WO2015149584A1 - 超高分辨率光子晶体超棱镜及其设计方法 - Google Patents

超高分辨率光子晶体超棱镜及其设计方法 Download PDF

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WO2015149584A1
WO2015149584A1 PCT/CN2015/072194 CN2015072194W WO2015149584A1 WO 2015149584 A1 WO2015149584 A1 WO 2015149584A1 CN 2015072194 W CN2015072194 W CN 2015072194W WO 2015149584 A1 WO2015149584 A1 WO 2015149584A1
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photonic crystal
region
superprism
ultra
self
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French (fr)
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蒋寻涯
李伟
张小刚
林旭林
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Shanghai Institute of Microsystem and Information Technology of CAS
Fudan University
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Shanghai Institute of Microsystem and Information Technology of CAS
Fudan University
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials
    • G02B1/005—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials made of photonic crystals or photonic band gap materials
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/10—Beam splitting or combining systems
    • G02B27/1006—Beam splitting or combining systems for splitting or combining different wavelengths
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/10—Beam splitting or combining systems
    • G02B27/12—Beam splitting or combining systems operating by refraction only
    • G02B27/126—The splitting element being a prism or prismatic array, including systems based on total internal reflection

Definitions

  • the invention belongs to the field of optoelectronics and optical communication, and relates to an ultra-high resolution photonic crystal superprism and a design method thereof.
  • Photonic crystals were independently proposed by S. John and E. Yablonovitch in 1987. They are artificial microstructures that are periodically arranged by media of different refractive indices. Due to the spatial periodicity of the dielectric constant, a periodic variation of the spatial refractive index is caused. When the change in the dielectric constant is large enough and the period of change is equal to the wavelength of the light, the dispersion relationship of the light waves will have a band-like structure, which is a photonic band structure. These terminated frequency intervals are called "Photonic Band Gap" (PBG), and light or electromagnetic waves whose frequencies fall within the forbidden band cannot propagate.
  • PBG Photonic Band Gap
  • the refractive index of a photonic crystal changes periodically in space, which can effectively control the propagation behavior of photons. Since the concept of photonic crystals has been proposed, attention has been paid to the application of photonic crystals. Especially in the field of optical communication technology, photonic crystal fibers, micro-resonator lasers, filters, integrated optical circuits and other photonic crystal devices have broad application prospects. The continuous improvement of semiconductor material micro-machining technology has greatly promoted the application of two-dimensional or even three-dimensional photonic crystal devices in practice. In recent years, photonic crystal superprisms and their application in high performance spectrometers and wavelength division multiplexers have become the focus of attention in the industry, because spectrometers and wavelength division multiplexers are the core devices in the fields of optical communication and optical detection. One.
  • Photonic crystal superprisms have the ability to separate continuous frequency electromagnetic waves within a photonic crystal by a certain number of channels. It is characterized in that on the one hand, such a wavelength division multiplexer is small in size and easy to integrate, and on the other hand, it has a high frequency (wavelength) resolution capability.
  • the prior art discloses a photonic crystal superprism that operates using regions of the photonic crystal with sharply varying frequency lines. Such super-prisms inevitably have problems such as lack of frequency, easy crosstalk, and large device area, which are not conducive to the application of the device in the integrated optical path.
  • an object of the present invention is to provide an ultra-high resolution photonic crystal superprism and a design method thereof for solving the problem that the photonic crystal superprism has a missing frequency and a high crosstalk level in the prior art.
  • the problem is that the device area is relatively large.
  • the present invention provides a method for designing an ultra-high resolution photonic crystal superprism comprising at least the following steps:
  • Step S1 selecting a dielectric material to determine a structure type and a structural parameter of the photonic crystal
  • Step S2 obtaining an equal-frequency map of the photonic crystal, and searching for a self-collimation region in the equal-frequency map;
  • Step S3 obtaining a group velocity distribution of each point in the isobaric image, and searching for a low group velocity region;
  • Step S4 optimizing the structural parameters of the photonic crystal such that the self-collimation region and the low group velocity region in the photonic crystal iso-frequency map overlap as much as possible, and the overlapping region is defined as a working region;
  • Step S5 Obtain an equal incident angle line, rotate the photonic crystal, intersect the incident angle line with the working area, and select a suitable incident angle in the intersection to complete the design of the photonic crystal superprism.
