Irregular resonant cavity based on transformation optics

Abstract

This invention discloses an irregularly shaped resonant cavity based on transformation optics. An array of holes is formed on the substrate of a whispering-gallery resonant cavity. The spatial distribution of the array hole diameters satisfies the equation, and the refractive index distribution n(x,y) of the medium on the substrate satisfies the equation. This application uses transformation optics design methods to design an irregularly shaped resonant cavity, overcoming the limitations of traditional symmetrical cavity designs. This allows for an improvement in the Q-value of the resonant cavity through optimization of the cavity structure and material selection. Combining transformation optics optical field optimization technology and the high refractive index characteristics of lithium niobate material, edge scattering of light and material absorption loss are effectively reduced, further lowering the total loss of the resonant cavity. Utilizing the electro-optic effect of lithium niobate, dynamic tuning of the resonant cavity frequency is achieved through an external electric field, providing more flexible resonance characteristics.

Description

Technical Field

[0001] This invention belongs to the field of optical device technology, and particularly relates to irregular resonant cavities based on transformation optics. Background Technology

[0002] Optical resonant cavities have become a research hotspot in the field of optics due to their high frequency selectivity and long photon dwell time in optical signal processing and optical communication. Typically, circular or elliptical whispering-gallery resonant structures can achieve high Q values ​​due to their symmetry. However, traditional resonant cavity designs often have limitations in terms of resonant frequency tuning and shape diversity. Furthermore, cavity losses significantly affect the Q value, making them inadequate for high-frequency applications and complex environments. Summary of the Invention

[0003] Lithium niobate (LiNbO3) is a material with excellent electro-optic, acousto-optic, and nonlinear optical properties, and is widely used in optical modulators, optical waveguides, and frequency conversion devices. Transformation optics is an emerging optical design tool that enables flexible manipulation of light fields by controlling their propagation path in a medium. By combining the principles of transformation optics with lithium niobate, the design of resonant cavities can be optimized, creating irregularly shaped resonant cavity structures, thereby improving the Q value and achieving more flexible resonance characteristics.

[0004] This application proposes an irregularly shaped resonant cavity based on transformation optics to address the aforementioned technical problems. The specific technical solution is as follows:

[0005] Based on transformation optics, an irregularly shaped resonant cavity is constructed by setting an array of holes on the substrate of a whispering resonant cavity. The spatial distribution of the diameters of the array of holes satisfies equation (1):

[0006]

[0007] In equation (1), n(x,y) represents the refractive index distribution of the medium on the substrate, p represents the period of the structural unit, and n air n is the refractive index of air. LN Let d be the refractive index of the substrate, and d(x,y) be the spatial diameter distribution of the structural unit.

[0008] The refractive index distribution n(x,y) of the medium on the substrate satisfies equation (2):

[0009]

[0010] In equation (2), a is a parameter characterizing the deformation of the resonant cavity, and n0 is the refractive index of the background medium; x = (1 + 2a * cosθ) * cosθ, y = (1 + 2a * cosθ) * sinθ.

[0011] Furthermore, a waveguide layer is formed on the surface of the substrate.

[0012] In some specific implementations, the thickness of the waveguide layer is controlled to be 500 nm.

[0013] In some specific implementations, the waveguide layer is formed by ion diffusion or proton exchange processes.

[0014] Preferably, the substrate is a lithium niobate single crystal wafer.

[0015] Preferably, the lithium niobate single crystal is subjected to an external electric field, and the electric field parameters are adjusted to change the refractive index of lithium niobate, thereby dynamically tuning the resonant frequency of the irregularly shaped resonant cavity.

[0016] In some specific implementations, the refractive index of lithium niobate is adjusted to 2.2, the resonant frequency is 406.38 THz, the resonant wavelength is 738 nm, and the quality factor reaches the order of 10^11.

[0017] In some specific implementations, the refractive index of lithium niobate is adjusted to 2, the resonant frequency is 456.05 THz, the resonant wavelength is 657 nm, and the quality factor reaches the order of 10^10.

[0018] Preferably, the surface of the resonant cavity has a passivation layer.

