CN111308582B

CN111308582B - Two-dimensional photonic crystal slab, design method and optical device using the slab

Info

Publication number: CN111308582B
Application number: CN202010151013.4A
Authority: CN
Inventors: 侯金; 杨春勇; 陈少平
Original assignee: South Central University for Nationalities
Current assignee: South Central Minzu University
Priority date: 2020-03-06
Filing date: 2020-03-06
Publication date: 2021-10-01
Anticipated expiration: 2040-03-06
Also published as: WO2021175310A1; CN111308582A

Abstract

The invention relates to a two-dimensional photonic crystal flat plate, a design method and an optical device using the flat plate. The two-dimensional photonic crystal flat plate comprises an upper cladding layer, a lower cladding layer and a two-dimensional photonic crystal core layer positioned between the upper cladding layer and the lower cladding layer. The two-dimensional photonic crystal core layer is a two-dimensional photonic crystal with limited height. The two-dimensional photonic crystal slab has a complete photonic band gap, is positioned below the cladding light rays determined by the upper cladding and the lower cladding and the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab and is positioned above the lowest-order photonic band curve of the TM-like mode, and the infinite-height ideal two-dimensional photonic crystal corresponding to the finite-height two-dimensional photonic crystal has a photonic band gap of a TM polarization state between the lowest-order energy band curve of the TM mode and the second lower-order energy band curve. The two-dimensional photonic crystal slab can form a complete photonic band gap with a relatively low maximum refractive index.

Description

Two-dimensional photonic crystal slab, design method and optical device using the slab

Technical Field

The present invention relates to a two-dimensional photonic crystal slab, a method for designing the same, and an optical device formed by using the two-dimensional photonic crystal slab, and more particularly, to a two-dimensional photonic crystal slab that forms a complete photonic band gap for electromagnetic waves of a specific wavelength range, and an optical device such as an optical waveguide and a resonator formed by using the two-dimensional photonic crystal slab.

Background

Photonic band gap phenomena in photonic crystals can prevent electromagnetic waves, such as light, within a certain frequency range from propagating in the periodic structure of the photonic crystal. The introduction of suitable defects in a photonic crystal having a photonic band gap will produce a specific defect pattern in the photonic band gap region, in which only electromagnetic waves of a specific frequency corresponding to this pattern can appear. In general, point defects are formed in a photonic crystal to produce optical devices such as resonators, line defects are formed to produce optical devices such as waveguides, and both point and line defects can be formed to produce optical devices with greater functionality.

According to the difference of the light polarization control capability, the photonic band gap types of the ideal two-dimensional photonic crystal can be divided into three types: a TE bandgap that does not support TE modes, a TM bandgap that does not support TM modes, and a full photonic bandgap that does not support both TE and TM modes. The complete photonic band gap can limit light of two polarizations simultaneously, so that the light limiting capability is stronger, and optical devices related to various polarizations can be designed on the basis of the complete photonic band gap. Generally, the wider the photonic band gap width, the more controllable the photonic band gap has to the light. For example, the wider the photonic band gap, the wider the band in which the control light operates, the smaller the transmission loss, the higher the quality factor of the photonic crystal resonator or laser, the better the confinement effect on the spontaneous emission, and the higher the reflection efficiency of the photonic crystal mirror.

However, a complete bandgap in an ideal two-dimensional photonic crystal typically requires that the photonic crystal be constructed of optical materials with a high refractive index ratio. For example, as described in non-patent documents Oskooi, a.f., Joannopoulos, j.d., and Johnson, s.g.: Zero-group-chromaticity modules in a crystal halogen photonic-crystal fibers', Opt Express,2009,17, (12), pp.10082-10090, and U.S. patent document US 2010/0221537 a1, for a connected cylindrical ideal two-dimensional photonic crystal of a triangular lattice, an optimized fully normalized photonic band gap width of at most 5.4% is obtained when the rod radius is 0.16a (a is the lattice constant of the photonic crystal) and the rod width is 0.2a, at a refractive index ratio of the column to the filler material in the photonic crystal of 2.8: 1; when the refractive index ratio is below 2.6:1, the complete photonic band gap disappears in this ideal two-dimensional photonic crystal. For another example, as described in non-patent documents Cerjan, A., and Fan, S.: Complete photonic bands and gates in supercell photonic crystals', PHYSICAL REVIEW A,2017,96, pp.051802(R), an optimized normalized Complete photonic band gap width of 8.6% at a refractive index ratio of 2.4:1 is obtained for a connected hexagonal annular superlattice two-dimensional photonic crystal of a triangular lattice; when the refractive index ratio is lower than 2.1:1, the complete photonic band gap disappears in such an ideal two-dimensional photonic crystal. The refractive index ratio in the present disclosure is the ratio of the maximum refractive index value and the minimum refractive index value in all materials constituting the photonic crystal or the photonic crystal slab.

In an ideal two-dimensional photonic crystal, the photonic crystal is assumed to be infinite and constant in the third dimension, so that only the light confinement in two dimensions is considered, and the light confinement in the third dimension is not considered. In order to obtain the optical confinement capability in the third dimension, a two-dimensional photonic crystal slab is developed on the basis of an ideal two-dimensional photonic crystal. Unlike an ideal two-dimensional photonic crystal with infinite and constant third-dimension assumption, the two-dimensional photonic crystal slab generally has a sandwich structure composed of a thick upper cladding layer, a thick lower cladding layer and a relatively thin two-dimensional photonic crystal core layer. For a two-dimensional photonic crystal panel with photonic band gaps, the properties of light in the middle photonic crystal core layer in the panel plane are mainly limited by the photonic band gap effect, and the properties in the direction perpendicular to the photonic crystal panel plane are mainly limited by the total reflection effect at the interfaces of the photonic crystal core layer and the upper and lower cladding layers, so that the full three-dimensional limitation of light is realized. From the photonic band diagram, the light confinement in the direction perpendicular to the plane of the photonic crystal is mainly determined by adding light rays (cones) of the upper and lower cladding layers to the photonic band dispersion diagram, i.e., the optical mode above the cladding light rays leaks into the corresponding cladding layer, and the optical mode below the two cladding light rays together is confined in the central photonic crystal core layer due to the total reflection effect. Therefore, the photonic band gap in the two-dimensional photonic crystal flat plate is under the common part of the two cladding light rays, and the light limitation in the three-dimensional direction of the space can be obtained; in contrast, an ideal two-dimensional photonic crystal does not have upper and lower cladding layers, and does not have this requirement.

Furthermore, in a two-dimensional photonic crystal slab, due to the introduction of the upper and lower cladding layers, especially when the upper and lower cladding layers are different materials or also composed of photonic crystals, the polarization state of light can not be strictly classified as pure TE or pure TM polarization. However, considering that the core layer has a relatively thin thickness and the effective refractive indices of the upper and lower cladding layers generally differ little, the optical wave in such a two-dimensional photonic crystal slab has properties similar to those of TE polarization or TM polarization, and is thus generally classified into TE-like (or z-even-like) waves and TM-like (or z-odd-like) waves. Therefore, for the photonic band gap in the two-dimensional photonic crystal flat plate, in the region below the cladding light cone, a TE-like band gap which does not support a TE-like mode, a TM-like band gap which does not support a TM-like mode, and a complete photonic band gap which does not support either the TE-like mode or the TM-like mode can be correspondingly divided. The TE or TE-like mode refers to an electromagnetic wave mode that an electric field E is parallel to an XY plane on the central plane of the flat plate; the TM or TM-like mode refers to an electromagnetic wave mode that an electric field E is perpendicular to an XY plane (a magnetic field H is parallel to the XY plane) on a central plane of a flat plate.

