Photon lattice capable of cutting boundaries in various modes and method for generating boundary states

Abstract

The invention belongs to the technical field of photonic crystals, and particularly relates to a photonic lattice capable of cutting boundaries in various modes and a method for generating a boundary state. In order to provide crystal lattices with a larger existence range, the evanescent coupling straight waveguides comprise a plurality of uniformly distributed crystal lattice points, the evanescent coupling straight waveguides are arranged on the crystal lattice points, every three crystal lattice points form a primitive cell, and the three crystal lattice points in each primitive cell form an equilateral triangle. The interfaces on the two sides of the evanescent coupling straight waveguide are arranged to be one or two of an alpha-zigzag shape, a beta-zigzag shape and a beam shape. According to the method, construction is simple, various boundaries can be cut, and two different types of boundary states are supported.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of photonic crystals, and particularly relates to a photonic lattice with multiple tailorable boundaries and a method for generating boundary states. BACKGROUND

[0002] Due to the advantages that the photonic lattice structure can be freely designed, the initial conditions can be accurately controlled, and there are no structural defects or adsorption pollution like atomic lattices, the photonic lattice has attracted more and more attention. In addition, the photonic lattice has the transmission characteristics of low loss and high integration, the robust transmission ability of topological protection, and the enhancement and controllability of nonlinear optical effects, and is significantly superior to traditional optical devices in performance, function and application adaptability. The photonic lattice has many practical research results and application examples in many fields such as nonlinear optics, optical communication, biomedicine and information storage, covering lasers, harmonic enhancement devices, biosensors and many other types.

[0003] When an infinite periodic lattice structure is truncated, a localized boundary state will be formed at the truncated boundary. Tamm and Shockley published a pioneering paper, marking the beginning of the field of solid surface physics. After that, the boundary state is usually divided into Tamm state and Shockley state. Due to the boundary state, especially the boundary state with topological protection, it plays an important role in the transport process, such as quantitative detection of picomolar biological molecules, dynamic routing and beam splitting of optical signals, spintronic devices and non-dissipative transistors, etc. If the nonlinear effect is introduced into the photonic lattice, countless strange phenomena that cannot be observed in a pure linear or uniform nonlinear system can be generated.

[0004] At present, the research on the boundary state of the two-dimensional photonic lattice mostly focuses on the Tamm boundary state and the Shockley boundary state artificially introduced defects, and the research on the Tamm state without artificially introduced defects and the two kinds of boundary states is very little. Since the existence range of the Tamm state of the lattice honeycomb lattice with two kinds of boundary states is very small in the momentum space, it is difficult to observe, so a lattice with a larger existence range is needed. SUMMARY

[0005] The application provides a photonic lattice with multiple tailorable boundaries and a method for generating boundary states.

[0006] In order to achieve the above purpose, the application adopts the following technical scheme:

[0007] The application provides a photonic lattice with multiple tailorable boundaries, which comprises a plurality of uniformly distributed lattice points, and evanescent coupling straight waveguides are arranged on the lattice points, every three lattice points form a unit cell, and the three lattice points in each unit cell form an equilateral triangle.

[0008] Further, the two side interfaces of the evanescent coupling straight waveguide are set as one or both of a-zigzag shape, β-zigzag shape and bearded shape, and the interfaces between the two side boundaries and air are respectively set as a first waveguide channel and a second waveguide channel, and the first waveguide channel and the second waveguide channel are used to support the boundary state.

[0009] Further, the distance between adjacent lattice points is , and the diameter of each lattice point is .

[0010] Further, the refractive index of the evanescent coupling straight waveguide is order of magnitude, and the background is an optical material with a refractive index of 1.45 or 2.35.

[0011] The application also provides a method for generating a boundary state based on the photonic lattice with multiple tailored boundaries, comprising the following steps:

[0012] Step 1, the propagation of the light beam in the photonic lattice waveguide array is described by a nonlinear Schrödinger equation:

[0013] ;

[0014] wherein, is the complex envelope function of the light field, and is the normalized transverse coordinate, is the normalized propagation distance, and the potential function represents the waveguide array, and the propagation of the light in the waveguide array is along the direction;

[0015] Step 2, the profile of each waveguide in the photonic lattice waveguide array is described by a Gaussian function with a beam waist diameter of :

[0016] ;

[0017] wherein, is the average refractive index modulation depth, is the lattice point coordinate of the lattice;

[0018] Step 3, considering the configuration periodic along the y-axis and limited along the x-axis, it satisfies , wherein , and a is the distance between the lattice points.

