# Grating Coupler Design for Vertical Light Coupling in Silicon Thin Films on Lithium Niobate

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}, LN) crystal, which is more promising in this role [2,3,4] because of its wide transparency range and excellent electro-optic, nonlinear, acousto-optic, piezoelectric, photorefractive, and elasto-optic properties. However, contrary to photonics based on Si, the manufacturing of LN photonic devices is still in its infancy. The integration of a Si thin film on a thin LN cladding layer, combines the mature micro- and nano- technology properties of Si and the optical properties of LN. This produces an enhanced optical material that has a good confinement, and strong guidance, of light due to the high-refractive-index contrast between Si and LN [5,6]. When the light propagates in the Si waveguide, the energy of the light is distributed within both the Si thin film and the LN layer. Electro-optic modulators in Si on LN can be prepared by applying voltage to the LN layer [7,8,9,10,11]. Previously, based on a hybrid Si/LN material, many photonic devices have been developed such as Mach-Zehnder interferometer [7,8], photonic crystals [9] and micro-ring resonator [10,11].

## 2. Device Design and Methods

_{0}) as a source. In this simulation, the thickness of the Si thin film and the etch depth were all chosen to be 0.22 μm; the parameters T, Lx, Ly, Lz, θ, Λ, and DC were varied to maximize the light from the single-mode fiber coupling into the waveguide.

_{eff}/λ is the real part of the propagation constant and n

_{eff}is the effective index of the guided mode in the grating coupler. The above equation was used to obtain the range of grating periods (Λ).

_{LN}≤ n

_{eff}≤ n

_{Si}, where n

_{LN}/n

_{Si}was the refractive index of LN (2.138)/Si (3.478). By substituting the inequality into Equation (1), an estimated range of Λ with respect to the fiber angle would be obtained: λ/(3.478 − sinθ) ≤ Λ ≤ λ/(2.138 − sinθ). The Λ could be in the estimated range of 0.465 μm ≤ Λ ≤ 0.775 μm.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Witzens, J.; Baehr-Jones, T.; Hochberg, M. Silicon photonics: On-chip OPOs. Nat. Photonics
**2010**, 4, 10–12. [Google Scholar] [CrossRef] - Weis, R.S.; Gaylord, T.K. Lithium niobate: Summary of physical properties and crystal structure. Appl. Phys. A
**1985**, 37, 191–203. [Google Scholar] [CrossRef] - Lawrence, M. Lithium niobate integrated optics. Rep. Prog. Phys.
**1993**, 56, 363–429. [Google Scholar] [CrossRef] - Syms, R.R.A. Advances in channel waveguide lithium niobate integrated optics. Opt. Quant. Electron.
**1988**, 20, 189–213. [Google Scholar] [CrossRef] - Rao, A.; Fathpour, S. Compact lithium niobate electrooptic modulators. IEEE J. Sel. Top. Quantum Electron.
**2018**, 24, 340014. [Google Scholar] [CrossRef] - Rao, A.; Fathpour, S. Heterogeneous thin-film lithium niobate integrated photonics for electrooptics and nonlinear optics. IEEE J. Sel. Top. Quantum Electron.
**2018**, 24, 8200912. [Google Scholar] [CrossRef] - Chiles, J.; Fathpour, S. Mid-infrared integrated waveguide modulators based on silicon-on-lithium-niobate photonics. Optica
**2014**, 1, 350–355. [Google Scholar] [CrossRef] - Cao, L.; Aboketaf, A.; Wang, Z.; Preble, S. Hybrid amorphous silicon (a-Si:H)–LiNbO
_{3}electro-optic modulator. Opt. Commun.**2014**, 330, 40–44. [Google Scholar] [CrossRef] - Witmer, J.D.; Hill, J.T.; Safavi-Naeini, A.H. Design of nanobeam photonic crystal resonators for a silicon-on-lithium-niobate platform. Opt. Express
**2016**, 24, 5876. [Google Scholar] [CrossRef] [Green Version] - Witmer, J.D.; Valery, J.A.; Arrangoiz-Arriola, P.; Sarabalis, C.J.; Hill, J.T.; Safavi-Naeini, A.H. High-Q photonic resonators and electro-optic coupling using silicon-on-lithium-niobate. Sci. Rep.
**2016**, 7, 46313. [Google Scholar] [CrossRef] [Green Version] - Han, H.; Xiang, B. Simulation and analysis of electro-optic tunable microring resonators in silicon thin film on lithium niobate. Sci. Rep.
**2019**, 9, 6302. [Google Scholar] [CrossRef] [PubMed] - Schmid, B.; Petrov, A.; Eich, M. Optimized grating coupler with fully etched slots. Opt. Express
**2009**, 17, 11066–11076. [Google Scholar] [PubMed] - Laere, F.V.; Roelkens, G.; Ayre, M.; Schrauwen, J.; Taillaert, D.; Thourhout, D.V.; Krauss, T.F.; Baets, R. Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides. J. Lightw. Technol.
**2007**, 25, 151–156. [Google Scholar] [CrossRef] [Green Version] - Roelkens, G.; Vermeulen, D.; Thourhout, D.V.; Baets, R.; Brision, S.; Lyan, P.; Gautier, P.; Fédéli, J.M. High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit. Appl. Phys. Lett.
**2008**, 92, 131101. [Google Scholar] [CrossRef] [Green Version] - Chen, Z.; Wang, Y.; Jiang, Y.; Kong, R.; Hu, H. Grating coupler on single-crystal lithium niobate thin film. Opt. Mater.
**2017**, 72, 136–139. [Google Scholar] [CrossRef] - Cai, L.; Piazza, G. Low-loss chirped grating for vertical light coupling in lithium niobate on insulator. J. Opt.
**2019**, 21, 065801. [Google Scholar] [CrossRef] - Nisar, M.S.; Zhao, X.; Pan, A.; Yuan, S.; Xia, J. Grating coupler for an on-chip lithium niobate ridge waveguide. IEEE Photonics J.
**2017**, 9, 1–8. [Google Scholar] [CrossRef] - Tavlove, A.; Hagness, S.C. Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed.; Artech House: Norwood, MA, USA, 2005. [Google Scholar]
- Matthew, S.; Shi, R.; Novack, A.; Cher, R.T.P.; Lim, A.E.-J.; Lo, P.G.-Q.; Baehr-Jones, T.; Hochberg, M. A compact bi-wavelength polarization splitting grating coupler fabricated in a 220 nm SOI platform. Opt. Express
**2013**, 21, 31019–31028. [Google Scholar] - Wang, Y.; Gao, S.; Wang, K.; Li, H.; Skafidas, E. Ultra-broadband, compact, and high-reflectivity circular Bragg grating mirror based on 220 nm silicon-on-insulator platform. Opt. Express
**2017**, 25, 6653–6663. [Google Scholar] [CrossRef] - Vivien, L.; Pascal, D.; Lardenois, S.; Marris-Morini, D.; Cassan, E.; Grillot, F.; Laval, S.; Fédéli, J.-M.; Melhaoui, L.M. Light injection in SOI microwaveguides using high-efficiency grating couplers. J. Lightw. Technol.
**2006**, 24, 3810–3814. [Google Scholar] [CrossRef] - Berenger, J.P. A perfectly matched layer for absorption of electromagnetic wave. J. Comput. Phys.
**1994**, 114, 185–200. [Google Scholar] [CrossRef] - Suhara, T.; Nishihara, H. Integrated optics components and devices using periodic structures. IEEE J. Quantum Electron.
**1986**, 22, 845–867. [Google Scholar] [CrossRef] [Green Version] - Emmons, R.M.; Hall, D.G. Buried-oxide silicon-on-insulator structures. II. Waveguide grating couplers. IEEE J. Quantum Electron.
**1992**, 28, 164–175. [Google Scholar] [CrossRef]

