Apparatus for topology boundary state modulation and harmonic generation based on voltage regulation

Abstract

This invention discloses a device for generating topological boundary states and harmonic frequencies based on voltage-controlled lithium niobate. Lithium niobate is arranged in an ordered manner in free space at specific intervals. By applying positive and negative voltages to the left and right sides of the lithium niobate respectively, the refractive index of the lithium niobate material can be changed using electro-optic modulation. Unlike previous studies, the enhancement of nonlinear optical effects is due to the strong local field at the boundary of the topological structure. Furthermore, the topological boundary states generated by this structure are uniformly distributed in an arithmetic progression, meaning that when the fundamental frequency light is in one of the boundary modes, the harmonic light is also in the topological boundary state mode. This makes all generated harmonic light immune to impurities or defects in the structure and prevents backscattering, thus the structure is topologically protected. This nonlinear optical effect based on topologically protected states provides a new approach for generating higher harmonics and other nonlinear optical effects.

Description

Technical Field

[0001] This invention specifically relates to the field of nonlinear topological photonics, and in particular to a device for topological boundary state manipulation and harmonic generation based on voltage regulation. Background Technology

[0002] In recent years, the concept of optical topologies has attracted considerable research interest. Optical topology originates from topological insulators, which are bulk insulators with conductive surfaces. The topological properties of these structures are determined by their bulk structure, exhibiting unique immunity to impurities and defects. They have been applied in numerous optical research areas, such as laser cavities, gratings, metasurfaces, and waveguide structures. The application of topological structures in optics allows light to bend at arbitrary angles or bypass obstacles, suppresses backscattering, reduces heat loss, and significantly improves light transmission efficiency. The topologically protected band structure properties and various novel optical phenomena have further promoted the development of topological photonic crystals. The most important characteristic of topological photonic crystals is the unique topological phase on each band, which supports strong localized fields at topological boundaries or surfaces, as well as properties protected by the structural system. The propagation of topologically protected boundary states has also led to broader research into various optical systems, such as resonant cavities, waveguides, plasmon crystals, and metamaterials.

[0003] Until now, most research on topological insulators has been limited to linear optical systems, but combining nonlinear optics with topological photonics is a promising research direction. First, the topological phase in a topological structure can be modulated by a strong external optical field in a nonlinear optical system, a phenomenon different from the inherent topological phase determined by the system itself. Second, the strong local fields at the topological boundaries and the topologically protected properties are used to enhance nonlinear optical effects, generating second and third harmonics. Related studies have shown that the generation efficiency of harmonics in nonlinear optical topological structures is three orders of magnitude higher than in non-topological structures. Although the harmonic conversion efficiency is enhanced, most harmonics in previous studies are not located at the topological boundary states, therefore the generated harmonics lack topological protection properties and are not immune to impurities and defects introduced during the structure manufacturing process.

[0004] Lithium niobate, a multifunctional material exhibiting electro-optic, acousto-optic, and nonlinear optical effects, and possessing a wide transparency range of 420 nm to 5200 nm, is widely used in integrated optics. Due to its relatively large second-order nonlinear optical coefficient, lithium niobate is also used to generate nonlinear harmonic signals, and nonlinear harmonic technology has become an important means of expanding frequency windows. This patent utilizes both the electro-optic and nonlinear optical effects of lithium niobate to alter the topological phase of the structure by applying an external voltage, thereby generating topological boundary states. By adjusting the width of the lithium niobate structure, the harmonic signals are also positioned within these topological boundary states. Unlike previous studies, the topological boundary states generated in this patent are uniformly distributed with equal intervals, making the generation of topologically protected higher harmonics possible.

[0005] Research on nonlinear topological photonics, which combines nonlinear optics with topological photonics, is in its early stages. Therefore, it is meaningful and necessary to combine topological structures and nonlinear optical structures for research. Summary of the Invention

[0006] Technical Problem: To address the aforementioned problems, this invention proposes a device for topological boundary state manipulation and harmonic generation based on voltage regulation. This invention combines the electro-optic effect and nonlinear optical effect of a one-dimensional topological structure and lithium niobate material. Utilizing the electro-optic effect of lithium niobate, topological phase reversal is achieved by applying positive and negative voltages to both sides of the structure, leading to the generation of topological boundary states. All topological boundary states are distributed in an arithmetic sequence. Furthermore, the nonlinear optical effect of lithium niobate crystal is utilized; when laser light is incident, harmonic frequencies are generated in addition to the fundamental frequency, and these harmonics also possess topological protection properties, thus generating topologically protected harmonic light.

