Method for realizing optical switch in PT symmetric potential well by using symmetric Pearls beam

Abstract

The invention discloses a method for realizing an optical switch in a PT symmetric potential well by using a symmetric Pearls beam, and belongs to the technical field of integrated optics. The method aims at solving the problem that a traditional PT symmetric optical switch is static in function and cannot periodically work in the propagation direction. The method comprises the following core steps: generating a symmetric Pearls beam and injecting the symmetric Pearls beam into a dual-channel PT symmetric optical waveguide; by regulating and controlling the gain / loss intensity of the potential well, the beam energy is actively induced to generate periodic and reciprocal coupling exchange between the two channels; and the periodic fluctuation of the light intensity of any channel is defined as on and off states of the switch, so that the dynamic optical switch is realized. By adjusting the potential well modulation depth, the gain / loss intensity and the light beam space distribution factor, the contrast ratio and the work period of the switch can be independently regulated and controlled, and the multi-dimensional tunability is achieved. The method is novel in principle, and a new scheme is provided for developing a dynamic reconfigurable non-Hermite photonic device.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of optical technology, and particularly relates to a method for realizing periodic and tunable optical switch in a PT symmetric potential well based on symmetric Poynting beam, which is suitable for the field of optical communication, optical calculation and integrated photonic device. BACKGROUND

[0002] Optical switch is a core device in optical communication, optical calculation and optical interconnection system. Traditional optical switch mechanism, such as electro-optical, thermo-optical switch based on Mach-Zehnder interferometer or directional coupler, is limited in size, power consumption and response speed by material properties and structural design. In recent years, the non-Hermite optical system based on PT symmetry principle provides a new paradigm for optical switch design. PT symmetry requires that the complex refractive index distribution of the system satisfies n(x)=n^*(-x), and through introducing carefully designed gain and loss distribution in the waveguide, novel optical phenomena such as non-reciprocal transmission, abnormal point enhanced sensing can be realized.

[0003] Traditional PT symmetric optical switch is usually based on a double waveguide coupler structure, one of which has gain and the other has loss. Its switching action depends on the evolution of the light beam in the coupling length, and the switch state ('on' or 'off') is determined by the light intensity distribution of the output port. However, the function of such switch is static, i.e. for a fixed device length, the output state is usually determined, and it cannot realize periodic and dynamic switch switching in the propagation direction of the light beam. In addition, its performance is severely dependent on the precise matching of the coupling length and the total propagation length, and the tunable dimension is limited.

[0004] On the other hand, self-focusing beams (such as Airy beams, Poynting beams) have attracted widespread attention due to their non-diffraction, self-healing and self-accelerating properties. As a new type of self-focusing beam, symmetric Poynting beam has fourfold symmetry, super focusing ability and highly adjustable light field distribution. When it is introduced into a specific potential field (such as optical lattice, potential well), its transmission trajectory and energy distribution can be controlled. The existing technology (such as Shakti Singh et al.) studies the evolution of circular Airy beam in PT symmetric potential well, and realizes the regulation of beam focal length and intensity, but does not reveal or utilize the physical mechanism of periodic reciprocal energy exchange between two channels to construct dynamic optical switch.

[0005] Therefore, how to overcome the shortcomings of the existing PT symmetric optical switch that cannot work periodically and has poor tunability, and provide a new type of optical switch scheme with flexible structure and dynamically adjustable performance, is a technical problem to be solved in the field. SUMMARY

[0006] In order to solve the problems of strong dependence of the length of the longitudinal coupling of the traditional optical switch and the inability to work periodically, the present application provides a method for realizing an optical switch by using a symmetric Pearcey beam in a PT symmetric potential well, the method comprising the following steps: designing a double-channel PT symmetric potential well with gain / loss distribution, inducing periodic reciprocal energy exchange between channels of the optical beam, and realizing the function of the optical switch, and the switch performance can be flexibly regulated by multiple parameters.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is:

[0008] A method for realizing an optical switch by using a symmetric Pearcey beam in a PT symmetric potential well, comprising the following steps:

