Method for constructing non-diffracting pst wave packets

Abstract

The application discloses a kind of construction methods of non-diffraction PST wave packet, it is related to non-diffraction beam technical field.The method includes the following steps: constructing pseudo time dimension by spatial scale transformation;Conical surface approximation is constructed pseudo light cone in the region on equal frequency sphere using spatial scale transformation, wherein and respectively x direction transverse wave number and y direction transverse wave number of spatial spectrum;Spectrum plane intersects with pseudo light cone, and the intersection line track determines the spectrum of PST wave packet;Using complex amplitude modulation method based on spatial light modulator generates non-diffraction PST wave packet.Compared with the space-time optical pulse scheme needing pulse laser source, 4f pulse shaping system and complex field scanning device, the efficient generation of wave packet is realized by simplifying configuration.

Description

Technical Field

[0001] This invention relates to the field of diffraction-free beam technology, and more particularly to a method for constructing a diffraction-free PST wave packet. Background Technology

[0002] Diffraction, an inherent property of free-space beam propagation, causes beam broadening in the lateral direction, thus limiting the resolution of imaging systems, restricting the transmission capacity of optical communications, and weakening the critical intensity required for light-matter interaction. To overcome this physical limitation, researchers have long been dedicated to exploring beams with diffraction-free properties—beams whose lateral intensity distribution remains constant during long-distance propagation. Most two-dimensional monochromatic diffraction-free solutions described by the Helmholtz equations (including Bessel beams, Mathieu beams, and Weber beams) follow a simple and elegant fundamental principle: the lateral wavenumber component of its spatial spectrum (… and The components are constrained to a thin circular ring in the frequency domain, thus ensuring that all spectral components have a consistent axial wavenumber. While this ring spectrum model is intuitive and easy to process, its inherent geometric constraints also create significant limitations. Apart from Airy beams with transverse acceleration characteristics, almost all existing designs for two-dimensional monochromatic non-diffraction beams have failed to break through the framework of this ring spectrum structure. Therefore, whether monochromatic non-diffraction beams can transcend the limitations of the ring spectrum remains a crucial and unresolved issue in the field of optics.

[0003] In recent years, significant breakthroughs have been achieved in the study of two-dimensional multicolor spatiotemporal wave packets (i.e., structured light fields constructed by replacing spatial dimensions with time dimensions), providing new insights into solving this problem. Among these, spatiotemporal light sheets, as a typical example, can achieve diffraction-free propagation at any tunable group velocity. Notably, their propagation invariance stems from their unique spectral structure: the spectrum lies on the conic section intersection of the light cone (a surface describing the dispersion relation of multicolor beams in free space) and the spectral plane, thus eliminating the need to maintain a constant axial wavenumber.

[0004] The dispersion relations of polychromatic light and monochromatic light differ fundamentally: the former corresponds to a light cone structure in the frequency domain, while the latter exhibits an equal-frequency sphere. This geometric characteristic eliminates the possibility of obtaining a conical spectrum through planar tangency. This fundamental difference in physical mechanism and geometric structure constitutes the fundamental obstacle to achieving diffraction-free propagation of monochromatic conical spectrum beams. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to provide a method that simplifies experimental setup and enables efficient generation of diffraction-free PST wave packets.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for constructing a diffraction-free PST wave packet, comprising the following steps:

[0007] S1-1: By adjusting the spatial scale of the beam, an equivalent pseudo-time dimension is constructed in the spatial domain;

[0008] S1-2: Using spatial scaling transformation on an equal-frequency sphere A pseudocone is constructed by approximating the region with a cone-shaped surface;

[0009] S1-3: The spectral plane intersects with the pseudocone, and the trajectory of the intersection line determines the spectrum of the PST wave packet;

[0010] S1-4: PST wave packets are generated using a complex amplitude modulation method based on spatial light modulators.

