All-dielectric metamaterial ultrahigh Q-guided mode resonator based on symmetrical structure

Abstract

The invention discloses an all-dielectric metamaterial ultrahigh Q guided mode resonator based on a symmetrical structure. The resonator is composed of homocentric-square-shaped dielectric resonance units which are distributed periodically in a two-dimensional mode, each unit comprises a left vertical part, a right vertical part, an upper transverse part and a lower transverse part, the vertical parts and the transverse parts are perpendicular to each other, and the distance between the vertical parts and the transverse parts is adjustable. By adjusting the distance between the upper transverse part and the lower transverse part, ultrahigh Q-value resonance is realized on the premise of keeping the symmetry of the structure. When the terahertz wave is vertically incident and the polarization direction of the electric field is vertical to the transverse cuboid dielectric strip, the Q value can be obviously improved by reducing the transverse distance. Under the condition that the structural symmetry is kept, the ultra-high Q value is easy to appear, the structure is simple, the processing tolerance is high, interface bonding or complex asymmetric design is not needed, and the ultra-high-Q-value terahertz wave band filter is suitable for a high-sensitivity sensor, a narrow-band filter and a nonlinear optical device of a terahertz wave band.

Description

Technical Field

[0001] The present invention relates to an all-dielectric metamaterial ultra-high Q guided-mode resonator based on a symmetric structure, and belongs to the technical field of metamaterials. Background Art

[0002] Metamaterials have attracted the attention of many researchers due to their peculiar properties such as negative refractive index and negative permittivity. Fano resonance is a fundamental property of metamaterials and a basic physical concept, which can be evaluated by the resonance quality factor (Q), defined as the center frequency of the resonance peak divided by the resonance peak width (FWHM). The Q value is an important evaluation criterion for the resonance peak. No matter what mechanism excites the resonance peak, its performance can be reflected by the Q value. A high Q value has important practical significance because a high Q value represents a narrow full width at half maximum, which can further be reflected as high sensitivity and can be applied in narrowband filters, high-precision measurements, etc.

[0003] The eddy current loss of metals is proportional to the square of the operating frequency. As the operating frequency of metamaterials increases, the loss of electromagnetic waves passing through metal materials increases significantly, which limits the application of metal metamaterials to a certain extent. Since dielectric materials themselves have characteristics such as high permittivity and low loss, dielectric metamaterials are of great research significance. The overall structure of dielectric metamaterials is simple, and some non-metallic dielectric materials themselves have properties such as temperature sensitivity, electric field sensitivity, and magnetic field sensitivity.

[0004] High-Q resonances play a crucial role in many applications. However, the high-Q resonance structures of most traditional dielectric resonators not only require high precision to control the structural asymmetry, but also change significantly with the asymmetry, which is not conducive to obtaining stable high-Q resonances and has limited practicality. Here, we can obtain an ultra-high Q value by changing the structural parameters while maintaining symmetry. At the same time, this structure is easy to manufacture without interface bonding or complex asymmetric design. Therefore, the proposed resonator has many potential applications in nonlinear optics, optical filters, and biosensors. Summary of the Invention

[0005] The purpose of the present invention is to provide an all-dielectric metamaterial ultra-high Q guided-mode resonator based on a symmetric structure, and to provide a new technology for generating high Q.

[0006] To achieve the above purpose, the technical solutions adopted by the present invention are as follows:

[0007] A kind of all-dielectric metamaterial ultra-high Q guided-mode resonator based on a symmetric structure according to the present invention is characterized in that: the resonator is composed of "hui"-shaped dielectric resonator units distributed periodically in two dimensions. Each dielectric resonator unit is composed of a left vertical part, a right vertical part, an upper horizontal part and a lower horizontal part, and the vertical parts are parallel to each other, and the horizontal parts are parallel to each other. The horizontal part is perpendicularly connected to the vertical part, and the turning angles at the connection points are all 90°.

[0008] Further, the dielectric constant of the dielectric resonator unit of the present invention is greater than or equal to 6.

[0009] Further, the cross-sections of the vertical dielectric strips and the horizontal dielectric strips of the all-dielectric resonator unit of the present invention are both rectangular.

[0010] Further, the turning angle at the joint of the right end of the upper horizontal part and the upper end of the right vertical part of the present invention is 90°, the turning angle at the joint of the lower end of the right vertical part and the right end of the lower horizontal part is 90°, and the lower horizontal part is The turning angle at the joint of the left end and the lower end of the left vertical part is 90°, and the turning angle at the joint of the upper end of the left vertical part and the right end of the upper horizontal part is 90°.

[0011] Further, the lengths of the upper horizontal part and the lower horizontal part of the present invention are equal, and the lengths of the left vertical part and the right vertical part are equal.

[0012] Further, the resonant device of the present invention is periodically distributed in both the X and Y directions, and the distribution period is p. The incident electromagnetic wave is in the Z direction, and the electric field polarization direction of the incident electromagnetic wave is in the Y direction. Among them, all the longitudinal rectangular dielectric strips are parallel to the electric field polarization direction of the incident electromagnetic wave, and all the transverse rectangular dielectric strips are perpendicular to the electric field polarization direction of the incident electromagnetic wave.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] (1) The structure design of the resonator of the present invention is simple, and the precision requirement for the processing technology is relatively low; on the one hand, the interface combination of two major materials is not required, which is beneficial to avoiding the material loss of the substrate and realizing high-Q resonance. On the other hand, there are no grooves and gaps that are difficult to process as in the prior art, and the processing is extremely convenient.

