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	Fondazione Bruno Kessler, National Institute of Optics
Analysis	Full AI Review Included

Executive Summary

This analysis focuses on designing robust silicon microring resonator geometries for efficient Second-Harmonic Generation (SHG), specifically addressing limitations imposed by typical fabrication tolerances in integrated photonics.

Core Value Proposition: The study identifies specific microring geometries that exhibit SHG efficiency nearly independent of small variations in waveguide thickness and radius, thereby relaxing stringent fabrication requirements.
Mechanism: SHG is achieved by exploiting the intrinsic 4-bar symmetry of the silicon lattice, enabling a quasi-phase matching condition (m_SH = 2m_f + 2).
Robust Geometry Identified: The optimal robust geometry occurs where the internal radius (R_in) as a function of thickness (e) exhibits a flat maximum (e ≈ 330 nm, R_in ≈ 60.755 µm).
Tolerance Improvement: This robust design maintains high efficiency (η ≥ 10^-4) across a thickness variation range of 16 nm, a significant improvement over non-optimized geometries which tolerate only about 1 nm of variation.
Performance: Theoretical conversion efficiencies up to 1.7 x 10^-4 were calculated for 1 mW pump power, using a pump wavelength (λ_f) greater than 2.2 µm to avoid Two-Photon Absorption (TPA).
Transferability: The methodology, which relies on analyzing modal confinement dependence on geometry, can be easily transferred to other material systems (like GaAs or AlN) that also exhibit 4-bar symmetry.
Application Focus: The resulting devices are ideal for integrated quadratic frequency comb sources and on-chip frequency conversion for metrology and sensing applications.

Technical Specifications

Parameter	Value	Unit	Context
Material System	Strained Silicon (Si)	N/A	Core material, assumed X⁽²⁾_zxy ≠ 0
Cladding Material	Si₃N₄	N/A	Cladding layer thickness: 140 nm
Waveguide Width (w)	800	nm	Width used for robustness analysis
Optimal Robust Thickness (e)	330	nm	Thickness yielding maximum tolerance
*Optimal Robust Internal Radius (R_in)*	60.755	µm	Radius corresponding to optimal thickness
Pump Wavelength (λ_f)	> 2.2	µm	Minimum wavelength to prevent Two-Photon Absorption (TPA)
Second Harmonic Wavelength (λ_SH)	~1.15	µm	Generated frequency
Maximum Conversion Efficiency (η_max)	1.7 x 10^-4	N/A	Calculated for P_in = 1 mW, Q = 10⁴
Robust Thickness Tolerance Range	16	nm	Range where η ≥ 10^-4 (around e = 330 nm)
Non-Robust Thickness Tolerance Range	1	nm	Range where η ≥ 10^-4 (around e = 440 nm)
Assumed Second-Order Susceptibility (X⁽²⁾_zxy)	1	pm/V	Value used for efficiency modeling
Assumed Quality Factor (Q)	10⁴	N/A	Used for both intrinsic (Q_int) and coupling (Q_cpl)
Pump Power (P_in)	1	mW	Used for efficiency calculations

Key Methodologies

The design and optimization relied on Finite Element Method (FEM) simulations combined with experimental material data to ensure both energy and angular momentum conservation for SHG.

Electromagnetic Simulation: Finite Element Method (FEM) simulations using COMSOL Multiphysics were employed to determine the resonant modes and effective indices of the microring structure.
Material Dispersion Modeling: Refractive index dispersions for Si, SiO₂, and Si₃N₄ were derived from Sellmeier fits of experimental ellipsometry measurements performed at the fabrication facility (Fondazione Bruno Kessler).
Mode Selection and Conservation:
- Energy Conservation: Enforced λ_f = 2λ_SH.
- Angular Momentum Conservation (QPM): Enforced m_SH = 2m_f + 2, utilizing the 4-bar symmetry of the Si lattice.
- Polarization/Mode Order: Focused on a Hz-polarized fundamental mode (p_f = 1) generating an Ez-polarized SH mode (p_SH = 3).
Geometry Iteration: For fixed width (w) and thickness (e), the internal radius (R_in) was iteratively adjusted until the SHG phase-matching conditions were satisfied.
Efficiency Calculation: Conversion efficiency (η) was calculated using the undepleted pump approximation, incorporating the field overlap integral (K) between the fundamental and SH modes, and assuming critical coupling (Q = 10⁴).
Robustness Analysis: The relationship between the required radius and thickness (R_in = f(e)) for SHG was plotted. The geometry corresponding to the flat maximum of this curve (e ≈ 330 nm) was selected as the robust design, as small thickness variations near this point require minimal radius adjustment, minimizing efficiency degradation.

Commercial Applications

The development of robust, integrated SHG devices in silicon is critical for advancing integrated nonlinear photonics, targeting applications where stability and mass manufacturability are essential.

Integrated Frequency Combs: Enables the creation of integrated quadratic frequency comb sources (OFCs) that utilize second-order nonlinearities to achieve octave-spanning spectra, crucial for high-precision measurements.
Metrology and Sensing: The stability and precision offered by integrated OFCs are fundamental for advanced on-chip metrology and high-sensitivity optical sensing systems.
Radio-on-Fiber (RoF): Frequency conversion capabilities are essential for high-speed data transmission and signal processing in radio-on-fiber networks.
Material Characterization: The SHG measurement technique serves as a tool to scout and characterize new materials suitable for quadratic OFCs by measuring their effective second-order nonlinear dielectric susceptibility (X⁽²⁾).
Integrated Nonlinear Optics: General on-chip frequency conversion, such as converting telecom wavelengths (2.3 µm) to visible wavelengths (1.15 µm), for use in compact photonic circuits.

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

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2015 - Silicon-chip mid-infrared frequency comb generation [Crossref]
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2014 - Integrated high quality factor lithium niobate microdisk resonators [Crossref]
2016 - Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency [Crossref]