  • the dielectric material is at least one selected from the group consisting of silicon, silicon dioxide, germanium, gallium arsenide, and gallium nitride.
  • the type of structure comprises a two-dimensional structure or a three-dimensional structure.
  • the type of structure comprises a pore structure or a dielectric pillar structure.
  • the structure type comprises a square lattice cell structure, a rectangular lattice cell structure, a triangular lattice cell structure or a hexagonal lattice cell structure.
  • the structural parameters include a filling ratio, a lattice constant, a thickness of the photonic crystal, and a length of the photonic crystal, and are optimized by changing at least one of the structural parameters.
  • the self-collimating region includes a self-collimating region or a partial self-collimating region throughout the Brillouin zone.
  • the self-collimating region comprises a strict self-collimating region and an approximate self-collimating region in the vicinity thereof.
  • the low group velocity is a group velocity of light propagating in the photonic crystal of less than 3E7 meters per second.
  • the equal-frequency diagram, group velocity, and equal incident angle are obtained by theoretical calculation or experimentally obtained.
  • the present invention also provides a photonic crystal superprism in which an auto-collimation region coincides with a low group velocity region, and an equal incident angle intersects the coincident region.
  • the photonic crystal superprism is a pore structure or a dielectric pillar structure.
  • the ultra-high resolution photonic crystal superprism of the present invention and the method for designing the same have the following beneficial effects: the present invention optimizes the structural parameters of the photonic crystal to make the self-collimation region and the low group in the iso-frequency diagram of the photonic crystal.
  • the velocity region is overlapped as much as possible, the coincident region is defined as the working region, and the photonic crystal is appropriately rotated so that the incident angle line and the working region intersect, and the appropriate incident angle is selected so that the incident angle is as close as possible to the vertical, which is convenient for the optical path design of the applied instrument.
  • the photonic crystal superprism designed by the present invention is very sensitive to the frequency of light incident at the above incident angle, and can significantly separate light of different frequencies.
  • the photonic crystal superprism of the invention has good integration and wide application range, and can be applied to high-resolution spectrometers, wavelength division multiplexers, high-sensitivity detectors and the like, and has important practical value.
  • 1 is a flow chart showing a method of designing an ultra-high resolution photonic crystal superprism of the present invention.
  • FIG. 2 is a schematic view showing the separation of incident light rays by the ultra-high resolution photonic crystal superprism of the present invention.
  • Figure 3 shows a schematic view of the arrangement of dielectric columns in a photonic crystal.
  • Figure 4 shows an isometric diagram of a photonic crystal.
  • Figure 5 shows the equal incident angle and low group velocity distribution.
  • Figures 6a-6c show the distribution of the photonic crystal superprism parameters.
  • Figures 7a-7c show a three-channel crossover plot for a photonic crystal superprism.
  • the present invention provides a method for designing an ultra-high resolution photonic crystal superprism.
  • a flow chart showing the method includes at least the following steps:
  • Step S1 selecting a dielectric material to determine a structure type and a structural parameter of the photonic crystal
  • Step S2 obtaining an equal-frequency map of the photonic crystal, and searching for a self-collimation region in the equal-frequency map;
  • Step S3 obtaining a group velocity distribution of each point in the isobaric image, and searching for a low group velocity region;
  • Step S4 optimizing the structural parameters of the photonic crystal such that the self-collimation region and the low group velocity region in the photonic crystal iso-frequency map overlap as much as possible, and the overlapping region is defined as a working region;
  • Step S5 Obtain an equal incident angle line, rotate the photonic crystal, intersect the incident angle line with the working area, and select a suitable incident angle in the intersection to complete the design of the photonic crystal superprism.
  • FIG. 2 there is shown a schematic diagram of the ultra-high resolution photonic crystal superprism of the present invention separating incident light.
  • the photonic crystal is very sensitive to the frequency of the light, and can significantly separate incident light of different frequencies.
  • the three star marks on the outer edge of the superprism in Fig. 2 represent three light exiting positions.
  • the photonic crystal superprism in Figure 2 consists of a number of dielectric columns.
  • step S1 is performed: selecting a dielectric material to determine the structure type and structural parameters of the photonic crystal.
  • the dielectric material is at least one selected from the group consisting of silicon, silicon dioxide, germanium, and gallium nitride.
