A method for realizing multimode quasi-phase-matched four-wave mixing in a multimode waveguide

Abstract

The present invention discloses a method for realizing multi-mode quasi-phase matching four-wave mixing in a multi-mode waveguide. The present invention first determines the target signal light wavelength of the four-wave mixing process corresponding to the fundamental mode and the high-order mode, and then uses simulation software to simulate the eigenmodes of straight waveguides of different widths, and then calculates and obtains the relationship curve of the straight waveguide width-phase mismatch amount in the four-wave mixing process corresponding to the fundamental mode and the high-order mode, respectively, and then uses the multi-mode phase mismatch amount equation proposed by the present invention to determine the straight waveguide width, and uses the relationship between the straight waveguide length and the phase mismatch amount to determine the straight waveguide length, and finally realizes the quasi-phase matching of the four-wave mixing process of the fundamental mode and the high-order mode in the multi-mode waveguide at the same time. The present invention uses silicon waveguide as an example to carry out simulation calculation, and the results show that high-efficiency multi-mode wavelength conversion can be achieved within the range covering the entire C band and most of the L band, overcoming the problem of narrow conversion bandwidth existing in the existing multi-mode wavelength conversion research.

Description

Technical Field

[0001] The invention relates to a method for realizing phase-matched four-wave mixing in a waveguide, belonging to the technical field of optical communication, and specifically to a method for realizing multi-mode quasi-phase-matched four-wave mixing in a multi-mode waveguide. Background Art

[0002] Wavelength conversion is indispensable in wavelength-routed optical communication systems. When two signals with the same wavelength arrive at the same node, the wavelengths will be blocked. In order to achieve wavelength reuse, wavelength conversion can be performed at this node to copy the information carried on one wavelength to another idle wavelength for continued transmission. With the rapid development of integrated optical waveguide technology in the past decade, research on all-optical wavelength conversion based on on-chip optical waveguide devices has gradually emerged. Among them, the four-wave mixing effect (FWM) has received a lot of attention because it is transparent to high-order modulation formats.

[0003] To achieve high-efficiency FWM in waveguides, phase matching must be achieved first. The mainstream phase matching method is to adjust the waveguide size for dispersion management and obtain near-zero dispersion within the target band. At present, most studies only focus on the fundamental mode in the waveguide, and the dispersion management technology for the fundamental mode is relatively mature. With the introduction of the concept of on-chip hybrid multiplexing, research on multimode waveguides has become increasingly popular, and research on multimode wavelength conversion has also been put on the agenda. In 2014, Ding Yunhong et al. realized mode-selective all-optical wavelength conversion in multimode silicon waveguides and attempted to manage dispersion for both TE0 and TE1 modes at the same time. However, the poor dispersion characteristics of high-order modes make it extremely difficult to achieve phase matching of the fundamental mode and high-order modes simultaneously within a broadband. Therefore, the current research on multimode wavelength conversion can only remain in the demonstration stage and is still far from practical application.

[0004] In 2013, Yannick Lefevre proposed a solution to achieve high-efficiency FWM in the presence of a large phase mismatch, called quasi-phase matching (QPM). This method borrows the idea of ​​quasi-phase matching commonly used in second-order nonlinear processes, but unlike periodic polarization inversion, it achieves periodic variation of dispersion through a grating-like structure with periodic changes in waveguide width, which has a similar effect to periodic domain inversion, thereby achieving high-efficiency FWM (wavelength conversion efficiency greater than -23dB) at any wavelength in the near-infrared range of 1.3μm to 1.9μm in silicon waveguides. In 2014, Yannick Lefevre proposed a method to achieve quasi-phase matching for two arbitrary FWM processes at the same time, but it is still only for FWM processes with two different pump wavelengths in a waveguide mode. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for realizing multimode quasi-phase matching four-wave mixing in a multimode waveguide. The final multimode waveguide of the present invention adopts a grating-like structure with periodic variation of the waveguide width, which can simultaneously realize quasi-phase matching of the FWM process of the TE0 and TE1 modes of the multimode waveguide. The simulation results show that the wavelength conversion efficiency of the two modes can reach -16dB, and the bandwidth can cover the entire C band.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] The multimode waveguide includes two straight waveguides and a tapered waveguide between the two straight waveguides. The specific steps of the present invention are as follows:

[0008] 1) Determine the wavelengths of the target signal light, pump light and idler light of the fundamental mode and the higher-order mode, and then obtain the relationship curves of the straight waveguide width-phase mismatch amount in the four-wave mixing process corresponding to the fundamental mode and the higher-order mode under the current target signal light based on the current target signal light, pump light and idler light processing;

[0009] 2) According to the relationship curve between the straight waveguide width and the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode under the current target signal light, two straight waveguide widths W1 and W2 are selected so that the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguides of the two widths at the current target signal light satisfies the multi-mode phase mismatch equation;

[0010] 3) Determine the length of the tapered waveguide according to the width difference between the two straight waveguides to achieve adiabatic conversion of modes between straight waveguides of different widths;

[0011] 4) The larger phase mismatch of each straight waveguide in the four-wave mixing process corresponding to the fundamental mode and the higher-order mode is taken as the target phase mismatch of the current straight waveguide. The length of the current two straight waveguides is determined according to the product of the length of each straight waveguide and the target phase mismatch of the current straight waveguide being equal to π. The two straight waveguides in step 2) and the tapered waveguide in step 3) constitute a multimode waveguide basic unit. A plurality of multimode waveguide basic units are sequentially connected to form a periodic structure, thereby constituting a final multimode waveguide. Quasi-phase matching of the four-wave mixing process of the fundamental mode and the higher-order mode is simultaneously achieved in the final multimode waveguide.

[0012] The step 1) is specifically as follows:

[0013] First, the wavelength of the signal light for quasi-phase matching in the four-wave mixing process corresponding to the fundamental mode and the high-order mode is determined, and then the wavelength of the pump light is determined. The wavelength of the idler light is determined based on the wavelength of the signal light and the wavelength of the pump light; then, based on the current signal light, pump light and idler light, the eigenmodes of the straight waveguides of different widths are simulated using simulation software to obtain the effective refractive indexes corresponding to the current signal light, pump light and idler light in the straight waveguide of each width in the fundamental mode and the high-order mode, respectively. Based on the effective refractive index, the phase mismatch amount of the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguide of the current width is calculated, and the phase mismatch amount of the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguide of different widths is traversed and calculated, so as to establish a relationship equation between the width of the straight waveguide and the phase mismatch amount in the four-wave mixing process corresponding to the fundamental mode and the high-order mode under the current target signal light.

[0014] The simulation software in step 1) is finite element analysis software Comsol.

[0015] The multimode phase mismatch equation in step 2) is specifically:

[0016] Δβ0(W1) / Δβ0(W2)=Δβ1(W1) / Δβ1(W2)

[0017] Among them, Δβ0(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ0(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, and Δβ1(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the high-order mode.

[0018] The product of the length of each straight waveguide in step 4) and the target phase mismatch of the current straight waveguide is equal to π, specifically:

[0019] max{Δβ0(W1),Δβ1(W1)}×L1=max{Δβ0(W2),Δβ1(W2)}×L2=π

[0020] Among them, Δβ0(W1) represents the phase mismatch of the straight waveguide of the first width W1 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W1) represents the phase mismatch of the straight waveguide of the first width W1 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, Δβ0(W2) represents the phase mismatch of the straight waveguide of the second width W2 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W2) represents the phase mismatch of the straight waveguide of the second width W2 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, max{} represents the maximum value operation, L1 represents the length of the straight waveguide of the first width W1, and L2 represents the length of the straight waveguide of the second width W2.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. The present invention extends the quasi-phase matching method from the fundamental mode to the high-order mode, proposes a multi-mode quasi-phase matching four-wave mixing method for the first time, and verifies its feasibility through simulation;

[0023] 2. The present invention can perform all-optical wavelength conversion on a signal containing two modes at the same time, and the conversion bandwidth can cover the entire C-band, which is of great significance to the integration of the mode division multiplexing system and the existing wavelength division multiplexing system. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a method flow chart of an embodiment of the present invention.

