CN107037507A - A kind of all dielectric Meta Materials resonance device of high-quality-factor - Google Patents
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Abstract
本发明公开了一种高品质因子的全介质超材料谐振装置，包括基底和位于基底的上表面上的二维周期性介质谐振单元。基底由介质材料制作，每个介质谐振单元为横截面为矩形的介质条，介质条的长、宽和高满足以下条件：a≥2b,a≥2.5h,1.6a≤λ≤2.4a，其中，a、b、h分别表示介质条的长、宽、高，λ为谐振装置的谐振中心波长，介质谐振单元的介电常数大于基底的介电常数。在电磁波垂直于介质条的上表面入射且电场偏振方向垂直介质条的第一侧面的情况下，可产生Mie电、磁谐振，实现极高的Q值。
The invention discloses a high quality factor all-dielectric metamaterial resonant device, which comprises a base and a two-dimensional periodic dielectric resonant unit located on the upper surface of the base. The substrate is made of dielectric material, and each dielectric resonance unit is a dielectric strip with a rectangular cross section. The length, width and height of the dielectric strip meet the following conditions: a≥2b, a≥2.5h, 1.6a≤λ≤2.4a, where , a, b, h represent the length, width and height of the dielectric strip respectively, λ is the resonance center wavelength of the resonance device, and the dielectric constant of the dielectric resonance unit is greater than that of the substrate. When the electromagnetic wave is incident perpendicular to the upper surface of the dielectric strip and the polarization direction of the electric field is perpendicular to the first side of the dielectric strip, Mie electric and magnetic resonance can be generated to achieve a very high Q value.
Description
技术领域technical field
本发明涉及一种谐振装置，属于超材料技术领域。The invention relates to a resonance device and belongs to the technical field of metamaterials.
背景技术Background technique
全介质超材料是一种人工设计制作的亚波长周期性介质谐振结构材料。由于全介质超材料能够非常容易操控电磁波的响应和极低的损耗，可以获得自然界介质不能获得的特性而受到广泛重视。目前在生物传感、隐身衣、负折射率、光子器件等领域具有非常重要的应用。All-dielectric metamaterial is a kind of artificially designed sub-wavelength periodic dielectric resonant structure material. Because all-dielectric metamaterials can easily manipulate the response of electromagnetic waves and have extremely low loss, and can obtain characteristics that cannot be obtained by natural media, they have been widely valued. At present, it has very important applications in the fields of biosensing, invisibility clothing, negative refractive index, and photonic devices.
目前对金属超材料谐振器，由于金属的欧姆损耗和谐振辐射损耗使提高Q值(quality factory，品质因子，谐振峰中心频率除以谐振峰宽度，谐振宽度以FWHM(FullWidth at Half Maxium)计算)成为非常难以解决的问题。而全介质超材料可以克服金属损耗和辐射损耗，为实现高Q谐振提供了可能性。但目前高品质因子及实现高Q电磁谐振的全介质超材料设计方法还很少。At present, for metal metamaterial resonators, due to the metal ohmic loss and resonance radiation loss, the Q value (quality factory, quality factor, the center frequency of the resonant peak divided by the width of the resonant peak, and the resonant width is calculated by FWHM (FullWidth at Half Maxium)) become a very difficult problem to solve. However, all-dielectric metamaterials can overcome metal loss and radiation loss, which provides the possibility to realize high-Q resonance. However, there are still few design methods for all-dielectric metamaterials with high quality factor and high-Q electromagnetic resonance.
发明内容Contents of the invention
本发明的目的是提供一种具有高品质因子的全介质超材料谐振装置。The purpose of the present invention is to provide an all-dielectric metamaterial resonance device with high quality factor.