[0011] The beneficial effects of adopting the above technical solution are as follows: This application introduces pseudo-spacetime (PST) wave packets—a new type of monochromatic diffraction-free beam that transcends the ring spectrum paradigm—by breaking the symmetry of spatial diffraction and constructing a pseudocone for a monochromatic beam. The spectrum of this type of beam originates from the intersection of the pseudocone with conic sections of various spectral planes, while spectral phase modulation further generates a variety of diffraction-free beams, demonstrating the versatility of the PST platform. This expands the scope of diffraction-free fields and paves the way for its applications in microscopy, holography, nonlinear light-matter interactions, and long-distance optical communication. Compared to spatiotemporal optical pulse schemes that require pulsed laser sources, 4f pulse shaping systems, and complex field scanning devices, this method achieves efficient wave packet generation through simplified configuration. Attached Figure Description

[0012] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0013] Figure 1 This is an overall flowchart of the method for constructing diffraction-free PST wave packets according to Embodiment 1 of the present invention;

[0014] Figure 2a This is a spectral projection diagram of a conventional non-diffraction beam in Embodiment 1 of the present invention;

[0015] Figure 2b This is a spectral projection diagram of the spatiotemporal optical film in Embodiment 1 of the present invention;

[0016] Figure 2c This is a schematic diagram of the construction of the pseudocone in Embodiment 1 of the present invention;

[0017] Figure 2d This is a schematic diagram of the unaccelerated PST Airy packet located on the pseudocone in Embodiment 1 of the present invention;

[0018] Figure 3This is a schematic diagram of the PST wave packet generation optical path system in Embodiment 1 of the present invention;

[0019] Figure 4a The spatial intensity distribution measurement results of the Airy wave packet without acceleration in Embodiment 1 of the present invention;

[0020] Figure 4b The result of the spectral amplitude measurement of the PST wave packet in Embodiment 1 of the present invention;

[0021] Figure 4c The phase measurement results of the PST wave packet in Embodiment 1 of the present invention;

[0022] Figure 4d In Embodiment 1 of the present invention and Location measured Distribution and Correspondence time Spatial profile;

[0023] Figure 5 This is the method for constructing the accelerated PST Airy packet as described in Embodiment 2 of the present invention;

[0024] Figure 6a This is a spatial intensity distribution diagram of an Airy wave packet with uniform spectral amplitude in the method described in Embodiment 2 of the present invention;

[0025] Figure 6b This is a spatial intensity distribution diagram of Airy packet with cubic phase in the method described in Embodiment 2 of the present invention;

[0026] Figure 6c The Airy wave packet edge in the method described in Embodiment 2 of the present invention Phase measurement results of the axis;

[0027] Figure 6d This is a diagram demonstrating the self-healing properties of the Airy wave packet within a propagation distance of approximately 190 mm in the method described in Embodiment 2 of the present invention.

[0028] Figure 6e This is a diagram showing the predicted propagation trajectory of the PST Airy packet in the method described in Embodiment 2 of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0030] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0031] Example 1

[0032] Overall, such as Figure 1 As shown in the figure, an embodiment of the present invention discloses a method for constructing a diffraction-free PST wave packet, the method comprising the following steps:

[0033] S1-1: Constructing the pseudo-time dimension of the beam by transforming its spatial scale, i.e., by transforming its spatial scale. Constructing a pseudo-time dimension ;

[0034] S1-2: Using spatial scaling transformation on an equal-frequency sphere A pseudocone is constructed by approximating the region with a cone-shaped surface, where... and These are the transverse wavenumbers in the x and y directions of the spatial spectrum, respectively.

[0035] S1-3: The spectral plane intersects with the pseudocone, and the trajectory of the intersection line determines the spectrum of the PST (pseudo-space-time) wave packet;

[0036] S1-4: Generate unaccelerated PST Airy packets using a complex amplitude modulation method based on spatial light modulators.

