Superoscillation Generation and Control Method and Device Based on Coherent Control

Abstract

The present invention discloses a method and device for generating and controlling super oscillations based on coherent control. The device includes a laser, a beam expander, a polarizer, a spatial light modulator, a 4f filter system, a radial polarization light converter and a high numerical aperture objective lens arranged along an optical path. By introducing a cosine pseudo-Schermer correlation structure, a Gaussian light beam is modulated into a radially polarized Gaussian cosine mode beam through a spatial light modulator, and the initial parameters of the beam source plane are reasonably selected, so that the light beam produces strong interference between the modes in the focal plane, thereby generating a super oscillation phenomenon based on coherent control. The present invention breaks through the resolution size limitation of the traditional partially coherent correlation structure light beam imaging limited by the diffraction limit, and has superior adjustment flexibility and stable performance characteristics. By precisely controlling the coherence parameters of the light field, precise control of the super oscillation focusing spot of the beam focal field in the lateral direction can be achieved.

Description

Technical Field

[0001] The present invention belongs to the field of light field manipulation, and in particular relates to a method and device for generating and controlling super oscillations based on coherent control. Background Art

[0002] In the field of traditional optics, due to the nature of light beam diffraction, the spot size that can be formed by the optical system is limited to no less than half the wavelength. This can be attributed to the fact that the oscillation speed of the "band-limited" function cannot exceed the highest Fourier harmonic in its spectrum.

[0003] In the prior art, the superoscillation phenomenon has attracted widespread attention in the study of band-limited signals. Superoscillation refers to the situation where the oscillation frequency of a signal exceeds the frequency of the fastest oscillation in its Fourier component in a local area. The application of superoscillation is mainly reflected in the field of optics, especially in super-resolution imaging technology. Through the carefully designed superposition of wave functions, a "hotspot" with a size much smaller than the diffraction limit can be formed in a local area.

[0004] However, in superoscillation research, the partial coherence structure is usually regarded as a relatively constant parameter. But in practical applications, most light sources are not completely coherent. For example, random phase changes introduced by temperature, mechanical vibration or other reasons will inevitably reduce the coherence of light. Therefore, the generation of superoscillation phenomenon based on the partial coherence correlation structure and even the regulation of superoscillation phenomenon have become urgent problems to be solved in current super-resolution imaging technology. Summary of the invention

[0005] In order to solve the resolution limitation caused by the diffraction limit in traditional focusing systems, the present invention provides a super-oscillation generation and control method and device based on coherent regulation, and introduces a new variable, the partial coherent correlation structure, in the field of super-resolution imaging based on super-oscillation technology. It can significantly reduce or eliminate image distortion caused by interference and scattering of light, thereby significantly improving the contrast, clarity and quality of the image, and reducing the impact of optical artifacts and noise.

[0006] The technical solution to achieve the purpose of the present invention is: a super oscillation generation and control method based on coherent control, by introducing a cosine correlation structure, the light beam is modulated into a radially polarized Gaussian cosine mode light beam; the initial parameters of the beam source plane are selected so that the light beam produces strong interference between the modes in the focal plane, and the strong interference means that the frequency of the oscillation of the generated spectral signal is greater than the frequency of the fastest oscillation in the band-limited Fourier component generated by the lens aperture, thereby generating a super oscillation phenomenon based on coherent control.

[0007] Furthermore, the radially polarized Gaussian cosine mode light beam constructs a partially coherent light field cross spectral density matrix with a cosine correlation structure on the source plane, and the cross spectral density matrix expression is:

[0008]

[0009]

[0010]

[0011]

[0012] Among them, r 1 and r 2 Represents the position vector of any two points on the source plane, r 1 and r 2 represents the radial coordinate size of any two points on the source plane, S(r) represents the spectral density of the beam, r represents the radial coordinate size of any point on the source plane, w 0 is the initial beam waist width; θ(φ 1 ,φ 2 ) is the polarization matrix that characterizes the radial polarization of the light beam, φ 1 and φ 2 is the azimuth of the transverse plane;

[0013] g(Δr) represents the coherence of the light beam, Δr = r 1 -r 2 , a is a positive value that represents the coherence of the light source.