[0007] Technical Solution: To achieve the above objectives, this invention employs a device for topological boundary state modulation and harmonic frequency generation based on voltage regulation. The device consists of lithium niobate crystals periodically emitted into the air at certain intervals. The number of cycles is 14. A positive voltage is applied above and below the lithium niobate crystals in the left 7 cycles, and a negative voltage is applied above and below the lithium niobate crystals in the right 7 cycles. The incident light source is a femtosecond pulsed laser, incident from the far left.

[0008] The light source selected in this invention (hereinafter the same) has a light intensity of 20 GW / cm². 2 Femtosecond pulsed laser.

[0009] The lithium niobate selected in this invention is an x-cut uniaxial crystal with its c-axis parallel to the z-axis.

[0010] The width of the lithium niobate crystals in the left seven cycles selected in this invention is da = 0.632 μm, and the width of the air layer in the left seven cycles is db = 0.684 μm.

[0011] The width of the lithium niobate crystals in the right seven cycles selected in this invention is da1 = 0.644 μm, and the width of the air layer in the right seven cycles is db1 = 0.696 μm.

[0012] The linear refractive index of the lithium niobate material selected in this invention is ε. xx =ε yy =4.97, ε zz =4.67. Its electro-optic coefficient is 62 pm / V. The second-order nonlinear optical coefficient is 168 pm / V.

[0013] The wave used in this invention is TM(E) z H x H y The wave in the ) mode propagates along the x-axis.

[0014] The boundary selected in this invention is the interface formed by lithium niobate with a positive voltage and lithium niobate with a negative voltage.

[0015] Beneficial Effects: This invention combines topological photonics and nonlinear optics, utilizing the electro-optic effect and second-order nonlinear optical effect of lithium niobate material to dynamically control the topological phase on both sides of the structure, so that the field intensity is mainly concentrated at the boundary of the two structures, and harmonic frequencies are generated under strong laser light. This technology makes both the fundamental and harmonic frequencies topologically protected and eliminates the need for phase matching techniques, making light transmission immune to structural defects and impurities. This technology has application value in optical integration, robust reconfigurable circuits, and enhanced nonlinear optical effects. Compared with existing technologies, the advantages of this invention are as follows:

[0016] (1) The device for topological boundary state modulation and harmonic generation based on voltage regulation proposed in this invention can generate harmonic waves protected by topology. By utilizing the electro-optic effect and nonlinear optical effect of lithium niobate material as two modulation methods, the refractive index and nonlinear optical effect of the material can be dynamically controlled.

[0017] (2) This method increases the difference in refractive index distribution between the two sides by changing the sign of the voltage on both sides of the structure, ultimately resulting in a topological phase reversal between the structure with positive voltage and the structure with negative voltage, forming a topological boundary state at the boundary between the two. The topological boundary state enhances the field at the boundary, and since the nonlinear optical effect is related to the field strength, this effectively enhances the nonlinear optical effect.

[0018] (3) Generally, harmonic generation devices in the terahertz band are not immune to defects and impurities during light transmission. However, the harmonics generated by this device are in the topological boundary state, so the light is topologically protected during transmission. It is immune to defects and impurities in the structure and does not produce backscattering, which greatly enhances the light transmission efficiency. Attached Figure Description

[0019] Figure 1 The present invention provides a device diagram for topological boundary state control and harmonic frequency generation based on voltage regulation.

[0020] Wherein: The rectangular cuboid represents lithium niobate. The width of the positive voltage applied on the left is db, and the width of the negative voltage applied on the right is db1. The medium between adjacent lithium niobate particles is air, with widths of da and da1 on the left and right sides, respectively. A period of da (air) and db (lithium niobate) on the left constitutes one cycle, with a period of a. A period of da1 (air) and db1 (lithium niobate) on the right constitutes one cycle, with a period of a1. A "+" above the lithium niobate indicates a positive voltage applied in the vertical direction (y-axis), and a "-" indicates a negative voltage applied in the vertical direction.

[0021] Figure 2 (a) shows the band structure of lithium niobate with a positive voltage, and (b) shows the band structure of lithium niobate with a negative voltage. The horizontal axis represents the wave vector in the x-direction, and the vertical axis represents the frequency of light. The Zak phase is marked on each band. The gray and black rectangles represent different topological band gaps. The insets in (a) and (b) are enlarged views of the dashed portion of the band gap ellipse ④.

[0022] Figure 3 The image shows the one-dimensional transmission spectrum of a 14-period structure with a positive voltage applied to the left 7 periods and a negative voltage applied to the right 7 periods. The boundary states in the figure correspond to... Figure 2 The positions of band gaps ①②③④ in the diagram.

