基于非线性光学材料的波导设计及其波长转换研究
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摘要
非线性波长转换在全光信号处理、数据存储、生物医学、彩色显示、生物工艺学、环境监测处理分析等方面扮演着重要的角色。基于三阶非线性效应的三次谐波和四波混频与基于二阶线非线性效应的差频、和频、倍频，能通过波长转换把半导体激光器的波长范围拓展到紫外、可见光、中红外和太赫兹波段。另一方面四波混频、差频、级联倍频差频、级联和频差频能把光信号从一个波长转移到另一个波长上，在密集波分复用光通信网络能得到应用。本论文通过灵活地设计几种波导结构来实现这些非线性效应，并对其中的波长转换进行了理论研究。具体内容如下：
(1)研究了损耗情况下AlGaAs准相位匹配波导的波长转换。在非耗尽近似下求出一个有损耗的准相位匹配波导中差频、级联倍频差频转换光功率的解析表达式。对于较大损耗的光波导，此表达式与直接进行数值求解的耗尽情况下转换效率一致。基于这些解析表达式，得出有损耗差频、级联倍频差频过程的优化波导长度公式。同时，我们设计了一个AlGaAs准相位匹配桥状波导，并详细研究和比较了无损耗和有损耗情况下两种非线性过程的转换效率、转换带宽、泵浦光波长容忍度和温度稳定性。
(2)研究了AlGaAs微环谐振腔中二次谐波的产生。为了避免周期反转结构造成的损耗，我们研究了弯曲AlGaAs波导实现相位匹配的原理，并且分析了微环谐振腔中的有效非线性系数。结果表明微环谐振腔能够实现相位匹配的倍频过程。我们设计了一个高折射率差的AlGaAs微环谐振腔，其中泵浦波长和倍频光波长都处在谐振波长上。在泵浦非耗尽近似下，得出一个转换效率的解析表达式。从此表达式看出，转换效率由于腔场的增强而得到增加。考虑到泵浦光耗尽的情况，采用分段法进行数值模拟。结果表明在无损耗情况下，转换效率可以接近1。
(3)研究了光子晶体波导中太赫兹波的差频产生。我们通过把近红外光波导放置在太赫兹波光子晶体波导的线缺陷里面，利用近红外光源的差频过程产生太赫兹波。在这种结构中，光子晶体波导能紧紧地限制住太赫兹波的模场，使相互作用的三个光波实现好的模场重叠。两个泵浦光与太赫兹Bloch波奇特的相位匹配条件能够通过合适选择波导参数和泵浦光波长来满足。根据模式理论推导了差频过程的耦合模方程和有效作用面积公式。首先，我们设计了一个AlGaAs光子晶体波导。数值模拟出连续光泵浦的太赫兹波归一化转换效率为0.7632×104W1。其次，我们设计出一个LiNbO3光子晶体波导结构实现了频率为1THz的太赫兹波高效差频产生。由于光子晶体波导结构在太赫兹领域得到了广泛研究，这些太赫兹波产生方案给太赫兹技术提供了参考。
(4)研究了光子晶体波导中慢光增强的四波混频。利用模式理论，我们推导出光子晶体波导中的三阶非线性作用的耦合模方程组。这些非线性作用包括自相位调制、交叉相位调制和简并四波混频。这些耦合模方程组的形式与非线性光纤光学中的一致，并且可以应用于其他周期波导结构中的三阶非线性效应。基于这些方程，我们系统分析了一个慢光工程的硅基光子晶体波导的群速度色散、光传输损耗、有效作用面积、慢光增强因子和相位失配。考虑到双光子吸收和自由载流子效应，利用有限差分法数值模拟了此光子晶体波导两个色散平坦区域的四波混频转换效率。最后研究了慢光增强的多重四波混频对波长转换的影响。
Nonlinear wavelength conversion had played a key role in all-optical signal processing,optical data storage, biomedicine, color display, biotechnology, environmental monitoringand process analysis and so on. The third-harmonic generation (THG), four wave mixing(FWM) based on the third-order nonlinear interactions and the difference frequency gen-eration (DFG), sum-frequency generation (SFG), second-harmonic generation (SHG) fromthe second-order nonlinear effects, may convert the wavelength of semiconductor lasers tothe ultraviolet (UV), visible light, mid-infrared (IR) light and terahertz regions. On theother hand, the FWM, DFG, cascaded second-harmonic generation and difference frequen-cy generation (cSHG/DFG), cascaded sum-frequency generation and difference frequencygeneration (cSFG/DFG) can move the signal from one wavelength to another, and this maybe applied in the dense wavelength division multiplexing (DWDM) optical communicationnetwork. In this thesis, we design some appropriate waveguide structures to achieve thesenonlinear processes, and theoretically investigate the characters of wavelength conversion.The detailed research contents can be found as follows.
