WO2021175310A1 - 二维光子晶体平板、设计方法及利用此平板的光器件 - Google Patents

二维光子晶体平板、设计方法及利用此平板的光器件 Download PDF

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WO2021175310A1
WO2021175310A1 PCT/CN2021/079243 CN2021079243W WO2021175310A1 WO 2021175310 A1 WO2021175310 A1 WO 2021175310A1 CN 2021079243 W CN2021079243 W CN 2021079243W WO 2021175310 A1 WO2021175310 A1 WO 2021175310A1
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photonic crystal
dimensional photonic
dimensional
energy band
crystal plate
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French (fr)
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侯金
杨春勇
陈少平
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中南民族大学
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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

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  • the invention relates to a two-dimensional photonic crystal plate and a design method thereof, and an optical device formed by the two-dimensional photonic crystal plate, in particular to a two-dimensional photonic crystal plate that forms a complete photonic band gap for electromagnetic waves in a specific wavelength range, and uses this Optical devices such as optical waveguides and resonators formed by two-dimensional photonic crystal plates.
  • the photonic band gap phenomenon in photonic crystals can prevent electromagnetic waves such as light in a certain frequency range from propagating in the periodic structure of photonic crystals. Introducing appropriate defects into a photonic crystal with a photonic band gap will produce a specific defect mode in the photonic band gap region, and only electromagnetic waves of a specific frequency corresponding to this mode can appear in the defect.
  • point defects are formed in the photonic crystal to produce optical devices such as resonators, and line defects are formed to produce optical devices such as waveguides. It is also possible to form point defects and line defects to produce more powerful optical devices at the same time.
  • the photonic band gap types of ideal two-dimensional photonic crystals can be divided into three types: TE band gap that does not support TE mode, TM band gap that does not support TM mode, and neither TE mode. It also does not support the full photonic band gap of the TM mode. Because the complete photonic band gap can simultaneously limit the light of two polarizations, it has a stronger ability to limit light. Therefore, it is possible to design various polarization-related optical devices on this basis. Generally speaking, the wider the photonic band gap, the stronger the photonic band gap's control performance on light.
  • the wider the photonic band gap, the wider the frequency band for controlling optical work the smaller the transmission loss, the higher the quality factor of photonic crystal resonators or lasers, the better the restraint effect on spontaneous radiation, and the better the reflection efficiency of photonic crystal mirrors. high.
  • the complete band gap in an ideal two-dimensional photonic crystal usually requires a higher refractive index ratio optical material to form the photonic crystal.
  • Oskooi AF, Joannopoulos, JD, and Johnson
  • the refractive index ratio in the present disclosure is the ratio of the maximum refractive index value and the minimum refractive index value among all materials constituting the photonic crystal or the photonic crystal plate.
  • a two-dimensional photonic crystal plate In an ideal two-dimensional photonic crystal, it is assumed that the photonic crystal is infinite and constant in the third dimension, so only the light confinement of two dimensions is considered, and the light confinement ability is not considered in the third dimension. In order to obtain the same light confinement capability in the third dimension, a two-dimensional photonic crystal plate was developed on the basis of an ideal two-dimensional photonic crystal. Unlike the ideal two-dimensional photonic crystal, which is assumed to be infinite and constant in the third dimension, a two-dimensional photonic crystal plate generally consists of a thick upper cladding layer, a thick lower cladding layer, and a relatively thin two-dimensional photonic crystal core layer. structure.
  • the properties of the light in the middle photonic crystal core layer in the plane of the plate mainly depend on the limitation of the photonic band gap effect, and the properties in the direction perpendicular to the plane of the photonic crystal plate mainly depend on the photon
  • the total reflection effect at the interface between the crystal core layer and the upper and lower cladding layers is limited, thus realizing the full three-dimensional confinement of light.
  • the light confinement ability in the direction perpendicular to the photonic crystal plane is mainly determined by adding the upper and lower cladding light (cone) to the photon energy band dispersion diagram, that is, the light mode above the cladding light will change Leaking into the corresponding cladding layer, only the light mode under the common light of the two cladding layers will be confined in the middle photonic crystal core layer due to the total reflection effect.
  • the photonic band gap in the two-dimensional photonic crystal plate must be under the common light of the two claddings to obtain the light confinement in the three-dimensional direction of space; in contrast, the ideal two-dimensional photonic crystal has no upper and lower cladding, which means There is no such requirement.
  • the polarization state of light cannot be strictly classified into pure TE or pure TM polarization.
  • the core layer has a relatively thin thickness and the effective refractive index of the upper and lower cladding layers are generally very small
  • the light waves in this two-dimensional photonic crystal plate have properties similar to TE polarization or TM polarization, and are usually Divided into class TE (TE-like or z-even-like) wave and class TM (TM-like or z-odd-like) wave.
  • the TE-like band gap that does not support the TE-like mode and the TE-like band gap that does not support the TM-like mode can be divided accordingly.
  • TE or TE-like mode refers to the electromagnetic wave mode in which the electric field E is parallel to the XY plane on the central plane of the plate;
  • the TM or TM-like mode refers to the electromagnetic wave mode on the central plane of the plate where the electric field E is perpendicular to the XY plane (magnetic field H Parallel to the XY plane) electromagnetic wave mode.
  • the photonic band structure of the two-dimensional photonic crystal plate is calculated first, and then the two-dimensional photonic crystal plate with the complete photonic band gap under the cladding light cone is obtained. This is very time-consuming and requires a lot of consumption. Computing resources. Therefore, the traditional empirical method is to first calculate and analyze the photonic band structure and its laws of the ideal two-dimensional photonic crystal corresponding to the two-dimensional photonic crystal plate. If the photonic band structure of the corresponding ideal two-dimensional photonic crystal can be Obtain a sufficiently wide complete photonic band gap, and then transition to calculating the energy band structure of a two-dimensional photonic crystal plate.
  • the photonic band gap included in the photonic band structure of the corresponding two-dimensional photonic crystal plate has similar properties and changing laws; at the same time, due to the two-dimensional photonic crystal
  • the plate needs to consider the light limitation in the third dimension, so it is more difficult to obtain a complete photonic band gap in a two-dimensional photonic crystal plate, and the normalized band gap width of the photonic band gap that can be obtained in a two-dimensional photonic crystal plate is narrower ; If in an ideal two-dimensional photonic crystal, the complete photonic band gap cannot be obtained or the obtained complete photonic band gap is very small, it is difficult to obtain a complete photonic band gap with practical value in the corresponding two-dimensional photonic crystal plate.
  • the refractive index ratio is 2.4:1
  • the normalized full photonic band gap width of 8.6% is obtained in the optimized two-dimensional photonic crystal of the connected hexagonal ring supercell of the optimized triangular lattice, and for the same 2.4
  • the complete photonic band gap determined by the 7th and 8th order bands only obtains a normalization of 4.3%
  • the width of the band gap is lower than the normalized full photonic band gap obtained in the corresponding ideal two-dimensional photonic crystal.
  • the upper and lower cladding layers of the two-dimensional photonic crystal plate with complete photonic band gap are air
  • the photonic crystal core layer in the middle is a non-connected annular dielectric rod.
  • This design means that the annular dielectric pillar in the middle core layer is not supported. , Hung in the air, so the two-dimensional photonic crystal plate cannot actually be fabricated, so it has no practical application value.
  • the radius of the supporting column composing the two-dimensional photonic crystal in the lower cladding layer is smaller than the ring radius of the two-dimensional photonic crystal in the middle core layer, so Very difficult to make.
  • the bandwidth of the complete photonic band gap in the photonic crystal plate is generally taken as the absolute difference between the lowest frequency point of the high-order photonic band curve forming the complete photonic band gap and the highest frequency point of the low-order photonic band curve;
  • the bandwidth of the complete photonic band gap is taken as the low-frequency point of the cladding light cone that forms the complete photonic band gap and the low-order photon energy band curve.
  • the absolute difference between the highest frequency points is the above-mentioned absolute difference and then divided to obtain the average of the two frequency values of the absolute difference, and the result is taken as a percentage.
  • the current state of the art is that when the refractive index ratio is lower than 2.4:1, there is no disclosure of a two-dimensional photonic crystal slab with a complete photonic band gap; when the refractive index ratio is 2.57:1, it is still There is no publication of a two-dimensional photonic crystal plate with a complete photonic band gap that is simple and easy to manufacture.
  • the two-dimensional photonic crystal plates are all obtained by further plate design when the corresponding ideal two-dimensional photonic crystal has a large complete photonic band gap. If it is found that a certain ideal two-dimensional photonic crystal does not have a complete photonic band gap of use value, those skilled in the art will not further consider and design the complete photonic band gap of the corresponding two-dimensional photonic crystal plate. Therefore, in the prior art, it has not been possible to design a two-dimensional photonic crystal plate with a complete photonic band gap and a relatively low refractive index.
  • the invention relates to a two-dimensional photonic crystal plate capable of realizing a complete photonic band gap under the condition of a lower refractive index ratio.
  • a two-dimensional photonic crystal plate which includes an upper cladding layer, a lower cladding layer, and a two-dimensional photonic crystal core layer located between the upper cladding layer and the lower cladding layer, wherein
  • the two-dimensional photonic crystal core layer is a two-dimensional photonic crystal with a finite height and is composed of a plurality of columns arranged periodically and a filled area. The columns are formed of the material with the highest refractive index in the two-dimensional photonic crystal plate.
  • the filling area surrounds the column and is formed of a material with a refractive index lower than that of the column, the under-cladding layer includes a solid support structure, and the two-dimensional photonic crystal plate has a complete photonic band gap, which is located at The cladding light determined by the upper cladding layer and the lower cladding layer and the lowest order photon band curve of the TE-like mode of the two-dimensional photonic crystal plate are located below the TM-like energy band curve of the two-dimensional photonic crystal plate.
  • the infinitely high ideal two-dimensional photonic crystal corresponding to the finite-height two-dimensional photonic crystal has between the lowest-order energy band curve of the TM mode and the second-lower-order energy band curve TM polarization state photonic band gap.
  • the infinite-height ideal two-dimensional photonic crystal corresponding to the finite-height two-dimensional photonic crystal does not have a complete photonic band gap or does not have a complete photon formed by the lowest-order photon energy band curve and the second-order photon energy band curve The band gap or a complete photonic band gap that does not meet the predetermined width requirement.
  • an optical device formed by using the two-dimensional photonic crystal plate according to the first aspect of the present invention.
  • the optical device is formed by forming point defects and/or lines in the two-dimensional photonic crystal plate. defect.
  • a method for designing a two-dimensional photonic crystal slab according to the first aspect of the present invention including: calculating the photonic band curve of an infinitely high ideal two-dimensional photonic crystal under a predetermined refractive index ratio, and In the case where there is a TM photonic band gap between the lowest-order TM mode and the second low-order TM mode in the photonic band curve of the infinite-height ideal two-dimensional photonic crystal that meets the first predetermined width requirement, the infinite-height
  • the structural parameters of the ideal two-dimensional photonic crystal are used as the initial two-dimensional structure parameters of the two-dimensional photonic crystal core layer, and the two-dimensional photonic crystal is designed and optimized based on the initial two-dimensional structure parameters of the two-dimensional photonic crystal core layer
  • the structural parameters of the core layer and the structural parameters of the upper cladding layer and the lower cladding layer, and the photonic band curve of the two-dimensional photonic crystal plate is calculated, so that the two-dimensional photonic crystal plate obtains
  • the two-dimensional photonic crystal plate of the present invention under the cladding light or light cone area determined by the upper cladding layer and the lower cladding layer, the two-dimensional photonic crystal plate is located under the lowest order photonic band curve of the TE-like mode of the two-dimensional photonic crystal plate.
  • the region above the lowest order photonic band curve of the TM-like mode of the two-dimensional photonic crystal plate forms a complete photonic band gap, which can form a complete photonic band gap when the maximum refractive index of the two-dimensional photonic crystal plate is relatively low, especially A complete photonic band gap is formed when the refractive index ratio is as low as the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap or a usable complete photonic band gap.
  • Fig. 1 shows a schematic structural diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 2 shows a photonic band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • FIG. 3 shows a photon energy band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 4 shows a photon energy band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • FIG. 5 shows a photon energy band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 6 shows a schematic structural diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 7 shows a photonic band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • FIG. 8 shows a photonic energy band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 9 shows a photon energy band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention.
  • FIG. 10 shows a photon energy band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 11 shows a photon energy band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • FIG. 12 shows a photon energy band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 13 shows a schematic structural diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • Fig. 14 shows a photonic band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention
  • FIG. 16 shows a schematic structural diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention.
  • Fig. 17 shows a photonic band diagram of a two-dimensional photonic crystal plate according to an embodiment of the present invention.
  • an ideal two-dimensional photonic crystal does not have a complete photonic band gap of use value, it can be designed to have a larger complete photonic band gap.
