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Giant enhancement of harmonic generation in all-dielectric resonant waveguide gratings of quasi-bound states in the continuum

Tingyin Ning, Xin Li, Yan Zhao, Luying Yin, Yanyan Huo, Lina Zhao, and Qingyang Yue

Open Access Open Access

Abstract

We report the giant enhanced optical harmonic generation in all-dielectric silicon nitride (SiN) based resonant waveguide gratings (RWGs) of quasi-bound states in the continuum (BICs) of ultra-high Q factor and localized field. The BICs are realized by tuning the excitation of the guided modes modulated by geometry parameters of four-part grating layer. At a feasible structure of quasi-BIC for nanofabrication, the SHG and THG are enhanced by 103 and 106, compared with those from the RWGs of traditional two-part grating layer, respectively, and even up to 108 and 1010 compared with those from the planar SiN film, respectively. The resonance wavelength of quasi-BICs can be effectively tuned by the angle of incidence, while almost not affect the enhancement of SHG and THG response. Our results show that the efficiency harmonic generation from all-nonlinear-dielectric RWGs of quasi-BICs has potential applications for the integrated nonlinear photonic devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (6)
Fig. 1.
Fig. 1. (a) Schematic diagram of the section of RWG structure as a simulation domain. da is the width of SiN, db and dc are the width of air. hg and hw are the height of grating layer and waveguide layer, respectively. The incidence light of TM-polarization and angle of incidence θ is excited on port 1. k, E and H are the wavevector, electric- and magnetic-field of the incident light, respectively. The periodic boundary condition is used for the left- and right-boundary. (b) Guided mode resonance of the grating waveguide structure. 0 and −1 represents the 0th and −1st order of diffraction. β is the propagating constant of the guided mode. (c) Dispersion relation of the TM0 guided mode in the waveguide layer (black solid line), and kx=kx,i (i=-1,-2) under different angle of incidence, 1° (red dashed lines), 5° (green dashed lines), 10° (blue dashed lines), and 15° (cyan dashed lines), respectively.

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Fig. 2.
Fig. 2. (a)The reflectance spectra of RWGs of different parameter δ at the different angles of incidence θ=1°. The inset shows the magnetic field |Hy/H0| distribution at the resonance modes in the structure of δ=0.1 and 1.0, respectively. (b) The dependence of reflectance of RWGs of δ=0.4 on the angle of incidence. (c) The relation of resonance wavelength with the angle of incidence at the RWG structure of δ=0.4. (d) The detail of reflectance spectra changing with the angle of incidence in the range of 0° to 1° in the RWG structure of δ=0.4.

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Fig. 3.
Fig. 3. Dependence of Q factor on δ. The dash line is a guide for the eye. The inset shows the linear relationship between Q factor and δ−2, and the dash line is a linear fitting.

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Fig. 4.
Fig. 4. (a) SHG enhancement factor in the RWGs of different parameter δ at angle of incidence θ=1°. (b) Hy(2ω) distribution of SHG at θ=1° under the fundamental field E0=1×106 V/m. The unit s A/m. (c) SHG spectra in the RWG structure of δ=0.4 at different angles of incidence. (d) The SHG spectra changing with the angle of incidence in the range of 0° to 1° in the RWG structure of δ=0.4. The colorbar shows the logarithm of SHG enhancement factor.

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Fig. 5.
Fig. 5. (a) THG enhancement factor in the RWGs of different parameter δ at angle of incidence θ=1°. (b) Hy(3ω) distribution of SHG at θ=1° under the fundamental field E0=1×106 V/m. The unit is A/m. (c) THG spectra in the RWG structure of δ=0.4 at different angles of incidence. (d) The THG spectra changing with the angle of incidence in the range of 0° to 1° in the RWG structure of δ=0.4. The colorbar shows the logarithm of THG enhancement factor.

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Fig. 6.
Fig. 6. Conversion efficiency of SHG and THG dependence on the fundamental input intensity. The slope 1 and 2 indicate the second- and third-order nonlinear process, respectively.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

∇ × ∇ × E ( ω ) − k 0 2 E ( ω )  =  μ 0 ω 2 P ( 1 ) ( ω )
∇ × ∇ × E ( 2 ω ) − ε 2 k 2 2 E ( 2 ω )  =  μ 0 ( 2 ω ) 2 P ( 2 ) ( 2 ω )
∇ × ∇ × E ( 3 ω ) − ε 3 k 3 2 E ( 3 ω )  =  μ 0 ( 3 ω ) 2 P ( 3 ) ( 3 ω )
h w k 0 2 n w 2 − β 2 = atan ( n w 2 n c 2 β 2 − k 0 2 n c 2 k 0 2 n w 2 − β 2 ) + atan ( n w 2 n s 2 β 2 − k 0 2 n s 2 k 0 2 n w 2 − β 2 )
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