新型波导光栅技术及在波分复用光子集成中的应用
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摘要
通讯业务的发展对光通讯容量的需求越来越大。目前光网络的核心的器件,如激光器、调制器、光探测器,若依旧以分立的形式进行生产、封装和使用,随着光网络的容量的进一步增加,将使得传统的光系统体积非常庞大、结构复杂,可靠性降低,能耗和管理成本大幅增加。这些困难将使光通讯系统难于维持。光子集成把数十个甚至几百个光子元件集成在单一芯片上。无论体积,功耗还是管理等都具很大的优越性,因而被认为是解决这些问题的唯一途径,并广泛被认为光器件的主流发展方向。
波分复用(WDM)技术是目前应用最为广泛的一种增加信息容量的技术,其中核心光子器件是WDM集成芯片。它是由多波长分布反馈(DFB)激光器阵列和各种无源滤波器的单片集成。多波长DFB激光器阵列的制作最为困难。本文简单回顾了光子集成的发展,并讨论了目前各种DFB激光器阵列的制造技术。最后介绍了利用重构——等效啁啾(Reconstruction-equivalent-chirp,i.e. REC)技术制作DFB激光器阵列的优势,即利用等效相移、等效啁啾提高单模成品率,工艺流程仅仅增加一步微米量级的光刻,其他与常规制作一致,成本低。本文一部分重要工作是致力于基于REC技术的特殊激光器以及多波长激光器阵列的理论与实验研究；另一部分重要工作是提出微结构准相位匹配技术(Microstructure quasi-phase matching technology, i.e. MS-QPM), REC技术仅为其一维特例；研究了其物理本质,讨论了其潜在应用价值。
第一章绪论中,简单介绍了光子集成的发展历程,波导光栅以及多波长DFB半导体激光器阵列制造面临的问题以及相关的制造方法。最后给出了本论文的只要工作以及整体安排。
第二章首先介绍了波导光栅的基本原理。随后,介绍了REC技术的基本原理。文中说明了取样改变傅立叶子光栅的光栅形貌的根本在于,取样相位的改变能改变傅立叶子光栅的相对相位,取样周期的改变能改变子光栅的周期。所以只要合理设计取样图案,子光栅的任意的光栅形貌都能由取样图案来控制。最后给出了REC技术设计的整体思路和流程。
第三章研究了基于REC技术的特殊DFB半导体激光器和DFB半导体激光器阵列。对于特殊DFB半导体激光器本文主要实现了以下几个激光器：
(1)首次实验实现了等效λ/8相移DFB半导体激光器,并对其小信号频率响应特性,1dB压缩点,3阶交调失真进行了测试。同时实验实现了分别25℃和60℃,基带信号为1.0-Gb/s和1.4-Gb/s,本征信号频率7.64GHz的背靠背直调无误码光载无线系统(RoF)传输。
(2)首次实验实现了等效3相移(3PS)DFB半导体激光器,并测试了从20mA到100mA的光谱特性。实验发现,该激光器具有很好的单模特性,在偏置电流100mA时,边模抑制比(SMSR)为56dB。
(3)本文先从横向切趾波导光栅开始入手,首次提出了高性能的Y分支波导。进而进一步提出和理论研究了等效切趾DFB半导体激光器。该激光器分为两种类型：其一为两边切趾,研究发现该结构能抑制激光器的边模而提高激光器的单模特性；其二为中间切趾,理论研究发现,该结构也能抑制空间烧孔效应(spatial hole burning, i.e. SHB)从而改善该激光器在高电流下的单模特性。同时,实验发现,该激光器在100mA偏置电流下,SMSR为50dB。另外理论研究发现,如果合理设计两边切趾,该激光器也能有效抑制0级r光栅的潜在激射。
根据文献报道,这是首次实现了用传统全息曝光在同一晶片上实现不同光栅结构的半导体激光器。
本文还提出了另一种高性能特殊激光器结构——啁啾补偿激光器,即利用预先设计的啁啾光栅补偿空间烧孔效应引起的折射率变化。理论研究发现与3PSDFB半导体激光器相比较,该激光器单模特性好,线宽窄,动态特性好。这种激光器可以用等效啁啾来实现。
对于等效DFB半导体激光器阵列本文主要实现了以下几个激光器阵列：
(1)3.2nm×11波长和6.4nm×7波长的等效λ4相移半导体激光器。
(2)0.4nm×50波长和1.6nm×30波长的等效3PS相移半导体激光器。
实验研究发现,实际波长间隔比设计要普遍缩小90%,但是若以拟合的直线为准,波长的控制精度等达到+1nm～-1nm之内。根据目前的制造工艺,这个控制精度已经很高。若配以热调谐,电流调谐等微调,则有望很好对准ITU—-T标准。其中,3PS半导体激光器阵列,实验实现了除开2个不能正常工作,其他48个激光器都能正常工作,而且.具有比较好的单模特性(SMSR>35dB)。根据目前文献报道,这是实验制作波长数最多的结果。
在第四章,本文进一步研究了基于REC技术的激光器阵列。研究了取样光刻板的误差对激射波长的影响,发现这种影响和激光器腔长,取样周期大小都有关系,但是就目前的光刻板制作精度能将DFB激光器波长控制在1nm以内。这个值很小,这对于REC技术制作激光器是非常有利的。分析了制作取样时侧向腐蚀对激光器有效折射率的影响,研究结果表明这个影响是可以忽略的。最后,实验研究发现实际波长间隔的缩小是由于激光器波导的色散的影响引起的。本文实验测出了色散值,计算了波长间隔,并和实际测出的结果吻合。
在第五章,首次提出了交错取样结构提高REC技术的性能。研究发现,该结构能使±1级反射峰蓝移。若+1级用作工作光栅,那么有效远离0级反射峰,避免0级谐振的干扰。随后,从交错取样出发,进一步提出了MS-QPM技术,并对该技术进行了数学分析与仿真验证。REC技术是该技术的一维特例。本章解释了MS-QPM/REC的物理本质,即利用取样形成的附加光栅矢量来补偿种子光栅矢量与目标光栅实现的差,这个过程和非线性光学中的准相位匹配技术非常类似。对于其应用,该技术能等效实现复杂多维光栅,有望降低制造工艺。本章中讨论了其应用前景,同时提出了多种基于MS-QPM的光子集成器件。最后研究了多维取样结构的重构算法。由于取样图案往往复杂而非解析,所以重构算法对于MS-QPM在实际的应用中尤为重要。