  • the band gap corresponds to a two-dimensional photonic crystal plate.
  • the inventor found that under the cladding light or light cone region defined by the upper and lower cladding layers, the use of the lowest-order photon band curve of the TE-like mode of the two-dimensional photonic crystal plate and the two-dimensional photonic crystal plate The region above the lowest-order photonic band curve of the TM-like mode can realize a two-dimensional photonic crystal plate with a large complete photonic band gap, even when the corresponding ideal two-dimensional photonic crystal does not have a complete photonic band gap.
  • the present invention can effectively solve the problem that it is difficult to obtain a complete photonic band gap in a two-dimensional photonic crystal plate with a lower refractive index ratio.
  • a two-dimensional photonic crystal plate with a complete photonic band gap can be obtained in the range, and a greater complete photonic band gap can be obtained under the condition that the existing technology can obtain a complete photonic band gap but the complete photonic band gap is very narrow due to the low refractive index ratio.
  • Photonic band gap bandwidth the two-dimensional photonic crystal plate according to the present invention has a simple structure and is easy to manufacture.
  • the embodiments of the present invention adopt the following design principles.
  • first TM energy band ie, the lowest-order energy band curve of the TM mode
  • the second TM energy band ie, the second lower-order energy band curve of the TM mode
  • Energy band curve can form a TM photonic band gap, so that a similar first TM-like energy band (ie, the lowest-order energy band curve of the TM-like mode) can be easily obtained in its corresponding two-dimensional photonic crystal plate And the second TM-like energy band (ie, the second lower-order energy band curve of the TM-like mode) of the TM-like mode photonic band gap.
  • first TM-like energy band ie, the lowest-order energy band curve of the TM-like mode
  • the second TM-like energy band ie, the second lower-order energy band curve of the TM-like mode
  • the first TE-like energy band ie, the lowest-order energy band curve of the TE-like mode
  • the first TE-like energy band in the two-dimensional photonic crystal plate Compared with a TM-like energy band, it usually has a larger difference, that is, the interval is very large.
  • the first photonic band (lowest-order band curve) is generally TM-like mode. Therefore, the band curve of the first TE-like mode is not only the same as the first band curve of TE-like mode.
  • the energy band curve of a TM-like mode is widely spaced and will appear in the upper region of the photon energy band of the first TM-like mode energy band curve. Therefore, there is a TM-like photonic band gap on the band curve of the first TM-like mode, and there is also a large gap between the first TE-like mode and the upper cladding layer. Below the cladding light cone area determined by the cladding, above the first TM-like mode and below the first TE-like mode, an area where TM-like mode and TE-like mode do not exist at the same time is formed, that is, complete photon Band gap area.
  • the parameters and the structural parameters of the cladding can form a complete photonic band gap that meets the width requirements at a lower refractive index ratio.
  • the complete photonic band gap is surrounded by the lowest order photonic band curve and the cladding light.
  • the region is determined, or determined by the lowest-order photon energy band curve, the second-order photon energy band curve and the area enclosed by the cladding light.
  • the lowest-order photon energy band curve is the lowest-order energy band curve of the TM-like mode of the two-dimensional photonic crystal plate
  • the second-order photon energy band curve is the two-dimensional photon
  • the second low-order photon energy band curve of the TM-like mode of the crystal plate, or the lowest order energy band curve of the TE-like mode of the two-dimensional photonic crystal plate, or the TE-like mode of the two-dimensional photonic crystal plate A part of the lowest order energy band curve and a part of the second lower order photon energy band curve of the TM-like mode are formed.
  • the embodiment of the present invention provides a two-dimensional photonic crystal plate.
  • the two-dimensional photonic crystal plate includes an upper cladding layer, a lower cladding layer, and a two-dimensional photonic crystal core layer located between the upper cladding layer and the lower cladding layer.
  • the core layer of the two-dimensional photonic crystal is a two-dimensional photonic crystal with a finite height, and is composed of a plurality of pillars arranged periodically and a filled area, and the pillars are formed of the material with the highest refractive index in the two-dimensional photonic crystal plate,
  • the filling area surrounds the column and is formed of a material having a refractive index lower than that of the column.
  • the under-cladding layer includes a solid support structure.
  • the two-dimensional photonic crystal plate has a complete photonic band gap, and the complete photonic band gap of the two-dimensional photonic crystal plate is located at the cladding light determined by the upper cladding layer and the lower cladding layer, and the two-dimensional photonic crystal plate Below the lowest order photon energy band curve of the TE-like mode of the crystal plate and above the lowest order photon energy band curve of the TM-like mode of the two-dimensional photonic crystal plate.
  • the infinite-height ideal two-dimensional photonic crystal corresponding to the finite-height two-dimensional photonic crystal has a TM polarization state photonic band gap between the lowest-order energy band curve and the second low-order energy band curve of the TM mode.
  • the maximum refractive index ratio of the two-dimensional photonic crystal plate may be as low as the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap or does not have the lowest order photonic band curve and the second order (ie, the first order).
  • the predetermined width can be determined according to the needs of actual applications. For example, it is generally considered that a normalized full photonic band gap width of less than 3% is of no use value. Therefore, the predetermined width requirement here can be selected as a normalized width greater than 3%. ⁇ Width.
  • the lowest order photon energy of the TE-like mode located in the two-dimensional photonic crystal plate is used because it is located under the light cone of the cladding layer defined by the upper and lower cladding layers.
  • the area below the band curve and above the lowest order photonic band curve of the TM-like mode of the two-dimensional photonic crystal plate forms a complete photonic band gap, which can be formed when the maximum refractive index of the two-dimensional photonic crystal plate is relatively low Usable complete photonic band gap, especially when the refractive index ratio is low to the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap or does not have a usable complete photonic band gap can also be used Complete photonic band gap.
  • a usable full photonic band gap can be realized when the maximum refractive index ratio is lower than 2.4 or even lower than 2.0.
  • the under-cladding layer includes a solid support structure
  • the two-dimensional photonic crystal slab can be actually manufactured.
  • the under-cladding layer is composed of a solid homogeneous material
  • the solid-state homogeneous material is a solid support structure
  • the under-cladding layer is also a two-dimensional photonic crystal structure, the columns and/or columns in the two-dimensional photonic crystal structure
  • the filled area is a solid material, which plays a supporting role.
  • FIG. 1 shows a schematic structural diagram of a two-dimensional photonic crystal plate 100 according to an embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of the XY plane, and (c) is a cross-sectional view of the XZ plane.
  • the upper cladding layer 101 is air
  • the lower cladding layer is silicon dioxide 102
  • the two-dimensional photonic crystal core layer 103 is a two-dimensional photonic crystal of finite height, which is composed of periodically arranged silicon nitride ( Si x N y ) cylinders and filled areas filled with air.
  • the values of Si x N y x and y are determined according to the designed refractive index, and Si x N y has the largest refractive index among the materials forming the two-dimensional photonic crystal plate 100.
  • the upper cladding layer 101, the core layer 103, and the lower cladding layer 102 constitute a sandwich structure.
  • the two-dimensional photonic crystal of the core layer 103 is a two-dimensional photonic crystal with a triangular lattice and a circular column, as shown in FIG. 1(b).
  • FIG. 2 is a photonic energy band diagram corresponding to an embodiment of the two-dimensional photonic crystal plate 100 of FIG. 1.
  • the main structural parameters of the two-dimensional photonic crystal plate 100 are: the column material (Si x N y ) of the core layer has the highest refractive index, which is 2.5, and the air in the upper cladding layer and the filling area has the lowest refractive index.
  • the refractive index of the under-cladding layer (silicon dioxide) is 1.45.
  • the maximum refractive index ratio is 2.5:1; the thickness h of the core layer is 1.9a, and the radius r of the Si x N y cylinder is 0.33a, where a is the lattice constant of the photonic crystal, and the lattice constant a is selected according to the applicable electromagnetic spectrum frequency.
  • the thickness of the upper cladding layer and the lower cladding layer can be designed according to needs, and usually reaches 4-10 wavelengths or more to be considered as infinitely thick. According to the above structural parameters, the photon energy band diagram as shown in Figure 2 can be calculated.
  • the horizontal axis is the wave vector, labeled ⁇ , M, and K
  • the vertical axis is the normalized frequency, with the unit c/a, where c is the speed of light, and a is the lattice constant of the photonic crystal.
  • the gray uniform shaded area is the light cone area determined by the light of the silica cladding with a refractive index of 1.45;
  • the energy band curve (energy band 1) shown by the solid dot and solid line is the lowest order The energy band curve, which is the lowest-order energy band curve of the TM-like mode;
  • the energy band curve (energy band 2) shown by the square dotted line is the second-order energy band curve, which is the second low-energy band curve of the TM-like mode ;
  • the energy band curve (energy band 3) shown by the triangular dashed line is the third-order energy band curve, which includes TE-like mode and TM-like mode, and is the lowest energy band curve containing TE-like mode under the light cone.
  • the above-mentioned second-order energy band curve may be the second low-energy band curve of TM-like mode, or the lowest energy band curve of TE-like mode, or it may be TM A part of the second low energy band curve of the -like mode and a part of the lowest energy band curve of the TE-like mode are formed.
  • the energy band curve of each photon in the energy band diagram is the first order (the lowest order), the second order (the second low order), etc. from bottom to top.
  • the lowest-order energy band curve, the second-order energy band curve and the cladding light jointly define a complete photonic band gap region, as shown in the gray shaded area with vertical lines (the band is vertical The area where the gray shaded area of the line overlaps with the blank area in the figure is the complete photonic band gap area).
  • the complete photonic band gap region There is no optical mode in this complete photonic band gap region, that is, there is neither TM-like mode nor TE-like mode.
  • the complete photonic band gap is located below the energy band 3 of the lowest order photon energy band curve containing the TE-like mode, and above the lowest order photon energy band curve (energy band 1) of the TM-like mode .
  • Figure 3 is a photonic band diagram of an infinitely high ideal two-dimensional photonic crystal corresponding to Figure 2.
  • the structural parameters of the infinitely high ideal two-dimensional photonic crystal and the structural parameters of the finitely high two-dimensional photonic crystal in the core layer of the photonic crystal plate in Figure 2 The same, the only difference is that the ideal two-dimensional photonic crystal has no cladding and the height is infinite. Since the ideal two-dimensional photonic crystal has no cladding, its photonic band diagram does not have a light cone region that represents the optical confinement of the cladding.
  • the energy band curve shown by the solid dotted line is the energy band curve of TM mode
  • the energy band curve shown by the hollow dotted line is the energy band curve of TE mode.
  • the maximum refractive index ratio is as low as 2.5:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal slab can still be relatively high. Large complete photonic band gap.
  • the maximum refractive index ratio is 2.5:1
  • the cylindrical radius and the height of the core layer in the triangular lattice two-dimensional photonic crystal plate shown in FIG. 1 different two-dimensional images can be obtained.
  • the normalization of the photonic crystal plate is completely wide, so that the structural parameters of the two-dimensional photonic crystal plate can be optimized, as shown in Table 1 below:
  • FIG. 4 is a photonic energy band diagram corresponding to another embodiment of the two-dimensional photonic crystal plate 100 of FIG. 1.
  • the maximum refractive index ratio is further reduced to 2:1, and its main structural parameters are: the pillar material (Si x N y ) of the core layer has the highest refractive index, which is 2.0, the upper cladding layer and The air in the filled area has the lowest refractive index, which is 1, and the refractive index of the under-cladding layer (silicon dioxide) is 1.45. Therefore, the maximum refractive index ratio is 2:1; the thickness h of the core layer is 3.0a, and Si x N The radius r of the y cylinder is 0.33a.
  • the photon energy band diagram as shown in Fig. 4 can be calculated.
  • the gray uniform shaded area is the light cone area determined by the light of the silica cladding;
  • the energy band curve (energy band 1) shown by the solid line is the lowest-order energy band curve, which is TM-like The lowest-order energy band curve of the mode;
  • the energy band curve (energy band 2) shown by the dotted line is the second-order energy band curve, which is the lowest-order energy band curve of the TE-like mode, and some of the modes are in the light cone.
  • the lowest-order energy band curve, the second-order energy band curve and the cladding light jointly define a complete photonic band gap, as shown in the gray shaded area with vertical lines.
  • the complete photonic band gap is located below the lowest order photon energy band curve of the TE-like mode and above the lowest order photon energy band curve of the TM-like mode.
  • the calculation shows that the normalized full photonic band gap width of the photonic crystal plate shown in Figure 2 is 3.68%. Therefore, when the center wavelength is 1550nm, the bandwidth is about 57nm; when the center wavelength is 650nm, the bandwidth is about 23.9 nm. Such a bandwidth can realize a variety of practical optical devices.
  • Figure 5 is a photonic energy band diagram of an infinitely high ideal two-dimensional photonic crystal corresponding to Figure 4.
