Progress of silicon photonic devices-based Fano resonance

Lu Li-Dan; Zhu Lian-Qing; Zeng Zhou-Mo; Cui Yi-Ping; Zhang Dong-Liang; Yuan Pei

doi:10.7498/aps.70.20200550

Abstract

The development of silicon photonics provides a method of implementing high reliability and high precision for new micro-nano optical functional devices and system-on-chips. The asymmetric Fano resonance phenomenon caused by the mutual coupling of optical resonant cavities is extensively studied. The spectrum of Fano resonance has an asymmetric and sharp slope near the resonance wavelength. The wavelength range for tuning the transmission from zero to one is much narrow in Fano lineshape, therefore improving the figure of merits of power consumption, sensing sensitivity, and extinction ratio. The mechanism can significantly improve silicon-based optical switches, detectors, sensors, and optical non-reciprocal all-optical signal processing. Therefore, the mechanism and method of generating the Fano resonance, the applications of silicon-based photonic technology, and the physical meaning of the Fano formula’s parameters are discussed in detail. It can be concluded that the primary condition for creating the Fano resonance is that the dual-cavity coupling is a weak coupling, and the detuning of resonance frequency of the two cavities partly determines Fano resonance lineshapes. Furthermore, the electromagnetically induced transparency is generated when the frequency detuning is zero. The methods of generating Fano resonance by using different types of devices in silicon photonics (besides the two-dimensional photonic crystals) and the corresponding evolutions of Fano resonance are introduced and categorized, including simple photonic crystal nanobeam, micro-ring resonator cavity without sacrificing the compact footprint, micro-ring resonator coupling with other structures (mainly double micro-ring resonators), adjustable Mach-Zehnder interferometer, and others such as slit waveguide and self-coupling waveguide. Then, we explain the all-optical signal processing based on the Fano resonance phenomenon, and also discuss the differences among the design concepts of Fano resonance in optimizing optical switches, modulators, optical sensing, and optical non-reciprocity. Finally, the future development direction is discussed from the perspective of improving Fano resonance parameters. The topology structure can improve the robustness of the Fano resonance spectrum; the bound states in continuous mode can increase the slope of Fano spectrum; the Fano resonance can expand the bandwidth of resonance spectrum by combining other material systems besides silicon photonics; the multi-mode Fano resonances can enhance the capability of the spectral multiplexing; the reverse design methods can improve the performance of the device. We believe that this review can provide an excellent reference for researchers who are studying the silicon photonic devices.

Keywords:

Authors and contacts

1.
State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China
2.
Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science & Technology University, Beijing 100192, China
3.
Advanced Photonics Center, Southeast University, Nanjing 210096, China

Corresponding author: Zhu Lian-Qing, lqzhu_bistu@sina.com ; Zeng Zhou-Mo, zhmzeng@tju.edu.cn ;

Funds: Project supported by the 111 Project of China (Grant No. D17021), the Beijing New-star Plan of Science and Technology of China (Grant No. Z191100001119052), and the Vertical Subject of Beijing Laboratory of China (Grant No. GXKF2019002)

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图 1 (a) q与相移δ之间的关系曲线; (b)—(f) q → $ -\infty $, q = –1, q = 0, q = +1, q → $ +\infty $时对应的传输光谱; (g)不同半高宽Γ对Fano线形的影响; (h)不同共振波长ω₀对应的光谱

Figure 1. (a) Relationship between q and the phase shift δ; (b)–(f) transmitted spectra corresponding to q → $ -\infty $, q =–1, q = 0, q = + 1, q → $ +\infty $, respectively; (g) effect of different half-widths Γ on Fano lineshapes; (h) different spectra corresponding to different resonance wavelengths ω₀.

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图 2 硅基光子谐振腔不同耦合方式的简化模型　(a)—(c) 侧边直接耦合腔; (d) 端面耦合腔; (e)侧边间接耦合腔

Figure 2. A simplified model of different coupling modes of the silicon-based photonic resonator: (a)–(c) Directly side coupled cavities; (d) end-coupled cavities; (e) indirectly side coupled cavities.

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图 3 (a) Fano共振形成条件; (b) ω₂– ω₁的失谐量对Fano共振线形的影响

Figure 3. (a) Formation conditions for Fano resonance; (b) the effect of ω₂– ω₁ on Fano resonance.

