Waveguide mode converter based on joint regulation and control of artificial standard field and loss

Abstract

The invention provides a waveguide mode converter based on joint regulation and control of an artificial standard field and loss, and relates to the technical field of integrated photonics and optical communication, the device introduces a geometric phase e + / -2i theta (wherein theta is a mode rotation angle induced by a notch groove) through a notch groove engineered orbital angular momentum waveguide structure, and constructs an equivalent artificial standard field; and the generated resultant magnetic flux phi is equal to 2theta. By utilizing non-Hermite chiral symmetry protection induced by the artificial standard field, stable third-order EP (i.e., three-state degeneration) is realized, and controllable conversion between second-order EP and third-order EP is realized by adjusting waveguide coupling strength. According to the method, polymorphic degeneracy can be induced and stabilized by utilizing an artificial standard field, and the implementation difficulty of a high-order degeneracy point is reduced, so that the requirement on non-Hermite degeneracy control in practical application is met.

Description

Technical Field

[0001] This invention relates to the field of integrated photonics and optical communication technology, and in particular to a waveguide mode converter based on the joint modulation of artificial gauge field and loss. Background Technology

[0002] Orbital Angular Momentum (OAM) beams have a helical phase distribution e ilφ Constructing an infinite-dimensional orthogonal mode space, OAM modes have shown great application potential in fields such as mode-multiplexed optical communication and optical micromanipulation. However, achieving stable transmission and flexible control of OAM modes on integrated photonic platforms faces a key challenge: when the cross-section of the optical waveguide has ideal rotational symmetry, OAM modes with topological charges ι = +1 and ι = -1 are degenerate states, sharing the same propagation constant. While this degeneracy, stemming from the continuous rotational symmetry of the system, is beneficial for mode multiplexing, it limits the independent control of the relative phase between modes, becoming an obstacle to constructing on-chip non-Hermitian photonic devices.

[0003] By introducing geometric grooving engineering into the waveguide cross-section to break the aforementioned rotational symmetry, the originally degenerate OAM modes can be coupled and energy-split, inducing an equivalent rotation in the azimuth direction of the guided wave modes. This geometric rotation is equivalent to introducing a spatially varying gauge potential, i.e., an artificial gauge field, into the system. This gauge field alters the effective transmission boundary conditions of photons in the waveguide, equivalent to applying a designable equivalent magnetic flux in a tight-binding model. Thus, without relying on an external magnetic field, it provides new physical degrees of freedom for controlling the symmetry of photon behavior and constructing higher-order degeneracy points in non-Hermitian systems.

[0004] In non-Hermitian optical systems, when multiple eigenvalues ​​and their corresponding eigenvectors simultaneously become degenerate, an exceptional point (EP) is formed. EPs exhibit rich physical effects, such as nonlinear responses to perturbations and enhanced mode selectivity, making them valuable for applications in ultra-high sensitivity sensing and mode-selective manipulation. However, achieving multi-state degeneracy typically requires satisfying multiple complex parameter matching conditions simultaneously, demanding extremely high degrees of freedom from the system, making it difficult to maintain stability in practical physical systems. Existing technologies mainly rely on gain-loss modulation or specific symmetries to reduce the implementation difficulty, but these schemes often require precise control of multiple independent parameters, resulting in high system complexity, poor stability, and a lack of effective technical solutions that can stably realize high-order degenerate states on integrated photonic platforms and support controllable switching between different orders.

