Generation, regulation and control system and method for partially coherent space-time light field

Abstract

The invention discloses a system and method for generating, regulating and controlling a partially coherent space-time light field. The system comprises a pulse shaping assembly composed of a plurality of optical elements and an incident light source used for providing a completely coherent ultrafast pulse light field. An optical element in the pulse shaping assembly comprises a first blazed grating, a first cylindrical lens, a two-dimensional dynamic holographic modulator, a second cylindrical lens and a second blazed grating which are sequentially arranged in the light field propagation direction. The focal lengths of the first cylindrical lens and the second cylindrical lens are the same, and the distance between the adjacent optical elements is equal to the focal lengths of the first cylindrical lens and the second cylindrical lens; the two-dimensional dynamic holographic modulator is used for loading a specific complex amplitude modulation function to reconstruct the spatial-spectral characteristics of the light field. According to the invention, the two-dimensional space-spectrum function of the pulse is dynamically modulated, the generation of the partially coherent space-time wave packet is realized, and the amplitude and structure distribution of the space-time coherence can be designed and regulated as required.

Description

Technical Field

[0001] This invention relates to the field of partially coherent spatiotemporal optical field technology, and in particular to a system and method for generating and controlling partially coherent spatiotemporal optical fields. Background Technology

[0002] Coherence, as a core property of partially coherent optical fields, determines the transmission behavior and application performance of light beams through its spatial and temporal correlation characteristics. Compared to fully coherent beams, partially coherent beams possess unique advantages in areas such as disturbance-resistant transmission and uniform energy distribution, making them irreplaceable in multiple fields including optical communication, materials processing, particle manipulation, and information encryption, thus driving continuous iteration and upgrading of related technologies.

[0003] Coherence is a unique property of partially coherent optical fields, distinct from first-order deterministic optical parameters such as frequency and amplitude, and described by the second-order statistical properties of the optical field. It is divided into spatial coherence and temporal coherence, characterizing the degree of correlation between light waves at different locations in space and at different points in time, respectively. Coherence is not only reflected in differences in the degree of coherence but can also exhibit specific structural distributions. This characteristic provides key technical support for scenarios such as high-security information encryption.

[0004] Existing methods for generating partially coherent optical fields include using dynamic scatterers such as high-speed rotating frosted glass to convert fully coherent laser light into incoherent light, and then controlling the spatial coherence based on the van Sitter-Zenick theorem. Furthermore, digital holography using spatial light modulators can also directly generate partially coherent optical fields with specific spatial coherence structures. And because ultrafast laser pulses possess both spatial and temporal dimensions, their pulse widths are typically extremely short (femtosecond to picosecond range). Existing techniques also utilize 4f pulse shaping schemes to achieve complex amplitude modulation of various deterministic optical parameters of fully coherent pulses in the temporal or spatiotemporal domains.

[0005] In summary, existing technologies primarily target the pure spatial coherence manipulation of continuous laser beams, making it difficult to achieve coordinated control of coherence magnitude and structural distribution across the spatiotemporal dimensions. Furthermore, existing 4f pulse shaping schemes are based on deterministic parametric control of a fully coherent optical field, failing to generate partially coherent spatiotemporal wave packets with specific spatiotemporal coherence distributions, and even less capable of on-demand control over the magnitude and structure of their spatiotemporal coherence. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a system and method for generating and controlling partially coherent spatiotemporal optical fields. By dynamically modulating the two-dimensional spatial-spectral function of a pulse, partially coherent spatiotemporal wave packets are generated, and the amplitude and structural distribution of their spatiotemporal coherence can be designed and controlled as needed.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a system for generating and controlling a partially coherent spatiotemporal optical field, comprising: A pulse shaping assembly consisting of multiple optical elements and an incident light source for providing a fully coherent ultrafast pulsed light field; The optical elements in the pulse shaping assembly include a first blazed grating, a first cylindrical lens, a two-dimensional dynamic holographic modulator, a second cylindrical lens, and a second blazed grating arranged sequentially along the light field propagation direction; and the first cylindrical lens and the second cylindrical lens have the same focal length, and the spacing between adjacent optical elements is equal to the focal length of the first cylindrical lens and the second cylindrical lens. The two-dimensional dynamic holographic modulator is used to load a specific complex amplitude modulation function to reconstruct the spatial-spectral characteristics of the light field.

