Defect quasi-periodic photonic crystal structure for enhancing gh shift and applications thereof

Abstract

This invention discloses a defect-laden quasi-periodic photonic crystal structure for enhancing GH shift. It is a hybrid structure formed by combining four media with different refractive indices according to a specific arrangement rule. This arrangement rule is defined as follows: a symmetrical medium structure in the middle, and quasi-periodic photonic crystal structures on either side of the symmetrical medium structure. The symmetrical medium structure consists of a single layer of MoS2 and two layers of HfO2 symmetrically distributed on either side of the single-layer MoS2. The quasi-periodic photonic crystal structures consist of alternating Li2O and Si layers templated by Pell sequences, with the quasi-periodic photonic crystal structures on either side stacked at periods N and M, respectively. In this structure, the single-layer MoS2 is sandwiched between two quasi-periodic photonic crystals arranged by Pell sequences. By optimizing the thickness of all components and the number of periods in the sequences, the GH shift of the designed structure is significantly enhanced at a specific operating wavelength.

Description

Technical Field

[0001] This invention relates to the field of optical devices, specifically to a defective quasi-periodic photonic crystal structure for enhancing Goos- Applications of (GH) displacement. Related to the physical properties of monolayer MoS2 and optoelectronic devices. Background Technology

[0002] The Goos-Hanshin shift is an anomalous optical phenomenon that occurs when a beam of light with a finite cross-sectional area undergoes total internal reflection at the interface between two media with different refractive indices. This results in a lateral displacement, meaning the reflection point and the incident point are not at the same point. This displacement is called the Goos-Hanshin shift. GH displacement. In the field of optics, the GH displacement effect can be applied to optical waveguides. By utilizing the properties of GH displacement, such as angle and focal point shift, the beam in the waveguide can be adjusted and waveguide sensors can be manufactured.

[0003] In existing technologies, monolayer MoS2 has attracted widespread attention due to its limited band gap and has become a potential candidate material for exploring GH displacement. However, the small magnitude of the GH displacement in pure monolayer MoS2 greatly hinders its application in optoelectronic sensors and detectors. Therefore, a new method is needed to enhance its GH displacement.

[0004] A defective quasi-periodic photonic crystal refers to a structure containing one or more defects within a photonic crystal. A photonic crystal is an optical structure capable of controlling light transmission through a periodic arrangement of media with different dielectric constants. In this structure, the wavelength of light is comparable to the lattice constant, allowing the photonic crystal to form a bandgap structure containing a photonic bandgap. When defects are introduced into a photonic crystal, light propagation is suppressed or altered, resulting in interesting optical effects. For example, defective photonic crystals can enable high-efficiency optical coupling, high-sensitivity optical sensing, and high-quality-factor microcavity optical devices. Defective quasi-periodic photonic crystals can be generated through various methods, such as introducing defects into the existing lattice or splicing two different photonic crystals together to form a defect. These defect structures interact with the photonic bandgap structure in the crystal, leading to a variety of complex optical effects in light transmission. These effects have broad application prospects in optical device design and optical sensing. Therefore, designing a defective quasi-periodic photonic crystal structure to improve the amplitude of the GH shift is a problem that needs to be solved in this field. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to address the shortcomings of existing technologies by providing a defect quasi-periodic photonic crystal structure for enhancing GH displacement.

[0006] Technical solution: The defect quasi-periodic photonic crystal structure for enhancing GH displacement described in this invention is a hybrid structure formed by combining four media with different refractive indices according to an arrangement rule;

[0007] The arrangement rule is defined as: a symmetrical medium structure in the middle, and quasi-periodic photonic crystal structures on both sides of the symmetrical medium structure;

[0008] The symmetrical medium structure consists of a single layer of MoS2 and two layers of HfO2 symmetrically distributed on both sides of the single layer of MoS2.

[0009] The quasi-periodic photonic crystal structure consists of alternating Li2O and Si layers using Pell sequences as templates, with the quasi-periodic photonic crystal structures on both sides superimposed with periods N and M, respectively.

[0010] A further preferred embodiment of the present invention is that the thickness of the single-layer Si layer is 77 nm, the thickness of the single-layer Li2O layer is 46 nm, the thickness of the single-layer HfO2 layer is 50 nm, and the thickness of the single-layer MoS2 layer is 0.65 nm.

[0011] Preferably, the refractive index of Li2O is 1.65, the refractive index of Si is 3.42, and the refractive index of HfO2 is 1.975.

