A waveguide structure for generating complex coupling strength and its design method

Abstract

The present invention discloses a waveguide structure for generating complex coupling intensity and its design method, belonging to the technical field of integrated optoelectronic devices. The method comprises: designing a waveguide structure that meets the complex coupling coefficient requirement based on the expression of the equivalent coupling coefficient caused by an artificial gauge field in a dual-waveguide coupling system transmitting along the z-direction; constructing different waveguide structures based on the waveguide function that meets the complex coupling coefficient requirement, and modeling and simulating the different constructed waveguide structures. The present invention extends the direct coupling coefficient between optical waveguides from the real number domain to the complex number domain by introducing artificial gauge field modulation into the waveguide structure; the so-called artificial gauge field modulates the geometric structure of the optical system to affect the photon transmission in the optical system; and by designing a suitable optical waveguide structure using the equivalent coupling coefficient calculation formula, the complex coupling coefficient is obtained. The complex coupling coefficient can then be used to realize complex photon state conversion and light intensity control in the optical waveguide array.

Description

Technical Field

[0001] The present invention belongs to the technical field of integrated optoelectronic devices, and in particular relates to a waveguide structure for generating complex coupling strength and a design method thereof. Background Art

[0002] As the fundamental structure of integrated optoelectronic devices, the development of optical waveguide arrays is driving advancements in optoelectronic technology, providing a foundation for high-speed communications and the realization of complex optical systems. They play a crucial role in the implementation of a variety of functional devices, including lasers, modems, wavelength division multiplexers / demultiplexers, and optical switches. Coupling between optical waveguides, which enables the partial or complete transfer of an optical signal from one waveguide to another through the propagation and interference of light, is a crucial mechanism for optical signal transmission and processing in optical systems.

[0003] However, coupling between optical waveguides also has some limitations. The coupling coefficient can effectively control the properties of photon states (including symmetry and light intensity distribution), but the coupling coefficients between common optical waveguides are generally limited to positive real numbers, which greatly limits the richness of photon state transmission within the waveguide. Furthermore, the means of controlling the light intensity transmitted by different waveguides in a waveguide array are relatively simple. Existing technologies do not exist for waveguide structures capable of generating complex coupling coefficients. Summary of the Invention

[0004] In response to the lack of waveguide structures capable of generating complex coupling coefficients in the prior art, the present invention provides a waveguide structure for generating complex coupling strength and a design method thereof. The present invention extends the direct coupling coefficient between optical waveguides from the real domain to the complex domain by introducing artificial gauge field modulation into the waveguide structure. The so-called artificial gauge field modulates the geometric structure of the optical system to affect the photon transmission in the optical system. By designing a suitable optical waveguide structure using an equivalent coupling coefficient calculation formula, the complex coupling coefficient is obtained, and the complex coupling coefficient can be used to realize complex photon state conversion and light intensity control in the optical waveguide array. The method of the present invention is beneficial for further enriching the functions of the optical waveguide array, greatly enriching the control of photon states in the waveguide, and also can better regulate the transmission of light in the waveguide. That is, by designing the complex coupling coefficient between waveguides, directional transmission of light can be achieved, thereby providing a basis for the design of various functional devices such as directional couplers and optical switches.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for designing a waveguide structure for generating complex coupling strength comprises the following steps:

[0007] Step 1: Based on the expression of the equivalent coupling coefficient caused by the artificial gauge field in the dual-waveguide coupling system transmitting along the z direction, design a waveguide structure that meets the complex coupling coefficient requirements. The specific steps include the following:

[0008] The expression of the equivalent coupling coefficient of the dual-waveguide coupling system transmitted along the z direction caused by the artificial gauge field is as follows:

[0009]

[0010] in, Parameter κ eff is the calculated equivalent coupling coefficient between waveguides, parameter κ is the straight waveguide coupling coefficient, which is a positive real number, P is the period, which represents the length of one period of the function corresponding to the designed waveguide, d is the center distance between the two waveguides, λ is the wavelength of the light propagating in the waveguide, and n0 is the ambient refractive index. Represents the partial derivative of the function x(z) with respect to the variable z.

