Special-shaped resonant cavity based on transformation optics

Abstract

The invention discloses a special-shaped resonant cavity based on transformation optics, array holes are formed in a base material of an echo wall type resonant cavity, and the diameter space distribution of the array holes meets the formula # imgabs 0 # base material medium refractive index distribution n (x, y) meets the formula # imgabs 1 #. The special-shaped resonant cavity is designed by applying a transformation optics design method, the limitation of a traditional symmetric cavity design is overcome, and the design efficiency is improved. The Q value of the resonant cavity can be improved by optimizing the cavity structure and selecting materials; the light field optimization technology of conversion optics and the high refractive index characteristic of the lithium niobate material are combined, so that the edge scattering of light and the absorption loss of the material are effectively reduced, and the total loss of the resonant cavity is further reduced; dynamic tuning of the frequency of the resonant cavity is achieved through an external electric field by means of the electro-optical effect of lithium niobate, and more flexible resonance characteristics are provided.

Description

Technical Field

[0001] The invention belongs to the technical field of optical devices, and in particular relates to a special-shaped resonant cavity based on transformation optics. Background Art

[0002] Optical resonators have become a research hotspot in the field of optics due to their high frequency selectivity and long photon residence time in optical signal processing and optical communications. Generally, circular or elliptical whispering gallery resonator structures can achieve high Q values ​​due to their symmetry. However, traditional resonant cavity designs often have limitations in resonant frequency tuning and shape diversity. In addition, the loss of the resonant cavity can also significantly affect the Q value, making it insufficient in high-frequency applications and complex environments. Summary of the invention

[0003] Lithium niobate (LiNbO3) is a material with excellent electro-optical, acousto-optical, 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 can flexibly control the light field by controlling the propagation path of the light field in the medium. By combining the principles of transformation optics with lithium niobate materials, the design of the resonant cavity can be optimized and a special-shaped resonant cavity structure can be created, thereby improving the Q value and achieving more flexible resonant characteristics.

[0004] In view of the above technical problems, this application proposes a special-shaped resonant cavity based on transformation optics. The specific technical solution is as follows:

[0005] Based on the special-shaped resonant cavity of transformation optics, an array hole is set on the substrate of the whispering gallery resonant cavity, and the spatial distribution of the diameter of the array hole satisfies formula (1):

[0006]

[0007] In formula (1), n(x, y) is the refractive index distribution of the medium on the substrate, p is the period of the structural unit, and n air is the refractive index of air, n LN is the refractive index of the substrate, d(x,y) is 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 formula (2), a is a parameter characterizing the deformation of the resonant cavity, 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 embodiments, the thickness of the waveguide layer is controlled to be 500 nm.

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

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

[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 the lithium niobate, thereby dynamically tuning the resonant frequency of the special-shaped resonant cavity.

[0016] In some specific embodiments, 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 embodiments, 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 the present invention are as follows: the present application designs a special-shaped resonant cavity by applying a transformation optics design method, thereby overcoming the limitations of a traditional symmetrical cavity design, so that the Q value of the resonant cavity can be improved by optimizing the cavity structure and material selection; combining the light field optimization technology of transformation optics and the high refractive index characteristics of lithium niobate materials, effectively reducing the edge scattering of light and material absorption loss, and further reducing the total loss of the resonant cavity; utilizing the electro-optical effect of lithium niobate, dynamically tuning the resonant cavity frequency through an applied electric field, and providing more flexible resonant characteristics;

[0020] The resonant cavity design of the present application can be widely used in the fields of optical communication, optical sensing, optical signal processing and nonlinear optics, and is particularly suitable for scenarios such as highly selective optical filtering, precise frequency control and high-sensitivity sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 What is shown is a schematic diagram of the structure of a special-shaped resonant cavity;

[0022] Figure 2 Shown are the boundary and refractive index distribution of the special-shaped resonant cavity in Example 1;

[0023] Figure 3 The actual structure of the special-shaped resonant cavity in Example 1 (front view) is shown;

[0024] Figure 4 The actual structure (three-dimensional state) of the special-shaped resonant cavity in Example 1 is shown;

[0025] Figure 5 The diagram shows the light field distribution after the optimization of the special-shaped resonant cavity in Example 1;

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

[0027] Figure 7 What is shown is the light field distribution diagram of the perfect circular resonant cavity in comparative example 1;

[0028] Figure 8 What is shown is the variation of the quality factor of the resonant cavity with frequency in the simulation calculation in comparative example 1.