Since the two-dimensional photonic crystal slab is essentially of a three-dimensional structure, the two-dimensional photonic crystal slab which obtains the complete photonic band gap below the cladding light cone is further searched by calculating the photonic band structure of the two-dimensional photonic crystal slab, which is time-consuming and needs to consume large computing resources. Therefore, the traditional empirical method is to calculate and analyze the photonic band structure of the ideal two-dimensional photonic crystal corresponding to the two-dimensional photonic crystal slab and the rule thereof, and if a complete photonic band gap with sufficient width can be obtained in the photonic band structure of the ideal two-dimensional photonic crystal corresponding to the photonic band structure, the calculation of the energy band structure of the two-dimensional photonic crystal slab is performed. The traditional theoretical experience considers that: compared with the corresponding ideal two-dimensional photonic crystal, the photonic band gap included in the photonic band structure of the corresponding two-dimensional photonic crystal flat plate has similar properties and change rules; meanwhile, because the two-dimensional photonic crystal panel needs to consider the light limitation in the third dimension, it is more difficult to obtain the complete photonic band gap in the two-dimensional photonic crystal panel, and the normalized band gap width of the photonic band gap which can be obtained in the two-dimensional photonic crystal panel is narrower; if a complete photonic band gap cannot be obtained or is obtained only in a small amount in an ideal two-dimensional photonic crystal, it is difficult to obtain a complete photonic band gap having a practical value in a two-dimensional photonic crystal slab corresponding thereto. In other words, in conventional theoretical experience, if an ideal two-dimensional photonic crystal is found to have no useful full photonic band gap, i.e., there is no overlapping TM band gap and TE band gap or the overlapping TM band gap and TE band gap regions are small, the full photonic band gap of the corresponding two-dimensional photonic crystal slab will not be considered and designed further.

For example, as described in non-patent document arXiv:1704.08374[ physics. optics ] (https:// arXiv. org/abs/1704.08374), after a sufficiently wide complete photonic band gap is obtained in an ideal two-dimensional photonic crystal, the design of a two-dimensional photonic crystal slab is started. When the refractive index ratio is 2.4:1, a normalized complete photonic band gap width of 8.6% is obtained in the optimized triangular lattice hexagonal ring super-cellular ideal two-dimensional photonic crystal, while for the same refractive index ratio of 2.4:1, in the corresponding triangular lattice hexagonal ring super-cellular two-dimensional photonic crystal flat plate, the complete photonic band gap determined by the 7 th and 8 th order energy bands only obtains a normalized band gap width of 4.3%, which is lower than the normalized complete photonic band gap width obtained in the corresponding ideal two-dimensional photonic crystal. In addition, the upper cladding layer and the lower cladding layer of the two-dimensional photonic crystal flat plate with the complete photonic band gap are both air, and the central photonic crystal core layer is a non-connected annular dielectric rod. The authors of this document subsequently describe a more realistic design of one of such two-dimensional photonic crystal slabs in another non-patent document Cerjan, a., and Fan, s.: Complete photonic bands in supercell photonic crystals', PHYSICAL REVIEW A,2017,96, pp.051802(R), but which requires a further increase in refractive index ratio: at a maximum refractive index ratio of 2.57:1, a maximum normalized complete photonic band gap width of 5.6% is obtained in the optimized hexagonal-ring superlattice two-dimensional photonic crystal slab (the upper cladding is air, and the lower cladding is silica photonic crystal), which is also lower than the normalized complete photonic band gap of the corresponding hexagonal-ring two-dimensional ideal photonic crystal under the same refractive index ratio shown in fig. 2 of the document. Moreover, in the hexagonal ring superlattice two-dimensional photonic crystal slab described in this document, the radius of the support pillars constituting the two-dimensional photonic crystal in the lower cladding layer is smaller than the radius of the ring constituting the two-dimensional photonic crystal in the intermediate core layer, so that it is very difficult to manufacture. The bandwidth of the complete photonic band gap in the photonic crystal slab 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; when the lowest frequency point of the higher order photonic band curve is above the cladding cone low frequency point, the bandwidth of the full photonic band gap is taken as the absolute difference between the cladding cone low frequency point forming the full photonic band gap and the highest frequency point of the lower order photonic band curve. The normalized frequency width in the photonic crystal slab is the absolute difference divided by the average of the two frequency values of the absolute difference, and the result is taken as a percentage.

In summary, the current state of the art is that, in the case of refractive index ratios below 2.4:1, there is no disclosure of two-dimensional photonic crystal slabs with complete photonic band gaps; at a refractive index ratio of 2.57:1, there has been no disclosure of a two-dimensional photonic crystal slab with a complete photonic band gap that is simple to fabricate. In the prior art, two-dimensional photonic crystal slabs are obtained by further slab design under the condition that an ideal two-dimensional photonic crystal corresponding to the slab has a larger complete photonic band gap. If an ideal two-dimensional photonic crystal is found to have a complete photonic band gap that is not of value for use, those skilled in the art will not further consider and design the complete photonic band gap of the corresponding two-dimensional photonic crystal slab. Therefore, the prior art fails to design a two-dimensional photonic crystal slab with a complete photonic band gap and a relatively low refractive index.

Disclosure of Invention

The invention relates to a two-dimensional photonic crystal flat plate capable of realizing complete photonic band gap under the condition of lower refractive index ratio.

According to an aspect of the present invention, there is provided a two-dimensional photonic crystal slab comprising 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 finite-height two-dimensional photonic crystal and is composed of a plurality of columns arranged periodically and a filler region, the columns are formed of a material having a highest refractive index in the two-dimensional photonic crystal slab, the filler region surrounds the columns and is formed of a material having a lower refractive index than that of the columns, the lower cladding layer comprises a solid support structure, the two-dimensional photonic crystal slab has a complete photonic band gap located below a cladding light ray defined by the upper cladding layer and the lower cladding layer and below a lowest-order photonic band curve of a TE-like mode of the two-dimensional photonic crystal slab and above a lowest-order photonic band curve of a TM-like mode of the two-dimensional photonic crystal slab, and the infinite high ideal two-dimensional photonic crystal corresponding to the finite high two-dimensional photonic crystal has a TM polarized optical sub-band gap between the lowest-order energy band curve and the second low-order energy band curve of the TM mode. Optionally, the infinite high ideal two-dimensional photonic crystal corresponding to the finite high two-dimensional photonic crystal does not have a complete photonic band gap or a complete photonic band gap formed by the lowest order photonic band curve and the second order photonic band curve or a complete photonic band gap which does not meet the requirement of a predetermined width.

According to another aspect of the present invention there is provided an optical device formed using a two-dimensional photonic crystal slab according to the first aspect of the present invention, the optical device being formed by forming point defects and/or line defects in the two-dimensional photonic crystal slab.

According to another aspect of the present invention, there is provided a method of designing a two-dimensional photonic crystal slab according to the first aspect of the present invention, comprising: calculating a photon energy band curve of an infinite high ideal two-dimensional photonic crystal under a preset refractive index ratio, taking the structural parameters of the infinite high ideal two-dimensional photonic crystal as initial two-dimensional structural parameters of a two-dimensional photonic crystal core layer under the condition that a TM optical sub-band gap meeting a first preset width requirement is arranged between a lowest-order TM mode and a second lower-order TM mode in the photon energy band curve of the infinite high ideal two-dimensional photonic crystal, designing and optimizing the structural parameters of the two-dimensional photonic crystal core layer and the structural parameters of an upper cladding layer and a lower cladding layer based on the initial two-dimensional structural parameters of the two-dimensional photonic crystal core layer, and calculating a photon energy band curve of the two-dimensional photonic crystal flat plate to enable the two-dimensional photonic crystal flat plate to obtain a complete photon band gap meeting a second preset width requirement, and the complete photonic band gap is positioned below the lowest-order photonic band curves of the cladding light rays determined by the upper cladding and the lower cladding and the TE-like mode of the two-dimensional photonic crystal flat plate and is positioned above the lowest-order photonic band curves of the TM-like mode of the two-dimensional photonic crystal flat plate.