为实现上述目的，本发明所采取的技术方案是：本发明高品质因子的全介质超材料谐振装置包括基底和位于基底的上表面上的二维周期性介质谐振单元，所述基底由介质材料制作，每个所述介质谐振单元为横截面为矩形的介质条，所述介质条的长度、宽度和高度满足以下条件：a≥2b,a≥2.5h,1.6a≤λ≤2.4a，其中，a表示介质条的长度，b表示介质条的宽度，h表示介质条的高度，λ为所述谐振装置的谐振中心波长，所述介质谐振单元的介电常数大于基底的介电常数。In order to achieve the above object, the technical solution adopted by the present invention is: the all-dielectric metamaterial resonance device with high quality factor of the present invention comprises a base and a two-dimensional periodic dielectric resonator unit positioned on the upper surface of the base, the base is made of a dielectric material Each of the dielectric resonance units is a dielectric strip with a rectangular cross section, and the length, width and height of the dielectric strip meet the following conditions: a≥2b, a≥2.5h, 1.6a≤λ≤2.4a, where , a represents the length of the dielectric strip, b represents the width of the dielectric strip, h represents the height of the dielectric strip, λ is the resonance center wavelength of the resonance device, and the dielectric constant of the dielectric resonance unit is greater than that of the substrate.
进一步地，入射电磁波与所述介质条的上表面垂直，且入射电磁波的电场偏振方向与所述介质条的第一侧面垂直，第一侧面的长度为a、宽度为h。Further, the incident electromagnetic wave is perpendicular to the upper surface of the dielectric strip, and the electric field polarization direction of the incident electromagnetic wave is perpendicular to the first side of the dielectric strip. The length of the first side is a and the width is h.
与现有技术相比，本发明具有以下优点：本发明的二维周期性介质谐振单元结构简单，由于介质条的横截面为矩形，当介质条的几何参数满足以下条件：a≥2b,a≥2.5h,1.6a≤λ≤2.4a(a、b、h分别表示介质条的长度、宽度、高度，λ为所述谐振装置的谐振中心波长)并且谐振单元的介电常数高于基底时，若入射电磁波与介质条的上表面垂直，且入射电磁波的电场偏振方向与介质条的第一侧面垂直，能够产生Mie高阶电磁谐振，获得很高的谐振品质因子。本发明实现了在传感、滤波及光纳米器件等方面的重要应用。Compared with the prior art, the present invention has the following advantages: the structure of the two-dimensional periodic dielectric resonant unit of the present invention is simple, since the cross section of the dielectric strip is rectangular, when the geometric parameters of the dielectric strip meet the following conditions: a≥2b, a ≥2.5h, 1.6a≤λ≤2.4a (a, b, h respectively represent the length, width, and height of the dielectric strip, and λ is the resonance center wavelength of the resonance device) and the dielectric constant of the resonance unit is higher than that of the substrate , if the incident electromagnetic wave is perpendicular to the upper surface of the dielectric strip, and the electric field polarization direction of the incident electromagnetic wave is perpendicular to the first side of the dielectric strip, Mie high-order electromagnetic resonance can be generated and a high resonance quality factor can be obtained. The invention realizes important applications in sensing, filtering, optical nanometer devices and the like.
附图说明Description of drawings
图1为本发明高品质因子的全介质超材料谐振装置的一种结构示意图。FIG. 1 is a schematic structural view of an all-dielectric metamaterial resonator device with a high quality factor of the present invention.
图2为图1的俯视图。FIG. 2 is a top view of FIG. 1 .
图3为图1的左视图。Fig. 3 is a left side view of Fig. 1 .
图4为本发明全介质超材料谐振装置在入射电磁波的电场偏振方向为X方向的情况下由有限元算法计算得到在580纳米—740纳米的透射率谱曲线。Fig. 4 is the transmittance spectrum curve at 580nm-740nm calculated by the finite element algorithm when the electric field polarization direction of the incident electromagnetic wave is in the X direction of the all-dielectric metamaterial resonator device of the present invention.
图5为本发明全介质超材料谐振装置在介质条的高度和宽度固定，长度变化时，入射电磁波的电场偏振方向为X方向的情况下由有限元法计算得到在585纳米—740纳米的透射率谱曲线。Fig. 5 is the all-dielectric metamaterial resonator device of the present invention, when the height and width of the dielectric strip are fixed and the length is changed, and the electric field polarization direction of the incident electromagnetic wave is in the X direction, the transmission at 585 nanometers to 740 nanometers is calculated by the finite element method rate spectrum curve.