[0009] S1, inputting a symmetric Pearcey beam with a Gaussian truncation, generating an initial energy-limited symmetric Pearcey beam by means of a spatial light modulator by using a four-fold symmetric Pearcey beam;

[0010] S2, injecting the symmetric Pearcey beam into a double-channel PT symmetric optical waveguide; the refractive index distribution of the double-channel PT symmetric optical waveguide constitutes a PT symmetric potential well, at least one channel of the potential well contains an optical gain, and the other channel contains an optical loss balanced therewith;

[0011] S3, controlling the parameters of the PT symmetric potential well and the symmetric Pearcey beam, so that the energy of the optical beam is periodically and reciprocally coupled and exchanged between the two channels when the optical beam is transmitted;

[0012] S4, periodically distributing the light intensity of any one of the two channels in the propagation direction as an output, wherein the periodic peak and valley values of the light intensity correspond to the "on" state and the "off" state of the optical switch, respectively.

[0013] Further, the symmetric Pearcey beam in the step S1 is represented as follows:

[0014] ;

[0015] wherein is a Pearcey function;

[0016] is an initial amplitude, is a spatial distribution factor, is a Gaussian truncation coefficient.

[0017] Further, in the step S2, the transmission of the optical beam is described by the following standard Schrodinger equation with a PT symmetric waveguide:

[0018] ;

[0019] wherein, an optical field envelope representing a symmetric Pearcey beam, and is a normalized transverse coordinate, is a normalized longitudinal propagation distance, parameter is a modulation depth of the PT-symmetric potential well;

[0020] ; ;

[0021] corresponding to its real and imaginary parts, respectively, the real part providing beam confinement and the imaginary part providing a balanced gain and loss distribution, is a potential well width modulation factor, is a potential well spacing, is a gain / loss effect.

[0022] Further, by increasing the modulation depth P, the peak intensity of the periodic energy exchange can be enhanced and the exchange period can be prolonged simultaneously.

[0023] Further, by increasing the absolute value of the gain / loss intensity, the peak intensity of the periodic energy exchange can be enhanced and the exchange period can be shortened.

[0024] Further, the sign of the gain / loss intensity determines the initial order of the periodic energy exchange, which is used to set the initial working state of the optical switch.

[0025] Further, by increasing the spatial distribution factor, the peak intensity of the periodic energy exchange can be enhanced without changing its exchange period substantially.

[0026] The core idea of the present application is to inject a symmetric Pearcey beam with special spatial modes into a two-channel PT-symmetric potential well with a specific gain / loss spatial distribution; to actively induce periodic and reciprocal energy exchange between the two channels by the synergistic effect between the self-focusing property of the beam and the non-Hermitian property of the potential well; and to define the periodic fluctuation of the light intensity in either channel during the energy exchange process as the "on" (high light intensity) and "off" (low light intensity) states of the optical switch, thereby realizing an optical switch that works dynamically along the propagation direction.

[0027] Compared with the prior art, the present application realizes the function of an optical switch through the periodic energy exchange of a symmetric Pearcey beam in a two-channel PT-symmetric potential well, and has the following advantages:

[0028] 1. Achieved dynamic periodic switching function: This invention utilizes the inherent periodic energy exchange behavior of the symmetrical Pierce beam in the PT symmetrical potential well, so that the "on" and "off" states of the optical switch can be periodically repeated along the beam propagation direction z, breaking through the limitations of the traditional PT symmetrical coupler optical switch function being static and dependent on a fixed coupling length.

[0029] 2. Multidimensional tunability: The key performance indicators of the optical switch of this invention, such as the peak intensity (contrast) in the "on" state and the "on-off" switching period (frequency), can be independently and flexibly adjusted by the potential well parameters (P, W0) and the beam parameters (b), which greatly enhances the adaptability and design freedom of the device.

[0030] 3. Novel principle and simple structural concept: This invention creatively combines the unique transmission characteristics of symmetric Pierce beams with the non-Hermitian control capability of PT symmetric potential traps, revealing a new physical mechanism for dynamic optical switching, and providing new ideas for the development of novel functional devices based on complex optical fields and non-Hermitian photonic structures.