[0014] Furthermore, in order to be physically feasible, the elements of the CSD matrix Must have an integral representation:

[0015]

[0016] Among them, α, β = x, y, x and y are the horizontal plane coordinates of any two points on the source plane, respectively, to construct the weight function p required for the radially polarized Gaussian cosine mode beam. αβ (v) and kernel function Φ α (r,v) is expressed as:

[0017]

[0018]

[0019] Among them, δ is the Dirac function, v is a one-dimensional unitless vector, and r represents the position vector of any point on the source plane.

[0020] Furthermore, the method of phase control of the light beam by the spatial light modulator is: through mode expansion, the light beam is divided into a set of discrete modes, and different random phases are added to each mode to form a hologram; in order to ensure that the obtained modes are independent of each other, more than 200 holograms with random phases must be generated; the spatial intensity distribution of the light beam is adjusted to achieve incoherent superposition between different modes.

[0021] Furthermore, the lateral size of the focal spot of the light field is controlled by adjusting the waist width of the initial spot of the light beam.

[0022] The present invention also provides a super-oscillation generation and control device based on coherent control, which is used to implement the above method, and the device includes a laser, a beam expander, a linear polarizer, a reflector, a spatial light modulator, a 4f filter system, a radial polarization converter, a high numerical aperture objective lens and a CCD camera;

[0023] The laser beam emitted by the laser passes through a beam expander and then a linear polarizer to form a linearly polarized laser beam, which then passes through a reflector to reflect the beam onto a reflective phase spatial light modulator to generate a partially coherent linearly polarized beam. The partially coherent beam then passes through a 4f filter system to obtain a collimated and filtered first-order diffracted light, which then passes through a radial polarization converter to control the arrangement of liquid crystal units through a computer to convert the linear polarized light into radially polarized light. The partially coherent beam is focused through a high numerical aperture objective lens 16, and a partially coherent super-oscillating focused light spot of controllable size is observed on a CCD camera.

[0024] Furthermore, the 4f filtering system is composed of a thin lens 1, a pinhole aperture, and a thin lens 2 which are arranged in sequence.

[0025] Furthermore, the numerical aperture NA of the high numerical aperture objective lens is greater than 0.8.

[0026] Furthermore, the laser is a helium-neon laser with a wavelength of 632.8 nm and a power of 400 mW.

[0027] Furthermore, the focal lengths of the thin lens 1 and the thin lens 2 are both 150 mm, and the focal length of the high numerical aperture objective lens is 3 mm.

[0028] Compared with the prior art, the significant advantages of the present invention are as follows: the core innovation of the present invention is to introduce the partial coherent correlation structure into the study of super-oscillation phenomenon. The super-oscillation phenomenon refers to the oscillation frequency of the signal exceeding the frequency of the fastest oscillation in its Fourier component in a local area; by performing the first correlation structure regulation and the second polarization distribution modulation on the pre-processed laser beam, a radially polarized Gaussian cosine mode beam with a periodic correlation structure is obtained. When the beam propagates in a tightly focused optical system, the superposition interference between different modes realizes a focused light field with a sub-wavelength feature morphology resolution, which is not possible with the traditional partial coherent light correlation structure, providing a new variable for controlling the super-oscillation effect, and providing a new idea for the application of super-oscillation technology in the field of super-resolution imaging. What is more noteworthy is that by regulating the parameters of the partial coherent correlation structure, the size of the partially coherent super-oscillation focusing spot can be accurately controlled, which greatly saves the iterative calculation time in the traditional super-oscillation imaging, and the introduction of the partial coherent correlation structure can effectively reduce the artifact problem caused by the high-coherence laser in the imaging application, providing more possibilities for the application of super-oscillation technology in the field of super-resolution imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of a super oscillation generation and control method based on coherent control of the present invention.

