Robust Geometries for Second-Harmonic-Generation in Microrings Exhibiting a 4-Bar Symmetry

At a Glance

Metadata	Details
Publication Date	2020-12-17
Journal	Applied Sciences
Authors	Pierre Guillemé, Chiara Vecchi, Claudio Castellan, Stefano Signorini, Mher Ghulinyan
Institutions	National Institute of Optics, Fondazione Bruno Kessler
Analysis	Full AI Review Included

Technical Documentation & Analysis: Robust Geometries for Second-Harmonic Generation

Reference Paper: Guillemé et al., “Robust Geometries for Second-Harmonic-Generation in Microrings Exhibiting a 4-Bar Symmetry,” Appl. Sci. 2020, 10, 9047.

Executive Summary

Core Achievement: Identification of robust microring resonator geometries that maintain high Second-Harmonic Generation (SHG) efficiency despite unavoidable fabrication tolerances (variations in thickness and radius).
Mechanism: Exploitation of the 4-bar symmetry inherent in zinc-blend or diamond lattice materials to achieve quasi-phase matching (QPM) for second-order optical nonlinearities ($\chi^{(2)}$).
Material Limitation: The study used silicon, a centrosymmetric material, requiring complex strain engineering or p-i-n junctions to induce the necessary $\chi^{(2)}$ susceptibility.
Performance Metrics: Achieved conversion efficiencies ($\eta$) up to $1.7 \times 10^{-4}$ for a 1 mW pump, with robust geometries tolerating up to 16 nm thickness variation and 45 nm radius variation while maintaining $\eta \geq 10^{-4}$.
Wavelength Range: Pump wavelengths ($\lambda_{f}$) were constrained to 2.2 µm to 2.55 µm to avoid efficiency degradation due to Two-Photon Absorption (TPA) in silicon.
6CCVD Value Proposition: The methodology is directly transferable to diamond, a superior material system (diamond lattice) that inherently possesses the required symmetry and eliminates TPA limitations, enabling significantly higher conversion efficiencies and power handling.

Technical Specifications

The following data points were extracted from the theoretical modeling and simulation results:

Parameter	Value	Unit	Context
Fundamental Wavelength ($\lambda_{f}$) Range	2.2 to 2.55	µm	Pump source, constrained to avoid Si TPA
Second Harmonic Wavelength ($\lambda_{SH}$) Range	1.1 to 1.275	µm	Generated signal
Waveguide Thickness ($e$)	280 to 440	nm	Optimized range for robust SHG
Waveguide Width ($w$)	800 to 1000	nm	Tested geometries
Internal Radius ($R_{in}$) Range	14.275 to 60.755	µm	Microring dimensions
Maximum Conversion Efficiency ($\eta$)	1.7 x 10^-4	Unitless	Achieved with $P_{in}$ = 1 mW
Minimum Robust Efficiency ($\eta_{min}$)	1.0 x 10^-4	Unitless	Threshold for robust operation
Thickness Tolerance (Robust Geometry)	16	nm	Range maintaining $\eta \geq 10^{-4}$
Radius Tolerance (Robust Geometry)	45	nm	Range maintaining $\eta \geq 10^{-4}$
Assumed Q-factor ($Q_{int}$, $Q_{cpl}$)	10⁴	Unitless	Critical coupling condition
Second-Order Susceptibility ($\chi^{(2)}_{zxy}$)	1	pm/V	Assumed induced value in Si

Key Methodologies

The research relied heavily on computational modeling and specific material constraints to identify optimal geometries:

Simulation Platform: Finite Element Method (FEM) simulations were performed using COMSOL Multiphysics (v 5.3) to model mode profiles and determine geometries satisfying SHG conservation laws.
Phase Matching Condition: The study focused on the quasi-phase matching condition exploiting the 4-bar symmetry of the diamond lattice structure, requiring angular momentum conservation ($m_{SH} = 2m_{f} + 2$).
Mode Constraints: Simulations were limited to the fundamental mode (Hz polarization, radial number $p_{f}=1$) and the SH mode (Ez polarization, radial number $p_{SH}=3$).
TPA Avoidance: A critical constraint was imposed on the pump wavelength ($\lambda_{f}$ > 2.2 µm) to mitigate Two-Photon Absorption (TPA) in the silicon core, which drastically degrades conversion efficiency.
Refractive Index Modeling: Material dispersion for Si, SiO₂, and Si₃N₄ was modeled using Sellmeier fits derived from experimental ellipsometry measurements.
Efficiency Calculation: Conversion efficiency ($\eta$) was calculated using the undepleted pump approximation, assuming a critical coupling condition with Q-factors fixed at $10^{4}$.
Robustness Analysis: Geometries were optimized by analyzing the variation of $\eta$ as a function of small changes in thickness ($e$) and internal radius ($R_{in}$), identifying flat-top regions where SHG performance is insensitive to fabrication defects.