[0019] The beneficial effects of this invention are as follows: This application uses transformation optics design methods to design irregularly shaped resonant cavities, overcoming the limitations of traditional symmetrical cavity designs. This allows for an improvement in the Q value of the resonant cavity through optimization of the cavity structure and material selection. Combining transformation optics' optical field optimization technology with the high refractive index characteristics of lithium niobate material, edge scattering of light and material absorption losses are effectively reduced, further lowering the total loss of the resonant cavity. Utilizing the electro-optic effect of lithium niobate, dynamic tuning of the resonant cavity frequency is achieved through an external electric field, providing more flexible resonance characteristics.

[0020] The resonant cavity design of this application can be widely used in optical communication, optical sensing, optical signal processing and nonlinear optics, and is especially suitable for scenarios such as high-selectivity optical filtering, precise frequency control and high-sensitivity sensors. Attached Figure Description

[0021] Figure 1 The diagram shown is a schematic of the irregularly shaped resonant cavity.

[0022] Figure 2 The diagram shows the boundary and refractive index distribution of the irregularly shaped resonant cavity in Example 1;

[0023] Figure 3 The actual structure (front view) of the irregular resonant cavity in Embodiment 1 is shown;

[0024] Figure 4 The diagram shows the actual structure (three-dimensional state) of the irregular resonant cavity in Example 1;

[0025] Figure 5 The diagram shown is the optical field distribution after optimization of the irregular resonant cavity in Example 1;

[0026] Figure 6 The figure shows the variation of the quality factor of the resonant cavity with frequency in the simulation calculation of Example 1;

[0027] Figure 7 The diagram shown is the optical field distribution of the circular resonant cavity in Comparative Example 1;

[0028] Figure 8 The figure shows the variation of the quality factor of the resonant cavity with frequency in the simulation calculation of Comparative Example 1.

[0029] Figure 9 The figure shows the variation of the quality factor of the resonant cavity with frequency in the simulation calculation of Example 2. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments.

[0031] This application provides an irregularly shaped resonant cavity based on transformation optics. The irregularly shaped resonant cavity includes a circular sheet substrate 100, which serves as the resonant cavity. An array of holes is provided on the substrate 100. The array of holes will also be present at the boundary of the substrate 100 based on their array state, thereby transforming the traditional circular resonant cavity into an irregularly shaped resonant cavity. The spatial distribution of the diameter of the array of holes on the substrate 100 satisfies equation (1):

[0032]

[0033] In equation (1), p is the period of the structural unit, which is the center-to-center distance between adjacent holes; nair is the refractive index of air; nLN is the refractive index of the background medium (i.e., the refractive index of substrate 100); and d(x,y) is the spatial diameter distribution of the structural unit. Based on this distribution and the period p, the spatial distribution of the hole diameter can be obtained. A circular hole is used as an example; any shape of hole structure can be used, as long as the following conditions are met:

[0034] f is the duty cycle of the hole area relative to the area of ​​the structural unit, n(x,y) is the refractive index distribution of the medium on the substrate 100, and satisfies equation (2):

[0035]

[0036] In equation (2), i is the imaginary unit, a is a parameter characterizing the deformation of the resonant cavity; the larger the value of a, the greater the degree of deformation of the resonant cavity; when a = 0, the resonant cavity is perfectly circular. n0 is the refractive index of the background medium, which is the same as n in equation (1). LN Similarly, based on equation (2), the boundary and refractive index distribution of the irregular resonant cavity can be obtained, and based on the refractive index distribution, according to the equivalent medium theory, the diameter spatial distribution of the hole array can be calculated by combining equation (1) through the method of opening holes.

[0037] Transforming a traditional circular resonant cavity into an irregularly shaped resonant cavity is based on the principle of transformation optics. The boundary calculation formula for the irregularly shaped resonant cavity is as follows:

[0038] x=(1+2a*cosθ)*cosθ

[0039] y = (1 + 2a * cosθ) * sinθ.