[0008] In a further technical solution, the two-dimensional dynamic holographic modulator is a two-dimensional dynamic hologram with complex amplitude modulation capability, and the two-dimensional dynamic hologram is composed of a liquid crystal spatial light modulator or a digital micromirror array.

[0009] In a further technical solution, the modulation surface of the two-dimensional dynamic holographic modulator is set perpendicular to the central axis of the first cylindrical lens and the second cylindrical lens.

[0010] Secondly, the present invention provides a method for generating and controlling a partially coherent spatiotemporal optical field, based on the system for generating and controlling a partially coherent spatiotemporal optical field as described in any one of the first aspects, comprising: After the incident light source emits a completely coherent ultrafast pulse light field, it passes through the first blazed grating for dispersion and the first cylindrical lens for collimation in sequence. The collimated ultrafast pulse light field forms a two-dimensional space-spectral plane in the plane where the two-dimensional dynamic holographic modulator is located. By loading a specific complex amplitude modulation function on the two-dimensional dynamic holographic modulator, the space-spectral plane of the ultrafast pulse light field is reconstructed. The reconstructed ultrafast pulsed light field then passes through the second cylindrical lens and the second blazed grating in sequence to combine, completing the inverse Fourier transform in the time and spatial domains, and outputting a partially coherent spatiotemporal wave packet with target coherence.

[0011] A further technical solution is that the fully coherent ultrafast pulse optical field, under the conditions of paraxial approximation and slow-varying envelope approximation, is expressed as the product of the carrier and the complex envelope function.

[0012] A further technical solution is that the instantaneous transmittance function expression of the two-dimensional dynamic holographic modulator is: ; in, It is the inverse singer function. The frequency of the linear grating phase. The dynamic phase hologram distribution function loaded for the spatial light modulator. To satisfy the random phase of the Dirac correlation, The spatial coordinates of the plane where the spatial light modulator is located. To eliminate harmonic frequencies, is the power spectral density function.

[0013] A further technical solution is that the mutual coherence function of the partially coherent spatiotemporal wave packets is expressed as: ; in, , Let the three-dimensional coordinates of any two points in space and time on the plane where the spatial light modulator is located be given. , The three-dimensional coordinates of any two points in space and time on the output plane of the pulse shaper. For differential, It is the mutual coherence function of the light field after the ultrafast pulse light field passes through a two-dimensional dynamic holographic modulator.

[0014] A further technical solution is that the expression for the mutual coherence function of the ultrafast pulsed light field after passing through the two-dimensional dynamic holographic modulator is: ; in, and Let be the instantaneous electric field of the incoherent electric field at the plane where the spatial light modulator is located, and * be the complex conjugate. and Let be the power spectral density function of the incoherent electric field. and To satisfy the dynamic random phase of the Dirac correlation.

[0015] A further technical solution is that when the output partially coherent spatiotemporal wave packet is a Gaussian-Sher model spatiotemporal wave packet, the spatiotemporal coherence function of the Gaussian-Sher model spatiotemporal wave packet is expressed as: ; in, and These represent the position and time difference between any two points in space and time, respectively. and for .

[0016] A further technical solution is that when the output partially coherent spatiotemporal wave packet is a Hermitian-Gaussian correlated spatiotemporal wave packet, the spatiotemporal coherence function of the Hermitian-Gaussian correlated spatiotemporal wave packet is expressed as: ; in, ( ) is a Hermitian polynomial of order 2m.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: Existing technologies can only individually control spatial coherence or temporal deterministic parameters, failing to coordinate the control of coherence characteristics across the spatiotemporal dimensions. This invention designs a pulse shaping component based on a 4f structure. By loading a complex amplitude modulation function onto the two-dimensional space-spectral plane, it can simultaneously and synergistically control the spatial and temporal coherence of the optical field. This solves the technical pain point of "spatiotemporal separation control," enabling flexible adjustment of coherence across the entire spatiotemporal domain.