[0005] Artificial gauge fields provide new physical degrees of freedom for controlling photon behavior by constructing equivalent magnetic flux, altering the energy spectrum properties of the system and inducing degenerate states that are impossible to achieve in traditional crystal lattices. In photonic systems, artificial gauge fields can simulate the vector potential of charged particles through complex coupling coefficients, introducing non-reciprocal phases between optical modes using spatial or temporal modulation, thereby creating equivalent synthetic magnetic fields. Orbital angular momentum modes, due to their helical phase wavefronts, provide a natural basis for generating gauge fields through controlled interference. However, research on the combination of artificial gauge fields and higher-order degeneracy points is still in its early stages. There is an urgent need to develop novel photonic devices that are simple in structure, controllable in parameters, and easy to integrate, capable of inducing and stabilizing multi-state degeneracy using artificial gauge fields to meet the needs of manipulating non-Hermitian systems in practical applications. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a waveguide mode converter based on the joint control of artificial gauge field and loss.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: This device introduces geometric phase e through a grooved, engineered orbital angular momentum waveguide structure. ±2iθ (where θ is the mode rotation angle induced by the groove), constructing an equivalent artificial gauge field, the resulting composite magnetic flux is: Φ = 2 θ By utilizing the non-Hermitian chiral symmetry protection induced by this artificial gauge field, a stable third-order EP (i.e., three-state degeneracy) is achieved, and the controllable transition between the second-order and third-order EP is realized by adjusting the waveguide coupling strength.

[0008] The photonic device of this invention employs an asymmetric dual-waveguide coupling structure, comprising a grooved few-mode waveguide and a single-mode waveguide with controllable optical loss. The grooved few-mode waveguide serves as the first optical waveguide, and its cross-section features a grooved structure with a specific geometric configuration. This grooved structure disrupts the rotational symmetry of the waveguide, inducing TE (transient optical loss). 10 and TE 01 The transverse electric mode undergoes azimuth rotation, resulting in a rotation angle of... θ The equivalent local coordinate system is used, and this geometric rotation introduces an equivalent gauge potential in mode coupling, generating an artificial gauge field. A single-mode waveguide serves as the second optical waveguide, equipped with a loss-tuning layer. The loss coefficient γ of the waveguide is controlled by adjusting the thickness or material properties of the loss layer, ensuring the system satisfies the non-Hermitian condition. The two waveguides are arranged parallel to each other, extending along the light propagation direction, and there is controllable evanescent field coupling between them. The coupling strength... c The waveguide spacing can be adjusted. d Change.

[0009] Based on the above structure, this invention achieves a high-dimensional degeneracy state through the following mechanism. When the rotation angle... θ = π When / 4, the corresponding artificial gauge field quantization is: Φ = π / 2, at which point the system's Hamiltonian satisfies non-Hermitian chiral symmetry. (in The symmetry-forced characteristic polynomial coefficients are real numbers, reducing the realization conditions of the third-order degeneracy point from four real constraints to two, thus enabling the third-order EP to be realized in the three-dimensional parameter space (γ, c , c 1) A stable one-dimensional manifold is formed in the middle. Specifically, the third-order degeneracy point satisfies and ,in This is half the difference in propagation constant of the rotating TE mode in the grooved waveguide. When the coupling strength satisfies the above relationship, the system is at the third-order degeneracy point, and the three eigenstates are simultaneously degenerate. When the coupling strength deviates from this condition, the third-order degeneracy point splits into two second-order degeneracy points, thereby achieving controllable switching between degeneracy points of different orders.

[0010] Preferably, the device is fabricated on a silicon-on-insulator platform. The first optical waveguide has a main width of 0.95 μm, a height of 0.85 μm, a groove depth of 0.03 μm, and a width of 0.66 μm. These geometric parameters correspond to the mode rotation angle. θ = π / 4; the width of the second optical waveguide is approximately 0.46 μm and the height is 0.85 μm; the distance between the two waveguides is 0.11 μm, corresponding to a coupling strength of... c The effective refractive index spectrum of the device is approximately 0.0484 μm⁻¹; the operating wavelength is 1550 nm; the cladding material is silicon dioxide (refractive index 1.46); and the core material is silicon (refractive index 3.47). Finite element numerical simulations verified that the effective refractive index spectrum of the device under the above parameter configuration is consistent with the theoretical model prediction, confirming the artificial gauge field. Φ = π The effective realization of / 2 and the stable existence of the third-order EP.

