CN114221124A - A resonance-enhanced terahertz antenna for electro-optic modulation - Google Patents

Abstract

The invention discloses a resonance-enhanced terahertz antenna for electro-optic modulation, which comprises a receiving device, a first resonant circuit and a second resonant circuit, wherein the receiving device comprises a metal element surface resonator which is a double-capacitor and double-loop metal structure; an electro-optical modulation element is arranged between the capacitors, the distance between the electro-optical modulation element and the capacitor on the right side is 5 mu m, and a silicon dioxide buffer layer and a lithium niobate substrate are arranged on the lower portion of the metal primary surface resonator. The electro-optical modulation element is made of lithium niobate, and the electro-optical modulation element adopts a ridge waveguide under a single-mode condition. The invention has the advantages that the structure of the element surface metal RLC resonator ensures that the resonance frequency is positioned at 232GHz, and a local gain electric field is obtained in the capacitor structure of the resonator, thereby finally realizing the electric field enhancement of 40 times of a specific frequency band.

Description

A resonance-enhanced terahertz antenna for electro-optic modulation

technical field

The invention belongs to the technical field of electro-optical modulation, and in particular relates to a resonance-enhanced terahertz antenna used for electro-optical modulation.

Background technique

With the maturity and popularization of 5G (fifth generation mobile communication technology) communication technology and the increasing demand for communication rates, terahertz frequency band communication technology is gradually becoming the focus of research. At present, most of the 5G communication frequency bands are located below 6GHz, and the bandwidth is narrow. With the increase in communication requirements, communication resources are increasingly tight. The terahertz frequency band between 0.1THz-10THz has a higher data transmission rate and wider frequency band resources. However, there is a lack of effective receiving devices in the terahertz band. For the electronic detection methods commonly used in microwave detection, the terahertz band has approached the limit response frequency of microwave electronic components. For the common semiconductor detection methods commonly used in the optical band, terahertz light No apparent optical response.

To achieve efficient terahertz detection, we design a method based on resonance-enhanced microstructured antennas combined with lithium niobate waveguides for efficient measurement of electro-optical modulation of terahertz signals. This method can realize the enhancement of electro-optical modulation in the terahertz frequency band with tunable resonance frequency by changing the structural parameters.

SUMMARY OF THE INVENTION

In order to solve the defects existing in the prior art, the present invention provides a resonance-enhanced terahertz antenna for electro-optic modulation.

In order to solve the above-mentioned technical problems, the present invention provides the following technical solutions:

A resonance-enhanced terahertz antenna for electro-optic modulation, comprising a receiving device, characterized in that the receiving device comprises a metal element surface resonator, and the metal element surface resonator is a double capacitor and double loop metal structure; An electro-optical modulation element is arranged between the capacitors, and the distance from the capacitor on the right is 5 μm. A silicon dioxide buffer layer and a lithium niobate substrate are arranged at the lower part of the metal original surface resonator.

Preferably, the material of the electro-optical modulation element is lithium niobate, and the electro-optical modulation element adopts a single-mode ridge waveguide.

Preferably, the single-mode condition satisfies the following formula:

in,

Preferably, the buffer thickness of the silicon dioxide layer is 400nm-500nm.

Preferably, the thickness of the lithium niobate substrate is 700nm-900nm.

Preferably, the structural parameters are h=0.7 μm, H=0.68 μm, W=0.42 μm, θ=60°, n ₁ =n _{o, e} =2.21, 2.14, n ₀ =n ₂ =1.5,b= h/2λ.

Compared with the prior art, the present invention has the following beneficial effects:

1) The structure of the metal element surface resonator makes its resonance frequency at 232 GHz, and a local gain electric field is obtained in the resonator capacitance structure to achieve a 40-fold electric field enhancement in a specific frequency band.

2) The directions of the two loops are opposite, and the change of the magnetic flux causes the induced currents in the two loops to change in opposite directions, and the magnetic response characteristics of the structure are suppressed; the series connection of the double capacitors has a compensating effect.

3) During resonance, most of the energy is localized between the capacitor structures, so that there is a strong local resonant electric field near the capacitor, which is beneficial to the collection and gain of signals.

Description of drawings

FIG. 1 is a schematic diagram of the terahertz electro-optical detector of the present invention.

FIG. 2 is a partial enlarged view of the terahertz electro-optical detector A of the present invention.

FIG. 3 is a schematic diagram of the terahertz electro-optical detector of the present invention.