[0011] Design the waveguide function expression x(z) of different structures, and select the appropriate waveguide spacing, with amplitude as the independent variable, and the ratio of the equivalent coupling coefficient to the corresponding waveguide spacing straight waveguide coupling coefficient κ eff κ is the dependent variable. MATLAB is used to draw the curve of the equivalent coupling coefficient of the waveguide structure corresponding to different waveguide functions as a function of amplitude according to the above expression. eff The real and imaginary parts of κ are plotted separately, and the change curve is used to determine whether it is a waveguide function that meets the complex coupling coefficient requirements;

[0012] Step 2: Based on the waveguide function obtained in step 1 that meets the complex coupling coefficient requirements, different waveguide structures are constructed and modeled and simulated. By setting up a monitor to detect the light intensity during the propagation of light in each waveguide structure, the waveguide structure with the smallest loss is selected and compared with the theoretical calculated value.

[0013] Furthermore, in step 1, the different waveguide functions include symmetric and asymmetric functions in the form of sine and cosine, and symmetric and asymmetric functions in the form of broken lines, and corresponding waveguide structures are constructed respectively.

[0014] Furthermore, the function expression x(z) in the form of sine and cosine includes a function of the center position x of the dual waveguides of the symmetrical structure changing with the period z and a function of the center position x of the dual waveguides of the asymmetrical structure changing with the period z;

[0015] The function of the center position x of the dual waveguides of the symmetrical structure changing with the z period is:

[0016] The function of the center position x of the dual waveguides of the asymmetric structure changing with the z period is:

[0017]

[0018] Where A is the amplitude and P is the length of one period of the waveguide function.

[0019] Furthermore, the function expression x(z) in the form of a broken line includes a function of the center position x of the dual waveguides of the symmetrical structure changing with the z period and a function of the center position x of the dual waveguides of the asymmetrical structure changing with the z period;

[0020] The function of the center position x of the dual waveguides of the symmetrical structure changing with the z period is:

[0021] The function of the center position x of the dual waveguides of the asymmetric structure changing with the z period is:

[0022]

[0023] Furthermore, in step 1, when the imaginary part curve of the equivalent coupling coefficient corresponding to the waveguide function no longer always remains at 0, it is a waveguide function that meets the requirements of the complex coupling coefficient.

[0024] Furthermore, in step 2, the constructed waveguide structure is modeled and simulated using Rsoft simulation software.

[0025] Compared with the prior art, the advantages of the present invention are as follows:

[0026] 1. The present invention proposes a design method for a waveguide structure for generating complex coupling strength. This method extends the coupling coefficient between waveguides to the complex domain through artificial gauge fields, namely, waveguide shape modulation. By selecting a suitable structure, the loss of light propagating in the waveguide is minimized, thus enriching the means for photon state control and light intensity modulation in waveguide arrays.

[0027] 2. The coupling coefficient is indirectly characterized by light intensity. When the coupling coefficient is a real number, the normalized intensity of light in both waveguides is 0.5. When the coupling coefficient is a complex number, the normalized intensity of light transmitted in the waveguides exhibits a periodic variation with an intensity of 0.5 as the dividing line, and the number of cycles is closely related to the magnitude of the coupling coefficient. The larger the modulus of the complex coupling coefficient, the greater the number of cycles. The accuracy and rationality of the design were verified by comparing the theoretical calculation results with the actual modeling and simulation of the light intensity distribution in the dual waveguides. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly describes the drawings required for the specific embodiments or the description of the prior art. Similar elements or parts are generally identified by similar reference numerals throughout the drawings. Elements or parts in the drawings are not necessarily drawn to scale.