[0025] Figure 2 It is a schematic diagram of the structure of a multimode QPM waveguide provided in an embodiment of the present invention.

[0026] Figure 3 It is a mode field distribution diagram of the two modes TE0 and TE1 provided in an embodiment of the present invention.

[0027] Figure 4 1 is a curve showing the relationship between the phase mismatch of the TE0 and TE1 modes and the waveguide width provided in an embodiment of the present invention.

[0028] Figure 5 It is a curve showing the change of idler optical power corresponding to the target signal optical wavelength with transmission distance in the FWM process of the two modes TE0 and TE1 provided in the example of the present invention.

[0029] Figure 6 This is the relationship between the idler light conversion efficiency and the signal light wavelength in the FWM process of the two modes TE0 and TE1 provided in the example of the present invention. DETAILED DESCRIPTION

[0030] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0031] Figure 2 Schematic diagram of the multimode waveguide structure used in the present invention. Figure 2 (a) is a schematic diagram of the cross-section of a multimode waveguide. The waveguide substrate is silicon dioxide, the core layer is silicon, the thickness of the core layer silicon is 220nm, which is the same as the thickness of the core layer of a general SOI waveguide, and the upper cladding is air. Figure 2 (b) is a top view of a multimode waveguide, which is formed by alternating two straight waveguides of different widths, where the straight waveguide with a width of W1 is L2 long, and the straight waveguide with a width of W2 is L2 long. Adjacent straight waveguides are connected by an adiabatic tapered waveguide to achieve lossless transition of waveguide modes with different widths. A 25μm long tapered waveguide can achieve adiabatic mode conversion between two straight waveguides with a waveguide width difference of 120nm. Figure 3 (a) and (b) are the mode field distribution diagrams of the simulated multimode waveguides TE0 and TE1 respectively.

[0032] like Figure 1 As shown, the multimode waveguide includes two straight waveguides and a tapered waveguide between the two straight waveguides. The present invention includes the following steps:

[0033] 1) Determine the wavelengths of the target signal light, pump light, and idler light of the fundamental mode and the higher-order mode, and then obtain the relationship curves of the straight waveguide width-phase mismatch amount in the four-wave mixing process corresponding to the fundamental mode and the higher-order mode under the current target signal light based on the current target signal light, pump light, and idler light processing;

[0034] Step 1) is specifically as follows:

[0035] First, determine the wavelength of the signal light for quasi-phase matching in the four-wave mixing process corresponding to the fundamental mode and the high-order mode, then determine the wavelength of the pump light, and determine the wavelength of the idler light based on the wavelength of the signal light and the wavelength of the pump light; then, based on the current signal light, pump light and idler light, use simulation software to simulate the eigenmodes of straight waveguides of different widths, and obtain the effective refractive indexes corresponding to the current signal light, pump light and idler light in the fundamental mode and the high-order mode in the straight waveguide of each width, respectively, and calculate the phase mismatches Δβ0 and Δβ1 of the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguide of the current width based on the effective refractive index, and traverse and calculate the phase mismatches Δβ0 and Δβ1 of the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguide of different widths, so as to establish a relationship curve between the width of the straight waveguide and the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode under the current target signal light; Figure 4 shown.

[0036] The phase mismatch is calculated by the following formula:

[0037]

[0038] Where Δβ is the phase mismatch Δβ0 or Δβ1 of the four-wave mixing process corresponding to the fundamental mode or high-order mode, n eff,s 、n eff,i 、n eff,p Represent the effective refractive index of signal light, idler light, and pump light, respectively, s , i , p are the wavelengths of signal light, idler light, and pump light, respectively. The pump light wavelength is fixed at 1.55μm. The target signal light wavelengths of the TE0 and TE1 modes are selected as 1.75μm and 1.6μm, respectively. The idler light wavelength can be determined by the following formula:

[0039]

[0040] The simulation software in step 1) is finite element analysis software Comsol; the material refractive index of silicon as the waveguide core layer and silicon dioxide as the waveguide substrate is calculated by the Sellmeier equation.