图6为本发明全介质超材料谐振装置在介质条的高度和长度固定，宽度变化时，入射电磁波的电场偏振方向为X方向的情况下由有限元法计算得到在585纳米—780纳米的透射率谱曲线。Fig. 6 is the all-dielectric metamaterial resonator device of the present invention, when the height and length of the dielectric strip are fixed and the width changes, and the electric field polarization direction of the incident electromagnetic wave is in the X direction, the transmission at 585 nanometers to 780 nanometers is calculated by the finite element method rate spectrum curve.
具体实施方式detailed description
以下结合附图进一步详细说明本发明全介质超材料谐振装置的结构。The structure of the all-dielectric metamaterial resonator device of the present invention will be further described in detail below in conjunction with the accompanying drawings.
如图1至图3所示，本发明全介质超材料谐振装置包括基底21和位于基底21的上表面上的二维周期性介质谐振单元。基底21由介质材料制作而成。所谓二维周期性介质谐振单元是由多个介质谐振单元按二维周期性分布构成(参见图2)。在本发明中，每个介质谐振单元为一介质条12，该介质条12的横截面为矩形。具体地说，如图1至图3所示，若以a表示介质条12的长度，b表示介质条12的宽度，h表示介质条12的高度，则介质条12的横截面的长度为a、宽度为b。并且，介质条12的长度、宽度和高度满足以下条件：a≥2b,a≥2.5h,1.6a≤λ≤2.4a，其中，λ为本发明全介质超材料谐振装置的谐振中心波长。此外，在本发明中，介质谐振单元的介电常数大于基底21的介电常数。As shown in FIGS. 1 to 3 , the all-dielectric metamaterial resonator device of the present invention includes a base 21 and a two-dimensional periodic dielectric resonator unit located on the upper surface of the base 21 . The base 21 is made of dielectric material. The so-called two-dimensional periodic dielectric resonant unit is composed of multiple dielectric resonant units according to two-dimensional periodic distribution (see Figure 2). In the present invention, each dielectric resonance unit is a dielectric strip 12, and the cross section of the dielectric strip 12 is rectangular. Specifically, as shown in Figures 1 to 3, if a represents the length of the dielectric strip 12, b represents the width of the dielectric strip 12, and h represents the height of the dielectric strip 12, then the length of the cross section of the dielectric strip 12 is a , the width is b. Moreover, the length, width and height of the dielectric strip 12 satisfy the following conditions: a≥2b, a≥2.5h, 1.6a≤λ≤2.4a, where λ is the resonance center wavelength of the all-dielectric metamaterial resonance device of the present invention. Furthermore, in the present invention, the dielectric constant of the dielectric resonance unit is larger than that of the substrate 21 .
如图3所示，本发明全介质超材料谐振装置使用时，入射电磁波朝着介质条12的上表面射入，并且与介质条12的上表面垂直，且入射电磁波的电场偏振方向与介质条12的第一侧面121垂直。如图3所示，第一侧面121的长度为a、宽度为h。在图1和图2中，第一侧面121为介质条12的左侧面。需要说明的是，如图1至图3所示，入射电磁波的电场偏振方向与介质条12的第一侧面121垂直是指入射电磁波的电场偏振方向与X轴方向相同。图3中，K为波矢，即为入射电磁波的传播方向，E为电场偏振方向，H为磁场偏振方向。As shown in Figure 3, when the all-dielectric metamaterial resonator device of the present invention is in use, the incident electromagnetic wave is incident towards the upper surface of the dielectric strip 12, and is perpendicular to the upper surface of the dielectric strip 12, and the electric field polarization direction of the incident electromagnetic wave is the same as that of the dielectric strip The first side 121 of 12 is vertical. As shown in FIG. 3 , the length of the first side 121 is a and the width is h. In FIGS. 1 and 2 , the first side 121 is the left side of the dielectric strip 12 . It should be noted that, as shown in FIG. 1 to FIG. 3 , the electric field polarization direction of the incident electromagnetic wave is perpendicular to the first side 121 of the dielectric strip 12 means that the electric field polarization direction of the incident electromagnetic wave is the same as the X-axis direction. In Figure 3, K is the wave vector, that is, the propagation direction of the incident electromagnetic wave, E is the polarization direction of the electric field, and H is the polarization direction of the magnetic field.
