Method and system for generating ultra-intense donut-shaped airy beam laser pulses

Abstract

The application provides a method and system for generating superstrong circular ring Airy light laser pulses, comprising: determining a phase delay distribution function according to a Fourier transform approximate formula of a near-field light intensity distribution of the circular ring Airy light to be generated; calculating a gray scale pattern corresponding to the phase delay distribution; experimentally verifying the gray scale pattern of the phase delay distribution; preparing a phase plate according to the verified gray scale pattern of the phase delay distribution; building an experimental device for generating the circular ring Airy light using the phase plate, and generating the superstrong circular ring Airy light laser pulses by modulating the output pulses of a superstrong femtosecond laser. The application adopts a glass substrate phase plate with a high damage threshold, breaks through the limitation of traditional methods that can only generate weak light intensity circular ring Airy light laser pulses due to the low damage threshold of a liquid crystal spatial light modulator. The superstrong circular ring Airy light laser pulses can be generated only by using a simple optical system, which creates the possibility for further application.

Description

Technical Field

[0001] This invention relates to the field of laser pulses, and more specifically, to a method and system for generating ultra-intense circular Airy laser pulses. Background Technology

[0002] The paper "Fourier space generation of abruptly autofocusing beams and optical bottle beams," published in Volume 36, Issue 18 of *Optics Letters* in 2011, proposed a Fourier transform method for generating ring-shaped Airy beams. This method generates ring-shaped Airy beams in the spatial domain by phase modulation of a Gaussian beam followed by a Fourier transform. This method is traditional and the most widely used for generating ring-shaped Airy beams. Its drawback lies in the fact that the phase modulation device used is a liquid crystal spatial light modulator, which has a low damage threshold and limited effective modulation area. This makes it unsuitable for femtosecond lasers with high energy and large spot sizes, thus limiting its application.

[0003] Circular Airy beams are rotationally symmetric Airy beams, exhibiting the known characteristics of Airy beams: no diffraction, transverse free acceleration leading to maximum intensity along a parabolic trajectory, interference resistance, and self-healing upon encountering obstacles. Simultaneously, the rotational symmetry about the propagation axis enables long-distance controllable focusing. By modulating the initial waveform, the initial laser pulse energy is distributed on a large circular ring, avoiding the nonlinear losses of strong laser pulses propagating in air, and then focusing at a specified long distance, utilizing the self-focusing phenomenon of strong light to focus the ultra-intense light onto the target. Therefore, it is an ideal waveform for ultra-intense lasers to propagate over long distances in media including the atmosphere. Currently, circular Airy beams are mainly generated by modulating the Gaussian light output from the laser using a spatial light modulator (SLM). This approach is limited by the damage threshold of the spatial light modulator, especially for femtosecond laser pulses, whose ultra-high instantaneous power can cause nonlinear responses in liquid crystals and reflective media films, leading to ionization and permanent damage. For typical 800nm ​​wavelength pulses with pulse widths of tens of femtoseconds, when the beam cross-section is around 10mm, the damage threshold of the incident laser pulse energy is approximately 3mJ (pulse width 30fs). This damage threshold severely limits the generation of ultrafast and ultraintense circular Airy pulses. Therefore, there is an urgent need to develop new methods for generating circular Airy pulses.

[0004] A design method for an optical geometric phase element and a self-focusing lens device for generating a circular Airy beam using complex amplitude modulation (CN115598837A) is disclosed. This invention uses an optical geometric phase element and a polarization filter to directly generate a circular Airy beam through complex amplitude modulation, avoiding the low efficiency of traditional Fourier transform methods. However, optical geometric phase elements require complex micro-nano fabrication techniques for fabrication, and those designed for femtosecond laser spot sizes are expensive due to their large required dimensions, hindering practical applications.

[0005] A system and method for generating terahertz waves using a circular Airy tri-field laser (CN114389125A); This invention directly generates a circular beam by phase modulation using a liquid crystal spatial light modulator. This circular beam also has the property of circular self-focusing and is a similar beam to the circular Airy beam. However, due to the limitation of the effective area of ​​the spatial light modulator, it is impossible to generate a circular beam with a large initial radius. Therefore, the self-focusing distance of the circular beam is limited. At the same time, the energy of the generated circular Airy beam is also limited by the damage threshold of the liquid crystal spatial light modulator, and it is impossible to generate a circular Airy femtosecond laser pulse with large energy. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for generating ultra-intense circular Airy laser pulses.