[0031] 4. The present invention has a simple structure and various control methods, and is suitable for integrated optical and tunable photonic devices. Attached Figure Description

[0032] Figure 1 This is a transmission characteristic diagram of a symmetrical Pierce beam under a dual-channel PT symmetrical waveguide without gain / loss effects;

[0033] Figure 2 This is a transmission characteristic diagram of a symmetrical Pierce beam under a dual-channel PT symmetrical waveguide with introduced gain / loss effects;

[0034] Figure 3 This is a diagram showing the transmission characteristics of a symmetrical Pierce beam at different potential well depths;

[0035] Figure 4 This is a transmission characteristic diagram of a symmetrical Pierce beam under different gain / loss intensities;

[0036] Figure 5 It is at different modulation depths With gain / loss intensity Below, spatial distribution factor The impact on peak intensity and period. Detailed Implementation

[0037] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0038] The beam propagation model based on this embodiment is the standard Schrödinger equation with a PT-symmetric potential well, as follows:

[0039] ;

[0040] denotes the light field envelope of a symmetric Pearcey beam, and is the normalized transverse coordinate, denotes the normalized longitudinal propagation distance.

[0041] Generation of a symmetric Pearcey beam: As the input light source, the initial light field of a symmetric Pearcey beam can be characterized by the following formula:

[0042] ;

[0043] where is the Pearcey integral function, representing the core phase structure of the beam; is the initial amplitude, is the spatial distribution factor, used to scale the transverse dimension of the beam, is the Gaussian truncation coefficient, used to ensure the finite energy of the beam. In practice, the corresponding combination of fourth-order phase and linear phase can be loaded by a spatial light modulator, and a Gaussian-type diaphragm can be used to physically generate this beam.

[0044] Design of a two-channel PT-symmetric potential well: The potential function in the standard Schrödinger equation of a PT-symmetric potential well and is specifically defined as:

[0045] ;

[0046] ;

[0047] Here, denotes two Gaussian potential wells located at x = -B and x = +B, respectively, used to confine the beam in the transverse direction, is an odd function that provides a net gain in the x = -B channel (when W0> 0) and an equal amount of net loss in the x = +B channel, thereby achieving PT symmetry. The parameter w controls the width of the potential well, B controls the distance between the two channels, and W0is the gain / loss strength.

[0048] Working principle and regulation of the optical switch:

[0049] As shown in Figure 1 , when W0= 0 (no gain / loss), the main lobe of the symmetric Pearcey beam is split into two beams under the confinement of the two real potential wells V(x, y), which are independently and stably transmitted in the two channels. The light intensity in the two channels is equal and does not change with z, and the switch does not have the function.

[0050] As shown in Figure 2As shown, when introducing nonzero W0 (e.g. W0 = 0.8), the gain and loss break the system balance, leading to non-Hermitian coupling between the two channel modes. The four-fold symmetry and strong gradient field of the symmetric Pearcey beam efficiently interact with this non-Hermitian coupling, facilitating the periodic and complete energy exchange between the two channels. At this moment, monitoring the light intensity I(z) of either channel, one can observe its periodic oscillation with z, and the peak (high light intensity) defines the switch "on" and the valley (low light intensity) defines the switch "off", thus realizing a dynamic optical switch.

[0051] Figures 3-5 The tunability of the optical switch is demonstrated:

[0052] The control of the potential well depth P: Increasing P enhances the confinement of the potential well to the beam and the strength of the non-Hermitian coupling. As shown, Figure 3 with P increasing from 1 to 1.6, the peak intensity of the energy exchange increases significantly, and the propagation distance corresponding to a complete exchange cycle (i.e. the switching period) also becomes longer. This means that by changing the refractive index modulation depth of the waveguide (e.g. by changing P through electro-optic or thermo-optic effects), one can simultaneously adjust the contrast ratio and the working frequency of the switch.

