A flight focus focusing element based on spatial discrete focusing and time delay control

Abstract

This invention discloses a flight focus element based on spatial discrete focusing and time delay control, belonging to the field of optical device technology. It employs a multi-ring stepped lens to achieve spatial discrete focusing, with each ring having a different focal length, causing the incident laser to converge at different positions along the optical axis, forming an extended discrete focal zone. Simultaneously, the stepped thickness of each ring introduces different optical path delays, forming a staggered time sequence. This spatial and temporal coordination achieves a flight focus with controllable propagation speed. As a specific embodiment, the focusing element is preferably fabricated using acrylic material, but optical glass can also be used. A five-focal design is adopted, with an adjacent focal distance of 2.5 mm. The tested flight focus velocity is -2.6 × 10⁸ m / s, close to the reverse light speed -c. This invention does not require broadening the pump pulse width, has a simple structure, is easy to fabricate, and has high laser utilization efficiency, showing broad application prospects in back-air laser enhancement, atmospheric remote sensing, laser micromachining, and laser wake field acceleration.

Description

Technical Field

[0001] This invention belongs to the field of optical device technology and relates to the design of a flight focus element based on spatial discrete focusing and time delay control, specifically a multifocal Fresnel stepped lens made of acrylic material. This element achieves spatial discrete focusing through different focal lengths in each ring, and achieves time delay control through the stepped thickness variation of each ring. These two aspects work together to form a dynamically moving discrete flight focus, which is characterized by low cost and simple fabrication. Background Technology

[0002] Flying focus technology is an advanced laser control method that actively introduces spatiotemporal coupling to enable the laser focus to move at an arbitrary controllable speed (including superluminal and backward propagation) independent of the light group velocity within an extended focal area far exceeding the Rayleigh length. It has important application prospects in laser micromachining, laser wake field acceleration, terahertz wave control, and atmospheric remote sensing.

[0003] Traditional flying-focusing techniques combine diffraction elements with chirped pulses, controlling the focus velocity by adjusting the chirp and pulse width. However, this technique has significant limitations in applications such as laser filament generation and back-air laser enhancement: First, the laser utilization efficiency of diffraction elements is generally low, and they are expensive; more importantly, the focus velocity control in this approach depends on adjusting the chirped pulse width. For back-air laser enhancement, the pulse width of the femtosecond laser often needs to be extended to the tens of picoseconds, resulting in a significant decrease in peak pulse power. Under these conditions, the laser intensity at the focus often fails to reach the threshold required for atmospheric ionization, thus limiting the practical application of this technique in laser filament generation and back-air laser enhancement. Summary of the Invention

[0004] This invention addresses the challenges of low laser utilization efficiency and high fabrication costs in diffraction elements, as well as the dependence of flight focus velocity control on the incident laser pulse width. For back-to-air laser enhancement, the pulse width needs to be broadened to tens of picoseconds, but wide-pulse-width lasers are difficult to effectively generate filamentary and air lasers. To address these challenges, a flight focus focusing element based on spatial discrete focusing and time delay control is proposed. This focusing element is low-cost and easy to fabricate. By precisely controlling the spatiotemporal convergence characteristics of the laser pulse, it effectively overcomes the pulse width limitations of traditional methods, successfully achieving a high-intensity laser flight focus. This significantly improves the effective gain length of back-to-air lasers, thereby enhancing the output of back-to-air lasers.

[0005] The technical solution of the present invention is as follows:

[0006] This patent proposes a flight focus element based on spatial discrete focusing and time delay control. The focusing element includes: at least two stepped lenses with rings, each ring of the stepped lens having a preset focal length and thickness. By independently adjusting the focal length of each ring, the incident light forms different focal points after passing through different rings, thereby precisely controlling the convergence of the light emitted from each ring at a specified position on the receiving surface, providing adjustable spatial focusing; further adjusting the stepped thickness provides a radially varying time delay, achieving a flight focus of -c.

