硅基寬帶雙偏振單模狹縫波導(dǎo)

侯金，李博雅，王林枝，楊春勇，鐘志有，陳少平

(中南民族大學(xué) 電子信息工程學(xué)院，智能無線通信湖北省重點(diǎn)實(shí)驗(yàn)室，武漢430074)

摘要采用三維平面波法和三維有限時(shí)域差分法，研究了硅基單模狹縫波導(dǎo)的雙偏振特性.通過調(diào)節(jié)狹縫波導(dǎo)中硅介質(zhì)的寬度，獲得了寬達(dá)320.6 nm的雙偏振帶寬；并且發(fā)現(xiàn)在該帶寬范圍內(nèi)，準(zhǔn)TE模式的電場強(qiáng)度在狹縫中均具有增強(qiáng)效果，并且狹縫中光限制因子均大于60%.該研究結(jié)果可為設(shè)計(jì)其他與偏振相關(guān)的硅光子器件提供參考.

關(guān)鍵詞寬帶；偏振；狹縫波導(dǎo)

Silicon photonics built on a silicon-on-insulator (SOI) platform has enabled us to fabricate ultracompact optical waveguides and optical components[1]. Recently, a new kind of silicon waveguide, silicon slot waveguide, which can confine and enhance light in a low-index slot, has attracted great attentions[2, 3]. Making use of this feature, a lot of high performance optical devices have been developed, such as wavelength demultiplexer[3], sensor[4, 5], optical modulator[6], directional coupler[7]and multimode interference splitter[8]. For most optical devices, bandwidth and/or polarization are essential performance parameters to be considered[3-8]. To be powerful, sometimes devices having both wideband and polarization characteristics are needed[9, 10]. Although great research progresses associated with bandwidth and polarization have been achieved in devices based on conventional strip waveguide[7]and photonic crystal waveguide[10, 11], due to the large polarization divergence in the slot waveguides, only few devices based on slot waveguide take the issues into consideration[8]. And till now, wideband dual polarizations slot waveguide, which serves as a basis for diversity functional polarization slot devices, is not well investigated.

To solve the problem, wideband dual polarizations single mode characteristics in silicon slot waveguide is investigated by three dimensional plane-wave expansion method (PWEM)[12]and three dimensional finite difference time domain method (FDTD)[13]in this paper. Firstly, the results obtained by PWEM and FDTD are compared to find which methods are more efficiently for the analysis. Then, optimizing is done by PWEM to obtain a wide single mode bandwidth for both quasi-TE and quasi-TM 1polarizations. Through adjusting the width of the surrounding silicon region of the slot waveguides, 320.6 nm wide single mode bandwidth for dual polarizations is obtained in an optimized slot waveguide. Finally, normalized filed distributions and the optical confinement factors of the slot waveguides are distinguished and calculated, which demonstrate that the electric field enhanced in the low index slot zone for quasi-TE fundamental modes is still maintained in the whole bandwidth.

Fig.1　Cross section of the silicon slot waveguide 圖1　狹縫波導(dǎo)的截面示意圖

As shown in Fig. 1, a silicon-on-insulator (SOI) wafer is used as a basis for design of the wideband dual polarizations silicon single mode slot waveguide. The refractive index of SiO2is assumed to be 1.45. In the silicon layer, a low-refractive-index air slot is sandwiched between two high refractive-index silicon regions, in which the light intensity can be enhanced due to the large discontinuity of the electric permittivity at high index-contrast interfaces[2]. The refractive index of silicon is assumed to be 3.45 and that of air is unity. The thickness of the silicon layer is denoted as H and fixed with an unchanged value of 0.8a, where isareference unit constant. The width of the slot is denoted asWSand has a fixed value of 0.2a. The value is chosen through a preliminary optimizing of the slot width based on a previously investigation, which would support electric field enhancement in the low index slot zone of the waveguide[6]. And the width for the high-index silicon region on the sides is denoted asWH.

In order to obtain wideband dual polarization performance, the dispersion curves of the slot waveguides are firstly investigated. Fig.2 shows the band structures of a typical slot waveguide withWH=0.75a. The blue hollow square curves and the red hollow triangle curves denote the quasi-TM bands and the quasi-TE bands respectively, which are calculated by PWEM. And the corresponding computational results obtained by FDTD for the two polarizations are denoted as green hollow circle curves and pin dot curves, respectively. The black solid line denotes the light line for SiO2, above which the modes would be leaky to the silica layer. So it restricts the upward frequency for guided modes. From the figure, below the SiO2light line, the band structures obtained by the two different methods look approximately the same in almost all the part except a little discrepancy for the fundamental modes near the silica light line, which would be due to the inexactly leaky modes extraction in FDTD. Therefore, we can conclude that, for most of the time, the two methods are matched very well. Considering that, calculating modes for a slot waveguide by three dimensional FDTD spends much more time than that by three dimensional PWEM. So, PWEM is more efficient and thus is chosen to investigate the dual polarizations characteristics.

To widen the dual polarizations bandwidth of the silicon single mode slot waveguide, the width of the high-index silicon regionWHis tailored while other parameters are remaining. We start from a very small width value ofWHwith, which corresponds to 150 nm thickness centered at 1550 nm. As shown in Fig.2,WHis tuned from 150 nm to 300 nm. WhenWHis increased, the dual polarizations bandwidth centered at 1550 nm wavelength of the slot waveguide will firstly increase accordingly. And whenWHreaches around 235 nm, the bandwidth gets to its maximum. After that, further increasing ofWHwill make the dual polarizations bandwidth narrower. Thus, a suitable value ofWHfor a maximum dual polarizations bandwidth should be chosen.

