Method for achieving optical wave and terahertz near-zero refractive index based on nonlinear hybrid waveguide

Abstract

The application discloses a method for realizing optical wave and terahertz near-zero refractive index based on a nonlinear mixed waveguide, and steps are as follows: thin film lithium niobate is selected as a nonlinear material to process a mixed waveguide; a one-dimensional corrugated waveguide is used on the mixed waveguide to show a Dirac point-like dispersion characteristic at a Gamma point; an average nonlinear coupling coefficient of the mixed waveguide is calculated, and the quality factor of the zero-refractive-index waveguide is optimized by adjusting the thickness and period of the thin film lithium niobate; hollow rectangular metal waveguides are arranged around the thin film lithium niobate waveguide, and are used for guiding the propagation of terahertz waves and enhancing the nonlinear interaction in the difference frequency process; and the near-zero refractive index of various terahertz frequencies is realized by changing the width of the hollow rectangular metal waveguide. By jointly designing the nonlinear mixed waveguide of the terahertz and optical wave near-zero refractive index, the problems of phase mismatch and weak nonlinear interaction of the conversion of the optical wave to the terahertz wave are solved, so that the efficient conversion of the optical wave to the terahertz wave across the wave band is realized through on-chip optical difference frequency.

Description

Technical Field

[0001] This invention belongs to the fields of electronics and photonics, and particularly relates to a method for achieving near-zero refractive index of light waves and terahertz waves based on nonlinear hybrid waveguides. Background Technology

[0002] The terahertz band, typically ranging from 0.1 to 10 THz, is a transitional region between electrons and photons and is considered one of the "ten technologies that will change the future world," a key technology for 6G communication. Methods for generating terahertz waves primarily utilize electronic, photonic, and hybrid approaches, including quantum cascade lasers, free-electron lasers, photoconductive antennas, and nonlinear optical processes. However, finding a terahertz source that meets all the requirements of terahertz communication remains challenging. For example, traditional electronic methods for generating terahertz radiation have limitations in modulation speed; hybrid electron-photon methods encounter unresolved issues related to integration and miniaturization; and photonic methods need to improve the conversion efficiency from light waves to terahertz waves for practical applications. Among these, on-chip difference frequency generators (DFGs) offer unique advantages in terms of integration, low cost, and low noise. However, their low conversion efficiency urgently requires further optimization.

[0003] Metamaterials are composite materials designed with subwavelength components, possessing unique properties such as negative and zero refractive indices. By controlling or modifying the dielectric constant and permeability of these materials, specific functions can be achieved or device performance can be improved, leading to important applications in perfect lenses, invisibility cloaks, artificial black holes, and nonlinear optical processes. In recent years, broadband optically generated terahertz waves based on nonlinear optical rectification using zero-refractive-index materials have attracted considerable attention and have seen widespread applications in medical imaging and diagnosis. However, these terahertz sources are typically large and difficult to integrate, hindering their practical application in terahertz communication. Furthermore, the wide bandwidth of these optically generated terahertz sources cannot meet the narrow linewidth requirements of terahertz communication. Summary of the Invention

[0004] Objective of the Invention: The objective of this invention is to provide a method for achieving near-zero refractive index conversion of optical waves and terahertz waves based on a nonlinear hybrid waveguide. By jointly designing a nonlinear hybrid waveguide with near-zero refractive index for both terahertz and optical waves, the problems of phase mismatch and weak nonlinear interaction in the conversion of optical waves to terahertz waves are solved, thereby achieving efficient cross-band conversion of optical waves to terahertz waves through on-chip optical difference frequency modulation.

[0005] Technical solution: The present invention provides a method for achieving near-zero refractive index for optical waves and terahertz waves based on nonlinear hybrid waveguides, comprising the following steps:

[0006] Step 1: Select thin-film lithium niobate as the nonlinear material to fabricate hybrid waveguides;

[0007] Step 2: Using a one-dimensional corrugated waveguide on the hybrid waveguide, exhibit Dirac point dispersion characteristics at the Γ point;

[0008] Step 3: Calculate the average nonlinear coupling coefficient of the hybrid waveguide and optimize the quality factor of the zero-refractive-index waveguide by adjusting the thickness and period of the thin lithium niobate film;

[0009] Step 4: Hollow rectangular metal waveguides are set around the thin-film lithium niobate waveguide to guide the propagation of terahertz waves and enhance the nonlinear interaction in the difference frequency process.