FIG. 4 is (a) a metasurface resonator structure of the present invention, and (b) an RLC equivalent circuit.

Figure 5 is the absorptivity curve under different capacitance values simulated by COMSOL.

(a) Surface resonance spectra of elements with different capacitances. The left capacitor spacings are 17.5μm, 35μm, and 70μm, respectively, and the right capacitor spacings are 2.5μm, 5μm, and 10μm, respectively. The low frequency resonance peak corresponds to the LC resonance mode, and the high frequency resonance peak corresponds to the DP resonance mode;

(b) LC resonance mode conduction current density distribution

(c) Distribution of conduction current density in DP resonance mode. The arrows represent conduction current density vectors, and the size of arrows in b and c is normalized.

FIG. 6 shows the electric field distribution of the cross-section of the intermediate layer of the lithium niobate layer, wherein the metal thicknesses of (a), (b), and (c) are 50 nm, 100 nm, and 200 nm, respectively.

Figure 7 shows the electric field gain during resonance under different capacitor sizes. The left and right capacitor spacings are (a) 17.5μm, 2.5μm, (b) 35μm, 5μm, (c) 70μm, 10μm, respectively. The resonance frequencies are (a) 200GHz, (b) 232GHz, (c) 266GHz.

FIG. 8 is a schematic diagram of a ridge waveguide according to an embodiment of the present invention.

FIG. 9 is an electric field distribution diagram of the horizontal or vertical polarization corresponding to two sets of representative simulation results provided by the present invention.

FIG. 10 is a cross-sectional view of a terahertz electric field gain distribution.

Detailed ways

The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, but not to limit the present invention.

Example 1

This embodiment provides a resonance-enhanced terahertz antenna for electro-optical modulation, including a receiving device, the receiving device includes a metal element surface resonator, and the metal element surface resonator is a double capacitor and double loop metal structure; An electro-optical modulation element is arranged between the capacitors, and the distance from the capacitor on the right is 5 μm. A silicon dioxide buffer layer and a lithium niobate substrate are arranged at the lower part of the metal original surface resonator.

The material of the electro-optical modulation element is lithium niobate, and the electro-optical modulation element adopts a ridge waveguide with a single-mode condition.

Among them, the single-mode condition satisfies the following formula:

in,

The buffer thickness of the silicon dioxide layer is 400nm-500nm.

The thickness of the lithium niobate substrate is 700nm-900nm.

The structural parameters are h=0.7 μm, H=0.68 μm, W=0.42 μm, θ=60°, n ₁ =n _{o, e} =2.21, 2.14, n ₀ =n ₂ =1.5, b=h/2λ .

Example 2

In order to express the design idea of the present invention more clearly, the following specific explanations are made:

Electro-optic effect

The refractive index of the crystal will change under an external DC electric field, and the magnitude of the change is proportional to the magnitude of the electric field, which is called the Pockels effect (ie, the electro-optic effect). The physical essence of the electro-optic effect is the sum-frequency process of the DC electric field and the electromagnetic wave field under the action of the second-order nonlinear term χ ⁽²⁾ (ω=ω+0). Thus, the DC electric field equivalently changes the linear refractive index of the electromagnetic wave.

The crystal refractive index ellipsoid formula is:

η ₁₁ x ² +η ₂₂ y ² +η ₃₃ z ² +2η ₁₂ xy+2η ₂₃ yz+2η ₃₁ zx=1

The linear electro-optic coefficient term γ _mk is the electro-optic coefficient of the Pockels effect.

Properties of Lithium Niobate Electro-optic Crystals

Lithium niobate crystal has a very large linear electro-optic coefficient and is a commonly used electro-optic modulation crystal. The lithium niobate crystal belongs to the 3m group according to its symmetry, and its first-order electro-optic coefficient tensor is expressed as

At 500nm wavelength, the value of each coefficient is:

γ ₁₃ =8.6pm·V ^-1 γ ₂₂ =6.8pm·V ^-1

γ ₃₃ =30.9pm·V ^-1 γ ₄₂ =20pm·V ^-1

The refractive index ellipsoid of lithium niobate is

The z axis is the optical axis of the crystal, and no and ne are the ordinary light ( _o light) and extraordinary light ( _e light) refractive indices of lithium niobate, respectively.

In this embodiment, the x-cut lithium niobate crystal thin film is used as the electro-optic modulation crystal, and the x-cut represents the orientation of the crystal so that the probe light propagates in the crystal along the x-axis of the crystal.