[0012] Preferably, the dielectric constant of monolayer MoS2 at room temperature is 18.66-57.00 when the incident wavelength is in the range of 300-900 nm.

[0013] Preferably, the periods N and M of the Pell sequence are 2 and 3, respectively.

[0014] Preferably, the structure has a maximum amplification factor of 3445.3 for the GH displacement.

[0015] The defect quasi-periodic photonic crystal structure described above for enhancing GH displacement can be applied to the fabrication of optical modulators, sensors, or solar cells.

[0016] Beneficial Effects: This invention provides a defective quasi-periodic photonic crystal structure for enhancing GH shift. In this structure, a monolayer of MoS2 is sandwiched between two quasi-periodic photonic crystals arranged in Pell sequences. By optimizing the thickness of all components and the number of periods in the sequences, the GH shift of the designed structure is significantly enhanced at a specific operating wavelength.

[0017] Furthermore, this invention also explores the effect of dielectric composition thickness on GH displacement. This invention confirms that defective quasi-periodic photonic crystal structures possess the ability to enhance GH displacement, provides a novel platform for GH displacement research, and greatly promotes the application of this defective structure in optoelectronic devices. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of a defect quasi-periodic photonic crystal structure used to enhance GH displacement in the embodiment.

[0019] Figure 2 The graph shows the dielectric constant of monolayer MoS2 at room temperature as a function of incident wavelength.

[0020] Figure 3 middle, Figure 3 (a) is a graph showing the relationship between the GH displacement of the reflected wave and the wavelength in a hybrid structure with or without a monolayer of MoS2. Figure 3 (b) is a graph showing the relationship between the phase and wavelength of the reflected wave in a hybrid structure with or without a monolayer of MoS2. Figure 3 (c) is a graph showing the relationship between reflectivity and wavelength in a hybrid structure with or without a monolayer of MoS2.

[0021] Figure 4 The image shows a periodic photonic crystal (BBA) with a monolayer MoS2 mixed structure (solid line), a non-monolayer MoS2 mixed structure (dashed line), and defects at a wavelength of 490.8 nm. 2N / C / M / C / (BBA) M A graph showing the relationship between the magnetic field distribution of the structure (the broken line) and the distance.

[0022] Figure 5 middle, Figure 5 (a) represents the GH displacement of the reflected wave in the hybrid structure and d a Relationship change diagram; Figure 5 (b) represents the GH displacement of the reflected wave in the hybrid structure and d b Relationship change diagram; Figure 5 (c) represents the GH displacement of the reflected wave in the hybrid structure and d. c Relationship change diagram.

[0023] Figure 6 The graph shows the relationship between the GH displacement and wavelength of the reflected wave in the hybrid structure under different M and N conditions. Detailed Implementation

[0024] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the embodiments described.

[0025] Example: A defect quasi-periodic photonic crystal structure for enhancing GH displacement, which is a hybrid structure formed by combining four media with different refractive indices according to an arrangement rule.

[0026] a. The left and right parts are quasi-periodic photonic crystal structures, including Li2O and Si layers with Pell sequences as templates. The two constituent materials in the Pell sequence are Si and Li2O, with thicknesses of 77 nm and 46 nm, respectively, and they are stacked alternately with periods of N and M.

[0027] Quasi-periodic photonic crystals are composed of two dielectric materials labeled A and B, arranged according to the Pell sequence, which can be represented as: P n =2P n-1 P n-2 (n≥3), where P1=A, P2=B. In this embodiment, sequences P3 and P4 are used as two Pell sequences for single periods on the left and right sides. N and M are 2 and 3, respectively.

[0028] b. The middle part consists of a single layer of MoS2 and HfO2. The thickness of the single layer of MoS2 is 0.65 nm and the thickness of HfO2 is 50 nm. Both are arranged parallel to the quasi-periodic photonic crystal structures on both sides.

[0029] c. Si with a refractive index of 3.42, Li₂O with a refractive index of 1.65, HfO₂ with a refractive index of 1.975, and substances whose dielectric constant varies with incident wavelength, such as... Figure 2 The monolayer MoS2 shown is combined according to the above rules to form a hybrid structure.