以下以基底21的材料为石英、介质条12为硅条为例对本发明全介质超材料谐振装置作进一步的说明。Hereinafter, the all-dielectric metamaterial resonator device of the present invention will be further described by taking the material of the substrate 21 as quartz and the dielectric strip 12 as an example.
在本实施例中，硅条的介电常数为11.9，硅条的长度a为340纳米、宽度b为150纳米、高度h为100纳米。基底21的材料为石英，其折射率n为1.46(介电常数为2.1316)。如图2所示，在本实施例中，四个硅条构成二维周期性介质谐振单元，其中，沿Y轴方向的周期长度Py为440纳米，沿X轴方向的周期长度Px为400纳米。In this embodiment, the dielectric constant of the silicon strip is 11.9, the length a of the silicon strip is 340 nanometers, the width b is 150 nanometers, and the height h is 100 nanometers. The material of the substrate 21 is quartz, whose refractive index n is 1.46 (dielectric constant is 2.1316). As shown in Figure 2, in this embodiment, four silicon strips form a two-dimensional periodic dielectric resonant unit, wherein the period length Py along the Y-axis direction is 440 nanometers, and the period length Px along the X-axis direction is 400 nanometers .
将本实施例获得的全介质超材料谐振装置用有限元法计算得到在580纳米—740纳米范围的透射率谱图(如图4所示)。从图4中可以看出，在中心波长为594纳米和674.5纳米处各有一个谐振，即为介质Mie谐振。由Mie谐振理论和电磁场空间矢量图(未示出)可以判断，该两个谐振分别为Mie磁偶极谐振和电偶极谐振。其中，594纳米处磁谐振的Q值较低，为44，对谐振单元的几何参数不敏感；674.5纳米处电谐振的Q值较高，为218，受介质谐振单元的几何参数(如介质条的长、宽等几何参数)的影响较大。The all-dielectric metamaterial resonator device obtained in this embodiment is calculated using the finite element method to obtain a transmittance spectrum in the range of 580 nm to 740 nm (as shown in FIG. 4 ). It can be seen from Figure 4 that there is a resonance at the center wavelength of 594 nanometers and 674.5 nanometers, which is the dielectric Mie resonance. According to the Mie resonance theory and the electromagnetic field space vector diagram (not shown), the two resonances are Mie magnetic dipole resonance and electric dipole resonance respectively. Among them, the Q value of the magnetic resonance at 594 nanometers is low, 44, which is not sensitive to the geometric parameters of the resonance unit; the Q value of the electric resonance at 674.5 nanometers is relatively high, 218, which is affected by the geometric parameters of the dielectric resonance unit (such as dielectric strips). Geometric parameters such as length and width) have a greater influence.
图5为本实施例获得的全介质超材料谐振装置在介质条12的高度(100nm)和宽度(150nm)固定，而长度变化时，入射电磁波的电场偏振方向与介质条12的第一侧面121垂直(即沿着X轴方向)的情况下由有限元法计算得到在585纳米—740纳米的透射率谱曲线。从图5中可以看出，本实施例获得的全介质超材料谐振装置在中心波长590纳米～610纳米范围内为磁谐振，670纳米～720纳米范围内为电谐振；并且，本实施例获得的全介质超材料谐振装置的谐振中心波长随介质条12的长度增大而变大，其中电谐振的Q值随介质条12的长度的变化而有较大的变化。Fig. 5 is that the height (100nm) and width (150nm) of the dielectric strip 12 of the all-dielectric metamaterial resonator device obtained in the present embodiment are fixed, and when the length changes, the electric field polarization direction of the incident electromagnetic wave and the first side 121 of the dielectric strip 12 In the case of vertical (that is, along the X-axis direction), the transmittance spectrum curve at 585 nm to 740 nm is calculated by the finite element method. As can be seen from Figure 5, the all-dielectric metamaterial resonator device obtained in this embodiment is magnetic resonance in the range of central wavelength 590 nm to 610 nm, and electric resonance in the range of 670 nm to 720 nm; and, this embodiment obtains The resonance center wavelength of the all-dielectric metamaterial resonator device of the present invention increases with the length of the dielectric strip 12, and the Q value of the electric resonance changes greatly with the change of the length of the dielectric strip 12.