According to the two-dimensional photonic crystal flat plate, under the cladding light ray or light cone region determined by the upper cladding and the lower cladding, the region which is positioned below the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal flat plate and above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal flat plate is used for forming the complete photonic band gap, the complete photonic band gap can be formed under the condition that the maximum refractive index of the two-dimensional photonic crystal flat plate is relatively low, and particularly the complete photonic band gap can be formed under the condition that the refractive index is lower than that of a corresponding infinite high ideal two-dimensional photonic crystal does not have the complete photonic band gap or does not have the usable complete photonic band gap.

Drawings

These and/or other aspects, features and advantages of the present invention will become more apparent and readily appreciated from the following description of the embodiments taken in conjunction with the accompanying drawings of which:

FIG. 1 shows a schematic structural diagram of a two-dimensional photonic crystal slab according to an embodiment of the present invention;

FIG. 2 shows a photonic band diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 3 shows a photonic band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 4 shows a photonic band diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 5 shows a photonic band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 6 shows a schematic structural diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 7 shows a photonic band diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 8 shows a photonic band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 9 shows a photonic band diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 10 shows a photonic band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 11 shows a photonic band diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 12 shows a photonic band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 13 shows a schematic structural diagram of a two-dimensional photonic crystal slab, according to an embodiment of the present invention;

FIG. 14 shows a photonic band diagram of a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 15 shows a photonic band diagram of an ideal two-dimensional photonic crystal corresponding to a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention;

FIG. 16 shows a schematic structural diagram of a two-dimensional photonic crystal slab, according to an embodiment of the present invention;

FIG. 17 shows a photonic band diagram of a two-dimensional photonic crystal slab according to an embodiment of the present invention.

Detailed Description

The present invention will be described in detail below with reference to exemplary embodiments thereof. However, the invention is not limited to the embodiments described herein, which may be embodied in many different forms. The described embodiments are intended only to be exhaustive and complete of the disclosure and to fully convey the concept of the invention to those skilled in the art. Features of the various embodiments described may be combined with each other or substituted for each other unless expressly excluded or otherwise excluded in context.

As explained in the background section, in the prior design theory experience of two-dimensional photonic crystal slab, if an ideal two-dimensional photonic crystal is found to have no useful complete photonic band gap, i.e. there is no overlapping TM band gap and TE band gap or the overlapping TM band gap and TE band gap regions are small and have no useful value, the corresponding two-dimensional photonic crystal slab will not be considered and designed to have complete photonic band gap. Therefore, in the prior art, a two-dimensional photonic crystal slab with a complete photonic band gap and a relatively low refractive index has not been designed. However, the inventor has found through research that this theoretical experience is a technical bias, and in fact, even in the case that a certain ideal two-dimensional photonic crystal does not have a complete photonic band gap of use, a corresponding two-dimensional photonic crystal slab with a larger complete photonic band gap can be designed. The inventors have found that a two-dimensional photonic crystal slab with a large complete photonic bandgap can be realized with a region below the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab and above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal slab, even if the corresponding ideal two-dimensional photonic crystal does not have a complete photonic bandgap, below the cladding ray or cone region defined by the upper and lower cladding layers. Therefore, the invention can effectively solve the problem that the complete photonic band gap is difficult to obtain in the two-dimensional photonic crystal flat plate with lower refractive index ratio, can obtain the two-dimensional photonic crystal flat plate with the complete photonic band gap in the low refractive index ratio range in which the complete photonic band gap can not be obtained in the prior art, and can obtain larger complete photonic band gap bandwidth under the condition that the complete photonic band gap is very narrow due to the low refractive index ratio although the complete photonic band gap can be obtained in the prior art. And the two-dimensional photonic crystal flat plate has a simple structure and is easy to manufacture.

The embodiments of the present invention adopt the following design principles. First, for an ideal two-dimensional photonic crystal with a TM photonic bandgap, a photonic bandgap of a similar TM-like mode is also readily obtained in its corresponding two-dimensional photonic crystal slab. Accordingly, embodiments of the present invention first require that the first TM energy band (i.e., the lowest order energy band curve of the TM mode) and the second TM energy band (i.e., the second lower order energy band curve of the TM mode) of an ideal two-dimensional photonic crystal can constitute a TM photonic bandgap, such that a TM-like mode photonic bandgap between the similar first TM-like energy band (i.e., the lowest order energy band curve of the TM-like mode) and the second TM-like energy band (i.e., the second lower order energy band curve of the TM-like mode) can be more easily obtained in its corresponding two-dimensional photonic crystal slab. Then, on this basis, it is considered that the photonic crystal generally has a large polarization dispersion characteristic, and therefore, the first TE-like energy band (i.e., the lowest order energy band curve of the TE-like mode) in the two-dimensional photonic crystal slab generally has a larger difference, i.e., a larger interval, than the first TM-like energy band. For example, in a dielectric cylindrical two-dimensional photonic crystal slab, the first photonic band (lowest order band curve) is generally a TM-like mode, and thus, the first TE-like mode band curve is not only spaced apart from the first TM-like mode band curve but also appears in the upper region of the photonic band of the first TM-like mode band curve. Therefore, the first TM-like mode energy band curve has the TM-like photonic band gap and has a larger interval with the first TE-like mode, so that a region where the TM-like mode and the TE-like mode do not exist simultaneously, i.e. a complete photonic band gap region, can be formed above the first TM-like mode and below the first TE-like mode below the cladding light cone region determined by the upper cladding and the lower cladding. At this time, using the structural parameters of the ideal two-dimensional photonic crystal satisfying the conditions as the two-dimensional structural initial parameters of the core layer of the two-dimensional photonic crystal slab, and designing and optimizing the structural parameters of the core layer including the thickness and the structural parameters of the cladding layer based on the two-dimensional structural initial parameters, it is possible to form a complete photonic band gap satisfying the width requirement in the case of a lower refractive index ratio, for example, the complete photonic band gap is determined by a region surrounded by the lowest-order photonic band curve and the cladding light, or by the lowest-order photonic band curve, the second-order photonic band curve and the cladding light, in which neither TM-like mode nor TE-like mode exists. According to an embodiment of the present invention, the lowest order photonic band curve is a lowest order photonic band curve of a TM-like mode of the two-dimensional photonic crystal slab, and the second order photonic band curve is a second lower order photonic band curve of the TM-like mode of the two-dimensional photonic crystal slab, or is a lowest order photonic band curve of a TE-like mode of the two-dimensional photonic crystal slab, or is formed of a portion of the lowest order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab and a portion of the second lower order photonic band curve of the TM-like mode.

According to the above design principle, embodiments of the present invention provide a two-dimensional photonic crystal slab. The two-dimensional photonic crystal flat plate comprises an upper cladding layer, a lower cladding layer and a two-dimensional photonic crystal core layer positioned between the upper cladding layer and the lower cladding layer. The two-dimensional photonic crystal core layer is a two-dimensional photonic crystal with limited height and is composed of a plurality of columns and filling regions, wherein the columns are arranged periodically, the columns are formed by materials with the highest refractive indexes in the two-dimensional photonic crystal flat plate, and the filling regions surround the columns and are formed by materials with lower refractive indexes than those of the columns. The lower cladding layer includes a solid support structure. The two-dimensional photonic crystal slab has a complete photonic band gap, and the complete photonic band gap of the two-dimensional photonic crystal slab is located below the cladding light determined by the upper cladding and the lower cladding and the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab and above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal slab. And the infinite high ideal two-dimensional photonic crystal corresponding to the finite high two-dimensional photonic crystal has a TM polarized optical sub-band gap between the lowest-order energy band curve and the second low-order energy band curve of the TM mode. Optionally, the maximum refractive index ratio of the two-dimensional photonic crystal slab may be as low as that of a corresponding infinitely high ideal two-dimensional photonic crystal that does not have a full photonic band gap or a full photonic band gap formed by the lowest order photonic band curve and the second order (i.e., the second lower order) photonic band curve or a full photonic band gap that does not meet the predetermined width requirement. The predetermined width may be determined according to the requirements of the actual application, for example, a normalized full photonic bandgap width of less than 3% is generally considered to be of no use value, and therefore, the predetermined width requirement herein may be selected to be a normalized width of more than 3%.