With the development of the communication services, the demand for the capacity increases rapidly. At present, the key devices of the optical communication system, such as lasers, modulators and detectors, are usually separately fabricated, packaged and utilized. But as the optical network capacity will grow fast in the near future, if the devices keep discretely, the traditional optical communication systems will become very huge and complex, thus the cost of the energy consumption and management will be very high. So it would be hard to maintain the system. In contrast, dozens or hundreds of photonic elements are monolithically integrated on a single substrate to form the photonic integrated circuits (PICs). The main elements of PICs such as size, energy consumption and management are all superior to these with discrete devices. Therefore, PICs are widely considered as the only way to solve the problem and the main developing trend.
Wavelength division multiplexing (WDM) technology is widely used to increase the information capacity at present. The key device is the WDM photonic integrated circuits. It includes multi-wavelength DFB semiconductor laser array (MLA) and other various passive filters. The fabrication process of MLA is the most difficult among these elements. In the introduction of this thesis, we briefly review the development of the PICs and discuss some techniques to fabricate MLA presented up to now. Finally, we introduce the advantages of Reconstruction-equivalent-chirp (REC) technology for fabricating MLA. The equivalent phase shift and equivalent chirp are used to improve the yield of lasers working under single longitudinal mode condition. Only an additional μm level photo-lithography should be added comparing with the processes to fabricate the ordinary DFB lasers, so it would reduce the costs. In this thesis, one of the important works is the research of REC based DFB semiconductor laser with special grating structures and corresponding laser arrays. Another is the proposal and study of the Microstructure quasi-phase matching technology (MS-QPM). We found that the REC technology is a special case in one-dimensional. We also reveal its physical nature, and discuss the potential applications.
In the first chapter, the brief introduction of the development of the PICs is given. Then, the difficulty for fabricating the the waveguide grating and multi-wavelength DFB semiconductor laser array is described. The corresponding fabrication technologys are also given. At last, the main work and the arrangement of this thesis are given.
In the second chapter, the basic principle of the waveguide grating is introduced. In the following, the basic principle of the REC technology is also given. It shows that the change of the initial phase of the sampling structure changes the initial phase of the Fourier sub-gratings, and the change of the sampling period changes the period of the Fourier sub-grating. So the arbitrary grating profile can be equivalently formed if we carefully design the sampling structure. Finally, the whole design process is given.
