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CN112379485B - Integrated optical filter structure with ultra-large free spectral range - Google Patents

Integrated optical filter structure with ultra-large free spectral range Download PDF

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CN112379485B
CN112379485B CN202011278864.1A CN202011278864A CN112379485B CN 112379485 B CN112379485 B CN 112379485B CN 202011278864 A CN202011278864 A CN 202011278864A CN 112379485 B CN112379485 B CN 112379485B
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孙春雷
李兰
林宏焘
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    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/28Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29331Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by evanescent wave coupling
    • G02B6/29335Evanescent coupling to a resonator cavity, i.e. between a waveguide mode and a resonant mode of the cavity
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Abstract

本发明公开一种超大自由光谱范围的集成光学滤波器结构,该结构包括由入射波导、弯曲波导和出射波导依次相连构成的边耦合波导,以及依次相连的左侧布拉格波导光栅、拉锥渐变型波导光栅、反向拉锥渐变型波导光栅、右侧布拉格波导光栅。且弯曲波导的最低点的垂线过拉锥渐变型波导光栅、反向拉锥渐变型波导光栅的连接点。所有的波导光栅的周期相等,且布拉格波导光栅的禁带带宽小于两倍的F‑P谐振腔的自由光谱范围,F‑P谐振腔的谐振波长靠近布拉格波导光栅的禁带的中部。本发明将波导耦合器、布拉格波导光栅与F‑P谐振腔结合,利用布拉格光栅的有限禁带带宽以及F‑P谐振腔的大自由光谱范围可实现全光谱范围单纵模激励,从而实现单通道信号滤波。

Figure 202011278864

The invention discloses an integrated optical filter structure with an ultra-large free spectral range. The structure includes a side-coupling waveguide composed of an incident waveguide, a curved waveguide and an outgoing waveguide connected in sequence, and a left Bragg waveguide grating, a tapered gradient type, and a left Bragg waveguide grating connected in sequence. Waveguide grating, reverse taper gradient waveguide grating, right Bragg waveguide grating. And the vertical line of the lowest point of the curved waveguide passes through the connection point of the tapered tapered gradient waveguide grating and the reverse tapered tapered tapered waveguide grating. All the waveguide gratings have the same period, and the band gap of the Bragg waveguide grating is less than twice the free spectral range of the F‑P resonator, and the resonant wavelength of the F‑P resonator is close to the middle of the forbidden band of the Bragg waveguide grating. The invention combines the waveguide coupler, the Bragg waveguide grating and the F-P resonant cavity, and utilizes the limited band gap of the Bragg grating and the large free spectral range of the F-P resonant cavity to realize the excitation of the single longitudinal mode in the whole spectral range, thereby realizing the single longitudinal mode excitation of the whole spectral range. Channel signal filtering.

Figure 202011278864

Description

一种超大自由光谱范围的集成光学滤波器结构An integrated optical filter structure with a very large free spectral range

技术领域technical field

本发明涉及光学滤波器领域,具体涉及一种超大自由光谱范围的集成光学滤波器结构。The invention relates to the field of optical filters, in particular to an integrated optical filter structure with a super large free spectral range.

背景技术Background technique

在当今通讯网络和计算系统中,对高速率数据日益增长的需求推动了低成本、高速光学链路的发展。光互连中,各种先进的复用技术,如波分复用、偏振复用和模式复用已经相继被用来提高通光信容量。其中,在共享物理通道中使用不同波长的波分复用是近几十年来光互连中最流行的技术之一。这种基于波分复用技术的光子链路需要具有大量波长通道。因此,在基于波分复用的光互连中使用的滤波器波长的操作,多个滤波器级联实现多个波长通道的复用。自由光谱范围越大意味着可以支持越多独立的波长通道且通道之间互不干扰。利用光路可逆原理,大自由光谱范围的滤波器可以实现输入光谱进行下载,从而可以实现宽谱信号分析。In today's communication networks and computing systems, the growing demand for high-rate data drives the development of low-cost, high-speed optical links. In optical interconnection, various advanced multiplexing technologies, such as wavelength division multiplexing, polarization multiplexing and mode multiplexing, have been successively used to improve the optical communication capacity. Among them, wavelength division multiplexing using different wavelengths in a shared physical channel is one of the most popular technologies in optical interconnection in recent decades. Such a photonic link based on wavelength division multiplexing technology needs to have a large number of wavelength channels. Therefore, in the operation of filter wavelengths used in wavelength division multiplexing-based optical interconnects, multiple filters are cascaded to achieve multiplexing of multiple wavelength channels. A larger free spectral range means that more independent wavelength channels can be supported without interfering with each other. Using the principle of reversibility of the optical path, the filter with a large free spectral range can realize the download of the input spectrum, so that the wide-spectrum signal analysis can be realized.

另外一方面,近年以来,在物联网场景需求推动下,光传感器在医疗、油气、电力、军工、城建、食品安全和地质勘探等领域广泛应用,因而催生了数亿规模的市场。为了实现多位点多参量的传感,利用波分复用技术的分布式传感是构建传感网络的关键技术之一。分布式光探测技术,可以同时获得被测场的空间分布和随时间的变化信息。采用大自由光谱范围的滤波器可以有效增加单根传感链路上彼此独立传感器的数量,实现更多位点和参量的同时传感。On the other hand, in recent years, driven by the needs of IoT scenarios, optical sensors have been widely used in medical, oil and gas, electric power, military industry, urban construction, food safety and geological exploration, which has spawned a market of hundreds of millions. In order to realize multi-site and multi-parameter sensing, distributed sensing using wavelength division multiplexing technology is one of the key technologies for building a sensor network. Distributed light detection technology can simultaneously obtain the spatial distribution and time-dependent information of the measured field. Using a filter with a large free spectral range can effectively increase the number of independent sensors on a single sensing link, enabling simultaneous sensing of more sites and parameters.