[0040] θ is the angle between the line connecting the corresponding point and the origin and the x-axis, and its value ranges from [0, 2π]. In the embodiment, a waveguide layer 100 is also formed on the upper surface of the substrate 200, such as... Figure 1 As shown, the waveguide layer 100 is formed on the surface of the substrate 200 by ion diffusion or proton exchange process.

[0041] In some implementations, the waveguide layer 100 can be 500 nm thick, with the thickness depending on the design wavelength and the corresponding refractive index of the waveguide layer.

[0042] In this implementation scheme, the substrate 200 is a lithium niobate (LiNbO3) single crystal wafer. Lithium niobate (LiNbO3) exhibits excellent nonlinear optical, acousto-optic, and electro-optic effects, which can effectively improve the performance of the resonant cavity. Based on the electro-optic effect of lithium niobate, the resonant frequency can be dynamically tuned by applying an external electric field. Lithium niobate has a high refractive index, which can effectively confine the optical field within the cavity and reduce transmission loss. Other materials with tunable refractive indices can also be selected for the substrate, such as indium tin oxide (ITO), whose refractive index can be changed by electrical modulation, or the phase change material Sb2S3, whose refractive index can be changed by thermal modulation. In other words, materials whose refractive index can be changed at the same incident light wavelength by applying an external physical field can be selected.

[0043] In the implementation scheme, the substrate 200 is defined as a sound-gallery resonator structure including a circle. This type of sound-gallery resonator is a symmetrical resonator, and can also be elliptical. Through optical transformation, the sound-gallery resonator structure is transformed into an irregularly shaped resonator. This irregularly shaped resonator allows the light field to be effectively maintained within the cavity, reducing edge scattering losses and simultaneously modulating the resonant modes within the cavity. Using a coordinate transformation method, the propagation path of light is redirected to different regions of the cavity, thereby achieving precise control of the resonant frequency.

[0044] Based on the principle of transformation optics, the shape of the irregular resonant cavity of the present invention can be optimized according to different application requirements. These irregular cavities can concentrate the light field in a specific area through the coordinate transformation algorithm of transformation optics, reduce the scattering of light at the edge of the cavity, and thus improve the Q value.

[0045] By optimizing the structural parameters of the resonant cavity, including its size, shape, and material parameters, the cavity's quality factor (Q value) is maximized. Simultaneously, optical field optimization methods from transform optics design are used to reduce optical losses within the cavity, particularly edge scattering and material absorption losses.

[0046] In the implementation scheme, surface state losses can be reduced by passivating the surface of the resonant cavity.

[0047] In some implementations, passivation is performed using a sulfur-containing compound solution, and the passivation layer and the protective layer are formed in the same sulfur-containing compound solution, with the protective layer being made of a wide-bandgap sulfur oxide material.

[0048] In some implementations, an ion beam is used to bombard and clean the surface of the resonant cavity to remove oxide layers, contaminants, surface states, etc., and then an AlN passivation layer is deposited at low temperature using atomic layer deposition (ALD) technology.

[0049] In the implementation plan, tapered optical fibers can also be used to couple with irregularly shaped resonant cavities, thereby maximizing optical coupling efficiency and further reducing coupling loss.

[0050] Example 1

[0051] The circular lithium niobate (LiNbO3) single crystal is used as the substrate of the resonant cavity. A high-refractive-index waveguide layer is formed on the surface of the lithium niobate through ion diffusion process, with the thickness controlled at 500nm.

[0052] By taking a = 0.11, the boundary and refractive index distribution of the irregularly shaped resonant cavity can be obtained, such as... Figure 2 As shown.

[0053] Determine the refractive index n of lithium niobate LNGiven the refractive index n0 of the background medium, we can obtain... Figure 3 and Figure 4 The actual structure of the irregular resonant cavity shown is as follows: Figure 3 Main view, Figure 4 This is a 3D image.

[0054] Furthermore, the optimized optical field distribution map obtained through the irregularly shaped resonant cavity can be obtained, such as... Figure 5 As shown, the light field distribution of the visible resonant cavity is uniform and stable.