  • the structural parameters of the infinitely high ideal two-dimensional photonic crystal and the structural parameters of the finitely high two-dimensional photonic crystal in the core layer of the photonic crystal plate in Figure 4 The same, the only difference is that the ideal two-dimensional photonic crystal has no cladding and the height is infinite. Since the ideal two-dimensional photonic crystal has no cladding, its photonic band diagram does not have a light cone region that represents the optical confinement of the cladding.
  • the energy band curve shown by the solid dotted line is the energy band curve of TM mode
  • the energy band curve shown by the hollow dotted line is the energy band curve of TE mode.
  • the normalized band gap width between the first-order TM band and the second-order TM band is 16.63%, which is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal plate.
  • the maximum refractive index ratio is as low as 2:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal plate can still be relatively high. Large complete photonic band gap.
  • the maximum refractive index ratio is 2:1
  • the cylindrical radius and the height of the core layer in the triangular lattice two-dimensional photonic crystal plate shown in FIG. 1 different two-dimensional images can be obtained.
  • the normalized full photonic band gap of the photonic crystal plate is shown in Table 2 below:
  • both the upper cladding layer and the lower cladding layer are homogeneous layers formed of a material with a refractive index lower than the maximum refractive index in the two-dimensional photonic crystal slab.
  • An example in which at least one of the upper cladding layer and the lower cladding layer is also a two-dimensional photonic crystal structure is given below.
  • the upper cladding layer and/or the lower cladding layer may be a two-dimensional photonic crystal cladding layer composed of multiple materials with a refractive index lower than the maximum refractive index in the two-dimensional photonic crystal plate .
  • the two-dimensional photonic crystal of the upper cladding layer and/or the lower cladding layer may have the same lattice structure as the core layer of the two-dimensional photonic crystal.
  • the column radius in the two-dimensional photonic crystal of the under-cladding layer may be greater than or equal to the column radius of the two-dimensional photonic crystal core layer.
  • the column radius in the two-dimensional photonic crystal of the upper cladding layer may be smaller than or equal to the column radius of the two-dimensional photonic crystal core layer.
  • FIG. 6 shows a schematic structural diagram of a two-dimensional photonic crystal plate 600 according to another embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of the XY plane, and (c) is a cross-sectional view of the XZ plane .
  • the upper cladding layer 601 is a homogeneous material air
  • the lower cladding layer 602 is a two-dimensional photonic crystal cladding layer formed of a finite-height cylindrical silica and air
  • the core layer 603 is a finite-height cylinder Shaped silicon nitride (Si x N y ) and air form a two-dimensional photonic crystal core layer.
  • Si x N y has the largest refractive index among the materials forming the two-dimensional photonic crystal plate 600, and the refractive index of the column material silicon dioxide of the under-cladding layer 602 is lower than the aforementioned maximum refractive index.
  • the core layer 603 and the under-cladding layer 602 have the same crystal lattice and the shape and radius of the pillars, and both are triangular lattice circular pillar two-dimensional photonic crystals, as shown in FIG. 6(b).
  • FIG. 7 is a photonic energy band diagram corresponding to an embodiment of the two-dimensional photonic crystal plate 600 of FIG. 6.
  • the main structural parameters of the two-dimensional photonic crystal plate 600 are: the pillar material (Si x N y ) of the core layer has the highest refractive index, which is 1.8, and the air in the upper cladding layer and the filling area has the lowest refractive index. It is 1, the refractive index of the silica cylinder under the cladding layer is 1.45, therefore, the maximum refractive index ratio is 1.8:1; the thickness h of the core layer is 2.1a, the Si x N y cylinder and the silica The radius r is 0.33a.
  • the thickness of the upper cladding layer and the lower cladding layer can be designed according to needs, and usually reaches 4-10 wavelengths or more to be considered as infinitely thick.
  • the photon energy band diagram as shown in FIG. 7 can be calculated.
  • the gray uniform shaded area is the light cone area determined by the light of the undercladding layer;
  • the energy band curve (energy band 1) shown by the solid dotted line is the lowest-order energy band curve, which is TM-like The lowest-order energy band curve of the mode;
  • the energy band curve (energy band 2) shown by the dotted line is the second-order energy band curve, which is the lowest-order energy band curve of the TE-like mode and is completely in the light cone region .
  • the lowest-order band curve and the cladding light together define a complete photonic band gap, as shown in the gray shaded area with vertical lines in the figure.
  • the cladding is a two-dimensional photonic crystal cladding
  • the cladding light takes the lowest-order energy band curve of the two-dimensional photonic crystal cladding.
  • the complete photonic band gap is located below the lowest order photon energy band curve of the TE-like mode and above the lowest order photon energy band curve of the TM-like mode.
  • the calculation shows that the normalized full photonic band gap width of the photonic crystal plate shown in Figure 7 is 3.17%. Therefore, when the center wavelength is 1550nm, the bandwidth is about 49nm; when the center wavelength is 650nm, the bandwidth is about 20nm . Such a bandwidth can realize a variety of practical optical devices.
  • Fig. 8 is a photonic energy band diagram of an infinitely high ideal two-dimensional photonic crystal corresponding to the core layer of Fig. 7.
  • the structural parameters of the infinitely high ideal two-dimensional photonic crystal and the finite high two-dimensional photonic crystal of the core layer of the photonic crystal plate in Fig. 7 The structural parameters are the same, the only difference is that the ideal two-dimensional photonic crystal has no cladding and the height is infinite. Since the ideal two-dimensional photonic crystal has no cladding, its photonic band diagram does not have a light cone region that represents the optical confinement of the cladding. As shown in Fig.
  • the energy band curve shown by the solid dotted line is the energy band curve of TM mode
  • the energy band curve shown by the solid dotted line is the energy band curve of TE mode.
  • the energy band diagram of the ideal two-dimensional photonic crystal shown in the figure there are two TM band gaps (shown in the shaded area in the figure), but due to the relatively low refractive index (only 1.8:1), there is no complete photonic band Gap.
  • the normalized band gap width between the first-order TM band and the second-order TM band is 13.13%, which is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal plate.
  • the maximum refractive index ratio is as low as 1.8:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal plate can still be relatively high. Large complete photonic band gap.
  • the maximum refractive index ratio is 1.8:1
  • the cylindrical radius in the triangular lattice two-dimensional photonic crystal plate shown in FIG. 6 the cylindrical radius of the core layer and the cladding layer are the same
  • the height of the core layer the normalized full photonic band gap width of different two-dimensional photonic crystal plates can be obtained, as shown in Table 3 below:
  • FIG. 9 is a photonic energy band diagram corresponding to another embodiment of the two-dimensional photonic crystal plate 600 of FIG. 6.
  • the main structural parameters of the two-dimensional photonic crystal plate 600 are: the column material (Si x N y ) of the core layer has the highest refractive index, which is 2.4, and the air in the upper cladding layer and the filling area has the lowest refractive index.
  • the refractive index of the silica cylinder under the cladding layer is 1.45. Therefore, the maximum refractive index ratio is 2.4:1; the thickness h of the core layer is 1.4a, and the Si x N y cylinder and the silica The radius r of the cylinder is 0.21a.
  • the photon energy band diagram as shown in FIG. 9 can be calculated.
  • the gray uniform shaded area is the light cone area determined by the light of the under-cladding layer (take the lowest band curve of the two-dimensional photonic crystal cladding energy band curve as the light); the solid dots and solid lines are shown
  • the energy band curve of is the lowest order energy band curve (energy band 1), which is the lowest order energy band curve of the TM-like mode; the energy band curve shown by the dotted line is the second order energy band curve (energy band 2) , which is the lowest-order band curve of the TE-like mode, and is completely located in the optical cone of the cladding. It can be seen from Fig.
  • the lowest-order band curve and the cladding light together define a complete photonic band gap area, as shown in the gray shaded area with vertical lines.
  • the complete photonic band gap is located below the lowest order photon energy band curve of the TE-like mode and above the lowest order photon energy band curve of the TM-like mode.
  • the calculation shows that the normalized full photonic band gap width of the photonic crystal plate shown in Fig. 9 is 12.85%, so when the center wavelength is 1550nm, the bandwidth is about 199nm; when the center wavelength is 650nm, the bandwidth is about 83nm . Such a bandwidth can realize a variety of practical optical devices.
  • Fig. 10 is a photonic energy band diagram of an infinitely high ideal two-dimensional photonic crystal corresponding to the core layer of Fig. 9.
  • the structural parameters of the infinitely high ideal two-dimensional photonic crystal and the finite-height two-dimensional photonic crystal of the core layer of the photonic crystal plate in Fig. 9 The structural parameters are the same, the only difference is that the ideal two-dimensional photonic crystal has no cladding and the height is infinite. Since the ideal two-dimensional photonic crystal has no cladding, its photonic band diagram does not have a light cone region that represents the optical confinement of the cladding. As shown in FIG.
  • the energy band curve shown by the solid dotted line is the energy band curve of TM mode
  • the energy band curve shown by the solid dotted line is the energy band curve of TE mode.
  • the energy band diagram of the ideal two-dimensional photonic crystal shown in the figure there is a TM band gap (shown in the shaded area in the figure), but due to the relatively low refractive index (only 2.4:1), there is no complete photonic band Gap.
  • the normalized band gap width between the first-order TM band and the second-order TM band is 31.37%, which is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal plate.
  • the maximum refractive index ratio is as low as 2.4:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal slab can still be relatively high. Large complete photonic band gap.
  • the maximum refractive index ratio is 2.4:1
  • the cylindrical radius in the triangular lattice two-dimensional photonic crystal plate shown in FIG. 6 the cylindrical radius of the core layer and the cladding layer are the same
  • the height of the core layer the normalized full photonic band gap width of different two-dimensional photonic crystal plates can be obtained, as shown in Table 4 below:
  • FIG. 11 is a photonic energy band diagram corresponding to another embodiment of the two-dimensional photonic crystal plate 600 of FIG. 6.
  • the main structural parameters of the two-dimensional photonic crystal plate 600 are: the column material (Si x N y ) of the core layer has the highest refractive index, which is 2.57, and the air in the upper cladding layer and the filling area has the lowest refractive index.
  • the refractive index of the silica cylinder under the cladding layer is 1.45. Therefore, the maximum refractive index ratio is 2.57:1; the thickness h of the core layer is 1.25a, and the Si x N y cylinder and the silica The radius r of the cylinder is 0.21a.
  • the photon energy band diagram as shown in FIG. 11 can be calculated.
  • the gray uniform shaded area is the light cone area determined by the light of the lower cladding (take the lowest band curve of the two-dimensional photonic crystal cladding energy band curve as the light); shown by the solid dotted line
  • the energy band curve (energy band 1) of is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode
  • the energy band curve (energy band 2) shown by the dotted line in the open square is the second order energy band curve , Which is the lowest-order band curve of the TE-like mode, and is completely located in the optical cone of the cladding.
  • the lowest-order band curve and the cladding light together define a complete photonic band gap, as shown in the gray shaded area with vertical lines.
  • the complete photonic band gap is located below the lowest order photon energy band curve of the TE-like mode and above the lowest order photon energy band curve of the TM-like mode.
  • the calculation shows that the normalized full photonic band gap width of the photonic crystal plate shown in Figure 11 is 13.65%. Therefore, when the center wavelength is 1550nm, the bandwidth is about 211nm; when the center wavelength is 650nm, the bandwidth is about 88nm . Such a bandwidth can realize a variety of practical optical devices.
  • Fig. 12 is a photonic energy band diagram of an infinitely high ideal two-dimensional photonic crystal corresponding to the core layer of Fig. 11.
  • the structural parameters of the infinitely high ideal two-dimensional photonic crystal and the finite-height two-dimensional photonic crystal in the core layer of the photonic crystal plate in Fig. 11 The structural parameters are the same, the only difference is that the ideal two-dimensional photonic crystal has no cladding and the height is infinite. Since the ideal two-dimensional photonic crystal has no cladding, its photonic band diagram does not have a light cone region that represents the optical confinement of the cladding. As shown in Fig.
  • the energy band curve shown by the solid dotted line is the TM mode energy band curve
  • the energy band curve shown by the hollow dotted solid line is the TE mode energy band curve.
  • the normalized band gap width between the first-order TM band and the second-order TM band is 34.84%, which is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal plate.
  • the maximum refractive index ratio is as low as 2.57:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal slab can still be relatively high. Large complete photonic band gap.
  • the maximum refractive index ratio is 2.57:1
  • the cylindrical radius in the triangular lattice two-dimensional photonic crystal plate shown in FIG. 6 the cylindrical radius of the core layer and the cladding layer are the same
  • the height of the core layer the normalized full photonic band gap width of different two-dimensional photonic crystal plates can be obtained, as shown in Table 5 below:
  • FIG. 13 shows a schematic structural diagram of a two-dimensional photonic crystal plate 1300 according to another embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of the XY plane, and (c) is a cross-sectional view of the XZ plane .