[0007] In this invention, the adjustable spatial focusing element employs a multifocal Fresnel lens. The lens's refraction effect occurs only on the optical surface. During imaging, the Fresnel lens's surface curvature plays a decisive role in deflecting light, while the lens's thickness contributes little to the imaging. The Fresnel lens transforms the continuous, thick curved surface of a traditional convex lens by removing portions that have no impact on imaging, compressing them onto a flat substrate, and decomposing them into a series of concentric, serrated ring structures. Each ring corresponds to a segment of the original lens at that location. After these segments are aligned to the same plane, they retain the deflection angle of the corresponding portion of the original lens. When parallel light rays are incident, these serrated ring structures refract and converge the light to a single focal point, thus achieving a focusing effect similar to that of a traditional convex lens.

[0008] In this invention, each ring of the focusing element is designed with a different focal length, so that the incident parallel laser beam converges at different spatial positions along the optical axis after passing through different rings. The axial distribution of these discrete focal points together constitutes an extended focusing region, the total length of which is determined by the focal length difference between the innermost and outermost rings.

[0009] In this invention, the focusing element needs to optimize the surface curvature so that the diameter of the spot where each ring converges is smaller than the Airy disk, so that it can reach the atmospheric ionization threshold, thereby generating a filament and a laser beam against the air.

[0010] In this invention, acrylic (PMMA, polymethyl methacrylate) is the preferred material for the focusing element. It has the advantages of low cost, easy processing and good light transmittance, and is suitable for rapid prototyping and mass production. Optical glass (such as K9, quartz glass) or other transparent media materials can also be selected.

[0011] In this invention, the time delay module adjusts the thickness of different rings to focus lasers incident on the optical axis within a controllable time delay, forming an extended focusing area.

[0012] In this invention, the inner and outer radii of each ring of the lens need to be determined according to the energy distribution of the incident light spot to ensure that the laser energy transmitted through each ring remains uniform.

[0013] In this invention, the propagation speed v of the flight focus is comprehensively controlled by two factors: the focal length of each ring of the multifocal Fresnel lens and the radially varying thickness. The specific formula is as follows:

[0014] (1)

[0015] Where Δf is the focal length difference between two adjacent annular lenses of the designed multifocal Fresnel lens, ΔL is the thickness difference between two adjacent annular lenses, n1 is the refractive index of the lens material, and n0 is the refractive index of air.

[0016] In this invention, the propagation speed of the flight focus can be continuously adjusted from a standstill to several times the speed of light, including motion modes that are the same as or opposite to the direction of laser pulse propagation.

[0017] In this invention, the flight focus forms a dynamically moving high-intensity region in the medium, which can continuously maintain a power density higher than the excitation threshold of the medium, thereby achieving efficient population inversion.

[0018] The advantages and beneficial effects of this invention are:

[0019] This invention combines technological innovation with practical advantages. Through an innovative spatiotemporal coupling control mechanism, it achieves a flying focus without widening the pump pulse width, effectively avoiding the peak power reduction problem caused by pulse width widening in traditional technologies, and ensuring that the laser intensity at the focal point consistently reaches the medium ionization threshold. The focusing element is made of acrylic material, and the inner and outer radii of the rings are optimized by equal power division. This not only simplifies the fabrication process, reduces costs, and makes it suitable for mass production, but also achieves a laser utilization efficiency of over 95%, significantly reducing energy loss. By co-designing the focal length and thickness differences of each ring, it can achieve a focusing range from stationary to several times the speed of light. This device allows for precise control of the flight focus velocity within its range, supporting both forward and reverse propagation modes. The reverse propagation speed extends the effective gain length of the back-to-air laser from millimeters to centimeters, significantly enhancing its output intensity. Furthermore, this component eliminates the need for complex components such as external control fields and multiple laser paths, resulting in a simple, compact system structure that is easy to integrate and debug optically. It significantly improves the conversion efficiency, output intensity, and effective working distance of back-to-air lasers while maintaining excellent beam quality. This provides a novel technical solution for fields such as laser micromachining, laser wake field acceleration, atmospheric remote sensing, and environmental monitoring, demonstrating broad application prospects and outstanding practical value. Attached Figure Description

[0020] Figure 1 A schematic diagram of the focusing optical path of the focusing element for flight focus based on spatial discrete focusing and time delay control is shown.