目前已有多种实现大自由光谱范围滤波器的方案。微环谐振器通过选取超小半径可以实现较大的自由光谱范围,同时有紧凑的体积,但是自由光谱范围难以突破100nm,限制了其应用。为了在微环谐振器中实现扩展的自由光谱范围,人们使用了游标效应或两点耦合的多串耦合微环,但是这种方案敏感于实际器件尺寸变化,工艺容差小,通常需要热调进行微环谐振峰对准。在单环上级联反向耦合器也能实现宽的自由光谱范围,但这种方案中为了获取较窄的禁带宽度,要求反向耦合器中布拉格波导光栅刻槽宽度极小,工艺难度大,不利于工业生产,而且这种方案仍需要布拉格波导光栅的主峰和微环谐振峰对准,工艺容差小。理想的集成滤波器应具有大的自由光谱范围、高的抑制比和大的工艺容差,以避免精确的波长对准。At present, there are many schemes to realize the large free spectral range filter. Microring resonators can achieve a large free spectral range by selecting an ultra-small radius, and at the same time have a compact volume, but the free spectral range is difficult to exceed 100 nm, which limits its application. To achieve extended free spectral range in microring resonators, Vernier effect or two-point coupled multi-string coupled microrings have been used, but this scheme is sensitive to actual device size changes, has small process tolerances, and usually requires thermal tuning Perform microring resonance peak alignment. Cascading inverse couplers on a single ring can also achieve a wide free spectral range, but in order to obtain a narrow forbidden band width in this scheme, the groove width of the Bragg waveguide grating in the inverse coupler is required to be extremely small, and the process is difficult. , which is not conducive to industrial production, and this solution still requires alignment of the main peak of the Bragg waveguide grating with the resonant peak of the microring, and the process tolerance is small. An ideal integrated filter should have a large free spectral range, a high rejection ratio, and a large process tolerance to avoid precise wavelength alignment.

发明内容SUMMARY OF THE INVENTION

针对现有技术的不足,本发明提出一种超大自由光谱范围的集成光学滤波器结构,该滤波器结构能在宽谱范围甚至全光谱范围内实现单通道信号滤波。In view of the deficiencies of the prior art, the present invention proposes an integrated optical filter structure with a large free spectral range, which can realize single-channel signal filtering in a wide spectral range or even a full spectral range.

本发明的目的通过如下的技术方案来实现:The object of the present invention is achieved through the following technical solutions:

一种超大自由光谱范围的集成光学滤波器结构,其包括入射波导、出射波导、弯曲波导、左侧布拉格波导光栅、右侧布拉格波导光栅、拉锥渐变型波导光栅、反向拉锥渐变型波导光栅,其中:An integrated optical filter structure with an ultra-large free spectral range, comprising an incident waveguide, an outgoing waveguide, a curved waveguide, a left Bragg waveguide grating, a right Bragg waveguide grating, a tapered tapered waveguide grating, and a reverse tapered tapered waveguide grating, where:

所述入射波导、弯曲波导和出射波导依次相连,构成边耦合波导;The incident waveguide, the curved waveguide and the outgoing waveguide are connected in sequence to form an edge-coupling waveguide;

所述左侧布拉格波导光栅、拉锥渐变型波导光栅、反向拉锥渐变型波导光栅、右侧布拉格波导光栅依次相连,且所述左侧布拉格波导光栅与所述右侧布拉格波导光栅同轴;The left Bragg waveguide grating, the tapered tapered waveguide grating, the reverse tapered tapered waveguide grating, and the right Bragg waveguide grating are connected in sequence, and the left Bragg waveguide grating is coaxial with the right Bragg waveguide grating ;

所述弯曲波导的最低点的垂线过所述拉锥渐变型波导光栅、反向拉锥渐变型波导光栅的连接点;The vertical line of the lowest point of the curved waveguide passes through the connection point of the tapered tapered waveguide grating and the reverse tapered tapered waveguide grating;

所述入射波导、弯曲波导、出射波导、左侧布拉格波导光栅、拉锥渐变型波导光栅、反向拉锥渐变型波导光栅、右侧布拉格波导光栅均为单模波导;The incident waveguide, the curved waveguide, the outgoing waveguide, the left Bragg waveguide grating, the tapered tapered waveguide grating, the reverse tapered tapered waveguide grating, and the right Bragg waveguide grating are all single-mode waveguides;

所述左侧布拉格波导光栅、拉锥渐变型波导光栅、反向拉锥渐变型波导光栅、右侧布拉格波导光栅均为周期性结构,且四者的周期相等;The left Bragg waveguide grating, the tapered tapered waveguide grating, the reverse tapered tapered waveguide grating, and the right Bragg waveguide grating are all periodic structures, and the periods of the four are equal;

所述左侧布拉格波导光栅与所述右侧布拉格波导光栅构成F-P谐振腔;The left Bragg waveguide grating and the right Bragg waveguide grating form an F-P resonant cavity;

所述弯曲波导与所述F-P谐振腔构成侧边耦合F-P谐振腔;The curved waveguide and the F-P resonator form a side-coupled F-P resonator;

所述左侧布拉格波导光栅和右侧布拉格波导光栅的禁带带宽中的较大值为Δλsb,F-P腔的自由光谱范围FSRFP,则两者满足如下关系:The larger value of the forbidden band width of the left Bragg waveguide grating and the right Bragg waveguide grating is Δλ sb , and the free spectral range FSR FP of the FP cavity, then the two satisfy the following relationship:

Δλsb<2FSRFP Δλ sb < 2FSR FP

且所述F-P谐振腔的谐振波长靠近所述的左侧布拉格波导光栅和右侧布拉格波导光栅的禁带的中部。And the resonance wavelength of the F-P resonant cavity is close to the middle of the forbidden band of the left Bragg waveguide grating and the right Bragg waveguide grating.

进一步地,该滤波器结构为左右对称结构,且Δλsb<FSRFPFurther, the filter structure is a left-right symmetrical structure, and Δλ sb < FSR FP .

