A method for generating space-time coherent vortices and space-time dislocations

Abstract

The present invention relates to the field of optical technology, and specifically to a method for generating spatiotemporal coherent vortices and spatiotemporal dislocations. First, the cross spectral density function of a partially coherent pulsed light beam (PCPB) is expressed as an incoherent superposition of multiple spatial frequency domain eigenfunctions; then, a mutual coherence function expression of the PCPB is obtained using Fourier transform, and the expression is expressed as an incoherent superposition of multiple spatial time domain eigenfunctions; then, the spatiotemporal vortex phase is loaded into the eigenfunction of the time space domain to obtain an analytical expression of the mutual coherence function with the spatiotemporal vortex phase PCPB; then, the real part and imaginary part of the mutual coherence function with the spatiotemporal vortex phase PCPB are respectively set to zero; finally, the position where the spatiotemporal coherent vortex and spatiotemporal dislocation are generated is located at a position where both the real part and the imaginary part are zero, i.e., the spatiotemporal coherent vortex and spatiotemporal dislocation are generated. This method conveniently dynamically regulates the spatiotemporal coherent vortex and spatiotemporal dislocation by constructing a partially coherent pulsed light source with spatiotemporal coherent vortices.

Description

Technical Field

[0001] The present invention relates to the field of optical technology, and in particular to a method for generating space-time coherent vortex and space-time dislocation. Background Art

[0002] Manipulating the orbital angular momentum (OAM) of light beams has been a hot topic in recent years in laser technology. By manipulating the OAM degree of freedom on demand, various beam structures can be achieved, offering enormous potential for applications in optical communications, laser processing, optical tweezers, lidar, space exploration, and other fields.

[0003] Traditional OAM manipulation primarily focuses on the longitudinal OAM of steady-state optical beams. Recently, with the development of ultrashort pulse laser technology, OAM manipulation has achieved breakthroughs. Professor Zhan Qiwen's team has creatively combined temporal and spatial field manipulation of ultrashort pulse beams, demonstrating for the first time, both theoretically and experimentally, a novel optical beam with a spatiotemporal vortex phase and transverse OAM. This creates a new OAM degree of freedom and holds significant potential for research and application in optical communications, optical information processing, quantum optics, particle manipulation, alternative energy sources, and relativistic space physics. Unlike longitudinal OAM beams, where the OAM vector is parallel to the beam propagation direction, transverse OAM beams have an OAM vector perpendicular to the beam propagation direction. Because these beams are essentially multicolor light wave packets, they are often referred to as "spatiotemporal vortices." These transverse vortices are common in nature and science, such as tropical cyclones, tornadoes, and the motion of vortex domain walls in magnetic nanowires. Recently, Wan Chenhao et al. realized elegant vortex ring structures in optics based on Maxwell's equations and conformal optical transformations. Professor Lu Yanqing's team used dispersion engineering to achieve a transverse OAM beam with no temporal diffraction and a topological charge greater than 100. Researcher Liu Jun's team used a "step-by-step method" based on diffraction theory to generate a transverse OAM beam.

[0004] However, the above research is limited to the scope of fully coherent beams and does not consider the partial coherence of the beam, which restricts the rapid development of this field.

[0005] In practical applications, ideal, completely coherent light does not exist; commonly, light sources are partially coherent. According to optical coherence theory, the partial coherence of a light source can significantly impact the beam's far-field intensity distribution, polarization distribution, and imaging quality. Particularly in laser long-distance communications, target practice, and imaging, partially coherent beams can reduce bit error rates, eliminate speckle, and improve image clarity. Vortices residing in completely coherent light are called optical vortices, while partially coherent light is referred to as "coherent vortices." They contain more controllable degrees of freedom and offer many unique advantages in light capture, optical communication, and information encryption. For example, the spatial coherence width of a vortex beam can be manipulated to capture particles with different refractive indices. Partially spatially coherent vortex beams can effectively overcome transmission-induced light intensity flicker and beam broadening. The unique spatial or temporal correlation functions of partially coherent pulsed vortex beams not only provide more degrees of freedom for information encryption and transmission, but also offer a variety of new methods for beam shaping.