[0011] Compared with existing technologies, this invention has the following significant advantages. By utilizing artificial gauge fields to induce non-Hermitian chiral symmetry, the realization conditions for third-order degeneracy points are reduced from four independent constraints to two, significantly reducing the difficulty of realizing higher-order degeneracy points. This allows for the formation of a stable one-dimensional solution manifold in an experimentally achievable three-dimensional parameter space, significantly improving the structural stability and robustness of the system. By adjusting only the waveguide spacing—a single geometric parameter—deterministic switching between third-order and second-order EP can be achieved, avoiding the complex operation of simultaneously adjusting multiple independent parameters required in existing technologies, greatly simplifying the control of the device. This invention employs standard silicon-based photonic integration processes, and all structural parameters are within the range achievable by existing micro / nano fabrication technologies. No special materials or complex post-processing are required, demonstrating good scalability and practical application prospects. Based on the differences in eigenstate characteristics at degeneracy points of different orders, this invention can achieve selective excitation, conversion, and filtering of orbital angular momentum modes, providing a new technical approach for applications such as high-dimensional optical communication and on-chip optical signal processing. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the asymmetric waveguide coupler described in this invention and a schematic diagram of OAM synthesis.

[0013] Figure 2 This section compares the energy spectrum characteristics of the present invention under different artificial gauge field conditions. Figure 2 Figure (a) shows a gaugeless field. Φ Tight-binding model when (= 0); Figure 2 Figure (b) shows the gauge field. Φ = π A three-level ring coupling model at / 2; Figure 2 Figure (c) shows a gaugeless field. Φ When γ = 0, the real part of the eigenvalue varies with the loss coefficient γ. A graph showing the relationship between changes; Figure 2 Figure (d) in the diagram represents the gauge field. Φ = π The graph shows the relationship between the real part of the eigenvalue and the loss coefficient γ at / 2.

[0014] Figure 3 This describes the dynamic mode evolution and orbital angular momentum mode purity variation characteristics of the device described in this invention under different loss conditions. Figure 3 Figure (a) shows the cross-sectional field distribution and the evolution of the corresponding mode intensity with propagation distance when the loss is lower than the third-order EP (γ = 0.025 μm⁻¹); Figure 3 Figure (c) shows the cross-sectional field distribution and the evolution of the corresponding mode intensity with propagation distance when the loss is close to the third-order EP (γ = 0.1 μm⁻¹); Figure 3Figure (e) shows the cross-sectional field distribution and the evolution of the corresponding mode intensity with propagation distance when the loss is higher than the third-order EP (γ = 0.2 μm⁻¹); Figure 3 Figure (b) shows OAM0 (dashed line) and OAM when the loss is below the third-order EP (γ = 0.025 μm⁻¹). +1 (Solid line), OAM -1 (Dotted line) The evolution of the purity of the three modes with propagation distance shows high-frequency, short-period mode competition; Figure 3 Figure (d) shows the purity evolution of the three modes when the loss approaches the third-order EP (γ = 0.1 μm⁻¹); Figure 3 Figure (f) shows the purity evolution of the three modes when the loss is higher than the third-order EP (γ = 0.2 μm⁻¹), showing low-frequency oscillations and a decrease in the overall decay rate. Detailed Implementation

[0015] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings to further illustrate the technical solutions of the present invention. However, the present invention is not limited to these embodiments.

[0016] like Figure 1 The schematic diagram of the asymmetric waveguide coupler shown illustrates the coupling configuration of a grooved engineered orbital angular momentum waveguide and a lossy single-mode waveguide, as well as the principle of orbital angular momentum mode synthesis. Specifically, the rectangular groove at the top of the first optical waveguide disrupts the waveguide's four-fold rotational symmetry, causing the originally degenerate TE... 10 and TE 01 The transverse electric mode undergoes rotational mixing, with the rotation angle... θ = π / 4, corresponding to the total magnetic flux Φ = π / 2 artificial gauge field; the superposition of the two transverse electric modes produces an orbital angular momentum mode carrying a topological charge of ±1.