[0007] A method for generating ultra-intense circular Airy laser pulses according to the present invention includes:

[0008] Step S1: For the parameters of the ring Airy light pulse to be generated, determine its near-field light intensity distribution, and calculate the corresponding phase delay distribution function according to the Fourier transform approximation formula of the ring Airy light.

[0009] Step S2: Derive the phase delay grayscale pattern based on the phase delay distribution function;

[0010] Step S3: Experimentally verify the grayscale pattern of phase delay distribution;

[0011] Step S4: Prepare a phase plate based on the verified phase delay distribution grayscale image;

[0012] Step S5: Construct an experimental setup for generating a ring-shaped Airy beam using a phase plate. By modulating the output pulses of an ultra-intense femtosecond laser, an ultra-intense ring-shaped Airy beam laser pulse is generated.

[0013] Preferably, in step S1:

[0014] The required parameters include the initial radius r0 of the annular Airy light and the scale factor parameter w;

[0015] These two parameters are used to calculate the linear convergence distance f of Airy light. Ai for:

[0016]

[0017] Wherein, λ is the center wavelength of the femtosecond laser pulse;

[0018] Simultaneously, the Fourier transform approximation formula for the Airy light of the annulus is determined, expressed as a function of the initial radius r0 of the annulus and the scale factor parameter w:

[0019]

[0020] in, Let f be the radial spatial frequency, f be the focal length of the Fourier lens, r be the radial coordinate, C0 be a constant, and a be the attenuation coefficient. It is a Bessel function of the first kind of order 0;

[0021] Based on the requirements, the phase delay distribution function calculated using the Fourier transform approximation formula of the near-field intensity distribution of the circular Airy light is obtained through the formula... Transform the polar coordinates into a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates in the Cartesian coordinate system, respectively.

[0022] Preferably, in step S2:

[0023] The phase delay grayscale pattern is drawn by numerical discretization based on the number of pixels and the pixel size of the spatial light modulator; for the drawn phase delay grayscale pattern, grayscale values ​​from 0 to 255 correspond to phase delays from 0 to 2π.

[0024] Preferably, in step S3:

[0025] The phase delay distribution grayscale pattern was experimentally verified using an experimental setup that generates a ring of Airy light via a spatial light modulator.

[0026] Using a transmissive or reflective spatial light modulator, the grayscale pattern of the phase delay distribution to be verified is loaded into its control software to generate the corresponding phase delay distribution. The modulator is placed on the front focal plane of the Fourier lens.

[0027] The chirped amplified femtosecond laser emits a laser pulse, and the pulse energy is controlled to be less than the damage threshold of the spatial light modulator, which is then incident on the aforementioned spatial light modulator with a specific phase delay distribution.

[0028] The modulator output light passes through a Fourier lens;

[0029] A window with a blocking object is placed at a predetermined position before the back focal plane of the Fourier lens to completely block the intensity of the unmodulated zero-order light, thereby generating a near-field light intensity distribution of a ring of Airy light on the back focal plane of the lens.

[0030] The circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and the focusing distance of the ring is determined. The phase delay distribution function is verified by comparing it with the preset theoretical value.

[0031] Preferably, in step S4:

[0032] The modulation area of ​​the spatial light modulator used to verify the phase delay distribution function differs from the size of the phase sheet to be prepared. Therefore, the phase delay distribution function is recalculated based on the specific size of the phase sheet.

[0033] The phase plate is made of optical glass. Based on the phase delay variation function over the provided radius, a quasi-continuous phase delay distribution of 256th order is fabricated using a suitable process.

[0034] The specific manufacturing process depends on the manufacturer, including the liquid crystal beam splitting DOE method.

[0035] Preferably, in step S5:

[0036] An ultra-intense femtosecond laser pulse is sequentially passed through a phase plate with a preset phase delay distribution placed on the front focal plane of a Fourier lens, a Fourier lens, and a window plate with a zero-order light blocker, generating a circular Airy light near-field intensity distribution on the rear focal plane of the Fourier lens.

[0037] The ultra-intense circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and to determine the focusing distance of the ring, which is then compared with the preset theoretical design value.

[0038] A system for generating ultra-intense circular Airy laser pulses according to the present invention includes:

[0039] Module M1: For the parameters of the circular Airy light pulse to be generated, determine its near-field light intensity distribution, and calculate the corresponding phase delay distribution function according to the Fourier transform approximation formula of the circular Airy light;

[0040] Module M2: Derives a phase delay grayscale pattern based on the phase delay distribution function;

[0041] Module M3: Experimentally verify the grayscale pattern of phase delay distribution;

[0042] Module M4: Prepare a phase sheet based on the verified phase delay distribution grayscale pattern;

[0043] Module M5: Construct an experimental setup for generating circular Airy beams using phase plates. By modulating the output pulses of an ultra-intense femtosecond laser, ultra-intense circular Airy beam laser pulses are generated.

