A sawtooth grating non-reciprocal device based on bound states in the quasi-continuum

Abstract

This application provides a sawtooth grating non-reciprocal device based on bound states in a quasi-continuous domain, comprising a plurality of grating unit cells. Each grating unit cell includes a silicon triangular prism layer, a silicon slab layer, and a silicon dioxide substrate layer. The silicon slab layer is disposed on the silicon dioxide substrate layer, and the silicon triangular prism layer is disposed on the silicon slab layer. The silicon triangular prism is a right triangular prism with an asymmetric triangular cross-section to form an in-plane asymmetric structure. The plurality of grating unit cells are periodically arranged laterally to form a sawtooth grating structure. The in-plane asymmetric structure is used to transform bound states in the continuous domain into bound states in the quasi-continuous domain to excite high-quality factor resonance modes and achieve non-reciprocal transport under the nonlinear effects of materials. The device of this invention has a simple structure, is easy to integrate, and can be used in fields such as optical isolation, optical transmission modulation, and optical signal processing.

Description

Technical Field

[0001] This application relates to the field of optical non-reciprocal devices, and in particular to a sawtooth grating non-reciprocal device based on bound states in a quasi-continuous domain. Background Technology

[0002] In the field of integrated photonics, optical non-reciprocal devices have significant application value in on-chip optical isolation, optical ring transmission, laser protection, and optical signal processing. As photonic integration technology advances towards miniaturization, high density, and low power consumption, developing compact, easily integrated optical devices with good non-reciprocal transmission performance has become an important research direction in this field.

[0003] Existing methods for realizing non-reciprocal optical devices mainly include magneto-optical effect schemes and time-varying modulation schemes. Magneto-optical effect schemes usually require the introduction of external magnetic fields or magnetic materials, resulting in complex structures, large device sizes, and poor compatibility with existing CMOS processes. While time-varying modulation schemes can overcome the reciprocity limitation, they typically require an additional modulation system, making the design and implementation process more complex and hindering the miniaturization and integrated application of devices.

[0004] In recent years, schemes for achieving non-reciprocal transport based on the nonlinear effects of materials have attracted widespread attention. These schemes typically do not require an external magnetic field and offer advantages such as compact structure and ease of on-chip integration. However, due to the inherently weak nonlinear response of the materials, the devices often require relatively high incident light intensity to achieve a significant non-reciprocal effect, thus limiting their practicality.

[0005] To enhance nonlinear effects in devices, researchers often introduce high-quality-factor optical resonant structures to increase local electric field strength and amplify the material's nonlinear response. Bound-in-continuum (BIC) states in the continuous domain, due to their theoretically extremely high quality factor and excellent field localization capabilities, have become one of the important mechanisms for enhancing optical field effects. By introducing appropriate structural symmetry breaking, ideal BIC states can be transformed into bound-in-continuum (QBIC) modes that can be excited externally, achieving effective coupling with external radiation fields while maintaining high-quality-factor characteristics.

[0006] Therefore, how to design a micro / nano grating device that combines structural asymmetry with high quality factor QBIC resonance characteristics to achieve good non-reciprocal transport performance under material nonlinearity is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] In view of this, the main objective of this application is to solve one of the aforementioned problems.

[0008] This application provides a non-reciprocal sawtooth grating device based on bound states in a quasi-continuous domain, comprising:

[0009] A plurality of grating unit cells, each grating unit cell comprising a silicon triangular prism layer, a silicon slab layer, and a silicon dioxide substrate layer; the silicon slab layer is disposed on the silicon dioxide substrate layer, and the silicon triangular prism layer is disposed on the silicon slab layer; the silicon triangular prism is a right triangular prism, and the cross-section of the silicon triangular prism is an asymmetric triangle to form an in-plane asymmetric structure; the plurality of grating unit cells are periodically arranged in the transverse direction to form a sawtooth grating structure, the in-plane asymmetric structure being used to transform bound states in a continuous domain into bound states in a quasi-continuous domain to excite high quality factor resonance modes and achieve non-reciprocal transport under the nonlinear effect of materials.

[0010] Furthermore, both the silicon triangular prism layer and the silicon plate layer are made of silicon material, and the silicon dioxide substrate layer is made of silicon dioxide material.

[0011] Furthermore, in the cross-section of the silicon triangular prism, the edge closest to the silicon substrate is the bottom edge, the bottom edge is L1, the point furthest from the silicon substrate is the vertex, the distance of the vertex from the horizontal center of symmetry of the bottom edge is L2, and the asymmetry coefficient α is defined as L2 / L1, and α>0.