进一步地,该滤波器结构还包括位于拉锥渐变型波导光栅、反向拉锥渐变型波导光栅之间的单模波导,所述弯曲波导的最低点切线与所述单模波导平行且存在间隙,构成侧边耦合波导结构;且所述弯曲波导的最低点到所述单模波导的垂线过所述单模波导的中点。Further, the filter structure also includes a single-mode waveguide located between the tapered tapered waveguide grating and the reverse tapered tapered waveguide grating, and the lowest point tangent of the curved waveguide is parallel to the single-mode waveguide and has a gap. , forming a side-coupling waveguide structure; and the vertical line from the lowest point of the curved waveguide to the single-mode waveguide passes through the midpoint of the single-mode waveguide.

进一步地,所述F-P腔的自由光谱范围FSRFP的计算公式如下:Further, the calculation formula of the free spectral range FSR FP of the FP cavity is as follows:

Figure BDA0002780054030000021
Figure BDA0002780054030000021

Figure BDA0002780054030000031
Figure BDA0002780054030000031

其中,Lpd为所述左侧布拉格波导光栅和右侧布拉格波导光栅的穿透深度,Lt为拉锥渐变型波导光栅、反向拉锥渐变型波导光栅的长度,ng1表示单模波导的群折射率,ng2表示所述左侧布拉格波导光栅与右侧布拉格波导光栅的群折射率,ng3表示所述拉锥渐变型波导光栅、反向拉锥渐变型波导光栅的群折射率;neff,w和neff,n是左侧布拉格波导光栅、右侧布拉格波导光栅中周期性变化的有效折射率;λ为滤波器结构的工作波长。Wherein, L pd is the penetration depth of the left Bragg waveguide grating and the right Bragg waveguide grating, L t is the length of the tapered tapered waveguide grating and the reverse tapered tapered waveguide grating, and n g1 represents the single-mode waveguide , n g2 represents the group refractive index of the left Bragg waveguide grating and the right Bragg waveguide grating, n g3 represents the group refractive index of the tapered tapered waveguide grating and the reverse tapered tapered waveguide grating ; n eff,w and n eff,n are the effective refractive indices of the left Bragg waveguide grating and the right Bragg waveguide grating which change periodically; λ is the working wavelength of the filter structure.

本发明的有益效果如下:The beneficial effects of the present invention are as follows:

本发明的超大自由光谱范围的集成光学滤波器结构可以同时实现超大自由光谱范围操作、亚纳米光带宽和大工艺公差。也就意味着,可以支持越多独立的波长通道且通道之间互不干扰。这在光通信领域和分布式传感方面有着极大的应用价值。The integrated optical filter structure of the ultra-large free spectral range of the present invention can simultaneously realize operation in the ultra-large free spectral range, sub-nanometer optical bandwidth and large process tolerance. That is to say, more independent wavelength channels can be supported without interfering with each other. This has great application value in the field of optical communication and distributed sensing.

附图说明Description of drawings

图1为本发明的实施例一的超大自由光谱范围的滤波器结构的示意图;1 is a schematic diagram of a filter structure with a super large free spectral range according to Embodiment 1 of the present invention;

图2为本发明的实施例一的超大自由光谱范围的滤波器的工作原理图;Fig. 2 is the working principle diagram of the filter of the ultra-large free spectral range of the first embodiment of the present invention;

图3为实施例一的滤波器在1400-1620nm波长范围内的透射率示意图;3 is a schematic diagram of the transmittance of the filter in the first embodiment in the wavelength range of 1400-1620 nm;

图4为实施例一的滤波器在1400、1521、1522、1620nm处的模拟电场分布示意图,其中,白色箭头表示注入光的方向。FIG. 4 is a schematic diagram of the simulated electric field distribution at 1400, 1521, 1522, and 1620 nm of the filter of the first embodiment, wherein the white arrows indicate the direction of the injected light.

图5为本发明的实施例三的超大自由光谱范围的滤波器结构的示意图;5 is a schematic diagram of a filter structure with a super large free spectral range according to Embodiment 3 of the present invention;

图6为本发明的实施例五的超大自由光谱范围的滤波器结构的示意图;6 is a schematic diagram of a filter structure with a super large free spectral range according to Embodiment 5 of the present invention;

图7为图6左侧布拉格波导光栅104的波导截面图;FIG. 7 is a waveguide cross-sectional view of the Bragg waveguide grating 104 on the left side of FIG. 6;

图8为本发明的实施例六的超大自由光谱范围的滤波器结构的示意图;8 is a schematic diagram of a filter structure with a super large free spectral range according to Embodiment 6 of the present invention;

图9为图8左侧布拉格波导光栅104的波导截面图;FIG. 9 is a waveguide cross-sectional view of the Bragg waveguide grating 104 on the left side of FIG. 8;

图10为本发明的实施例七的超大自由光谱范围的滤波器结构的示意图;10 is a schematic diagram of a filter structure with a super large free spectral range according to Embodiment 7 of the present invention;

实施例一~七中,101为入射波导、102为出射波导、103为弯曲波导、104为左侧布拉格波导光栅、105为右侧布拉格波导光栅、106为拉锥渐变型波导光栅、107为反向拉锥渐变型波导光栅、108为单模波导、201为波导芯层,202为波导包层,203为被刻蚀的波导包层、301为波导芯层、302为波导包层、303为纳米柱。In the first to seventh embodiments, 101 is the incident waveguide, 102 is the outgoing waveguide, 103 is the curved waveguide, 104 is the left Bragg waveguide grating, 105 is the right Bragg waveguide grating, 106 is the tapered gradient waveguide grating, and 107 is the inverted waveguide grating. The tapered gradient waveguide grating, 108 is a single-mode waveguide, 201 is a waveguide core layer, 202 is a waveguide cladding layer, 203 is an etched waveguide cladding layer, 301 is a waveguide core layer, 302 is a waveguide cladding layer, 303 is Nanopillars.