[0017] like Figure 2 The image shows a comparison of the energy spectrum characteristics under different artificial gauge field conditions. (a) and (b) respectively show the energy spectrum characteristics under no gauge field ( Φ Tight-bound model and gauge field when = 0) Φ = π The three-level ring-coupled model at / 2; (c) and (d) are the real parts of the eigenvalues ​​as a function of the loss coefficient under the corresponding conditions. g The relationship between the changes is as follows. Without a gauge field, the energy spectrum only exhibits paired energy level repulsion and crossing, lacking the symmetry protection required for third-order degeneracy; introducing... π After the / 2 gauge field, the energy spectrum exhibits mirror symmetry, with two second-order degenerate points appearing where the real part is zero, verifying the establishment of non-Hermitian chiral symmetry.

[0018] like Figure 3The diagram shows the dynamic mode evolution and orbital angular momentum mode purity variation characteristics of the device under different loss conditions. (a), (c), and (e) show the cross-sectional field distribution and the evolution of the corresponding mode intensity with propagation distance under three conditions: loss below the third-order EP (γ = 0.025 μm⁻¹), near the third-order EP (γ = 0.1 μm⁻¹), and above the third-order EP (γ = 0.2 μm⁻¹), respectively; (b), (d), and (f) show the OAM0 (dashed line) and OAM under the corresponding conditions. +1 (Solid line) and OAM -1 (Dotted line) Evolution of purity of the three modes with propagation distance. At the third-order EP, the simultaneous degeneracy of the three eigenstates significantly suppresses mode oscillations, and the energy is ultimately localized in the left waveguide and converted into higher-purity OAM. +1 In regions far from the degeneracy point, energy level splitting re-triggers mode oscillations, with significant differences in oscillation period and mode decay characteristics. This figure visually illustrates the physical mechanism of selective excitation, conversion, and filtering of orbital angular momentum modes by adjusting loss parameters, verifying the crucial role of the third-order EP in mode manipulation.

[0019] Its working principle is as follows: The core innovation of this invention lies in using an artificial gauge field as an independent physical degree of freedom to control the symmetry category of a non-Hermitian system, breaking through the constraints of traditional gain-loss modulation on the realization of higher-order degeneracy points. Unlike existing technologies that rely on PT symmetry or antisymmetry, this invention establishes non-Hermitian chiral symmetry through gauge flux induced by geometric rotation, reducing the realization conditions of a third-order EP from four real constraints to two real constraints, enabling it to form a stable one-dimensional solution manifold in the experimentally accessible three-dimensional parameter space. Simultaneously, by selecting a specific propagation distance, mode-selective excitation and conversion can be achieved, providing a simple and effective single-parameter control scheme for on-chip dynamic mode manipulation. The specific physical mechanism is as follows: I. Gauge Field Induction and Symmetry Reconstruction When light propagates in the first optical waveguide, the rotational symmetry disrupted by the grooves causes TE 10 and TE 01 The mode undergoes a geometrical rotation, which is equivalent to the resultant magnetic flux. Φ = π A 2 / 2 artificial gauge field. This gauge field introduces pure imaginary coupling under the OAM basis, ensuring that the system's Hamiltonian satisfies non-Hermitian chiral symmetry. For example... Figure 2 As shown, the energy spectrum exhibits only energy level repulsion when there is no gauge field; introducing... π After the / 2 gauge field, the energy spectrum is mirror-symmetric about the real axis, and a second-order degeneracy point appears, marking the establishment of the symmetry protection mechanism.

[0020] The key to this mechanism lies in: geometric parameters. θ Continuously adjustable → Standardized flux Φ= 2 θ Continuously adjustable → Symmetry category continuously adjustable. When Φ When = 0, the system lacks the symmetry required to protect the third-order EP ( Figure 2 (c)); when Φ = π At / 2, the energy spectrum exhibits mirror symmetry, and a second-order EP appears ( Figure 2 (d) , marking the establishment of symmetry protection. Finite element simulation ( c = 0.0484 μm −1 , c 1 = 0.012 μm −1 This verifies the determinism of this symmetry regulation.