  • the upper cladding layer 1301 is a homogeneous material air
  • the lower cladding layer 1302 is a two-dimensional photonic crystal cladding layer formed of a finite height cylindrical silica and air
  • the core layer 1303 is a finite height cylindrical Shaped silicon nitride (Si x N y ) and air form a two-dimensional photonic crystal core layer.
  • Si x N y has the largest refractive index among the materials forming the two-dimensional photonic crystal slab 1300, and the refractive index of the column material of the under-cladding layer 1302 is lower than the above-mentioned maximum refractive index.
  • the core layer 1303 and the lower cladding layer 1302 have the same crystal lattice and column shape, both of which are two-dimensional photonic crystals, which are triangular lattices and circular column two-dimensional photonic crystals, but the column radius of the lower cladding layer 1302 The cylinder radius is larger than the core layer 1303, as shown in Figure 13(b) and (c).
  • FIG. 14 is a photonic energy band diagram corresponding to an embodiment of the two-dimensional photonic crystal plate 1300 of FIG. 13.
  • the main structural parameters of the two-dimensional photonic crystal slab 1300 are: the column material (Si x N y ) of the core layer has the highest refractive index, which is 2, and the air in the upper cladding layer and the filling area has the lowest refractive index.
  • the refractive index of the silica cylinder under the cladding layer is 1.45. Therefore, the maximum refractive index ratio is 2:1; the thickness h of the core layer is 1.8a, and the radius of the Si x N y cylinder is 0.28. a, the radius of silica is 0.33a.
  • the thickness of the upper cladding layer and the lower cladding layer can be designed according to needs, and usually reaches 4-10 wavelengths or more to be considered as infinitely thick. According to the above structural parameters, the photon energy band diagram as shown in FIG. 14 can be calculated.
  • the gray uniform shaded area is the light cone area determined by the light of the under cladding (take the lowest band curve of the two-dimensional photonic crystal cladding energy band curve as the light); the dotted solid line shows The energy band curve (energy band 1) is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve shown by the dotted line (energy band 2) is the second order energy band curve, which It is the lowest-order energy band curve of TE-like mode, and it is completely located in the light cone. It can be seen from Figure 14 that the lowest-order energy band curve and the cladding light together define a complete photonic band gap region, as shown by the gray shaded area with vertical lines in the figure.
  • the complete photonic band gap is located below the lowest order photon energy band curve of the TE-like mode and above the lowest order photon energy band curve of the TM-like mode.
  • the calculation shows that the normalized full photonic band gap width of the photonic crystal plate shown in Figure 14 is 4.74%. Therefore, when the center wavelength is 1550nm, the bandwidth is about 73nm; when the center wavelength is 650nm, the bandwidth is about 31nm . Such a bandwidth can realize a variety of practical optical devices.
  • Fig. 15 is a photonic band diagram of an infinitely high ideal two-dimensional photonic crystal corresponding to the core layer of Fig. 14.
  • the structural parameters of the infinitely high ideal two-dimensional photonic crystal and the finite-height two-dimensional photonic crystal of the core layer of the photonic crystal plate in Fig. 14 The structural parameters are the same, the only difference is that the ideal two-dimensional photonic crystal has no cladding and the height is infinite. Since the ideal two-dimensional photonic crystal has no cladding, its photonic band diagram does not have a light cone region that represents the optical confinement of the cladding. As shown in FIG.
  • the energy band curve shown by the solid dotted line is the TM mode energy band curve
  • the energy band curve shown by the hollow dotted solid line is the TE mode energy band curve.
  • the normalized band gap width between the first-order TM band and the second-order TM band is 21.08%, which is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal plate.
  • the maximum refractive index ratio is as low as 2:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal plate can still be relatively high. Large complete photonic band gap.
  • FIG. 16 shows a schematic structural diagram of a two-dimensional photonic crystal plate 1600 according to another embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of the XY plane, and (c) is a cross-sectional view of the XZ plane .
  • the upper cladding layer 1601 and the lower cladding layer 1602 are both two-dimensional photonic crystal cladding layers, each formed of a finite-height cylindrical silicon dioxide and air;
  • the core layer 1603 is made of a finite-height cylindrical nitride
  • Si x N y has the largest refractive index among the materials forming the two-dimensional photonic crystal slab 1600, and the refractive indexes of the pillar materials of the upper cladding layer 1601 and the lower cladding layer 1602 are lower than the aforementioned maximum refractive index.
  • the upper cladding layer 1601, the core layer 1603, and the lower cladding layer 1602 have the same crystal lattice and column shape, all of which are two-dimensional photonic crystals and triangular lattice circular column two-dimensional photonic crystals, and the upper cladding layer
  • the cylinder radius of 1601 is equal to the cylinder radius of the core layer 1603, but is smaller than the cylinder radius of the lower cladding layer 1602, as shown in Fig. 16(b) and (c).
  • FIG. 17 is a photonic energy band diagram corresponding to an embodiment of the two-dimensional photonic crystal plate 1600 of FIG. 16.
  • the main structural parameters of the two-dimensional photonic crystal slab 1600 are: the column material (Si x N y ) of the core layer has the highest refractive index, which is 2, and the air in the filled area has the lowest refractive index, which is 1.
  • the refractive index of the upper and lower cladding silica cylinders is 1.45, therefore, the maximum refractive index ratio is 2:1;
  • the thickness h of the core layer is 1.8a, the radius of the upper cladding silica and Si
  • the radius of the x N y cylinder is 0.28a, and the radius of the under-cladding silica is 0.33a.
  • the thickness of the upper cladding layer and the lower cladding layer can be designed according to needs, and usually reaches 4-10 wavelengths or more to be considered as infinitely thick.
  • the photon energy band diagram as shown in FIG. 17 can be calculated.
  • the gray uniform shaded area is the light cone area determined by the light of the lower cladding (take the lowest energy band curve of the upper and lower two-dimensional photonic crystal cladding energy band curve as the light);
  • the energy band curve (energy band 1) shown is the lowest-order energy band curve, which is the lowest-order energy band curve of the TM-like mode;
  • the energy band curve (energy band 2) shown by the hollow dotted line is the second-order energy band curve.
  • the belt curve which is the lowest-order energy band curve of the TE-like mode, is almost completely located in the light cone region. It can be seen from Figure 17 that the lowest-order band curve and the cladding light together define a complete photonic band gap region, as shown by the gray shaded area with vertical lines in the figure. In addition, it can be seen that the complete photonic band gap is located below the lowest order photon energy band curve of the TE-like mode and above the lowest order photon energy band curve of the TM-like mode. The calculation shows that the normalized full photonic band gap width of the photonic crystal plate shown in Figure 17 is 5.87%.
  • the bandwidth is about 91nm; when the center wavelength is 650nm, the bandwidth is about 38nm .
  • the infinitely high ideal two-dimensional photonic crystal corresponding to the core layer in FIG. 17 is the same as the infinitely high ideal two-dimensional photonic crystal corresponding to the core layer in FIG. 14, so its photonic band diagram is also shown in FIG. 15.
  • the maximum refractive index ratio is as low as 2:1, and the corresponding infinitely high ideal two-dimensional photonic crystal does not have a complete photonic band gap, but the two-dimensional photonic crystal plate can still be relatively high. Large complete photonic band gap.
  • an optical device formed by using the above-mentioned two-dimensional photonic crystal plate.
  • the optical device is formed by forming point defects and/or line defects in the two-dimensional photonic crystal plate.
  • introducing line defects into a two-dimensional photonic crystal plate can form an optical waveguide
  • introducing point defects into a two-dimensional photonic crystal plate can form a resonator
  • introducing point defects and line defects into a two-dimensional photonic crystal plate can form a more powerful function Optical devices.
  • a method of designing a two-dimensional photonic crystal plate according to an embodiment of the present invention.
  • the foundation of a two-dimensional photonic crystal slab The embodiments according to the present invention are generally applied when the refractive index is relatively low.
  • the predetermined refractive index ratio can be determined according to the design application scene and the material system, and the ideal two-dimensional photonic crystal is calculated in the predetermined refractive index ratio.
  • the photon energy band curve Specifically, in the case that there is a TM photonic band gap between the lowest-order TM mode and the second low-order TM mode in the photonic band curve of the infinitely high ideal two-dimensional photonic crystal that meets the first predetermined width requirement, the The structural parameters of the infinitely high ideal two-dimensional photonic crystal are used as the initial two-dimensional structure parameters of the two-dimensional photonic crystal core layer.
  • the first predetermined width requirement here can be set according to the requirements of specific applications. For example, it can be a requirement that the normalized photonic band gap is greater than 3%, 10%, etc., in order to obtain complete photons that meet the requirements in the two-dimensional photonic plate. Bandgap.
  • the first predetermined width requirement is similar to or slightly wider than the final required complete photonic band gap.
  • the structural parameters of an ideal two-dimensional photonic crystal can be used as the initial two-dimensional structure parameters of the core layer of the designed two-dimensional photonic crystal plate .
  • the two-dimensional structural parameters include the lattice structure of the two-dimensional photonic crystal; the material or refractive index, shape, and plane size (for example, radius) of the column; and the material or refractive index of the filled area.
  • the two-dimensional photonic crystal core layer design and optimize the structure parameters of the two-dimensional photonic crystal core layer, including the thickness, and the upper cladding layer and the lower cladding layer. Structure parameters, and calculate the photonic band curve of the two-dimensional photonic crystal plate, so that the two-dimensional photonic crystal plate obtains a complete photonic band gap that meets the second predetermined width requirement, and the complete photonic band gap is located on the upper
  • the cladding light determined by the cladding layer and the lower cladding layer and the lowest order photon band curve of the TE-like mode of the two-dimensional photonic crystal plate and located at the lowest order of the TM-like mode of the two-dimensional photonic crystal plate Above the photon band curve.
  • the structural parameters of the core layer include the thickness of the core layer in addition to the above-mentioned two-dimensional structural parameters.
  • the calculation and comparison of the parameter values around the initial two-dimensional structure parameters can be performed.
  • the thickness of the core layer and the structure of the cladding layer can be determined according to specific applications, for example, the selection of suitable materials and sizes. In addition, a variety of parameters can be calculated to determine the optimized parameters.
  • the optimized full photonic band gap width can be obtained by changing the corresponding size.
  • a two-dimensional photonic crystal plate with a complete photonic band gap meeting the second predetermined width requirement is finally obtained.
  • the second predetermined width requirement can be determined according to the bandwidth requirement of the designed optical device.
  • a two-dimensional photonic crystal slab with a complete photonic band gap can be formed with a relatively low refractive index, which can greatly promote a complete photonic band gap such as a two-dimensional photonic crystal slab.
  • the column shape in the two-dimensional photonic crystal plate is not limited to a column, and can be a column of any shape, for example, a triangular column, a square column, other polygonal columns and other different shapes.
  • the high refractive index material used for the core layer column is not limited to silicon nitride, for example, it can be selected from silicon, germanium, silicon nitride, silicon oxynitride, gallium arsenide, indium phosphide, titanium oxide, or a compound of these materials Or a mixture, or glass, or optical or electromagnetic polymers such as plastic; the low refractive index material used for the cladding or the filled area can be selected from silicon nitride, silicon oxynitride, silicon dioxide, air, etc., as long as it can meet the requirements of the design A predetermined refractive index ratio is sufficient.

