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针对提出的基于Si3N4波导和LRSPP波导的混合结构,对其温度特性进行分析。混合波导结构传输的相位为:
$$ \varphi =\frac{2\pi }{\lambda }\cdot ({n}_{\rm eff1}\cdot {L}_{1}+{n}_{\rm eff2}\cdot {L}_{2}) $$ (1) 式中:λ为波长;neff1为Si3N4波导的模式有效折射率;L1为Si3N4波导的长度;neff2为LRSPP波导的模式有效折射率的实部;L2为LRSPP波导的长度。
当温度发生变化时,相位随温度的漂移可用下式表征:
$$ \begin{split} \frac{\text{d}\varphi }{\text{d}T}=&\frac{2\pi }{\lambda }\cdot \left[\left(\frac{\text{d}{n}_{\rm eff1}}{\text{d}T}+{n}_{\rm eff1}\cdot {\alpha }_{1}\right)\cdot {L}_{1}\right.+\\&\left.\left(\frac{\text{d}{n}_{\rm eff2}}{\text{d}T}+{n}_{\rm eff2}\cdot {\alpha }_{2}\right)\cdot {L}_{2}\right] \end{split} $$ (2) 式中:T为环境温度;α1为Si3N4波导衬底的热膨胀系数;α2为LRSPP波导衬底的热膨胀系数。
由Drude模型可得金在1550 nm波长下的折射率随温度的变化关系为[9]:
$$ \begin{split} {n}_{\mathrm{A}\mathrm{u}}\left(T\right)=& {n}_{\mathrm{r}}\left(T\right)+{i}{n}_{\mathrm{i}}\left(T\right)\\ {n}_{\mathrm{r}}\left(T\right)=& 0.054\;3+0.001\;68T \\ {n}_{\mathrm{i}}\left(T\right)=& 11.617-3.204\times {10}^{-4}T-2.965\times {10}^{-7}{T}^{2} \end{split} $$ (3) 式中:nAu(T)为金在温度T下的折射率;nr(T)为金的折射率实部;ni(T)为金的折射率虚部。
根据材料的热光系数,利用有限元算法计算了Si3N4波导和LRSPP波导在不同温度下的模式有效折射率,如图5(a)所示。Si3N4波导和LRSPP波导的模式有效折射与温度呈线性关系,由此可得公式(2)中dneff1/dT和dneff2/dT分别为1×10−5和−1.86×10−4,与包层材料的热光系数接近,表明波导模式有效折射率的热光特性主要取决于包层材料的热光系数。Si3N4波导的包层为SiO2,热光系数为正;LRSPP波导的包层材料为聚合物,具有负的热光系数。当温度发生变化时,Si3N4波导和LRSPP波导折射率的变化趋势相反。因此,可利用LRSPP波导的负热光特性对Si3N4波导相位的漂移进行补偿。由公式(2)可知,通过设计Si3N4波导和LRSPP波导的长度实现温度不敏感。相位变化与波导长度比的关系如图5(b)所示。当LRSPP波导的热光系数为−1.86×10−4时,L2/L1 = 0.077,相位的漂移为0,即相位不随温度的变化而发生漂移。此外,LRSPP波导包层材料的热光系数可调,图5(b)还给出了不同热光系数下实现温度不敏感的条件。
图 5 (a) Si3N4波导和LRSPP波导模式有效折射率随温度的变化曲线;(b) 不同热光系数下,相位变化与Si3N4波导和LRSPP波导长度比的关系
Figure 5. (a) Effective mode refractive index of the Si3N4 waveguide and LRSPP waveguide under different temperatures; (b) Phase change of the Si3N4 waveguide and LRSPP waveguide under different length ratios
当不能满足最佳长度比时,利用LRSPP波导进行主动调谐,策略就是通过施加电压主动调节LRSPP波导的温度,以消除温度对相位的影响。LRSPP波导芯层材料为金,具有光电复用的特性,既能传输光,也是电的良导体,可通过电极直接将调谐电压施加到芯层上,利用热光效应改变LRSPP波导的传输特性,进而补偿温度对Si3N4波导的影响。当波导实际温度偏离设定工作温度时,由公式(2)可算得需要LRSPP波导的主动调谐量,进而得到LRSPP波导所需的升温或降温量。当需要LRSPP波导升温时,外加电压经电极加载到LRSPP波导芯层上,通过发热导致LRSPP波导温度上升,进而实现对相位的调谐。随着施加调制电压的升高,LRSPP波导的温度也越高,如图6(a)所示,其中2.5 V的电压就能实现10 ℃的升温。当向LRSPP波导芯层施加电压时,LRSPP波导的温度快速上升,随后上升速率减缓并逐步趋于稳定,达到所需的温度以实现温度不敏感,如图6(b)所示,可得升温的响应时间为0.78 ms。此外,根据对LRSPP施加的电压可得LRSPP波导升温1 ℃所需要的功率为0.45 mW。当需要LRSPP波导降温时,通过自然降温来实现,降温曲线如图6(c)所示,降温10 ℃仅需200 μs左右的时长,能迅速响应波导的调谐需求。
图 6 (a) LRSPP波导温度与施加电压的关系,插图是不同电压下LRSPP波导的温度场分布;(b) LRSPP波导的升温曲线,插图是升温曲线局部放大图;(c) LRSPP波导的降温曲线,插图是不同降温时间下LRSPP波导的温度场分布
Figure 6. (a) Temperature of the LRSPP waveguide under different voltages, inset: the temperature field distribution of the LRSPP waveguide under different voltages; (b) Heating curve of the LRSPP waveguide, inset: zoom in the heating curve; (c) Cooling curve of the LRSPP waveguide, inset: the temperature field distribution of the LRSPP waveguide
LRSPP波导为Si3N4波导的温度补偿提供了有效途径。进一步考虑到工程化应用,可构建自动伺服系统优化LRSPP波导的温度补偿过程,通过对波导输出的检测、比较、反馈、补偿实现对Si3N4波导的主动补偿。具体过程大致如下:在不满足最佳长度比的前提下,当环境温度发生变化时,检测波导的输出,并与设定工作温度下的输出进行比较,结合公式(2)求得需要LRSPP波导补偿的模式有效折射率,将此补偿量转化为芯层调制的电压,然后将电压施加于LRSPP波导的芯层上,构成伺服回路,实现对整个波导结构温度特性的主动补偿。
Temperature-insensitive waveguide based on Si3N4 and LRSPP