表1中示出了在硅条的宽度和高度不变时，本实施例获得的全介质超材料谐振装置的电谐振中心波长和品质因子随硅条长度的变化而发生变化。Table 1 shows that when the width and height of the silicon strips are constant, the electrical resonance center wavelength and quality factor of the all-dielectric metamaterial resonator device obtained in this embodiment change with the length of the silicon strips.
表1Table 1
由表1可以看出，本实施例获得的全介质超材料谐振装置当介质谐振单元的长度a从340纳米增大到430纳米时，相应的电谐振品质因子从218增大至25660，且介质谐振单元的长度a越接近Py时，电谐振Q值越大。It can be seen from Table 1 that when the length a of the dielectric resonant unit of the all-dielectric metamaterial resonator device obtained in this embodiment increases from 340 nanometers to 430 nanometers, the corresponding electrical resonance quality factor increases from 218 to 25660, and the dielectric When the length a of the resonant unit is closer to Py, the Q value of the electrical resonance is larger.
图6为本实施例获得的谐振装置在介质谐振单元的高度(100nm)和长度(420nm)固定，而宽度变化时，入射电磁波E的电场偏振方向为X轴方向的情况下，由有限元法计算得到在585纳米—780纳米的透射率谱曲线。从图6中可以看出，全介质超材料谐振装置在580纳米—630纳米范围内为磁谐振，在670纳米—760纳米范围内为电谐振，其中，全介质超材料谐振装置的谐振中心波长随着介质谐振单元的宽度的变化而变化，且电谐振Q值的变化较大，可以实现很高Q值。Fig. 6 shows that the height (100nm) and length (420nm) of the dielectric resonance unit of the resonant device obtained in this embodiment are fixed, and when the width changes, the electric field polarization direction of the incident electromagnetic wave E is in the X-axis direction, by the finite element method The transmittance spectrum curve at 585nm-780nm is obtained by calculation. It can be seen from Figure 6 that the all-dielectric metamaterial resonator device is a magnetic resonance in the range of 580 nm to 630 nm, and it is an electrical resonance in the range of 670 nm to 760 nm. Among them, the resonance center wavelength of the all-dielectric metamaterial resonator device is As the width of the dielectric resonance unit changes, and the Q value of the electric resonance varies greatly, a very high Q value can be realized.
表2中示出了硅条在不同宽度时，全介质超材料谐振装置的电谐振中心波长和品质因子的变化。Table 2 shows the change of the electrical resonance center wavelength and quality factor of the all-dielectric metamaterial resonator device when the silicon strips have different widths.
表2Table 2
由表2可以看出，当介质谐振单元的宽度变小时，全介质超材料谐振装置的电谐振品质因子变大；当介质谐振单元的宽度为120纳米时，全介质超材料谐振装置的电谐振品质因子为12100，已具有极高的电谐振品质因子。It can be seen from Table 2 that when the width of the dielectric resonant unit becomes smaller, the electrical resonance quality factor of the all-dielectric metamaterial resonant device becomes larger; when the width of the dielectric resonant unit is 120 nanometers, the electrical resonance of the all-dielectric metamaterial resonator The quality factor is 12100, which already has a very high electrical resonance quality factor.
由上可知，本发明全介质超材料谐振装置通过改变介质条12的长、宽、高等几何参数，可以在不同程度上调节电谐振中心波长的大小和电谐振品质因子的大小，获得极高的电谐振品质因子。本发明高品质因子的全介质谐振装置可以应用于滤波器、超灵敏传感器、负折射率等领域，用于制作光波段、太赫兹及微波等波段的高性能器件和超灵敏度传感器等。It can be seen from the above that the all-dielectric metamaterial resonator device of the present invention can adjust the size of the central wavelength of electrical resonance and the size of the electrical resonance quality factor to different degrees by changing the geometric parameters such as the length, width, and height of the dielectric strip 12, and obtain extremely high Electrical resonance quality factor. The all-dielectric resonant device with high quality factor of the present invention can be applied to the fields of filters, ultra-sensitive sensors, negative refractive index, etc., and can be used to manufacture high-performance devices and ultra-sensitive sensors in optical, terahertz, and microwave bands.
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