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图 4 各种PCNC产生Fano共振的方法　(a)单PCNC^[38]; (b) PCNC侧耦合F-P谐振器^[39]; (c)纳米微机电结构动态控制Fano共振光谱^[37]; (d) PCN的带隙边缘模式耦合PCNC^[40]; (e)具有简并带隙边缘模式的双PCNC^[43]; (f)双排PCN构建的布拉格反射结构的(i)整体结构图和(ii)俯视图^[44]

Figure 4. Various PCNC structures for Fano resonance: (a) Single PCNC^[38]; (b) PCNC side coupled F-P resonator^[39]; (c) dynamic control of Fano resonance with a nanoelectromechanical structure^[37]; (d) band edge mode of PCN couple with PCNC^[40]; (e) double PCNCs with degenerate band edges mode^[43]; (f) the overall structure (i) and top view (ii) Bragg reflection structure constructed with double-row PCN^[44].

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图 5 紧凑型MRR产生Fano共振的方法　(a)错位总线波导耦合MRR^[46]; (b)双模式总线波导耦合MRR^[47]; (c)直波导端面反射耦合MRR^[48]; (d) 反馈直波导耦合MRR^[50]; (e)直波导耦合带有相移布拉格光栅的MRR^[51]; (f)总线波导结合光栅/空气孔/狭缝耦合MRR^{[20,34,54-56]}

Figure 5. Various MRRs with compact footprint for Fano resonance: (a) Straight waveguide with misalignment^[46]; (b) dual-mode bus waveguide^[47]; (c) straight waveguide with end face reflection^[48]; (d) straight waveguide with feedback^[50]; (e) MRR with phase-shifted Bragg grating^[51]; (f) bus waveguide combined Bragg grating/air holes/slits^{[20,34,54-56]}.

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图 6 各种复合MRR产生Fano共振的方法　(a)耦合模式理论分析双MRR结构^[57]; (b)等效F-P单元分析多环耦合结构^[36]; (c)双环嵌套结构^[59-64]; (d)双环反馈耦合结构^[67,68]; (e) Sagnac形成F-P腔耦合MRR^[75]; (f)等效双马赫-曾德尔干涉仪^[35,76-78]

Figure 6. Various complex MRRs for Fano resonance: (a) Analysis of double MRR using coupling mode theory^[57]; (b) analysis of multi-ring coupling with equivalent F-P unit^[36]; (c) double-MRRs nested structure^[59-64]; (d) double-MRRs with feedback configuration^[67,68]; (e) Sagnac formed F-P cavity couples MRR^[75]; (f) equivalent double Mach-Zehnder interferometer^[35,76-78].

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图 7 MRR与各种变异结构MZI耦合产生Fano共振的方法　(a) MZI耦合MRR模型^[79]; (b) MZI侧边耦合MRR^[83]; (c) 双4 × 4多模耦合器组成双MZI^[85]; (d) MZI双臂耦合交叉环^[86]; (e) MZI双臂耦合MRR及交叉波导^[87]; (f)双MZI耦合双MRR^[22]

Figure 7. MRR coupled with variant MZI for Fano resonance: (a) Model for MZI coupled MRR^[79]; (b) MZI side coupled MRR^[83]; (c) dual 4 × 4 multimode couplers form dual MZI^[85]; (d) dual-arm of MZI coupled cross-loop waveguide^[86]; (e) dual-arm of MZI coupled MRR and cross waveguide^[87]; (f) dual MZI coupled dual MRR^[22].

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图 8 (a)自耦合波导^[90]; (b)狭缝波导耦合光栅式F-P^[92]

Figure 8. (a) Self-coupling waveguide^[90]; (b) slot waveguide coupling F-P composed by Bragg grating^[92].

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图 9 Fano共振与Lorentzian线形的开关性能

Figure 9. Switching performance of Fano resonance and Lorentzian lineshapes.

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图 10 Fano共振硅光开关^[42]　(a) PCNC耦合PCN; (b) PCNC耦合PCN的光谱

Figure 10. Silicon optical switch based on Fano resonant^[42]: (a) PCNC couple PCN; (b) corresponding spectra.

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图 11 Fano共振硅基电光调制器　(a) MZI耦合MRR^[80]; (b)单波导PCNC^[98]

Figure 11. Silicon electro-optic modulator based on Fano resonant: (a) MZI couple MRR^[80]; (b) single waveguide PCNC^[98].

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图 12 Fano共振传感　(a)波导截面^[46]; (b)光栅式MRR^[68]; (c)传感测试装置^[63,64]; (d) Fano共振光谱随折射率传感变化曲线, 图中RI (refractive index)代表折射率^[56]

Figure 12. Fano resonance for sensing applications: (a) Cross section of waveguide^[46]; (b) MRR composed of grating^[68]; (c) setup for sensor^[63,64]; (d) spectrum of Fano resonance versus refractive index (RI)^[56].