Firstly, we study the wavelength conversion in the lossy quasi-phase-matched (QPM)AlGaAs waveguide. We obtain the analytical expressions of converted wave power for DFG,cSHG/DFG processes under the non-depletion approximation in lossy QPM waveguides. Itis shown that the analytical results and the numerical simulation with depletion agree verywell for lossy waveguides. Employing the analytical solutions, the formulas of optimizedwaveguide lengths are obtained for lossy DFG and cSHG/DFG processes. After designingan AlGaAs QPM ridge waveguide, we detailly investigate and compare the characteristicsof the second-order nonlinear effects with and without loss, such as conversion efficiency,conversion bandwidth, pump wavelength tolerance and temperature stability.
Secondly, we study the SHG in AlGaAs microring resonator. In order to avoid theloss of QPM structures, we investigate the principle of curved AlGaAs waveguide for phasematch, and analyze the effective nonlinear coefficient of microring resonator. It is foundthat microring resonator can be employed to satisfy the phase matching condition of SHG. We design a high-index-contrast AlGaAs microring resonator with the wavelengths of pumpand second-harmonic in resonator wavelength. Under the non-depletion approximation, theanalytical solution of conversion efficiency is obtained. Based on the analytical solutions,it is clearly that the enhanced field in the microring resonator can improved the conversionefficiency. Considering the depletion situation, we numerically simulate the SHG processusing the fragment method. The results show that the conversion efficiency may be reach1in lossless case.
Thirdly, we study the THz wave DFG form photonic crystal waveguides (PCWs). Weplace the near-infrared light waveguide in the line defect of THz PCW to achieve THzwave DFG from near-infrared light sources. In this structure，PCW structure provides atight confinement of THz-wave field, resulting in a good mode field overlap of three waves.The unique phase matching condition between two pump waves and THz Bloch wave canbe satisfied through choosing appropriate waveguide parameters and pump wavelengths.The couple-mode equations and the effective interaction area formula for DFG processesis obtained from the modal theory. Firstly, we design a AlGaAs PCW, the high power-normalized conversion efficiency of0.7632×104W1for3THz generation is obtainedthrough simulating the continuous THz DFG process. Secondly, we design a LiNbO3PCWfor efficient1THz DFG. Since the photonic crystal structures have been widely exploitedfor THz researches, these approaches have the potential to open a new window for THztechnology.
Fourthly, we study the slow light enhanced FWM in PCW. By employing the modaltheory, we derive the couple-mode equations for third-order nonlinear effects in PCWs.These nonlinear interactions include self-phase modulation, cross-phase modulation anddegenerate FWM. The equations similar to that in nonlinear fiber optics could be expandedand applied for third-order nonlinear processes in other periodic waveguides. Based onthe equations, we systematically analyze the group-velocity dispersion, optical propagationloss, effective interaction area, slow light enhanced factor and phase mismatch for a slowlight engineered silicon PCW. Considering the two-photon absorption and free-carrier ef-fects, the wavelength conversion efficiencies in two low-dispersion regions are numerically simulated by utilizing finite difference method. Finally, we investigate the influence of slowlight enhanced multiple FWM process on the conversion efficiency.
(1)研究了损耗情况下AlGaAs准相位匹配波导的波长转换。在非耗尽近似下求出一个有损耗的准相位匹配波导中差频、级联倍频差频转换光功率的解析表达式。对于较大损耗的光波导，此表达式与直接进行数值求解的耗尽情况下转换效率一致。基于这些解析表达式，得出有损耗差频、级联倍频差频过程的优化波导长度公式。同时，我们设计了一个AlGaAs准相位匹配桥状波导，并详细研究和比较了无损耗和有损耗情况下两种非线性过程的转换效率、转换带宽、泵浦光波长容忍度和温度稳定性。
(2)研究了AlGaAs微环谐振腔中二次谐波的产生。为了避免周期反转结构造成的损耗，我们研究了弯曲AlGaAs波导实现相位匹配的原理，并且分析了微环谐振腔中的有效非线性系数。结果表明微环谐振腔能够实现相位匹配的倍频过程。我们设计了一个高折射率差的AlGaAs微环谐振腔，其中泵浦波长和倍频光波长都处在谐振波长上。在泵浦非耗尽近似下，得出一个转换效率的解析表达式。从此表达式看出，转换效率由于腔场的增强而得到增加。考虑到泵浦光耗尽的情况，采用分段法进行数值模拟。结果表明在无损耗情况下，转换效率可以接近1。
(3)研究了光子晶体波导中太赫兹波的差频产生。我们通过把近红外光波导放置在太赫兹波光子晶体波导的线缺陷里面，利用近红外光源的差频过程产生太赫兹波。在这种结构中，光子晶体波导能紧紧地限制住太赫兹波的模场，使相互作用的三个光波实现好的模场重叠。两个泵浦光与太赫兹Bloch波奇特的相位匹配条件能够通过合适选择波导参数和泵浦光波长来满足。根据模式理论推导了差频过程的耦合模方程和有效作用面积公式。首先，我们设计了一个AlGaAs光子晶体波导。数值模拟出连续光泵浦的太赫兹波归一化转换效率为0.7632×104W1。其次，我们设计出一个LiNbO3光子晶体波导结构实现了频率为1THz的太赫兹波高效差频产生。由于光子晶体波导结构在太赫兹领域得到了广泛研究，这些太赫兹波产生方案给太赫兹技术提供了参考。
(4)研究了光子晶体波导中慢光增强的四波混频。利用模式理论，我们推导出光子晶体波导中的三阶非线性作用的耦合模方程组。这些非线性作用包括自相位调制、交叉相位调制和简并四波混频。这些耦合模方程组的形式与非线性光纤光学中的一致，并且可以应用于其他周期波导结构中的三阶非线性效应。基于这些方程，我们系统分析了一个慢光工程的硅基光子晶体波导的群速度色散、光传输损耗、有效作用面积、慢光增强因子和相位失配。考虑到双光子吸收和自由载流子效应，利用有限差分法数值模拟了此光子晶体波导两个色散平坦区域的四波混频转换效率。最后研究了慢光增强的多重四波混频对波长转换的影响。