[0012] Furthermore, by adjusting the asymmetry coefficient α, the symmetry-protected continuous-domain bound state BIC in the device is transformed into a quasi-continuous-domain bound state QBIC mode with a finite quality factor.

[0013] Furthermore, the resonant wavelength of the QBIC mode of the silicon grating does not change with the asymmetry coefficient α; the quality factor of the QBIC mode is proportional to the negative square of the asymmetry coefficient α.

[0014] The beneficial effects of this application are as follows:

[0015] 1. The device of the present invention adopts a sawtooth grating structure composed of a silicon triangular prism layer, a silicon plate layer and a silicon dioxide substrate layer. The overall configuration is clear, suitable for micro-nano fabrication, and can be well compatible with silicon-based integrated photonics platforms.

[0016] 2. The sawtooth grating non-reciprocal device provided by this invention supports multiple symmetry-protected QBICs, has a high Q value and a strong electric field enhancement effect, and can significantly enhance the third-order nonlinear effect of silicon. It can achieve strong non-reciprocal response of multiple wavelengths without the need for external bias. The device has a simple structure, is easy to miniaturize and integrate, and has broad application prospects. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the non-reciprocal device structure of the quasi-continuous domain bound-state sawtooth grating based on the present invention, wherein, Figure 1 (a) in the diagram is a three-dimensional structure diagram. Figure 1 (b) in the diagram is a two-dimensional structure diagram.

[0018] Figure 2 This is a comparison of the transmission spectra of the silicon grating under in-plane symmetric and asymmetric conditions of the present invention.

[0019] Figure 3 This is a graph showing the functional relationship between different QBIC values ​​and the asymmetry coefficient α in an embodiment of the present invention. Figure 3 (a) in the figure is a graph showing the functional relationship between the three QBIC resonant frequencies and the asymmetry coefficient α in an embodiment of the present invention. Figure 3 (b) in the figure shows the functional relationship between the three QBIC quality factors and α.

[0020] Figure 4 These are the forward and reverse transmission spectra of different QBIC modes under linear and nonlinear conditions in embodiments of the present invention, wherein... Figure 4 (a) in the figure shows the forward and reverse transport spectra of QBIC1 under linear and nonlinear conditions in an embodiment of the present invention. Figure 4 (b) in the figure shows the forward and reverse transport spectra of QBIC2 under linear and nonlinear conditions in an embodiment of the present invention. Figure 4 (c) in the figure is the forward and reverse transmission spectrum of QBIC3 under linear and nonlinear conditions in the embodiment of the present invention.

[0021] Figure 5 This is a graph showing the functional relationship between forward and reverse transmittance and incident light intensity under different wavelengths of incident light in an embodiment of the present invention. Figure 5 (a) in the figure is a graph showing the functional relationship between forward and reverse transmittance and incident light intensity under incident light intensity at a wavelength of 1038.8 nm in an embodiment of the present invention. Figure 5 (b) in the figure is a graph showing the functional relationship between forward and reverse transmittance and incident light intensity under incident light intensity at a wavelength of 1293.3 nm in an embodiment of the present invention. Figure 5 (c) in the figure is a graph showing the relationship between forward and reverse transmittance and incident light intensity under incident light intensity at a wavelength of 1595.6 nm in an embodiment of the present invention.

[0022] Figure 6 This is a graph showing the functional relationship between the isolation of different QBIC modes and the incident wavelength and light intensity in an embodiment of the present invention. Figure 6 (a) in the figure is a graph showing the functional relationship between the isolation of the QBIC1 mode and the incident wavelength and light intensity in an embodiment of the present invention. Figure 6 (b) in the figure is a graph showing the functional relationship between the isolation of the QBIC2 mode and the incident wavelength and light intensity in an embodiment of the present invention. Figure 6 (c) in the figure is a function graph showing the relationship between the isolation of the QBIC3 mode and the incident wavelength and light intensity in an embodiment of the present invention. Detailed Implementation

[0023] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the application. Furthermore, it should be noted that, for ease of description, only the parts relevant to the application are shown in the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features described in the present application can be combined with each other.

[0024] like Figure 1 (a) and Figure 1 As shown in (b) of the figure, this embodiment provides a non-reciprocal sawtooth grating device based on bound states in a quasi-continuous domain. The device consists of several grating unit cells arranged periodically along the transverse direction, and each grating unit cell includes a silicon triangular prism layer, a silicon slab layer, and a silicon dioxide substrate layer.