[0037] The above steps will be explained in detail below with specific methods:

[0038] By altering the xy dimensions of a light beam (where the x-direction is much smaller than the y-direction), the beam's behavior in the y-dimensional space can be simulated to mimic its time-dimensional behavior. Simply put, this simulates time using space, and the spatial dimension of this time simulation is called the pseudo-time dimension. The diffraction behavior of light can be more intuitively understood in the spectral domain. For a monochromatic light beam, its dispersion relation in free space forms an isofrequency sphere. ,in For wave number, and These are the transverse wavenumbers in the x-direction and y-direction of the spatial spectrum, respectively. This represents the axial wavenumber of the spatial spectrum. For example... Figure 2a As shown, a traditional non-diffractive beam is characterized by its spectral components being concentrated in a ring-shaped region, which consists of monochromatic plane wave components. ( (It is the frequency of light waves). This ring spectrum is essentially an equal-frequency sphere and an equal-frequency sphere. The intersection of the planes; if this condition is deviated from, the beam will inevitably undergo diffraction broadening and intensity distribution diffusion. By applying complex amplitude modulation to the ring spectrum, various types of diffraction-free beams can be derived—for example, a uniform amplitude and phase distribution corresponds to a zero-order Bessel beam.

[0039] For a multicolor spacetime wave packet, the free-space dispersion relation becomes a light cone: ,(because Shaft without modulation, take ),in Indicates time frequency. The speed of light in a vacuum. Based on this, a diffraction-free spacetime optical sheet was developed, whose spectrum is constrained to the light cone and various spectral planes (parallel to...). axis and with Shaft On the conic section formed by the intersection of the included angles ( Figure 2b These intersections are in plane and The projection on the plane determines the spatiotemporal spectral characteristics and group velocity, which constitute the physical basis for the spatiotemporal light sheet to maintain propagation invariance.

[0040] Inspired by the diffraction-free spacetime wave packet in free space, this application extends the concept of two-dimensional spacetime duality to the dispersion-free spectral domain of monochromatic light. Monochromatic beams obey the paraxial Helmholtz equations:

[0041] ,

[0042] Represents the light field of a monochromatic beam;

[0043] By introducing coordinate transformations inspired by the contraction of Lorentz space ( This achieves the breaking of symmetry in the horizontal dimension.

[0044] The transformed equation becomes:

[0045] ,

[0046] in Represents higher-order terms, ignored After applying the second derivative in the direction, the equation simplifies to:

[0047]

[0048] Here This constructs a pseudo-time dimension, and the equation's form is completely consistent with the paraxial wave equation of the spacetime wave packet. This transformation achieves selective suppression. Axis (i.e., original) The diffraction broadening along the (axis) direction breaks the symmetry of two-dimensional space, and its compression efficiency is determined by the parameter. Regulation. In the construction In the domain (i.e., the PST domain), increase Can enhance Suppressing diffraction along the axial direction while maintaining The axial diffraction properties remain unchanged. Especially when hour, Axial diffraction was significantly suppressed.

[0049] Figures 2a-2d This is a conceptual diagram of an Airy wave packet without acceleration using PST. Figure 2a The spectrum of a conventional non-diffractive beam lies on an isofrequency sphere and is projected onto... plane and On a plane; arrows of the same length indicate that the lateral spatial frequencies are the same. Value. The right side shows the range of propagation 10 times Rayleigh ( The corresponding light field after ). Figure 2b The spectrum of the spacetime light plate lies on the light cone and is projected onto... plane and On a plane; arrows of different lengths and colors represent different time frequencies. value. Figure 2c This is a schematic diagram of the construction of the pseudocone. The gray dashed cone represents the inverse pseudocone. Figure 2d ,and Figure 2a Similarly, but showing the unaccelerated PST Airy packet located on the pseudocone, with its spectral plane having an adjustable tilt angle, the projection corresponding to the intersection of the blue highlight plane and the pseudocone.