具体实施方式Detailed ways

下面将结合示意图对本发明的超大自由光谱范围的滤波器结构进行更详细的描述,其中示意图表示了本发明的优选实施例,应该理解本领域技术人员可以修改在此描述的本发明,而仍然实现本发明的有利效果。因此,下列描述应当被理解为对于本领域技术人员的广泛知道,而并不作为对本发明的限制。The filter structure of the present invention with a large free spectral range will be described in more detail below with reference to the schematic diagram, wherein the schematic diagram represents a preferred embodiment of the present invention, and it should be understood that those skilled in the art can modify the present invention described herein, and still achieve Advantageous effects of the present invention. Therefore, the following description should be construed as widely known to those skilled in the art and not as a limitation of the present invention.

在本发明的描述中,需要说明的是,对于方位词,如有术语“中心”,“横向”、“纵向”、“长度”、“宽度”、“厚度”、“上”、“下”、“前”、“后”、“左”、“右”、“竖直”、“水平”、“顶”、“底”、“内”、“外”、“顺时针”、“逆时针”等指示方位和位置关系为基于附图所示的方位或位置关系,仅是为了便于叙述本发明和简化描述,而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定方位构造和操作,不能理解为限制本发明的具体保护范围。In the description of the present invention, it should be noted that, for orientation words, such as the terms "center", "horizontal", "longitudinal", "length", "width", "thickness", "upper", "lower" , "Front", "Back", "Left", "Right", "Vertical", "Horizontal", "Top", "Bottom", "Inside", "Outside", "Clockwise", "Counterclockwise" ” etc. indicating the orientation and positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation or a specific orientation. The structure and operation should not be construed as limiting the specific protection scope of the present invention.

在下列段落中参照附图以举例方式更具体地描述本发明。根据下面说明,本发明的优点和特征将更清楚。需说明的是,附图均采用非常简化的形式且均使用非精准的比例,仅用以方便、明晰地辅助说明本发明实施例的目的。The invention is described in more detail by way of example in the following paragraphs with reference to the accompanying drawings. The advantages and features of the present invention will become more apparent from the following description. It should be noted that, the accompanying drawings are all in a very simplified form and in inaccurate scales, and are only used to facilitate and clearly assist the purpose of explaining the embodiments of the present invention.

如图1所示,本发明的超大自由光谱范围的滤波器结构,包括入射波导101、出射波导102、弯曲波导103、左侧布拉格波导光栅104、右侧布拉格波导光栅105、拉锥渐变型波导光栅106、反向拉锥渐变型波导光栅107和单模波导108;As shown in FIG. 1 , the filter structure of the present invention with a large free spectral range includes an incident waveguide 101 , an exit waveguide 102 , a curved waveguide 103 , a left Bragg waveguide grating 104 , a right Bragg waveguide grating 105 , and a tapered tapered waveguide. grating 106, reverse taper gradient waveguide grating 107 and single-mode waveguide 108;

所述入射波导101、弯曲波导103和出射波导102依次相连,构成边耦合波导;The incident waveguide 101, the curved waveguide 103 and the outgoing waveguide 102 are connected in sequence to form an edge-coupling waveguide;

所述左侧布拉格波导光栅104、拉锥渐变型波导光栅106、单模波导108、反向拉锥渐变型波导光栅107、右侧布拉格波导光栅105依次相连,且所述左侧布拉格波导光栅104与所述右侧布拉格波导光栅同轴;左侧布拉格波导光栅104与右侧布拉格波导光栅105之间存在单模波导108,并构成F-P谐振腔;弯曲波导103的最低点切线与单模波导108平行且存在间隙,构成侧边耦合波导结构;单模波导108的长度可以为零。弯曲波导103的最低点到单模波导108的垂线过单模波导108的中点;弯曲波导103与F-P谐振腔构成侧边耦合F-P谐振腔。The left Bragg waveguide grating 104 , the tapered tapered waveguide grating 106 , the single-mode waveguide 108 , the reverse tapered tapered waveguide grating 107 , and the right Bragg waveguide grating 105 are connected in sequence, and the left Bragg waveguide grating 104 It is coaxial with the right Bragg waveguide grating; a single-mode waveguide 108 exists between the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105 to form an F-P resonant cavity; the lowest point tangent of the curved waveguide 103 is connected to the single-mode waveguide 108 Parallel and there is a gap to form a side-coupling waveguide structure; the length of the single-mode waveguide 108 can be zero. The vertical line from the lowest point of the curved waveguide 103 to the single-mode waveguide 108 passes through the midpoint of the single-mode waveguide 108; the curved waveguide 103 and the F-P resonator form a side-coupled F-P resonator.

此外,入射波导101、弯曲波导103、出射波导102、左侧布拉格波导光栅104、拉锥渐变型波导光栅106、反向拉锥渐变型波导光栅107、右侧布拉格波导光栅105均为单模波导,且左侧布拉格波导光栅104、拉锥渐变型波导光栅106、反向拉锥渐变型波导光栅107、右侧布拉格波导光栅105均为周期性结构,且四者的周期相等。In addition, the incident waveguide 101 , the curved waveguide 103 , the outgoing waveguide 102 , the left Bragg waveguide grating 104 , the tapered tapered waveguide grating 106 , the reverse tapered tapered waveguide grating 107 , and the right Bragg waveguide grating 105 are all single-mode waveguides. , and the left Bragg waveguide grating 104 , the tapered tapered waveguide grating 106 , the reverse tapered tapered waveguide grating 107 , and the right Bragg waveguide grating 105 are all periodic structures with equal periods.