[0030] Figure 2 It is a schematic diagram of a super oscillation generation and control device based on coherent control of the present invention.

[0031] Figure 3 It is a schematic diagram of the change of the intensity of the super-oscillating focused light spot based on coherent control with the change of parameter a, and the total light intensity in the longitudinal direction and the light spot in the xy direction in the focal plane.

[0032] Figure 4 It is a schematic diagram of the change of the intensity of the super-oscillating focused light spot based on coherent control with the change of parameter β, and the total light intensity in the longitudinal direction and the light spot in the xy direction in the focal plane.

[0033] Figure 5 This is a trend diagram of the super-oscillating focusing spot size based on coherent control as the parameter a changes.

[0034] Figure 6 This is a trend diagram of the super-oscillating focusing spot size based on coherent control as the parameter β changes.

[0035] Figure numerals: 7 - laser, 8 - beam expander, 9 - linear polarizer, 10 - reflector, 11 - spatial light modulator, 12 - thin lens 1, 13 - pinhole aperture, 14 - thin lens 2, 15 - radial polarization converter, 16 - high numerical aperture objective lens, 17 - CCD camera. DETAILED DESCRIPTION

[0036] The present invention provides a super-oscillation generation and control device based on coherent regulation, comprising the following components: a beam expander, a polarizer, a spatial light modulator (or DMD), a 4f filtering system, a radial polarization converter and a high numerical aperture objective lens. In the system, the beam expander is used to expand and collimate the laser beam, and the polarizer adjusts the expanded beam to a horizontally polarized linear polarized light to ensure that the polarization direction is consistent with the working direction of the spatial light modulator (or DMD). The phase of the special correlation structure is modulated by the spatial light modulator (or DMD) to achieve the regulation of the light field correlation structure. The 4f filtering system is used to ensure that the 0th order diffraction light is filtered out. The radial polarization converter controls the arrangement of liquid crystal units by a computer to convert linear polarization into radial polarized light. Finally, the high numerical aperture objective lens is used for focusing and generating. The entire system realizes the controllable size of the partially coherent super-oscillation focusing spot through precise optical elements and phase regulation.

[0037] Based on the above device, a super oscillation generation and control method based on coherent control of the present invention comprises the following steps:

[0038] Laser beam expansion and collimation include:

[0039] Step 1: First, a He-Ne laser 7 (wavelength 632.8 nm, power 400 mW) emits a laser beam for writing; after passing through a beam expander 8, the required beam waist width is achieved.

[0040] The formation of linear polarized light includes:

[0041] Step 2: The laser beam passes through a linear polarizer 9 to form a linearly polarized laser beam, and then passes through a reflector 10 to reflect the beam onto a reflective spatial light modulator (or DMD);

[0042] The spatial light modulator (or DMD) modulation phase and 4f filtering system include:

[0043] Step 3: The linearly polarized light beam is irradiated onto the spatial light modulator (or DMD) 11. The light beam on the SLM spatial light modulator (German ViALUX V series USB3.0 data transmission interface, onboard memory can store 170,000 1-bit binary graphic data, ultra-high resolution 2560×1600, ultra-high speed: the delay from reading to displaying the graphic data is less than 1500μs, and the non-real-time graphic refresh rate is as high as 22.272kHz) is already a shaped light beam, a partially coherent linearly polarized light beam with special statistical characteristics. The generated partially coherent modulated light beam passes through the 4f system composed of a thin lens 12, a pinhole aperture 13, and a thin lens 14 to obtain a beam of first-order diffracted light after collimation and filtering, where this 4f filter system can also be replaced by an aperture;

[0044] Generating radially polarized light includes:

[0045] Step 4: The filtered linearly polarized partially coherent light beam is converted into radially polarized light by a computer-controlled radial polarization converter 15 .