[0029] Figure 1 The curve of the equivalent coupling coefficient corresponding to the sine-cosine structure design of the present invention versus amplitude;

[0030] Among them: (a) Curve of the equivalent coupling coefficient of the sine-cosine symmetrical structure changing with the amplitude;

[0031] (b) Curve of the equivalent coupling coefficient of the asymmetric structure in the sine-cosine form versus amplitude;

[0032] Figure 2 The curve of the equivalent coupling coefficient versus amplitude corresponding to the broken line structure design in the present invention;

[0033] Among them: (a) Curve of the equivalent coupling coefficient of the broken line symmetrical structure changing with the amplitude;

[0034] (b) Curve of the equivalent coupling coefficient of the asymmetric structure in the form of a broken line versus amplitude;

[0035] Figure 3 Schematic diagram of the optical waveguide structure that generates complex coupling in the present invention, including a function of the waveguide center position x changing with the z period and a single-period actual structure diagram;

[0036] Where: (a) is the function curve of the waveguide center position x changing with z, P represents one period and P = 2mm, A represents the amplitude and A = 5.5um;

[0037] (b) Schematic diagram of a single period of structure fabricated in an optical glass chip using femtosecond laser direct writing technology;

[0038] Figure 4 Graph showing simulation results of the dual-waveguide system constructed in the present invention;

[0039] Figure 5 Schematic diagram of the light intensity distribution (a) obtained by simulating the Rsoft waveguide constructed in the present invention and the light intensity distribution of the theoretically calculated complex coupling coefficient (b). DETAILED DESCRIPTION

[0040] In order to clearly and completely describe the technical solution and specific working process of the present invention, the specific implementation methods of the present invention are as follows in conjunction with the accompanying drawings:

[0041] Example 1

[0042] This embodiment provides a design method for a waveguide structure for generating complex coupling strength. By designing periodic bending variations in the waveguide along the propagation direction, an artificial gauge field and a complex coupling coefficient are introduced. The structure is fabricated in an optical glass chip using femtosecond laser direct writing technology. Considering a dual-waveguide coupling system transmitting along the z-direction, the equivalent coupling coefficient caused by the artificial gauge field is expressed as follows: in, The parameters in the expression are period P = 2 mm, center distance between the two waveguides d = 7 μm, wavelength λ = 0.81 μm, and ambient refractive index n0 = 1.504. Using Matlab to substitute the parameters in the expression, with amplitude as the independent variable, the equivalent coupling coefficient κ is eff κ is the dependent variable and the equivalent coupling coefficient of different structures is plotted as a function of amplitude, such as Figure 1 As shown. Among them, the symmetric function 1 of the change of the center position x of the dual waveguide of the symmetrical structure with the z period is: The asymmetric function 2 of the dual waveguide center position x of the asymmetric structure changes with the z period is:

[0043]

[0044] When the function corresponding to the structure is a symmetric function in the form of sine and cosine, the corresponding equivalent coupling coefficient varies with the amplitude as follows: Figure 1 As shown in (a), it can be seen that the equivalent coupling coefficient does not have an imaginary part at this time, but it changes positively and negatively with the amplitude. When the function corresponding to the structure is an asymmetric function, the corresponding equivalent coupling coefficient changes with the amplitude as shown in Figure 1 As shown in (b), the coupling coefficient has an imaginary part. It can be seen that the asymmetric function 2 is selected as the waveguide function to generate the complex coupling coefficient, and the actual waveguide structure is constructed based on it. For the actual modeling and simulation of this waveguide structure, a 7-period waveguide with a total length of 1.4 cm is selected for modeling. According to the loss calculation formula The calculated loss of light propagating in the waveguide is 4.54dB.