[0029] Fig. 9 The figure shows the variation of the quality factor of the resonant cavity with frequency calculated by simulation in Example 2. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments.

[0031] The present application provides a special-shaped resonant cavity based on transformation optics. The special-shaped resonant cavity includes a circular sheet substrate 100, the circular sheet substrate 100 is used as a resonant cavity, and array holes are arranged on the substrate 100. The array holes also appear at the boundary of the substrate 100 based on their array state, thereby transforming a traditional circular resonant cavity into a special-shaped resonant cavity, wherein the diameter spatial distribution of the array holes on the substrate 100 satisfies formula (1):

[0032]

[0033] In formula (1), p is the period of the structural unit, that is, the distance between the centers of adjacent holes, nair is the refractive index of air, nLN is the refractive index of the background medium (that is, the refractive index of the 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. The circular hole is an example, and any shape of hole structure can be used as long as the following conditions are met:

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

[0035]

[0036] In formula (2), i is an imaginary unit, and a is a parameter that characterizes the deformation of the resonant cavity. The larger the a value, the greater the deformation of the resonant cavity. When a = 0, the resonant cavity is a perfect circle. n0 is the refractive index of the background medium, which is the same as n in formula (1). LN Similarly, based on formula (2), the boundary and refractive index distribution of the special-shaped 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 opening holes in combination with formula (1).

[0037] The transformation of the traditional circular resonant cavity into a special-shaped resonant cavity is based on the principle of transformation optics. The boundary calculation formula of the special-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 of the coordinate system and the x-axis, and its value range is [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 embodiments, the thickness of the waveguide layer 100 may be 500 nm, with the thickness being related to the design wavelength and the corresponding waveguide layer refractive index.

[0042] In the implementation scheme, the substrate 200 is a lithium niobate (LiNbO3) single crystal. Lithium niobate (LiNbO3) has excellent nonlinear optical, acousto-optical and electro-optical effects, which can effectively improve the performance of the resonant cavity. Based on the electro-optical effect of lithium niobate, dynamic tuning of the resonant frequency can be achieved through an external electric field. The lithium niobate material has a high refractive index and can effectively constrain the light field in the cavity to reduce transmission losses. The substrate can also be made of other materials with tunable refractive index, such as indium tin oxide (ITO), which can change the refractive index through electrical modulation, or phase change material Sb2S3, which can change the refractive index through thermal modulation, that is, a material that can achieve a change in the refractive index at the same wavelength of incident light through an external physical field.

[0043] In the embodiment, the substrate 200 is defined as a whispering gallery resonant cavity structure including a circular shape. This type of whispering gallery resonant cavity is a symmetrical resonant cavity, for example, it can also be an elliptical shape. Through transformation optics design, the whispering gallery resonant cavity structure is transformed into a special-shaped resonant cavity with a specific shape. This special-shaped resonant cavity enables the light field to be effectively maintained in the special-shaped cavity, reduces edge scattering losses, and regulates the resonant mode in the cavity. The coordinate transformation method is used to redirect the propagation path of light to different areas of the cavity, thereby achieving precise control of the resonant frequency.

[0044] Based on the principle of transformation optics, the shape of the special-shaped resonant cavity of the present invention can be optimized according to different application requirements. These special-shaped 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 the size, shape, and material parameters of the cavity, the quality factor (Q value) of the cavity is maximized. At the same time, the light field optimization method in transformation optics design is used to reduce the light loss in the cavity, especially the edge scattering and material absorption loss.

[0046] In an embodiment, the surface state loss can be reduced by passivating the surface of the resonant cavity.

[0047] In some embodiments, a sulfur-containing compound solution is used for passivation, the passivation layer and the protective layer are formed in the same sulfur-containing compound solution, and the material of the protective layer is a wide bandgap sulfur oxide material.