[0018] Existing 4f pulse shaping schemes can only control the deterministic parameters of fully coherent pulses, failing to generate partially coherent wave packets with specific spatiotemporal coherence distributions. This invention designs a two-dimensional dynamic hologram with complex amplitude control capability within a 4f-based pulse shaping component, enabling precise generation of partially coherent spatiotemporal wave packets with target coherence at the output. Stable generation is possible for both Gaussian coherent distributions and non-Gaussian coherent structures such as Hermetic-Gaussian distributions, filling the technological gap in "generation of wave packets with specific spatiotemporal coherent distributions."

[0019] The two-dimensional dynamic hologram of this invention is composed of programmable devices such as liquid crystal spatial light modulators or digital micromirror arrays. The coherence characteristics of the output light field can be set as needed, and the coherence magnitude and structure can be customized to meet diverse application requirements. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0021] Figure 1 This invention relates to a system for generating and controlling partially coherent spatiotemporal optical fields; Figure 2 The distribution of the power spectral density function loaded by the spatial light modulator of the present invention and the generated partially coherent spatiotemporal optical field are shown; where a is the complex amplitude distribution of the power spectral density function, b is the light intensity distribution of the generated partially coherent spatiotemporal optical field, and c is the coherent structure distribution of the generated partially coherent spatiotemporal optical field. Figure 3For the present invention…; experimental results of controlling the coherence of a partially coherent spatiotemporal optical field; where a represents the spatial and temporal coherence widths (572 μm, 268 fs), b represents the spatial and temporal coherence widths (614 μm, 288 fs), c represents the spatial and temporal coherence widths (717 μm, 336 fs), d represents the spatial and temporal coherence widths (958 μm, 449 fs), and e represents the arbitrary control curves of the spatial and temporal coherence magnitude as a function of the power spectral density. Figure 4 The results are experimental results of coherent structure modulation of partially coherent spatiotemporal optical fields according to the present invention; where a is the Hermitian-Gaussian correlation coherent structure distribution (m=1, n=0), b is the Hermitian-Gaussian correlation coherent structure distribution (m=0, n=1), and c is the Hermitian-Gaussian correlation coherent structure distribution (m=0, n=2). Detailed implementation method: The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0024] Example 1 This embodiment provides a system for generating and controlling partially coherent spatiotemporal optical fields, such as... Figure 1 As shown, the system for generating and controlling a partially coherent spatiotemporal optical field includes a pulse shaping assembly composed of multiple optical elements and an incident light source for providing a fully coherent ultrafast pulsed optical field.

[0025] The optical elements in the pulse shaping assembly include a first blazed grating, a first cylindrical lens, a two-dimensional dynamic holographic modulator, a second cylindrical lens, and a second blazed grating, arranged sequentially along the light field propagation direction. The first and second cylindrical lenses have the same focal length: A two-dimensional dynamic holographic modulator is disposed between the first cylindrical lens and the second cylindrical lens, and the modulation surface of the two-dimensional dynamic holographic modulator is perpendicular to the central axis of the first cylindrical lens and the second cylindrical lens. It is used to load a specific complex amplitude modulation function to reconstruct the spatial-spectral characteristics of the light field. The two-dimensional dynamic holographic modulator is a two-dimensional dynamic hologram with complex amplitude control capability. The two-dimensional dynamic hologram is composed of a programmable modulator such as a liquid crystal spatial light modulator or a digital micromirror array.

[0026] The spacing between adjacent optical elements is equal to the focal length of the first cylindrical lens and the second cylindrical lens. This constitutes a configuration based on 4 in this embodiment. Pulse shaping components for the structure.