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图 13 基于EIT的光非互易性传输　(a) 微环形成双MZI结构^[35]; (b)非互易性光谱特征^[35]; (c)端口1波长随输入功率变化曲线^[35]; (d) 端口2波长随输入功率变化曲线^[101]

Figure 13. EIT-based optical nonreciprocal transmission: (a) Microrings forming a dual MZIs^[35]; (b) characteristics of optical nonreciprocity spectral^[35]; (c) wavelength of port 1 versus input power^[35]; (d) wavelength of port 2 versus input power^[101].

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表 1 不同PCNC产生Fano共振的参数表

Table 1. Parameters for Fano resonance based on different PCNCs.

结构	尺寸/(μm × μm)	消光比/dB	斜率/(dB·nm^–1)	应用	文献
PCNC结合光纤	～13.2 × 0.47	17			[38]
F-P 侧边耦合 PCNC	～6 × 0.45	7.3	5.3		[39]
F-P 侧边耦合 PCNC	～18 × 0.72	14—18			[37]
F-P 侧边耦合 PCNC	～10.5 × 1.5	22			[40]
F-P 侧边耦合狭缝 PCNC	～10.5 × 1.5	24		折射率灵敏度778 nm/RIU	[41]
双 PCNs	～5.18 × 0.74	20			[43]
交叉耦合四端口PCNC	～4	16		光开关	[45]

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表 2 不同紧凑型MRR产生Fano共振的参数表

Table 2. Parameters for Fano resonance based on different compact MRRs.

结构	尺寸/(μm×μm)	消光比/dB	斜率	性能	文献
总线错位波导耦合MRR	～20×30	30		葡萄糖灵敏度24 mg/dl	[46]
多模总线波导耦合MRR	～1020×230	6	27.1/nm		[47]
端面反射总线波导耦合MRR	～22×10000	30		折射率探测极限～10^–8 RIU	[48]
MRR耦合反馈总线波导	～20×350	30.8	226.5 dB/nm		[49,50]
MRR耦合相移光栅	～60×60	20			[51]
MRR耦合由两个布拉格光栅形成的F-P腔	～17×140	22.54	250.4 dB/nm		[52]
MRR耦合由光子晶体形成的F-P腔	～6×10	23		折射率灵敏度～1.76 × 10^–4	[56]
亚波长光栅耦合MRR	～6×10	12		折射率灵敏度366 nm/RIU	[54]
狭缝F-P耦合狭缝MRR	～4×10	20		折射率灵敏度297.13 nm/RIU	[55]
PCNC侧耦合结合Kerr 非线性材料的PCN	～16			关开关功耗0.76 pJ, 切换时间0.707 ps	[42]

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表 3 多MRR产生Fano共振的参数表

Table 3. Parameters for Fano resonance based on multiple MRRs.

结构	尺寸/(μm×μm)	消光比/dB	斜率	性能	文献
MRR嵌入跑道微环	～5×40	20			[59]
热调MRR嵌入跑道微环	～5 × 40	40	35—93 dB/nm		[60]
亚波长光栅式MRR嵌入跑道微环	～20×100	21.53		折射率灵敏度500 nm/RIU	[68]
Sagnac形成的双F-P耦合	～100×300	20	770 dB/pm		[30]
Sagnac形成的F-P耦合MRR	～25×30	23.22	252 dB/nm		[75]

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表 4 不同基于MZI 单元产生Fano共振的参数表

Table 4. Parameters for Fano resonance based on MZI unit.

结构	尺寸/(μm×μm)	消光比/dB	斜率/(dB·nm^–1)	应用	文献
多模MZI耦合MRR	～65×85	33	113	模式开关	[82]
双总线耦合交叉MRR形成的等效MZI				光开关	[86]
MRR结合“十”交叉波导作为MZI的干涉臂	～100×370	20			[87]
MRR的两总线波导反馈形成MZI	～390×850	30.2	41		[88]
双MRR辅助双MZI		56.8	3388.1		[22]

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表 5 各种硅光器件产生Fano共振的方法对比

Table 5. Comparation of diffrent silicon waveguide unit for Fano resonance.

方法	尺寸	消光比	斜率	工艺要求	应用
PCNC	小	适中	小	高	光开关/传感
MRR	中	适中	大	一般	传感/滤波器
MZI	大	大	大	一般	调制器/隔离器

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