[0006] Taking into account the time domain, space domain, transverse OAM and partial coherence of the pulsed vortex beam at the same time, it is called "space-time coherent vortex". The existing technology for generating space-time coherent vortex is to load the space-time vortex phase to the source plane, use the diffraction integral formula to obtain the mutual coherence function expression of the far field, and further obtain the space-time vortex phase distribution and space-time intensity distribution. However, this method is not easy to obtain an analytical solution, cannot handle the case where the topological charge is greater than 1, and the calculation is cumbersome and time-consuming. At the same time, it is also very difficult to control the space-time coherent vortex using pulse parameters, and space-time dislocations cannot be generated.

[0007] In view of the above-mentioned technical problems, new methods are needed to solve them. Summary of the Invention

[0008] The purpose of the present invention is to solve the problems involved in the above-mentioned background technology and provide a method for generating spatiotemporal coherent vortices and spatiotemporal dislocations. The present invention utilizes a combination of a coherent mode representation method and a Fourier transform method to construct a partially coherent pulse light source with spatiotemporal coherent vortices, obtains an analytical expression for the mutual coherence function of the pulse light source, demonstrates the influence of pulse parameters on spatiotemporal coherent vortices and spatiotemporal dislocations, and very conveniently dynamically regulates spatiotemporal coherent vortices and spatiotemporal dislocations. This method solves the current problems existing in the transmission and regulation of spatiotemporal coherent vortices.

[0009] Specifically, the present invention adopts the following technical solutions:

[0010] A method for generating space-time coherent vortices and space-time dislocations comprises the following steps:

[0011] The cross spectral density function of partially coherent pulsed beam (PCPB) is expressed as the incoherent superposition of multiple spatial frequency domain eigenfunctions.

[0012] The mutual coherence function expression of PCPB is obtained by Fourier transform, and the expression is expressed as the incoherent superposition of multiple space-time domain eigenfunctions.

[0013] The space-time vortex phase is loaded into the time-space domain eigenfunction, and the analytical expression of the mutual interference function with the space-time vortex phase PCPB is obtained;

[0014] Let the real and imaginary parts of the PCPB mutual interference function with the space-time vortex phase be equal to zero respectively;

[0015] The position where space-time coherent vortex and space-time dislocation are generated is where both the real part and the imaginary part are zero, that is, space-time coherent vortex and space-time dislocation are generated.

[0016] Based on the above method, the specific further scheme is as follows.

[0017] Furthermore, the expression of the cross spectral density function of PCPB is:

[0018]

[0019] In the above formula:

[0020] λ mnk is the weight function of the pattern, which is generally a non-negative real function;

[0021] Subscripts m, n, and k are positive integers greater than 1.

[0022] r represents the horizontal space coordinate vector,

[0023] z represents the transmission distance,

[0024] φ mnk (r,ω,z) is the Hermite-Gaussian norm, defined as:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] d=(a 2 +2ab) 1 / 2 (8);

[0032]

[0033]

[0034] In formula (2):

[0035] H m(n) is an m or n order Hermitian polynomial,

[0036] z0 represents the position of the beam waist plane,

[0037] ω0 represents the pulse carrier frequency,

[0038] w0 and σ0 represent the root mean square beam width and spatial coherence length, respectively.

[0039] T0 and T c represent the pulse width and pulse temporal coherence length, respectively.

[0040] Ω0 and Ω c represent the pulse spectrum width and pulse spectrum coherence length respectively,

[0041] φk(ω) is the source spectral distribution.