[0045] Example 2

[0046] This embodiment introduces a waveguide structure and a design method for generating complex coupling strength. By designing the periodic bending change of the waveguide along the propagation direction, an artificial gauge field and a complex coupling coefficient are introduced. The symmetric function form and the asymmetric function form selected at this time are both broken line forms. Considering the expression of the equivalent coupling coefficient caused by the artificial gauge field in the dual waveguide coupling system transmitting along the z direction, the parameter selection in the expression is consistent with that in Example 1. Using Matlab to substitute the parameters in the formula, with the amplitude as the independent variable, the equivalent coupling coefficient κ eff κ is the dependent variable and the equivalent coupling coefficient of different structures is plotted as a function of amplitude, such as Figure 2 As shown. Among them, the function 3 of the change of the center position x of the dual waveguide of the symmetrical structure with the z period is:

[0047]

[0048] The function 4 of the center position x of the dual waveguides in the asymmetric structure changes with the z period is:

[0049]

[0050] When the function corresponding to the structure is a symmetrical function in the form of a broken line, the corresponding relationship between the equivalent coupling coefficient and the amplitude is as follows: Figure 2 As shown in (a), it can be seen that the equivalent coupling coefficient does not have an imaginary part at this time, but it changes positively and negatively with the amplitude. When the function corresponding to the structure is an asymmetric function, the corresponding equivalent coupling coefficient changes with the amplitude as shown in Figure 2 As shown in (b), the coupling coefficient has an imaginary part. This indicates that the asymmetric function 4 was chosen as the waveguide function to generate the complex coupling coefficient, and the actual waveguide structure was constructed based on this. For actual modeling and simulation of this waveguide structure, a seven-period waveguide with a total length of 1.4 cm was selected for modeling. The calculated light loss in the waveguide was 12.68 dB.

[0051] This shows that asymmetric waveguide structures cause light loss during waveguide propagation. Asymmetric structures using sine and cosine deformation functions have relatively low losses compared to other asymmetric structures, including broken lines. Therefore, asymmetric function 2 was selected as the waveguide function to generate the complex coupling coefficient and the waveguide structure was constructed.

[0052] Example 3

[0053] This example describes a method for constructing a waveguide model with an asymmetric function structure and verifying its coupling coefficient. Based on the discussion above, an asymmetric function derived from a modified sine and cosine function is chosen because it results in lower light transmission losses in the waveguide. The amplitude is chosen so that the real and imaginary parts of the equivalent coupling coefficient are close. Therefore, the asymmetric waveguide amplitude A is set to 5.5 μm. Figure 3Taking the amplitude of 5.5um as an example, a schematic diagram of the function of the waveguide center position x changing with the z period in the asymmetric structure and a schematic diagram of the actual structure of a single period are given. The total length of the established simulation model is 3cm. Open the Rsoft simulation software, click Edit Globel Settings, select the Beampro module, select Fiber in 3D Struct Type, enter 0.81 in Free SpaceWavelength, enter 1.504 in Background Index, enter 0.004 in Component Delta-N, enter 6 in Component width, enter 6 in Component height, click Edit symbol and then click New Symbol, enter length as the name, and the expression is 2000. Click Accept Symbol. Click Seqment to model in the blank space of Rosft. Its basic structure is the same as Figure 2 Consistent, and repeat 15 cycles, the center distance between the two waveguides is 7. Click EditsPathways, select all waveguides on the left as path one, click New, repeat the operation to select all waveguides on the right as path two, and click OK. Click Edits Lanuch to build two Lanuchs, Lanuch1 and Lanuch2, and set the Power in Lanuch1 and Lanuch2 to 1. In order to monitor the intensity of light transmitted in the two waveguides, a monitor is needed. Click Edit Pathway Monitors, select Fiber Mode Power for Type, select 1 for Pathway, and set the monitor to monitor the light intensity of the first waveguide; in the same way, set the monitor for the light intensity of the second waveguide, and select 2 for Pathway. Click Simulation to simulate, and the simulation results are as follows Figure 4 As shown in .

[0054] The light intensity detected by the monitor of the dual waveguide system after modeling and simulation is consistent with the theoretically calculated light intensity. Figure 4 The intensity information of the complex coupling coefficient can be characterized by the period of light intensity variation. The light intensity variation period calculated theoretically using the complex coupling coefficient is the same as the simulation result period, which proves that the actual coupling strength is basically consistent with the theoretical result. In addition, the reason why the light intensity monitored by the monitor in the simulation model gradually decreases is that under actual circumstances, there will be loss when light is transmitted in the asymmetric structure waveguide, which does not need to be considered in the theoretical calculation. The simulation results are basically consistent with the theoretical results in form and the number of periods is basically the same, which confirms the existence of the complex coupling coefficient and also shows the rationality of this verification method.