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Abstract

本发明涉及一种二维光子晶体平板、设计方法以及利用此平板的光器件。所述二维光子晶体平板包括上包层、下包层和位于所述上包层和所述下包层之间的二维光子晶体核心层。二维光子晶体核心层为有限高的二维光子晶体。所述二维光子晶体平板具有完全光子带隙，其位于上包层和下包层所确定的包层光线以及二维光子晶体平板的类TE模式的最低阶光子能带曲线下方并位于类TM模式的最低阶光子能带曲线上方，并且所述有限高的二维光子晶体所对应的无限高理想二维光子晶体在TM模式的最低阶能带曲线与第二低阶能带曲线之间具有TM偏振态的光子带隙。所述二维光子晶体平板可以在最大折射率比较低的情况下形成完全光子带隙。

Description

二维光子晶体平板、设计方法及利用此平板的光器件 技术领域
本发明涉及二维光子晶体平板及其设计方法、以及利用二维光子晶体平板形成的光器件，尤其涉及一种对特定波长范围的电磁波形成完全光子带隙的二维光子晶体平板，以及利用此类二维光子晶体平板形成的光波导、谐振器等光器件。
背景技术
光子晶体中的光子带隙现象能够使得在某一频率范围内的诸如光的电磁波不能在光子晶体的周期性结构中传播。在具有光子带隙的光子晶体中引入合适的缺陷，将会在光子带隙区中产生特定的缺陷模式，只有相应于这个模式的特定频率的电磁波能够在缺陷中出现。通常，在光子晶体中形成点缺陷来产生诸如谐振器之类的光器件，形成线缺陷来产生诸如波导之类的光器件，也可以同时形成点缺陷和线缺陷产生功能更强大的光器件。
根据对光偏振控制能力的不同，可以将理想二维光子晶体的光子带隙类型分为三种：不支持TE模式的TE带隙、不支持TM模式的TM带隙和同时既不支持TE模式也不支持TM模式的完全光子带隙。完全光子带隙因为能同时对两种偏振的光进行限制，对光的限制能力更强，因而能以此为基础设计各种偏振有关的光器件。一般而言，光子带隙宽度越宽，光子带隙对光的控制性能越强。例如，光子带隙越宽，控制光工作的频带越宽、传输损耗越小，光子晶体谐振器或激光器的品质因子越高，对自发辐射的约束效果越好，光子晶体反射镜的反射效率越高。
然而，理想二维光子晶体中的完全带隙通常要求由较高折射率比的光学材料来构成光子晶体。例如，据非专利文献Oskooi,A.F.,Joannopoulos,J.D.,and Johnson,S.G.:‘Zero-group-velocity modes in chalcogenide holey photonic-crystal fibers’,Opt Express,2009,17,(12),pp.10082-10090和美国专利文献US 2010/0221537 A1所说明，对三角晶格的连接圆柱型理想二维光子晶体，当圆柱杆半径为0.16a(a为光子晶体的晶格常数)，连接杆宽度为0.2a时，在光子晶体中的柱体与填充材料的折射率比为2.8:1时，获得最大5.4％的优化归一化完全光子带隙宽度；当折射率比低于2.6:1时，完全光子带隙在这种理想二维光子晶体中消失。再例如，据非专利文献Cerjan,A.,and Fan,S.:‘Complete photonic band gaps in supercell photonic crystals’,PHYSICAL REVIEW A,2017,96,pp.051802(R)中所说明，对三角晶格的连接六边形环形超元胞二维光子晶体，在折射率比为2.4:1时，获得最大8.6％的优化归一化完全光子带隙宽度；当折射率比低于2.1:1时，完全光子带隙在这种理想二维光子晶体中消失。本公开中的折射率比为构成光子晶体或光子晶体平板的所有材料中的最大折射率值和最小折射率值的比值。
在理想二维光子晶体中，假设光子晶体在第三个维度上是无穷且恒定不变的，因而只 考虑了两个维度的光限制情况，在第三个维度上没有考虑光的限制能力。为了能够在第三个维度上同样获得光限制能力，在理想二维光子晶体的基础上发展出二维光子晶体平板。与第三维假定为无穷且恒定不变的理想二维光子晶体不同，二维光子晶体平板一般由厚的上包层和厚的下包层以及相对较薄的二维光子晶体核心层共同组成三明治结构。对于具有光子带隙的二维光子晶体平板，中间光子晶体核心层中的光在平板平面中的性质主要依赖光子带隙效应限制，而在垂直于光子晶体平板平面方向上的性质主要依赖在光子晶体核心层和上下包层界面处的全反射效应所限制，这样实现了光的全三维限制。从光子能带图上来讲，垂直于光子晶体平面方向上的光限制能力主要通过在光子能带色散图上增加上下包层的光线(锥)来确定，即在包层光线上方的光模式会泄漏到相应的包层中去，只有在两个包层光线共同下方的光模式才会因为全反射效应而被限制在中间的光子晶体核心层内。这样，二维光子晶体平板中的光子带隙要在两个包层光线的共同下方，才能获得空间三维方向上的光限制；与之相对的，理想二维光子晶体没有上下包层，也就没有这个要求。
此外，在二维光子晶体平板中，由于上下包层的引入，特别是当上下包层为不同的材料或者也由光子晶体构成时，光的偏振态不能再严格划分为纯TE或纯TM偏振。然而，考虑到核心层具有相对较薄的厚度和上下包层的有效折射率一般相差很小，这种二维光子晶体平板中的光波具有与TE偏振或TM偏振相类似的性质，因而通常被分为类TE(TE-like或z-even-like)波和类TM(TM-like或z-odd-like)波。从而，对于二维光子晶体平板中的光子带隙，在包层光锥下方的区域中，也可以相应地划分出不支持TE-like模式的TE-like带隙、不支持TM-like模式的TM-like带隙、以及既不支持TE-like模式也不支持TM-like模式的完全光子带隙。TE或TE-like模式是指在平板中心平面上，电场E平行于XY平面的电磁波模式；所述的TM或TM-like模式是指在平板中心平面上，电场E垂直于XY平面(磁场H平行于XY平面)的电磁波模式。
由于二维光子晶体平板本质是三维结构，所以通过先计算其光子能带结构再进一步寻找获得包层光锥下方的完全光子带隙的二维光子晶体平板，非常耗时，且需要消耗很大的计算资源。因此，传统的经验方法是首先计算并分析二维光子晶体平板所对应的理想二维光子晶体的光子能带结构和其规律，如果在其对应的理想二维光子晶体的光子能带结构中能够获得足够宽的完全光子带隙，再过渡到计算二维光子晶体平板的能带结构。传统理论经验认为：与对应的理想二维光子晶体相比，其对应的二维光子晶体平板的光子能带结构所包括的光子带隙具有相似的性质和变化规律；同时，由于二维光子晶体平板需要考虑第三个维度上的光限制，所以在二维光子晶体平板中获取完全光子带隙更加困难，在二维光子晶体平板中能获得的光子带隙的归一化带隙宽度更窄；如果在理想二维光子晶体中，不能得到完全光子带隙或者获得的完全光子带隙很小时，与其对应的二维光子晶体平板中难以获得具有实用价值的完全光子带隙。换言之，在传统理论经验中，若发现某个理想二维光子晶体不具有使用价值的完全光子带隙，即不存在重叠的TM带隙和TE带隙或重叠的TM带隙和TE带隙区域很小，则不会进一步考虑和设计对应的二维光子晶体平板的完全 光子带隙。
例如，据非专利文献arXiv:1704.08374[physics.optics](https://arxiv.org/abs/1704.08374)中所述，在理想二维光子晶体中获得足够宽的完全光子带隙后，开始二维光子晶体平板的设计。当折射率比为2.4:1时，在优化的三角晶格的连接六边形环超元胞理想二维光子晶体中获得了8.6％的归一化完全光子带隙宽度，而对同样的2.4:1的折射率比，在对应的三角晶格六边形环超元胞二维光子晶体平板中，由第7和第8阶能带确定的完全光子带隙仅获得了4.3％的归一化带隙宽度，低于其对应的理想二维光子晶体中获得的归一化完全光子带隙宽度。此外，该具有完全光子带隙的二维光子晶体平板的上下包层均为空气，中间的光子晶体核心层为非连接的环形介质杆，这样的设计意味着中间核心层的环形介质柱没有支撑，空悬在空气中，所以该二维光子晶体平板实际无法制作出来，因而不具有实际应用价值。该文献的作者随后在另一篇非专利文献Cerjan,A.,and Fan,S.:‘Complete photonic band gaps in supercell photonic crystals’,PHYSICAL REVIEW A,2017,96,pp.051802(R)中描述了该类二维光子晶体平板中的一个更现实的设计，但其要求的折射率比进一步提高：在最大折射率比为2.57:1时，在优化的三角晶格的六边形环超元胞二维光子晶体平板中(上包层为空气，下包层为二氧化硅光子晶体)获得了最大5.6％的归一化完全光子带隙宽度，这一结果同样低于该文献图2所示的同等折射率比下对应的连接六边形环二维理想光子晶体的归一化完全光子带隙。而且，在该文献所描述的六边形环超元胞二维光子晶体平板中，下包层中组成二维光子晶体的支撑柱半径小于中间核心层中组成二维光子晶体的环形半径，所以非常难于制作。光子晶体平板中的完全光子带隙的频带宽度一般取为形成完全光子带隙的高阶光子能带曲线的最低频率点和低阶光子能带曲线的最高频率点之间的绝对差；当高阶光子能带曲线的最低频率点在包层光锥低频率点之上时，完全光子带隙的频带宽度取为形成完全光子带隙的包层光锥低频率点和低阶光子能带曲线的最高频率点之间的绝对差。光子晶体平板中的归一化频率宽度则为上述绝对差再除以获得该绝对差的两个频率值的平均值，结果取百分数。
综上可知，现有技术的现状是，在折射率比低于2.4:1的情况下，还没有具有完全光子带隙的二维光子晶体平板的公开；在折射率比2.57:1时，还没有简单易制作的具有完全光子带隙的二维光子晶体平板的公开。在现有技术中，二维光子晶体平板都是在其对应的理想二维光子晶体具有较大完全光子带隙的情况下进行进一步的平板设计而获得的。若发现某个理想二维光子晶体不具有使用价值的完全光子带隙，本领域的技术人员则不会进一步考虑和设计对应的二维光子晶体平板的完全光子带隙。因此，现有技术中未能设计出具有完全光子带隙的折射率比较低的二维光子晶体平板。
发明内容
本发明涉及一种能够在较低折射率比值的情况下实现完全光子带隙的二维光子晶体平板。
根据本发明的一个方面，提供了一种二维光子晶体平板，包括上包层、下包层和位于所述上包层和所述下包层之间的二维光子晶体核心层，其中所述二维光子晶体核心层为有限高的二维光子晶体，由周期排列的多个柱体和填充区域构成，所述柱体由所述二维光子晶体平板中折射率最高的材料形成，所述填充区域包围所述柱体并且由折射率低于所述柱体的折射率的材料形成，所述下包层包括固态支撑结构，所述二维光子晶体平板具有完全光子带隙，其位于所述上包层和所述下包层所确定的包层光线以及所述二维光子晶体平板的类TE模式的最低阶光子能带曲线的下方并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方，并且所述有限高的二维光子晶体所对应的无限高理想二维光子晶体在TM模式的最低阶能带曲线与第二低阶能带曲线之间具有TM偏振态光子带隙。可选的，所述有限高的二维光子晶体所对应的无限高理想二维光子晶体不具有完全光子带隙或不具有最低阶光子能带曲线与第二阶光子能带曲线形成的完全光子带隙或具有不满足预定宽度要求的完全光子带隙。
根据本发明的另一方面，提供一种利用根据本发明第一方面的二维光子晶体平板形成的光器件，所述光器件为在所述二维光子晶体平板中形成点缺陷和/或线缺陷。
根据本发明的另一方面，提供一种设计根据本发明第一方面的二维光子晶体平板的方法，包括：在预定折射率比下计算无限高理想二维光子晶体的光子能带曲线，在所述无限高理想二维光子晶体的光子能带曲线中的最低阶TM模式与第二低阶TM模式之间具有满足第一预定宽度要求的TM光子带隙的情况下，将所述无限高理想二维光子晶体的结构参数作为所述二维光子晶体核心层的初始二维结构参数，以及基于所述二维光子晶体核心层的二维结构初始参数，设计和优化所述二维光子晶体核心层的结构参数以及所述上包层和所述下包层的结构参数，并计算所述二维光子晶体平板的光子能带曲线，使得所述二维光子晶体平板获得满足第二预定宽度要求的完全光子带隙，且所述完全光子带隙位于所述上包层和所述下包层所确定的包层光线以及所述二维光子晶体平板的类TE模式的最低阶光子能带曲线的下方并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方。
根据本发明二维光子晶体平板，在上包层、下包层所确定的包层光线或光锥区域下方，利用位于二维光子晶体平板的类TE模式的最低阶光子能带曲线下方并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方的区域形成完全光子带隙，可以在二维光子晶体平板的最大折射率比较低的情况下形成完全光子带隙，尤其是在折射率比低到对应的无限高理想二维光子晶体不具有完全光子带隙或者不具有可使用的完全光子带隙的情况下形成完全光子带隙。
附图说明
通过下面结合附图对实施例的描述，本发明的这些和/或其他方面、特征和优点将变得更加清楚和容易理解，其中：