[0050] In the PST domain, a cylindrical surface is first used. Approximately equal frequency sphere (e.g.) Figure 2c (As shown). This approximation only applies to... area (i.e.) Figure 2c The spherical gray ring holds true, where the curvature of the sphere is negligible. Further, a conical surface is used for a more detailed approximation:

[0051]

[0052] in The slope of the cone. Let be the vertex of the cone. According to the paraxial approximation requirements, the cone surface must satisfy the constraint conditions. ,Right now ,and This means and This construction can lead to other equivalent conical surfaces (such as...). A cone with its positive vertex on the axis. Figure 2c(dashed cone). Within the neighborhood, this conical surface can still approximate a sphere with high accuracy. For ease of observation, the sphere exhibits ellipsoidal characteristics from the perspective of the spectral compression domain, while the conical surface simulates the behavior of a light cone—hence the name "pseudo-cone." It should be emphasized that this pseudo-cone model is only applicable in certain regions. Effective within the region, the lateral broadening of the paraxial beam in one dimension is strongly suppressed, perfectly reproducing the dispersive characteristics of the spatiotemporal pulse.

[0053] The spectrum studied in this application is constrained to the pseudocone and the tilted spectral plane (parallel). Axis, relative Axis tilt Angle, and always passes through a fixed point. The intersection of the lines:

[0054]

[0055] Substituting equation (3) into equation (2) and ignoring higher-order minor quantities, we get: And ignore the sub-items:

[0056]

[0057] This equation precisely defines the monochromatic PST wave packet. Spectrum , for Figure 2d The tilt angle of the mid-spectral plane is derived from this:

[0058] .

[0059] This indicates that the PST wave packet satisfies That is, PST wave packet propagation except Lateral movement of the axis Irrelevant. This lateral shift can be eliminated by spectral shifting, or it can be understood as... Dependent on pseudogroup velocity. It is worth noting that equation (4) in The domain can be precisely approximated as a parabola, but it must be clarified that the parabolic spectrum alone is insufficient to guarantee propagation invariance. The core mechanism lies in the synergistic effect of the specific trajectory of the pseudocone and the broadening caused by symmetry breaking. Therefore, other trajectories on the pseudocone (such as hyperbolas or ellipses) may also achieve diffraction-free propagation under symmetry breaking conditions.

[0060] Test experiment:

[0061] To generate PST wave packets, a pure phase-type spatial light modulator is used, directly in... The domain is loaded with an encoded complex amplitude modulation phase map. For example... Figure 3 As shown, through a 4f optical system (consisting of two focal lengths) The diffraction field is filtered using a lens and spatial filter (comprising mm lenses and a spatial filter), extracting only the complex amplitude distribution of the target. The diffraction components are analyzed and wavefront reconstruction is performed. Furthermore, by adding a spherical lens in front of the CCD camera to construct a 2f imaging system, real-time measurement of the wave packet spatial spectrum can be achieved. For the acquisition of spectral phase information, a Mach-Zehnder interferometer is used for measurement, and phase reconstruction is completed based on the interferometric data.

[0062] The experimentally generated PST wave packets exhibit an approximately parabolic spectral trajectory, which originates from the pseudocone and tilt angle. Their spectral planes intersect. Figure 4a The PST domain was displayed. The intensity distribution measured within the ) shows a Gaussian-shaped main lobe and a flight envelope composed of side lobes; Figure 4b and 4c These correspond to the amplitude and phase distributions of the spectrum, respectively. The spectral bandwidth ratio is given by the following formula: Therefore, the value was set to 8.4 in this experiment. After precise lateral displacement compensation, the light field satisfies... And without diffraction propagation. For example... Figure 4d As shown, the transverse cross-sectional distribution was measured over a propagation distance of approximately 610 mm (equivalent to 100 times the Rayleigh range of a Gaussian beam of equal width, beyond which the peak intensity decreases sharply). half height full width It only widens to 1.45 times its original width. It is worth noting that the beam... The two sides of the plane evolve symmetrically along the propagation direction, and along... The axial distribution also remained stable. The experimental results are in high agreement with the theoretical predictions.

[0063] Figures 4a-4d For the characterization of Airy wave packets without acceleration PST, among which Figure 4a The spatial intensity distribution of Airy wave packets without acceleration is measured. Figures 4b-4c The results show the spectral amplitude and phase measurements of the PST wave packet. Figure 4d In order to be in and Location measured Distribution and Correspondence time Spatial profile. Transverse profile of the central main lobe at half height and full width. It is approximately 35 micrometers long, and widens to 1.45 micrometers after propagating 100 times the Rayleigh distance. After that, the peak intensity dropped sharply.