[0027] In this embodiment, the working principle of the partially coherent spatiotemporal optical field generation and control system is as follows: After being dispersed by the first blazed grating and collimated by the first cylindrical lens, the spectral components of the fully coherent ultrafast pulsed light field are stretched and expanded along the one-dimensional direction in the plane of the two-dimensional dynamic holographic modulator. At the same time, the spatial dimension orthogonal to it forms a two-dimensional space-spectral plane. By loading a specific complex amplitude modulation function on the two-dimensional dynamic holographic modulator, the space-spectral characteristics of the light field can be reconstructed. After being combined by the second cylindrical lens and the second blazed grating, the inverse Fourier transforms of the time domain and the spatial domain are completed respectively, so that a partially coherent spatiotemporal wave packet with target coherence can be formed at the output end. The magnitude of the coherence of the output light field and its spatiotemporal structure distribution are precisely set by the complex amplitude modulation function recorded on the two-dimensional dynamic holographic modulator.

[0028] Example 2 This embodiment provides a method for generating and controlling a partially coherent spatiotemporal optical field, based on the system for generating and controlling a partially coherent spatiotemporal optical field provided in Embodiment 1. The specific method is as follows: First, after the incident light source emits a completely coherent ultrafast pulse light field, it passes through the first blazed grating for dispersion and the first cylindrical lens for collimation in sequence. Then, the collimated ultrafast pulse light field forms a two-dimensional space-spectral plane on the plane where the two-dimensional dynamic holographic modulator is located. By loading a specific complex amplitude modulation function on the two-dimensional dynamic holographic modulator, the space-spectral plane of the ultrafast pulse light field is reconstructed. Finally, the reconstructed ultrafast pulse light field is then combined with the second cylindrical lens and the second blazed grating to complete the inverse Fourier transform in the time and spatial domains, outputting a partially coherent spatiotemporal wave packet with target coherence.

[0029] In this embodiment, the fully coherent ultrafast pulsed optical field, under the paraxial approximation and slowly varying envelope approximation conditions, is represented as the product of the carrier wave and the complex envelope function, specifically as follows: ; in, It is a spatial lateral position vector. , The center angular frequency of the incident fully coherent pulse beam. The transmission distance after the second blazed grating. For wave number.

[0030] Based on optical coherence theory and the partially coherent spatiotemporal optical field generation and manipulation system provided in Example 1, the mutual coherence function of the output partially coherent spatiotemporal optical field is... Represented as: ; in, and Let the three-dimensional coordinates of any two points in space and time on the plane where the spatial light modulator is located be given. and The three-dimensional coordinates of any two points in space and time on the output plane of the pulse shaper. Let be the system impulse response function, j=1,2. For wave number, Let z be the dispersion coefficient, and z be the transmission distance after the second blazed grating. The coordinates of the plane where the spatial light modulator is located are denoted as . To represent the differential, It is the mutual coherence function of the light field after the ultrafast pulse light field passes through a two-dimensional dynamic holographic modulator.

[0031] ; For 4 The impulse response function of the impulse shaping component of the structure. To eliminate harmonic frequencies, ; and These represent the spatiotemporal three-dimensional coordinates of the plane where the two-dimensional dynamic holographic modulator is located and the output plane, respectively.

[0032] The coherence function of the ultrafast pulsed light field after passing through a two-dimensional dynamic holographic modulator The expression is: ; in, and Let be the instantaneous electric field of the incoherent electric field at the plane where the spatial light modulator is located, and * denotes complex conjugate. and Let be the power spectral density function of the incoherent electric field. and To satisfy the dynamic random phase of the Dirac correlation.

[0033] in This represents an instantaneous random electric field of the incoherent light field, such as Figure 2 As shown in (a). Amplitude Let be the power spectral density function, and its dynamic phase. The statistics satisfy the Dirac correlation function: .Will Substitute the expression From the expression, we can obtain its normalized form of the coherence function. :

[0034] The magnitude and structure of the spatiotemporal coherence of the generated partially coherent spatiotemporal wave packets are both based on 4 The power spectral density function of the incoherent source behind the dynamic hologram in the pulse shaping component of the structure. Decide.