[0019] Step 4, the interfaces between the two side boundaries and air are respectively set as a first waveguide channel and a second waveguide channel, and based on the photonic lattice, the evanescent coupling straight waveguide is introduced to realize the support of the boundary state with two opposite propagation directions in the first waveguide channel and the second waveguide channel.

[0020] Compared with the prior art, the present application has the following advantages:

[0021] The present application obtains a variety of tailored boundary states based on a new trimer lattice, and two different types of boundary states appear at the same time, which enriches the regulation mode of boundary transmission. In theory, nonlinearity can lead to boundary solitons and bistability, thereby expanding the means of manipulating optical wave packets. In addition, the structure design of the present application is simple and novel, and the Tamm state appears only depending on the spatial structure of the lattice based on the design of the trimer lattice. The present application has mature processing and manufacturing technology, and the boundary state scheme is more practical based on the femtosecond laser direct writing waveguide system. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 It is a schematic diagram of a waveguide array.

[0023] Figure 2 It is a cross-sectional structure diagram of a variety of tailored boundary photonic lattice.

[0024] Figure 3 It is the band structure and boundary state of the alpha-zigzag boundary and the bearded boundary.

[0025] Figure 4 It is the band structure, derivative curve of propagation constant and boundary state of the beta-zigzag boundary.

[0026] Figure 5 It is the propagation of the Shockley boundary state and the Tamm boundary state on the beta-zigzag boundary. DETAILED DESCRIPTION

[0027] In order to further illustrate the technical scheme of the present application, the present application will be further described below through examples.

[0028] As shown in Figure 1 and Figure 2 , a variety of tailored boundary photonic lattice of the present embodiment includes a plurality of uniformly distributed lattice points, and evanescent coupling straight waveguides are arranged on the lattice points. Every three lattice points form a unit cell, and the three lattice points in each unit cell form an equilateral triangle.

[0029] The two side interfaces of the evanescent coupling straight waveguide are set as one or two of alpha-zigzag, beta-zigzag and bearded, and the junctions of the two side boundaries and air are respectively set as a first waveguide channel and a second waveguide channel, and the first waveguide channel and the second waveguide channel are used to support boundary states.

[0030] The distance between adjacent lattice points is , and the diameter of each lattice point is .

[0031] The refractive index of the evanescently coupled straight waveguide is of the order of magnitude, and the background is an optical material with a refractive index of 1.45 or 2.35.

[0032] A method for generating a boundary state according to the embodiment comprises the following steps:

[0033] Step 1: The propagation of the light beam in the photonic lattice waveguide array is described by a nonlinear Schrödinger equation:

[0034]

[0035] wherein, is the complex envelope function of the optical field, and is the normalized transverse coordinate, is the normalized propagation distance, and the potential function represents the waveguide array, and the waveguide acts as a potential well, similar to the atomic nucleus in a solid. Therefore, the propagation of light in the waveguide array along the direction is equivalent to the evolution of an electron over time;

[0036] The photonic lattice waveguide array according to the embodiment is composed of a set of evanescently coupled straight waveguides, which has the advantages of miniaturization and easy manufacturing.

[0037] Step 2: The profile of each waveguide in the photonic lattice waveguide array is described by a Gaussian function with a beam waist diameter of :

[0038]

[0039] wherein, is the average refractive index modulation depth, which is in the range of 3-12, is the lattice point coordinate of the lattice;

[0040] Step 3: Considering the configuration that is periodic along the y-axis and limited along the x-axis, it satisfies wherein , a is the distance between the lattice points, and the waveguide channel is located at the outer boundary on both sides of the y-axis.

[0041] Step 4: The interface between the two side boundaries and the air is respectively set as the first waveguide channel and the second waveguide channel, and based on the photonic lattice, by introducing the evanescently coupled straight waveguide, the first waveguide channel and the second waveguide channel are realized to support two boundary states with opposite propagation directions.

[0042] The photonic lattice is prepared in molten silica by femtosecond laser writing technology, and the above parameters are converted into experimental values; the wavelength of the laser radiation is and the lateral characteristic dimension is set as​​ Corresponding dimensionless coordinate units The photonic lattice is a evanescently coupled straight waveguide with a lattice constant of . The width of a single lattice is .