[0055] The preferred embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the scope of protection of the present invention.

[0056] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any appropriate manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

[0057] In addition, the various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.

Claims

1. A method for designing a waveguide structure for generating a complex coupling strength, characterized in that: The specific steps include: Step 1: Based on the expression of the equivalent coupling coefficient caused by the artificial gauge field in the dual-waveguide coupling system transmitting along the z direction, design a waveguide structure that meets the complex coupling coefficient requirements. The specific steps include the following: The expression of the equivalent coupling coefficient of the dual-waveguide coupling system transmitted along the z direction caused by the artificial gauge field is as follows: in, Parameter κ eff is the calculated equivalent coupling coefficient between waveguides, parameter κ is the straight waveguide coupling coefficient, which is a positive real number, P is the period, which represents the length of one period of the function corresponding to the designed waveguide, d is the center distance between the two waveguides, λ is the wavelength of the light propagating in the waveguide, and n0 is the ambient refractive index. represents the partial derivative of the function x(z) with respect to the variable z; Design the waveguide function expression x(z) of different structures, and select the appropriate waveguide spacing, with amplitude as the independent variable, and the ratio of the equivalent coupling coefficient to the corresponding waveguide spacing straight waveguide coupling coefficient κ eff / κ is the dependent variable, and MATLAB is used to draw the curve of the equivalent coupling coefficient of the waveguide structure corresponding to different waveguide functions as a function of amplitude according to the above expression. eff The real and imaginary parts of / κ are plotted separately, and the change curve is used to determine whether it is a waveguide function that meets the complex coupling coefficient requirements; Step 2: Based on the waveguide function obtained in step 1 that meets the complex coupling coefficient requirements, different waveguide structures are constructed and modeled and simulated. By setting up a monitor to detect the light intensity during the propagation of light in each waveguide structure, the waveguide structure with the smallest loss is selected and compared with the theoretical calculated value.

2. The method for designing a waveguide structure for generating a complex coupling strength according to claim 1, wherein: In step 1, the different waveguide functions include symmetric and asymmetric functions in the form of sine and cosine, and symmetric and asymmetric functions in the form of broken lines, and corresponding waveguide structures are constructed respectively.

3. The method for designing a waveguide structure for generating a complex coupling strength according to claim 2, wherein: The function expression x(z) in the form of sine and cosine includes the function of the center position x of the dual waveguides of the symmetrical structure changing with the z period and the function of the center position x of the dual waveguides of the asymmetrical structure changing with the z period; The function of the center position x of the dual waveguides of the symmetrical structure changing with the z period is: The function of the center position x of the dual waveguides of the asymmetric structure changing with the z period is: Where A is the amplitude and P is the length of one period of the waveguide function.

4. The method for designing a waveguide structure for generating a complex coupling strength according to claim 2, wherein: The function expression x(z) in the form of a broken line includes the function of the center position x of the dual waveguides of the symmetrical structure changing with the z period and the function of the center position x of the dual waveguides of the asymmetrical structure changing with the z period; The center position x of the dual waveguides of the symmetrical structure varies with the period z. for: The function of the center position x of the dual waveguides of the asymmetric structure changing with the z period is: Where A is the amplitude and P is the length of one period of the waveguide function.

5. The method for designing a waveguide structure for generating a complex coupling strength according to claim 1, wherein: In step 1, when the imaginary part curve of the equivalent coupling coefficient corresponding to the waveguide function no longer always remains at 0, it is a waveguide function that meets the requirements of the complex coupling coefficient.

6. The method for designing a waveguide structure for generating a complex coupling strength according to claim 1, wherein: In step 2, the constructed waveguide structure is modeled and simulated using Rsoft simulation software.

7. A waveguide structure for generating a complex coupling strength, characterized in that Obtained by the design method according to any one of claims 1 to 6.

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