[0035] To modulate the spatial spectral wavefront of a fully coherent ultrafast pulsed light field onto the aforementioned instantaneous random electric field, the instantaneous transmittance function of the two-dimensional dynamic holographic modulator is expressed as follows: ; in, It is the inverse singer function. The frequency of the linear grating phase. The dynamic phase hologram distribution function loaded for the spatial light modulator. To satisfy the random phase of the Dirac correlation, The spatial coordinates of the plane where the spatial light modulator is located. To eliminate harmonic frequencies, is the power spectral density function.

[0036] In this embodiment, the fully coherent ultrafast pulsed light field is a Gaussian pulsed laser beam with a center wavelength of 1030 nm and a bandwidth of 20 nm, and its spatial size is 2 mm. The parameters of the first and second blazed gratings used are 1200 lines / mm, and the focal lengths of the first and second cylindrical lenses are... =100mm.

[0037] On-demand adjustment of the magnitude of spatiotemporal coherence: When the output partially coherent spatiotemporal wave packet is a Gauss-Schner model spatiotemporal wave packet, the spatiotemporal coherence function of the Gauss-Schner model spatiotemporal wave packet is expressed as: ; in, and These are the coherence widths in space and time, respectively. and These represent the position and time difference between any two points in space and time, respectively. and for .

[0038] Figure 3 This indicates that the coherence magnitude of the generated Gauss-Sher model spatiotemporal wave packet is adjustable. Figure 3(a)–(d) present the experimentally measured spatiotemporal coherence function results when power spectral density functions with different spatial and spectral widths are loaded onto two-dimensional dynamic holograms.

[0039] In the figure, the dashed and solid lines represent the experimental measurement and theoretical fitting curves, respectively, both exhibiting Gaussian envelope distributions. The full width at half maximum (FWHM) of the Gaussian fitting curves can quantitatively characterize the coherence length (or coherence time) in the spatial and temporal dimensions. The spatial and spectral widths of the corresponding loaded power spectral density functions are: (a) 1.5 mm / 0.802 THz, (b) 1.25 mm / 0.684 THz, (c) 1.00 mm / 0.535 THz, and (d) 0.75 mm / 0.401 THz. It can be observed that as the power spectral distribution width decreases, the spatial and temporal coherence of the generated spatiotemporal coherent wave packets gradually increases. Figure 3 (e) A comparison between numerical simulation and experimental results of coherence modulation is presented. The two are highly consistent, which fully demonstrates that the method of this embodiment can achieve flexible and on-demand modulation of the coherence magnitude of the spatiotemporally coherent optical field.

[0040] Spatiotemporal coherence structure distribution regulation: When the output partially coherent spatiotemporal wave packet is a Hermitian-Gaussian correlated spatiotemporal wave packet, the spatiotemporal coherence function of the Hermitian-Gaussian correlated spatiotemporal wave packet is expressed as: ; in, ( ) is a Hermitian polynomial of order 2m.

[0041] Figure 4 Experimental and simulation results were presented to output the spatiotemporal wave packet of Hermitian-Gaussian correlation. The results show that by setting the Hermitian-Gaussian order (m and n) in the spatial and temporal directions of the power spectral density function in the two-dimensional dynamic hologram, coherent distributions with specific Hermitian-Gaussian structural characteristics can be generated in both the spatial and temporal dimensions. The experimental measurements and numerical simulations are in high agreement, verifying that the method in this embodiment can achieve on-demand design and precise control of the spatiotemporally coherent optical field coherent structure.

[0042] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0043] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A system for generating and controlling a partially coherent spatiotemporal optical field, characterized in that, include: A pulse shaping assembly consisting of multiple optical elements and an incident light source for providing a fully coherent ultrafast pulsed light field; The optical elements in the pulse shaping group include a first blazed grating, a first cylindrical lens, a two-dimensional dynamic holographic modulator, a second cylindrical lens, and a second blazed grating arranged sequentially along the light field propagation direction; and the first cylindrical lens and the second cylindrical lens have the same focal length, and the spacing between adjacent optical elements is equal to the focal length of the first cylindrical lens and the second cylindrical lens. The two-dimensional dynamic holographic modulator is used to load a specific complex amplitude modulation function to reconstruct the spatial-spectral characteristics of the light field.