具体地,在滤波器在使用时,激光注入到滤波器的入射波导101中,激光通过弯曲波导103耦合到F-P谐振腔中。非谐振波长从F-P谐振腔耦合到出射波导102中,谐振波长耦合进入在F-P谐振腔中并增强,直到输入功率,外耦合功率,腔损耗功率达到动态平衡,光像是被腔体束缚住,无法从F-P谐振腔耦合到出射波导102,从而实现特定波长光的滤波。通过在左侧布拉格光栅104和右侧布拉格光栅105之间引入拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107,降低左侧布拉格光栅104、右侧布拉格光栅105和单模波导108的模式失配,从而降低腔内损耗,抑制边带抖动和增加谐振腔的品质因子。单模波导108连接拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107。通过控制拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107的周期数和单模波导108的长度可以调控F-P谐振腔的自由光谱范围。如图2所示,选择拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107尽量少的周期数和单模波导108的长度(单模波导108的长度可以为零),使得左侧布拉格波导光栅104和右侧布拉格波导光栅105的禁带带宽小于两倍的F-P谐振腔腔的自由光谱范围,便可以实现单纵模的激发,从而实现全光谱范围单个峰或者单个谷超大自由光谱范围的滤波器。其中,Δλsb表示布拉格波导光栅的禁带带宽,FSRFP为F-P腔的自由光谱范围则两者满足如下关系:Specifically, when the filter is in use, laser light is injected into the incident waveguide 101 of the filter, and the laser light is coupled into the FP resonator through the curved waveguide 103 . The non-resonant wavelength is coupled from the FP resonator into the outgoing waveguide 102, and the resonant wavelength is coupled into the FP resonator and intensifies until the input power, out-coupling power, and cavity loss power reach a dynamic balance, and the optical image is bound by the cavity, There is no way to couple from the FP resonator to the exit waveguide 102, enabling filtering of specific wavelengths of light. By introducing the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 between the left Bragg grating 104 and the right Bragg grating 105, the left Bragg grating 104, the right Bragg grating 105 and the single-mode waveguide are lowered 108 mode mismatch, thereby reducing intracavity losses, suppressing sideband jitter and increasing the quality factor of the resonator. The single-mode waveguide 108 connects the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 . The free spectral range of the FP resonator can be regulated by controlling the number of periods of the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 and the length of the single-mode waveguide 108 . As shown in FIG. 2 , the number of periods of the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 and the length of the single-mode waveguide 108 (the length of the single-mode waveguide 108 can be zero) are selected as small as possible, so that the left The band gap of the side Bragg waveguide grating 104 and the right Bragg waveguide grating 105 is less than twice the free spectral range of the FP resonator cavity, so that the excitation of a single longitudinal mode can be realized, thereby realizing a single peak or a single valley in the full spectral range. Filter for spectral range. Among them, Δλ sb represents the forbidden band bandwidth of the Bragg waveguide grating, and FSR FP is the free spectral range of the FP cavity, and the two satisfy the following relationship:

Δλsb<2FSRFPΔλ sb <2FSR FP ;

且所述F-P谐振腔的谐振波长靠近所述的左侧布拉格波导光栅(104)和右侧布拉格波导光栅(105)的禁带的中部。And the resonance wavelength of the F-P resonant cavity is close to the middle of the forbidden band of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105).

其中,FSRFP的计算公式如下:Among them, the calculation formula of FSR FP is as follows:

Figure BDA0002780054030000051
Figure BDA0002780054030000051

Figure BDA0002780054030000052
Figure BDA0002780054030000052

其中,Lpd为所述左侧布拉格波导光栅104和右侧布拉格波导光栅105的穿透深度,Lt为拉锥渐变型波导光栅106、反向拉锥渐变型波导光栅107的长度,ng1表示单模波导108的群折射率,ng2表示所述左侧布拉格波导光栅104与右侧布拉格波导光栅105的群折射率,ng3表示所述拉锥渐变型波导光栅106、反向拉锥渐变型波导光栅107的群折射率;neff,w和neff,n是左侧布拉格波导光栅104、右侧布拉格波导光栅105中周期性变化的有效折射率;λ为滤波器结构的工作波长。Wherein, L pd is the penetration depth of the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105 , Lt is the length of the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 , and n g1 represents The group refractive index of the single-mode waveguide 108, n g2 represents the group refractive index of the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105, n g3 represents the tapered waveguide grating 106, the reverse tapered tapered The group refractive index of the waveguide grating 107; n eff, w and n eff, n are the effective refractive indices of the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105 that change periodically; λ is the working wavelength of the filter structure.

下面给出本发明的滤波器结构的多个实施例。Several embodiments of the filter structure of the present invention are given below.

实施例一Example 1

基于220nm绝缘层上硅平台制备集成的超大自由光谱范围的滤波器。入射波导101、出射波导102、弯曲波导103和单模波导108宽度为500nm,波导为脊波导,刻蚀深度(波导高度)为150nm,弯曲波导的弯曲半径为20μm。左侧布拉格波导光栅104和右侧布拉格波导光栅105由宽波导和窄波导周期性交替而成,宽波导宽度为500nm,窄波导为300nm,周期数为150,周期为317nm。拉锥渐变型波导光栅106由宽波导和窄波导周期性交替而成,宽波导宽度为500nm,宽度不变,窄波导宽度从300nm线性变宽至500nm,周期数为5,周期为317nm;反向拉锥渐变型波导光栅107由宽波导和窄波导周期性交替而成,宽波导宽度为500nm,宽度不变,窄波导宽度从500nm线性变为300nm,周期数为5,周期为317nm;单模波导108长度为零,弯曲波导103和单模波导108的间隙为250nm。An integrated ultra-large free spectral range filter was fabricated based on a 220 nm silicon-on-insulator platform. The width of the incident waveguide 101 , the outgoing waveguide 102 , the curved waveguide 103 and the single-mode waveguide 108 is 500 nm, the waveguide is a ridge waveguide, the etching depth (waveguide height) is 150 nm, and the bending radius of the curved waveguide is 20 μm. The left Bragg waveguide grating 104 and the right Bragg waveguide grating 105 are formed by periodically alternating wide waveguides and narrow waveguides. The width of the wide waveguide is 500 nm, the width of the narrow waveguide is 300 nm, the number of periods is 150, and the period is 317 nm. The tapered gradient waveguide grating 106 is formed by periodically alternating wide waveguides and narrow waveguides. The width of the wide waveguide is 500nm, and the width is unchanged. The tapered gradient waveguide grating 107 is formed by periodically alternating wide waveguides and narrow waveguides. The width of the wide waveguide is 500nm, and the width is unchanged. The width of the narrow waveguide changes linearly from 500nm to 300nm, the number of periods is 5, and the period is 317nm; The mode waveguide 108 has a length of zero, and the gap between the curved waveguide 103 and the single mode waveguide 108 is 250 nm.