Fig.2　Band structures of the slot waveguide obtained by the PWEM and the FDTD, respectively. The structure parameters of the slot waveguide are with W S=0.2a and W H=0.75a 圖2　狹縫波導(dǎo)的能帶曲線圖

Fig.2 shows the band structure of the slot waveguide with the optimized maximum dual polarizations bandwidth. The structure parameters are withWS=0.2a,WH=0.75aandH=0.8a, which correspond toWS=62.5 nm,WH=234.4 nm andH=250 nm for a center wavelength of 1550 nm. In Fig. 2, the light green region denotes the border normalized frequencies for quasi-TE and quasi-TM fundamental modes, respectively, which are with values of 0.24 and 0.195. Within the bandwidth region, both the quasi-TE and quasi-TM polarizations are single modes. And it indicates a large dual polarizations bandwidth range from 1710.3 nm to 1389.7 nm, which is broader than that in [9]. Therefore, about 320.6 nm dual polarizations bandwidth can be achieved in the optimized slot waveguide.

Fig.3　Dual polarizations bandwidth as a function of W H 圖3　雙偏振帶寬隨W H的變化圖

To distinguish whether there still exists field enhancement in the whole wideband range of the dual polarizations silicon slot waveguide, normalizedEydistributions for the quasi-TE fundamental modes and normalizedHydistributions for the quasi-TM fundamental modes in the optimized waveguide for various wavelengths are investigated. Fig.4(a) shows theEydistribution for the quasi-TE fundamental mode at wavelength of 1550 nm, while Fig.4(b) shows theHydistribution for the quasi-TM fundamental mode at the same wavelength. Because of the existing of high dielectric contrast interfaces,Eywhich is the major component of the quasi-TE mode, as shown in Fig.4(a), also undergoes a large discontinuity[2]. And that discontinuity results in a strong electric field enhancement. Therefore, a large optical confinement factor of 70% is obtained in the low dielectric slot zone. Here, the optical confinement factor is expressed as |ES|2/|ET|2, whereESis the integral intensity of electric field in the slot zone andETis the electric field integral intensity in the whole slot waveguide[14]. However, as shown in Fig. 4(b), for the fundamental quasi-TM mode, there is no magnetic field enhancement in the low dielectric slot zone, andHylooks continuous in the slot waveguide along the Y axis direction. Correspondingly, the optical confinement factor for the quasi-TM fundamental mode is only 9% in the low dielectric slot zone, which is much smaller than that for the quasi-TE fundamental mode. The phenomenon can be explained that the magnetic permeability of silicon is almost equal to that of air, and thus there is no discontinuity for magnetic permeability. Therefore, there is no magnetic field discontinuity at the dielectric interfaces. And that’s also why the electric filed is heavily investigated in slot waveguides.

(a) Normalized E y distribution for the quasi-TE mode; (b) Normalized H y distribution for the quasi-TM mode Fig.4　Field distributions at 1550 nm wavelength for the quasi-TE and quasi-TM fundamental mode 圖4　準(zhǔn)TE和TM模式的電場分布圖(波長為1550nm)

In order to further validate the strong electric field enhancement for the quasi-TE fundamental mode in the whole dual polarizations bandwidth region, as shown in Fig.5, the optical confinement factors in the low dielectric slot zone at various wavelengths are also calculated. In the dual polarizations bandwidth region, the optical confinement factor is kept above a high value of 64%, which confirms that there exists field confinement in the slot zone for the quasi-TE fundamental modes. However, we can also observe that, as the wavelength increases, the associated optical confinement factor undergoes a slightly decreasing. That is mainly due to the dielectric discontinuity arising from a fixed thickness of the thin slot. For a short wavelength, it would undergo a heavily discontinuity due to the thin low dielectric slot. Thus the optical confinement factor has a larger value. As the wavelength increased, in one wavelength length, the same thin low dielectric slot will take a smaller potion. And the dielectric discontinuity gets weaker. Thus, the optical confinement also gets weaker. So in contrast, the field confinement factors for longer wavelengths are only with smaller values.

Fig.5　Optical confinement factor for the dual polarization bandwidth of the optimized slot waveguide 圖5　優(yōu)化狹縫波導(dǎo)中雙偏振帶寬內(nèi)的光限制因子

In conclusion, wideband dual polarizations single mode characteristics in silicon slot waveguide is theoretically investigated. In order to obtain a wide dual polarizations bandwidth, the width of the high region silicon is tailored. From our three dimensional PWEM calculation and three dimensional FDTD analysis, 320.6 nm dual polarizations bandwidth can be obtained in an optimized slot waveguide. The electric field enhancement in the low dielectric slot zone is also verified by the field distribution analysis and the optical confinement factor computation in the slot waveguide. The investigation would be used as a basis for developing polarization related slot devices in polarization diversity system, such as polarization bending, couplers, splitters, and so on.

Acknowledgments

This work was partly supported by National Natural Science Foundation of China under Grant Nos. 11147014 & 11491240105, the Natural Science Foundation of Hubei Province under Grant No. 2013CFA052, and the Central Universities Fundamental Research Funds of South-Central University for Nationalities under Grant No. CZW14020.

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