According to the two-dimensional photonic crystal slab of the above embodiment of the invention, since the complete photonic band gap is formed by using the region below the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab and above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal slab below the cladding light cone region defined by the upper cladding and the lower cladding, the complete photonic band gap that can be used can be formed in the case where the maximum refractive index of the two-dimensional photonic crystal slab is relatively low, and particularly, the complete photonic band gap that can be used can be formed in the case where the refractive index is lower than the corresponding infinitely high ideal two-dimensional photonic crystal does not have the complete photonic band gap or does not have the complete photonic band gap that can be used. For example, according to embodiments of the present invention, a usable full photonic bandgap may be achieved with a maximum refractive index ratio below 2.4 or even below 2.0. In addition, since the lower cladding layer includes the solid support structure, the two-dimensional photonic crystal slab can be practically manufactured. For example, if the lower cladding layer is made of a solid homogenous material, the solid homogenous material is a solid support structure; if the lower cladding is also in a two-dimensional photonic crystal structure, the columns and/or the filling areas in the two-dimensional photonic crystal structure are made of solid materials, so that a supporting effect is achieved.

Fig. 1 shows a schematic structural diagram of a two-dimensional photonic crystal slab 100 according to an embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of an XY plane, and (c) is a cross-sectional view of an XZ plane. In the two-dimensional photonic crystal slab 100, the upper cladding layer 101 is air, the lower cladding layer is silicon dioxide 102, and the two-dimensional photonic crystal core layer 103 is a two-dimensional photonic crystal with finite height, which is composed of periodically arranged silicon nitride (SixNy) pillars and filled regions filled with air. The values of x and y in SixNy are determined by the designed refractive index, with SixNy having the largest refractive index of the materials forming the two-dimensional photonic crystal slab 100. The upper cladding layer 101, the core layer 103, and the lower cladding layer 102 constitute a sandwich structure. In fig. 1, the two-dimensional photonic crystal of the core layer 103 is a triangular lattice circular column two-dimensional photonic crystal, as shown in fig. 1 (b).

Fig. 2 is a photonic band diagram corresponding to one embodiment of the two-dimensional photonic crystal slab 100 of fig. 1. In this embodiment, the main structural parameters of the two-dimensional photonic crystal slab 100 are: the cylinder material (SixNy) of the core layer has the highest refractive index, which is 2.5, the air of the upper cladding and the filled region has the lowest refractive index, which is 1, the refractive index of the lower cladding (silica) is 1.45, and thus 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 SixNy 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 thicknesses of the upper and lower cladding layers can be designed as desired, and typically up to 4-10 wavelengths or more, which can be considered infinitely thick. The photon energy band diagram shown in fig. 2 can be calculated according to the above structural parameters. In fig. 2, the horizontal axis is the wavevector denoted Γ, M, K, and the vertical axis is the normalized frequency in units of c/a, where c is the speed of light and a is the lattice constant of the photonic crystal. As shown in fig. 2, the gray uniformly shaded area is the light cone defined by the light rays of the silica cladding with the refractive index of 1.45; the energy band curve (energy band 1) shown by the solid dot solid line is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve (band 2) shown by the dotted square line is a second-order energy band curve, which is a second low energy band curve of the TM-like mode; the energy band curve (energy band 3) shown by the triangular dotted line is a third-order energy band curve which comprises a TE-like mode and a TM-like mode and is the lowest energy band curve comprising the TE-like mode under the light cone. It should be noted that, in the case of changing the slab parameters, the second-order band curve may be a second low-band curve of the TM-like mode, may also be a lowest-band curve of the TE-like mode, and may also be a portion of the second low-band curve of the TM-like mode and a portion of the lowest-band curve of the TE-like mode. In the present invention, each photonic band curve in the band diagram is, from bottom to top, the first order (lowest order), the second order (second lowest order), … …, and so on. As can be seen from fig. 2, the lowest order energy band curve, the second order energy band curve and the cladding light rays together define a complete photonic band gap region, as indicated by the gray shaded region with vertical lines in the figure (the region where the gray shaded region with vertical lines overlaps the white region in the figure is the complete photonic band gap region). There is no optical mode in this full photonic bandgap region, i.e., there is neither TM-like nor TE-like mode. Furthermore, it can be seen that the full photonic bandgap is located below band 3, which contains the lowest order photonic band curve of the TE-like mode, and above the lowest order photonic band curve (band 1) of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 2 is 12.83%, thus, at a center wavelength of 1550nm, the bandwidth is about 198 nm; at a central wavelength of 650nm, the bandwidth is about 83 nm. Such bandwidths may enable a variety of practical optical devices.

Fig. 3 is a photonic band diagram of an infinite high ideal two-dimensional photonic crystal corresponding to fig. 2, having the same structural parameters as the finite high two-dimensional photonic crystal of the photonic crystal slab core layer of fig. 2, except that the ideal two-dimensional photonic crystal has no cladding layer and an infinite height. Since an ideal two-dimensional photonic crystal has no cladding, there is no cone region in its photonic band diagram that represents cladding light confinement. As shown in fig. 3, the band curve shown by the solid dotted line is a TM mode band curve, and the band curve shown by the open dotted line is a TE mode band curve. In the illustrated energy band diagram of an ideal two-dimensional photonic crystal, there are 3 TM bandgaps (as shown by the shaded regions in the diagram), but due to the relatively low refractive index (only 2.5:1), there is no complete photonic bandgap, i.e., there is no region that is both a TM bandgap and a TE bandgap in the same frequency range. The normalized bandgap width between the first (lowest) order TM band and the second (second lowest) order TM band in the figure is 22.33%, which is used to obtain a complete photonic bandgap in the aforementioned two-dimensional photonic crystal slab.

It can thus be seen that in this embodiment, 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 full photonic bandgap, but the two-dimensional photonic crystal slab can still achieve a larger full photonic bandgap.

According to the embodiment of the invention, under the condition that the maximum refractive index ratio is 2.5:1, by changing the cylindrical radius and the core layer height in the triangular lattice two-dimensional photonic crystal panel shown in fig. 1, the normalized complete photonic band gap widths of different two-dimensional photonic crystal panels can be obtained, so that the structural parameters of the two-dimensional photonic crystal panel can be optimized as shown in the following table 1:

TABLE 1

Fig. 4 is a photonic band diagram corresponding to another embodiment of the two-dimensional photonic crystal slab 100 of fig. 1. In this example, the maximum refractive index ratio is further reduced by 2:1, with the main structural parameters: the pillar material (SixNy) of the core layer has the highest refractive index, which is 2.0, the air of the upper cladding and the filling region has the lowest refractive index, which is 1, the refractive index of the lower cladding (silica) is 1.45, and thus the maximum refractive index ratio is 2: 1; the thickness h of the core layer was 3.0a and the radius r of the SixNy cylinder was 0.33 a. The photonic band diagram shown in fig. 4 can be calculated from the above structural parameters. As shown in fig. 4, the gray uniformly shaded area is the light cone defined by the light rays of the silica cladding; the energy band curve (band 1) shown by the solid line is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve (band 2) shown by the dotted line is a second order energy band curve, which is the lowest order energy band curve of the TE-like mode, with a portion of the modes in the light cone. As can be seen in FIG. 4, the lowest order energy band curve, the second order energy band curve and the cladding light combine to define a complete photonic band gap region, as indicated by the gray shaded area with vertical lines. The full photonic bandgap is located below the lowest order photonic band curve of the TE-like mode and above the lowest order photonic band curve of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 2 is 3.68%, and thus, at a center wavelength of 1550nm, the bandwidth is about 57 nm; at a central wavelength of 650nm, the bandwidth is about 23.9 nm. Such bandwidths may enable a variety of practical optical devices.

