A space-time pulse shaping method based on a cascaded 4f system

Abstract

The application relates to a space-time pulse shaping method based on a cascade 4f system. The method adopts a space-time pulse shaping device based on a cascade 4f system, and the method comprises the following steps: setting an incident pulse light beam, separating different frequency components of the incident pulse light beam to different spatial positions through a first diffraction grating, then the pulse enters a plurality of cascaded 4f systems, the 4f systems perform phase modulation on the pulse, and finally the different frequency components of the pulse output by the last 4f system are combined through a second diffraction grating to complete pulse shaping. Compared with the prior art, the application has the advantages of completing an arbitrary y-t domain space-time light pulse shaping task and the like.

Description

Technical Field

[0001] This invention relates to the technical field of spacetime pulse shaping, and in particular to a spacetime pulse shaping device and method based on a cascaded 4f system. Background Technology

[0002] Pulse shaping technology is widely used in theoretical research and engineering applications in fields such as optical communication, biooptics, and quantum optics. Unlike spatial domain waveform transformation, time domain waveform modulation involves the separate modulation of different frequency components. Since Newton discovered dispersion, various dispersive devices have been invented, among which gratings are commonly used optical devices. At a suitable incident angle, a grating can diffract incident light of different frequencies (different wavelengths) to different angles, thus separating the frequencies of light waves and achieving separate modulation of different frequencies.

[0003] For example, in reference 1, “Space-Time Profiles of Shaped Ultrafast Optical Waveforms” (Wefers MM, Nelson K A. IEEE Journal of Quantum Electronics, 1996, 32(1): 161-172.), a diffraction grating is combined with a one-dimensional phase modulation device. The diffraction grating is used to diffract the incident light wave to different positions on the x-axis for separate modulation. The theoretical analysis and experimental verification of the time-domain shaping effect of the incident pulse are shown.

[0004] Reference 1 mainly maps the time domain of the pulse to the x-axis of the spatial domain and then achieves pulse shaping effect through one-dimensional phase modulation. Soon, researchers extended the phase modulation from one-dimensional to two-dimensional xy-domain phase modulation. In this process, a diffraction grating is used to map the pulse time domain to the x-axis of the spatial domain for modulation, while the pulse is simultaneously modulated on the y-axis of the spatial domain to achieve pulse yt-domain modulation.

[0005] For example, in reference 2, “Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum” (Chong A, Wan C, Chen J, et al. Nature Photonics, 2020, 14(6): 350-354.), Professor Zhan Qiwen’s research group at Shanghai University of Science and Technology used a single-stage reflective 4f system to perform helical phase modulation on the pulsed yt domain to generate a transverse vortex beam carrying the orbital angular momentum of the yt domain, thus experimentally generating a spacetime optical vortex (STOV) for the first time.

[0006] In the aforementioned reference 2, only a single-stage 4f system was used to perform a single spiral phase modulation. The pulse modulation task completed was to generate a longitudinal orbital angular momentum vortex with relatively regular intensity and phase distribution.

[0007] However, existing technologies cannot complete the task of shaping light pulses in arbitrary yt domain spacetime, nor can they complete the task of generating complex light field distributions such as OPTICA strings. At the same time, the STOV generated by existing methods has serious distortion and trailing phenomena, with significant differences from the ideal light spot and large mean square error, which affects the potential application effect of STOV. Summary of the Invention

[0008] The purpose of this invention is to overcome the defects of the prior art by providing a space-time pulse shaping device and method based on a cascaded 4f system.

[0009] The objective of this invention can be achieved through the following technical solutions:

[0010] A space-time pulse shaping method based on a cascaded 4f system is disclosed. The method employs a space-time pulse shaping device based on a cascaded 4f system. The device includes a first diffraction grating at the incident position, several cascaded 4f systems, and a second diffraction grating at the exit position, all placed sequentially.

[0011] The method includes the following steps:

[0012] An incident pulse beam is set up and passes through a first diffraction grating, which separates the different frequency components of the incident pulse beam to different spatial positions. Then the pulse enters several cascaded 4f systems, which perform phase modulation on the pulse. After passing through a second diffraction grating, the different frequency components of the pulse output by the last 4f system are combined to complete pulse shaping.

[0013] Furthermore, the 4f system consists of a first cylindrical lens, a transmissive spatial light modulator, and a second cylindrical lens arranged sequentially, with the distance between the three being the focal length of the cylindrical lens.