[0025] The silicon slab layer is disposed on the silicon dioxide substrate layer, and the silicon triangular prism layer is disposed on the silicon slab layer. The silicon triangular prism is a right triangular prism structure with an asymmetrical triangular cross-section to form an in-plane asymmetrical structure. Multiple grating unit cells are arranged periodically in the transverse direction to collectively form a sawtooth grating structure.

[0026] In this embodiment, both the silicon triangular prism layer and the silicon plate layer are made of silicon material, and the silicon dioxide substrate layer is also made of silicon dioxide material. This structure facilitates integration with existing silicon-based photonic devices and allows for the utilization of the nonlinear optical effects of silicon material to achieve non-reciprocal transport functionality in the device.

[0027] To more clearly illustrate the structural features of the present invention, in the cross-section of the silicon triangular prism, the edge closest to the silicon substrate is defined as the base edge, and the length of the base edge is denoted as L1; the corner point furthest from the silicon substrate is defined as the vertex. The vertex is laterally offset relative to the horizontal center of symmetry of the base edge, and the offset distance is denoted as L2. Thus, the in-plane asymmetry coefficient α is defined as α = L2 / L1, and α > 0. By setting the vertex offset, the in-plane symmetry of the structure can be broken, thereby forming an asymmetric sawtooth unit cell supporting quasi-continuous domain bound states.

[0028] In this embodiment, as a preferred but not limited structural parameter setting, the grating unit cell period P is 500 nm, the base length L1 of the silicon triangular prism is 400 nm, the vertex offset distance L2 is 60 nm, and the corresponding asymmetry coefficient α is 0.15. The height H1 of the silicon triangular prism is 320 nm, the thickness H2 of the silicon substrate is 300 nm, and the thickness H3 of the silicon dioxide substrate is 1 μm.

[0029] Under these structural parameters, the sawtooth grating device supports multiple quasi-continuous bound-state (QBIC) modes in the infrared band, induced by symmetry protection. Compared to in-plane symmetric structures, when the vertices are not shifted, the correlated modes in the structure exhibit ideal continuous bound-state (BIC) modes, which are difficult to be effectively excited by external incident light. When the vertex shift is introduced, the symmetry is broken, and the ideal BIC state is transformed into a QBIC mode with a finite quality factor, thereby enabling coupling with the external radiation field and forming obvious resonance characteristics in the transmission spectrum.

[0030] Numerical simulation can be used to further illustrate the working mechanism of this invention. Figure 2 The transmission spectra of the in-plane symmetric and in-plane asymmetric structures are compared. When the structure maintains in-plane symmetry, no obvious QBIC resonance peaks appear in the transmission spectrum; when the in-plane asymmetry is introduced, multiple narrow-linewidth resonance peaks appear in the transmission spectrum, indicating that the structure can support multiple QBIC modes.

[0031] Furthermore, the quality factor Q of the QBIC mode can be controlled by adjusting the asymmetry coefficient α. Figure 3 Figure (a) shows the relationship between the resonant wavelength and different asymmetry coefficients α. Figure 3 Figure (b) shows the relationship between the quality factor Q and different asymmetry coefficients α. Simulation results show that the resonant wavelength of the QBIC mode remains essentially constant with the change of the asymmetry coefficient α, while the quality factor Q is proportional to the negative square of the asymmetry coefficient α. Therefore, this invention can effectively control the resonant quality factor by adjusting the degree of structural asymmetry without significantly changing the operating wavelength.

[0032] Under the given parameters in this embodiment, the device supports three relatively typical QBIC modes in the infrared band, with resonant wavelengths around 1038.8 nm, 1293.3 nm, and 1595.6 nm, respectively, corresponding to quality factors of 480, 714, and 1878. Under linear conditions, all three QBIC modes exhibit significant high-Q resonance characteristics and strong local electric field enhancement capabilities. The above parameters and results are merely illustrative of the invention and do not constitute a limitation on the scope of protection of the invention.

[0033] The non-reciprocal transmission characteristic of the device in this invention mainly stems from the combined effect of structural asymmetry and material nonlinearity. On one hand, the QBIC mode has a high quality factor, which can significantly enhance the local electric field under resonant conditions, thereby amplifying the nonlinear optical response of silicon material. On the other hand, due to the in-plane asymmetry of the device structure, the coupling conditions between the forward and reverse incident light and the QBIC mode differ. Therefore, under nonlinear effects, the device exhibits different transmission responses to forward and reverse incident light, achieving non-reciprocal transmission.