[0043] like Figure 2 As shown, each unit cell includes three lattice points that form an equilateral triangle. Other specific parameters are as follows: , The refractive index of the waveguide is The background refractive index is 1.45, and molten silica is used. Depending on the cutting method, the edges on the left and right sides are α-zigzag, β-zigzag, and bearded, respectively. Furthermore, the x-direction is finite, and the y-direction is periodic; the first waveguide channel (Channel 1) and the second waveguide channel (Channel 2) of the boundary state are represented by solid and dashed lines, respectively.

[0044] like Figure 3 As shown in the figure above, the band structure and boundary states of an α-zigzag boundary are illustrated. It can be seen that the α-zigzag boundary supports one type of Shockley boundary state. Since both the left and right channels are α-zigzag boundaries, they support the same boundary state on both sides. The figure below shows the band structure and boundary states of a bearded boundary. The bearded boundary supports two different Shockley boundary states.

[0045] like Figure 4 As shown in the figure above, the band structure and boundary states of a β-zigzag boundary are as follows: the topmost boundary state is the Shockley boundary state, while the other two are Tamm boundary states. The bottom figure shows the Shockley boundary state of the β-zigzag boundary and the Tamm boundary state between the second and third bands. and . The group velocity reflects the boundary state, and it can be seen that the Shockley boundary state in... hour From positive to negative, therefore The temporal boundary state propagates along the negative y-axis. Similarly, the Tamm boundary state... hour Therefore, the boundary state will propagate along the positive y-axis.

[0046] like Figure 5 As shown, the propagation result is indeed as described. Figure 4 As mentioned, with The Shockley boundary state propagates along the negative y-axis and the Tamm boundary state propagates along the positive y-axis, and can stably propagate.

[0047] The foregoing merely illustrates the principles of the application. It will thus be appreciated that those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the application and are thus within its spirit and scope. Furthermore, any

[0048] In addition, it should be understood that although the description herein is based on embodiments, not every embodiment contains only one independent technical solution, and the description herein is only for the sake of clarity, and those skilled in the art should consider the description as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that those skilled in the art can understand.

Claims

1. A photonic lattice with multiple shaped boundaries, characterized in that, It includes several uniformly distributed lattice points, each of which is provided with an evanescent coupled straight waveguide. Every three lattice points form a unit cell, and the three lattice points in each unit cell form an equilateral triangle.

2. The photonic lattice with multiple trimmed boundaries according to claim 1, characterized in that, The two side interfaces of the evanescent coupled straight waveguide are set to one or two of the following: α-zigzag, β-zigzag, and bearded. The junctions between the two side boundaries and the air are respectively set as the first waveguide channel and the second waveguide channel. The first waveguide channel and the second waveguide channel are used to support the boundary state.

3. A photonic lattice with multiple trimmed boundaries according to claim 1, characterized in that, The distance between adjacent lattice points is The diameter of each of the lattice points .

4. A photonic lattice with multiple cut boundaries according to claim 1, characterized in that, The refractive index of the evanescent coupled straight waveguide is The magnitude is on the order of magnitude, with the background being optical materials with a refractive index of 1.45 or 2.

35.

5. A method for generating boundary states based on a photonic lattice with multiple trimmed boundaries as described in any one of claims 1-4, characterized in that, Includes the following steps: Step 1: The propagation of the light beam in the photonic lattice waveguide array is described by a nonlinear Schrödinger-like equation: ； in, It is the complex envelope function of the light field. and For normalized horizontal coordinates, It is the normalized transmission distance, potential function. This represents a waveguide array, where light travels along... Directional propagation; Step 2, the contours of each waveguide in the photonic lattice waveguide array are defined by a beam waist diameter of... Described using a Gaussian function: ； in, The average refractive index modulation depth, These are the lattice point coordinates of the crystal lattice; Step 3, consider a configuration that is periodic along the y-axis and constrained along the x-axis, satisfying... ,in , where a is the distance between lattice points; Step 4: The junctions of the two side boundaries and the air are respectively set as the first waveguide channel and the second waveguide channel. Based on the photonic lattice, by introducing evanescent coupled straight waveguides, the first waveguide channel and the second waveguide channel can realize the support of two boundary states with opposite propagation directions.

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