[0014] Furthermore, the specific process of phase modulation of the pulse using a 4f system is as follows:

[0015] The incident pulse is sequentially phase-modulated by a 4f system consisting of a first cylindrical lens, a transmissive spatial light modulator with pre-loaded phase modulation, and a second cylindrical lens.

[0016] Furthermore, the 4f system consists of a beam splitter, a cylindrical lens, and a reflective spatial light modulator arranged sequentially, with the interval between the cylindrical lens and the reflective spatial light modulator being the focal length of the cylindrical lens.

[0017] Furthermore, the 4f system also includes a reflector located between the beam splitter and the cylindrical lens, forming a multi-reflection structure. The distance between the reflector, the cylindrical lens, and the reflective spatial light modulator is the focal length of the cylindrical lens.

[0018] Furthermore, the specific process of phase modulation of the pulse using a 4f system is as follows:

[0019] The incident pulse is sequentially phase-modulated by a 4f system consisting of an optical beam splitter, a cylindrical lens, a pre-loaded phase-modulated reflective spatial light modulator, and a reflector.

[0020] Furthermore, the spatial light modulator has phase modulation capability. The phase mask loaded on it is trained using gradient descent based on the incident pulse light field distribution and the target field distribution. The training process is as follows:

[0021] The output optical field is obtained by modeling the optical field transmission in the yt domain of the multi-stage 4f system. The loss function is constructed by the L2 norm of the output optical field and the target field. The partial derivative of the loss function with respect to the phase loaded by the spatial light modulator in each stage of the 4f system is calculated using the backpropagation algorithm. The phase is then updated until convergence is achieved using the gradient descent method.

[0022] Furthermore, the output light field is:

[0023]

[0024] Where U0 represents the input light field, U N+1 This represents the output light field after passing through the grating twice. A 4f system has N levels, where the subscript index k indicates the k-th level 4f system. M k This represents the spatial light modulator loaded on the k-th level 4f system in the N-level 4f system. Phase modulation of the incident light wavefront and The frequency and spatial domain propagation operators representing the propagation of the light field from the input plane to the first spatial light modulator. and The frequency and spatial domain transmission operators represent the transmission of the optical field from the (k-1)th spatial light modulator to the kth spatial light modulator. and The frequency and spatial domain transmission operators represent the transmission of the light field from the Nth spatial light modulator to the output plane.

[0025] Furthermore, the loss function is:

[0026]

[0027] Where L represents the loss function, U N+1Let T represent the output light field, i.e., the output light field after passing through the grating twice, and let T represent the target field distribution. The partial derivative calculated using the error backpropagation algorithm is: Indicates the phase being loaded.

[0028] Furthermore, the first diffraction grating separates the different frequency components of the incident pulse beam to different positions on the x-axis, realizing the mapping of the frequency domain to the spatial x-domain.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] (1) This invention improves the shaping capability of space-time pulses in the yt domain by introducing a multi-level cascaded 4f system and using a multi-layer phase-type spatial light modulator. It can complete the task of generating complex light field distributions such as OPTICA strings and produces good space-time vortex effects.

[0031] (2) The present invention uses the backpropagation algorithm to obtain the required multi-layer phase modulation parameters through a two-dimensional gradient descent training process, and loads them into a multi-layer phase-type spatial light modulator, which can complete the task of spatial light pulse shaping in any yt domain. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the structure of the present invention;

[0033] Figure 2 This is a diagram showing the intensity and phase distribution of the incident pulse beam in the yt domain according to the present invention, wherein, Figure 2 (a) represents the intensity of the incident pulse beam in the yt domain. Figure 2 (b) is a phase distribution diagram of the incident pulse beam;

[0034] Figure 3 A schematic diagram of a single reflective 4f system;

[0035] Figure 4 A schematic diagram of a 4f SLM multiplexing system using multiple reflections from a mirror;

[0036] Figure 5 The target pulse field distribution diagram;

[0037] Figure 6 The phase distribution training results are shown in the SLM loading diagram for a seven-level cascaded 4f system.

[0038] Figure 7 The output pulse-shaped data is shown as the intensity and phase distribution in the yt domain. Figure 7 (a) represents the pulse-shaped output yt domain intensity. Figure 7 (b) is the pulse shaping output phase distribution diagram;

[0039] In the figure, at the incident position, there is a diffraction grating 1, a first 4f system 2, a second 4f system 3, a third 4f system 4, at the exit position, there is a diffraction grating 5, a first cylindrical lens 6, a transmissive SLM 7, a second cylindrical lens 8, a beam splitter 9, a third cylindrical lens 10, a first reflective SLM 11, a reflector 12, a fourth cylindrical lens 13, and a second reflective SLM 14. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0041] Definitions:

[0042] SLM: Spatial Light Modulator.