[0044] Preferably, in module M1:

[0045] The required parameters include the initial radius r0 of the annular Airy light and the scale factor parameter w;

[0046] These two parameters are used to calculate the linear convergence distance f of Airy light. Ai for:

[0047]

[0048] Wherein, λ is the center wavelength of the femtosecond laser pulse;

[0049] Simultaneously, the Fourier transform approximation formula for the Airy light of the annulus is determined, expressed as a function of the initial radius r0 of the annulus and the scale factor parameter w:

[0050]

[0051] in, Let f be the radial spatial frequency, f be the focal length of the Fourier lens, r be the radial coordinate, C0 be a constant, and a be the attenuation coefficient. It is a Bessel function of the first kind of order 0;

[0052] Based on the requirements, the phase delay distribution function calculated using the Fourier transform approximation formula of the near-field intensity distribution of the circular Airy light is obtained through the formula... Transform the polar coordinates into a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates in the Cartesian coordinate system, respectively.

[0053] In module M2:

[0054] The phase delay grayscale pattern is drawn by numerical discretization based on the number of pixels and the pixel size of the spatial light modulator; for the drawn phase delay grayscale pattern, grayscale values ​​from 0 to 255 correspond to phase delays from 0 to 2π.

[0055] Preferably, in module M3:

[0056] The phase delay distribution grayscale pattern was experimentally verified using an experimental setup that generates a ring of Airy light via a spatial light modulator.

[0057] Using a transmissive or reflective spatial light modulator, the grayscale pattern of the phase delay distribution to be verified is loaded into its control software to generate the corresponding phase delay distribution. The modulator is placed on the front focal plane of the Fourier lens.

[0058] The chirped amplified femtosecond laser emits a laser pulse, and the pulse energy is controlled to be less than the damage threshold of the spatial light modulator, which is then incident on the aforementioned spatial light modulator with a specific phase delay distribution.

[0059] The modulator output light passes through a Fourier lens;

[0060] A window with a blocking object is placed at a predetermined position before the back focal plane of the Fourier lens to completely block the intensity of the unmodulated zero-order light, thereby generating a near-field light intensity distribution of a ring of Airy light on the back focal plane of the lens.

[0061] The circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and the focusing distance of the ring is determined. The phase delay distribution function is verified by comparing it with the preset theoretical value.

[0062] Preferably, in module M4:

[0063] The modulation area of ​​the spatial light modulator used to verify the phase delay distribution function differs from the size of the phase sheet to be prepared. Therefore, the phase delay distribution function is recalculated based on the specific size of the phase sheet.

[0064] The phase plate is made of optical glass. Based on the phase delay variation function over the provided radius, a quasi-continuous phase delay distribution of 256th order is fabricated using a suitable process.

[0065] The specific manufacturing process depends on the manufacturer, including the liquid crystal beam splitting DOE method;

[0066] In module M5:

[0067] An ultra-intense femtosecond laser pulse is sequentially passed through a phase plate with a preset phase delay distribution placed on the front focal plane of a Fourier lens, a Fourier lens, and a window plate with a zero-order light blocker, generating a circular Airy light near-field intensity distribution on the rear focal plane of the Fourier lens.

[0068] The ultra-intense circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and to determine the focusing distance of the ring, which is then compared with the preset theoretical design value.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. The present invention prepares a phase sheet with a specific phase delay distribution. Since it is based on optical glass material, it has a higher damage threshold than liquid crystal spatial light modulator. At the same time, it can adapt to femtosecond laser pulses with larger spot size, thus enabling the generation of circular Airy femtosecond laser pulses with higher energy.

[0071] 2. This invention addresses the generation of ring Airy light with specific requirements. First, a reflective liquid crystal spatial light modulator is used to obtain the phase diagram required for the generation of ring Airy light through computer coding calculation. The input test light is then adjusted. After successful adjustment, a phase sheet is prepared according to the corresponding phase delay distribution grayscale pattern, which reduces the trial and error cost of phase sheet preparation.