[0064] In the design of diffraction-free beams, achieving a balance between increasing the diffraction-free distance and maintaining the central energy has long been a critical challenge. To address this, this application further monitored the energy localization characteristics of the PST wave packet during propagation. Experiments show that its central energy is approximately 50% higher than that of a zero-order Bessel beam, exhibiting a superior energy confinement mechanism while maintaining a comparable diffraction-free distance, effectively suppressing the dissipation of central energy. This novel monochromatic diffraction-free beam maintains the integrity of the central main lobe morphology by allowing the natural evolution of the outer flight envelope. During propagation, the central main lobe and side lobe envelopes maintain partial overlap, the main lobe scale remains stable, while the envelope slowly shifts; once they separate, the optical field rapidly distorts.

[0065] Furthermore, the non-diffraction length—the propagation distance at which the central main lobe and the guiding envelope maintain effective overlap—is determined by the spectral uncertainty. With bandwidth The ratio of these factors determines the outcome. In this experiment, Limited by practical factors such as the pixel size of the spatial light modulator. In a fixed Under the same experimental conditions, different numerical simulations were used to analyze... Based on the propagation behavior under these conditions, it can be deduced that the ideal diffraction-free length of the PST wave packet is likely to exceed 460 times the Rayleigh range. Under the ideal condition of infinite energy, i.e., when the flight envelope extends infinitely, the PST wave packet will be able to achieve distortion-free permanent propagation.

[0066] Example 2

[0067] like Figure 5 As shown in the figure, this invention discloses a method for constructing an accelerated PST Airy packet, comprising the following steps:

[0068] S2-1: Defines the Lorentz acceleration of the beam in the PST domain;

[0069] S2-2: Apply Lorentz acceleration to a beam with a parabolic spectrum in the PST domain;

[0070] S2-3: Superimpose a cubic phase onto the parabolic spectrum in the PST domain described above;

[0071] S2-4: Generate unaccelerated PST Airy packets using a complex amplitude modulation method based on spatial light modulators.

[0072] The above steps will be explained in detail below with specific methods:

[0073] By introducing universal complex amplitude modulation to modulate the spectral trajectory on the pseudocone, novel physical properties can be imparted to the PST wave packet, leading to a series of novel diffraction-free beams. As a typical example, in... Figures 6a-6eThis demonstrates the implementation of PST Airy packet without acceleration. It uses PST wave packet expressions. Starting from the PST domain, apply the Lorentz transformation:

[0074] and ;

[0075] in , , Indicates along The velocity of the reference frame relative to the axis moving in the laboratory coordinate system. and Representing the coordinates after the Lorentz transformation, we can obtain the light field in the new coordinate system:

[0076] ;

[0077] in , , The transformed wavenumber, and This represents the coordinates and light field after the Lorentz transformation.

[0078] When the system operates at a characteristic pseudogroup rate During motion, the expression simplifies to:

[0079] ,

[0080] It is proven that the PST wave packet retains its non-diffraction properties after undergoing the Lorentz transformation, in which... Indicates the tilt angle of the spectral plane. The compression factor representing the spatial transformation, i.e. .

[0081] Figures 6a-6b The spatial intensity distribution of Airy wave packets with uniform spectral amplitude and cubic phase are shown below. The blue curve corresponds to profile. Figure 6c For along The phase measurement results of the axis (red dots represent experimental data, and brown solid lines represent fitted curves) are in high agreement with the theoretical predictions (blue dashed lines). Figure 6d Demonstration of the self-healing properties of Airway packets over a propagation distance of approximately 190 mm: when the main lobe is blocked, through... The measured intensity distribution at the three locations illustrates the reconstruction process. Figure 6e The predicted propagation trajectory of the PST Airy wave packet (solid brown line) and experimental observations (orange dots) both show no lateral acceleration. In contrast, the blue curve shows the acceleration trajectory of a conventional Airy beam with the same initial profile.