[0030] In this scenario, incident light strikes the surface of the hybrid structure at an angle θ. Materials A and B are Si and Li₂O, respectively, with refractive indices n0 and n0, respectively. A and n B Their thicknesses are d A and d B Material C is HfO2, and its refractive index and thickness are n, respectively. c and d C The dielectric constant and thickness of a single-layer MoS2 are ε and d, respectively. M .

[0031] Experiments have shown that the dielectric constant of monolayer MoS2 at room temperature (T = 300 K) is given by the pentaelectrode critical point model:

[0032]

[0033] The Transfer Matrix Method (TMM) is a numerical simulation method used to calculate the behavior of light waves propagating in complex multilayer media. The TMM method divides the medium into a series of cells and calculates the transfer matrix of each cell, ultimately determining the transfer matrix of the entire system. The transfer matrix describes the behavior of light waves propagating between cells, including reflection, transmission, and phase changes. Using the TMM method, light transmission characteristics in complex multilayer media, such as reflectivity, transmittance, propagation time, and phase, can be calculated. The TMM method is widely used in optics, such as optical device design, thin-film optics, and refractive index measurement. Essentially, this method connects the electric and magnetic fields of one layer to the magnetic and electric fields of adjacent layers in matrix form. Assume M... j If is the characteristic matrix of layer j in a multi-layer structure, then the total transition matrix can be obtained by formula (2).

[0034]

[0035] in, Parameters c and ε j and are the speed of light in air and the dielectric constant of the j-th layer, respectively. For the corresponding transverse electric wave (TE,s) and transverse magnetic wave (TM,p), respectively... and

[0036]

[0037] For the s(p) wave, q0 = q s =cosθ(q0=q s =1 / cosθ); m ij (i,j=1,2) are the components of the total matrix M of the multilayer defect quasi-periodic photonic crystal structure.

[0038] After obtaining the reflection coefficient, the GH displacement of the defective quasi-periodic photonic crystal structure can be calculated using the fixed phase method through formula (3).

[0039]

[0040] Where S represents the GH offset of the reflection, The phase of the reflection coefficient, k x This represents the transverse component of the incident light vector.

[0041] The fixed-phase method is a method used to calculate the Gushanshin displacement in optical interference. In the fixed-phase method, the relative intensity and relative phase difference of the light are measured, and then the Gushanshin displacement is determined by calculating the change in the relative phase difference. The fixed-phase method requires the use of an interferometer, typically a laser interferometer. During measurement, a sample and a reference sample are placed in the path of the laser beam. As the light passes through the sample and the reference sample, interference fringes are generated due to the optical path difference between them. The Gushanshin displacement is calculated by observing the changes in the interference fringes. In the fixed-phase method, the relative phase difference is calculated by dividing the interference fringes into several regions of equal width. In each region, the relative phase difference of the interference fringes is considered fixed, and therefore can be used to calculate the Gushanshin displacement. This method has high accuracy and reliability, and is particularly suitable for measuring minute displacements or deformations.

[0042] Figure 3 (a) shows the relationship between the GH displacement (S) and wavelength of the reflected wave in a hybrid structure with a single layer of MoS2 (solid line). Figure 3 In (a), a positive peak with a value of 3445.3λ is observed in the GH shift spectrum of the hybrid structure at an operating wavelength of 490.8 nm. For comparison, the GH shift of the reflected wave as a function of wavelength is shown (dashed line) in the hybrid structure without monolayer MoS2. A relatively wide and shallow dip with a value of only -139.6λ is observed at 490.63 nm when monolayer MoS2 is absent in the hybrid structure. Clearly, the GH peak in the hybrid structure with monolayer MoS2 is almost 24.7 times the absolute value of the GH peak and valley in the hybrid structure without monolayer MoS2, confirming that combining a defective quasi-periodic photonic crystal structure with monolayer MoS2 can significantly enhance the GH shift. This result demonstrates the potential of Pell quasi-periodic photonic crystals in improving the GH performance of monolayer MoS2, which may promote the application of quasi-periodic photonic crystals in sensor and detector devices.

[0043] Figure 3(b) shows the relationship between the phase and wavelength of the reflected wave in hybrid structures with and without a single layer of MoS2 (solid line) and without MoS2 (dashed line). It can be seen that the locations of abrupt phase changes in the hybrid structures with and without a single layer of MoS2 coincide with the locations of the peak or trough values ​​of the GH displacement, but their trends differ. In the hybrid structure with a single layer of MoS2, the phase of the reflected wave increases sharply with increasing wavelength, but in the hybrid structure without a single layer of MoS2, the phase of the reflected wave gradually decreases with increasing wavelength. This directly leads to the different signs of the GH displacement in the hybrid structures with and without MoS2. These conclusions indicate that the amplitude and sign of the GH displacement of the hybrid structure are determined by the phase change of its reflection coefficient.