[0021] Figure 2 A schematic diagram of the focusing element ring structure is shown.

[0022] Figure 3 The figure shows the division of the rings in a focusing element that achieves equal intensity distribution when the incident light energy has a Gaussian distribution.

[0023] Figure 4 A physical image of the focusing element for multifocal flight is shown.

[0024] Figure 5 A schematic diagram of a Fresnel lens-based discrete flight focus focusing element for a back-to-air laser enhancement experimental setup is shown.

[0025] Figure 6 The experimental results of a five-focal-flying-focal femtosecond filament based on a Fresnel lens are shown.

[0026] Figure 7 The flight focus speed test diagram is shown.

[0027] In the diagram: 1. Laser; 2. Beam splitter; 3. Delay line; 4. Beam expander lens group; 5. Multifocal flying focus focusing element; 6. Multifocal filament; 7. Mirror; 8. BBO; 9. Filter; 10. Mirror; 11. Beam expander lens group; 12. Plano-convex lens; 13. CCD camera. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings and preliminary embodiments, so that those skilled in the art can more clearly understand the present invention.

[0029] This invention proposes a flying focus focusing element based on spatial discrete focusing and time delay control. The flying focus focusing element described in this invention achieves coordinated control of spatial focusing and time delay through an innovative stepped lens structure. It achieves flying focus while maintaining a constant pump pulse width, effectively avoiding the peak power reduction problem caused by pulse width broadening in traditional technologies, and ensuring that the laser intensity at the focal point reaches the ionization threshold. The focusing element uses acrylic material, and the inner and outer radii of each ring are optimized through an equal power division method, achieving a laser utilization efficiency of over 95%. It is low-cost, easy to fabricate, and suitable for mass production. By designing the focal length and thickness differences of each ring, the flying focus speed can be precisely controlled from rest to several times the speed of light. Experiments show that the flying focus speed of the five-focal focusing element is close to the speed of light in the reverse propagation direction -c, which can extend the effective gain length from the millimeter level to the centimeter level, significantly enhancing the laser output intensity against the air. Furthermore, the system has a simple structure and is easy to integrate, showing broad application prospects in laser micromachining, laser wake field acceleration, atmospheric remote sensing, and laser enhancement against the air.

[0030] The following are the specific design steps for the five-focal-focusing flight focus element:

[0031] Step 1: Calculate the thickness of each annular lens according to the required time delay.

[0032] To achieve the flight focus, this invention provides radial delay by varying the thickness L of different rings. Light has a refractive index of n0 in air and n1 in the stepped lens medium. Therefore, the resulting time delay is Δt = L / c(n1 - n0).

[0033] Step 2: Calculate the inner and outer radii of each ring based on the energy distribution of the incident light spot. Taking Gaussian light as an example, to ensure equal light intensity at the focal point, the transmitted light intensity of the stepped lens ring needs to be calculated. The default input laser is a standard Gaussian type, with the intensity I(r) distribution as follows:

[0034] (2)

[0035] Where r is the radial distance to the center of the beam spot, and ω is the beam waist radius of the Gaussian beam. The total power P of the incident focusing element... total As shown in formula (3), where I0 is the peak light intensity, R max This represents the maximum radius of the focusing element.

[0036] (3)

[0037] Step 3: To avoid excessive spherical aberration in the outer rings, resulting in a large focused spot that makes it difficult to reach the ionization threshold at the focal point, a suitable lens needs to be selected, typically an aspherical lens. Each ring lens is optimized to make its output spot approximate the Airy disk, ensuring that the power density at each focal point reaches the ionization threshold of air.