[0021] II. Non-Hermitian chiral symmetry and dimensionality reduction of higher-order EP Third-order EP requirements Typically, four real constraints need to be satisfied, but in the three-dimensional parameter space (γ, c , c 1) Providing only three degrees of freedom results in a constraint number exceeding the number of degrees of freedom, making it difficult for the third-order EP to exist stably in general non-Hermitian systems.

[0022] The system characteristic polynomial of this invention is The last term is a normatively induced correction term. When Φ = π / 2 o'clock, The correction term disappears, and the coefficients of the characteristic polynomial are forced to be real numbers. This symmetry protection reduces the real and imaginary parts of each complex constraint equation to a single equation, halving the total number of constraints from 4 to 2, and decreasing the codimensionality. D codim = 2, solution manifold dimension d = 1. Thus, the third-order EP is transformed from an isolated, unrealizable point into a continuously adjustable one-dimensional working line in the parameter space.

[0023] In contrast, the time correction term Δ = in the ungauge field c ² c 1 is a non-zero term, and the two constraint equations cannot be satisfied simultaneously; the third-order EP is strictly prohibited; gauge field Φ = π When Δ = 0 at / 2, the constraints can be satisfied simultaneously, transforming the realization of higher-order EP from impossible to experimentally attainable. This working line is determined by the Sylvester junction method and satisfies... and Based on this deterministic relationship, fixed c 1 = 0.012 μm −1 γ = 0.062 μm −1 ,whenc = 0.034 μm −1 ( d When μm = 0.11 μm, the system is in third-order EP; c Deviation to 0.048 μm −1 The third-order EP splits into two second-order EPs. Because c 1 is fixed by the groove geometry; only the waveguide spacing is adjusted. c It can move along the working line to achieve deterministic switching between second-order and third-order EP without the need to adjust multiple independent parameters simultaneously.

[0024] III. Mode Conversion with Degeneracy Auxiliary When the system is exactly at the third-order degeneracy point condition, triple degeneracy effectively eliminates the phase difference between modes, thereby suppressing coherent oscillations and enabling directional energy transport along an exponentially decaying path. At this point, the three eigenstates are completely degenerate in the complex energy spectrum, and the collinearity of the eigenstates allows the system dynamics to be dominated by the dominant mode with the minimum net loss. Specifically, when the loss parameter γ ≈ 0.1 μm⁻¹ and the coupling strength satisfies... At approximately 0.0339 μm⁻¹, the energy initially coupled from the left waveguide to the right lossy waveguide and then rapidly decays. The energy component in the left waveguide is retained because it is not subject to loss, and tends to a steady state after a propagation distance of about 250 μm. Finally, it is localized in the left waveguide and converted into a high-purity OAM₊1 mode, realizing a deterministic conversion from the fundamental mode to a single orbital angular momentum mode.

[0025] Once the coupling strength deviates from this condition, the third-order degeneracy point will split into two second-order degeneracy points. The recovered energy level difference re-drives coherent oscillations between modes, thus achieving mode beam splitting. In the low-loss region (γ = 0.025 μm⁻¹), the large energy level splitting leads to high-frequency, short-period mode oscillations, with energies in OAM0, OAM₊1, and OAM₊1. -1 The periodic transitions between the three modes significantly reduce the purity of the output mode. In the high-loss region (γ = 0.2 μm⁻¹), although level splitting triggers mode oscillations again, the oscillation period is significantly longer than in the low-loss region. Furthermore, due to the change in the complex energy spectrum structure in the high-loss mode, the overall energy decay rate is actually lower than at the third-order EP. Therefore, under the premise of fixed gauge flux and mode splitting, the system can achieve deterministic switching between different states, such as mode locking and purification in the third-order EP and mode beam splitting in the second-order EP, simply by adjusting the waveguide spacing to change the coupling strength. This provides a simple and effective single-parameter control scheme for on-chip dynamic mode manipulation.