In the third chapter, some special types of DFB semiconductor lasers and DFB laser arrays based on REC technology are studied. The following are some special types of DFB lasers studied and experimentally realized.
1. The equivalent A/8phase shifted DFB semiconductor laser was experimentally realized for the first time. Its performances such as small signal frequency response,1dB compression point and input3rd intercept point were tested. The directly modulated back to back error free transmissions in radio over fiber (RoF) system with operation temperatures of25"C and60"C, baseband signal frequencies of1.0-Gb/s and1.4-Gb/s and local oscillator signal frequency of7.64GHz are experimentally realized respectively.
2. The equivalent3PS DFB semiconductor laser was experimentally realized for the first time. The spectral characteristics were tested when the bias currents varied from20mA to100mA. It is found that the laser has good single longitudinal mode (SLM) performance. The side mode suppress ratio (SMSR) is56dB under the bias current of100mA.
3. Initialing with the a firstly proposed high performance Y branch waveguide based on the transverse apodized grating, the equivalent apodized DFB semiconductor lasers based on the sampled grating were proposed and theoretically analyzed. This type of lasers can be grouped into two kinds. The one is the apodization with two sides; the other is the apodization with middle. It is found that the sidelobes can be suppressed so that the side modes of the lasers can be suppressed accordingly when the first kind of apodization is applied. The second kind of apodization can suppress the spatial hole burning (SHB). Therefore the SLM operation can be maintained under high bias current. The experiment results show good SLM performance with SMSR of50dB when the bias current is100mA. If the apodiztion with two sides is designed reasonablely, it also can be used to suppress the potential lasing of the0th order Fourier sub-grating.
In addition, another novel DFB laser structure which is called SHB compensation (SHBC) DFB semiconductor laser is proposed. That is to say, use the predesigned chirped grating to compensate the index change caused by the SHB. Theoretical analysis shows that it has better SLM performance, narrower linewidth and better dynamic properties compared with the3PS DFB laser. This kind of lasers can also be realized by REC technology.
Some kinds of DFB laser arrays based on REC technology were also experimentally realized:
1.3.2nm×11wavelengths and6.4nm×7wavelengths A/4equivalent phase shifted DFB laser arrays;
2.0.4nm×50wavelengths and1.6nm×30wavelengths equivalent3PS DFB laser arrays.
The experimental results show that the measured wavelength spaces are smaller than that of designed to the extent of90%. According to the linear fitting line, the wavelength residuals are within+1nm～-1nm. These results are accurate enough to control the wavelength grid in the future. If the heart fine tune or the current fine tune is used, it is promising to meet the ITU-T standard precisely. For the3PS laser array, up to48lasers can work with SMSR larger than35dB except that two of them fail. According to the reports about the DFB laser arrays, the results exhibit the maximum lasing number.
In the fourth chapter, the further study for the DFB laser arrays based on REC technology is given. The influence of the sample mask error on the lasing wavelength is analyzed. Some conclusions can be drawn that the lasing wavelength error is related to the laser cavity length and the sampling period. However, even though this error is considered, the precision can only be controlled within1nm. Fortunately, this value is accurate enough for the laser arrays. The effluence on the effective index cansed by the lateral etch of the samping structure during the fabrication of the sampled grating is also analyzed. The results show this effluence is very small. On the other hand, the measured lasing wavelength space shrinked error is caused by the dispersion of the laser waveguide. The value of the dispersion was measured and the actual wavelength space considering dispersion is calculated. It matches well with the measured results.
In the fifth chapter, the crossed sampled grating is proposed for the first time. The±1st order reflective wavelengths are blue shifted of this grating. So the performance of this grating can be improved if the+1st order Fourier sub-grating is used. It is because that the0th order of this grating is farther away from the+1st sub-grating than that of traditional gratings so the unwanted resonance of the0th order can be avoided. Then based on the theoretical analysis for the crossed sampled grating, the MS-QPM is firstly proposed and theoretical analyzed and simulated. The REC technology becomes a one dimensional case of the MS-QPM. In the following, the physical nature of MS-QPM/REC is also revealed. That is to say, an additional grating vector produced by the sampling structure is applied to compensate the difference between the vectors of the working light and the seed grating. This principle is very similar with that of QPM in nonlinear optics. MS-QPM is expected to equivalently fabricate various complex multi-dimensional gratings with low cost. Its potential applications are discussed and some photonic devices are also proposed. Finally, the reconstruction algorithm of the MS-QPM is studied. Because the sampling pattern is usually very complex and hard to give an analytical expression, the reconstruction algorithm appears more important.