[0072] 3. The method and apparatus proposed in this invention have a simple optical path structure and are easy to implement. Compared with the traditional low-energy ring Airy light generation device, it only requires replacing the spatial light modulator with a phase plate made of optical glass material with a specific phase delay distribution, which is very convenient in practical applications. Attached Figure Description

[0073] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0074] Figure 1 Schematic diagrams of the experimental setups used to verify the grayscale pattern of the phase delay distribution and to apply the prepared phase plate;

[0075] Figure 2 A grayscale pattern of phase delay of a ring-shaped Airy beam for testing Airy beam generation in a liquid crystal spatial light modulator.

[0076] Figure 3 A ring-shaped Airy phase delay grayscale pattern for use in phase sheet fabrication;

[0077] Figure 4 Experimental results characterizing the circular Airy light generated by phase plate modulation: the spot images of the circular Airy light at the focal point (0cm) of the Fourier lens and at 100cm, 150cm, and 230cm behind the focal point, and the corresponding radial intensity distribution. Detailed Implementation

[0078] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0079] Example 1:

[0080] This invention proposes a method and apparatus for generating ultra-intense circular Airy laser pulses. A chirped amplified femtosecond laser emits ultra-intense femtosecond laser pulses, and phase modulation required for generating circular Airy light is achieved through a phase plate with a preset phase delay distribution. The phase plate is made of optical glass, such as N-BK7 glass, which has an extremely high damage threshold. The phase delay distribution is calculated according to the Fourier transform approximation formula for circular Airy light, and after being fabricated, it is placed on the front focal plane of a Fourier lens. The femtosecond laser pulse modulated by the phase plate undergoes a Fourier transform through the lens. The back focal plane forms a near-field intensity distribution of a ring-shaped Airy beam. After blocking the zero-order intensity, the ring-shaped Airy beam propagates freely. It converges towards the axis at a distance determined by its near-field, and nonlinear self-focusing occurs when the intensity reaches the self-focusing threshold, accelerating the convergence of the intensity and achieving ultra-intense intensity at a designed distance. The input laser pulse energy of the device is only limited by the damage threshold of the phase plate material. Ordinary optical glass can achieve a damage threshold on the order of 100 mJ for incident femtosecond laser pulses with a beam cross-section of about 10 mm, which is tens to hundreds of times higher than that of typical spatial light modulators. Therefore, using the method and device proposed in this invention, ultra-intense ring-shaped Airy femtosecond laser pulses can be generated with only a simple optical system, creating possibilities for its further applications.

[0081] The present invention provides a method for generating ultra-intense circular Airy laser pulses, such as... Figures 1-4 As shown, it includes:

[0082] Step S1: For the parameters of the ring Airy light pulse to be generated, determine its near-field light intensity distribution, and calculate the corresponding phase delay distribution function according to the Fourier transform approximation formula of the ring Airy light.

[0083] Specifically, in step S1:

[0084] The required parameters include the initial radius r0 of the annular Airy light and the scale factor parameter w;

[0085] These two parameters are used to calculate the linear convergence distance f of Airy light. Ai for:

[0086]

[0087] Wherein, λ is the center wavelength of the femtosecond laser pulse;

[0088] Simultaneously, the Fourier transform approximation formula for the Airy light of the annulus is determined, expressed as a function of the initial radius r0 of the annulus and the scale factor parameter w:

[0089]

[0090] in, Let f be the radial spatial frequency, f be the focal length of the Fourier lens, r be the radial coordinate, C0 be a constant, and a be the attenuation coefficient. It is a Bessel function of the first kind of order 0;

[0091] Based on the requirements, the phase delay distribution function calculated using the Fourier transform approximation formula of the near-field intensity distribution of the circular Airy light is obtained through the formula... Transform the polar coordinates into a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates in the Cartesian coordinate system, respectively.

[0092] Step S2: Derive the phase delay grayscale pattern based on the phase delay distribution function;

[0093] Specifically, in step S2:

[0094] The phase delay grayscale pattern is drawn by numerical discretization based on the number of pixels and the pixel size of the spatial light modulator; for the drawn phase delay grayscale pattern, grayscale values ​​from 0 to 255 correspond to phase delays from 0 to 2π.

[0095] Step S3: Experimentally verify the grayscale pattern of phase delay distribution;

[0096] Specifically, in step S3:

[0097] The phase delay distribution grayscale pattern was experimentally verified using an experimental setup that generates a ring of Airy light via a spatial light modulator.

[0098] Using a transmissive or reflective spatial light modulator, the grayscale pattern of the phase delay distribution to be verified is loaded into its control software to generate the corresponding phase delay distribution. The modulator is placed on the front focal plane of the Fourier lens.