[0046] The high numerical aperture objective focusing includes:

[0047] Step 5: The generated partially coherent light beam is focused by a high numerical aperture objective focusing lens 16. The numerical aperture NA of the objective lens should be greater than 0.8 to ensure that the focusing condition is tight focusing.

[0048] The implementation principle of the method of the present invention is described in detail below.

[0049] By definition, super-oscillatory spots appear due to oscillations faster than the fastest Fourier component of a band-limited function. When light is focused with a lens, the fastest oscillating Fourier component corresponds to the annular component coming from the outer edge of the lens. The vector diffraction theory based on cylindrical vector beams provides an accurate way to describe this phenomenon. In this theoretical framework, for infinitely thin annular radially polarized beams, the strict intensity distribution I(r) at the focus can be described by a more complex mathematical expression.

[0050]

[0051] Among them, n 0 is the refractive index of the medium behind the lens, k is the wave vector of the light wave, J 0 and J 1 In this case, the light field distribution at the focus can be represented by the Bessel function of the first kind J 1 It can be described by the expression where n is the refractive index of the lens medium. The first and second terms in the equation correspond to the longitudinal and sagittal components at the focus, respectively.

[0052] For a system with numerical aperture NA = 1.4 and refractive index n 0 = 1.52, the full width at half maximum (FWHM) value of the superoscillation standard corresponds to 0.412λ m , where λ m is the wavelength in the medium, given by the wavelength λ in air 0 Divide by the refractive index n to get.

[0053] The present invention proposes a method and device for generating and controlling super oscillations based on coherent control, such as Figure 1 As shown, including:

[0054] First, the laser output beam is expanded and collimated, and its polarization direction is modulated to horizontal polarization through a polarizer.

[0055] Secondly, the light beam is modulated by a spatial light modulator into a radially polarized Gaussian cosine mode beam with a cosine periodic correlation structure, and its cross spectral density matrix can be expressed as:

[0056]

[0057]

[0058]

[0059]

[0060] Among them, r 1 and r 2 represents the position vector of any two points on the source plane, S(r) represents the spectral density of the beam, w 0 is the initial beam waist width, when w 0 When it is very large, it is equivalent to plane wave incidence. g(Δr) represents the coherence of the light beam, Δr = r 1 -r 2 , a is a positive value that represents the coherence of the light source. 1 ,φ 2 ) is the polarization matrix that characterizes the radial polarization of the light beam, φ 1 and φ 2 is the azimuth in the transverse plane.

[0061] To be physically realizable, the elements of the CSD matrix must have an integral representation:

[0062]

[0063] where Φ α and Φ β are two arbitrary kernel functions, p αβ (v) is a non-negative weight function, and * represents a conjugate operation. αβ (v), kernel function Φ α (r, v) has the following form:

[0064]

[0065]

[0066] At the same time, in order to measure the waist width of the initial spot of the beam, we define the dimensionless parameter β 0 :

[0067]

[0068] Where R is the radius of the lens.

[0069] From (6), we can see that the essence of mode decomposition is that the (spectral) spatial partially coherent field can be decomposed into the sum of completely coherent but uncorrelated basic modes. Therefore, the propagation and light-matter interaction problems with partially coherent fields can be analyzed by coherent optics.

[0070] After the light beam described by equation (2) passes through a tightly focused optical system, its electric field expression near the focal field of the lens is: n (x, y, z) can be expressed by the Richards-Wolf integral:

[0071]

[0072] Φ n (r) = Φ nx (r)n x +Φ ny (r)n y . (11)

[0073] Where f is the focal length, represents the inverse Fourier transform, z represents the axial distance from the focus to calculate the electric field, and are the far-field representations of the x and y components of the focused field of the incident field function (i.e., the field at the lens surface), Φ nx (r) and Φ ny They represent the electric field distribution of the incident field, n x and n y denotes the unit length vectors in the x and y directions respectively, Θ(k x ,k y ) represents the transmittance function of the lens, and n represents that it is the nth mode in the mode decomposition.