在本实施例中,滤波器在使用时,扫频连续激光注入到滤波器的入射波导101中,激光通过边耦合波导结构耦合到F-P谐振腔中。谐振波长1521nm一直在谐振腔中振荡无法从谐振腔耦合到出射波导102,非谐振波长(除1521nm外)从F-P谐振腔耦合到出射波导102中,以实现对1521nm波长激光的滤除。In this embodiment, when the filter is in use, the swept-frequency continuous laser is injected into the incident waveguide 101 of the filter, and the laser is coupled into the F-P resonator through the side-coupling waveguide structure. The resonant wavelength of 1521 nm has been oscillating in the resonator and cannot be coupled from the resonator to the exit waveguide 102, and the non-resonant wavelengths (except 1521 nm) are coupled from the F-P resonator into the exit waveguide 102, so as to realize the filtering of the 1521 nm wavelength laser.

图3给出了实施例一的滤波器的光谱传输图,从图中可以看出,在220nm的超大波长范围内,只能看到在1521nm有一个深的凹陷,而在非共振波长处平坦的响应。图4展示了在工作波长为1400、1521、1522和1620nm时整个结构的电场分布。对于禁带外波长为1400和1620nm的光,该滤波器被认为是传统的双波导耦合器。因此,光在F-P腔中不能增强,而是耦合到右侧的布拉格光栅中。对于阻带内1522nm而非谐振处的波长,光被耦合到腔内,然后被布拉格光栅反射,最后传输到直通端口。对于1521nm的谐振波长,光耦合进入腔内,增强腔内的功率,直到耦合功率、外耦合功率和损耗功率之间实现动态平衡。因此,光就像被困在腔内,几乎没有功率耦合到直通端口。Figure 3 shows the spectral transmission diagram of the filter of Example 1. It can be seen from the figure that in the ultra-large wavelength range of 220 nm, only a deep depression can be seen at 1521 nm, while it is flat at the non-resonant wavelength. the response to. Figure 4 shows the electric field distribution of the whole structure at operating wavelengths of 1400, 1521, 1522 and 1620 nm. For light with out-of-band wavelengths of 1400 and 1620 nm, the filter is considered a conventional dual-waveguide coupler. Therefore, the light cannot be enhanced in the F-P cavity, but is coupled into the Bragg grating on the right. For wavelengths within the stopband of 1522 nm but not at resonance, light is coupled into the cavity, then reflected by the Bragg grating, and finally transmitted to the thru port. For the resonant wavelength of 1521 nm, light is coupled into the cavity, enhancing the power in the cavity until a dynamic balance is achieved between coupled power, outcoupling power, and loss power. Therefore, the light appears to be trapped inside the cavity, with little power coupled into the thru port.

实施例二Embodiment 2

实施例二与实施例一的不同之处仅在于将实施例一中的脊波导变成条波导。The difference between the second embodiment and the first embodiment is only that the ridge waveguide in the first embodiment is changed into a strip waveguide.

实施例三Embodiment 3

实施例三与实施例一的不同之处仅在于将实施例一中的左侧布拉格波导光栅104、右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107由宽波导和窄波导交替的方案更改为波导内刻蚀小孔的方案。如图5所示,左侧布拉格波导光栅104和右侧布拉格波导光栅105均由普通单模波导和打孔的单模波导周期性交替形成;拉锥渐变型波导光栅106由单模波导和打孔的单模波导周期性交替而成,单模波导宽度不变,圆孔的半径逐渐变小;反向拉锥渐变型波导光栅107由单模波导和打孔的单模波导周期性交替而成,单模波导宽度不变,圆孔的半径逐渐变大。The difference between the third embodiment and the first embodiment is only that the left Bragg waveguide grating 104 , the right Bragg waveguide grating 105 , the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 in the first embodiment are changed. The scheme of alternating wide waveguides and narrow waveguides is changed to the scheme of etching small holes in the waveguide. As shown in FIG. 5 , the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105 are both formed by a common single mode waveguide and a perforated single mode waveguide periodically alternately; the tapered gradient waveguide grating 106 is composed of a single mode waveguide and a punched single mode waveguide The single-mode waveguides of the holes are periodically alternated, the width of the single-mode waveguides remains unchanged, and the radius of the circular holes gradually decreases; the reverse taper gradient waveguide grating 107 is composed of the single-mode waveguides and the perforated single-mode waveguides periodically alternated. The width of the single-mode waveguide remains unchanged, and the radius of the circular hole gradually increases.

实施例四Embodiment 4

实施例四与实施例三的不同之处仅在于将实施例三中的左侧布拉格波导光栅104、右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107种的圆孔替换成非圆形孔,如矩形孔、方形孔、椭圆形孔等。The difference between the fourth embodiment and the third embodiment is only that the left Bragg waveguide grating 104, the right Bragg waveguide grating 105, the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 in the third embodiment are replaced. The round holes of this kind are replaced with non-circular holes, such as rectangular holes, square holes, oval holes, etc.