[0099] The chirped amplified femtosecond laser emits a laser pulse, and the pulse energy is controlled to be less than the damage threshold of the spatial light modulator, which is then incident on the aforementioned spatial light modulator with a specific phase delay distribution.

[0100] The modulator output light passes through a Fourier lens;

[0101] A window with a blocking object is placed at a predetermined position before the back focal plane of the Fourier lens to completely block the intensity of the unmodulated zero-order light, thereby generating a near-field light intensity distribution of a ring of Airy light on the back focal plane of the lens.

[0102] The circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and the focusing distance of the ring is determined. The phase delay distribution function is verified by comparing it with the preset theoretical value.

[0103] Step S4: Prepare a phase plate based on the verified phase delay distribution grayscale image;

[0104] Specifically, in step S4:

[0105] The modulation area of ​​the spatial light modulator used to verify the phase delay distribution function differs from the size of the phase sheet to be prepared. Therefore, the phase delay distribution function is recalculated based on the specific size of the phase sheet.

[0106] The phase plate is made of optical glass. Based on the phase delay variation function over the provided radius, a quasi-continuous phase delay distribution of 256th order is fabricated using a suitable process.

[0107] The specific manufacturing process depends on the manufacturer, including the liquid crystal beam splitting DOE method.

[0108] Step S5: Construct an experimental setup for generating a ring-shaped Airy beam using a phase plate. By modulating the output pulses of an ultra-intense femtosecond laser, an ultra-intense ring-shaped Airy beam laser pulse is generated.

[0109] Specifically, in step S5:

[0110] An ultra-intense femtosecond laser pulse is sequentially passed through a phase plate with a preset phase delay distribution placed on the front focal plane of a Fourier lens, a Fourier lens, and a window plate with a zero-order light blocker, generating a circular Airy light near-field intensity distribution on the rear focal plane of the Fourier lens.

[0111] The ultra-intense circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and to determine the focusing distance of the ring, which is then compared with the preset theoretical design value.

[0112] Example 2:

[0113] Example 2 is a preferred embodiment of Example 1, and is used to illustrate the present invention in more detail.

[0114] The present invention also provides a system for generating ultra-intense circular Airy laser pulses. The system for generating ultra-intense circular Airy laser pulses can be implemented by executing the process steps of the method for generating ultra-intense circular Airy laser pulses. That is, those skilled in the art can understand the method for generating ultra-intense circular Airy laser pulses as a preferred embodiment of the system for generating ultra-intense circular Airy laser pulses.

[0115] A system for generating ultra-intense circular Airy laser pulses according to the present invention includes:

[0116] Module M1: For the parameters of the circular Airy light pulse to be generated, determine its near-field light intensity distribution, and calculate the corresponding phase delay distribution function according to the Fourier transform approximation formula of the circular Airy light;

[0117] Specifically, in module M1:

[0118] The required parameters include the initial radius r0 of the annular Airy light and the scale factor parameter w;

[0119] These two parameters are used to calculate the linear convergence distance f of Airy light. Ai for:

[0120]

[0121] Wherein, λ is the center wavelength of the femtosecond laser pulse;

[0122] Simultaneously, the Fourier transform approximation formula for the Airy light of the annulus is determined, expressed as a function of the initial radius r0 of the annulus and the scale factor parameter w:

[0123]

[0124] in, Let f be the radial spatial frequency, f be the focal length of the Fourier lens, r be the radial coordinate, C0 be a constant, and a be the attenuation coefficient. It is a Bessel function of the first kind of order 0;

[0125] Based on the requirements, the phase delay distribution function calculated using the Fourier transform approximation formula of the near-field intensity distribution of the circular Airy light is obtained through the formula... Transform the polar coordinates into a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates in the Cartesian coordinate system, respectively.

[0126] Module M2: Derives a phase delay grayscale pattern based on the phase delay distribution function;

[0127] In module M2:

[0128] The phase delay grayscale pattern is drawn by numerical discretization based on the number of pixels and the pixel size of the spatial light modulator; for the drawn phase delay grayscale pattern, grayscale values ​​from 0 to 255 correspond to phase delays from 0 to 2π.

[0129] Module M3: Experimentally verify the grayscale pattern of phase delay distribution;

[0130] Specifically, in module M3:

[0131] The phase delay distribution grayscale pattern was experimentally verified using an experimental setup that generates a ring of Airy light via a spatial light modulator.