2. The system for generating and controlling a partially coherent spatiotemporal optical field as described in claim 1, characterized in that, The two-dimensional dynamic holographic modulator is a two-dimensional dynamic hologram with complex amplitude modulation capability, and the two-dimensional dynamic hologram is composed of a liquid crystal spatial light modulator or a digital micromirror array.

3. The system for generating and controlling a partially coherent spatiotemporal optical field as described in claim 1, characterized in that, The modulation surface of the two-dimensional dynamic holographic modulator is set perpendicular to the central axis of the first cylindrical lens and the second cylindrical lens.

4. A method for generating and controlling a partially coherent spatiotemporal optical field, based on the system for generating and controlling a partially coherent spatiotemporal optical field as described in any one of claims 1-3, characterized in that, include: After the incident light source emits a completely coherent ultrafast pulse light field, it passes through the first blazed grating for dispersion and the first cylindrical lens for collimation in sequence. The collimated ultrafast pulse light field forms a two-dimensional space-spectral plane in the plane where the two-dimensional dynamic holographic modulator is located. By loading a specific complex amplitude modulation function on the two-dimensional dynamic holographic modulator, the space-spectral plane of the ultrafast pulse light field is reconstructed. The reconstructed ultrafast pulsed light field then passes through the second cylindrical lens and the second blazed grating in sequence to combine, completing the inverse Fourier transform in the time and spatial domains, and outputting a partially coherent spatiotemporal wave packet with target coherence.

5. The method for generating and controlling a partially coherent spatiotemporal optical field as described in claim 4, characterized in that, The fully coherent ultrafast pulsed optical field, under the paraxial approximation and the slowly varying envelope approximation, is expressed as the product of the carrier and the complex envelope function.

6. The method for generating and controlling a partially coherent spatiotemporal optical field as described in claim 4, characterized in that, The instantaneous transmittance function expression of the two-dimensional dynamic holographic modulator is: ; in, It is the inverse singer function. The frequency of the linear grating phase. The dynamic phase hologram distribution function loaded for the spatial light modulator. To satisfy the random phase of the Dirac correlation, The spatial coordinates of the plane where the spatial light modulator is located. To eliminate harmonic frequencies, is the power spectral density function.

7. The method for generating and controlling a partially coherent spatiotemporal optical field as described in claim 4, characterized in that, The mutual coherence function of the partially coherent spatiotemporal wave packets is expressed as: ; in, , Let the three-dimensional coordinates of any two points in space and time on the plane where the spatial light modulator is located be given. , The three-dimensional coordinates of any two points in space and time on the output plane of the pulse shaper. For differential, It is the mutual coherence function of the light field after the ultrafast pulse light field passes through a two-dimensional dynamic holographic modulator.

8. The method for generating and controlling a partially coherent spatiotemporal optical field as described in claim 7, characterized in that, The expression for the mutual coherence function of the ultrafast pulsed light field after passing through the two-dimensional dynamic holographic modulator is: ; in, and Let be the instantaneous electric field of the incoherent electric field at the plane where the spatial light modulator is located, and * be the complex conjugate. and Let be the power spectral density function of the incoherent electric field. and To satisfy the dynamic random phase of the Dirac correlation.

9. The method for generating and controlling a partially coherent spatiotemporal optical field as described in claim 4, characterized in that, When the output partially coherent spatiotemporal wave packet is a Gauss-Schelle model spatiotemporal wave packet, the spatiotemporal coherence function of the Gauss-Schelle model spatiotemporal wave packet is expressed as: ； in, and These represent the position and time difference between any two points in space and time, respectively. and for .

10. The method for generating and controlling a partially coherent spatiotemporal optical field as described in claim 4, characterized in that, When the output partially coherent spatiotemporal wave packet is a Hermitian-Gaussian correlated spatiotemporal wave packet, the spatiotemporal coherence function of the Hermitian-Gaussian correlated spatiotemporal wave packet is expressed as: ； in, ( ) is a Hermitian polynomial of order 2m.

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