实施例五Embodiment 5

实施例五与实施例一的不同之处仅在于将实施例一中的左侧布拉格波导光栅104、右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107由宽波导和窄波导交替的方案更改为刻蚀波导包层的方案。如图6所示,左侧布拉格波导光栅104和右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107均由普通单模波导和周期性刻蚀的包层组成。图7所示为图6左侧布拉格波导光栅104的波导截面图。201为波导芯层,202为波导包层,203为被刻蚀的波导包层。The difference between the fifth embodiment and the first embodiment is only that the left Bragg waveguide grating 104 , the right Bragg waveguide grating 105 , the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 in the first embodiment are replaced. The scheme of alternating wide and narrow waveguides is changed to the scheme of etching the waveguide cladding. As shown in FIG. 6, the left Bragg waveguide grating 104, the right Bragg waveguide grating 105, the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 are all made of ordinary single-mode waveguides and periodically etched packages. layer composition. FIG. 7 is a cross-sectional view of the waveguide of the Bragg waveguide grating 104 on the left side of FIG. 6 . 201 is the waveguide core layer, 202 is the waveguide cladding layer, and 203 is the etched waveguide cladding layer.

实施例六Embodiment 6

实施例六与实施例五的不同之处仅在于将实施例五的左侧布拉格波导光栅104、右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107由刻蚀波导包层的方案改为波导旁边刻蚀纳米柱。如图8所示,左侧布拉格波导光栅104和右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107均由普通单模波导和周期性刻蚀的纳米柱组成。图9所示为图8左侧布拉格波导光栅104的波导截面图。601为波导芯层,302为波导包层,303为纳米柱。纳米柱303可以是矩形柱、方形柱、圆柱、椭圆柱。The difference between the sixth embodiment and the fifth embodiment is only that the left Bragg waveguide grating 104, the right Bragg waveguide grating 105, the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 of the fifth embodiment are replaced by The scheme for etching the waveguide cladding is changed to etching nanopillars next to the waveguide. As shown in FIG. 8 , the left Bragg waveguide grating 104 , the right Bragg waveguide grating 105 , the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 are all made of ordinary single-mode waveguides and periodically etched nanometers. Column composition. FIG. 9 is a cross-sectional view of the waveguide of the Bragg waveguide grating 104 on the left side of FIG. 8 . 601 is a waveguide core layer, 302 is a waveguide cladding layer, and 303 is a nanocolumn. The nanopillars 303 can be rectangular, square, cylindrical, or elliptical.

实施例七Embodiment 7

实施例七与实施例一的不同之处仅在于将实施例一的左侧布拉格波导光栅104、右侧布拉格波导光栅105、拉锥渐变型波导光栅106和反向拉锥渐变型波导光栅107和单模波导108由普通波导改为狭缝波导,如图10所示。The difference between the seventh embodiment and the first embodiment is only that the left Bragg waveguide grating 104 , the right Bragg waveguide grating 105 , the tapered tapered waveguide grating 106 and the reverse tapered tapered waveguide grating 107 of the first embodiment are combined with each other. The single-mode waveguide 108 is changed from an ordinary waveguide to a slit waveguide, as shown in FIG. 10 .

此外,对于本技术领域的普通技术人员来说,在不脱离本发明原理的前提下,还可以做出若干改进和润饰,采用其他集成光学平台,如绝缘层上硅平台、无机硫系玻璃平台、氧化钛平台、氮化硅平台、绝缘层上铌酸锂平台和三五族磷化铟平台等;采用不同的光学工作波段,比如紫外波段、可见光波段、近红外波导、中红外波导和远红外波段等。In addition, for those of ordinary skill in the art, without departing from the principles of the present invention, several improvements and modifications can also be made, and other integrated optical platforms, such as silicon-on-insulator platforms, inorganic chalcogenide glass platforms, can be used. , titanium oxide platform, silicon nitride platform, lithium niobate platform on insulating layer and indium phosphide platform, etc.; using different optical working bands, such as ultraviolet band, visible light band, near-infrared waveguide, mid-infrared waveguide and far Infrared band, etc.

综上,在本实施例中,提出的超大自由光谱范围的滤波器结构,本发明将波导耦合器、布拉格波导光栅与F-P谐振腔结合,利用布拉格光栅的有限禁带带宽以及F-P谐振腔的大自由光谱范围的特点,控制F-P谐振腔的腔长使得布拉格波导光栅的禁带带宽小于两倍的F-P谐振腔腔的自由光谱范围,便可以实现单纵模的激发,从而实现全光谱范围单个峰或者单个谷超大自由光谱范围的滤波器。To sum up, in this embodiment, the proposed filter structure with a large free spectral range, the present invention combines a waveguide coupler, a Bragg waveguide grating and an F-P resonant cavity, and utilizes the limited band gap of the Bragg grating and the large F-P resonant cavity. The characteristics of the free spectral range, controlling the cavity length of the F-P resonator so that the band gap of the Bragg waveguide grating is less than twice the free spectral range of the F-P resonator cavity, so that the excitation of a single longitudinal mode can be achieved, thereby realizing a single peak in the full spectral range. Or a single-valley filter with a very large free spectral range.

本领域普通技术人员可以理解,以上所述仅为发明的优选实例而已,并不用于限制发明,尽管参照前述实例对发明进行了详细的说明,对于本领域的技术人员来说,其依然可以对前述各实例记载的技术方案进行修改,或者对其中部分技术特征进行等同替换。凡在发明的精神和原则之内,所做的修改、等同替换等均应包含在发明的保护范围之内。Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still understand the Modifications are made to the technical solutions described in the foregoing examples, or equivalent replacements are made to some of the technical features. All modifications and equivalent replacements made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims (3)