[0042] Furthermore, according to Fourier transform, in the time-space domain, the mutual interference function of PCPB can be expressed as:

[0043]

[0044] In formula (11),

[0045] is φ mnk The Fourier transform of (r,ω,z) is denoted as FT[·], that is:

[0046]

[0047] Furthermore, consider the spacetime vortex phase with topological charge q:

[0048]

[0049] In formula (13):

[0050] t and x are time and space coordinates respectively,

[0051] t s and x s is the normalization coefficient;

[0052] Loading the spatiotemporal vortex phase into the eigenfunction of the light field in the time-space domain at the z plane In the build function:

[0053]

[0054] Furthermore, the expression of the PCPB mutual interference function with the space-time vortex phase is:

[0055]

[0056] Equation (15) represents the superposition of multiple coherent modes;

[0057] In actual calculations, for convenience, we consider the mutual interference function of the PCPB composed of two modes to be expressed as:

[0058]

[0059] Formula (16) represents the incoherent superposition of a Gaussian pulse beam at the beam waist z=0 plane and a Hermite-Gaussian pulse beam of order mn at the beam waist z=z0 plane.

[0060] Furthermore, considering the one-dimensional case, that is, y = 0, the expressions of the first mode and the second mode are:

[0061]

[0062]

[0063] Furthermore, Equation (16) is used to study the spatiotemporal coherent vortices and spatiotemporal dislocations of PCPB at z1 = z2 = z. The spatiotemporal locations of the spatiotemporal coherent vortices and spatiotemporal dislocations are determined by the real and imaginary parts of the mutual coherence function:

[0064] Re[Γ′(x1,x2,t1,t2,z1,z2)]=0 (19);

[0065] Im[Γ′(x1,x2,t1,t2,z1,z2)]=0 (20);

[0066] In formulas (19) and (20):

[0067] Re and Im represent the real and imaginary parts of the mutual interference function Γ′(x1,x2,t1,t2,z1,z2), respectively;

[0068] The topological charge of a coherent vortex and its sign are determined by the sign principle;

[0069] When x1=x2, t1=t2, z1=z2, the expression of space-time intensity is I(x2, t2, z2):

[0070]

[0071] Using Equations (16) to (21), the phase distribution of the PCPB mutual coherence function, the function curves with the real and imaginary parts equal to zero, the modulus of the mutual coherence function, and the spatiotemporal intensity distribution of the PCPB are numerically calculated to obtain the relevant distribution diagrams. At the same time, the effects of pulse parameters such as the waist spacing z0 between the two modes, the reference point (x1, t1), the beam order m, the source spectral distribution (determined by the k parameter), the topological charge q, and the mode weight λ1 / λ2 on the spatiotemporal coherent vortices and spatiotemporal dislocations are displayed.

[0072] With respect to the above-mentioned method, the present invention demonstrates in detail the influence of pulse parameters on spatiotemporal coherent vortices and spatiotemporal dislocations.

[0073] Firstly, the cross-spectral density function of a partially coherent pulsed beam (PCPB) is expressed as the incoherent superposition of multiple spatial frequency domain eigenfunctions. The mutual coherence function expression of the PCPB is obtained by Fourier transform, and this expression is expressed as the incoherent superposition of multiple spatial time domain eigenfunctions.

[0074] Then, the space-time vortex phase is loaded into the time-space domain eigenfunction to obtain the analytical expression of the mutual interference function with the space-time vortex phase PCPB, and the real and imaginary parts of the mutual interference function with the space-time vortex phase PCPB are set to zero respectively;

[0075] Then, the phase structure and intensity distribution of the spatiotemporal coherent vortex and spatiotemporal dislocation are plotted; the positions of the spatiotemporal coherent vortex and spatiotemporal dislocation are determined using the intersection of the real part equal to zero curve and the imaginary part equal to zero curve;