[0038] The focusing element of this invention is preferably made of acrylic (PMMA, polymethyl methacrylate) material, but other transparent media such as optical glass (e.g., K9, quartz) can also be used as needed. Acrylic material has advantages such as low cost, good light transmittance, and ease of processing and molding, making it suitable for mass production.

[0039] The specific processing steps are as follows:

[0040] 1. 3D modeling: Based on the focal length, thickness, and inner and outer radii of each ring, a 3D structural model of the focusing element is established.

[0041] 2. CNC Precision Machining: Multi-axis CNC precision engraving machines (such as diamond single-point cutting machines) are used to process the acrylic blanks. The machining accuracy is controlled within ±0.01 mm, and the surface roughness Ra < 20 nm. The stepped structure and surface curvature of each ring are formed sequentially through layered cutting.

[0042] 3. Optical polishing: The curved surface of each ring is locally polished to eliminate machining marks, reduce light scattering loss, and ensure that the converging light spot approaches the Airy disk to reach the dielectric ionization threshold.

[0043] 4. Cleaning and drying: Use anhydrous ethanol or isopropanol to ultrasonically clean the surface of the component to remove oil and debris, and then air dry or blow dry with nitrogen.

[0044] 5. Antireflection coating deposition: If it is necessary to further improve the transmittance or damage resistance threshold, an antireflection coating (such as MgF2 or SiO2 / TiO2 multilayer film in the 800 nm band) can be deposited on the surface of the component.

[0045] The focusing element prepared by the above process has high structural precision, good surface quality, and a significantly lower unit cost than traditional diffractive optical elements, making it suitable for laboratory research and industrial application.

[0046] On the other hand, the present invention also provides a method for characterizing femtosecond filaments and testing flight focus velocities based on multifocal flight focus focusing elements:

[0047] The beam distribution of the back-to-air laser was measured using a CCD camera to analyze its beam quality and divergence angle. The spectral characteristics of the back radiation, including the center wavelength, bandwidth, and spectral line shape, were recorded using a high-resolution spectrometer. The pulse energy and average power of the back laser were measured using an energy meter to calculate the energy conversion efficiency. The temporal characteristics of the back signal were recorded using a high-speed oscilloscope and a photodetector to analyze its temporal relationship with the motion of the flight focus.

[0048] The spatiotemporal evolution characteristics of the flight focus were measured using a pump-probe plasma diffraction method. The specific configuration was as follows: a frequency-doubled femtosecond laser beam with a center wavelength of 400 nm was used as the probe beam, illuminating the interaction region perpendicular to the flight focus propagation direction. The probe beam pulse width was 50 fs, the repetition frequency was the same as the pump laser, and the single-pulse energy was 100 μJ. A precision optical delay line was incorporated into the probe beam path, with a delay adjustment range of 0-500 ps and a resolution of 10 fs, to precisely control the time delay between the pump and probe beams.

[0049] When the probe light passes through the plasma channel generated by the focal point of flight, the refractive index change caused by the plasma modulates the wavefront phase of the probe light, producing a diffraction effect. The diffraction pattern carrying information about the spatial distribution of plasma density is collected by an imaging lens and recorded by a scientific-grade CCD camera.

[0050] During measurement, pump light parameters are fixed, and the pump-probe time delay is continuously varied using a delay line. Multiple diffraction images are acquired at each delay position and averaged. By analyzing the spatial evolution characteristics of the diffraction pattern, the spatiotemporal dynamics of the flight focus propagating along the optical axis are reconstructed. In particular, the propagation velocity of the flight focus can be calculated by extracting the relationship between the spatial position of the diffraction fringe initiation point and the time delay.