[0053] The control of the gain / loss strength W0: The absolute value of W0 directly determines the strength of the non-Hermitian coupling. As shown, Figure 4 (a), increasing W0 leads to more intense energy exchange (increasing peak intensity) but faster completion of the exchange (shorter period). In particular, the sign of W0 determines which channel is in the gain state at the initial time. In contrast to Figure 4 (a2) W0 = 1.1 and Figure 4 (a3) W0 = -1.1, one can find that the light intensity evolution curves of the two channels are completely "interchanged", i.e. the order of energy exchange is reversed. This means in practical applications that one can preset the initial state of the optical switch (which channel opens first) by reversing the distribution of gain / loss, increasing the flexibility of control.

[0054] The control of the beam spatial factor b: Factor b scales the transverse width of the beam. Increasing b makes the initial energy of the beam more concentrated, and the overlap integral with the potential well increases, leading to an increase in the peak intensity of the coupled energy exchange. However, since b does not change the intrinsic mode coupling coefficients of the system, the exchange period remains essentially unchanged. This provides a unique means to independently adjust the contrast ratio of the switch without affecting its frequency.

[0055] In summary, by the synergistic design of symmetric Poynting vector beam and double-channel PT symmetric potential well, a dynamic optical switch with highly adjustable performance is realized. Those skilled in the art can make adaptive changes to the specific form of the potential well (such as non-Gaussian type), the generation method or control means of the light beam without departing from the principles of the present application. These changes should fall within the scope of protection defined by the claims of the present application.

Claims

1. A method for realizing an optical switch in a PT-symmetric potential well using a symmetric Pierce beam, characterized in that, Includes the following steps: S1. Input a Gaussian-trunculated symmetrical Pierce beam, and use a quadruple symmetrical Pierce beam with a spatial light modulator to generate a symmetrical Pierce beam with finite initial energy. S2. The symmetrical Pierce beam is injected into a dual-channel PT symmetrical optical waveguide; the refractive index distribution of the dual-channel PT symmetrical optical waveguide forms a PT symmetrical potential well, at least one channel of the potential well contains optical gain, and the other channel contains optical loss that balances it. S3. Control the parameters of the PT symmetric potential well and the symmetric Pierce beam so that the energy of the beam undergoes periodic reciprocal coupling exchange between the two channels during transmission. S4. The periodic distribution of light intensity in the propagation direction of any one of the dual channels is taken as the output, wherein the periodic peak and valley values ​​of the light intensity correspond to the "on" and "off" states of the optical switch, respectively.

2. The method according to claim 1, characterized in that, The symmetrical Pierce beam in step S1 is represented as follows: ； in It is the Pierce function; The initial amplitude, Spatial distribution factor, is the Gaussian cutoff coefficient.

3. The method according to claim 1, characterized in that, In step S2, the propagation of the beam is described by the following standard Schrödinger equation with a PT-symmetric waveguide: ； in, This represents the optical field envelope of a symmetrical Pierce beam. and For normalized horizontal coordinates, Represents the normalized longitudinal propagation distance, parameter The modulation depth of the PT-symmetric potential well; ； ； These correspond to the real and imaginary parts, respectively. The real part provides beam confinement, while the imaginary part provides a balanced distribution of gain and loss. It is the potential well width modulation factor. It is the potential well spacing. It is a gain / loss effect.

4. The method according to claim 3, characterized in that, By increasing the modulation depth P, the peak intensity of the periodic energy exchange can be enhanced and its exchange period can be extended simultaneously.

5. The method according to claim 3, characterized in that, By increasing the absolute value of the gain / loss intensity, the peak intensity of the periodic energy exchange can be enhanced and its exchange cycle shortened.

6. The method according to claim 5, characterized in that, The sign of the gain / loss intensity determines the initial sequence of the periodic energy exchange, which is used to set the initial operating state of the optical switch.

7. The method according to claim 3, characterized in that, By increasing the spatial distribution factor, the peak intensity of the periodic energy exchange can be enhanced without significantly altering its exchange period.

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