波分复用(WDM)技术是目前应用最为广泛的一种增加信息容量的技术,其中核心光子器件是WDM集成芯片。它是由多波长分布反馈(DFB)激光器阵列和各种无源滤波器的单片集成。多波长DFB激光器阵列的制作最为困难。本文简单回顾了光子集成的发展,并讨论了目前各种DFB激光器阵列的制造技术。最后介绍了利用重构——等效啁啾(Reconstruction-equivalent-chirp,i.e. REC)技术制作DFB激光器阵列的优势,即利用等效相移、等效啁啾提高单模成品率,工艺流程仅仅增加一步微米量级的光刻,其他与常规制作一致,成本低。本文一部分重要工作是致力于基于REC技术的特殊激光器以及多波长激光器阵列的理论与实验研究；另一部分重要工作是提出微结构准相位匹配技术(Microstructure quasi-phase matching technology, i.e. MS-QPM), REC技术仅为其一维特例；研究了其物理本质,讨论了其潜在应用价值。
第一章绪论中,简单介绍了光子集成的发展历程,波导光栅以及多波长DFB半导体激光器阵列制造面临的问题以及相关的制造方法。最后给出了本论文的只要工作以及整体安排。
第二章首先介绍了波导光栅的基本原理。随后,介绍了REC技术的基本原理。文中说明了取样改变傅立叶子光栅的光栅形貌的根本在于,取样相位的改变能改变傅立叶子光栅的相对相位,取样周期的改变能改变子光栅的周期。所以只要合理设计取样图案,子光栅的任意的光栅形貌都能由取样图案来控制。最后给出了REC技术设计的整体思路和流程。
第三章研究了基于REC技术的特殊DFB半导体激光器和DFB半导体激光器阵列。对于特殊DFB半导体激光器本文主要实现了以下几个激光器：
(1)首次实验实现了等效λ/8相移DFB半导体激光器,并对其小信号频率响应特性,1dB压缩点,3阶交调失真进行了测试。同时实验实现了分别25℃和60℃,基带信号为1.0-Gb/s和1.4-Gb/s,本征信号频率7.64GHz的背靠背直调无误码光载无线系统(RoF)传输。
(2)首次实验实现了等效3相移(3PS)DFB半导体激光器,并测试了从20mA到100mA的光谱特性。实验发现,该激光器具有很好的单模特性,在偏置电流100mA时,边模抑制比(SMSR)为56dB。
(3)本文先从横向切趾波导光栅开始入手,首次提出了高性能的Y分支波导。进而进一步提出和理论研究了等效切趾DFB半导体激光器。该激光器分为两种类型：其一为两边切趾,研究发现该结构能抑制激光器的边模而提高激光器的单模特性；其二为中间切趾,理论研究发现,该结构也能抑制空间烧孔效应(spatial hole burning, i.e. SHB)从而改善该激光器在高电流下的单模特性。同时,实验发现,该激光器在100mA偏置电流下,SMSR为50dB。另外理论研究发现,如果合理设计两边切趾,该激光器也能有效抑制0级r光栅的潜在激射。
根据文献报道,这是首次实现了用传统全息曝光在同一晶片上实现不同光栅结构的半导体激光器。
本文还提出了另一种高性能特殊激光器结构——啁啾补偿激光器,即利用预先设计的啁啾光栅补偿空间烧孔效应引起的折射率变化。理论研究发现与3PSDFB半导体激光器相比较,该激光器单模特性好,线宽窄,动态特性好。这种激光器可以用等效啁啾来实现。
对于等效DFB半导体激光器阵列本文主要实现了以下几个激光器阵列：
(1)3.2nm×11波长和6.4nm×7波长的等效λ4相移半导体激光器。
(2)0.4nm×50波长和1.6nm×30波长的等效3PS相移半导体激光器。
实验研究发现,实际波长间隔比设计要普遍缩小90%,但是若以拟合的直线为准,波长的控制精度等达到+1nm～-1nm之内。根据目前的制造工艺,这个控制精度已经很高。若配以热调谐,电流调谐等微调,则有望很好对准ITU—-T标准。其中,3PS半导体激光器阵列,实验实现了除开2个不能正常工作,其他48个激光器都能正常工作,而且.具有比较好的单模特性(SMSR>35dB)。根据目前文献报道,这是实验制作波长数最多的结果。
在第四章,本文进一步研究了基于REC技术的激光器阵列。研究了取样光刻板的误差对激射波长的影响,发现这种影响和激光器腔长,取样周期大小都有关系,但是就目前的光刻板制作精度能将DFB激光器波长控制在1nm以内。这个值很小,这对于REC技术制作激光器是非常有利的。分析了制作取样时侧向腐蚀对激光器有效折射率的影响,研究结果表明这个影响是可以忽略的。最后,实验研究发现实际波长间隔的缩小是由于激光器波导的色散的影响引起的。本文实验测出了色散值,计算了波长间隔,并和实际测出的结果吻合。
在第五章,首次提出了交错取样结构提高REC技术的性能。研究发现,该结构能使±1级反射峰蓝移。若+1级用作工作光栅,那么有效远离0级反射峰,避免0级谐振的干扰。随后,从交错取样出发,进一步提出了MS-QPM技术,并对该技术进行了数学分析与仿真验证。REC技术是该技术的一维特例。本章解释了MS-QPM/REC的物理本质,即利用取样形成的附加光栅矢量来补偿种子光栅矢量与目标光栅实现的差,这个过程和非线性光学中的准相位匹配技术非常类似。对于其应用,该技术能等效实现复杂多维光栅,有望降低制造工艺。本章中讨论了其应用前景,同时提出了多种基于MS-QPM的光子集成器件。最后研究了多维取样结构的重构算法。由于取样图案往往复杂而非解析,所以重构算法对于MS-QPM在实际的应用中尤为重要。
With the development of the communication services, the demand for the capacity increases rapidly. At present, the key devices of the optical communication system, such as lasers, modulators and detectors, are usually separately fabricated, packaged and utilized. But as the optical network capacity will grow fast in the near future, if the devices keep discretely, the traditional optical communication systems will become very huge and complex, thus the cost of the energy consumption and management will be very