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

[0049] In the implementation scheme, a tapered optical fiber can also be used to couple with a special-shaped resonant cavity, thereby maximizing the light coupling efficiency and further reducing the coupling loss.

[0050] Example 1

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

[0052] Taking a = 0.11, we can obtain the boundary and refractive index distribution of the special-shaped resonant cavity, such as Figure 2 shown.

[0053] Determine the refractive index n of lithium niobate LNFor the refractive index n0 of the background medium, we can get Figure 3 and Figure 4 The actual structure of the special-shaped resonant cavity is shown in Figure 3 For the main view, Figure 4 It is a three-dimensional picture.

[0054] Furthermore, the light field distribution diagram after optimization by the special-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 by simulation as the frequency changes, such as Figure 6 As shown in the figure, under this condition, 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 achieved through the electro-optical effect of lithium niobate.

[0056] Comparative Example 1

[0057] A circular sheet of lithium niobate (LiNbO3) single crystal is used as the substrate of the resonant cavity. Taking a=0, the boundary of the perfect 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 diagram through the perfect circular resonant cavity can be obtained, such as Figure 7 As shown. The simulation further calculates the change of the quality factor (Q value) of the resonant cavity with frequency, as shown in Figure 8 As shown in the figure, under this condition, 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. Compared with the calculated results of the special-shaped resonant cavity, it can be shown that the optimized special-shaped resonant cavity designed by transformation optics theory can greatly improve the Q value.

[0059] Example 2

[0060] Based on the excellent electro-optical effect of lithium niobate, dynamic tuning of the resonant frequency can be achieved through an external electric field, providing more flexible resonant characteristics.

[0061] On the basis of Example 1, the refractive index n of lithium niobate is LN By adjusting the setting to 2, the simulation further calculates the change of the quality factor (Q value) of the resonant cavity with frequency, such as Fig. 9As shown, under this condition, 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 the characteristics of high quality factor can still be maintained.

[0062] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them.

Claims

1. A special-shaped resonant cavity based on transformation optics, characterized in that: An array hole is arranged on the substrate of the whispering gallery resonant cavity, and the spatial distribution of the diameter of the array hole satisfies formula (1): In formula (1), n(x, y) is the refractive index distribution of the medium on the substrate, p is the period of the structural unit, and n air is the refractive index of air, n LN is the refractive index of the substrate, d(x,y) is 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 formula (2), a is a parameter characterizing the deformation of the resonant cavity, n0 is the refractive index of the background medium; x = (1 + 2a*cosθ)*cosθ, y = (1 + 2a*cosθ)*sinθ.

2. The special-shaped resonant cavity based on transformation optics according to claim 1, characterized in that: A waveguide layer is formed on the surface of the substrate.

3. The special-shaped resonant cavity based on transformation optics according to claim 2, characterized in that: The thickness of the waveguide layer is controlled to be 500 nm.

4. The special-shaped resonant cavity based on transformation optics according to claim 2, characterized in that: The waveguide layer is formed by ion diffusion or proton exchange process.

5. The special-shaped resonant cavity based on transformation optics according to claim 1, characterized in that: The substrate is a lithium niobate single crystal wafer.

6. The special-shaped resonant cavity based on transformation optics according to claim 5, characterized in that: 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 the lithium niobate, thereby dynamically tuning the resonant frequency of the special-shaped resonant cavity.

7. The special-shaped resonant cavity based on transformation optics according to claim 6, characterized in that: The refractive index of lithium niobate is adjusted to 2.2, the resonant frequency is 406.38THz, the resonant wavelength is 738nm, and the quality factor reaches the order of 10^11.

8. The special-shaped resonant cavity based on transformation optics according to claim 6, characterized in that: The refractive index of lithium niobate is adjusted to 2, the resonant frequency is 456.05THz, the resonant wavelength is 657nm, and the quality factor reaches the order of 10^10.

9. The special-shaped resonant cavity based on transformation optics according to claim 1, characterized in that: The surface of the resonant cavity is provided with a passivation layer.

Images