[0055] The refractive index n of lithium niobate LN By adjusting the setting to 2.2, the quality factor (Q value) of the resonant cavity is further calculated using simulation as a function of frequency, such as... Figure 6 As shown, under these conditions, the resonant frequency is 406.38 THz, and the corresponding resonant wavelength is 738 nm. At the resonant frequency, the quality factor (Q value) of the resonant cavity can reach the order of 10^11, indicating that a tunable high Q value resonant cavity can be realized through the electro-optic effect of lithium niobate.

[0056] Comparative Example 1

[0057] A circular sheet-shaped lithium niobate (LiNbO3) single crystal is used as the substrate of the resonant cavity. By taking a=0, the boundary of the circular resonant cavity can be obtained.

[0058] The refractive index n of lithium niobate LN By adjusting the setting to 2.2, the light field distribution pattern through the circular resonant cavity can be obtained, such as... Figure 7 As shown. Further simulation calculations are performed to determine how the quality factor (Q value) of the resonant cavity changes with frequency, as shown below. Figure 8 As shown, under these conditions, the resonant frequency is 502.8 THz, and the corresponding resonant wavelength is 597 nm. At the resonant frequency, the quality factor (Q value) of the resonant cavity is on the order of 10^5. Comparison with the calculation results of the irregular resonant cavity shows that the optimized irregular resonant cavity designed through conversion optics theory can significantly improve the Q value.

[0059] Example 2

[0060] Based on the excellent electro-optic effect of lithium niobate, the resonant frequency can be dynamically tuned by applying an external electric field, providing more flexible resonant characteristics.

[0061] Based on Example 1, by adjusting the refractive index n of lithium niobate... LN By adjusting the setting to 2, the quality factor (Q value) of the resonant cavity is further calculated using simulation as a function of frequency, such as... Figure 9As shown, under these conditions, the resonant frequency is 456.05 THz, and the corresponding resonant wavelength is 657 nm. At the resonant frequency, the quality factor (Q value) of the resonant cavity can reach the order of 10^10, and it can still maintain the characteristics of high quality factor.

[0062] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it.

Claims

1. An irregularly shaped resonant cavity based on transformation optics, characterized in that, An array of holes is formed on the substrate of a sound-gallery resonator, and the spatial distribution of the diameters of the array holes satisfies equation (1): In equation (1), n(x,y) represents the refractive index distribution of the medium on the substrate, p represents the period of the structural unit, and n air n is the refractive index of air. LN Let d be the refractive index of the substrate, and d(x,y) be the spatial diameter distribution of the structural unit. The refractive index distribution n(x,y) of the medium on the substrate satisfies equation (2): In equation (2), a is a parameter characterizing the deformation of the resonant cavity, and n0 is the refractive index of the background medium, which is the same as nLN in equation (1); x = (1 + 2a * cosθ) * cosθ, y = (1 + 2a * cosθ) * sinθ; A waveguide layer is formed on the surface of the substrate. The substrate is a lithium niobate single crystal. The lithium niobate single crystal is subjected to an external electric field. The electric field parameters are adjusted to change the refractive index of lithium niobate, thereby dynamically tuning the resonant frequency of the irregular resonant cavity.

2. The irregular resonant cavity based on transformation optics according to claim 1, characterized in that, The thickness of the waveguide layer is controlled to be 500 nm.

3. The irregular resonant cavity based on transformation optics according to claim 1, characterized in that, The waveguide layer is formed by ion diffusion or proton exchange processes.

4. The irregular resonant cavity based on transformation optics according to claim 1, characterized in that, By adjusting the refractive index of lithium niobate to 2.2, the resonant frequency was 406.38 THz, the resonant wavelength was 738 nm, and the quality factor reached the order of 10^11.

5. The irregular resonant cavity based on transformation optics according to claim 1, characterized in that, By adjusting the refractive index of lithium niobate to 2, the resonant frequency is 456.05 THz, the resonant wavelength is 657 nm, and the quality factor reaches the order of 10^10.

6. The irregular resonant cavity based on transformation optics according to claim 1, characterized in that, The surface of the resonant cavity has a passivation layer.

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