[0041] 2) According to the relationship curve between the straight waveguide width and the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode under the current target signal light, two suitable straight waveguide widths W1 and W2 are selected so that the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguides of the two widths at the current target signal light satisfies the multi-mode phase mismatch equation;

[0042] The multimode phase mismatch equation in step 2) is specifically:

[0043] Δβ0(W1) / Δβ0(W2)≈Δβ1(W1) / Δβ1(W2)

[0044] Among them, Δβ0(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ0(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, and Δβ1(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the high-order mode. In the specific implementation, the widths of the two straight waveguides are W1=710nm and W2=820nm, respectively, and the phase mismatches at the target wavelengths are Δβ0(W1)=-5568.56nm. -1, Δβ0(W2)=5594.36m -1 , Δβ1(W1)=9543.87m -1 , Δβ1(W2)=-9677.64m -1 .

[0045] 3) Determine the length of the tapered waveguide between the two straight waveguides according to the width difference between the two straight waveguides, so as to realize the adiabatic conversion of modes between straight waveguides with different widths;

[0046] 4) The larger phase mismatch of each straight waveguide in the four-wave mixing process corresponding to the fundamental mode and the higher-order mode is taken as the target phase mismatch of the current straight waveguide. The length of the current two straight waveguides is determined according to the product of the length of each straight waveguide and the target phase mismatch of the current straight waveguide being equal to π. The two straight waveguides in step 2) and the tapered waveguide in step 3) constitute a multimode waveguide basic unit. A plurality of multimode waveguide basic units are sequentially connected to form a periodic structure, thereby constituting a final multimode waveguide. Quasi-phase matching of the four-wave mixing process of the fundamental mode and the higher-order mode is simultaneously achieved in the final multimode waveguide.

[0047] The product of the length of each straight waveguide in step 4) and the target phase mismatch of the current straight waveguide is equal to π, specifically:

[0048] max{Δβ0(W1),Δβ1(W1)}×L1=max{Δβ0(W2),Δβ1(W2)}×L2=π

[0049] Among them, Δβ0(W1) represents the phase mismatch of the straight waveguide of the first width W1 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W1) represents the phase mismatch of the straight waveguide of the first width W1 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, Δβ0(W2) represents the phase mismatch of the straight waveguide of the second width W2 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W2) represents the phase mismatch of the straight waveguide of the second width W2 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, max{} represents the maximum value operation, L1 represents the length of the straight waveguide of the first width W1, and L2 represents the length of the straight waveguide of the second width W2. In the specific implementation, L1=329.2μm, L2=324.6μm.

[0050] In the simulation, the signal light wavelength varies from 1.35μm to 1.8μm, and the four-wave mixing process corresponding to the two modes is simulated respectively. The total length L of the multimode waveguide is determined to maximize the conversion efficiency, and the 3dB conversion bandwidth is calculated. The conversion efficiency is defined as:

[0051]

[0052] Among them, P i,output Indicates the output power of idler light, P s,input represents the input power of the signal light, and the result is expressed in dB. The conversion bandwidth is defined as the wavelength range corresponding to a 3dB drop in conversion efficiency. The simulation results are shown in Figure 5 and Figure 6 shown. Figure 5 This is the relationship between conversion efficiency and transmission distance. Before the transmission distance reaches 12 mm, the conversion efficiency increases rapidly with the transmission distance. After the transmission distance exceeds 12 mm, the conversion efficiency increases slowly and basically does not change after reaching 12 mm. Figure 5 The spectrum diagram for transmitting 20 cycles (i.e., L=20×(L1+L2)=13.076mm) shows that the conversion bandwidths of the TE0 and TE1 modes are 410nm and 90nm respectively, and the conversion efficiency can reach -16dB. The common conversion bandwidth covers the entire C-band and most of the L-band, which is sufficient to meet the frequency band requirements of the wavelength division multiplexing system. For the existing research on quasi-phase matching FWM, they only target the fundamental mode and cannot simultaneously achieve quasi-phase matching of the high-order mode FWM process; for the existing research on realizing four-wave mixing of two modes in a multimode waveguide, their wavelength conversion bandwidths are relatively limited and it is difficult to meet the frequency band requirements of the actual communication system. Compared with the existing research, the present invention provides a method for realizing broadband multimode wavelength conversion.