[0034] Figure 4 (a) Figure 4 (b) Figure 4 Figure (c) shows the forward and reverse transmission spectra of the three QBIC modes under linear and nonlinear conditions, respectively. Simulation results show that under linear conditions, the forward and reverse transmission spectra of the device are basically coincident; however, after considering the material nonlinearity, the forward and reverse transmission spectra show significant differences, indicating that the device has significant non-reciprocal transmission characteristics near the corresponding resonant wavelengths.

[0035] Figure 5 (a) Figure 5 (b) Figure 5 Figure (c) shows the curves showing the relationship between the forward and reverse transmittance of the device and the incident light intensity at different operating wavelengths. It can be seen that the forward and reverse transmittance show different trends as the incident light intensity changes, indicating that the device can exhibit different degrees of non-reciprocal response range at different operating points.

[0036] Figure 6 (a) Figure 6 (b) Figure 6 Figure (c) shows the relationship between the device isolation and the incident wavelength and incident light intensity. Simulation results show that, under the structural parameters of this embodiment, the device can achieve high isolation near multiple operating wavelengths. Specifically, the maximum isolation reaches 50 dB when incident near 1038.8 nm; 67 dB when incident near 1293.3 nm; and 4 dB when incident near 1595.6 nm. Correspondingly, under nonlinear conditions, the non-reciprocal intensity range (NRIR) of the device near the above three wavelengths are 2.99, 2.81, and 1.27, respectively. The above results demonstrate that the sawtooth grating non-reciprocal device provided by this invention can achieve strong non-reciprocal transmission effects in multiple infrared bands.

[0037] The device performance in this embodiment can be analyzed using electromagnetic simulation software, such as the finite element method, to solve for the device's transmission spectrum, resonance mode, electric field distribution, and forward and reverse transmission characteristics. In the simulation, the area above the device can be designated as port 1, and the area below as port 2, to define the forward and reverse incident conditions, respectively. By comparing the transmission responses under different incident directions, the non-reciprocal performance of the device can be evaluated.

[0038] The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of this application as claimed. The scope of protection of this application is defined by the appended claims and their equivalents.

Claims

1. A non-reciprocal sawtooth grating device based on bound states in a quasi-continuous domain, characterized in that, include: A plurality of grating unit cells, wherein the grating unit cell includes a silicon triangular prism layer, a silicon plate layer and a silicon dioxide substrate layer; The silicon plate layer is disposed on the silicon dioxide substrate layer, and the silicon triangular prism layer is disposed on the silicon plate layer; The silicon triangular prism is a right triangular prism, and the cross-section of the silicon triangular prism is an asymmetrical triangle to form an in-plane asymmetrical structure; A number of the aforementioned grating unit cells are arranged periodically along the transverse direction to form a sawtooth grating structure. The in-plane asymmetric structure is used to transform the bound states in the continuous domain into bound states in the quasi-continuous domain, so as to excite the high quality factor resonance mode and realize non-reciprocal transport under the nonlinear effect of the material.

2. The sawtooth grating non-reciprocal device based on bound states in a quasi-continuous domain according to claim 1, characterized in that, Both the silicon triangular prism layer and the silicon plate layer are made of silicon material, and the silicon dioxide substrate layer is made of silicon dioxide material.

3. The sawtooth grating non-reciprocal device based on bound states in a quasi-continuous domain according to claim 1, characterized in that, In the cross-section of the silicon triangular prism, the side closest to the silicon substrate is the base, the base is L1, the point furthest from the silicon substrate is the vertex, and the distance of the vertex from the horizontal center of symmetry of the base is L2. The asymmetry coefficient α is defined as L2 / L1, and α>0.

4. The sawtooth grating non-reciprocal device based on bound states in a quasi-continuous domain according to claim 3, characterized in that, By adjusting the asymmetry coefficient α, the symmetry-protected continuous-domain bound state BIC in the device is transformed into a quasi-continuous-domain bound state QBIC mode with a finite quality factor.

5. A non-reciprocal sawtooth grating device based on bound states in a quasi-continuous domain according to claim 1, characterized in that, The resonant wavelength of the QBIC mode of the silicon grating does not change with the asymmetry coefficient α; the quality factor of the QBIC mode is proportional to the negative square of the asymmetry coefficient α.

Images