[0044] Figure 3 (c) Shows graphs illustrating the relationship between reflectivity (solid and dashed lines) and wavelength for hybrid structures with and without monolayer MoS2. Figure 3 As shown in (c), due to the ultrathin thickness of the monolayer MoS2, the reflectance curves in the hybrid structures with and without monolayer MoS2 are basically similar, with values ​​first decreasing and then increasing with increasing wavelength. The main difference lies in the minimum reflectance values, which are 0 and 0.048, respectively. Furthermore, for the hybrid structures with and without monolayer MoS2, the wavelengths at which the minimum reflectance occurs are slightly different, located at 490.8 nm and 490.63 nm, respectively, which also coincide with the locations of the GH peak / valley values ​​and significant phase changes. The comparison of GH shift, phase, and reflectance between the hybrid structures with and without monolayer MoS2 also demonstrates the important role of monolayer MoS2 in generating a large GH shift in quasi-periodic photonic crystals, opening new prospects for achieving enhanced GH shift in monolayer TMDC within the visible light wavelength range.

[0045] To reveal the underlying mechanism behind GH displacement enhancement Figure 4The graph shows the relationship between magnetic field distribution and distance in a hybrid structure containing a monolayer MoS2 (solid line) at a wavelength of 490.8 nm. It can be observed that the magnetic field strength oscillates along the z-direction as electromagnetic waves propagate within the hybrid structure. The interaction between the standing wave within the defect layer and the electromagnetic wave in the quasi-periodic photonic crystal ensures that the strongest magnetic field strength occurs inside the left-hand quasi-periodic photonic crystal, very close to the location of the defect layer. As the electromagnetic wave enters the Pell quasi-periodic photonic crystal, moving away from the location of the strongest magnetic field strength, the maximum value of the magnetic field strength decreases. A comparison is made with the magnetic field distribution versus distance graph in a hybrid structure without a monolayer MoS2 (dashed line). Clearly, due to the ultrathin thickness of the monolayer MoS2, the magnetic field distribution curves of the hybrid structures with and without a monolayer MoS2 are very similar, but the maximum magnetic field strength of the hybrid structure containing a monolayer MoS2 is greater than that of the hybrid structure without a monolayer MoS2. This is compared with a defect-periodic photonic crystal (BBA). 2N / C / M / C / (BBA) M Compared to the kink line, the maximum magnetic field strength near the left defect layer of the defective quasi-periodic photonic crystal is significantly greater than that of the defective periodic photonic crystal. These results indicate that in the hybrid structure with a monolayer of MoS2, the coupling between the incident wave and the strong localized modes within the quasi-periodic photonic crystal near the left defect layer enhances the absorptivity of the hybrid structure, i.e., reduces its reflectivity, and causes a dramatic phase change at the specified wavelength, thereby enhancing its GH shift.

[0046] To explore the effect of the thickness of dielectric materials A, B, or C on the displacement of the hybrid structure GH, the results were plotted on... Figure 5 In, all other parameters remain the same as Figure 3 same. Figure 5 (a) shows the variation of GH displacement with wavelength for the hybrid structure at different thicknesses of material A, with thicknesses d and d respectively. a =76nm, 76.5nm, 77nm, 77.5nm, and 78nm. It can be observed that for each thickness of dielectric material A, the hybrid structure exhibits either a GH displacement peak or a GH displacement valley. With d a From 76 nm to 77 nm, the GH shift spectrum of the hybrid structure shows a GH shift peak, and its value continuously increases; when d a When the wavelength is 77.5 nm, the original GH displacement peak value of the hybrid structure becomes the GH displacement valley value. a When the thickness of the A layer increases further to 78 nm, the absolute value of the GH displacement valley in the hybrid structure decreases. Furthermore, with the increase of the thickness of the A layer, the location of the GH displacement peak or valley in the hybrid structure shifts towards increasing wavelength. When the thickness of the B layer changes from 44 nm to 48 nm, the relationship between the GH displacement of the hybrid structure and wavelength is plotted, and the results are as follows: Figure 5 As shown in (b). From Figure 5 As can be seen in (b), for each d b The hybrid structure still has a GH displacement peak or a GH displacement valley, and as d b As d increases, the location of the GH displacement peak or GH displacement valley will redshift. The difference is that as d... b As the wavelength increased from 44nm to 48nm, the original GH displacement valley value of the hybrid structure became the GH displacement peak value, and the GH displacement amplitude increased from -468.5λ to 292.6λ. Figure 5 (c) shows the hybrid structure at different d c The GH displacement varies with wavelength. It can be seen that when d... c When the wavelength changes from 48 nm to 52 nm, the sign of the GH displacement of the hybrid structure changes from negative to positive. Along with this sign change, the location of the GH displacement valley or peak still exhibits a redshift, but the shift in the valley location is relatively small. The results indicate that the thickness of dielectric materials A, B, or C not only affects the magnitude of the GH displacement of the hybrid structure but also alters its sign, thus making it possible to control the GH displacement in quasi-periodic photonic crystals.