[0010] Step 5: Achieve near-zero refractive index for various terahertz frequencies by changing the width of the hollow rectangular metal waveguide.

[0011] Furthermore, step 1 specifically includes the following steps:

[0012] Step 1.1: Spin-coat photoresist onto thin-film lithium niobate, expose it using electron beam lithography (EBL), and then etch the lithium niobate waveguide using ion beam etching (IBE).

[0013] Step 1.2: Deposit a silicon dioxide protective layer using plasma-enhanced chemical vapor deposition (PECVD) to complete the fabrication of the optical waveguide;

[0014] Step 1.3: Gold plating is performed on the surface using electron beam evaporation (EBE) deposition.

[0015] Step 1.4: Perform end-face polishing to promote the coupling of light waves and the external coupling of terahertz waves.

[0016] Furthermore, the etched lithium niobate waveguide has a thickness of 300-900 nm, the deposited silicon dioxide protective layer has a thickness of 1-3 μm, and the upper metal layer has a thickness of 0.1-2 μm.

[0017] Furthermore, step 2 specifically involves: utilizing a one-dimensional corrugated waveguide to exhibit Dirac point dispersion characteristics at point Γ, i.e., one pair of linear dispersions at k... o =0 (Γ point) intersection, the intersection of the mixed modes at Γ point contains orthogonal electric dipole and magnetic dipole resonances, and the symmetry provides the electric and magnetic responses required for zero refractive index; for metallic terahertz zero refractive index waveguides, the intrinsic structural dispersion depends on the simulation of the metallic rectangular waveguide, for TE 01 The dispersion relation of the waveguide in the mode is:

[0018] ε eff =1-(π / k0w) 2 =1-(f T,c / f T ) 2

[0019] Assume the waveguide behaves with an effective dielectric constant εeff The equivalent medium, k o =2π / λ T The wavenumber is the wavelength in free space, w is the width of the hollow rectangle, and f is the wavenumber in free space. T f is the terahertz frequency. T,c For TE 01 The cutoff frequency of the mode.

[0020] Furthermore, step 3 specifically involves:

[0021] Assuming that the intensities of the pump light ω1 and the signal light ω2 do not change significantly during the terahertz generation process, the terahertz wave (ω T The conversion efficiency of (ω1-ω2) is expressed as:

[0022]

[0023] Among them, I T The generated terahertz intensity is given by I1 and I2, where I1 and I2 are the pump and signal light intensities, respectively, and L is the nonlinear interaction length. α j The absorption coefficient is Δα = α1 + α2 - α T Δk is the phase mismatch; Phase mismatch:

[0024] Δk=(n1ω1 / c-n2ω2 / cn T ω T / c)

[0025] c represents the speed of light in a vacuum, n j For effective refractive index, average nonlinear coupling coefficient

[0026]

[0027] Where ε0 is the permittivity of free space, e j For the intrinsic model field, χ is the modulus power, a is the period length, and χ is the modulus power. (2) For the nonlinear coefficients, mode power, and group velocity v in the terahertz band g,j The relationship between them is:

[0028] P j =W j v g,j / a

[0029] W j Let represent the mode energy within one period. Considering the waveguide structure, the zero refractive index point is realized at the band edge, and the group velocity is close to zero, leading to a strong slow-light effect. This slow-light effect enhances the nonlinear interaction between the light wave and the terahertz wave. Under approximate conditions, the mode power is expressed as:

[0030] Pj ≈ε0cn j ∫∫ A |e j | 2 dxdy / 2

[0031] n j Indicates the effective refractive index.

[0032] The quality factor indicates that the oscillator loses energy at a slower rate and the vibration can continue for a longer period of time. The expression for the quality factor is:

[0033]

[0034] Where h is the waveguide thickness, λ is the wavelength, n is the effective refractive index, and α is the loss. As can be seen from the above equation, the quality factor depends on the waveguide thickness and the group velocity. The group velocity is related to dispersion. By adjusting the lithium niobate thickness and period, the quality factor can be optimized, thereby reducing the energy leaked into free space.

[0035] Further, step 4 specifically involves: after fabricating a waveguide on a thin-film lithium niobate chip containing metal electrodes at the bottom, depositing a silicon dioxide protective layer using plasma chemical vapor deposition, and then plating metal on the top and sidewalls, combining it with the metal at the bottom to form a rectangular metal waveguide.