Nonlinear wavelength conversion had played a key role in all-optical signal processing,optical data storage, biomedicine, color display, biotechnology, environmental monitoringand process analysis and so on. The third-harmonic generation (THG), four wave mixing(FWM) based on the third-order nonlinear interactions and the difference frequency gen-eration (DFG), sum-frequency generation (SFG), second-harmonic generation (SHG) fromthe second-order nonlinear effects, may convert the wavelength of semiconductor lasers tothe ultraviolet (UV), visible light, mid-infrared (IR) light and terahertz regions. On theother hand, the FWM, DFG, cascaded second-harmonic generation and difference frequen-cy generation (cSHG/DFG), cascaded sum-frequency generation and difference frequencygeneration (cSFG/DFG) can move the signal from one wavelength to another, and this maybe applied in the dense wavelength division multiplexing (DWDM) optical communicationnetwork. In this thesis, we design some appropriate waveguide structures to achieve thesenonlinear processes, and theoretically investigate the characters of wavelength conversion.The detailed research contents can be found as follows.
Firstly, we study the wavelength conversion in the lossy quasi-phase-matched (QPM)AlGaAs waveguide. We obtain the analytical expressions of converted wave power for DFG,cSHG/DFG processes under the non-depletion approximation in lossy QPM waveguides. Itis shown that the analytical results and the numerical simulation with depletion agree verywell for lossy waveguides. Employing the analytical solutions, the formulas of optimizedwaveguide lengths are obtained for lossy DFG and cSHG/DFG processes. After designingan AlGaAs QPM ridge waveguide, we detailly investigate and compare the characteristicsof the second-order nonlinear effects with and without loss, such as conversion efficiency,conversion bandwidth, pump wavelength tolerance and temperature stability.
Secondly, we study the SHG in AlGaAs microring resonator. In order to avoid theloss of QPM structures, we investigate the principle of curved AlGaAs waveguide for phasematch, and analyze the effective nonlinear coefficient of microring resonator. It is foundthat microring resonator can be employed to satisfy the phase matching condition of SHG. We design a high-index-contrast AlGaAs microring resonator with the wavelengths of pumpand second-harmonic in resonator wavelength. Under the non-depletion approximation, theanalytical solution of conversion efficiency is obtained. Based on the analytical solutions,it is clearly that the enhanced field in the microring resonator can improved the conversionefficiency. Considering the depletion situation, we numerically simulate the SHG processusing the fragment method. The results show that the conversion efficiency may be reach1in lossless case.
Thirdly, we study the THz wave DFG form photonic crystal waveguides (PCWs). Weplace the near-infrared light waveguide in the line defect of THz PCW to achieve THzwave DFG from near-infrared light sources. In this structure，PCW structure provides atight confinement of THz-wave field, resulting in a good mode field overlap of three waves.The unique phase matching condition between two pump waves and THz Bloch wave canbe satisfied through choosing appropriate waveguide parameters and pump wavelengths.The couple-mode equations and the effective interaction area formula for DFG processesis obtained from the modal theory. Firstly, we design a AlGaAs PCW, the high power-normalized conversion efficiency of0.7632×104W1for3THz generation is obtainedthrough simulating the continuous THz DFG process. Secondly, we design a LiNbO3PCWfor efficient1THz DFG. Since the photonic crystal structures have been widely exploitedfor THz researches, these approaches have the potential to open a new window for THztechnology.
Fourthly, we study the slow light enhanced FWM in PCW. By employing the modaltheory, we derive the couple-mode equations for third-order nonlinear effects in PCWs.These nonlinear interactions include self-phase modulation, cross-phase modulation anddegenerate FWM. The equations similar to that in nonlinear fiber optics could be expandedand applied for third-order nonlinear processes in other periodic waveguides. Based onthe equations, we systematically analyze the group-velocity dispersion, optical propagationloss, effective interaction area, slow light enhanced factor and phase mismatch for a slowlight engineered silicon PCW. Considering the two-photon absorption and free-carrier ef-fects, the wavelength conversion efficiencies in two low-dispersion regions are numerically simulated by utilizing finite difference method. Finally, we investigate the influence of slowlight enhanced multiple FWM process on the conversion efficiency.
引文
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