[0026] In summary, this invention establishes a method for realizing higher-order degeneracy points with symmetry control. By using artificial gauge fields to realize and manipulate higher-order non-Hermitian degeneracy in an integrated photonic platform, it provides a new technical solution for applications such as high-sensitivity optical sensing, photonic optical devices, and on-chip optical signal processing.

[0027] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A waveguide mode converter based on joint modulation of artificial gauge field and loss, characterized in that, The waveguide mode converter is a photonic device with an asymmetric dual-waveguide coupling structure, comprising a grooved few-mode waveguide and a single-mode waveguide with controllable optical loss. The grooved few-mode waveguide serves as the first optical waveguide; the grooved structure disrupts the rotational symmetry of the waveguide, inducing TE. 10 and TE 01 The transverse electric mode undergoes azimuth rotation, resulting in a rotation angle of... i The equivalent local coordinate system, this rotation makes TE 10 and TE 01 The coupling coefficients between modes carry a direction-dependent phase factor e ±2iθ This is equivalent to introducing a resultant magnetic flux into the system. F = 2 i The artificial gauge field; the single-mode waveguide serves as the second optical waveguide, and it is equipped with a loss modulation layer. The loss coefficient of the waveguide is controlled by adjusting the thickness or material properties of the loss layer. g This ensures the system satisfies the non-Hermitian condition; the first and second optical waveguides are arranged in parallel, extending along the direction of light propagation, and there is controllable evanescent field coupling between them, with a coupling strength of [missing information]. c The waveguide spacing can be adjusted. d By changing and adjusting c and γ, the system can satisfy non-Hermitian chiral symmetry and achieve a stable third-order EP point.

2. The waveguide mode converter based on joint control of artificial gauge field and loss according to claim 1, characterized in that, High-dimensional degeneracy is achieved through the following mechanism: when the rotation angle... i = π When / 4, the corresponding artificial gauge field quantization is: Φ=π / 2, at this point, the system's Hamiltonian satisfies non-Hermitian chiral symmetry. This symmetry forces the coefficients of the system's characteristic polynomial to be real, reducing the realization conditions of the third-order degeneracy point from four real constraints to two real constraints, allowing the third-order EP to be in the three-dimensional parameter space (γ, c , c 1) A stable one-dimensional manifold is formed in which c 1 is half of the difference in the propagation constant of the rotating TE mode, which is uniquely determined by the groove geometry; when the coupling strength deviates beyond this condition, the third-order degeneracy point splits into two second-order degeneracy points, thereby realizing the controllable switching between degeneracy points of different orders.

3. A waveguide mode converter based on joint modulation of artificial gauge field and loss according to claim 1, characterized in that, The photonic device is fabricated on a silicon-on-insulator platform. The first optical waveguide has a main width of 0.95 μm, a height of 0.85 μm, a groove depth of 0.03 μm, and a width of 0.66 μm. These geometric parameters correspond to the mode rotation angle. i = π / 4; the width of the second optical waveguide is approximately 0.46 μm and the height is 0.85 μm; the spacing between the two waveguides d The coupling strength can be adjusted within the range of 0.11-0.14 μm. c In the range of 0.034–0.048 μm -1 Variation within the range; when c ≈ 0.034 μm -1 And the loss coefficient γ ≈ 0.064 μm -1 When, the system is at a third-order degeneracy point; when c Deviation from this value (e.g.) c ≈ 0.048 μm -1 When the third-order degeneracy point splits into two second-order degeneracy points, controllable switching between degeneracy points of different orders is achieved; the working wavelength is 1550 nm; the cladding material is silicon dioxide with a refractive index of 1.46; the core material is silicon with a refractive index of 3.47.

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