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摘要: 光子集成芯片将多种功能器件进行片上集成,具有损耗低、带宽大、抗电磁干扰等优势,是当前光电领域发展的主流方向。集成光学器件的温度稳定性是影响其光学性能的重要因素之一。为了提高集成光学器件温度稳定性,提出了基于氮化硅(Si3N4)和长程表面等离激元(Long-Range Surface Plasmon Polariton,LRSPP)波导的温度不敏感结构,对器件性能随温度的漂移进行抑制和补偿。首先,分析了Si3N4波导和LRSPP波导对接的模式耦合效率,当满足最佳匹配条件时,可实现耦合效率99.9%以上的高效耦合。对混合波导的温度特性进行了分析,结果表明,当LRSPP波导和Si3N4波导的最佳长度比为 0.077,相位不随温度的变化而发生漂移,实现了温度不敏感的波导。当波导不能满足最佳长度比时,对LRSPP波导芯层施加电压实现主动补偿,亦可实现温度不敏感。此外,对LRSPP波导的传输特性进行了测试,测得偏振消光比为64 dB,具有良好的单偏振特性。文中提出的温度不敏感结构具有可主动调谐、损耗低、单偏振、普适性高等优点,能有效地解决Si3N4波导性能随温度变化发生漂移的问题,在Si3N4基光子集成芯片中具有广泛的应用前景。Abstract:
Objective Photonic integrated circuits composed of a variety of integrated functional devices on one chip have become the mainstream of the photoelectric fields due to their low loss, large bandwidth, and anti-electromagnetic interference properties, which are widely applied in optical sensing, radar, photon computing and medical testing. Due to the inherent thermo-optic characteristics of optical waveguide materials, the refractive index of the core and cladding materials will change with the temperature fluctuation, leading to the temperature stability which is one of the main problems in the engineering application of the photonic integrated circuits. Therefore, it is necessary to suppress and compensate for the drift of optical device performance with temperature to improve the temperature stability of the photonic integrated circuits. In this respect, a temperature-insensitive hybrid structure based on silicon nitride and long-range surface plasmon polariton (LRSPP) waveguides was proposed to suppress and compensate for the performance drift caused by temperature variation. Methods For the studies of the proposed temperature insensitive hybrid waveguide based on silicon nitride and LRSPP, the propagation properties, temperature stability and polarization characteristics were investigated. Firstly, considering the coupling efficiency between silicon nitride waveguide and LRSPP waveguide, the propagation model of silicon nitride waveguide and SPP waveguide was established. The mode coupling efficiencies and the optical propagation filed under different waveguide sizes were analyzed by using the finite difference time domain method. Then, the temperature stability was analyzed by the calculation of the phase change when the temperature fluctuated. Moreover, the polarization properties of the fabricated LRSPP waveguide were measured by the output spot and optical power under the transverse magnetic (TM) and the transverse electric (TE) mode. Results and Discussions The mode coupling efficiencies between the silicon nitride waveguide and LRSPP waveguide were more than 99.9% in the optimal cases (Fig.3), resulting in the almost negligible coupling losses. What's more, the proposed hybrid waveguide still showed good propagation characteristics even with 100 nm offset in vertical direction between the silicon nitride waveguide and LRSPP waveguide (Fig.4). For the temperature characteristics of the hybrid waveguide, there was an optimal length ratio of the LRSPP and silicon nitride waveguide for the defined waveguide to realize temperature insensitivity. Specifically, when the thermo-optic coefficient of the LRSPP waveguide was −1.86×10−4/℃, the optimal length ratio was 0.077, leading to zero phase drift when the temperature changes (Fig.5). However, when the optimal length ratio