[0015] (2) At present, most of the high-Q resonant structures achieve ultra-high Q values by breaking symmetry and then using low asymmetry. However, this method requires high processing accuracy, which brings great difficulties to actual processing. Based on the premise of a symmetric structure, the present invention can easily achieve high-Q resonance by changing the structural parameters. Here, we introduce a simple method to achieve high-Q resonance in dielectric structures. The structure consists of an all-dielectric structure. Keeping the spacing between the left and right vertical parts fixed, the smaller the spacing between the upper and lower horizontal parts is changed, the higher the obtained Q value is. When the spacing between the upper and lower horizontal parts is equal to the dielectric resonance period, the resonance mode degenerates into a dark guided mode, supporting an infinite Q value and being suitable for ultra-sensitive sensing. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of an ultra-high Q guided-mode resonator provided by a specific embodiment of the present invention;

[0017] Figure 2 is Figure 1 the side view in

[0018] Figure 3 is Figure 1 the transmittance curve calculated when the length l of the ultra-high Q guided-mode resonator shown in

[0019] Figure 4 is Figure 1 the transmittance curve calculated when l = 300 microns for the ultra-high Q guided-mode resonator shown in

[0020] Figure 5 is Figure 1 the ultra-high Q graph calculated when each resonance of the ultra-high Q guided-mode resonator shown in DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] To better understand the present invention, the following further detailed description is provided in conjunction with the accompanying drawings.

[0022] Figure 1 and Figure 2 show an all-dielectric metamaterial ultra-high Q guided-mode resonator based on a symmetric structure of the present invention. As shown in Figure 1 and Figure 2 shown, the all-dielectric metamaterial ultra-high Q guided-mode resonator only includes "hui"-shaped dielectric resonance units distributed two-dimensionally periodically. As shown in Figure 1As shown, the "hui"-shaped dielectric resonator unit is composed of a left vertical part 11, a right vertical part 12, an upper horizontal part 21, and a lower horizontal part 22 connected in sequence as a whole, and the corner at each connection is 90°. The left vertical part 11 and the right vertical part 12 are parallel to each other; the upper horizontal part 21 and the lower horizontal part 22 are parallel to each other, and the vertical part and the horizontal part are perpendicular to each other. The distance between the left vertical part 11 and the right vertical part 12 is w, and the distance between the upper horizontal part 21 and the lower horizontal part 22 is l. The transverse dielectric strip and the vertical dielectric strip are both preferably in the form of rectangular strips (i.e., the cross-sections of the vertical dielectric strip and the transverse dielectric strip are both rectangular), that is, the cross-sections of the vertical dielectric strip and the transverse dielectric strip are both rectangular as the preferred embodiment. The dielectric constant of the material for constructing these dielectric strips is greater than or equal to 6.

[0023] Figure 1 In the "hui"-shaped dielectric resonator unit shown, the angle between the upper end of the left vertical part 11 and the left end of the upper horizontal part 21 is 90°, the angle between the lower end of the left vertical part 11 and the left end of the lower horizontal part 22 is 90°, the angle between the right end of the upper horizontal part 21 and the upper end of the right vertical part 12 is 90°, and the angle between the right end of the lower horizontal part 22 and the lower end of the right vertical part 12 is 90°, making the overall resonator unit present a shape similar to the Chinese character "hui".

[0024] As Figure 1 and Figure 2 shown, the "hui"-shaped dielectric resonator unit is periodically distributed in both the X and Y directions, and its distribution period is p. Among them, the length direction of the horizontal part is the X-axis direction, the length direction of the vertical part is the Y-axis direction, and the height h direction of the "hui"-shaped dielectric resonator unit is the Z-axis direction. The length of the vertical part is p, the length of the horizontal part is also p, the distance between the left vertical part and the right vertical part is w, and the distance between the upper horizontal part and the lower horizontal part is l.

[0025] The width of the left vertical part 11 is a1, the width of the right vertical part 12 is a2, the width of the upper horizontal part 21 is b1, the width of the lower horizontal part 22 is b1, w is the distance between the left vertical part 11 and the right vertical part 12, and l is the distance between the upper horizontal part 21 and the lower horizontal part 22.

[0026] In this embodiment, the left vertical part 11 and the right vertical part 12 have the same width, that is, a1 = a2 = a; the upper horizontal part 21 and the lower horizontal part 22 have the same width, that is, b1 = b2 = b; all the dielectric strips have the same height h, where a1 + a2 + w = p; b1 + b2 + l = p.

[0027] The following uses specific embodiments to illustrate the technical effects of the present invention:

[0028] In this embodiment, the dielectric constant of the silicon strip is 11.67, the horizontal spacing l of the silicon strip is 240 μm, the vertical spacing w of the silicon strip is 160 μm, the height h is 150 μm, and the period p is 300 μm. The incident electromagnetic wave is in the Z-axis direction, and the electric field polarization direction of the incident electromagnetic wave is in the Y-axis direction.