图1示出根据本发明实施例的二维光子晶体平板的结构示意图；
图2示出根据本发明实施例的二维光子晶体平板的光子能带图；
图3示出根据本发明实施例的二维光子晶体平板对应的理想二维光子晶体的光子能带图；
图4示出根据本发明实施例的二维光子晶体平板的光子能带图；
图5示出根据本发明实施例的二维光子晶体平板对应的理想二维光子晶体的光子能带图；
图6示出根据本发明实施例的二维光子晶体平板的结构示意图；
图7示出根据本发明实施例的二维光子晶体平板的光子能带图；
图8示出根据本发明实施例的二维光子晶体平板对应的理想二维光子晶体的光子能带图；
图9示出根据本发明实施例的二维光子晶体平板的光子能带图；
图10示出根据本发明实施例的二维光子晶体平板对应的理想二维光子晶体的光子能带图；
图11示出根据本发明实施例的二维光子晶体平板的光子能带图；
图12示出根据本发明实施例的二维光子晶体平板对应的理想二维光子晶体的光子能带图；
图13示出根据本发明实施例的二维光子晶体平板的结构示意图；
图14示出根据本发明实施例的二维光子晶体平板的光子能带图；
图15示出根据本发明实施例的二维光子晶体平板对应的理想二维光子晶体的光子能带图；
图16示出根据本发明实施例的二维光子晶体平板的结构示意图；
图17示出根据本发明实施例的二维光子晶体平板的光子能带图。
具体实施方式
下面将参考本发明的示例性实施例对本发明进行详细描述。然而，本发明不限于这里所描述的实施例，其可以以许多不同的形式来实施。所描述的实施例仅用于使本公开彻底和完整，并全面地向本领域的技术人员传递本发明的构思。所描述的各个实施例的特征可以互相组合或替换，除非明确排除或根据上下文应当排除。
如背景技术部分所说明的，在二维光子晶体平板的现有设计理论经验中，若发现某个理想二维光子晶体不具有使用价值的完全光子带隙，即不存在重叠的TM带隙和TE带隙或重叠的TM带隙和TE带隙区域较小而不具有使用价值，则不会进一步考虑和设计对应的二维光子晶体平板使其具有完全光子带隙。因此，在现有技术中，未能设计出折射率比较低的、具有完全光子带隙的二维光子晶体平板。然而，发明人经过研究发现，这一理论经验为技术偏见，实际上，即使在某个理想二维光子晶体不具有使用价值的完全光子带隙 的情况下，也可以设计出具有较大完全光子带隙的对应二维光子晶体平板。发明人发现在上包层、下包层所确定的包层光线或光锥区域下方，利用位于二维光子晶体平板的类TE模式的最低阶光子能带曲线下方且位于二维光子晶体平板的类TM模式的最低阶光子能带曲线上方的区域可以实现具有较大完全光子带隙的二维光子晶体平板，即使在对应的理想二维光子晶体不具有完全光子带隙的情况下也是如此。从而，本发明可有效地解决在具有较低折射率比的二维光子晶体平板中获得完全光子带隙比较困难的问题，其既可以在现有技术无法获得完全光子带隙的低折射率比范围中获得具有完全光子带隙的二维光子晶体平板，还可以在现有技术虽能获得完全光子带隙但由于折射率比低而导致完全光子带隙很窄的情况下获得更大的完全光子带隙带宽。并且，根据本发明的二维光子晶体平板结构简单、易于制造。
本发明的实施例采用如下设计原理。首先，对于具有TM光子带隙的理想二维光子晶体，其对应的二维光子晶体平板中也容易获得类似的TM-like模式的光子带隙。因此，本发明的实施例首先要求理想二维光子晶体的第一条TM能带(即，TM模式的最低阶能带曲线)和第二条TM能带(即，TM模式的第二低阶能带曲线)能构成TM光子带隙，从而可以在其对应的二维光子晶体平板中较容易地获得类似的第一条TM-like能带(即，类TM模式的最低阶能带曲线)和第二条TM-like能带(即，类TM模式的第二低阶能带曲线)之间的TM-like模式光子带隙。继而，在此基础上，考虑光子晶体通常具有大的偏振色散特性，因此，二维光子晶体平板中的第一条TE-like能带(即，类TE模式的最低阶能带曲线)与第一条TM-like能带相比，通常具有较大的差异性，即间隔很大。例如，在介质柱型的二维光子晶体平板中，第一条光子能带(最低阶能带曲线)一般都是TM-like模式，从而，第一条TE-like模式能带曲线不仅与第一条TM-like模式能带曲线间隔很大并且还会出现在第一条TM-like模式能带曲线的光子能带的上方区域。因此，在第一条TM-like模式能带曲线上既有TM-like的光子带隙，并且和第一条TE-like模式之间也具有较大的间隔，从而可以在上包层、下包层所确定的包层光锥区域下方，在第一条TM-like模式上方、第一条TE-like模式下方形成一个同时不存在TM-like模式和TE-like模式的区域，即完全光子带隙区域。此时，使用满足条件的理想二维光子晶体的结构参数作为二维光子晶体平板的核心层的二维结构初始参数，并基于该二维结构初始参数设计和优化核心层包括厚度在内的结构参数以及包层的结构参数，可以在较低折射率比的情况下形成满足宽度要求的完全光子带隙，例如，该完全光子带隙由最低阶的光子能带曲线和包层光线围成的区域确定，或者由最低阶的光子能带曲线、第二阶的光子能带曲线和包层光线围成的区域确定，在该完全光子带隙的区域中既不存在TM-like模式也不存在TE-like模式。根据本发明的实施例，所述最低阶光子能带曲线为所述二维光子晶体平板的类TM模式的最低阶能带曲线，并且所述第二阶光子能带曲线为所述二维光子晶体平板的类TM模式的第二低阶光子能带曲线，或者为所述二维光子晶体平板的类TE模式的最低阶能带曲线，或者为所述二维光子晶体平板的类TE模式的最低阶能带曲线的一部分和类TM模式的第二 低阶光子能带曲线的一部分形成。
根据上述设计原理，本发明的实施例提供一种二维光子晶体平板。所述二维光子晶体平板包括上包层、下包层和位于所述上包层和所述下包层之间的二维光子晶体核心层。所述二维光子晶体核心层为有限高的二维光子晶体，由周期排列的多个柱体和填充区域构成，所述柱体由所述二维光子晶体平板中折射率最高的材料形成，所述填充区域包围所述柱体并且由折射率低于所述柱体的折射率的材料形成。所述下包层包括固态支撑结构。所述二维光子晶体平板具有完全光子带隙，并且所述二维光子晶体平板的完全光子带隙位于所述上包层和所述下包层所确定的包层光线以及所述二维光子晶体平板的类TE模式的最低阶光子能带曲线的下方，并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方。所述有限高的二维光子晶体所对应的无限高理想二维光子晶体在TM模式的最低阶能带曲线与第二低阶能带曲线之间具有TM偏振态光子带隙。可选的，所述二维光子晶体平板的最大折射率比可以低至对应的无限高理想二维光子晶体不具有完全光子带隙或不具有最低阶光子能带曲线与第二阶(即第二低阶)能带光子曲线形成的完全光子带隙或具有不满足预定宽度要求的完全光子带隙。所述预定宽度可以根据实际应用的需要确定，例如，通常认为小于3％的归一化完全光子带隙宽度不具有使用价值，因此，这里的预定宽度要求可以选定为大于3％的归一化宽度。
根据本发明的上述实施例的二维光子晶体平板，由于在位于上包层、下包层所确定的包层光锥区下方，利用位于二维光子晶体平板的类TE模式的最低阶光子能带曲线下方并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方的区域形成完全光子带隙，从而可以在二维光子晶体平板的最大折射率比较低的情况下形成可使用的完全光子带隙，尤其是在折射率比低到对应的无限高理想二维光子晶体不具有完全光子带隙或者不具有可使用的完全光子带隙的情况下也可以形成可使用的完全光子带隙。例如，根据本发明的实施例，可以在最大折射率比低于2.4甚至低于2.0的情况下实现可用的完全光子带隙。此外，由于下包层包括固态支撑结构，因而所述二维光子晶体平板可以实际制造。例如，若下包层由固态匀质材料构成，该固态匀质材料即为固态支撑结构；若下包层也为二维光子晶体结构，则该二维光子晶体结构中的柱体和/或填充区域为固态材料，从而起到支撑作用。
图1示出了根据本发明实施例的二维光子晶体平板100的结构示意图，其中(a)为三维侧视图，(b)为XY平面的俯视图，(c)为XZ平面的截面图。在二维光子晶体平板100中，上包层101为空气，下包层为二氧化硅102，二维光子晶体核心层103为有限高的二维光子晶体，其由周期排列的氮化硅(Si xN y)柱体以及由空气填充的填充区域构成。Si xN y x和y的取值根据所设计的折射率确定，Si xN y具有形成二维光子晶体平板100的材料中最大的折射率。上包层101、核心层103和下包层102构成三明治结构。在图1中，核心层103的二维光子晶体为三角晶格圆形柱二维光子晶体，如图1(b)所示。
图2是对应于图1的二维光子晶体平板100的一实施例的光子能带图。在该实施例中， 二维光子晶体平板100的主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为2.5，上包层以及填充区域的空气具有最低折射率，其为1，下包层(二氧化硅)的折射率为1.45，因此，最大折射率比为2.5:1；核心层的厚度h为1.9a，Si xN y圆柱体的半径r为0.33a，其中，a为光子晶体的晶格常数，晶格常数a根据适用的电磁波谱频率进行选择。上包层和下包层的厚度可以根据需要设计，通常达到4-10个波长以上即可认为其为无限厚。根据上述结构参数可以计算出如图2所示的光子能带图。在图2中，横轴为波矢，标注为Γ、M、K，纵轴为正规化频率，单位为c/a，其中c为光速，a为光子晶体的晶格常数。如图2所示，其中的灰色均匀阴影区为折射率为1.45的二氧化硅包层的光线所确定的光锥区；实心点实线所示的能带曲线(能带1)为最低阶能带曲线，其为TM-like模式的最低阶能带曲线；方块虚线所示的能带曲线(能带2)为第二阶能带曲线，其为TM-like模式的第二低能带曲线；三角虚线所示的能带曲线(能带3)为第三阶能带曲线，其包含有TE-like模式和TM-like模式，是光锥下包含TE-like模式的最低能带曲线。需要说明的是，在改变平板参数的情况下，上述第二阶能带曲线可能是TM-like模式的第二低能带曲线，也可能是TE-like模式的最低能带曲线，还可能是TM-like模式的第二低能带曲线的一部分和TE-like模式的最低能带曲线的一部分形成。在本发明中，能带图中各光子能带曲线从下至上依次为第一阶(最低阶)、第二阶(第二低阶)……等等。从图2中可以看出，最低阶能带曲线、第二阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示(该带竖线的灰色阴影区与图中空白区重叠的区域为该完全光子带隙区)。在该完全光子带隙区中没有任何光模式，即，既不存在TM-like模式也不存在TE-like模式。此外，可以看出，该完全光子带隙位于含有TE-like模式的最低阶光子能带曲线的能带3的下方，并位于TM-like模式的最低阶光子能带曲线(能带1)上方。通过计算可知，图2所示的光子晶体平板的归一化完全光子带隙宽度为12.83％，从而，在中心波长为1550nm时，带宽约为198nm；在中心波长为650nm时，带宽约为83nm。这样的带宽可以实现多种实用的光器件。
图3是与图2对应的无限高理想二维光子晶体的光子能带图，该无限高理想二维光子晶体的结构参数与图2光子晶体平板核心层的有限高二维光子晶体的结构参数相同，区别仅在于理想二维光子晶体没有包层，且高度为无限大。由于理想二维光子晶体没有包层，因此其光子能带图中没有代表包层光限制的光锥区域。如图3所示，实心点线所示的能带曲线为TM模式能带曲线，空心圆点线所示的能带曲线为TE模式能带曲线。在图示的理想二维光子晶体的能带图中，存在3个TM带隙(如图中阴影区域所示)，但由于折射率比较低(仅有2.5:1)，不存在完全光子带隙，即没有在同一频率范围内同时为TM带隙和TE带隙的区域。图中第一阶(最低的)TM能带和第二阶(第二低的)TM能带之间的归一化带隙宽度为22.33％，被用于在前述二维光子晶体平板中获得完全光子带隙。
由此可以看出，在该实施例中，最大折射率比低至2.5:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带 隙。
根据本发明的实施例，在最大折射率比为2.5:1的情况下，通过改变图1所示的三角晶格二维光子晶体平板中的圆柱半径和核心层高度，可以获得不同的二维光子晶体平板的归一化完全光子带隙宽，从而可以优化二维光子晶体平板的结构参数，如下表1所示：
表1
Figure PCTCN2021079243-appb-000001