[0053] It should be understood that the embodiments herein are intended to help readers understand the principles of the present invention, and the protection scope of the present invention is not limited to such embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the enlightenment provided by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for realizing multimode quasi-phase-matched four-wave mixing in a multimode waveguide, wherein the multimode waveguide comprises two straight waveguides and a tapered waveguide between the two straight waveguides, characterized in that: The steps include: 1) Determine the wavelengths of the target signal light, pump light and idler light of the fundamental mode and the higher-order mode, and then obtain the relationship curves of the straight waveguide width-phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the higher-order mode under the current target signal light based on the current target signal light, pump light and idler light; 2) According to the relationship curve between the straight waveguide width and the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode under the current target signal light, the widths W1 and W2 of the two straight waveguides are selected so that the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and the high-order mode of the straight waveguides of the two widths at the current target signal light satisfies the multi-mode phase mismatch equation; 3) Determine the length of the tapered waveguide according to the width difference between the two straight waveguides to achieve adiabatic conversion of modes between straight waveguides of different widths; 4) The larger phase mismatch of the phase mismatch of each straight waveguide in the four-wave mixing process corresponding to the fundamental mode and the high-order mode is used as the target phase mismatch of the current straight waveguide. The length of the current two straight waveguides is determined according to the product of the length of each straight waveguide and the target phase mismatch of the current straight waveguide being equal to π. The two straight waveguides in step 2) and the tapered waveguide in step 3) constitute a multimode waveguide basic unit. A plurality of multimode waveguide basic units are sequentially connected to form a periodic structure, thereby constituting a final multimode waveguide. Quasi-phase matching of the four-wave mixing process of the fundamental mode and the high-order mode is simultaneously achieved in the final multimode waveguide. The multimode phase mismatch equation in step 2) is specifically: Δβ0(W1) / Δβ0(W2)=Δβ1 (W1) / Δβ1(W2) Among them, Δβ0(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ0(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, and Δβ1(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the high-order mode.

2. A method for realizing multi-mode quasi-phase-matched four-wave mixing in a multi-mode waveguide according to claim 1, characterized in that: The step 1) is specifically as follows: Firstly, the wavelength of the signal light for quasi-phase matching in the four-wave mixing process corresponding to the fundamental mode and the high-order mode is determined, and then the wavelength of the pump light is determined, and the wavelength of the idler light is determined based on the wavelength of the signal light and the wavelength of the pump light; Then, based on the current signal light, pump light and idler light, the eigenmodes of straight waveguides of different widths are simulated using simulation software to obtain the effective refractive indices corresponding to the current signal light, pump light and idler light in the fundamental mode and high-order mode in the straight waveguide of each width, respectively. The phase mismatch of the four-wave mixing process corresponding to the fundamental mode and high-order mode of the straight waveguide of the current width is calculated based on the effective refractive index, and the phase mismatch of the four-wave mixing process corresponding to the fundamental mode and high-order mode of straight waveguides of different widths is traversed and calculated, so as to establish a relationship equation between the width of the straight waveguide and the phase mismatch in the four-wave mixing process corresponding to the fundamental mode and high-order mode under the current target signal light.

3. The method for realizing multi-mode quasi-phase-matched four-wave mixing in a multi-mode waveguide according to claim 1, characterized in that: The simulation software in step 1) is finite element analysis software Comsol.

4. The method for realizing multimode quasi-phase-matched four-wave mixing in a multimode waveguide according to claim 1, characterized in that: The product of the length of each straight waveguide in step 4) and the target phase mismatch of the current straight waveguide is equal to π, specifically: max{Δβ0(W1),Δβ1(W1)}×L1=max{Δβ0(W2),Δβ1(W2)}×L2=π Among them, Δβ0(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W1) represents the phase mismatch of the straight waveguide with the first width W1 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, Δβ0(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the fundamental mode, Δβ1(W2) represents the phase mismatch of the straight waveguide with the second width W2 at the current target signal light in the four-wave mixing process corresponding to the high-order mode, max{} represents the maximum value operation, L1 represents the length of the straight waveguide with the first width W1, and L2 represents the length of the straight waveguide with the second width W2.

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