[0076] Finally, the regulation and influence of pulse parameters on spatiotemporal coherent vortices and spatiotemporal dislocations are demonstrated.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] A method for generating spatiotemporal coherent vortices and spatiotemporal dislocations is provided. By combining the coherent module representation method with the Fourier transform method, a partially coherent pulse light source with spatiotemporal coherent vortices is constructed, and an analytical expression of the mutual coherence function of the pulse light source is obtained. The influence of pulse parameters on the spatiotemporal coherent vortices and spatiotemporal dislocations is demonstrated, and the spatiotemporal coherent vortices and spatiotemporal dislocations can be dynamically controlled very conveniently. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 Given are the phase distribution (a)-(d) of the PCPB mutual interference function under different spacing z0 between the two mode waist positions, the curves with the real and imaginary parts equal to zero (e)-(h), the modulus (i)-(l) of the mutual interference function, and the spatiotemporal intensity distribution (m)-(p) of the PCPB.

[0080] Figure 2The phase distribution of the PCPB mutual interference function and the distribution of the corresponding modes are given under different reference points.

[0081] Figure 3 The phase distribution of the PCPB mutual coherence function and the corresponding mode distribution are given for different beam orders.

[0082] Figure 4 The phase distribution of the PCPB mutual coherence function and the distribution of the corresponding modes under different k parameters are given.

[0083] Figure 5 Normalized source spectra and temporal intensities for different k parameters are given.

[0084] Figure 6 The phase distribution of the PCPB mutual coherence function and the distribution of the corresponding modes under different topological charges are given.

[0085] Figure 7 The phase distributions of the PCPB mutual interference functions under different mode weights are given (a)-(c), (g)-(i) and the corresponding graphs of the real and imaginary parts equal to zero (d)-(f), (j)-(l). DETAILED DESCRIPTION

[0086] Representative embodiments will now be further refined. It should be understood that the following description is not intended to limit the embodiments to a preferred embodiment. On the contrary, it is intended to encompass alternatives, modifications, and equivalents that may be included within the spirit and scope of the embodiments defined by the appended claims.

[0087] Embodiment: Specific examples are used to illustrate in detail.

[0088] A method for generating space-time coherent vortices and space-time dislocations comprises the following steps:

[0089] The cross spectral density function of partially coherent pulsed beam (PCPB) is expressed as the incoherent superposition of multiple spatial frequency domain eigenfunctions.

[0090] The mutual coherence function expression of PCPB is obtained by Fourier transform, and the expression is expressed as the incoherent superposition of multiple space-time domain eigenfunctions.

[0091] The space-time vortex phase is loaded into the time-space domain eigenfunction, and the analytical expression of the mutual interference function with the space-time vortex phase PCPB is obtained;

[0092] Let the real and imaginary parts of the PCPB mutual interference function with the space-time vortex phase be equal to zero respectively;

[0093] The position where space-time coherent vortex and space-time dislocation are generated is where both the real part and the imaginary part are zero, that is, space-time coherent vortex and space-time dislocation are generated.

[0094] Based on the above method, the specific further scheme is as follows.

[0095] First, the cross-spectral density function of the partially coherent pulsed beam (PCPB) is expressed as the incoherent superposition of multiple spatial frequency domain eigenfunctions; the expression of the cross-spectral density function of the PCPB is:

[0096]

[0097] In the above formula:

[0098] λ mnk is the weight function of the pattern, which is generally a non-negative real function;

[0099] Subscripts m, n, and k are positive integers greater than 1.

[0100] r represents the horizontal space coordinate vector,

[0101] z represents the transmission distance,

[0102] φ mnk (r,ω,z) is the Hermite-Gaussian norm, defined as:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] d=(a 2 +2ab) 1 / 2 (8);

[0110]

[0111]

[0112] In formula (2):

[0113] H m(n) is an m or n order Hermitian polynomial,

[0114] z0 represents the position of the beam waist plane,

[0115] ω0 represents the pulse carrier frequency,

[0116] w0 and σ0 represent the root mean square beam width and spatial coherence length, respectively.

[0117] T0 and T c represent the pulse width and pulse temporal coherence length, respectively.

[0118] Ω0 and Ω c represent the pulse spectrum width and pulse spectrum coherence length respectively,

[0119] φ k (ω) is the source spectral distribution.