Fig. 5 is a photonic band diagram of an infinite high ideal two-dimensional photonic crystal corresponding to fig. 4, having the same structural parameters as the finite high two-dimensional photonic crystal of the photonic crystal slab core layer of fig. 4, except that the ideal two-dimensional photonic crystal has no cladding layer and an infinite height. Since an ideal two-dimensional photonic crystal has no cladding, there is no cone region in its photonic band diagram that represents cladding light confinement. As shown in fig. 5, the band curve shown by the solid dotted line is a TM mode band curve, and the band curve shown by the open dotted line is a TE mode band curve. In the band diagram of the ideal two-dimensional photonic crystal illustrated, there are 2 TM bandgaps (as shown by the shaded regions in the diagram), but there are no complete photonic bandgaps due to the relatively low refractive index (only 2: 1). The normalized band gap width between the first order TM band and the second order TM band of the graph is 16.63%, which is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal slab.

It can thus be seen that in this embodiment, the maximum refractive index ratio is as low as 2:1, corresponding to an infinite height where the two-dimensional photonic crystal does not have a full photonic bandgap, but the two-dimensional photonic crystal slab can still achieve a larger full photonic bandgap.

According to the embodiment of the present invention, in the case that the maximum refractive index ratio is 2:1, by changing the cylindrical radius and the core layer height in the triangular lattice two-dimensional photonic crystal slab shown in fig. 1, the normalized complete photonic bandgap widths of different two-dimensional photonic crystal slabs can be obtained as shown in table 2 below:

TABLE 2

In the above embodiment, both the upper cladding and the lower cladding are homogeneous layers formed of a material having 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. According to an embodiment of the present invention, the upper cladding and/or the lower cladding may be a two-dimensional photonic crystal cladding composed of a plurality of materials having a refractive index lower than the maximum refractive index in the two-dimensional photonic crystal slab. Alternatively, the two-dimensional photonic crystal of the upper cladding layer and/or the lower cladding layer may have the same lattice structure as the two-dimensional photonic crystal core layer. The cylinder radius in the two-dimensional photonic crystal of the lower cladding layer may be greater than or equal to the cylinder radius of the two-dimensional photonic crystal core layer. The cylinder radius in the two-dimensional photonic crystal of the upper cladding layer may be less than or equal to the cylinder radius of the two-dimensional photonic crystal core layer.

Fig. 6 shows a schematic structural diagram of a two-dimensional photonic crystal slab 600 according to another embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of an XY plane, and (c) is a cross-sectional view of an XZ plane. In this embodiment, the upper cladding 601 is a homogeneous material of air, the lower cladding 602 is a two-dimensional photonic crystal cladding formed of a cylindrical silica of finite height and air, and the core 603 is a two-dimensional photonic crystal core formed of a cylindrical silicon nitride of finite height (SixNy) and air. The SixNy has the largest index of refraction among the materials forming the two-dimensional photonic crystal slab 600, and the index of refraction of the pillar material silica of the lower cladding 602 is lower than the above-mentioned largest index of refraction. In fig. 6, the core layer 603 and the lower cladding layer 602 have the same lattice and pillar shape and radius, and are both triangular lattice circular pillar two-dimensional photonic crystals, as shown in fig. 6 (b).

Fig. 7 is a photonic band diagram corresponding to one embodiment of the two-dimensional photonic crystal slab 600 of fig. 6. In this embodiment, the main structural parameters of the two-dimensional photonic crystal slab 600 are: the pillar material of the core layer (SixNy) has the highest refractive index, which is 1.8, the air of the upper cladding and the filled region has the lowest refractive index, which is 1, the refractive index of the lower cladding silica pillar is 1.45, and thus the maximum refractive index ratio is 1.8: 1; the thickness h of the core layer was 2.1a and the radius r of the SixNy cylinder and the silica were both 0.33 a. The thicknesses of the upper and lower cladding layers can be designed as desired, and are typically up to 4-10 wavelengths or more, which can be considered infinitely thick. From the above structural parameters, a photon energy band diagram as shown in fig. 7 can be calculated. As shown in fig. 7, the gray uniformly shaded area is the light cone defined by the light rays of the lower cladding layer; the energy band curve (energy band 1) shown by the solid-dotted solid line is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve (band 2) shown by the dotted dot line is a second order energy band curve, which is the lowest order energy band curve of the TE-like mode and is entirely within the cone of light. As can be seen in FIG. 7, the lowest order band curve and the cladding light combine to define a complete photonic band gap region, as shown by the gray shaded area with vertical bars in the figure. And under the condition that 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. Furthermore, it can be seen that the full photonic bandgap lies below the lowest order photonic band curve of the TE-like mode and above the lowest order photonic band curve of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 7 is 3.17%, so that the bandwidth is about 49nm at a center wavelength of 1550 nm; at a central wavelength of 650nm, the bandwidth is about 20 nm. Such bandwidths may enable a variety of practical optical devices.

Fig. 8 is a photonic band diagram of an infinite high ideal two-dimensional photonic crystal corresponding to the core layer of fig. 7, having the same structural parameters as the finite high two-dimensional photonic crystal of the photonic crystal slab core layer of fig. 7, except that the ideal two-dimensional photonic crystal has no cladding layer and an infinite height. Since an ideal two-dimensional photonic crystal has no cladding, there is no cone region in its photonic band diagram that represents cladding light confinement. As shown in fig. 8, the band curve shown by the solid dotted line is a TM mode band curve, and the band curve shown by the solid dotted line is a TE mode band curve. In the band diagram of the ideal two-dimensional photonic crystal shown, there are 2 TM bandgaps (as shown by the shaded regions in the diagram), but no complete photonic bandgap exists due to the lower refractive index (only 1.8: 1). The normalized bandgap width between the first order TM band and the second order TM band of the graph is 13.13%, and is used to obtain the complete photonic bandgap in the aforementioned two-dimensional photonic crystal slab.

It can thus be seen that in this embodiment, 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 full photonic bandgap, but the two-dimensional photonic crystal slab can still achieve a larger full photonic bandgap.

According to the embodiment of the present invention, by changing the cylindrical radius (the cylindrical radius of the core layer and the cladding layer is the same) and the core layer height in the triangular lattice two-dimensional photonic crystal slab shown in fig. 6 in the case that the maximum refractive index ratio is 1.8:1, the normalized complete photonic band gap widths of different two-dimensional photonic crystal slabs can be obtained as shown in table 3 below:

TABLE 3

Fig. 9 is a photonic band diagram corresponding to another embodiment of the two-dimensional photonic crystal slab 600 of fig. 6. In this embodiment, the main structural parameters of the two-dimensional photonic crystal slab 600 are: the pillar material of the core layer (SixNy) has the highest refractive index, which is 2.4, the air of the upper cladding and the filled region has the lowest refractive index, which is 1, the refractive index of the lower cladding silica pillar is 1.45, and thus the maximum refractive index ratio is 2.4: 1; the thickness h of the core layer was 1.4a and the radius r of the SixNy cylinder and the silica cylinder was 0.21 a. The photonic band diagram shown in fig. 9 can be calculated from the above structural parameters. As shown in fig. 9, the gray uniformly shaded area is a light cone area determined by the light rays of the lower cladding (the lowest energy band curve of the energy band curves of the two-dimensional photonic crystal cladding is taken as the light rays); the energy band curve shown by the solid dotted solid line 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 dot line is the second order energy band curve (band 2), which is the lowest order energy band curve of the TE-like mode and is located entirely within the cladding taper region. As can be seen in FIG. 9, the lowest order band curve and the cladding light combine to define a complete photonic band gap region, as indicated by the gray shaded area with vertical bars in the figure. The full photonic bandgap is located below the lowest order photonic band curve of the TE-like mode and above the lowest order photonic band curve of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 9 is 12.85%, so that the bandwidth is about 199nm at a center wavelength of 1550 nm; at a central wavelength of 650nm, the bandwidth is about 83 nm. Such a bandwidth may enable a variety of practical optical devices.