high. So it would be hard to maintain the system. In contrast, dozens or hundreds of photonic elements are monolithically integrated on a single substrate to form the photonic integrated circuits (PICs). The main elements of PICs such as size, energy consumption and management are all superior to these with discrete devices. Therefore, PICs are widely considered as the only way to solve the problem and the main developing trend.
Wavelength division multiplexing (WDM) technology is widely used to increase the information capacity at present. The key device is the WDM photonic integrated circuits. It includes multi-wavelength DFB semiconductor laser array (MLA) and other various passive filters. The fabrication process of MLA is the most difficult among these elements. In the introduction of this thesis, we briefly review the development of the PICs and discuss some techniques to fabricate MLA presented up to now. Finally, we introduce the advantages of Reconstruction-equivalent-chirp (REC) technology for fabricating MLA. The equivalent phase shift and equivalent chirp are used to improve the yield of lasers working under single longitudinal mode condition. Only an additional μm level photo-lithography should be added comparing with the processes to fabricate the ordinary DFB lasers, so it would reduce the costs. In this thesis, one of the important works is the research of REC based DFB semiconductor laser with special grating structures and corresponding laser arrays. Another is the proposal and study of the Microstructure quasi-phase matching technology (MS-QPM). We found that the REC technology is a special case in one-dimensional. We also reveal its physical nature, and discuss the potential applications.
In the first chapter, the brief introduction of the development of the PICs is given. Then, the difficulty for fabricating the the waveguide grating and multi-wavelength DFB semiconductor laser array is described. The corresponding fabrication technologys are also given. At last, the main work and the arrangement of this thesis are given.
In the second chapter, the basic principle of the waveguide grating is introduced. In the following, the basic principle of the REC technology is also given. It shows that the change of the initial phase of the sampling structure changes the initial phase of the Fourier sub-gratings, and the change of the sampling period changes the period of the Fourier sub-grating. So the arbitrary grating profile can be equivalently formed if we carefully design the sampling structure. Finally, the whole design process is given.
In the third chapter, some special types of DFB semiconductor lasers and DFB laser arrays based on REC technology are studied. The following are some special types of DFB lasers studied and experimentally realized.