[0051] Example:

[0052] Design and fabricate a five-focal-focusing element for flight according to the steps described above, and test its flight focus speed:

[0053] The flying focus focusing element designed in this embodiment is applied to the field of femtosecond filament back-to-air laser enhancement. Therefore, the flying focus velocity generated by the element is -c. The focal interval Δf = 2.5 mm is the convergence of adjacent rings of the multifocal Fresnel lens. The thickness of each ring of the lens is calculated by formula (1): L1 ≈ 3.45 mm, L2 ≈ 14.37 mm, L3 ≈ 25.23 mm, L4 ≈ 36.04 mm, L5 ≈ 46.81 mm. The designed radial stepped lens structure and its focusing situation are as follows. Figure 1 As shown.

[0054] The specific example of the design given here has a focusing element radius of 4.4 cm. Each ring divides the lens power into five equal parts. Therefore, the incident power P of each ring... step :

[0055] (4)

[0056] Substitute R max = 2.2 cm, beam radius ω = 2.2 cm:

[0057] (5)

[0058] (6)

[0059] Substituting the data, we obtain the r of each ring. n The inner and outer radii are determined to ensure that the intensity distribution of the focused beam passing through each annulus is the same. The inner and outer radius values ​​of each annulus are shown in Table 1. The annulus structure of the focusing element is as follows: Figure 2 As shown, the obtained annular zone distribution is as follows: Figure 3 As shown, the final processed multi-focusing element is shown in the following figure. Figure 4 As shown.

[0060] Table 1. Inner and outer radii of each annulus of the stepped lens

[0061] 1 0 8.86 2 8.86 12.82 3 12.82 16.1 4 16.1 19.1 5 19.1 22

[0062] Finally, a femtosecond filament characterization system for the flight focus was configured, and the flight focus velocity was tested. The test optical path diagram is shown below. Figure 5 As shown:

[0063] First, a laser source system is configured, using a Ti:sapphire femtosecond laser amplifier as the excitation source. This laser 1 has an output center wavelength of 800 nm, a spectral width of 9.2 nm, a pulse duration of 50 fs, a single pulse energy of 5 mJ, and a repetition rate of 500 Hz. The laser beam diameter is 10 mm, and the divergence angle is less than 0.5 mrad. The source is split into pump and probe beams by a beam splitter 2. The pump beam passes through a delay line 3 and then through a beam expander lens group 4 to expand the beam diameter to 44 mm. Finally, it is perpendicularly incident on a multifocal flying focal focusing element 5 to form a multifocal filament 6. The probe beam is reflected by a mirror 7, frequency-doubled by a BBO 8, and then crosses non-collinearly with the pump beam through a beam expander assembly 11. The time delay between the two beams is precisely controlled by the delay line 3. When the pump photoionizes the air to generate plasma, a shadow is projected against the background of the probe beam, and the shadow image is simultaneously captured by a CCD camera 13. By scanning the delay line, the dynamic evolution of the plasma can be recorded within a time range of 100 ps to 10 ns.

[0064] The system was started and experiments were conducted. First, the entire optical path was precisely calibrated to ensure that all optical components were strictly aligned. At the same time, the beam expander lens group 4, located in front of the multifocal flying focus focusing element 5 in the pump optical path, was finely adjusted to optimize the focusing effect and lay the foundation for the subsequent generation of a stable flying focus. Subsequently, the laser system was turned on, and the CCD camera 13 was used to receive the probe light signal. By adjusting the delay line 3, images of the ionization front evolution of the filament at different times were obtained to reveal the dynamic propagation characteristics of the flying focus.

[0065] To quantitatively characterize the displacement of the ionization front induced by the focusing element of the flight focus, this invention uses transverse diffraction as a diagnostic method. By gradually adjusting the delay line 3, the filaments generated by each focusing stage appear sequentially, and the experimental results are as follows. Figure 6 As shown in the figure, it can be clearly observed that the plasma propagates in the negative z-direction, exhibiting backward propagation characteristics. The appearance times of each filament were recorded, with corresponding delays of t0=0, t1=10 ps, ​​t2=18.3 ps, t3=30 ps, ​​and t4=40.6 ps, respectively. The diffraction images recorded by CCD camera 13 are attached. Figure 6 .