Fig. 10 is a photonic band diagram of an infinite high ideal two-dimensional photonic crystal corresponding to the core layer of fig. 9, having the same structural parameters as the finite high two-dimensional photonic crystal of the photonic crystal slab core layer of fig. 9, except that the ideal two-dimensional photonic crystal has no cladding layer and has an infinite height. Since an ideal two-dimensional photonic crystal has no cladding, there is no cone region in its photonic band diagram that represents cladding light confinement. As shown in fig. 10, the band curve shown by the solid dotted line is a TM mode band curve, and the band curve shown by the dotted solid line is a TE mode band curve. In the energy band diagram of the ideal two-dimensional photonic crystal shown in the figure, there are 1 TM bandgaps (as shown by the shaded area in the figure), but there are no complete photonic bandgaps due to the lower refractive index (only 2.4: 1). The normalized band gap width between the first order TM band and the second order TM band in the figure is 31.37% and is used to obtain a complete photonic band gap in the aforementioned two-dimensional photonic crystal slab.

It can thus be seen that in this embodiment, 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 full photonic bandgap, but the two-dimensional photonic crystal slab can still achieve a larger full photonic bandgap.

According to the embodiment of the present invention, by changing the cylindrical radius (the cylindrical radius of the core layer and the cladding layer is the same) and the core layer height in the triangular lattice two-dimensional photonic crystal slab shown in fig. 6 in the case that the maximum refractive index ratio is 2.4:1, the normalized complete photonic band gap widths of different two-dimensional photonic crystal slabs can be obtained as shown in table 4 below:

TABLE 4

Fig. 11 is a photonic band diagram of another embodiment of a two-dimensional photonic crystal slab 600 corresponding to fig. 6. In this embodiment, the main structural parameters of the two-dimensional photonic crystal slab 600 are: the core layer pillar material (SixNy) has the highest refractive index, which is 2.57, the upper cladding and the air in the filler region has the lowest refractive index, which is 1, the lower cladding silica pillar has a refractive index of 1.45, and thus the maximum refractive index ratio is 2.57: 1; the thickness h of the core layer was 1.25a and the radius r of the SixNy cylinder and the silica cylinder was 0.21 a. The photonic band diagram shown in fig. 11 can be calculated from the above structural parameters. As shown in fig. 11, the gray uniformly shaded area is a light cone area determined by the light rays of the lower cladding (the lowest energy band curve of the energy band curves of the two-dimensional photonic crystal cladding is taken as the light rays); the energy band curve (energy band 1) shown by the solid line is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve (band 2) shown by the open square dashed line is the second order energy band curve, which is the lowest order energy band curve of the TE-like mode and is located entirely within the cladding taper region. As can be seen in FIG. 11, the lowest order band curve and the cladding light combine to define a complete photonic band gap region, as indicated by the gray shaded area with vertical bars in the figure. The full photonic bandgap is located below the lowest order photonic band curve of the TE-like mode and above the lowest order photonic band curve of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 11 is 13.65%, so that the bandwidth is about 211nm at a center wavelength of 1550 nm; at a central wavelength of 650nm, the bandwidth is about 88 nm. Such bandwidths may enable a variety of practical optical devices.

Fig. 12 is a photonic band diagram of an infinite high ideal two-dimensional photonic crystal corresponding to the core layer of fig. 11, having the same structural parameters as the finite high two-dimensional photonic crystal of the photonic crystal slab core layer of fig. 11, except that the ideal two-dimensional photonic crystal has no cladding layer and an infinite height. Since an ideal two-dimensional photonic crystal has no cladding, there is no light cone region in its photonic band diagram that represents cladding light confinement. As shown in fig. 12, the band curve shown by the solid dotted line is a TM mode band curve, and the band curve shown by the solid open-dotted line is a TE mode band curve. In the illustrated energy band diagram of an ideal two-dimensional photonic crystal, there are 1 TM bandgap (as shown by the shaded area without diagonal lines in the diagram) and one TE bandgap (as shown by the shaded area with diagonal lines in the diagram), but there is no complete photonic bandgap due to the lower refractive index (only 2.57: 1). The normalized bandgap width between the first order TM band and the second order TM band of the graph is 34.84%, which is used to obtain the complete photonic bandgap in the two-dimensional photonic crystal slab described above.

It can thus be seen that in this embodiment, the maximum refractive index ratio is as low as 2.57:1, corresponding to an infinitely high ideal two-dimensional photonic crystal that does not have a full photonic bandgap, but the two-dimensional photonic crystal slab can still achieve a larger full photonic bandgap.

According to the embodiment of the present invention, by changing the cylindrical radius (the same cylindrical radius of the core layer and the cladding layer) and the core layer height in the triangular lattice two-dimensional photonic crystal slab shown in fig. 6 in the case that the maximum refractive index ratio is 2.57:1, the normalized complete photonic bandgap widths of different two-dimensional photonic crystal slabs can be obtained as shown in table 5 below:

TABLE 5

Fig. 13 shows a structural schematic diagram of a two-dimensional photonic crystal slab 1300 according to another embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of an XY plane, and (c) is a cross-sectional view of an XZ plane. In this embodiment, the upper cladding layer 1301 is a homogeneous material of air, the lower cladding layer 1302 is a two-dimensional photonic crystal cladding layer formed of a finite height cylindrical silica and air, and the core layer 1303 is a two-dimensional photonic crystal core layer formed of a finite height cylindrical silicon nitride (SixNy) and air. The SixNy has the largest index of refraction among the materials forming the two-dimensional photonic crystal slab 1300, and the refractive index of the columnar material of the lower cladding 1302 is lower than the above-mentioned largest index of refraction. In fig. 13, the core layer 1303 and the lower cladding layer 1302 have the same lattice and pillar shape, both being two-dimensional photonic crystals that are triangular lattice circular pillar two-dimensional photonic crystals, but the pillar radius of the lower cladding layer 1302 is larger than that of the core layer 1303, as shown in fig. 13(b) and (c).

Fig. 14 is a photonic band diagram of an embodiment of a two-dimensional photonic crystal slab 1300 corresponding to fig. 13. In this embodiment, the main structural parameters of the two-dimensional photonic crystal slab 1300 are: the core layer's bulk material (SixNy) has the highest refractive index, which is 2, the upper cladding and the air in the filled region has the lowest refractive index, which is 1, the lower cladding silica bulk has a refractive index of 1.45, and thus the maximum refractive index ratio is 2: 1; the thickness h of the core layer was 1.8a, the radius of the SixNy cylinder was 0.28a, and the radius of the silicon dioxide was 0.33 a. The thicknesses of the upper and lower cladding layers can be designed as desired, and are typically up to 4-10 wavelengths or more, which can be considered infinitely thick. The photonic band diagram shown in fig. 14 can be calculated from the above structural parameters. As shown in fig. 14, the gray uniformly shaded area is the light cone area determined by the light rays of the lower cladding (the lowest energy band curve of the two-dimensional photonic crystal cladding energy band curves is taken as the light rays); the energy band curve (energy band 1) shown by the dotted solid line is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve (band 2) shown by the dotted line is a second order energy band curve, which is the lowest order energy band curve of the TE-like mode and is located entirely within the light cone. As can be seen in FIG. 14, the lowest order band curve and the cladding light combine to define a complete photonic band gap region, as shown by the gray shaded area with vertical bars in the figure. Furthermore, it can be seen that the full photonic bandgap lies below the lowest order photonic band curve of the TE-like mode and above the lowest order photonic band curve of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 14 is 4.74%, and thus, at a center wavelength of 1550nm, the bandwidth is about 73 nm; at a central wavelength of 650nm, the bandwidth is about 31 nm. Such bandwidths may enable a variety of practical optical devices.