[0132] Using a transmissive or reflective spatial light modulator, the grayscale pattern of the phase delay distribution to be verified is loaded into its control software to generate the corresponding phase delay distribution. The modulator is placed on the front focal plane of the Fourier lens.

[0133] The chirped amplified femtosecond laser emits a laser pulse, and the pulse energy is controlled to be less than the damage threshold of the spatial light modulator, which is then incident on the aforementioned spatial light modulator with a specific phase delay distribution.

[0134] The modulator output light passes through a Fourier lens;

[0135] A window with a blocking object is placed at a predetermined position before the back focal plane of the Fourier lens to completely block the intensity of the unmodulated zero-order light, thereby generating a near-field light intensity distribution of a ring of Airy light on the back focal plane of the lens.

[0136] The circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and the focusing distance of the ring is determined. The phase delay distribution function is verified by comparing it with the preset theoretical value.

[0137] Module M4: Prepare a phase sheet based on the verified phase delay distribution grayscale pattern;

[0138] Specifically, in module M4:

[0139] The modulation area of ​​the spatial light modulator used to verify the phase delay distribution function differs from the size of the phase sheet to be prepared. Therefore, the phase delay distribution function is recalculated based on the specific size of the phase sheet.

[0140] The phase plate is made of optical glass. Based on the phase delay variation function over the provided radius, a quasi-continuous phase delay distribution of 256th order is fabricated using a suitable process.

[0141] The specific manufacturing process depends on the manufacturer, including the liquid crystal beam splitting DOE method;

[0142] Module M5: Construct an experimental setup for generating circular Airy beams using phase plates. By modulating the output pulses of an ultra-intense femtosecond laser, ultra-intense circular Airy beam laser pulses are generated.

[0143] In module M5:

[0144] An ultra-intense femtosecond laser pulse is sequentially passed through a phase plate with a preset phase delay distribution placed on the front focal plane of a Fourier lens, a Fourier lens, and a window plate with a zero-order light blocker, generating a circular Airy light near-field intensity distribution on the rear focal plane of the Fourier lens.

[0145] The ultra-intense circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and to determine the focusing distance of the ring, which is then compared with the preset theoretical design value.

[0146] Example 3:

[0147] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0148] This invention provides a method and apparatus for generating ultra-intense circular Airy laser pulses, and its optimized embodiment specifically includes the following steps and parameters:

[0149] (1) Based on the parameters of the desired annular Airy light, determine the initial radius r0 = 2 mm and the scale factor parameter w = 0.2 mm for the annular light in this embodiment.

[0150] (2) The phase distribution of the liquid crystal spatial light modulator is calculated and designed according to the Fourier transform approximation formula of the circular Airy light in step 1. The number of pixels of the liquid crystal spatial light modulator used is 1920×1080, and the pixel size is 8μm. The radial spatial frequency k required in the formula is calculated accordingly. The center wavelength of the femtosecond laser used is λ=800nm, the focal length of the Fourier lens is f=2000mm, the attenuation coefficient is a=0.05, and C0=1. The phase delay distribution calculated according to the approximation formula is proportionally normalized to generate a grayscale image with gray values ​​distributed in the range [0,255]. In the image, gray value 0 represents a phase delay of 0, and gray value 255 represents a phase delay of 2π. The phase delay grayscale image is shown below. Figure 1 As shown.

[0151] (3) Following step 2, the calculated phase delay pattern is loaded into the reflective liquid crystal spatial light modulator.

[0152] (4) Following step 3, construct the optical path required for phase delay pattern testing. The femtosecond laser pulse repetition frequency used in the testing step is 10Hz. Beam expansion is performed, and an adjustable aperture is used to limit the spot size of the incident reflective liquid crystal spatial light modulator to adapt to the effective modulation area of ​​the spatial light modulator. The incident pulse energy is also reduced to less than the damage threshold to verify that the incident laser pulse energy of the liquid crystal spatial light modulator is 3mJ.

[0153] (5) Following step 3, verify the generated ring-shaped Airy light. The verification includes the pulse energy of the generated ring-shaped Airy light, the initial ring radius, and the ring convergence distance. The results show that the converted Airy light pulse energy is 0.3 mJ.

[0154] (6) After determining the validity of the phase pattern in step 3, recalculate the phase retardation pattern of the phase plate used to generate the circular Airy light. According to the requirements of this embodiment, the phase plate size is set to 1 inch, and the phase retardation pattern of the phase plate used to generate the circular Airy light is as follows: Figure 2 As shown.