[0029] When the vertical spacing w is fixed at 160 μm and remains unchanged, the transmission spectra of the guided-mode resonator calculated by the finite element method for l = 240 μm and 270 μm in the range of 0.55 - 0.73 THz are shown as Figure 3 follows. It can be seen from Figure 3 that there are four resonances in this frequency range, which are respectively labeled as R 1 、R 2 、R 3 and R 4 . Resonances R 2 ~R 4 exhibit high Q-factors, while R 1 exhibits a low Q-factor. When l = 240 μm, the four resonances are located at 0.62 THz, 0.65 THz, 0.69 THz, and 0.71 THz respectively, and the Q value of R 3 is less than 10 3 . When the horizontal spacing l of the silicon strip increases to 270 μm, all its resonances will undergo a blue shift, and the linewidth of its Fano resonance is narrower and the Q value is higher. The Q value of R 3 can reach 10 5 .

[0030] During the process of increasing the horizontal spacing l of the silicon strip, the R 1 resonance is more sensitive to the change of parameters than the R 2 resonance, and its blue shift speed is faster with the increase of l. When l increases to 270 μm, the R 1 resonance and the R 2 resonance will interact to produce the EIT effect.

[0031] When the vertical spacing w is fixed at 160 μm and remains unchanged, the transmission spectra of the guided-mode resonator calculated by the finite element method for l = 300 μm in the range of 0.55 - 0.73 THz are shown as Figure 4 follows. At this time, the spacing l is equal to the resonance period p, and the two-dimensional dielectric resonance unit is equivalent to a one-dimensional grating structure. It can be seen from Figure 4 that the resonances R 2 、R 3 and R 4 disappear in the transmission spectrum, and only the R 1 resonance remains.

[0032] The fixed vertical part spacing w is kept at 160 microns. When the upper and lower horizontal part spacings l vary within the range of 240 - 300 microns, we calculated the Q factor of the resonance at the Γ point through eigenmode analysis, as Figure 5 shown. It can be seen from Figure 5 that as l continuously increases (the upper horizontal part width b1 and the lower horizontal part width b2 will decrease simultaneously), the Q values of the resonances R 2 , R 3 and R 4 constantly increase. When the horizontal part spacing l of the dielectric strip is equal to the dielectric resonance period p of 300 microns, their Q values tend to infinity (corresponding to the disappearance of the resonance in Figure 4 ).

[0033] Specifically, the grating in the Y direction disappears, resulting in the resonances R 2 , R 3 and R 4 becoming a dark guided mode resonance with an infinite Q factor, which means that the terahertz wave cannot be coupled with terahertz radiation whether it is normally incident or obliquely incident on the metamaterial. Its advantages are that high-Q factors can be achieved without precisely controlling the asymmetry of the structure, and it can be applied to high-performance devices and ultrasensitive sensors in the microwave band, terahertz band, and optical band, etc.

Claims

1. An all-dielectric metamaterial ultra-high Q guided mode resonator based on a symmetrical structure, characterized in that: The resonator is composed of two-dimensional periodically distributed "Yu"-shaped dielectric resonant units. Each dielectric resonant unit consists of a left vertical part, a right vertical part, an upper horizontal part and a lower horizontal part, and the vertical parts and the horizontal parts are parallel to each other, and the horizontal parts are vertically connected to the vertical parts, and the angle of the connection is 90°.

2. The all-dielectric metamaterial ultra-high Q guided mode resonator based on a symmetrical structure according to claim 1, characterized in that: The lengths of the upper horizontal part and the lower horizontal part are equal, and the lengths of the left vertical part and the right vertical part are equal. All the vertical rectangular dielectric strips are parallel to the electric field polarization direction of the incident electromagnetic wave, and all the horizontal rectangular dielectric strips are perpendicular to the electric field polarization direction of the incident electromagnetic wave.

3. The all-dielectric metamaterial ultra-high Q guided mode resonator based on a symmetrical structure according to claim 1, characterized in that: The material dielectric constant of the resonance unit is ≥6, the cross section is rectangular, and the spacing between the horizontal and vertical parts satisfies w≤l≤p, where w is the spacing between the left and right vertical parts, l is the spacing between the upper and lower horizontal parts, and p is the period length.

4. The all-dielectric metamaterial ultra-high Q guided mode resonator based on a symmetrical structure according to claim 1, characterized in that: The longitudinal spacing w remains unchanged, and only the transverse spacing l is changed, and the Q values ​​of multiple resonances will change. The larger the transverse spacing l, the higher the Q value, and thus the better the filtering effect.

5. The all-dielectric metamaterial ultra-high Q guided mode resonator based on a symmetrical structure according to claim 1, characterized in that: The Q value is controlled by adjusting the spacing l between the upper and lower transverse parts. When l approaches the period p, the resonator is equivalent to a one-dimensional grating structure, the resonant mode degenerates into a dark guided mode, and the Q value approaches infinity.

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