[0043] This invention proposes a space-time pulse shaping method based on a cascaded 4f system. The method employs a space-time pulse shaping device based on a cascaded 4f system, comprising a first diffraction grating at the incident position, several cascaded 4f systems, and a second diffraction grating at the exit position, placed sequentially. A structural diagram of the method is shown below. Figure 1 As shown.

[0044] The device includes a diffraction grating 1 at the incident position, several 4f systems (there can be three 4f systems: a first 4f system 2, a second 4f system 3, and a third 4f system 4), and a diffraction grating 5 at the exit position. The incident pulse beam passes through the diffraction grating 1, where different frequency components are separated to different spatial positions. Then, it sequentially passes through the first 4f system 2, the second 4f system 3, and the third 4f system 4 to modulate the phase of the pulse. Finally, it passes through the diffraction grating 5 to combine the different frequency components, completing pulse shaping.

[0045] Among them, the diffraction grating 1 at the incident position separates the different frequency components of the incident pulse to different positions on the x-axis, realizing the mapping of the frequency domain to the spatial x-domain.

[0046] The 4f system has two implementation methods depending on the phase-type SLM used. One is, as... Figure 1 The system shown consists of a first cylindrical lens 6, a transmissive SLM 7, and a second cylindrical lens 8, forming a transmissive 4f system. The distance between the three elements is the focal length f of the cylindrical lens. Secondly, as shown... Figure 3 The diagram shows a single reflective 4f system. The 4f system consists of a beam splitter 9, a third cylindrical lens 10, and a first reflective SLM 11. The distance between the cylindrical lens 10 and the reflective SLM 11 is equal to the focal length f of the cylindrical lens. Figure 4 A schematic diagram of a 4f multiplexing SLM system using multiple reflections from mirrors is shown below. Figure 4As shown, the reflective 4f system can use the reflector 12, the fourth cylindrical lens 13, and the second reflective SLM 14 to form a multi-reflection structure. The distance between the three elements is the focal length f of the cylindrical lens. The SLM is used in sections to improve efficiency and reduce system cost.

[0047] The phase-type SLM used in a 4f system can modulate the wavefront phase of the incident beam according to the loaded phase mask. The yt domain signal transmission of a multi-stage 4f system can be modeled as follows:

[0048]

[0049] Where U0 represents the input light field, U N+1 This represents the output light field after passing through the grating twice. A 4f system has N levels, and the subscript index k indicates the k-th level 4f system. This represents the spatial light modulator loaded on the k-th level 4f system in the N-level 4f system. The phase modulates the wavefront of the incident light wave. and The propagation operator representing the optical field's transmission from the input plane to the first SLM in both the frequency and spatial domains. and The frequency and spatial domain propagation operators representing the optical field's transmission from the (k-1)th SLM to the kth SLM. and This represents the propagation operator in both the frequency and spatial domains of the optical field as it travels from the Nth SLM to the output plane. The loss function is defined. T represents the target field distribution. Calculate the partial derivative of the modulation phase with respect to each stage of the 4f system. The phase loaded on the SLM is updated using gradient descent based on the partial derivative until the loss function converges.

[0050] The incident pulse beam used in this invention is as follows: Figure 2 As shown, Figure 2 (a) represents the intensity of the incident pulse beam in the yt domain. Figure 2 (b) shows the phase distribution of the incident pulse beam, which is as follows:

[0051] E1 = exp(-x 2 / a 2 )exp(-y 2 / b 2 )exp(-t 2 / c 2 )

[0052] Where a = 2 mm, b = 50 μm, and c = 0.1582 ps.

[0053] The following is an analysis of a practical example:

[0054] In this embodiment, an OPTICA character image is used as the target pulse field distribution, as shown in the distribution diagram below. Figure 5 As shown. The mask phase distribution parameters are obtained by training the input pulse field distribution using a gradient descent method, taking its two-dimensional yt domain distribution. In this embodiment, the seven-layer phase distribution obtained by training the seven-level cascaded 4f system is as follows: Figure 6 As shown.