  • the structure type of the photonic crystal includes a two-dimensional structure or a three-dimensional structure, and further, may include a pore structure or a dielectric pillar structure, and the arrangement thereof includes but is not limited to a tetragonal lattice cell structure and a rectangular lattice cell structure. , triangular lattice cell structure or hexagonal lattice cell structure.
  • the photonic crystal adopts a dielectric pillar structure having a radius of 0.32a, wherein a is a lattice period of the photonic crystal, and as shown in FIG. 3, the smallest arrangement unit of the dielectric pillar structure constitutes a rectangular shape.
  • the rectangular lattice has a width a, a length b, and an aspect ratio of 1.8.
  • step S2 is performed to obtain an equal-frequency map of the photonic crystal in which a self-collimation region is sought.
  • the equal-frequency diagram of the photonic crystal can be obtained by theoretical calculation or experimentally.
  • the dispersion relation of the photonic crystal structure is calculated by the plane wave expansion method, the second energy band is selected, and the equal-frequency diagram of the energy band is calculated.
  • the calculation of the iso-frequency diagram of the photonic crystal is a common knowledge in the field, such as the literature “Victor Liu and Shanhui Fan,” “Efficient computation of equifrequency surfaces and Density of states in photonic crystals using Dirichlet-to-Neumann maps, "Journal of the Optical Society of America B, Vol. 28, pp. 1837 (2011)” gives an example of calculating a frequency diagram of a photonic crystal, specifically The calculation process will not be described here.
  • FIG. 4 is an isometric view of the second energy band of the photonic crystal calculated by the plane wave expansion method in the present embodiment, wherein the abscissa is k x and the ordinate is k y , respectively representing the wave vector component of the x coordinate axis direction. And the wave vector component of the y coordinate axis direction, the unit is 2 ⁇ /a.
  • a plurality of equal-frequency lines are included, and the numbers in the figure represent the frequencies corresponding to the equal-frequency lines.
  • the self-collimating region includes a self-collimating region or a partial self-collimating region extending through the entire Brillouin zone.
  • the self-collimating region includes a strict self-collimating region and an approximate self-collimating region in the vicinity thereof.
  • the equal-frequency line corresponding to the frequency of 0.38 is a straight line, which belongs to a strict self-collimation region, and the direction of propagation of light at any incident angle on the line in the photonic crystal is perpendicular to the equal-frequency line. , that is, spread in the x direction.
  • the equal-frequency line with a frequency of 0.375 on the left side of the equal-frequency line and a frequency line of 0.385 on the right side are considered to be approximate self-collimation areas.
  • the dashed box in Figure 4 represents the self-collimating region selected in this embodiment.
  • step S3 is performed: obtaining a group velocity distribution of each point in the isobaric graph to find a low group velocity region.
  • the group speed can be obtained by theoretical calculation or experimentally obtained.
  • the theoretical calculation of group velocity is well known in the art, such as the literature "MJSteel, R. Zoli, C. Grillet, RCMc Phedran, C. Martijn de Sterke, A. Norton, P. Bassi, and BJ Eggleton, "Analytic properties
  • the specific calculation method of the photonic crystal group velocity is given in the photonic crystal superprism parameters, "Physical Review E, vol. 71, pp 056608 (2005)", and will not be described again here.
  • the low group velocity in the present invention means that the group velocity of light propagating in the photonic crystal is lower than 3E7 m/sec.
  • the shaded portion in Fig. 5 is the low group velocity region, and the darker the shaded portion, the lower the group velocity.
  • the parameter distribution of the photonic crystal superprism can also be calculated by the method in the above literature.
  • FIGS. 6a-6c shows the parameter distribution of the photonic crystal superprism.
  • the shadow in Fig. 6a is the distribution of the parameter value Log_1/p-, and the color depth reflects the change of its value, where p is the generalized angular resolution, reflecting the divergence of the exiting light of the prism, and the higher the angular resolution, representing the divergence.
  • the resolution parameter the larger the r value, the better the performance of the photonic crystal superprism.
  • step S4 is performed to optimize the structural parameters of the photonic crystal such that the self-collimation region and the low group velocity region in the photonic crystal iso-frequency map overlap as much as possible, and the coincident region is defined as the working region.
  • the structural parameters include a filling ratio, a lattice constant, a thickness of the photonic crystal, and a length of the photonic crystal, and the photonic crystal superprism resolution parameter r is improved by changing at least one of the structural parameters.