Fig. 15 is a photonic band diagram of an infinite high ideal two-dimensional photonic crystal corresponding to the core layer of fig. 14, having the same structural parameters as the finite high two-dimensional photonic crystal of the photonic crystal slab core layer of fig. 14, except that the ideal two-dimensional photonic crystal has no cladding layer and an infinite height. Since an ideal two-dimensional photonic crystal has no cladding, there is no light cone region in its photonic band diagram that represents cladding light confinement. As shown in fig. 15, the band curve shown by the solid dotted line is a TM mode band curve, and the band curve shown by the solid dotted line is a TE mode band curve. In the band diagram of the ideal two-dimensional photonic crystal shown, there are 2 TM bandgaps (as shown by the shaded regions in the diagram), but there are no complete photonic bandgaps due to the lower refractive index (only 2: 1). The normalized band gap width between the first order TM band and the second order TM band in the figure is 21.08% and is used to obtain a complete photonic band gap in the two-dimensional photonic crystal slab described above.

Fig. 16 shows a structural schematic diagram of a two-dimensional photonic crystal slab 1600 according to another embodiment of the present invention, in which (a) is a three-dimensional side view, (b) is a top view of an XY plane, and (c) is a cross-sectional view of an XZ plane. In this embodiment, both upper cladding 1601 and lower cladding 1602 are two-dimensional photonic crystal cladding, each formed of a cylindrical silica of finite height and air; core layer 1603 is a two-dimensional photonic crystal core layer formed of a finite height cylindrical silicon nitride (SixNy) and air. The SixNy has the largest index of refraction among the materials forming the two-dimensional photonic crystal slab 1600, and the refractive indices of the pillar materials of the upper cladding 1601 and the lower cladding 1602 are lower than the above-mentioned largest index of refraction. In fig. 16, upper cladding layer 1601, core layer 1603 and lower cladding layer 1602 have the same lattice and pillar shape, all are two-dimensional photonic crystals that are triangular lattice circular pillar two-dimensional photonic crystals, and the pillar radius of upper cladding layer 1601 is equal to the pillar radius of core layer 1603 but smaller than the pillar radius of lower cladding layer 1602, as shown in fig. 16(b) and (c).

FIG. 17 is a photonic band diagram of an embodiment of a two-dimensional photonic crystal slab 1600 corresponding to FIG. 16. In this embodiment, the main structural parameters of the two-dimensional photonic crystal slab 1600 are: the core layer's bulk material (SixNy) has the highest refractive index, which is 2, the air in the filled region has the lowest refractive index, which is 1, and the upper and lower cladding silica pillars have a refractive index of 1.45, thus, the maximum refractive index ratio is 2: 1; the thickness h of the core layer was 1.8a, the radius of the upper cladding silica and the radius of the SixNy cylinder was 0.28a, and the radius of the lower cladding silica was 0.33 a. The thickness of the upper and lower cladding layers can be designed as desired, typically up to 4-10 wavelengths or more, which can be considered infinitely thick. The photonic band diagram shown in fig. 17 can be calculated from the above structural parameters. As shown in fig. 17, the gray uniformly shaded area is a light cone area determined by the light rays of the lower cladding (taking the lowest energy band curve of the energy band curves of the upper and lower two-dimensional photonic crystal cladding as the light rays); the energy band curve (energy band 1) shown by the solid dot solid line is the lowest order energy band curve, which is the lowest order energy band curve of the TM-like mode; the energy band curve (band 2) shown by the dotted open line is the energy band curve of the second order, which is the lowest order energy band curve of the TE-like mode and is almost entirely in the light cone. As can be seen in FIG. 17, the lowest order band curve and the cladding light combine to define a complete photonic band gap region, as indicated by the gray shaded area with vertical bars in the figure. Furthermore, it can be seen that the full photonic bandgap is located below the lowest order photonic band curve of the TE-like mode and above the lowest order photonic band curve of the TM-like mode. It can be calculated that the normalized complete photonic band gap width of the photonic crystal slab shown in fig. 17 is 5.87%, so that the bandwidth is about 91nm at a center wavelength of 1550 nm; at a central wavelength of 650nm, the bandwidth is about 38 nm. The infinite height ideal two-dimensional photonic crystal corresponding to the core layer of fig. 17 is the same as the infinite height ideal two-dimensional photonic crystal corresponding to the core layer of fig. 14, and thus its photonic band diagram is also shown in fig. 15.

According to an embodiment of the present invention, there is also provided an optical device formed by using the two-dimensional photonic crystal slab, wherein the optical device is formed by forming a point defect and/or a line defect in the two-dimensional photonic crystal slab. For example, introducing a line defect in a two-dimensional photonic crystal slab can form an optical waveguide, introducing a point defect in a two-dimensional photonic crystal slab can form a resonator, or introducing a point defect and a line defect in a two-dimensional photonic crystal slab can form a more powerful optical device.

There is also provided, in accordance with an embodiment of the present invention, a method of designing a two-dimensional photonic crystal slab in accordance with an embodiment of the present invention. In the method, a photon energy band curve of an infinite high ideal two-dimensional photonic crystal is calculated in a preset refractive index ratio, and the ideal two-dimensional photonic crystal with a photon energy band meeting requirements is selected from the calculated ideal two-dimensional photonic crystals to serve as a basis for designing a two-dimensional photonic crystal panel. Embodiments according to the present invention are generally applicable to a case where the refractive index is relatively low, and a predetermined refractive index ratio in which a photonic band curve of an ideal two-dimensional photonic crystal is calculated may be determined according to a scenario and a material system to which the design is applied before the design starts. Specifically, under the condition that a TM photonic band gap meeting a first predetermined width requirement is formed between a lowest-order TM mode and a second lower-order TM mode in a photonic band curve of the infinite high ideal two-dimensional photonic crystal, the structural parameter of the infinite high ideal two-dimensional photonic crystal is used as an initial two-dimensional structural parameter of the two-dimensional photonic crystal core layer. The first predetermined width requirement here may be set according to the requirements of a specific application, for example, it may be a requirement that the normalized photonic band gap is greater than 3%, 10%, etc. in order to obtain a full photonic band gap satisfying the requirements in the two-dimensional photonic slab. Typically, the first predetermined width requirement is similar to, or slightly wider than, the final required full photonic bandgap. Under the condition that the structure parameter of a certain ideal two-dimensional photonic crystal is found to meet the first preset bandwidth requirement, the structure parameter of the ideal two-dimensional photonic crystal can be used as the initial two-dimensional structure parameter of the designed two-dimensional photonic crystal flat plate core layer. The two-dimensional structure parameters comprise a lattice structure of the two-dimensional photonic crystal; material or refractive index of the cylinder, shape, planar dimensions (e.g., radius); and the material or refractive index of the fill region. Then, based on the two-dimensional structure initial parameters of the two-dimensional photonic crystal core layer, designing and optimizing the structure parameters including the thickness of the two-dimensional photonic crystal core layer and the structure parameters of the upper cladding layer and the lower cladding layer, and calculating the photonic band curve of the two-dimensional photonic crystal panel, so that the two-dimensional photonic crystal panel obtains a complete photonic band gap meeting the second predetermined width requirement, and the complete photonic band gap is located below the cladding light rays determined by the upper cladding layer and the lower cladding layer and the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal panel and above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal panel. After the initial two-dimensional structural parameters of the two-dimensional photonic crystal core layer are determined, further determination and optimization of the structural parameters of the core layer and the cladding layer are needed. The structural parameters of the core layer include the thickness of the core layer in addition to the two-dimensional structural parameters described above. In particular, the optimization of the two-dimensional structural parameters for the two-dimensional photonic crystal core layer may calculate and compare the parameter values around the initial two-dimensional structural parameters. The thickness of the core layer and the structure of the cladding layer may be determined according to the specific application, for example, by selecting suitable materials and dimensions. In addition, various parameters may be calculated to determine the optimized parameters, and varying the respective dimensions may result in the optimized full photonic bandgap width, as shown in the tables above. By designing and optimizing the parameters, a two-dimensional photonic crystal flat plate with a complete photonic band gap satisfying the second predetermined width requirement is finally obtained. The second predetermined width requirement may be determined based on the bandwidth requirement of the designed optical device.