[0047] To further improve the flexibility of modulating GH displacement, this embodiment also explores the influence of the number of periods on both sides of the quasi-periodic photonic crystal on the GH displacement in the hybrid structure. Figure 6 The variation of the GH displacement of the hybrid structure with wavelength under different M and N conditions is shown, where the values ​​of M and N are M,N = 1, 2, M,N = 3, 2, M,N = 4, 2, and M,N = 1, 4. The study found that when N is fixed at 2, the value of M has a significant impact on the GH displacement of the hybrid structure. As expected, the hybrid structure with M,N = 3, 2 has the largest peak GH displacement in these three cases, since these two values ​​of M and N are optimized. When M,N = 1, 2, the GH displacement of the hybrid structure is negative within the wavelength range under discussion, and its absolute value first increases with increasing wavelength and then decreases, with a maximum negative value of -290.33λ. Conversely, when M,N = 4, 2, the GH displacement of the hybrid structure is positive, with a maximum value of 1174.6λ. Furthermore, simultaneous changes in the values ​​of M and N also have a significant impact on the GH displacement of the hybrid structure. When M = 1 and N = 4, the GH displacement values ​​are both positive, but the peak GH value is only 260.9λ. These results highlight the potential of the period number of quasi-periodic photonic crystals to generate controllable GH shifts in hybrid structures, which makes it possible for future applications of this structure in switchable sensors and other photonic devices.

[0048] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A defect quasi-periodic photonic crystal structure for enhancing GH shift, characterized in that, This structure is a hybrid structure formed by combining four media with different refractive indices according to an arrangement rule; The arrangement rule is defined as: a symmetrical medium structure in the middle, and quasi-periodic photonic crystal structures on both sides of the symmetrical medium structure; The symmetrical medium structure consists of a single layer of MoS2 and two layers of HfO2 symmetrically distributed on both sides of the single layer of MoS2. A quasi-periodic photonic crystal structure is constructed from two dielectric materials labeled A and B according to the Pell sequence, which is represented as: ,in , Materials A and B are made of Si and Li2O, respectively, and the quasi-periodic photonic crystal structures on both sides are superimposed with periods N and M, respectively.

2. The defect quasi-periodic photonic crystal structure for enhancing GH displacement according to claim 1, characterized in that, The thickness of a single Si layer is 77 nm, the thickness of a single Li2O layer is 46 nm, the thickness of a single HfO2 layer is 50 nm, and the thickness of a single MoS2 layer is 0.65 nm.

3. The defect quasi-periodic photonic crystal structure for enhancing GH displacement according to claim 1, characterized in that, The refractive index of Li₂O is 1.65, that of Si is 3.42, and that of HfO₂ is 1.

975.

4. The defect quasi-periodic photonic crystal structure for enhancing GH displacement according to claim 1, characterized in that, The dielectric constant of monolayer MoS2 at room temperature is 18.66-57.00 when the incident wavelength is in the range of 300-900 nm.

5. The defect quasi-periodic photonic crystal structure for enhancing GH displacement according to claim 1, characterized in that, The periods N and M of the Pell sequence are 2 and 3, respectively.

6. The defect quasi-periodic photonic crystal structure for enhancing GH displacement according to claim 1, characterized in that, The maximum amplification factor for the GH displacement of this structure is 3445.

3.

7. A defect quasi-periodic photonic crystal structure for enhancing GH displacement as described in claim 1, applied to the fabrication of optical modulators, sensors, or solar cells.

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