[0066] By analyzing the appearance time of each annular filament and combining it with the position x where the filament begins to appear in the CCD image, nThis allows us to determine the propagation trajectory of the plasma ionization front. Furthermore, based on the time interval T between the appearance of two adjacent filaments... n The focusing velocity of the flight focus was calculated as v = Δx / ΔT. The overall velocity fitting results for the flight focus are shown in the appendix. Figure 7 The measured velocity at the flight focal point was -2.6 × 10⁻⁶. 8 m / s. This result demonstrates that, while maintaining a constant pump pulse width, the designed lens can still effectively achieve a flying focus, and the velocity of the obtained flying focus is close to the speed of light -c. This characteristic provides an important foundation for subsequent enhancement of back-to-air laser or fluorescence signals, showing promising application prospects.

[0067] Finally, it should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. Those skilled in the art should understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the claims.

Claims

1. A flight focus focusing element based on spatial discrete focusing and time delay control, characterized in that, The focusing element includes: a stepped lens with at least two rings, each ring of the stepped lens having a preset focal length and thickness, used to make the incident laser form multiple discretely distributed focal points in space after passing through different rings, and form a sequentially delayed focusing sequence in time, thereby realizing a flying focus for reverse propagation.

2. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The focusing element is designed so that the incident laser beam converges along the optical axis at discrete spatial positions after passing through different rings, forming an extended focusing area. In terms of time, the incident laser beam experiences different optical path delays in different rings due to the stepped thickness of each ring, forming a controllable time delay sequence.

3. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The focusing element adjusts the surface curvature of each ring to make the diameter of the converging spot smaller than the Airy disk, thereby reaching the dielectric ionization threshold.

4. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The stepped lens is made of a transparent medium material, including but not limited to acrylic or optical glass.

5. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The inner and outer radii of each ring are determined based on the energy distribution of the incident light spot to ensure that the laser energy transmitted through each ring remains uniform.

6. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The propagation speed of the flight focus is jointly controlled by the focal length difference and thickness difference of adjacent rings, satisfying the following relationship: Where Δf is the focal length difference between two adjacent rings, ΔL is the thickness difference between two adjacent rings, n1 is the refractive index of the lens material, and n0 is the refractive index of air.

7. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The propagation speed of the flight focus is continuously adjustable from rest to several times the speed of light, including motion modes that are the same as or opposite to the direction of laser pulse propagation.

8. The flight focus focusing element based on spatial discrete focusing and time delay control according to claim 1, characterized in that, The flight focus forms a dynamically moving high-intensity region in the medium, which can continuously maintain a power density higher than the medium excitation threshold to achieve population inversion.

9. The method for fabricating a flight focus focusing element based on spatial discrete focusing and time delay control as described in any one of claims 1-8, characterized in that, The processing steps are as follows: (1) Three-dimensional modeling: Based on the focal length, thickness and inner and outer radius design parameters of each ring, a three-dimensional structural model of the focusing element is established; (2) CNC precision machining: The focusing element blank is machined by a multi-axis CNC precision engraving machine. The machining accuracy is controlled within ±0.01 mm and the surface roughness Ra < 20 nm. The stepped structure and surface curvature of each ring are formed sequentially by layer cutting. (3) Optical polishing: The curved surface of each ring is locally polished to eliminate machining marks, reduce light scattering loss, and ensure that the converging light spot approaches the Airy disk to reach the medium ionization threshold; (4) Cleaning and drying: Use anhydrous ethanol or isopropanol to ultrasonically clean the surface of the component to remove oil and debris, and air dry or blow dry with nitrogen. (5) Anti-reflection coating: An anti-reflection coating is deposited on the surface of the component to improve the transmittance or damage resistance threshold.

10. The application of the flight focus focusing element based on spatial discrete focusing and time delay control as described in any one of claims 1-8, characterized in that, Used in the fields of femtosecond laser filaments and air lasers, enabling laser micromachining, laser tail field acceleration, atmospheric remote sensing, and environmental monitoring.

Images