[0120] Second, the mutual interference function expression of PCPB is obtained by Fourier transform, and this expression is expressed as the incoherent superposition of multiple space-time domain eigenfunctions. According to Fourier transform, the mutual interference function of PCPB in the space-time domain can be expressed as:

[0121]

[0122] In formula (11),

[0123] is φ mnk The Fourier transform of (r,ω,z) is denoted as FT[·], that is:

[0124]

[0125] Third, consider the phase of a spacetime vortex with topological charge q:

[0126]

[0127] In formula (13):

[0128] t and x are time and space coordinates respectively,

[0129] t s and x s is the normalization coefficient;

[0130] Loading the spatiotemporal vortex phase into the eigenfunction of the light field in the time-space domain at the z plane In the build function:

[0131]

[0132] The expression of the PCPB mutual interference function with the space-time vortex phase is:

[0133]

[0134] Equation (15) represents the superposition of multiple coherent modes;

[0135] In actual calculations, for convenience, we consider the mutual interference function of the PCPB composed of two modes to be expressed as:

[0136]

[0137] Formula (16) represents the incoherent superposition of a Gaussian pulse beam at the beam waist z=0 plane and a Hermite-Gaussian pulse beam of order mn at the beam waist z=z0 plane.

[0138] Fourth, considering the one-dimensional case, that is, y = 0, the expressions of the first mode and the second mode are:

[0139]

[0140]

[0141] Fifth, the spatiotemporal coherent vortices and spatiotemporal dislocations of PCPB at z1 = z2 = z are studied using Equation (16). The spatiotemporal locations of the spatiotemporal coherent vortices and spatiotemporal dislocations are determined by the real and imaginary parts of the mutual coherence function:

[0142] Re[Γ′(x1,x2,t1,t2,z1,z2)]=0 (19);

[0143] Im[Γ′(x1,x2,t1,t2,z1,z2)]=0 (20);

[0144] In formulas (19) and (20):

[0145] Re and Im represent the real and imaginary parts of the mutual interference function Γ′(x1,x2,t1,t2,z1,z2), respectively;

[0146] The topological charge of a coherent vortex and its sign are determined by the sign principle;

[0147] When x1=x2, t1=t2, z1=z2, the expression of space-time intensity is I(x2, t2, z2):

[0148]

[0149] Using Equations (16) to (21), the phase distribution of the PCPB mutual coherence function, the function curves with the real and imaginary parts equal to zero, the modulus of the mutual coherence function, and the spatiotemporal intensity distribution of the PCPB are numerically calculated to obtain the relevant distribution diagrams. At the same time, the effects of pulse parameters such as the waist spacing z0 between the two modes, the reference point (x1, t1), the beam order m, the source spectral distribution (determined by the k parameter), the topological charge q, and the mode weight λ1 / λ2 on the spatiotemporal coherent vortices and spatiotemporal dislocations are displayed.

[0150] Assume that the calculation parameters z1=z2=0,z0=-0.1m,center wavelength λ=800nm,c=3×10 8 m / s,w0=σ=2mm,T0=T c =5fs,x s =1mm,τ s =1fs, x1=1mm, t1=1fs, k=0, q=1, λ1=1, λ2=1, m=1.

[0151] Based on the above method analysis, further detailed analysis is carried out in the form of icons.

[0152] Figure 1 The phase distribution (a)-(d) of the PCPB mutual interference function, the curves with the real and imaginary parts equal to zero (e)-(h), the modulus (i)-(l) of the mutual interference function and the spatiotemporal intensity distribution (m)-(p) of the PCPB are shown for different spacings z0 between the two mode waist positions.

