其中基波（FH）和三次谐波（TH）模式在同一膜内同时共振。设计了具有三角形气孔的六边形晶格平板，使K点带边FH模式和Γ点连续谱中的准束缚态（quasi - BIC）TH模式满足三倍频条件$3\omega_1\approx\omega_3$。将孔形状从圆形改为等边三角形打破了面内对称性，否则会使非线性耦合消失，从而将重叠可忽略的TH模式转换为具有有限重叠的模式，同时减小所需平板厚度。在耦合模理论导出的THG效率闭式表达式的指导下，设计了晶胞和PhC异质结构腔。对设计腔的三维模拟在中等品质因数下得到归一化THG效率$\eta = 2.7\times10^{-7}~\mathrm{W}^{-2}$，预计在制造限制的品质因数（Q = 200,000）下达到约$0.034~\mathrm{W}^{-2}$。由于工作波长由晶格常数设定，这种设计与金刚石的超宽透明窗口相结合，可在从电信波段到色心共振可见光和深紫外输出的各种可制造波长上映射单一几何结构。这些结果为量子和非线性光子学的全金刚石平台中高效、单片片上频率转换建立了一条稳健的途径。
英文摘要
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 $3ω_1\approxω_3$. 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 $η=2.7\times10^{-7}~\mathrm{W}^{-2}$ under moderate quality factors, which is projected to reach ~$0.034~\mathrm{W}^{-2}$ 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.