6CCVD Solutions & Capabilities

The research successfully demonstrated a robust geometric approach for SHG in integrated photonics. However, the reliance on silicon necessitates complex engineering (strain, p-i-n junctions) and imposes severe limitations (TPA) that restrict efficiency and power handling.

6CCVD offers MPCVD diamond materials that inherently overcome these limitations, providing a superior platform for replicating and extending this high-efficiency nonlinear research.

Applicable Materials

The 4-bar symmetry required for QPM is intrinsic to the diamond lattice structure. 6CCVD recommends the following materials for next-generation quadratic frequency comb sources:

Optical Grade Single Crystal Diamond (SCD): Ideal for high-power, low-loss microring resonators. SCD’s ultra-wide bandgap (5.5 eV) completely eliminates TPA in the near-IR/visible range ($\lambda_{f}$ > 2.2 µm), allowing for significantly higher pump powers and conversion efficiencies than achievable in Si.
Boron-Doped Diamond (BDD): For applications requiring an intrinsic $\chi^{(2)}$ without external strain. BDD is a superior alternative to induced $\chi^{(2)}$ in Si p-i-n junctions, offering stable, integrated nonlinear functionality.

Customization Potential

The paper highlights the need for precise, thin-film geometries (280 nm to 440 nm thickness) and integrated structures. 6CCVD’s custom fabrication capabilities are perfectly suited for this application:

Research Requirement	6CCVD Capability	Specification Match
Thin-Film SCD/PCD	Custom Thickness Control	SCD available from 0.1 µm up to 500 µm.
Large-Scale Integration	Custom Dimensions	Polycrystalline Diamond (PCD) plates/wafers up to 125 mm diameter.
High Q-Factor Resonators	Ultra-Smooth Polishing	SCD polished to Ra < 1 nm; Inch-size PCD polished to Ra < 5 nm. Essential for minimizing scattering losses in microrings.
Integrated Electrodes	Custom Metalization	In-house deposition of Au, Pt, Pd, Ti, W, and Cu, critical for implementing electro-optic modulation (Pockels effect) or p-i-n structures referenced in the paper.

Engineering Support

6CCVD’s in-house PhD team specializes in the material science and engineering of diamond for advanced photonics. We can assist researchers in transferring the robust geometric methodology demonstrated in this paper to the diamond platform, specifically optimizing:

Material Selection: Choosing the optimal SCD grade or BDD doping level to maximize the effective $\chi^{(2)}$ for similar Quadratic Frequency Comb Generation projects.
Strain Engineering: Consulting on methods to apply controlled strain to SCD substrates to further enhance $\chi^{(2)}$ via the Pockels effect, leveraging diamond’s exceptional mechanical properties.
Design for Fabrication: Ensuring that custom diamond dimensions and polishing specifications meet the stringent requirements for high-Q microring resonators.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Microring resonators made of materials with a zinc-blend or diamond lattice allow exploiting their 4-bar symmetry to achieve quasi-phase matching condition for second-order optical nonlinearities. However, fabrication tolerances impose severe limits on the quasi-phase matching condition, which in turn degrades the generation efficiency. Here, we present a method to mitigate these limitations. As an example, we studied the geometry and the pump wavelength conditions to induce the second-harmonic generation in silicon-based microrings with a second-order susceptibility χzxy(2)≠0. We found the best compromises between performances and experimental requirements, and we unveil a strategy to minimize the impacts of fabrication defects. The method can be easily transferred to other material systems.

Tech Support

Original Source

DOI: https://doi.org/10.3390/app10249047

References

2000 - Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb [Crossref]
2015 - Silicon-chip mid-infrared frequency comb generation [Crossref]
1999 - Broadband optical frequency comb generation with a phase-modulated parametric oscillator [Crossref]
2014 - Integrated high quality factor lithium niobate microdisk resonators [Crossref]
2016 - Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency [Crossref]