[0036] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0037] (1) This invention proposes the fabrication of a nonlinear hybrid integrated waveguide, which comprises a near-zero optical waveguide and a near-zero terahertz metallic waveguide made of nonlinear thin film materials. Simultaneously, this near-zero nonlinear hybrid waveguide exhibits a strong slow-light effect, enhancing the nonlinear interaction between optical waves and terahertz waves. Furthermore, terahertz waves are efficiently generated through on-chip nonlinear difference-frequency effects.

[0038] (2) Achieving efficient nonlinear processes requires conditions such as high effective nonlinear coefficients, large spatial mode overlap, small effective mode area, and phase matching. This invention proposes a cross-band phase matching technique that distinguishes itself from traditional quasi-phase matching and mode phase matching techniques by achieving near-zero refractive index in both the communication band and the terahertz band. This cross-band phase matching technique also exhibits a strong slow-light effect, enabling efficient generation of terahertz waves. Attached Figure Description

[0039] Figure 1 The diagram shows the near-zero refractive index nonlinear hybrid waveguide structure of this invention. (a) Schematic diagram of the hybrid waveguide, including an optical thin-film lithium niobate corrugated waveguide and a terahertz rectangular metal waveguide; (b) Schematic diagram of the optical thin-film lithium niobate corrugated waveguide; (c) Schematic diagram of the terahertz rectangular metal waveguide.

[0040] Figure 2 Design diagrams for zero-refractive-index waveguides for optical and terahertz waves. (a) Strip structure of thin-film lithium niobate zero-refractive-index waveguide; (b) Principal components of magnetic and electric fields at the Γ-point; (c) Effective refractive index of LN zero-refractive-index waveguide; (d) Cutoff frequencies of terahertz zero-refractive-index waveguides at different widths; (e) Effective refractive index of terahertz zero-refractive-index waveguide at W = 22 μm. The inset shows the mode profile of the terahertz wave.

[0041] Figure 3 This is a diagram showing the average nonlinear coupling coefficients of different terahertz waves generated by different pump lights near zero refractive index. Detailed Implementation

[0042] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0043] The nonlinear material is thin-film lithium niobate. Nonlinear materials include, but are not limited to, DAST, nonlinear organic materials, GaAs, and other materials with larger nonlinear coefficients.

[0044] The main characteristics of the above-mentioned nonlinear hybrid waveguide structure design are:

[0045] (1) The thin-film lithium niobate optical waveguide adopts a one-dimensional corrugated structure, and its dispersion at the Γ point has a refractive index of zero. The thin-film lithium niobate optical waveguide has a large second-order nonlinear polarizability and a small effective mode area;

[0046] (2) The quality factor (Q factor) of this zero-refractive-index waveguide is optimized by adjusting the thickness of lithium niobate and the period a, which significantly reduces the energy leaked into free space;

[0047] (3) Hollow rectangular metal waveguides are located around the thin-film lithium niobate waveguide to guide the propagation of terahertz waves and enhance the nonlinear interaction in the difference frequency process;

[0048] (4) Near-zero refractive index at various terahertz frequencies can be achieved by changing the width of the rectangular metal waveguide.

[0049] The process by which the hybrid waveguide with the above structure achieves zero refractive index and the principle of enhancing difference-frequency conversion efficiency are as follows: Assuming that the intensities of the pump light ω1 and the signal light ω2 do not change significantly during the THz generation process, the terahertz wave (ω... T The conversion efficiency of (ω1-ω2) can be expressed as:

[0050]

[0051] Among them, I T The generated terahertz intensity is given by I1 and I2, where I1 and I2 are the pump and signal light intensities, respectively, and L is the nonlinear interaction length. α jThe absorption coefficient is Δα = α1 + α2 - α T Δk is the phase mismatch. Typically, the phase mismatch Δk = (n1ω1 / c - n2ω2 / cn) T ω T / c), n j For effective refractive index, average nonlinear coupling coefficient

[0052]

[0053] Where ε0 is the permittivity of free space, e j For the intrinsic model field, χ is the modulus power, a is the period length, and χ is the modulus power. (2) For the nonlinear coefficients in the terahertz band. Mode power and group velocity v g,j The relationship between them is P j =W j v g,j / a, Considering our structure, the zero refractive index point is realized at the band edge, and the group velocity is close to zero, leading to a strong slow-light effect. This slow-light effect can enhance the nonlinear interaction between light waves and terahertz waves. Furthermore, under approximate conditions, the mode power can be expressed as P j ≈ε0cn j ∫∫ A |e j | 2 According to formula (2), dxdy / 2 indicates that the nonlinear coupling coefficient can be enhanced in the near-zero refractive index case. When all effective refractive indices are close to zero, phase matching and strong nonlinear interaction can be achieved, thereby enhancing the terahertz wave generation efficiency.