is not met, the hybrid waveguide can still achieve temperature insensitivity through the active phase compensation performed by the core modulation of the LRSPP waveguide. When a voltage signal was applied directly to the core layer of the LRSPP waveguide, the temperature of the LRSPP waveguide rose and gradually stabilized to the required temperature to compensate for the temperature drift (Fig.6). A voltage of 2.5 V can achieve a temperature rise of 10 °C with the response time of 0.78 ms, which can quickly respond to the tuning needs of the waveguide, resulting in high tuning efficiency. In addition, since the LRSPP waveguide only supports TM polarization state, the proposed hybrid waveguide inherited the single-polarization characteristic. In the TM polarization state, the output of the LRSPP waveguide is good with the output optical power of −46 dBm. While in the TE polarization state there is almost no output and the output optical power is −110 dBm (the lowest detection limit of the detector) (Fig.7). Accordingly, the polarization extinction ratio was calculated as 64 dB, indicating that the LRSPP waveguide has good single-polarization characteristics. Conclusions From the perspective of the basic waveguide, the proposed temperature-insensitive hybrid waveguide has the benefits of active tuning, low loss, single polarization and high universality, which can effectively address the performance drift of the silicon nitride waveguide caused by the temperature change and has broad application prospects in silicon-nitride-based photonic integrated circuits. -
图 3 (a) Si3N4波导和LRSPP波导的耦合效率与波导厚度的关系,插图是耦合效率的局部放大图;(b) Si3N4波导和LRSPP波导的耦合效率与波导宽度的关系,插图是最佳耦合效率下波导的厚度关系图;(c) Si3N4波导和LRSPP波导的模式面积差与波导厚度的关系;(d) Si3N4波导和LRSPP波导的耦合损耗与波导厚度的关系
Figure 3. (a) Coupling efficiencies of the Si3N4 waveguide and LRSPP waveguide with different core heights. Inset: the zoom of the coupling efficiency; (b) Coupling efficiencies of the Si3N4 waveguide and LRSPP waveguide with different core widths. Inset: optimal coupling efficiency with different core heights; (c) Mode area differences of the Si3N4 waveguide and LRSPP waveguide with different core heights; (d) Coupling losses of the Si3N4 waveguide and LRSPP waveguide with different core heights
图 4 (a) Si3N4波导和LRSPP波导在横向(x方向)和纵向(y方向)上的偏移;(b) Si3N4波导和LRSPP波导横向偏移时的传输场;(c)~(g) Si3N4波导和LRSPP波导在不同纵向偏移时的特性:(i) P1点的模式分布,(ii) P2的模式分布,(iii)传输场
Figure 4. (a) Offset between the Si3N4 waveguide and LRSPP waveguide in horizontal (x) and vertical (y) direction; (b) Transmission field of the Si3N4 waveguide and LRSPP waveguide with lateral offset; (c)-(g) Properties of the Si3N4 waveguide and LRSPP waveguide with longitudinal offset: (i) mode distribution in P1, (ii) mode distribution in P2, (iii) transmission field
图 6 (a) LRSPP波导温度与施加电压的关系,插图是不同电压下LRSPP波导的温度场分布;(b) LRSPP波导的升温曲线,插图是升温曲线局部放大图;(c) LRSPP波导的降温曲线,插图是不同降温时间下LRSPP波导的温度场分布
Figure 6. (a) Temperature of the LRSPP waveguide under different voltages, inset: the temperature field distribution of the LRSPP waveguide under different voltages; (b) Heating curve of the LRSPP waveguide, inset: zoom in the heating curve; (c) Cooling curve of the LRSPP waveguide, inset: the temperature field distribution of the LRSPP waveguide
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