  • the self-collimation region and the low-group velocity region of one of the equal-frequency maps are selected to have the highest degree of coincidence, and the structural parameters are taken as the optimal values, and the coincident regions are defined as the work areas.
  • step S5 is performed: obtaining an equal incident angle line, rotating the photonic crystal, intersecting the incident angle line with the working area, and selecting a suitable incident angle in the intersection to complete the design of the photonic crystal superprism.
  • the equal incident angle is calculated as follows:
  • ⁇ in is the given angle of incidence and ⁇ is the circular frequency of the light.
  • ⁇ is the circular frequency of the light.
  • the wavevectors k x and k y are different, and the wave vectors are connected to be equal to the incident angle.
  • the equal incident angle and the low group velocity distribution are shown in Fig. 5.
  • the arrows in the figure show the direction of light propagation at the intersection of the equal incident angle and the three equal frequency lines of the self-collimation region. Equal incident angle lines are also shown in Figures 6a-6c.
  • the so-called suitable incident angle refers to the incident angle as close as possible to the normal incidence. Selecting such an incident angle can avoid the incident angle from being too large, thereby reducing the complexity of the optical path design.
  • the photonic crystal superprism has been designed through the above steps.
  • the photonic crystal is very sensitive to the frequency of the light, and can significantly separate the light of different frequencies.
  • FIGS. 7a-7c the three-channel frequency division diagram of the photonic crystal superprism is shown, wherein the wavelengths of the incident light corresponding to FIG. 7a, FIG. 7b, and FIG. 7c are 1575.90 nm, 1550 nm, and 1537.90 nm, respectively.
  • the darker the area the stronger the light intensity.
  • the deflection angles of the different frequencies of light in the photonic crystal are different.
  • the present invention also provides a photonic crystal superprism in which an auto-collimation region coincides with a low group velocity region, and an equal incident angle intersects the coincident region.
  • the photonic crystal superprism may be a pore structure or a dielectric pillar structure.
  • the photonic crystal superprism can be designed using the above design method to determine the optimal structural parameters, including the fill ratio, lattice constant, thickness of the photonic crystal, and length of the photonic crystal.
  • the self-collimation region and the low group velocity region in the isomorphic image of the sub-crystal overlap as much as possible, define the coincident region as the working region, select an equal incident angle line intersecting the working region, and then select an appropriate one among the intersection points.
  • the angle of incidence is such that the angle of incidence is as close as possible to the incident angle of normal incidence, thereby reducing the complexity of the optical path design.
  • the photonic crystal superprism of the invention can be widely applied to devices such as spectrometers, interferometers, wavelength division multiplexers, detectors and the like.
  • the ultra-high resolution photonic crystal superprism of the present invention and its design method optimize the photonic crystal structure parameters so that the self-collimation region and the low group velocity region in the photonic crystal iso-frequency map overlap as much as possible.
  • the coincident region is defined as a working region, and the photonic crystal is appropriately rotated so that the incident angle line intersects the working region, and an appropriate incident angle is selected so that the incident angle is as close as possible to the vertical, which is convenient for the optical path design of the applied instrument.
  • the photonic crystal superprism designed by the present invention is very sensitive to the frequency of light incident at the above incident angle, and can significantly separate light of different frequencies.
  • the photonic crystal superprism of the invention has good integration and wide application range, and can be applied to high-resolution spectrometers, wavelength division multiplexers, high-sensitivity detectors and the like, and has important practical value. Therefore, the present invention effectively overcomes various shortcomings in the prior art and has high industrial utilization value.