1.一种超大自由光谱范围的集成光学滤波器结构,其特征在于,其包括入射波导(101)、出射波导(102)、弯曲波导(103)、左侧布拉格波导光栅(104)、右侧布拉格波导光栅(105)、拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107),其中:1. An integrated optical filter structure with a super large free spectral range, characterized in that it comprises an incident waveguide (101), an exit waveguide (102), a curved waveguide (103), a left Bragg waveguide grating (104), a right Bragg waveguide grating (105), tapered tapered waveguide grating (106), reverse tapered tapered waveguide grating (107), wherein: 所述入射波导(101)、弯曲波导(103)和出射波导(102)依次相连,构成边耦合波导;The incident waveguide (101), the curved waveguide (103) and the outgoing waveguide (102) are connected in sequence to form an edge-coupling waveguide; 所述左侧布拉格波导光栅(104)、拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)、右侧布拉格波导光栅(105)依次相连,且所述左侧布拉格波导光栅(104)与所述右侧布拉格波导光栅同轴;The left Bragg waveguide grating (104), the tapered tapered waveguide grating (106), the reverse tapered tapered waveguide grating (107), and the right Bragg waveguide grating (105) are connected in sequence, and the left Bragg The waveguide grating (104) is coaxial with the right Bragg waveguide grating; 所述弯曲波导(103)的最低点的垂线过所述拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)的连接点;The vertical line of the lowest point of the curved waveguide (103) passes through the connection point of the tapered tapered waveguide grating (106) and the reverse tapered tapered waveguide grating (107); 所述入射波导(101)、弯曲波导(103)、出射波导(102)、左侧布拉格波导光栅(104)、拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)、右侧布拉格波导光栅(105)均为单模波导;The incident waveguide (101), the curved waveguide (103), the outgoing waveguide (102), the left Bragg waveguide grating (104), the tapered tapered waveguide grating (106), and the reverse tapered tapered waveguide grating (107) , the Bragg waveguide grating (105) on the right side is a single-mode waveguide; 所述左侧布拉格波导光栅(104)、拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)、右侧布拉格波导光栅(105)均为周期性结构,且四者的周期相等;The left Bragg waveguide grating (104), the tapered tapered waveguide grating (106), the reverse tapered tapered waveguide grating (107), and the right Bragg waveguide grating (105) are all periodic structures, and the four period is equal; 所述左侧布拉格波导光栅(104)与所述右侧布拉格波导光栅(105)构成F-P谐振腔;The left Bragg waveguide grating (104) and the right Bragg waveguide grating (105) form an F-P resonant cavity; 所述弯曲波导(103)与所述F-P谐振腔构成侧边耦合F-P谐振腔;The curved waveguide (103) and the F-P resonator form a side-coupled F-P resonator; 所述左侧布拉格波导光栅(104)和右侧布拉格波导光栅(105)的禁带带宽中的较大值为Δλsb,F-P腔的自由光谱范围FSRFP,则两者满足如下关系:The larger value of the forbidden band width of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105) is Δλ sb , and the free spectral range FSR FP of the FP cavity, then the two satisfy the following relationship: Δλsb<2FSRFP Δλ sb < 2FSR FP 且所述F-P谐振腔的谐振波长靠近所述的左侧布拉格波导光栅(104)和右侧布拉格波导光栅(105)的禁带的中部;and the resonance wavelength of the F-P resonant cavity is close to the middle of the forbidden band of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105); 所述F-P腔的自由光谱范围FSRFP的计算公式如下:The calculation formula of the free spectral range FSR FP of the FP cavity is as follows:
Figure FDA0003782059220000011
Figure FDA0003782059220000011
Figure FDA0003782059220000012
Figure FDA0003782059220000012
其中,Lpd为所述左侧布拉格波导光栅(104)和右侧布拉格波导光栅(105)的穿透深度,Lt为拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)的长度,ng1表示单模波导(108)的群折射率,ng2表示所述左侧布拉格波导光栅(104)与右侧布拉格波导光栅(105)的群折射率,ng3表示所述拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)的群折射率;neff,w和neff,n是左侧布拉格波导光栅(104)、右侧布拉格波导光栅(105)中周期性变化的有效折射率;λ为滤波器结构的工作波长。Wherein, L pd is the penetration depth of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105), and L t is the tapered tapered waveguide grating (106) and the reverse tapered tapered waveguide grating The length of (107), n g1 represents the group refractive index of the single-mode waveguide (108), n g2 represents the group refractive index of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105), and n g3 represents Group refractive indices of the tapered tapered waveguide grating (106) and the reverse tapered tapered waveguide grating (107); n eff,w and n eff,n are the left Bragg waveguide grating (104), the right Bragg The effective refractive index of the waveguide grating (105) varies periodically; λ is the working wavelength of the filter structure.
2.根据权利要求1所述的超大自由光谱范围的集成光学滤波器结构,其特征在于,该滤波器结构为左右对称结构,且Δλsb<FSRFP2 . The integrated optical filter structure with a large free spectral range according to claim 1 , wherein the filter structure is a left-right symmetric structure, and Δλ sb < FSR FP . 3 . 3.根据权利要求1或2所述的超大自由光谱范围的集成光学滤波器结构,其特征在于,该滤波器结构还包括位于拉锥渐变型波导光栅(106)、反向拉锥渐变型波导光栅(107)之间的单模波导(108),所述弯曲波导(103)的最低点切线与所述单模波导(108)平行且存在间隙,构成侧边耦合波导结构;且所述弯曲波导(103)的最低点到所述单模波导(108)的垂线过所述单模波导(108)的中点3. The integrated optical filter structure with ultra-large free spectral range according to claim 1 or 2, characterized in that the filter structure further comprises a tapered tapered waveguide grating (106), a reverse tapered tapered waveguide A single-mode waveguide (108) between the gratings (107), the lowest point tangent of the curved waveguide (103) is parallel to the single-mode waveguide (108) and there is a gap, forming a side-coupling waveguide structure; and the curved The vertical line from the lowest point of the waveguide (103) to the single-mode waveguide (108) passes through the midpoint of the single-mode waveguide (108)
Figure FDA0003782059220000021
Figure FDA0003782059220000021
Figure FDA0003782059220000022
Figure FDA0003782059220000022
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