[0153] from Figure 1 (a) It can be seen that when z0 = -0.1m, a space-time coherent vortex appears at the origin (x2 = 0, t2 = 0), and a space-time dislocation line appears in the x2-t2 plane. The positions where they appear correspond to the positions where the modulus of the mutual coherence function is equal to zero, rather than the positions where the space-time intensity is equal to zero (as can be seen from the equation (17) describing the first mode, it is non-zero, and this characteristic is similar to the spatial coherent vortex). When the distance between the waist positions of the two modes increases, the position of the space-time coherent vortex does not change, but the space-time dislocation line gradually becomes shorter (see Figure 1 (f)-(h)), numerical calculations show that the space-time dislocation line disappears when z0 is less than -3. This is because when the distance between the two modes increases, their coupling effect weakens, eventually leading to the disappearance of the space-time dislocation line.

[0154] Figure 2 The phase distribution of the PCPB mutual coherence function and the distribution of the corresponding modes under different reference points are shown.

[0155] As can be seen from the figure, the reference point has a greater influence on the space-time dislocation line, but has an insignificant influence on the space-time coherent vortex. As the reference point position increases, the space-time dislocation line gradually approaches the space-time coherent vortex. When the reference point position is x1=10mm, t1=10fs, the space-time dislocation line and the space-time coherent vortex coincide.

[0156] At the same time, as the reference point position increases, the value of the mutual interference function modulus near the space-time dislocation line becomes larger and larger. This shows that the space-time dislocation line occupies an increasingly large proportion in the process of interaction with the space-time coherent vortex.

[0157] Figure 3 The phase distribution of the PCPB mutual coherence function and the distribution of the corresponding modes are shown under different beam orders.

[0158] It can be seen from Figures (a)-(f) that when the order m = 0, the space-time dislocation line does not exist. When the order m = 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 space-time dislocation lines appear respectively. The number of space-time dislocation lines appears in one-to-one correspondence with the value of m.

[0159] As can be seen from Figures (g)-(l), the space-time dislocation lines always appear at the position where the modulus of the PCPB mutual interference function is equal to zero, and the distribution of the modulus of the PCPB mutual interference function is symmetrical about the x2=0 axis.

[0160] This result can be seen from the eigenfunction of the second mode. m00 (·) contains the Hermitian polynomial H m (·), which contains m zero-value points and shows m space-time dislocation lines in the space-time plane. At the same time, this figure also shows that the space-time dislocation lines originate from the second mode.

[0161] Figure 4 The phase distribution of the PCPB mutual coherence function and the distribution of the corresponding modes are shown under different k parameters.

[0162] As can be seen from the figure, the k parameter has a significant impact on the space-time dislocation, causing the space-time dislocation line to be cut off. Depending on the value of k, the space-time dislocation line is cut into k+1 segments. This is also the result of space-time coupling.

[0163] This result can be further explained by formula (7), from which the expression of source spectral density can be obtained as S(ω)=|φ k (ω)| 2 , we can further obtain the time intensity S(t)=|FT[φ k (ω)]| 2 .

[0164] Figure 5The normalized source spectra and time intensity under different k parameters are shown. It can be seen from the figure that different k parameters correspond to different source spectra ( Figure 5 (a)-(c)), also corresponding to different time intensities ( Figure 5 (d)-(f)), by Figure 5 (d)-(f) show that when k = 1, the intensity zero value appears at t = 0, when k = 2, the intensity zero value appears at t = ± 2.7fs, and when k = 3, the intensity zero values ​​appear at t = 0 and t = ± 4.7fs respectively. The positions of these intensity zero values ​​are Figure 4 The positions where the space-time dislocation lines are truncated in (a)-(c) correspond.

[0165] Figure 6 The phase distribution of the PCPB mutual coherence function and the distribution of the corresponding modes under different topological charges are shown.

[0166] As can be seen from the figure, when the topological charge q = +1, the phase of the space-time coherent vortex rotates counterclockwise once and increases by 2π.

[0167] When the topological charge q = +2 and q = +3, the phase of the spacetime coherent vortex rotates counterclockwise, increasing by 4π and 6π respectively. When the topological charge q = -1, the phase of the spacetime coherent vortex rotates clockwise, increasing by 2π.