[0074]

[0075]

[0076] Among them, k = 2π / λ is the wave vector of the light beam, θ is the aperture angle, and k x , k y and k z are the components of the wave vector in the x, y and z directions respectively. After obtaining the mode vector near the focusing area, the CSD matrix W(r 1 ,z 1 ; r 2 ,z 2 ):

[0077]

[0078] where z1 and z 2 It represents the axial distance between any two points of the electric field and the focus, and T represents the transpose operation of the matrix.

[0079] The present invention is described in detail below with reference to the embodiments.

[0080] Example

[0081] In this embodiment, a system with a numerical aperture NA = 1.4 and a refractive index n = 1.52 is used. The corresponding superoscillation standard is a full width half maximum (FWHM) value corresponding to 0.412λ m .

[0082] like Figure 1 As shown in FIG. 1 , it is a system structure block diagram of a super oscillation generation and control method based on coherent control proposed by the present invention. Figure 2 This is a schematic diagram of an experimental device for the generation and control method of super oscillation based on coherent control of the present invention. First, the laser beam emitted by the laser 7 passes through a beam expander 8, and then passes through a linear polarizer 9 to form a linearly polarized laser beam, and then passes through a reflector 10, so that the beam is reflected on a reflective phase spatial light modulator 11, and a partially coherent linearly polarized beam with special statistical characteristics is generated; then the generated partially coherent beam passes through a 4f system composed of a thin lens 12, a pinhole aperture 13, and a thin lens 2 14 to obtain a collimated and filtered first-order diffracted light, and then passes through a radial polarization converter 15 to control the arrangement of liquid crystal units through a computer to convert the linear polarization into radial polarization. This beam is a partially coherent beam that can image the target, wherein the 4f filter system can also be replaced by an aperture; the generated partially coherent beam is focused by a high numerical aperture objective lens 16, so that a partially coherent super oscillation focused light spot with controllable size can be observed on the CCD 17 near the focus.

[0083] The focal length of the thin lens 12 is the same as that of the thin lens 2 14, 150 mm, and the focal length of the high numerical aperture objective lens 16 is 3 mm.

[0084] Figure 3 The change of the super-oscillating focusing spot size based on coherent control with the change of parameter a is shown. Where β=1.05(a)FWHM=0.383λ m (b) FWHM = 0.365λ m (c) FWHM = 0.389λ m . FWHM refers to the full width at half maximum, and the so-called full width at half maximum refers to the peak width at half the peak height of the spectrum. Figure 3 In case (a), the focused spot size is lower than the super-oscillation standard, indicating that super-oscillation can be generated by adjusting the partial coherent correlation structure.

[0085] Figure 4 The change of the super-oscillating focusing spot size based on coherent control with the change of parameter β is shown. a=3.8R(a)FWHM=0.389λ m (b) FWHM = 0.365λ m (n)FWHM=0.346λ m .

[0086] Figure 5 The trend of the super-oscillation focusing spot size based on coherent control as the parameter a changes is plotted. It can be seen that the minimum super-oscillation spot size can be obtained by selecting a suitable correlation structure parameter a.

[0087] Figure 6 The trend of the super-oscillating focusing spot size based on coherent control as the parameter β changes is plotted. By choosing a reasonable initial beam waist width, the full width at half maximum of the super-oscillating focusing spot can reach a sub-wavelength size, with a minimum of 0.3λ. m .

[0088] In summary, by introducing the partially coherent correlation structure, the size of the super-oscillation spot caused by the correlation structure can be flexibly controlled.