图4是对应于图1的二维光子晶体平板100的另一实施例的光子能带图。在该实施例中，最大折射率比进一步降低，降低为2:1，其主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为2.0，上包层以及填充区域的空气具有最低折射率，其为1，下包层(二氧化硅)的折射率为1.45，因此，最大折射率比为2:1；核心层的厚度h为3.0a，Si xN y圆柱体的半径r为0.33a。根据上述结构参数可以计算出如图4所示的光子能带图。如图4所示，灰色均匀阴影区为二氧化硅包层的光线所确定的光锥区；实线所示的能带曲线(能带1)为最低阶能带曲线，其为TM-like模式的最低阶能带曲线；点虚线所示的能带曲线(能带2)为第二阶能带曲线，其为TE-like模式的最低阶能带曲线，其部分模式在光锥中。从图4中可以看出，最低阶能带曲线、第二阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示。该完全光子带隙位于TE-like模式的最低阶光子能带曲线下方，并位于TM-like模式的最低阶光子能带曲线上方。通过计算可知，图2所示的光子晶体平板的归一化完全光子带隙宽度为3.68％，从而，在中心波长为1550nm时，带宽约为57nm；在中心波长为650nm时，带宽约为23.9nm。这样的带宽可以实现多种实用的光器件。
图5是与图4对应的无限高理想二维光子晶体的光子能带图，该无限高理想二维光子晶体的结构参数与图4光子晶体平板核心层的有限高二维光子晶体的结构参数相同，区别仅在于理想二维光子晶体没有包层，且高度为无限大。由于理想二维光子晶体没有包层，因此其光子能带图中没有代表包层光限制的光锥区域。如图5所示，实心点线所示的能带曲线为TM模式能带曲线，空心圆点线所示的能带曲线为TE模式能带曲线。在图示的理想二维光子晶体的能带图中，存在2个TM带隙(如图中阴影区域所示)，但由于折射率 比较低(仅有2:1)，不存在完全光子带隙。图中第一阶TM能带和第二阶TM能带之间的归一化带隙宽度为16.63％，被用于在前述二维光子晶体平板中获得完全光子带隙。
由此可以看出，在该实施例中，最大折射率比低至2:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带隙。
根据本发明的实施例，在最大折射率比为2:1的情况下，通过改变图1所示的三角晶格二维光子晶体平板中的圆柱半径和核心层高度，可以获得不同的二维光子晶体平板的归一化完全光子带隙宽，如下表2所示：
表2
Figure PCTCN2021079243-appb-000002
在以上实施例中，上包层和下包层都为折射率低于二维光子晶体平板中最大折射率的材料形成的均质层。下面给出上包层和下包层中至少一个也为二维光子晶体结构的实施例。根据本发明的实施例，所述上包层和/或所述下包层可以为由折射率低于所述二维光子晶体平板中最大折射率的多种材料组成的二维光子晶体包层。可选的，所述上包层和/或所述下包层的二维光子晶体可以具有和所述二维光子晶体核心层相同的晶格结构。所述下包层的二维光子晶体中的柱体半径可以大于或者等于所述二维光子晶体核心层的柱体半径。所述上包层的二维光子晶体中的柱体半径可以小于或者等于所述二维光子晶体核心层的柱体半径。
图6示出了根据本发明另一实施例的二维光子晶体平板600的结构示意图，其中(a)为三维侧视图，(b)为XY平面的俯视图，(c)为XZ平面的截面图。在该实施例中，上包层601为均质材料空气，下包层602为由有限高的圆柱形二氧化硅和空气形成的二维光子晶体包层，核心层603为由有限高的圆柱形氮化硅(Si xN y)和空气形成的二维光子晶体核心层。Si xN y具有形成二维光子晶体平板600的材料中最大的折射率，下包层602的柱体材料二氧化硅的折射率低于上述最大折射率。在图6中，核心层603和下包层602具有相同的晶格以及柱体形状和半径，都为三角晶格圆形柱二维光子晶体，如图6(b)所示。
图7是对应于图6的二维光子晶体平板600的一实施例的光子能带图。在该实施例中，二维光子晶体平板600的主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为1.8，上包层以及填充区域的空气具有最低折射率，其为1，下包层二氧化硅柱体的折射率为1.45，因此，最大折射率比为1.8:1；核心层的厚度h为2.1a，Si xN y圆柱体和二氧化硅的半径r均为0.33a。上包层和下包层的厚度可以根据需要设计，通常达到4-10个 波长以上即可认为其为无限厚。根据上述结构参数可以计算出如图7所示的光子能带图。如图7所示，灰色均匀阴影区为下包层的光线所确定的光锥区；实点实线所示的能带曲线(能带1)为最低阶能带曲线，其为TM-like模式的最低阶能带曲线；圆点虚线所示的能带曲线(能带2)为第二阶能带曲线，其为TE-like模式的最低阶能带曲线，并完全在光锥区中。从图7中可以看出，最低阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示。在包层为二维光子晶体包层的情况下，包层光线取二维光子晶体包层最低阶的能带曲线。此外，可以看出，该完全光子带隙位于TE-like模式的最低阶光子能带曲线下方，并位于TM-like模式的最低阶光子能带曲线上方。通过计算可知，图7所示的光子晶体平板的归一化完全光子带隙宽度为3.17％，从而，在中心波长为1550nm时，带宽约为49nm；在中心波长为650nm时，带宽约为20nm。这样的带宽可以实现多种实用的光器件。
图8是与图7的核心层对应的无限高理想二维光子晶体的光子能带图，该无限高理想二维光子晶体的结构参数与图7光子晶体平板核心层的有限高二维光子晶体的结构参数相同，区别仅在于理想二维光子晶体没有包层，且高度为无限大。由于理想二维光子晶体没有包层，因此其光子能带图中没有代表包层光限制的光锥区域。如图8所示，实心点虚线所示的能带曲线为TM模式能带曲线，圆点实线所示的能带曲线为TE模式能带曲线。在图示的理想二维光子晶体的能带图中，存在2个TM带隙(如图中阴影区域所示)，但由于折射率比较低(仅有1.8:1)，不存在完全光子带隙。图中第一阶TM能带和第二阶TM能带之间的归一化带隙宽度为13.13％，被用于在前述二维光子晶体平板中获得完全光子带隙。
由此可以看出，在该实施例中，最大折射率比低至1.8:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带隙。
根据本发明的实施例，在最大折射率比为1.8:1的情况下，通过改变图6所示的三角晶格二维光子晶体平板中的圆柱半径(核心层和包层的圆柱半径相同)和核心层高度，可以获得不同的二维光子晶体平板的归一化完全光子带隙宽，如下表3所示：
表3
Figure PCTCN2021079243-appb-000003
图9是对应于图6的二维光子晶体平板600的另一实施例的光子能带图。在该实施例 中，二维光子晶体平板600的主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为2.4，上包层以及填充区域的空气具有最低折射率，其为1，下包层二氧化硅柱体的折射率为1.45，因此，最大折射率比为2.4:1；核心层的厚度h为1.4a，Si xN y圆柱体和二氧化硅圆柱体的半径r为0.21a。根据上述结构参数可以计算出如图9所示的光子能带图。如图9所示，灰色均匀阴影区为下包层的光线(取该二维光子晶体包层能带曲线的最低一条能带曲线为光线)所确定的光锥区；实心点实线所示的能带曲线为最低阶能带曲线(能带1)，其为TM-like模式的最低阶能带曲线；圆点虚线所示的能带曲线为第二阶能带曲线(能带2)，其为TE-like模式的最低阶能带曲线，且完全位于包层光锥区中。从图9中可以看出，最低阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示。该完全光子带隙位于TE-like模式的最低阶光子能带曲线下方，并位于TM-like模式的最低阶光子能带曲线上方。通过计算可知，图9所示的光子晶体平板的归一化完全光子带隙宽度为12.85％，从而，在中心波长为1550nm时，带宽约为199nm；在中心波长为650nm时，带宽约为83nm。这样的带宽可以实现多种实用的光器件。
图10是与图9的核心层对应的无限高理想二维光子晶体的光子能带图，该无限高理想二维光子晶体的结构参数与图9光子晶体平板核心层的有限高二维光子晶体的结构参数相同，区别仅在于理想二维光子晶体没有包层，且高度为无限大。由于理想二维光子晶体没有包层，因此其光子能带图中没有代表包层光限制的光锥区域。如图10所示，实点虚线所示的能带曲线为TM模式能带曲线，点实线所示的能带曲线为TE模式能带曲线。在图示的理想二维光子晶体的能带图中，存在1个TM带隙(如图中阴影区域所示)，但由于折射率比较低(仅有2.4:1)，不存在完全光子带隙。图中第一阶TM能带和第二阶TM能带之间的归一化带隙宽度为31.37％，被用于在前述二维光子晶体平板中获得完全光子带隙。
由此可以看出，在该实施例中，最大折射率比低至2.4:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带隙。
根据本发明的实施例，在最大折射率比为2.4:1的情况下，通过改变图6所示的三角晶格二维光子晶体平板中的圆柱半径(核心层和包层的圆柱半径相同)和核心层高度，可以获得不同的二维光子晶体平板的归一化完全光子带隙宽，如下表4所示：
表4
Figure PCTCN2021079243-appb-000004
图11是对应于图6的二维光子晶体平板600的另一实施例的光子能带图。在该实施例中，二维光子晶体平板600的主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为2.57，上包层以及填充区域的空气具有最低折射率，其为1，下包层二氧化硅柱体的折射率为1.45，因此，最大折射率比为2.57:1；核心层的厚度h为1.25a，Si xN y圆柱体和二氧化硅圆柱体的半径r为0.21a。根据上述结构参数可以计算出如图11所示的光子能带图。如图11所示，灰色均匀阴影区为下包层的光线(取该二维光子晶体包层能带曲线的最低一条能带曲线为光线)所确定的光锥区；实点实线所示的能带曲线(能带1)为最低阶能带曲线，其为TM-like模式的最低阶能带曲线；空心方块虚线所示的能带曲线(能带2)为第二阶能带曲线，其为TE-like模式的最低阶能带曲线，且完全位于包层光锥区中。从图11中可以看出，最低阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示。该完全光子带隙位于TE-like模式的最低阶光子能带曲线下方，并位于TM-like模式的最低阶光子能带曲线上方。通过计算可知，图11所示的光子晶体平板的归一化完全光子带隙宽度为13.65％，从而，在中心波长为1550nm时，带宽约为211nm；在中心波长为650nm时，带宽约为88nm。这样的带宽可以实现多种实用的光器件。
图12是与图11的核心层对应的无限高理想二维光子晶体的光子能带图，该无限高理想二维光子晶体的结构参数与图11光子晶体平板核心层的有限高二维光子晶体的结构参数相同，区别仅在于理想二维光子晶体没有包层，且高度为无限大。由于理想二维光子晶体没有包层，因此其光子能带图中没有代表包层光限制的光锥区域。如图12所示，实点虚线所示的能带曲线为TM模式能带曲线，空心点实线所示的能带曲线为TE模式能带曲线。在图示的理想二维光子晶体的能带图中，存在1个TM带隙(如图中不带斜线的阴影区域所示)，一个TE带隙(如图中带斜线的阴影区域所示)，但由于折射率比较低(仅有2.57:1)，不存在完全光子带隙。图中第一阶TM能带和第二阶TM能带之间的归一化带隙宽度为34.84％，被用于在前述二维光子晶体平板中获得完全光子带隙。
由此可以看出，在该实施例中，最大折射率比低至2.57:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带隙。
根据本发明的实施例，在最大折射率比为2.57:1的情况下，通过改变图6所示的三角晶格二维光子晶体平板中的圆柱半径(核心层和包层的圆柱半径相同)和核心层高度，可以获得不同的二维光子晶体平板的归一化完全光子带隙宽，如下表5所示：
表5
Figure PCTCN2021079243-appb-000005
Figure PCTCN2021079243-appb-000006
图13示出了根据本发明另一实施例的二维光子晶体平板1300的结构示意图，其中(a)为三维侧视图，(b)为XY平面的俯视图，(c)为XZ平面的截面图。在该实施例中，上包层1301为均质材料空气，下包层1302为由有限高的圆柱形二氧化硅和空气形成的二维光子晶体包层，核心层1303为由有限高的圆柱形氮化硅(Si xN y)和空气形成的二维光子晶体核心层。Si xN y具有形成二维光子晶体平板1300的材料中最大的折射率，下包层1302的柱体材料的折射率低于上述最大折射率。在图13中，核心层1303和下包层1302具有相同的晶格以及柱体形状，都为二维光子晶体为三角晶格圆形柱二维光子晶体，但下包层1302的柱体半径大于核心层1303的柱体半径，如图13(b)和(c)所示。