[0023] Figure 4 (a), (b), and (c) are respectively: Figure 3 The diagram shows the one-dimensional field diagrams of the structures corresponding to boundary states ①, ③, and ④. The vertical dashed lines are the boundaries of each layer. L and N represent lithium niobate layers with positive and negative voltages, respectively, and A represents air.

[0024] Figure 5 (a), (b), and (c) are respectively: Figure 3 The Fourier transforms corresponding to boundary states ①③④ in the diagram. f0, f1, and f2 are the frequencies of the incident wave, respectively 2.179 × 10⁻⁴. 14 Hz, 6.537×10 14 Hz, 8.716×10 14Hz, the horizontal axis is frequency, and the vertical axis is Fourier coefficient. Detailed Implementation

[0025] The following description, in conjunction with the accompanying drawings and specific implementation methods, details how voltage changes the topological phase of the structure to achieve the harmonic frequency of the topological boundary state.

[0026] Figure 1 This diagram shows a device for generating topological boundary state harmonics based on voltage regulation. The rectangular cuboid represents lithium niobate with a width of da. The space between adjacent lithium niobate units is air with a width of db. The air space of width db and the lithium niobate unit of width da constitute one structural period with a period of a. On the right side, the lithium niobate unit has a width of da1, and the space between adjacent lithium niobate units is air with a width of db1. The air space of width db1 and the lithium niobate unit of width da1 constitute one structural period with a period of a1. In this device, the left half of the structure consists of lithium niobate and air with a positive voltage applied on the left, forming a structure with a period of 7; the right half consists of lithium niobate and air with a negative voltage applied on the right, forming a structure with a period of 7. A "+" sign above the lithium niobate indicates a positive voltage applied in the vertical direction (y-axis), and a "-" sign indicates a negative voltage applied in the vertical direction. The femtosecond laser in TM mode propagates along the x-axis with an intensity of 20 GW / cm². 2 .

[0027] Figure 2 (a) and (b) are the band structure diagrams for the left and right halves of the structure under positive and negative voltages, respectively. The voltage is 0.8 GV / m, which does not exceed the damage threshold voltage of lithium niobate (1 GV / m). Each band is marked with the magnitude of the corresponding topological phase, and the different topological properties of each bandgap are indicated by black and gray matrices. It can be seen from the diagram that the properties of the topological bandgap corresponding to the two structures are different at positions ①②③④, resulting in topological boundary states at these positions. When the voltage is 0.8 GV / m, because the refractive index difference between the structures under positive and negative voltages is very small, the bandgap opening width is also very small. In this case, we present an enlarged view of the elliptical dashed area of ​​bandgap ④, as shown below. Figure 2 As shown in the illustrations in (a) and (b), we can see that the band gap does indeed exist at this time.

[0028] exist Figure 2 Given the structural parameters, we plotted the transmission spectrum of the structure. Figure 3 ①, ②, ③, and ④ indicate the locations of the topological boundary states, which respectively correspond to Figure 2 The positions of band gaps ①, ②, ③, and ④ are determined. Calibration reveals that the frequencies of boundary states ①, ②, ③, and ④ form an arithmetic sequence. If... Figure 3As the range of the horizontal axis increases, an arithmetic sequence with the boundary state at point ① as the fundamental frequency will appear. This phenomenon means that the harmonics are also in the topological boundary states, thus providing topological protection. Furthermore, this structure no longer needs to satisfy the phase-matching condition for higher harmonics to ensure that all harmonics are in resonant mode, because the transmittance of the harmonics in this structure is all 1, already satisfying the resonance condition. From... Figure 3 As we can see, the higher the frequency, the larger the band gap, and the stronger the field localization. Figure 4 (a), (b), and (c) correspond to respectively Figure 3 One-dimensional field distribution under boundary state modes ①, ③, and ④. From Figure 4 (a) We can see that when the boundary state is in band gap ①, due to the small width of the band gap, the locality of the field at the boundary is not good, and the existence of the boundary state is basically not observed. Because Figure 3 The ② boundary state band gap is also very small, and its one-dimensional field distribution is not obvious, so it is not given here. When the boundary state is in Figure 3 At time ③, the field distribution is as follows Figure 4 (b) At this point, the boundary field exhibits its maximum distribution. The locality of the field is initially enhanced at the boundary. When we set the frequency of the incident light to... Figure 3 ④ When the position of the boundary state is reached, due to the further increase in the band gap width, from Figure 4 (c) It can be seen that the locality of the one-dimensional field is also enhanced.