[0168] When the topological charge q = +2 and q = +3, the phase of the spacetime coherent vortex rotates clockwise by one circle, increasing by 4π and 6π respectively. The topological charge q has no effect on the spacetime dislocation line. Figure 6 (g)-(i) show the modulus of the PCPB mutual interference function under different topological charges q = ±1, q = ±2, and q = ±3. It can be seen from the figure that as the topological charge |q| increases, the size of the spacetime vortex core increases.

[0169] Figure 7 The phase distributions of the PCPB mutual interference functions for different mode weights (a)-(c), (g)-(i) and the corresponding graphs with the real and imaginary parts equal to zero (d)-(f), (j)-(l) are shown.

[0170] Depend on Figure 7 (a)-(f) combination Figure 6 (a) It can be seen that as the weight λ1 of the first mode increases, the space-time dislocation line moves away from the origin. When the weight increases to a certain extent, the space-time dislocation line disappears ( Figure 7 (c)). This result also shows that the spatiotemporal dislocation line is mainly determined by the second mode. When the weight λ1 of the first mode increases, the influence of the second mode decreases. If the weight λ2 of the second mode is increased, as shown in Figure 7(g)-(l), the spacetime dislocation line is close to the spacetime coherent vortex and always exists. When the weight λ2 of the second mode is large enough, the position of the spacetime dislocation line and the spacetime coherent vortex (x2=0, t2=0) coincides. This is also a demonstration of the interaction between the two modes. In addition, the change of weight λ1 or λ2 also has a strong dependence on coherence. In principle, when λ1 / λ2 or λ2 / λ1 becomes infinite, the beam becomes completely coherent. When λ1 / λ2 takes a general value, the beam is partially coherent. This reflects the influence of coherence on spacetime coherent vortex or spacetime dislocation.

[0171] This paper, using coherent mode representation and Fourier transform methods, constructs a PCPB using the incoherent superposition of two beam modes, Gaussian and Hermite-Gaussian pulses. This demonstrates a new method for generating spatiotemporal coherent vortices and spatiotemporal dislocations. Using the superposition of two modes as an example, the authors reveal the influence of pulse parameters such as the waist spacing z0 between the two modes, the reference point (x1, t1), the beam order m, the source spectral distribution (determined by the k parameter), the topological charge q, and the mode weights λ1 and λ2 on the spatiotemporal coherent vortices and spatiotemporal dislocations. It is found that space-time coherent vortices and space-time dislocation lines appear in the space-time plane. When the topological charge q increases, the space-time coherent vortex phase distribution and the size of the vortex core change. When the beam waist spacing z0 or the weight λ1 is large, the space-time dislocation line disappears. The beam order m of the Hermite Gaussian pulse beam is consistent with the number of space-time dislocation lines. The source spectrum distribution has a greater impact on the space-time dislocation line. Depending on the k parameter, the space-time dislocation line is cut into k+1 line segments respectively. When the reference point position becomes larger or the weight λ1 becomes larger, the space-time dislocation line approaches the origin position and eventually coincides with the origin. The method provided by the present invention will solve the problems that space-time coherent vortices and space-time dislocations cannot handle the situation where the topological charge is greater than 1 and the calculation takes a long time. It is expected to have important application value in the fields of beam shaping, optical tweezers, spin-orbit angular momentum coupling, quantum communication, etc.

[0172] It is obvious to those skilled in the art that certain modifications, combinations and variations can be made based on the above teachings.