**Figure 2.**Coupling efficiency at different thicknesses of the LN cladding layer for TE polarization.

**Figure 3.**Coupling efficiency as a function of Lx (

**a**) and Ly (

**b**) and: coupling efficiency as a function of wavelength for different Lx (

**c**) and Ly (

**d**).

**Figure 5.**(

**a**) Coupling efficiency as a function of fiber angle, which is relative to the surface that is perpendicular to the Si substrate. (

**b**) Coupling efficiency as a function of wavelength for different fiber angles. (T = 2.1 μm Lx = 3.5 μm, Ly = 0 μm, Λ = 0.64 μm, and DC = 0.829).

**Figure 6.**(

**a**) Coupling efficiency as a function of period. (

**b**) Coupling efficiency as a function of wavelength for different period.

**Figure 7.**(

**a**) Coupling efficiency as a function of duty cycle. (

**b**) Coupling efficiency as a function of wavelength for different duty cycle.

**Figure 8.**Electric field distribution of the optical wave in the simulation region, in which the optimal values of T = 2.1 μm Lx = 3.5 μm, Ly = 0 μm, θ = 8°, Λ = 0.64 μm, DC = 0.829, and λ = 1.55 μm were employed.

T (μm) | Lx (μm) | Ly (μm) | θ (°) | Λ (μm) | DC |
---|---|---|---|---|---|

2.1 | 3.5 | 0 | 8 | 0.64 | 0.829 |

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**MDPI and ACS Style**

Han, H.; Xiang, B.
Grating Coupler Design for Vertical Light Coupling in Silicon Thin Films on Lithium Niobate. *Crystals* **2020**, *10*, 850.
https://doi.org/10.3390/cryst10090850

**AMA Style**

Han H, Xiang B.
Grating Coupler Design for Vertical Light Coupling in Silicon Thin Films on Lithium Niobate. *Crystals*. 2020; 10(9):850.
https://doi.org/10.3390/cryst10090850

**Chicago/Turabian Style**

Han, Huangpu, and Bingxi Xiang.
2020. "Grating Coupler Design for Vertical Light Coupling in Silicon Thin Films on Lithium Niobate" *Crystals* 10, no. 9: 850.
https://doi.org/10.3390/cryst10090850