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Abstract

一种超高分辨率光子晶体超棱镜的设计方法，包括以下步骤：S1：选定介质材料，确定光子晶体的结构类型和结构参数；S2：获得光子晶体的等频图，寻找自准直区域；S3：获得所述等频图中各点的群速度分布，寻找低群速度区域；S4：优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群速度区域尽可能重合，并把该重合区域定为工作区域；S5：获得等入射角线，并旋转所述光子晶体，使所述等入射角线与所述工作区域相交，并在交点中选取合适的入射角，完成光子晶体超棱镜的设计。当光以上述入射角入射时，光子晶体对光的频率非常敏感，能显著地把不同频率的光分开。该光子晶体超棱镜集成性好，适用范围广，具有重要实用价值。

Description

超高分辨率光子晶体超棱镜及其设计方法 技术领域
本发明属于光电子、光通信领域，涉及一种超高分辨率光子晶体超棱镜及其设计方法。
背景技术
光子晶体在1987年由S.John和E.Yablonovitch分别独立提出，它是由不同折射率的介质周期性排列而成的人工微结构。由于介电常数存在空间上的周期性，进而引起空间折射率的周期变化。当介电系数的变化足够大且变化周期与光波长相当时，光波的色散关系会出现带状结构，此即光子能带结构(Photonic Band structures)。这些被终止的频率区间称为“光子频率禁带”(Photonic Band Gap，PBG)，频率落在禁带中的光或电磁波是无法传播的。我们将具有“光子频率禁带”的周期性介电结构称作为光子晶体。
光子晶体的折射率在空间周期性变化，能够有效地控制光子的传播行为。自光子晶体的概念被提出以来，人们就对光子晶体的应用给予广泛关注。特别是在光通信技术领域，光子晶体光纤、微谐振腔激光器、滤波器、集成光路等光子晶体器件有着广阔的应用前景。半导体材料微细加工技术的不断提高大大地推动了二维甚至三维光子晶体器件在实际中的应用步伐。近年来，光子晶体超棱镜及其应用于高性能光谱仪和波分复用器的设计成为了业界关注的热点，因为光谱仪和波分复用器是光通信、光探测等领域中的核心器件之一。
光子晶体超棱镜有能力在光子晶体内部把连续频率的电磁波按照一定的频道数分开。它的特点是一方面这种波分复用器体积小易于集成，而另一方面它具有很高的频率(波长)分辨能力。现有文献公开了一种光子晶体超棱镜，它利用光子晶体等频线尖锐变化的区域来工作。这种超棱镜不可避免的存在频率缺失、易串话、器件面积比较大等问题，不利于器件在集成光路中的应用。
因此，为避免上述问题，我们必须从新的物理机制出发，通过新设计获取新型的光子晶体超棱镜。
发明内容
鉴于以上所述现有技术的缺点，本发明的目的在于提供一种超高分辨率光子晶体超棱镜及其设计方法，用于解决现有技术中光子晶体超棱镜存在频率缺失、串话水平高、器件面积比较大的问题。
为实现上述目的及其他相关目的，本发明提供一种超高分辨率光子晶体超棱镜的设计方法，至少包括以下步骤：
步骤S1：选定介质材料，确定光子晶体的结构类型和结构参数；
步骤S2：获得所述光子晶体的等频图，在所述等频图中寻找自准直区域；
步骤S3：获得所述等频图中各点的群速度分布，寻找低群速度区域；
步骤S4：优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群速度区域尽可能重合，并把该重合区域定为工作区域；
步骤S5：获得等入射角线，并旋转所述光子晶体，使所述等入射角线与所述工作区域相交，并在交点中选取合适的入射角，完成光子晶体超棱镜的设计。
可选地，所述介质材料选自硅、二氧化硅、锗、砷化镓及氮化镓中的至少一种。
可选地，所述结构类型包括二维结构或三维结构。
可选地，所述结构类型包括孔状结构或介质柱结构。
可选地，所述结构类型包括正方晶格原胞结构、长方晶格原胞结构、三角晶格原胞结构或六角晶格原胞结构。
可选地，于所述步骤S4中，所述结构参数包括填充比、晶格常数、光子晶体的厚度及光子晶体的长度，通过改变其中至少一个结构参数进行优化。
可选地，所述自准直区域包括贯穿整个布里渊区的自准直区域或局部自准直区域。
可选地，所述自准直区域包括严格的自准直区域及其附近的近似自准直区域。
可选地，所述低群速度为光在光子晶体中传播的群速度低于3E7米/秒。
可选地，所述等频图、群速度及等入射角线采用理论计算获得或采用实验方式测试获到。
本发明还提供一种光子晶体超棱镜，该光子晶体超棱镜等频图中的自准直区域与低群速度区域重合，且其等入射角与该重合区域相交。