The electric field component involved in the modulation is located in the yz plane. Since the _γ33 electro-optic coefficient of lithium niobate is the largest, we adjust the orientation of the crystal so that the direction of the modulated terahertz electric field falls on the z-axis of the crystal, that is, E ₁ ≈0, E ₂ ≈0, E ₃ =E _THz ,

Formula (1) is simplified to:

Note that the principal axes of the ellipsoid coordinate system are unchanged under electro-optic modulation, which will greatly simplify our calculations. The refractive indices in the y-direction and z-direction after modulation are

Assuming that the modulated light is linearly polarized light with a y offset of 45 degrees, it propagates along the x-axis of the crystal and the modulated distance is d, the phase difference in the yz direction caused by the different refractive indices in the y and z directions is

(2) The first term on the right side of the formula comes from the birefringence of the lithium niobate crystal, which has nothing to do with the modulation signal. A background signal will be generated during detection, which needs to be filtered out; the second term is proportional to the modulation signal. The phase difference caused by the term, we can restore the received terahertz signal. This method of measuring terahertz electric fields through the electro-optic effect is called electro-optic sampling.

1550nm probe light modulation signal intensity

Here we give some parameters of the actual device in advance to prove that the intensity of the modulated signal is sufficient to meet the detection requirements. The refractive indices of lithium niobate at 1550 nm for o light and e light are n _o =2.21, _ne =2.14, respectively. The modulation length is about d=96 μm, γ ₃₃ ≈30.9pm·V ^-1 , γ ₁₃ ≈8.6pm·V ^-1 , the gain of the resonator to the terahertz signal is about 20 times, assuming that the electric field of the terahertz signal propagating in free space is 10V·cm ^-1 . Substituting into equation 2.28, we can get the different polarization states of the light caused by the terahertz signal The phase difference is about

The light intensity change ratio of the polarization component caused by the phase difference is about 10 ^-3 , and the accuracy of the light intensity detector in the current experiment can reach 10 ^-6 , which is completely sufficient to detect the light intensity change of the polarization component caused by the phase difference.

As shown in Figure 3, in the actual modulation process, the terahertz signal experienced by the modulated light will vary with the time the light travels in the waveguide,

where C _LN includes all the coefficients related to the crystal, d is the length of the modulation region, which depends on the size of the resonator, and d determines the phase change of the terahertz signal during the modulation process, as shown in Figure 2.1.

We take the binary amplitude keying signal (2ASK) as an example to illustrate the detection process of the communication signal in the time domain. 2ASK is a random sequence composed of 1s and 0s (one byte per cycle) to modulate the harmonic carrier signal [ 5].

Where s(t) is a random variable, and A is the amplitude of the carrier signal. We assume that the terahertz signal transmits one binary byte of information per cycle on average. In order to distinguish the different information of adjacent cycles, we can allow the terahertz signal to generate a phase difference of half a cycle during the modulation process. The integral spectrum of the modulated signal within a half period of the signal can be expressed as:

where T=2π/ω. The time domain information corresponding to bytes 1 and 0 can be obtained by formula (3).

Microstructural Resonator Design

采用这种结构的共振器有若干优点：首先，两个回路的方向相反，磁通量变化引起两个回路中的感应电流变化方向相反，结构的磁响应特性被抑制了；其次，双电容串联具有补偿作用。假设电介质环境均匀∈(r)＝∈，作无限大平板电容器近似，则串联双电容的总电容表示为We adopt the metal element surface resonator structure as a double-capacitor, double-loop metal structure. Our structure is scaled up and fine-tuned based on the prototype of [12]. The planar structure of the resonator is shown in Figure 4(a). The size of the metal structure and the dielectric environment determine the size of the capacitance and inductance. Its equivalent circuit is an RLC oscillator circuit, as shown in Figure 4(b). The resonant frequency is

The resonator using this structure has several advantages: first, the directions of the two loops are opposite, and the change of the magnetic flux causes the induced current in the two loops to change in opposite directions, and the magnetic response characteristics of the structure are suppressed; secondly, the double capacitor series has compensation effect. Assuming that the dielectric environment is uniform ∈(r)=∈, as an approximation of an infinite plate capacitor, the total capacitance of the series-connected double capacitors is expressed as