[0155] (7) Following step 4, based on the recalculated phase delay distribution, prepare a phase sheet for generating the ring Airy light. The phase sheet is made of N-BK7 glass, has a diameter of 1 inch, and has 15,000 pixels in the radial direction. The phase sheet exhibits a quasi-continuous phase delay of 256 orders.

[0156] (8) Following step 5, construct the optical path required to generate the circular Airy beam. The energy of the incident laser pulse on the phase plate is 20 mJ.

[0157] (9) Following step 5, the generated ring-shaped Airy light is attenuated and then directly incident on the CCD camera to complete imaging. Move the CCD camera position to complete the spatial scan of the ring-shaped Airy light from its initial state to its complete convergence, thus verifying the generated ring-shaped Airy light. The measured energy of the converted Airy light pulse is 1.3 mJ. Figure 3 The images show the circular Airy light spot at the focal point (0cm) of the Fourier lens and at 100cm, 150cm, and 230cm behind the focal point, along with the corresponding radial intensity distribution.

[0158] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0159] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for generating ultra-intense circular Airy laser pulses, characterized in that, include: Step S1: For the parameters of the ring Airy light pulse to be generated, determine its near-field light intensity distribution, and calculate the corresponding phase delay distribution function according to the Fourier transform approximation formula of the ring Airy light. In step S1: Required parameters include the initial radius of the annular Airy light. and scale factor parameters ; These two parameters are used to calculate the linear convergence distance of Airy light. for: in, The center wavelength of the femtosecond laser pulse; Simultaneously, the Fourier transform approximation formula for the Airy light of the annulus is determined, expressed as a function of the initial radius of the annulus. and scale factor parameters Functions: in, Radial spatial frequency, Let be the focal length of the Fourier lens. Radial coordinates, It is a constant. The attenuation coefficient is... It is a Bessel function of the first kind of order 0; Based on the requirements, the phase delay distribution function calculated using the Fourier transform approximation formula of the near-field intensity distribution of the circular Airy light is obtained through the formula... Transform the polar coordinates into a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates in the Cartesian coordinate system, respectively. Step S2: Derive the phase delay grayscale pattern based on the phase delay distribution function; Step S3: Experimentally verify the grayscale pattern of phase delay distribution; Step S4: Prepare a phase plate based on the verified phase delay distribution grayscale image; the phase plate is made of optical glass. Step S5: Construct an experimental setup for generating a ring-shaped Airy beam using a phase plate. By modulating the output pulses of an ultra-intense femtosecond laser, an ultra-intense ring-shaped Airy beam laser pulse is generated. In step S5: An ultra-intense femtosecond laser pulse is sequentially passed through a phase plate with a preset phase delay distribution placed on the front focal plane of a Fourier lens, a Fourier lens, and a window plate with a zero-order light blocker, generating a circular Airy light near-field intensity distribution on the rear focal plane of the Fourier lens. The ultra-intense circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and to determine the focusing distance of the ring, which is then compared with the preset theoretical design value.

2. The method for generating ultra-intense circular Airy laser pulses according to claim 1, characterized in that, In step S2: The phase-delay grayscale pattern is drawn by numerical discretization based on the number of pixels and the pixel size of the spatial light modulator; for the drawn phase-delay grayscale pattern, grayscale values ​​from 0 to 255 correspond to 0 to 2 Phase delay.

3. The method for generating ultra-intense circular Airy laser pulses according to claim 1, characterized in that, In step S3: The phase delay distribution grayscale pattern was experimentally verified using an experimental setup that generates a ring of Airy light via a spatial light modulator. Using a transmissive or reflective spatial light modulator, the grayscale pattern of the phase delay distribution to be verified is loaded into its control software to generate the corresponding phase delay distribution. The modulator is placed on the front focal plane of the Fourier lens. The chirped amplified femtosecond laser emits a laser pulse, and the pulse energy is controlled to be less than the damage threshold of the spatial light modulator, which is then incident on the aforementioned spatial light modulator with a phase delay distribution. The modulator output light passes through a Fourier lens; A window with a blocking object is placed at a predetermined position before the back focal plane of the Fourier lens to completely block the intensity of the unmodulated zero-order light, thereby generating a near-field light intensity distribution of a ring of Airy light on the back focal plane of the lens. The circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and the focusing distance of the ring is determined. The phase delay distribution function is verified by comparing it with the preset theoretical value.