可选地，所述光子晶体超棱镜为孔状结构或介质柱结构。
如上所述，本发明的超高分辨率光子晶体超棱镜及其设计方法，具有以下有益效果：本发明通过优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群 速度区域尽可能重合，将该重合区域定义为工作区域，并适当旋转光子晶体使得等入射角线和工作区域相交，选择合适的入射角，使的入射角尽量接近垂直，便于应用仪器的光路设计。本发明设计的光子晶体超棱镜对以上述入射角入射的光的频率非常敏感，能显著地将不同频率的光分开。同时，本发明的光子晶体超棱镜集成性好，适用范围广，能应用于高分辨率光谱仪、波分复用器、高敏感探测器等器件，具有重要的实用价值。
附图说明
图1显示为本发明的超高分辨率光子晶体超棱镜的设计方法的流程图。
图2显示为本发明的超高分辨率光子晶体超棱镜将入射光线分开的示意图。
图3显示为光子晶体中介质柱的排列示意图。
图4显示为光子晶体的等频图。
图5显示为等入射角线与低群速度分布。
图6a-6c显示为光子晶体超棱镜参数分布。
图7a-7c显示为光子晶体超棱镜三频道分频图。
元件标号说明
S1～S5           步骤
具体实施方式
以下通过特定的具体实例说明本发明的实施方式，本领域技术人员可由本说明书所揭露的内容轻易地了解本发明的其他优点与功效。本发明还可以通过另外不同的具体实施方式加以实施或应用，本说明书中的各项细节也可以基于不同观点与应用，在没有背离本发明的精神下进行各种修饰或改变。
请参阅1至图7c。需要说明的是，本实施例中所提供的图示仅以示意方式说明本发明的基本构想，遂图式中仅显示与本发明中有关的组件而非按照实际实施时的组件数目、形状及尺寸绘制，其实际实施时各组件的型态、数量及比例可为一种随意的改变，且其组件布局型态也可能更为复杂。
本发明提供一种超高分辨率光子晶体超棱镜的设计方法，请参阅图1，显示为该方法的流程图，至少包括以下步骤：
步骤S1：选定介质材料，确定光子晶体的结构类型和结构参数；
步骤S2：获得所述光子晶体的等频图，在所述等频图中寻找自准直区域；
步骤S3：获得所述等频图中各点的群速度分布，寻找低群速度区域；
步骤S4：优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群速度区域尽可能重合，并把该重合区域定为工作区域；
步骤S5：获得等入射角线，并旋转所述光子晶体，使所述等入射角线与所述工作区域相交，并在交点中选取合适的入射角，完成光子晶体超棱镜的设计。
请参阅图2，显示为本发明的超高分辨率光子晶体超棱镜将入射光线分开的示意图。当光以上述入射角入射时，该光子晶体对光的频率非常敏感，能显著地把不同频率的入射光线分开，图2中超棱镜外缘的三个星型标记代表三个出光位置。作为示例，图2中光子晶体超棱镜由若干介质柱组成。
下面通过一个具体实施例来说明本发明的超高分辨率光子晶体超棱镜的设计方法。
首先请参阅图3，执行步骤S1：选定介质材料，确定光子晶体的结构类型和结构参数。
具体的，所述介质材料选自硅、二氧化硅、锗及氮化镓中的至少一种。本实施例中，所述介质材料以硅为例，其折射率n＝3.4，中心波长为1.55微米，该波长属于目前广泛应用光通信波段，而且硅材料的制备技术成熟。
具体的，光子晶体的结构类型包括二维结构或三维结构，进一步的，可包括孔状结构或介质柱结构，其排列方式包括但不限于正方晶格原胞结构、长方晶格原胞结构、三角晶格原胞结构或六角晶格原胞结构。
作为示例，所述光子晶体采用介质柱结构，所述介质柱的半径为0.32a，其中a为光子晶体的晶格周期，如图3所示，所述介质柱结构的最小排列单元组成长方晶格结构，长方晶格的宽度为a，长度为b，长宽比为1.8。
然后请参阅图4，执行步骤S2：获得所述光子晶体的等频图，在所述等频图中寻找自准直区域。
具体的，所述光子晶体的等频图可采用理论计算获得或采用实验方式测试获得。作为示例，本实施例中利用平面波展开法计算上述光子晶体结构的色散关系，选择第二个能带并计算该能带的等频图。光子晶体等频图的计算为本领域的公知常识，如文献“Victor Liu and Shanhui Fan，“Efficient computation of equifrequency surfaces and  density of states in photonic crystals using Dirichlet-to-Neumann maps，”Journal of the Optical Society of America B,Vol.28,pp.1837(2011)”中就给出了计算光子晶体等频图的例子，具体计算过程此处不再赘述。