In summary, according to the embodiments of the present invention, a two-dimensional photonic crystal slab having a complete photonic band gap can be formed with a relatively low refractive index, so that realization of optical devices such as light reflectors, optical resonators, optical waveguides, optical detectors, light emitting devices, solar cells, etc. in more electromagnetic spectrum based on the complete photonic band gap of the two-dimensional photonic crystal slab can be greatly facilitated, and the two-dimensional photonic crystal slab can be more widely applied to the fields of optical communication, optical sensing, light illumination, energy photons, etc.; and more adaptive optical materials can be selected to manufacture the two-dimensional photonic crystal flat plate with complete photonic band gap, so that the design space of the two-dimensional photonic crystal flat plate device is greatly enriched, and the application range of the two-dimensional photonic crystal flat plate photonic band gap device is expanded.

Those skilled in the art will appreciate that the particular embodiments described above are by way of example only, and not by way of limitation, and that various modifications, combinations, sub-combinations, and alternatives to those embodiments of the invention may be made in accordance with design requirements and other factors. For example, the column shape in the two-dimensional photonic crystal slab is not limited to a cylinder, and may be a column of any shape, for example, a triangular column, a square column, other polygonal columns, and the like. The high refractive index material used for the core layer cylinder is not limited to silicon nitride, and may be selected from, for example, silicon, germanium, silicon nitride, silicon oxynitride, gallium arsenide, indium phosphide, titanium oxide, or a compound or mixture of these materials, or an optical or electromagnetic polymer such as glass, or plastic; the low refractive index material for the cladding or the filling region may be selected from silicon nitride, silicon oxynitrides, silicon dioxide, air, etc., as long as the set refractive index ratio is satisfied.

Claims

1. A two-dimensional photonic crystal slab comprising an upper cladding layer, a lower cladding layer, and a two-dimensional photonic crystal core layer 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 finite height and is composed of a plurality of columns and filling regions, wherein the columns are arranged periodically, the columns are formed by materials with the highest refractive indexes in the two-dimensional photonic crystal flat plate, the filling regions surround the columns and are formed by materials with lower refractive indexes than those of the columns,

the lower cladding layer includes a solid support structure,

the two-dimensional photonic crystal slab has a complete photonic band gap, is located below the cladding light determined by the upper cladding and the lower cladding and the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab, is located above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal slab, and is

And the infinite high ideal two-dimensional photonic crystal corresponding to the finite high two-dimensional photonic crystal has a TM polarized optical sub-band gap between the lowest-order energy band curve and the second low-order energy band curve of the TM mode.

2. The two-dimensional photonic crystal slab of claim 1, wherein

The infinitely high ideal two-dimensional photonic crystal does not have a complete photonic bandgap.

3. The two-dimensional photonic crystal slab of claim 1, wherein

The infinite high ideal two-dimensional photonic crystal does not have a complete photonic band gap formed by a lowest-order photonic band curve and a second-order photonic band curve.

4. The two-dimensional photonic crystal slab of claim 1, wherein

The infinitely high ideal two-dimensional photonic crystal has a complete photonic bandgap that does not meet predetermined width requirements.

5. The two-dimensional photonic crystal slab of any one of claims 1 to 4, wherein

The complete photonic band gap of the two-dimensional photonic crystal slab is determined by a region defined by a lowest-order photonic band curve and cladding light rays, or by a region defined by the lowest-order photonic band curve, a second-order photonic band curve and the cladding light rays.

6. The two-dimensional photonic crystal slab of claim 5, wherein

The lowest-order photonic band curve is the lowest-order band curve of the TM-like mode of the two-dimensional photonic crystal flat plate, and

the second-order photonic band curve is a second low-order photonic band curve of a TM-like mode of the two-dimensional photonic crystal slab, or is a lowest-order photonic band curve of a TE-like mode of the two-dimensional photonic crystal slab, or is formed by a part of the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal slab and a part of the second low-order photonic band curve of the TM-like mode.

7. The two-dimensional photonic crystal slab of any one of claims 1 to 4, wherein

The maximum refractive index ratio of the material forming the two-dimensional photonic crystal slab is lower than 2.4.

8. The two-dimensional photonic crystal slab of any one of claims 1 to 4, wherein

The upper cladding and/or the lower cladding are two-dimensional photonic crystal claddings composed of a plurality of materials with refractive indexes lower than the maximum refractive index in the two-dimensional photonic crystal flat plate.

9. The two-dimensional photonic crystal slab of claim 8, wherein

The two-dimensional photonic crystal of the upper cladding layer and/or the lower cladding layer has the same lattice structure as the two-dimensional photonic crystal core layer,

the cylinder radius in the two-dimensional photonic crystal of the lower cladding layer is greater than or equal to the cylinder radius of the core layer of the two-dimensional photonic crystal, and

the radius of a cylinder in the two-dimensional photonic crystal of the upper cladding layer is smaller than or equal to that of a cylinder of the two-dimensional photonic crystal core layer.

10. The two-dimensional photonic crystal slab of any one of claims 1 to 4, wherein

The upper cladding and/or the lower cladding are homogeneous layers formed by materials with the refractive index lower than the maximum refractive index in the two-dimensional photonic crystal flat plate.

11. An optical device formed using the two-dimensional photonic crystal slab of any one of claims 1 to 10, the optical device being formed with point defects and/or line defects in the two-dimensional photonic crystal slab.

12. A method of designing a two-dimensional photonic crystal slab as claimed in any one of claims 1 to 10 comprising:

calculating the photon energy band curve of the infinitely high ideal two-dimensional photonic crystal under a preset refractive index ratio,

taking the structural parameters of the infinite high ideal two-dimensional photonic crystal as the initial parameters of the two-dimensional structure of the two-dimensional photonic crystal core layer under the condition that a TM photonic band gap meeting a first preset width requirement is arranged between a lowest-order TM mode and a second low-order TM mode in the photonic band curve of the infinite high ideal two-dimensional photonic crystal, and

designing and optimizing the structural parameters of the two-dimensional photonic crystal core layer and the structural parameters of the upper cladding layer and the lower cladding layer based on the two-dimensional structural initial parameters of the two-dimensional photonic crystal core layer, and calculating a photonic band curve of the two-dimensional photonic crystal panel, so that the two-dimensional photonic crystal panel obtains a complete photonic band gap meeting a second predetermined width requirement, and the complete photonic band gap is located below the cladding light rays determined by the upper cladding layer and the lower cladding layer and the lowest-order photonic band curve of the TE-like mode of the two-dimensional photonic crystal panel and is located above the lowest-order photonic band curve of the TM-like mode of the two-dimensional photonic crystal panel.