[0054] Example: Design of nonlinear hybrid waveguide structures. For example... Figure 1 As shown, two narrow-linewidth continuous lasers in the 1.5μm C-band are coupled into a nonlinear hybrid waveguide. The frequency interval between the two input light wavelengths is the terahertz frequency. The nonlinear dielectric film is lithium niobate and designed with a periodic corrugated structure. Terahertz radiation can be effectively generated in the thin-film lithium niobate waveguide through the difference frequency process.

[0055] In the specific design of the nonlinear zero-refractive-index optical waveguide, the Dirac point dispersion characteristics exhibited by the one-dimensional corrugated waveguide at point Γ are utilized, that is, a pair of linear dispersions at k o =0 (Γ point) intersects, such as Figure 2 As shown in (a), the intersection of the mixed modes at the Γ point contains orthogonal electric and magnetic dipole resonances. The symmetry of these modes provides the electric and magnetic responses required for zero refractive index, such as... Figure 2 As shown in (b). Compared to other near-zero dielectric materials (ENZ), due to the effective dielectric constant εeff and permeability μ eff With zero refractive index at the Γ point, the zero-refractive-index thin-film lithium niobate waveguide exhibits finite impedance, which is essential for effective waveguide coupling. Furthermore, the quality factor of the zero-refractive-index waveguide can be optimized by adjusting its thickness and period, significantly reducing energy leakage into free space.

[0056] For metallic terahertz zero-refractive-index waveguides, the intrinsic structural dispersion is simulated based on the metallic rectangular waveguide. For TE 01 The mode, the waveguide dispersion relation is ε eff =1-(π / k0w) 2 =1-(f T,c / f T ) 2 Assume the waveguide behaves with an effective dielectric constant ε. eff The equivalent medium, k o =2π / λ T The wavenumber is the wavelength in free space, w is the width of the hollow rectangle, and f is the wavenumber in free space. T f is the terahertz frequency. T,c For TE 01 The mode's cutoff frequency. From this equation, it can be seen that near the mode's cutoff frequency, ε... eff Approaching zero. Furthermore, the width of a hollow rectangular waveguide can be used to manipulate the terahertz cutoff frequency, resulting in zero exponents at various terahertz frequencies, such as... Figure 2 As shown in (d), when the width of the rectangular metallic waveguide is 22 μm, zero refractive index can be achieved at 3.21 THz, as... Figure 2 As shown in (e). When the terahertz frequency approaches the cutoff frequency f T,c At 3.21 THz, the nonlinear coupling coefficients increase overall under different pump light conditions. Furthermore, when the terahertz frequency remains constant at the cutoff frequency, these nonlinear coupling coefficients increase rapidly further by bringing the pump light closer to zero refractive index, such as... Figure 3 As shown.

[0057] The above hybrid waveguides can be implemented in the following ways:

[0058] Commercially available thin-film lithium niobate (TFLN) samples were selected for fabrication. First, photoresist was spin-coated onto the TFLN, followed by exposure using electron beam lithography (EBL). After development, the lithium niobate waveguide was etched using ion beam etching (IBE). Then, a silicon dioxide protective layer was deposited using plasma-enhanced chemical vapor deposition (PECVD) to complete the fabrication of the optical waveguide. Subsequently, gold was deposited on the surface using electron beam evaporation (EBE) to achieve a terahertz zero-refractive-index rectangular waveguide. Finally, end-face polishing was performed to promote optical wave coupling and external coupling of the terahertz wave.