图4显示为本实施例中通过平面波展开法计算得到的光子晶体第二个能带的等频图，其横坐标为kx，纵坐标为ky，分别代表x坐标轴方向的波矢分量及y坐标轴方向的波矢分量，单位均为2π/a。如图4所示，其中包括若干条等频线，图中的数字代表等频线所对应的频率。
具体的，所述自准直区域包括贯穿整个布里渊区的自准直区域或局部自准直区域。所述自准直区域包括严格的自准直区域及其附近的近似自准直区域。如图4所示，其中频率为0.38所对应的等频线为直线，属于严格的自准直区域，这条线上任意入射角度的光线在光子晶体中的传播方向均垂直于该等频线，即沿x方向传播。对于该等频线左侧频率为0.375的等频线及右侧频率为0.385等频线，可认为是近似自准直区域。图4中虚线框代表本实施例中选择的自准直区域。
接着请参阅图5，执行步骤S3：获得所述等频图中各点的群速度分布，寻找低群速度区域。
具体的，所述群速度可采用理论计算获得或采用实验方式测试获到。群速度的理论计算方法为本领域所公知，如文献“M.J.Steel,R.Zoli,C.Grillet,R.C.McPhedran,C.Martijn de Sterke,A.Norton,P.Bassi,and B.J.Eggleton，“Analytic properties of photonic crystal superprism parameters，”Physical Review E,vol.71,p.p 056608(2005)”中就给出了光子晶体群速度的具体计算方法，此处不再赘述。
需要指出的是，本发明中所述低群速度指的是光在光子晶体中传播的群速度低于3E7米/秒。图5中的阴影部分即为低群速度区域，阴影部分颜色越深，群速度越低。
同时，还可以采用上述文献中的方法计算出光子晶体超棱镜的参数分布，请参阅图6a～6c，显示为光子晶体超棱镜参数分布。其中，图6a中阴影为参数值Log︱1/p︱的分布，颜色深浅反映其值的变化，其中p为广义角分辨率，反映棱镜出射光的发散程度，角分辨率越高，代表发散程度越弱，超棱镜性能越好；图6b中阴影为参数值Log︱q︱的分布，其中q为广义色散；图6c中阴影为参数值Log︱r︱的分布，其中r＝q/p,为分辨率参数，r值越大，说明光子晶体超棱镜性能越好。
再执行步骤S4：优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群速度区域尽可能重合，并把该重合区域定为工作区域。
具体的，所述结构参数包括填充比、晶格常数、光子晶体的厚度及光子晶体的长度，通过改变其中至少一个结构参数进行优化，使得光子晶体超棱镜分辨率参数r提升。通过多组对比，选择其中一组等频图的自准直区域与低群速度区域重合程度最高的，将其结构参数作为最优值，并将其重合区域定义为工作区。
最后执行步骤S5：获得等入射角线，并旋转所述光子晶体，使所述等入射角线与所述工作区域相交，并在交点中选取合适的入射角，完成光子晶体超棱镜的设计。
具体的，等入射角的计算方式如下：
kx＝(ω/c)·cosθin，
ky＝(ω/c)·sinθin，
其中，θin为给定的入射角，ω为光的圆频率。对于给定的入射角，在不同的圆频率下，波矢kx、ky不同，把波矢连起来，就是等入射角线。当然，也可以采用实验方式测试并描线得到等入射角线。
图5中显示了等入射角线与低群速度分布，图中箭头示出了等入射角线与自准直区域的三条等频线交点处的光传播方向。图6a～6c中也示出了等入射角线。
需要指出的时，等入射角线存在多条，此处仅选择与所述工作区域相交的等入射角线。然后在交点中选择合适的入射角。需要指出的是，此处所谓合适的入射角是指尽量接近垂直入射的入射角，选择这样的入射角可以避免入射角过大，从而降低光路设计的复杂性。
至此，通过以上步骤设计得到了光子晶体超棱镜，当光以上述入射角入射时，该光子晶体对光的频率非常敏感，能显著地把不同频率的光分开。请参阅图7a～7c，显示为光子晶体超棱镜三频道分频图，其中图7a、图7b及图7c对应的入射光波长分别为1578.90nm、1550nm及1537.90nm。图7a～7c中，颜色越深的区域代表光强越强。显然，光入射之后，不同频率光在光子晶体中的偏向角不同，如图中箭头方向所示，当光以同样的入射角入射时，图7a中，光沿右下角方向传播，图7b中，光沿水平方向传播，图7c中，光沿右上角方向传播，从而导致不同频率的光传播路径被显著分开。这种跟频率相关的路径即为光子晶体超棱镜的频道。