Obviously, as long as the total capacitance interval d ₁ +d ₂ remains unchanged, changing the capacitance distance ratio d ₁ /d ₂ will not affect the total capacitance size and resonance frequency. This makes the design of the device more flexible; most of the energy is localized between the capacitor structures during resonance, so that there is a strong local resonant electric field near the capacitor, which is beneficial to the collection and gain of the signal.

resonance mode

There are two different resonance modes in this resonance structure, namely the LC mode and the DP mode. Figure 5(a) shows the absorptivity curves for different capacitance values simulated by COMSOL. When the metasurface resonates, a large amount of the incident electric field energy is localized in the capacitive structure, thereby forming an absorption peak. The absorption peak with lower frequency corresponds to the LC resonance mode, forming the loop current of the LC oscillation, as shown in Figure (b), the resonance frequency is characterized by

As the capacitance distance decreases and the total capacitance increases, it can be seen that the absorption peak corresponding to the LC resonance mode is shifted to the low frequency direction; the DP resonance mode is essentially an oscillation mode in which the structure generates electric dipoles under the driving of an external field, and does not generate The loop current is shown in (c), so increasing the capacitance has little effect on the absorption peak.

Figure 5. Surface resonance spectra of elements with different capacitances and sizes. The left capacitor spacings are 17.5μm, 35μm, and 70μm, respectively, and the right capacitor spacings are 2.5μm, 5μm, and 10μm, respectively. The low frequency resonance peak corresponds to the LC resonance mode, and the high frequency resonance peak corresponds to the DP resonance mode. (b) LC Resonant mode conduction current density distribution (c) DP resonant mode conduction current density distribution. The arrows represent conduction current density vectors, and the arrow sizes in b and c are normalized.

As shown in Figure 6, the electric field gain during resonance under different metal thicknesses, a 400nm silicon dioxide buffer layer and a 700nm lithium niobate substrate were placed under the metal successively (see 3.2.3 for the cross-sectional structure). The electric field shown in the figure is the electric field distribution of the middle layer of the lithium niobate layer,

As shown in Figure 7, the electric field gain during resonance under different capacitor sizes, the left and right capacitor distances are (a) 17.5μm, 2.5μm, (b) 35μm, 5μm, (c) 70μm, 10μm, and the resonance frequencies are (a) ) 200GHz (b) 232GHz (c) 266GHz, comparison experiment

Parameter selection and optimization

In order to achieve a large THz signal gain, the thickness of the metal structure and the size of the capacitance are optimized.

Figure 6 shows the magnitude of the electric field gain for different metal thicknesses. Thicker metals have larger capacitances, resulting in stronger localized electric fields in the capacitances.

Figure 7 shows the electric field gain size distribution on the capacitor cross section with different capacitor sizes. The electro-optical modulation element is designed under the capacitor structure on the right side. The smaller the spacing between the capacitors on the right side, the greater the gain of the local electric field and the stronger the inhomogeneity. An electric field that is too inhomogeneous has a large longitudinal component as well as a transverse gradient, which distorts the wavefront of the signal.

In the present invention, the spacing on the right side is selected as 5 μm.

Electro-optical modulation element design

We choose lithium niobate as the material of electro-optic modulation element. In electro-optic modulation, since we need to accurately measure the phase change of the probe light after modulation in the waveguide, the waveguide is required to be a single-mode waveguide, that is, only a single-mode propagation mode exists in the waveguide to ensure that the measured phase signal is not affected by high-order mode effect. Among various waveguide structures, the fabrication process of rectangular waveguides and ridge waveguides is relatively simple, in which the single-mode condition of ridge waveguides has fewer restrictions on the waveguide size than rectangular waveguides, higher-order modes are dissipated faster, and transversal The larger area is conducive to reducing the loss of the probe light coupling into the waveguide, so we choose the ridge waveguide as the waveguide structure design scheme.

Ridge waveguide

The schematic diagram and parameter definitions of the ridge waveguide are shown in Figure 8. In 1985, the single-mode condition requirements for ridge waveguides were proposed

in

Compared with the rectangular waveguide, the refractive index of the core and cladding of the ridge waveguide has less restriction on the single-mode condition, allowing a larger cross-sectional area.

_The thickness _h of the waveguide is defined according to the above to improve the coupling efficiency of the probe light. n ₀ =n ₂ =1.5, b=h/2λ, which satisfies the single-mode conditions given by equations 3.15 and 3.16.