[0055] Loading on SLM Figure 6 The phase distribution shown indicates that the incident pulse passes through... Figure 1 After the seven-layer cascaded 4f system shown, the final output pulse is obtained. The intensity and phase distribution of the final output pulse are as follows: Figure 7 As shown, Figure 7 (a) represents the pulse-shaped output yt domain intensity. Figure 7 (b) is the pulse shaping output phase distribution diagram, which clearly shows the six characters OPTICA, and is basically consistent with the target field.

[0056] This invention combines a diffraction grating with a multi-stage cascaded 4f system to form a spacetime diffraction neural network. The phase parameters of the 4f system phase modulator are obtained by training with backpropagation of error and gradient descent, demonstrating the ability to perform arbitrary spacetime pulse shaping tasks in the yt domain with low computational complexity.

[0057] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A space-time pulse shaping method based on a cascaded 4f system, characterized in that, The method employs a space-time pulse shaping device based on a cascaded 4f system. The device includes a first diffraction grating at the incident position, several cascaded 4f systems, and a second diffraction grating at the exit position, placed sequentially. The method includes the following steps: An incident pulse beam is set up and passes through a first diffraction grating. The first diffraction grating separates the different frequency components of the incident pulse beam to different positions on the x-axis, realizing the mapping of the frequency domain to the spatial x-domain. Then the pulse enters several cascaded 4f systems, with the number of 4f systems being greater than or equal to 2. The 4f systems perform phase modulation on the pulse, and then it passes through a second diffraction grating. The different frequency components of the pulse output by the last 4f system are combined to complete the spatial light pulse shaping task in the arbitrary yt domain; t is time, and the xy plane is the plane where the spatial light modulator is located. The 4f system consists of a first cylindrical lens, a transmissive spatial light modulator, and a second cylindrical lens arranged sequentially, with the distance between the three being the focal length of the cylindrical lens. The 4f system consists of a beam splitter, a cylindrical lens, and a reflective spatial light modulator arranged in sequence, with the interval between the cylindrical lens and the reflective spatial light modulator being the focal length of the cylindrical lens.

2. The space-time pulse shaping method based on a cascaded 4f system according to claim 1, characterized in that, The specific process of phase modulation of a pulse using a 4f system is as follows: The incident pulse is sequentially phase-modulated by a 4f system consisting of a first cylindrical lens, a transmissive spatial light modulator with pre-loaded phase modulation, and a second cylindrical lens.

3. The space-time pulse shaping method based on a cascaded 4f system according to claim 1, characterized in that, The specific process of phase modulation of a pulse using a 4f system is as follows: The incident pulse is sequentially phase-modulated by a 4f system consisting of an optical beam splitter, a cylindrical lens, a pre-loaded phase-modulated reflective spatial light modulator, and a reflector.

4. The space-time pulse shaping method based on a cascaded 4f system according to claim 1, characterized in that, The spatial light modulator has phase modulation capability. The phase mask loaded on it is trained using the gradient descent method based on the incident pulse light field distribution and the target field distribution. The training process is as follows: The output optical field is obtained by modeling the optical field transmission in the yt domain of the multi-stage 4f system. The loss function is constructed by the L2 norm of the output optical field and the target field. The partial derivative of the loss function with respect to the phase loaded by the spatial light modulator in each stage of the 4f system is calculated using the backpropagation algorithm. The phase is then updated until convergence is achieved using the gradient descent method.

5. The space-time pulse shaping method based on a cascaded 4f system according to claim 4, characterized in that, The output light field is: in, Represents the input light field. This represents the output light field after passing through the grating twice. The 4f system has a total of... Level, subscript index Indicates the first Level 4f system, express The 4f system Loaded on the spatial light modulator of the 4f-level system Phase modulation of the incident light wavefront and The frequency and spatial domain propagation operators representing the propagation of the light field from the input plane to the first spatial light modulator. and Representing the light field from the first The spatial light modulator transmits to the first The frequency domain and spatial domain transmission operators of a spatial optical modulator, and Representing the light field from the first A spatial optical modulator transmits frequency domain and spatial domain transmission operators to the output plane.

6. The space-time pulse shaping method based on a cascaded 4f system according to claim 4, characterized in that, The loss function is: in, Represents the loss function. This represents the output light field, specifically the output light field after passing through the grating twice. Representing the target field distribution, the partial derivative calculated using the error backpropagation algorithm is: , This indicates the phase being loaded.

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