本发明还提供一种光子晶体超棱镜，该光子晶体超棱镜等频图中的自准直区域与低群速度区域重合，且其等入射角与该重合区域相交。其中，所述光子晶体超棱镜可以为孔状结构或介质柱结构。该光子晶体超棱镜可采用上述设计方法设计，以确定最佳的结构参数，包括填充比、晶格常数、光子晶体的厚度及光子晶体的长度等，使光 子晶体等频图中的自准直区域与低群速度区域尽可能重合，将该重合区域定为工作区域，并选择与所述工作区域相交的等入射角线，然后在交点中选择合适的入射角，使得入射角尽量接近垂直入射的入射角，从而降低光路设计的复杂性。
本发明的光子晶体超棱镜可以广泛应用于光谱仪、干涉仪、波分复用器、探测器等器件上。
综上所述，本发明的超高分辨率光子晶体超棱镜及其设计方法通过优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群速度区域尽可能重合，将该重合区域定义为工作区域，并适当旋转光子晶体使得等入射角线和工作区域相交，选择合适的入射角，使的入射角尽量接近垂直，便于应用仪器的光路设计。本发明设计的光子晶体超棱镜对以上述入射角入射的光的频率非常敏感，能显著地将不同频率的光分开。同时，本发明的光子晶体超棱镜集成性好，适用范围广，能应用于高分辨率光谱仪、波分复用器、高敏感探测器等器件，具有重要的实用价值。所以，本发明有效克服了现有技术中的种种缺点而具高度产业利用价值。
上述实施例仅例示性说明本发明的原理及其功效，而非用于限制本发明。任何熟悉此技术的人士皆可在不违背本发明的精神及范畴下，对上述实施例进行修饰或改变。因此，举凡所属技术领域中具有通常知识者在未脱离本发明所揭示的精神与技术思想下所完成的一切等效修饰或改变，仍应由本发明的权利要求所涵盖。

Claims (12)

  1. 一种超高分辨率光子晶体超棱镜的设计方法，其特征在于，至少包括以下步骤：
    步骤S1：选定介质材料，确定光子晶体的结构类型和结构参数；
    步骤S2：获得所述光子晶体的等频图，在所述等频图中寻找自准直区域；
    步骤S3：获得所述等频图中各点的群速度分布，寻找低群速度区域；
    步骤S4：优化光子晶体的结构参数，使光子晶体等频图中的自准直区域与低群速度区域尽可能重合，并把该重合区域定为工作区域；
    步骤S5：获得等入射角线，并旋转所述光子晶体，使所述等入射角线与所述工作区域相交，并在交点中选取合适的入射角，完成光子晶体超棱镜的设计。
  2. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述介质材料选自硅、二氧化硅、锗、砷化镓及氮化镓中的至少一种。
  3. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述结构类型包括二维结构或三维结构。
  4. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述结构类型包括孔状结构或介质柱结构。
  5. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述结构类型包括正方晶格原胞结构、长方晶格原胞结构、三角晶格原胞结构或六角晶格原胞结构。
  6. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：于所述步骤S4中，所述结构参数包括填充比、晶格常数、光子晶体的厚度及光子晶体的长度，通过改变其中至少一个结构参数进行优化。
  7. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述自准直区域包括贯穿整个布里渊区的自准直区域或局部自准直区域。
  8. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述自准直区域包括严格的自准直区域及其附近的近似自准直区域。
  9. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述低群速度为光在光子晶体中传播的群速度低于3E7米/秒。
  10. 根据权利要求1所述的超高分辨率光子晶体超棱镜的设计方法，其特征在于：所述等频图、群速度及等入射角线采用理论计算获得或采用实验方式测试获到。
  11. 一种光子晶体超棱镜，其特征在于：该光子晶体超棱镜等频图中的自准直区域与低群速度区域重合，且其等入射角与该重合区域相交。
  12. 根据权利要求11所述的光子晶体超棱镜，其特征在于：所述光子晶体超棱镜为孔状结构或介质柱结构。
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