[0082] For the Airy beam, which is the only one-dimensional diffraction-free solution to the wave equation, its standard form can be expressed as: ,in It is the Airy function. Characterizing the trajectory of a parabola, This is the phase factor. Therefore, at the corresponding velocity... In the coordinate system, the transformed light intensity distribution satisfies: The formula shows that the acceleration trajectory is frozen in time. The wave packet propagates in a straight line without lateral acceleration, rather than exhibiting dynamic offset during propagation, due to the spatial curvature of the distribution. This characteristic contrasts sharply with the autonomous acceleration behavior of classical Airy beams. The physical essence of this lack of acceleration lies in the unique dynamic compression mechanism of the PST architecture—successfully simulating the behavior of a spatiotemporal pulse during temporal diffraction through diffraction suppression in a single spatial dimension.

[0083] Experimentally, by analyzing PST wave packets ( , ) spectrum applied Axial cubic phase modulation was used to successfully synthesize this novel type of wave packet. For example... Figure 6a As shown, the resulting light field exhibits a typical one-dimensional Airy distribution bent into a parabolic shape, with its transverse intensity distribution... (The blue curve) closely matches the Airy function. Measured phase distribution ( Figure 6b Clearly displayed Cubic phase modulation of the direction, and theoretical predictions ( Figure 6c (To maintain consistency) Figure 6d The transverse section strength shown This confirms that the wave packet always propagates in a straight line without acceleration. Furthermore, we verified its self-healing ability through an occlusion experiment: After several main lobes are blocked at a distance of mm, the wave packet achieves structural self-reconstruction within a propagation distance of approximately 60 mm. Compared to the classic Airy beam, the PST Airy wave packet not only eliminates lateral displacement during propagation ( Figure 6e Furthermore, it increases the non-diffraction propagation distance by 1.5 times, demonstrating significant performance advantages.

[0084] In summary, this application constructs a pseudocone structure by introducing a symmetry-breaking diffraction mechanism, and successfully demonstrates a novel type of diffraction-free beam—the PST wave packet—with approximately parabolic spectral characteristics. Arbitrary tilt angles can be adjusted via the spectral plane intersecting the pseudocone, providing unprecedented flexibility for spectrum modulation engineering. The PST theoretical framework not only breaks through the limitations of traditional ring spectra but also constructs a universal design platform, making the design of diffraction-free beams no longer dependent on exact analytical solutions to the Helmholtz equations. It is particularly noteworthy that the realization of propagation invariance does not solely depend on the parabolic spectrum but originates from the synergistic effect of symmetry-breaking diffraction and the pseudocone dispersion relation—a mechanism that opens a possible path for exploring novel monochromatic diffraction-free beams with variable spectral characteristics. Although the PST wave packet in this application satisfies the paraxial approximation condition, this platform is also applicable to non-paraxial systems, requiring only compensation for lateral displacement effects through coordinate reconstruction. This framework will significantly expand the design dimensions of diffraction-free beams, for example, enabling the realization of PST wave packets with arbitrary trajectories and one-dimensional field PST wave packets with higher interference phase stability. Compared to traditional non-diffraction beams, PST wave packets exhibit superior performance: they have higher energy localization and noise immunity than Bessel beams, and achieve longer non-diffraction propagation distances than Airy beams. These advantages lay a solid foundation for their application in fields such as microscopic imaging, holography, light-matter interaction, and long-distance optical transmission.

[0085] Beyond specific beam design, the PST method reveals a deep spatiotemporal duality between the spatial and temporal dimensions. Existing two-dimensional spatiotemporal duality theories only achieve spatiotemporal simulation of spatial dynamics under anomalous dispersion conditions. This application, however, innovatively proposes a PST non-diffraction beam in free space through relativistic analogy, achieving a reverse extension of the research paradigm. This breakthrough not only restores the bidirectional nature of spatiotemporal duality in free space but also profoundly reveals the essential connection between spatial diffraction and spatiotemporal dynamics. Most importantly, this method, through the effective simulation of the time dimension using spatial coordinates, achieves the spatial reproduction of the light cone structure and the Lorentz transformation in the PST domain. These findings indicate that physical phenomena unique to the spatiotemporal domain can be reconstructed in the PST domain, even providing a theoretical prototype for constructing a "space-pseudo-time-time" three-dimensional system containing the real time dimension.