Claims

1. A super-oscillation generation and control method based on coherent control, characterized in that: By introducing a cosine correlation structure, the light beam is modulated into a radially polarized Gaussian cosine mode light beam; the initial parameters of the beam source plane are selected so that the light beam generates strong interference between the modes in the focal plane. The strong interference refers to that the frequency of the oscillation of the generated spectral signal is greater than the frequency of the fastest oscillation in the band-limited Fourier component generated by the lens aperture, thereby generating a super-oscillation phenomenon based on coherent regulation; the radially polarized Gaussian cosine mode light beam constructs a partially coherent light field cross-spectral density matrix with a cosine correlation structure on the source plane, and the expression of the cross-spectral density matrix is: Where r1 and r2 represent the position vectors of any two points on the source plane, r1 and r2 represent the radial coordinates of any two points on the source plane, S(r) represents the spectral density of the light beam, r represents the radial coordinate of any point on the source plane, w0 is the initial beam waist width; θ(φ1, φ2) is the polarization matrix representing the radial polarization of the light beam, φ1 and φ2 are the azimuths of the transverse plane; g(Δr) represents the coherence of the light beam, Δr = r1-r2, a is a positive value representing the coherence of the light source; To be physically feasible, the elements of the CSD matrix Must have an integral representation: Among them, α, β = x, y, x and y are the horizontal plane coordinates of any two points on the source plane, respectively, to construct the weight function p required for the radially polarized Gaussian cosine mode beam. αβ (v) and the kernel function Φ α (r,v) is expressed as: Among them, δ is the Dirac function, v is a one-dimensional unitless vector, and r represents the position vector of any point on the source plane.

2. The method for generating and controlling super oscillations based on coherent control according to claim 1, characterized in that: The method of using a spatial light modulator to control the phase of a light beam is as follows: through pattern expansion, the light beam is divided into a set of discrete patterns, and different random phases are added to each pattern to form a hologram; in order to ensure that the obtained patterns are independent of each other, more than 200 holograms with random phases must be generated; the spatial intensity distribution of the light beam is adjusted to achieve incoherent superposition between different patterns.

3. The super-oscillation generation and control method based on coherent control according to claim 1, characterized in that: By adjusting the initial spot waist width of the light beam, the lateral size of the focal spot of the light field is controlled.

4. A super-oscillation generation and control device based on coherent control, characterized in that: For implementing the method described in any one of claims 1 to 3, the device comprises a laser, a beam expander, a linear polarizer, a reflector, a spatial light modulator, a 4f filter system, a radial polarization converter, a high numerical aperture objective lens and a CCD camera; The laser beam emitted by the laser passes through a beam expander and then a linear polarizer to form a linearly polarized laser beam, which then passes through a reflector to reflect the beam onto a reflective phase spatial light modulator to generate a partially coherent linearly polarized beam. The partially coherent beam then passes through a 4f filter system to obtain a collimated and filtered first-order diffracted light, which then passes through a radial polarization converter to control the arrangement of liquid crystal units through a computer to convert the linear polarized light into radially polarized light. The partially coherent beam is focused through a high numerical aperture objective lens, and a partially coherent super-oscillating focused light spot of controllable size is observed on a CCD camera.

5. The super-oscillation generation and control device based on coherent control according to claim 4, characterized in that: The 4f filtering system is composed of a thin lens 1, a pinhole aperture, and a thin lens 2 which are arranged in sequence.

6. The super-oscillation generation and control device based on coherent control according to claim 4, characterized in that: The numerical aperture NA of a high numerical aperture objective is greater than 0.

8.

7. The super-oscillation generation and control device based on coherent control according to claim 4, characterized in that: The laser is a helium-neon laser with a wavelength of 632.8 nm and a power of 400 mW.

8. The super-oscillation generation and control device based on coherent control according to claim 5, characterized in that: The focal lengths of the thin lens 1 and the thin lens 2 are both 150 mm, and the focal length of the high numerical aperture objective lens is 3 mm.

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