[0029] When the light intensity is 20GW / cm 2 When a femtosecond pulsed laser is incident on the structure, a Fourier transform is performed on the signal at the exit end. We use the COMSOL time-domain finite element method for calculation, such as... Figure 5 As shown. Figure 5 (a), (b), and (c) correspond to respectively Figure 3 The boundary states ①, ③, and ④ are shown in the diagram. The horizontal axis represents frequency, and the vertical axis represents Fourier coefficients. f0, f1, and f2 are the frequencies of the incident wave, which are 2.179 × 10⁻⁶ and 2.179 × 10⁻⁶ respectively. 14 Hz, 6.537×10 14 Hz, 8.716×10 14 Hz. When the band gap is relatively small, the locality of the field is relatively weak, such as Figure 4 As shown in (a), the field in the lithium niobate structure layer is very small at this time. The boundary state mode is located at this point. Figure 3 The first boundary state has a frequency of f0. However, because the intensity of the incident field is relatively large, after the light passes through the structure, under the influence of the optical nonlinearity of lithium niobate, the emitted light, in addition to the fundamental frequency f0, also exhibits a harmonic frequency 2f0, with Fourier coefficients of 2.326 × 10⁻⁶. 12 0.139×10 12Although the electric field strength in the lithium niobate structure is not high, the appearance of second harmonics was still observed. Besides the high incident light intensity, another reason for the appearance of second harmonics is that the higher the frequency, the better the localization of the field, and the harmonic field is also in a resonant mode, thus ensuring the generation efficiency of second harmonics in the structure. Keeping the incident light intensity constant, when the frequency of the incident light is in a relatively wide bandgap, such as... Figure 3 In the boundary mode of ③, the frequency is f1. In addition to the fundamental frequency f1 and the second harmonic 2f1, the emitted light also exhibits a third harmonic 3f1, with amplitudes of 2.174 × 10⁻⁶ respectively. 12 0.169×10 12 0.0249×10 12 Furthermore, when the frequency of the incident light is in a wider bandgap, such as... Figure 3 In the boundary mode of ④, the frequency is f2. In addition to the fundamental frequency f2, the second harmonic 2f2, the third harmonic 3f2, and 4f2, the emitted light also exhibits amplitudes of 1.920 × 10⁻⁶. 12 0.365×10 12 0.054×10 12 0.011×10 12 Even though the amplitude of the fourth harmonic is very small, we observed that the amplitude of the second harmonic increases with the width of the bandgap in which the fundamental mode is located. The presence of higher harmonics allows this structure to generate higher harmonics of switchable topological boundary states, and the harmonic waves possess topological protection properties.

Claims

1. A device for topological boundary state control and harmonic frequency generation based on voltage regulation, characterized in that, The device has incident light on the left and outgoing light on the right. The device structure consists of electro-optic materials arranged periodically at a set interval. The electro-optic material is a cuboid lithium niobate material with a rectangular parallelepiped structure, wherein the structure is a cuboid lithium niobate material arranged periodically at a set interval in free space. The device structure has a positive voltage applied above and below the lithium niobate on the left half, and a negative voltage applied above and below the lithium niobate on the right half. The length of the period of the left half of the lithium niobate structure is a， The length of the period of the right half of the lithium niobate structure is a 1, a and a 1. They are not equal.

2. The device for topological boundary state control and harmonic frequency generation based on voltage regulation according to claim 1, characterized in that, The device has a femtosecond laser on the left side, which can excite the second-order nonlinear optical effect of lithium niobate material.

3. The device for topological boundary state control and harmonic frequency generation based on voltage regulation according to claim 1, characterized in that, The lithium niobate on the left half of the device structure has a positive DC voltage of 0.8 to 1 GV / m applied to its upper and lower ends, while the lithium niobate on the right half has a negative DC voltage of -0.8 to -1 GV / m applied to its upper and lower ends.

4. The device for topological boundary state control and harmonic frequency generation based on voltage regulation according to claim 1, characterized in that, The lithium niobate mentioned is x - A cut uniaxial crystal, the c-axis of which is parallel to... z The lithium niobate along the axis x The axes are arranged at a set distance, and the incident light with frequency ω0 travels along... x The axis refers to the direction of arrangement of lithium niobate.

5. The device for topological boundary state control and harmonic frequency generation based on voltage regulation according to claim 1, characterized in that, The width da of the left half of the lithium niobate is 0.632 μm, and the width db of the air layer between the lithium niobates is 0.684 μm.

6. The device for topological boundary state control and harmonic frequency generation based on voltage regulation according to claim 5, characterized in that, The width da1 of the right half of the lithium niobate is 0.644 μm, and the width db1 of the air layer between the lithium niobates is 0.696 μm.

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