Buffer layer and waveguide thickness

In practical applications, a single-mode waveguide generates a localized gain electric field region through a metal resonator, located near the capacitive structure. Since the metal resonator is a closed double-loop structure, the waveguide will pass under the two metal frames of the loop, and may be affected by the metal (dense medium) to change the propagation mode of the waveguide, so it needs to be between the waveguide and the metal frame. Filling a sufficiently thick buffer layer of optically rarer media suppresses this effect. We employ a _SiO2 buffer layer consistent with the waveguide substrate. We used comsol to simulate images of the base film for different buffer layer thicknesses and waveguide thicknesses. Figure 9 shows the propagating mode electric field distributions for horizontal or vertical polarization for two representative simulations. When the thickness of the buffer layer is too small (<400 nm), the vertically polarized propagation mode will be coupled with the metal and leak into the gap between the waveguide and the metal to form the slot propagation mode, as shown in Figure 9(a). Due to the influence of the metal frame, when the thickness of the waveguide is less than 700nm, the fundamental mode of vertical polarization given by the calculation results of COMSOL is always accompanied by high-order horizontal polarization modes, which originate from the finite boundary in the simulated physical field. , we think that this means that the vertically polarized fundamental mode does not propagate stably in this case, but diverges in the horizontal direction, as shown in Figure 3.9(c).

由此计算得到垂直偏振基模的衰减系数大小为α＝κk₀＝1.34×10^-5×2π/1550nm＝54.3m^-1。金属共振器边框宽度为24μm，此时通过该边框区域的衰减1-e^-αΔz≈0.002，基本可以忽略。When the thickness of the waveguide reaches 700 nm, the fundamental mode can stably propagate in the waveguide. At this time, the electric field distributions of the horizontally polarized fundamental mode and the vertically polarized fundamental mode are shown in Figures 9(e) and 9(f). The effective refractive index is 2.08+2.39×10 ^-5 i, 2.04+1.34×10 ^-4 i. Propagation mode amplitude

According to this calculation, the magnitude of the attenuation coefficient of the vertically polarized fundamental mode is α=κk ₀ =1.34×10 ⁻⁵ ×2π/1550nm=54.3m ⁻¹ . The frame width of the metal resonator is 24 μm. At this time, the attenuation through the frame area is 1-e ^-αΔz ≈ 0.002, which can be basically ignored.

The working principle of the present invention is: the ridge waveguide has loose single-mode conditions, so that the cross section of the waveguide can be taken as a line width in the order of microns, which greatly increases the efficiency of the detection light coupling into the waveguide, but the gain electric field of the metal resonant structure is in the It is localized vertically and decays with increasing distance from the capacitive center.

The thickness of the waveguide is selected as H=0.7μm. At this time, the electric field gain at the center of the waveguide section is about 40 times. As shown in Figure 10, when using a 300nm metal structure, a 400nm buffer layer and a 700nm lithium niobate substrate, the numerical simulation gives Sectional electric field distribution structure in lithium niobate at resonance.

Finally, it should be noted that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (6)

1. A terahertz antenna for resonance enhancement of electro-optic modulation comprises a receiving device, and is characterized in that the receiving device comprises a metal element surface resonator which is a double-capacitor and double-loop metal structure; an electro-optical modulation element is arranged between the capacitors, the distance between the electro-optical modulation element and the capacitor on the right side is 5 mu m, and a silicon dioxide buffer layer and a lithium niobate substrate are arranged on the lower portion of the metal primary surface resonator.

2. The terahertz antenna for resonance enhancement of electro-optic modulation according to claim 1, wherein the material of the electro-optic modulation element is lithium niobate, and the electro-optic modulation element adopts a ridge waveguide in a single-mode condition.

3. The resonance enhanced terahertz antenna for electro-optic modulation according to claim 2, wherein the single mode condition satisfies the following formula:

wherein,

4. the resonance enhanced terahertz antenna for electro-optic modulation according to claim 1, wherein the silicon dioxide layer buffer thickness is 400nm-500 nm.

5. The resonance enhanced terahertz antenna for electro-optic modulation according to claim 1, wherein the lithium niobate substrate is 700nm-900nm thick.

6. A terahertz antenna for resonance enhancement of electro-optic modulation as claimed in claim 3, wherein the structural parameter is H-0.7 μm, H-0.68 μm, W-0.42 μm, θ -60 °, n₁＝n_o，e＝2.21，2.14，n₀＝n₂＝1.5，b＝h/2λ。

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