[0086] At the experimental implementation level, the PST wave packet generation mechanism has significant advantages: compared to spatiotemporal optical pulse schemes that require pulsed laser sources, 4f pulse shaping systems, and complex field scanning devices, this method achieves efficient generation by simplifying experimental configuration. Ultimately, the general framework established by the PST platform not only deepens the understanding of the essence of spatial and spatiotemporal optical fields, but its theoretical system can also be extended to wave physics systems such as acoustics and electronics, providing a new paradigm for interdisciplinary wave manipulation research.

Claims

1. A method of constructing a non-diffracting PST wave packet, characterized by The method comprises the following steps: S1-1: constructing an equivalent pseudo-time dimension in the spatial domain by regulating the spatial scale of the light beam; S1-2: Constructing pseudo-light cone by conical approximation of the region on the equal-frequency sphere using spatial scale transformation, wherein S1-3: Constructing pseudo-light cone by conical approximation of the region on the equal-frequency sphere using spatial scale transformation, wherein S1-4: Constructing pseudo-light cone by conical approximation of the region on the equal-frequency sphere using spatial scale transformation, wherein kx and ky are the x-direction transverse wave number and the y-direction transverse wave number of the spatial spectrum, respectively; S1-3: the spectrum plane intersects with the pseudo-light cone, and the intersection line locus determines the spectrum of the PST wave packet; S1-4: using a complex amplitude modulation method based on a spatial light modulator to generate a non-diffracting PST wave packet.

2. The method of constructing a non-diffracting PST wave packet of claim 1, wherein, The step S1-1 comprises the following steps: For a monochromatic light beam, the dispersion relationship in free space constitutes an equifrequency spherical surface: wherein is the wave number, the undiffracted beam is characterized by its spectral components being concentrated in an annular region, the annular region being composed of monochromatic plane wave components , is the light wave frequency, is the spatial spectral axial wave number; For a multi-color time-space wave packet, the free space dispersion relationship becomes a light cone: wherein denotes the time frequency, is the speed of light in vacuum; The monochromatic light beam follows the paraxial Helmholtz equation: ； wherein represents a monochromatic light beam light field; By introducing a coordinate transformation subject to Lorentz space contraction , , the symmetry breaking in the transverse dimensions is achieved, The transformed equation becomes: where represents the high order terms; neglecting After directional second derivative, the equation is simplified as: ； wherein constitute a pseudo-time dimension.

3. The method of constructing a non-diffracting PST wave packet of claim 1, wherein, The method for constructing the pseudo-light cone in the step S1-2 comprises the following steps: In the PST domain, the cylindrical surface approximation is valid only in the region A further approximation is performed using a conical surface: ； wherein is the conic slope, is the apex of the conic; according to the paraxial approximation requirement, the conic surface satisfies the constraint condition i.e. , and , then and ; in the neighborhood, the conic surface is called a pseudo-light cone.

4. The method of constructing a non-diffracting PST wave packet of claim 3, wherein, The method for obtaining the spectrum of the PST wave packet in the step S1-3 comprises the following steps: The spectrum is constrained to the intersection line of the pseudo-light cone and the tilted spectrum plane: ； After substituting equation (3) into equation (2) and neglecting high-order small quantities, the following equation is obtained: and ignore the minors: ； This equation is used to define the monochromatic PST wave packet of the spectrum , is the angle of inclination of the spectral plane.

5. The method of constructing a non-diffracting PST wave packet of claim 4, wherein, The PST wave packet generated in the step S1-4 is: ； The PST wave packets satisfy i.e. the PST wave packet propagation is independent of transverse movements of the axis, which are eliminated by spectral shifting. transverse movements of the axis, which are eliminated by spectral shifting.

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