Claims

1. A method for generating spatiotemporal coherent vortices and spatiotemporal dislocations, characterized by: The following steps are involved: The cross spectral density function of partially coherent pulsed beam (PCPB) is expressed as the incoherent superposition of multiple spatial frequency domain eigenfunctions. The mutual coherence function expression of PCPB is obtained by Fourier transform, and the expression is expressed as the incoherent superposition of multiple space-time domain eigenfunctions. The space-time vortex phase is loaded into the time-space domain eigenfunction, and the analytical expression of the mutual interference function with the space-time vortex phase PCPB is obtained; Let the real and imaginary parts of the PCPB mutual interference function with the space-time vortex phase be equal to zero respectively; The position where space-time coherent vortex and space-time dislocation are generated is where both the real part and the imaginary part are zero, that is, space-time coherent vortex and space-time dislocation are generated.

2. The method according to claim 1, wherein: The expression of the cross spectral density function of PCPB is: In the above formula: λ mnk is the weight function of the pattern, Subscripts m, n, and k are positive integers greater than 1. r represents the horizontal space coordinate vector, z represents the transmission distance, φ mnk (r,ω,z) is the Hermite-Gaussian norm, defined as: <h2 style=";text-align:left;direction:ltr">d=(a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2ab)<h2 style=";text-align:left;direction:ltr"> 1 / 2 <h2 style=";text-align:left;direction:ltr"> (8); In formula (2): H m(n) is an m or n order Hermitian polynomial, z0 represents the position of the beam waist plane, ω0 represents the pulse carrier frequency, w0 and σ0 represent the root mean square beam width and spatial coherence length, respectively. T0 and T c represent the pulse width and pulse temporal coherence length, respectively. Ω0 and Ω c represent the pulse spectrum width and pulse spectrum coherence length respectively, φ k (ω) is the source spectral distribution.

3. The method according to claim 1, wherein: According to Fourier transform, in the time-space domain, the mutual interference function of PCPB can be expressed as: In formula (11), is φ mnk The Fourier transform of (r,ω,z) is denoted as FT[·], that is:

4. The method according to claim 3, wherein: Consider the phase of a spacetime vortex with topological charge q: In formula (13): t and x are time and space coordinates respectively, t s and x s is the normalization coefficient; Loading the spatiotemporal vortex phase into the eigenfunction of the light field in the time-space domain at the z plane In the build function:

5. The method according to claim 4, characterized in that: The expression of the PCPB mutual interference function with the space-time vortex phase is: Equation (15) represents the superposition of multiple coherent modes; In actual calculations, the mutual interference function of the PCPB composed of two modes is expressed as: Formula (16) represents the incoherent superposition of a Gaussian pulse beam at the beam waist z=0 plane and a Hermite-Gaussian pulse beam of order mn at the beam waist z=z0 plane.

6. The method according to claim 5, characterized in that: In the one-dimensional case, that is, y = 0, the expressions of the first mode and the second mode are:

7. The method according to claim 6, characterized in that: Equation (16) is used to study the spatiotemporal coherent vortices and spatiotemporal dislocations of PCPB at z1 = z2 = z. The spatiotemporal locations of the spatiotemporal coherent vortices and spatiotemporal dislocations are determined by the real and imaginary parts of the mutual coherence function: Re[Γ′(x1,x2,t1,t2,z1,z2)]=0 (19); Im[Γ′(x1,x2,t1,t2,z1,z2)]=0 (20); In formulas (19) and (20): Re and Im represent the real and imaginary parts of the mutual interference function Γ′(x1,x2,t1,t2,z1,z2), respectively; The topological charge of a coherent vortex and its sign are determined by the sign principle; When x1=x2, t1=t2, z1=z2, the expression of space-time intensity is I(x2, t2, z2): Using Equations (16) to (21), the phase distribution of the PCPB mutual coherence function, the function curves with the real and imaginary parts equal to zero, the modulus of the mutual coherence function, and the spatiotemporal intensity distribution of the PCPB are numerically calculated to obtain the relevant distribution diagrams. At the same time, the effects of pulse parameters such as the waist spacing z0 between the two modes, the reference point (x1, t1), the beam order m, the source spectral distribution (determined by the k parameter), the topological charge q, and the mode weight λ1 / λ2 on the spatiotemporal coherent vortices and spatiotemporal dislocations are displayed.

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