4. The method for generating ultra-intense circular Airy laser pulses according to claim 1, characterized in that, In step S4: The modulation area of ​​the spatial light modulator used to verify the phase delay distribution function differs from the size of the phase sheet to be prepared. Therefore, the phase delay distribution function is recalculated based on the specific size of the phase sheet. Based on the provided phase delay variation function over the radius, a quasi-continuous phase delay distribution of order 256 is prepared using a pre-defined process. The specific manufacturing process depends on the manufacturer, including the liquid crystal beam splitting DOE method.

5. A system for generating ultra-intense circular Airy laser pulses, characterized in that, include: Module M1: For the parameters of the circular Airy light pulse to be generated, determine its near-field light intensity distribution, and calculate the corresponding phase delay distribution function according to the Fourier transform approximation formula of the circular Airy light; In module M1: Required parameters include the initial radius of the annular Airy light. and scale factor parameters ; These two parameters are used to calculate the linear convergence distance of Airy light. for: in, The center wavelength of the femtosecond laser pulse; Simultaneously, the Fourier transform approximation formula for the Airy light of the annulus is determined, expressed as a function of the initial radius of the annulus. and scale factor parameters Functions: in, Radial spatial frequency, Let be the focal length of the Fourier lens. Radial coordinates, It is a constant. The attenuation coefficient is... It is a Bessel function of the first kind of order 0; Based on the requirements, the phase delay distribution function calculated using the Fourier transform approximation formula of the near-field intensity distribution of the circular Airy light is obtained through the formula... Transform the polar coordinates into a Cartesian coordinate system, where x and y are the horizontal and vertical coordinates in the Cartesian coordinate system, respectively. Module M2: Derives a phase delay grayscale pattern based on the phase delay distribution function; Module M3: Experimentally verify the grayscale pattern of phase delay distribution; Module M4: Prepare a phase sheet based on the verified grayscale pattern of the phase delay distribution; the phase sheet is made of optical glass. Module M5: Construct an experimental setup for generating a ring-shaped Airy beam using a phase plate. By modulating the output pulses of an ultra-intense femtosecond laser, an ultra-intense ring-shaped Airy beam laser pulse is generated. In module M5: An ultra-intense femtosecond laser pulse is sequentially passed through a phase plate with a preset phase delay distribution placed on the front focal plane of a Fourier lens, a Fourier lens, and a window plate with a zero-order light blocker, generating a circular Airy light near-field intensity distribution on the rear focal plane of the Fourier lens. The ultra-intense circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and to determine the focusing distance of the ring, which is then compared with the preset theoretical design value.

6. The system for generating ultra-intense circular Airy laser pulses according to claim 5, characterized in that, In module M2: The phase-delay grayscale pattern is drawn by numerical discretization based on the number of pixels and the pixel size of the spatial light modulator; for the drawn phase-delay grayscale pattern, grayscale values ​​from 0 to 255 correspond to 0 to 2 Phase delay.

7. The system for generating ultra-intense circular Airy laser pulses according to claim 5, characterized in that, In module M3: The phase delay distribution grayscale pattern was experimentally verified using an experimental setup that generates a ring of Airy light via a spatial light modulator. Using a transmissive or reflective spatial light modulator, the grayscale pattern of the phase delay distribution to be verified is loaded into its control software to generate the corresponding phase delay distribution. The modulator is placed on the front focal plane of the Fourier lens. The chirped amplified femtosecond laser emits a laser pulse, and the pulse energy is controlled to be less than the damage threshold of the spatial light modulator, which is then incident on the aforementioned spatial light modulator with a phase delay distribution. The modulator output light passes through a Fourier lens; A window with a blocking object is placed at a predetermined position before the back focal plane of the Fourier lens to completely block the intensity of the unmodulated zero-order light, thereby generating a near-field light intensity distribution of a ring of Airy light on the back focal plane of the lens. The circular Airy femtosecond laser pulse propagates freely from the near field to the far field. After attenuation, the light spot is recorded by a CCD camera to measure the changes in the ring radius and pulse intensity with the propagation distance, and the focusing distance of the ring is determined. The phase delay distribution function is verified by comparing it with the preset theoretical value.

8. The system for generating ultra-intense circular Airy laser pulses according to claim 5, characterized in that: In module M4: The modulation area of ​​the spatial light modulator used to verify the phase delay distribution function differs from the size of the phase sheet to be prepared. Therefore, the phase delay distribution function is recalculated based on the specific size of the phase sheet. Based on the provided phase delay variation function over the radius, a quasi-continuous phase delay distribution of order 256 is prepared using a pre-defined process. The specific manufacturing process depends on the manufacturer, including the liquid crystal beam splitting DOE method.

Images