Claims

1. A method for achieving near-zero refractive index for optical waves and terahertz waves based on nonlinear hybrid waveguides, characterized in that, Includes the following steps: Step 1: Select thin-film lithium niobate as the nonlinear material to fabricate hybrid waveguides; Step 2: Using a one-dimensional corrugated waveguide on the hybrid waveguide, exhibit Dirac point dispersion characteristics at the Γ point; Step 3: Calculate the average nonlinear coupling coefficient of the hybrid waveguide and optimize the quality factor of the zero-refractive-index waveguide by adjusting the thickness and period of the thin lithium niobate film; The feature is that step 3 specifically includes: Assuming the pump light is generated during the terahertz process and signal light The intensity did not change significantly, terahertz waves ( The conversion efficiency of ) is expressed as: ； in, To produce terahertz intensity, and For the pump light and signal light intensity, The length of the nonlinear interaction. The absorption coefficient is... , Phase mismatch; Phase mismatch: ； c represents the speed of light in a vacuum. For effective refractive index, average nonlinear coupling coefficient : ； in, The dielectric constant of free space, For the intrinsic model field, For modulus power, The period length, For the nonlinear coefficients, mode power, and group velocity in the terahertz band The relationship between them is: ； W j Let represent the mode energy within one period. Considering the waveguide structure, the zero refractive index point is realized at the band edge, and the group velocity is close to zero, leading to a strong slow-light effect. This slow-light effect enhances the nonlinear interaction between the light wave and the terahertz wave. Under approximate conditions, the mode power is expressed as: ； n j Indicates the effective refractive index; The quality factor indicates that the oscillator loses energy at a slower rate and the vibration can continue for a longer period of time. The expression for the quality factor is: ； Where h is the waveguide thickness, Where λ is the wavelength and n is the effective refractive index. For losses; as can be seen from the above formula, the quality factor depends on the waveguide thickness and the group velocity, and the group velocity is related to dispersion. By adjusting the thickness and period of lithium niobate, the quality factor can be optimized, thereby reducing the energy leaked into free space. Step 4: Hollow rectangular metal waveguides are set around the thin-film lithium niobate waveguide to guide the propagation of terahertz waves and enhance the nonlinear interaction in the difference frequency process. Step 4 specifically involves: after fabricating a waveguide on a thin-film lithium niobate chip with metal electrodes at the bottom, depositing a silicon dioxide protective layer using plasma chemical vapor deposition, and then depositing metal on the top and sidewalls, combining it with the metal at the bottom to form a rectangular metal waveguide; Step 5: Achieve near-zero refractive index for various terahertz frequencies by changing the width of the hollow rectangular metal waveguide.

2. The method for achieving near-zero refractive index of optical waves and terahertz waves based on a nonlinear hybrid waveguide according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Spin-coat photoresist onto thin-film lithium niobate, expose it using electron beam lithography (EBL), and then etch the lithium niobate waveguide using ion beam etching (IBE). Step 1.2: Deposit a silicon dioxide protective layer using plasma-enhanced chemical vapor deposition (PECVD) to complete the fabrication of the optical waveguide; Step 1.3: Gold plating is performed on the surface using electron beam evaporation (EBE) deposition. Step 1.4: Perform end-face polishing to promote the coupling of light waves and the external coupling of terahertz waves.

3. The method for achieving near-zero refractive index of optical waves and terahertz waves based on a nonlinear hybrid waveguide according to claim 2, characterized in that, The etched lithium niobate waveguide has a thickness of 300-900 nm, the deposited silicon dioxide protective layer has a thickness of 1-3 μm, and the upper metal layer has a thickness of 0.1-2 μm.

4. The method for achieving near-zero refractive index of optical waves and terahertz waves based on a nonlinear hybrid waveguide according to claim 1, characterized in that, Step 2 specifically involves: utilizing a one-dimensional corrugated waveguide to exhibit Dirac point dispersion characteristics at point Γ, i.e., one pair of linear dispersions at... That is, the intersection at the Γ point, where the light waves at the intersection of the mixed modes contain orthogonal electric and magnetic dipole resonances, and the symmetry provides the electric and magnetic responses required for zero refractive index; for metallic terahertz zero-refractive-index waveguides, the intrinsic structural dispersion, which depends on the simulation of the metallic rectangular waveguide, is... 01 The dispersion relation of the waveguide in the mode is: ； Assume the waveguide behaves with an effective dielectric constant. The equivalent medium, The wavenumber at the wavelength in free space. The width of the hollow rectangle, Terahertz frequency, For TE 01 The cutoff frequency of the mode.

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