图14是对应于图13的二维光子晶体平板1300的一实施例的光子能带图。在该实施例中，二维光子晶体平板1300的主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为2，上包层以及填充区域的空气具有最低折射率，其为1，下包层二氧化硅柱体的折射率为1.45，因此，最大折射率比为2:1；核心层的厚度h为1.8a，Si xN y圆柱体的半径为0.28a，二氧化硅的半径为0.33a。上包层和下包层的厚度可以根据需要设计，通常达到4-10个波长以上即可认为其为无限厚。根据上述结构参数可以计算出如图14所示的光子能带图。如图14所示，灰色均匀阴影区为下包层的光线(取该二维光子晶体包层能带曲线的最低一条能带曲线为光线)所确定的光锥区；点实线所示的能带曲线(能带1)为最低阶能带曲线，其为TM-like模式的最低阶能带曲线；点虚线所示的能带曲线(能带2)为第二阶能带曲线，其为TE-like模式的最低阶能带曲线，并完全位于光锥区中。从图14中可以看出，最低阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示。此外，可以看出，该完全光子带隙位于TE-like模式的最低阶光子能带曲线下方，并位于TM-like模式的最低阶光子能带曲线上方。通过计算可知，图14所示的光子晶体平板的归一化完全光子带隙宽度为4.74％，从而，在中心波长为1550nm时，带宽约为73nm；在中心波长为650nm时，带宽约为31nm。这样的带宽可以实现多种实用的光器件。
图15是与图14的核心层对应的无限高理想二维光子晶体的光子能带图，该无限高理想二维光子晶体的结构参数与图14光子晶体平板核心层的有限高二维光子晶体的结构参数相同，区别仅在于理想二维光子晶体没有包层，且高度为无限大。由于理想二维光子晶体没有包层，因此其光子能带图中没有代表包层光限制的光锥区域。如图15所示，实心点虚线所示的能带曲线为TM模式能带曲线，空心点实线所示的能带曲线为TE模式能带曲线。在图示的理想二维光子晶体的能带图中，存在2个TM带隙(如图中阴影区域所示)，但由于折射率比较低(仅有2:1)，不存在完全光子带隙。图中第一阶TM能带和第二阶 TM能带之间的归一化带隙宽度为21.08％，被用于在前述二维光子晶体平板中获得完全光子带隙。
由此可以看出，在该实施例中，最大折射率比低至2:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带隙。
图16示出了根据本发明另一实施例的二维光子晶体平板1600的结构示意图，其中(a)为三维侧视图，(b)为XY平面的俯视图，(c)为XZ平面的截面图。在该实施例中，上包层1601和下包层1602均为二维光子晶体包层，各自由有限高的圆柱形二氧化硅和空气形成；核心层1603为由有限高的圆柱形氮化硅(Si xN y)和空气形成的二维光子晶体核心层。Si xN y具有形成二维光子晶体平板1600的材料中最大的折射率，上包层1601和下包层1602的柱体材料的折射率低于上述最大折射率。在图16中，上包层1601、核心层1603和下包层1602具有相同的晶格以及柱体形状，都为二维光子晶体为三角晶格圆形柱二维光子晶体，且上包层1601的柱体半径等于核心层1603的柱体半径，但小于下包层1602的柱体半径，如图16(b)和(c)所示。
图17是对应于图16的二维光子晶体平板1600的一实施例的光子能带图。在该实施例中，二维光子晶体平板1600的主要结构参数为：核心层的柱体材料(Si xN y)具有最高折射率，其为2，填充区域的空气具有最低折射率，其为1，上包层和下包层二氧化硅柱体的折射率为1.45，因此，最大折射率比为2:1；核心层的厚度h为1.8a，上包层二氧化硅的半径和Si xN y圆柱体的半径为0.28a，下包层二氧化硅的半径为0.33a。上包层和下包层的厚度可以根据需要设计，通常达到4-10个波长以上即可认为其为无限厚。根据上述结构参数可以计算出如图17所示的光子能带图。如图17所示，灰色均匀阴影区为下包层的光线(取该上下二维光子晶体包层能带曲线的最低一条能带曲线为光线)所确定的光锥区；实心点实线所示的能带曲线(能带1)为最低阶能带曲线，其为TM-like模式的最低阶能带曲线；空心点虚线所示的能带曲线(能带2)为第二阶的能带曲线，其为TE-like模式的最低阶能带曲线，并几乎完全位于光锥区中。从图17中可以看出，最低阶能带曲线和包层光线共同确定出一完全光子带隙区，如图中带竖线的灰色阴影区所示。此外，可以看出，该完全光子带隙位于TE-like模式的最低阶光子能带曲线下方，并位于TM-like模式的最低阶光子能带曲线上方。通过计算可知，图17所示的光子晶体平板的归一化完全光子带隙宽度为5.87％，从而，在中心波长为1550nm时，带宽约为91nm；在中心波长为650nm时，带宽约为38nm。图17的核心层对应的无限高理想二维光子晶体与图14的核心层对应的无限高理想二维光子晶体相同，因此其光子能带图同样如图15所示。
由此可以看出，在该实施例中，最大折射率比低至2:1，对应的无限高理想二维光子晶体不具有完全光子带隙，但所述二维光子晶体平板仍然可以获得较大的完全光子带隙。
根据本发明的实施例，还提供一种利用上述二维光子晶体平板形成的光器件，所述光器件为在所述二维光子晶体平板中形成点缺陷和/或线缺陷。例如，在二维光子晶体平板中引入线缺陷可以形成光波导，在二维光子晶体平板中引入点缺陷可以形成谐振器，或者 二维光子晶体平板中引入点缺陷和线缺陷可以形成功能更强大的光器件。
根据本发明的实施例，还提供一种设计根据本发明实施例的二维光子晶体平板的方法。在该方法中，首先在预定折射率比中计算无限高理想二维光子晶体的光子能带曲线，从所计算的理想二维光子晶体中选择光子能带满足要求的理想二维光子晶体作为设计二维光子晶体平板的基础。根据本发明的实施例一般应用在折射率比较低的情况下，设计开始前可以根据设计所应用的场景以及材料系统确定预定折射率比，在该在预定折射率比中计算理想二维光子晶体的光子能带曲线。具体的，在所述无限高理想二维光子晶体的光子能带曲线中的最低阶TM模式与第二低阶TM模式之间具有满足第一预定宽度要求的TM光子带隙的情况下，将所述无限高理想二维光子晶体的结构参数作为所述二维光子晶体核心层的初始二维结构参数。这里的第一预定宽度要求可以根据具体应用的要求而设定，例如，其可以是要求归一化光子带隙大于3％，10％等，以便在二维光子平板中获得满足要求的完全光子带隙。一般情况下，第一预定宽度要求与最终要求的完全光子带隙类似，或比其略宽。在找到某个理想二维光子晶体的结构参数满足第一预定带宽要求的情况下，可以将该理想二维光子晶体的结构参数作为所设计的二维光子晶体平板核心层的初始二维结构参数。二维结构参数包括二维光子晶体的晶格结构；柱体的材料或折射率、形状、平面尺寸(例如半径)；以及填充区域的材料或折射率。接着，基于所述二维光子晶体核心层的二维结构初始参数，设计和优化所述二维光子晶体核心层的包括厚度在内的结构参数以及所述上包层和所述下包层的结构参数，并计算所述二维光子晶体平板的光子能带曲线，使得所述二维光子晶体平板获得满足第二预定宽度要求的完全光子带隙，且所述完全光子带隙位于所述上包层和所述下包层所确定的包层光线以及所述二维光子晶体平板的类TE模式的最低阶光子能带曲线的下方并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方。在确定了二维光子晶体核心层的初始二维结构参数后，还需要进一步确定和优化核心层和包层的结构参数。核心层的结构参数除了包括上述二维结构参数之外还包括核心层的厚度。特别地，对于二维光子晶体核心层的二维结构参数的优化可以围绕初始二维结构参数对其周围的参数数值进行计算和比较。核心层的厚度以及包层的结构可以根据具体的应用予以确定，例如，选择适用的材料，尺寸。此外，可以对多种参数进行计算以确定优化的参数，如上文中各个表格所示，改变相应的尺寸可以获得优化的完全光子带隙宽度。通过设计和优化各个参数，最终获得具有满足第二预定宽度要求的完全光子带隙的二维光子晶体平板。第二预定宽度要求可以根据所设计的光器件的带宽要求予以确定。
综上所述，根据本发明的实施例，能够在折射率比较低的情况下形成具有完全光子带隙的二维光子晶体平板，从而可以大大促进诸如基于二维光子晶体平板的完全光子带隙的在更多的电磁频谱中实现光反射镜、光谐振器、光波导、光探测器、光发射器件、太阳能电池等光器件，以及更广泛地应用于光通信、光传感、光照明和能源光子等领域；并且使得可以选择更多适应的光学材料来制作具有完全光子带隙的二维光子晶体平板，大大丰富 了二维光子晶体平板器件设计的空间，扩展了二维光子晶体平板光子带隙器件的应用范围。
本领域技术人员应该理解，上述的具体实施例仅是例子而非限制，可以根据设计需求和其它因素对本发明的实施例进行各种修改、组合、部分组合和替换。例如，二维光子晶体平板中的柱状不限于圆柱，可以是任何形状的柱体，例如，三角柱，方柱，其它多边形柱等不同形状。用于核心层柱体的高折射率材料不限于氮化硅，例如可以选自硅、锗、氮化硅、氧氮化硅、砷化镓、磷化铟、氧化钛、或这些材料的化合物或混合物，或者玻璃，或者塑料等光学或电磁聚合物；用于包层或填充区的低折射率材料可以选自氮化硅、氧氮化硅、二氧化硅、空气等，只要能满足设定的折射率比即可。

Claims (10)

  1. 一种二维光子晶体平板，包括上包层、下包层和位于所述上包层和所述下包层之间的二维光子晶体核心层，其中
    所述二维光子晶体核心层为有限高的二维光子晶体，由周期排列的多个柱体和填充区域构成，所述柱体由所述二维光子晶体平板中折射率最高的材料形成，所述填充区域包围所述柱体并且由折射率低于所述柱体的折射率的材料形成，
    所述下包层包括固态支撑结构，
    所述二维光子晶体平板具有完全光子带隙，其位于所述上包层和所述下包层所确定的包层光线以及所述二维光子晶体平板的类TE模式的最低阶光子能带曲线的下方，并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方，并且
    所述有限高的二维光子晶体所对应的无限高理想二维光子晶体在TM模式的最低阶能带曲线与第二低阶能带曲线之间具有TM偏振态光子带隙。
  2. 如权利要求1所述的二维光子晶体平板，其中
    所述无限高理想二维光子晶体不具有完全光子带隙或不具有最低阶光子能带曲线与第二阶能带光子曲线形成的完全光子带隙或具有不满足预定宽度要求的完全光子带隙。
  3. 如权利要求1或2所述的二维光子晶体平板，其中
    所述二维光子晶体平板的完全光子带隙由最低阶光子能带曲线和包层光线围成的区域确定，或者由最低阶光子能带曲线、第二阶光子能带曲线和包层光线围成的区域确定。
  4. 如权利要求3所述的二维光子晶体平板，其中
    所述最低阶光子能带曲线为所述二维光子晶体平板的类TM模式的最低阶能带曲线，并且
    所述第二阶光子能带曲线为所述二维光子晶体平板的类TM模式的第二低阶光子能带曲线，或者为所述二维光子晶体平板的类TE模式的最低阶能带曲线，或者由所述二维光子晶体平板的类TE模式的最低阶能带曲线的一部分和类TM模式的第二低阶光子能带曲线的一部分形成。
  5. 如权利要求1或2所述的二维光子晶体平板，其中
    形成所述二维光子晶体平板的材料的最大折射率比低于2.4。
  6. 如权利要求1或2所述的二维光子晶体平板，其中
    所述上包层和/或所述下包层为由折射率低于所述二维光子晶体平板中最大折射率的多种材料组成的二维光子晶体包层。
  7. 如权利要求6所述的二维光子晶体平板，其中
    所述上包层和/或所述下包层的二维光子晶体具有和所述二维光子晶体核心层相同的晶格结构，
    所述下包层的二维光子晶体中的柱体半径大于或者等于所述二维光子晶体核心层的柱 体半径，并且
    所述上包层的二维光子晶体中的柱体半径小于或者等于所述二维光子晶体核心层的柱体半径。
  8. 如权利要求1或2所述的二维光子晶体平板，其中
    所述上包层和/或所述下包层为折射率低于所述二维光子晶体平板中最大折射率的材料形成的均质层。
  9. 一种利用如权利要求1-8中的任一项所述的二维光子晶体平板形成的光器件，所述光器件为在所述二维光子晶体平板中形成点缺陷和/或线缺陷。
  10. 一种设计如权利要求1-8中的任一项所述的二维光子晶体平板的方法，包括：
    在预定折射率比下计算无限高理想二维光子晶体的光子能带曲线，
    在所述无限高理想二维光子晶体的光子能带曲线中的最低阶TM模式与第二低阶TM模式之间具有满足第一预定宽度要求的TM光子带隙的情况下，将所述无限高理想二维光子晶体的结构参数作为所述二维光子晶体核心层的二维结构初始参数，以及
    基于所述二维光子晶体核心层的二维结构初始参数，设计和优化所述二维光子晶体核心层的结构参数以及所述上包层和所述下包层的结构参数，并计算所述二维光子晶体平板的光子能带曲线，使得所述二维光子晶体平板获得满足第二预定宽度要求的完全光子带隙，且所述完全光子带隙位于所述上包层和所述下包层所确定的包层光线以及所述二维光子晶体平板的类TE模式的最低阶光子能带曲线的下方并位于所述二维光子晶体平板的类TM模式的最低阶光子能带曲线上方。
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