1. The equivalent A/8phase shifted DFB semiconductor laser was experimentally realized for the first time. Its performances such as small signal frequency response,1dB compression point and input3rd intercept point were tested. The directly modulated back to back error free transmissions in radio over fiber (RoF) system with operation temperatures of25"C and60"C, baseband signal frequencies of1.0-Gb/s and1.4-Gb/s and local oscillator signal frequency of7.64GHz are experimentally realized respectively.
2. The equivalent3PS DFB semiconductor laser was experimentally realized for the first time. The spectral characteristics were tested when the bias currents varied from20mA to100mA. It is found that the laser has good single longitudinal mode (SLM) performance. The side mode suppress ratio (SMSR) is56dB under the bias current of100mA.
3. Initialing with the a firstly proposed high performance Y branch waveguide based on the transverse apodized grating, the equivalent apodized DFB semiconductor lasers based on the sampled grating were proposed and theoretically analyzed. This type of lasers can be grouped into two kinds. The one is the apodization with two sides; the other is the apodization with middle. It is found that the sidelobes can be suppressed so that the side modes of the lasers can be suppressed accordingly when the first kind of apodization is applied. The second kind of apodization can suppress the spatial hole burning (SHB). Therefore the SLM operation can be maintained under high bias current. The experiment results show good SLM performance with SMSR of50dB when the bias current is100mA. If the apodiztion with two sides is designed reasonablely, it also can be used to suppress the potential lasing of the0th order Fourier sub-grating.
In addition, another novel DFB laser structure which is called SHB compensation (SHBC) DFB semiconductor laser is proposed. That is to say, use the predesigned chirped grating to compensate the index change caused by the SHB. Theoretical analysis shows that it has better SLM performance, narrower linewidth and better dynamic properties compared with the3PS DFB laser. This kind of lasers can also be realized by REC technology.
Some kinds of DFB laser arrays based on REC technology were also experimentally realized:
1.3.2nm×11wavelengths and6.4nm×7wavelengths A/4equivalent phase shifted DFB laser arrays;
2.0.4nm×50wavelengths and1.6nm×30wavelengths equivalent3PS DFB laser arrays.
The experimental results show that the measured wavelength spaces are smaller than that of designed to the extent of90%. According to the linear fitting line, the wavelength residuals are within+1nm～-1nm. These results are accurate enough to control the wavelength grid in the future. If the heart fine tune or the current fine tune is used, it is promising to meet the ITU-T standard precisely. For the3PS laser array, up to48lasers can work with SMSR larger than35dB except that two of them fail. According to the reports about the DFB laser arrays, the results exhibit the maximum lasing number.
In the fourth chapter, the further study for the DFB laser arrays based on REC technology is given. The influence of the sample mask error on the lasing wavelength is analyzed. Some conclusions can be drawn that the lasing wavelength error is related to the laser cavity length and the sampling period. However, even though this error is considered, the precision can only be controlled within1nm. Fortunately, this value is accurate enough for the laser arrays. The effluence on the effective index cansed by the lateral etch of the samping structure during the fabrication of the sampled grating is also analyzed. The results show this effluence is very small. On the other hand, the measured lasing wavelength space shrinked error is caused by the dispersion of the laser waveguide. The value of the dispersion was measured and the actual wavelength space considering dispersion is calculated. It matches well with the measured results.
In the fifth chapter, the crossed sampled grating is proposed for the first time. The±1st order reflective wavelengths are blue shifted of this grating. So the performance of this grating can be improved if the+1st order Fourier sub-grating is used. It is because that the0th order of this grating is farther away from the+1st sub-grating than that of traditional gratings so the unwanted resonance of the0th order can be avoided. Then based on the theoretical analysis for the crossed sampled grating, the MS-QPM is firstly proposed and theoretical analyzed and simulated. The REC technology becomes a one dimensional case of the MS-QPM. In the following, the physical nature of MS-QPM/REC is also revealed. That is to say, an additional grating vector produced by the sampling structure is applied to compensate the difference between the vectors of the working light and the seed grating. This principle is very similar with that of QPM in nonlinear optics. MS-QPM is expected to equivalently fabricate various complex multi-dimensional gratings with low cost. Its potential applications are discussed and some photonic devices are also proposed. Finally, the reconstruction algorithm of the MS-QPM is studied. Because the sampling pattern is usually very complex and hard to give an analytical expression, the reconstruction algorithm appears more important.
引文
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