A method for generating a switchable optical ring lattice

Abstract

The present invention provides a method for generating a switchable optical ring lattice, the method comprising: preloading a preset complex amplitude mask onto a phase-type spatial light modulator, the complex amplitude mask being the complex amplitude mask corresponding to a superposition of circular Airy vortex beams with the same chirality and different topological charges; wherein a plurality of parameters of the complex amplitude mask are adjustable in real time; making a plane light wave incident on the spatial light modulator, and performing an inverse Fourier transform on the light emitted from the spatial light modulator to obtain an optical ring lattice with a chiral radial structure. The present invention utilizes complex amplitude modulation technology and digital propagation technology based on the angular spectrum theory, loads the complex amplitude mask of the superposition of circular Airy beams at a fixed plane onto the spatial light modulator, and then obtains a switchable optical ring lattice at the fixed plane through an inverse Fourier transform. The above-mentioned technology of the present invention has important value in the fields of holographic optical tweezers, laser processing, optical communication, etc.

Description

Technical Field

[0001] The present invention relates to a method for generating a switchable optical ring lattice, belonging to the field of optics. Background Art

[0002] An optical lattice is an array of periodic potential wells formed by multi-beam interference. Its array structure is editable and is similar to the lattice structure in solid physics. Due to its controllable and diverse structure, it has important applications in fields such as atomic trapping and cooling, photonic crystal lithography, micro-nano manipulation, super-resolution microscopy, and optical communication. The spatial structure of the optical lattice depends on the wave vectors of the interfering light waves, and the layout of the wave vectors determines the spatial morphology, period, and unit cell shape of the optical lattice. In the past, methods for generating optical lattices included the four-fiber method, the Talbot effect method, etc. The optical lattices generated by these methods are still limited in terms of spatial dimension, period, and arrangement pattern by the number and wave vectors of the interfering light waves. So far, optical ring lattices can be generated by superimposing circularly symmetric structured light fields carrying orbital angular momentum, such as Laguerre-Gaussian beams, Bessel beams, and perfect vortex beams. However, the ring lattices generated by the existing methods continuously expand during long-distance propagation, which is not conducive to applications such as spatial optical communication. Moreover, the generated ring lattices have a single spatial structure, and it is difficult to flexibly control the lattice structure. Therefore, there is still a need for a method with a simple device, convenient operation, and capable of forming a switchable complex lattice structure to solve this problem. Summary of the Invention

[0003] In view of the above problems, the present invention proposes a method for generating a switchable optical ring lattice to solve the problems in the prior art that the generated ring lattice has a single spatial structure and it is difficult to flexibly control the lattice structure.

[0004] According to one aspect of the present invention, there is provided a method for generating a switchable optical ring lattice, the method comprising: preloading a preset complex amplitude mask onto a phase-type spatial light modulator, the complex amplitude mask being the complex amplitude mask corresponding to a superimposed circular Airy vortex beam carrying the same chirality and different topological charges; wherein, a plurality of parameters of the complex amplitude mask are adjustable in real time; making a plane light wave incident on the spatial light modulator, and performing an inverse Fourier transform on the light emitted from the spatial light modulator to obtain an optical ring lattice with a chiral radial structure.

[0005] Further, the plurality of parameters are the adjustable parameters of the complex amplitude mask, wherein each adjustable parameter corresponds to a plurality of preset values; the method further comprises: selecting one or more of the adjustable parameters of the complex amplitude mask as the parameters to be adjusted, and adjusting the parameters to be adjusted from the current value to their respective target values to achieve the switching between the currently obtained optical ring lattice and the target optical ring lattice.

[0006] Further, the optical ring lattice obtained by the method is an optical ring bright-field lattice or an optical ring dark-field lattice.

[0007] Further, the step of preloading the preset complex amplitude mask onto the phase-type spatial light modulator includes: superimposing two circular Airy vortex beams with the same chirality and different topological charges, and using the complex amplitude modulation technology and the digital propagation technology based on the angular spectrum theory to obtain the Fourier spectral hologram of the superimposed circular Airy beam at a fixed plane, and encoding it on the spatial light modulator.

[0008] Further, the plurality of adjustable parameters include at least one of the following parameters: the propagation distance of the target light field; the respective initial emission angle parameters of the two circular Airy vortex beams; the respective topological charges of the two circular Airy vortex beams; wherein, the target light field is the light field corresponding to the superimposed circular Airy vortex beam.

[0009] Further, the expression of the complex amplitude mask loaded onto the spatial light modulator is:

[0010]

[0011] wherein represents the corresponding complex amplitude mask, represents the phase after Fourier transform of the superimposed circular Airy vortex beam, represents the frequency domain coordinates of the superimposed circular Airy vortex beam, is the phase of the blazed grating, and mod is the modulo operator, is the phase depth of the blazed grating.

[0012] Further, the step of performing inverse Fourier transform on the light emitted from the spatial light modulator includes: placing the spatial light modulator at the front focal plane of the lens, so that the light emitted from the spatial light modulator undergoes inverse Fourier transform through the lens to obtain the target superimposed circular Airy vortex beam on the rear focal plane of the lens.

[0013] Further, when the main ring radii and main ring widths of the two circular Airy vortex beams are the same, the obtained optical ring lattice is an optical ring bright-field lattice; when the main ring radii of the two circular Airy vortex beams are different but the main ring widths are the same, the obtained optical ring lattice is an optical ring dark-field lattice.

[0014] A method for generating a switchable optical ring lattice according to the present invention superimposes two circular Airy vortex beams with the same chirality and different topological charges, uses complex amplitude modulation technology and digital propagation technology based on the angular spectrum theory, loads the complex amplitude mask of the superimposed circular Airy beam at a fixed plane obtained onto a spatial light modulator, and then obtains a real-time switchable optical ring lattice at the fixed plane through inverse Fourier transform.

[0015] In the prior art, for the optical ring lattice generated by using its structured light field, since the interfering light waves may diverge during propagation, the lattice pattern cannot be stably propagated over long distances. Compared with the prior art, in the present invention, two circular Airy vortex beams with different topological charges are used for interference. Since this kind of beam propagates in a rotational self-focusing manner, it has a higher angular velocity compared with the superimposed Laguerre and Bessel beams, and generates a richer lattice structure. In addition, the present invention uses digital propagation technology. At a fixed operation plane, by changing the artificial propagation distance, it is possible to real-time switch the bright-field lattice, dark-field lattice with chiral radial structures, and multi-layer complex structure lattices without changing the beam settings. Therefore, the above technologies of the present invention have important value in fields such as holographic optical tweezers, laser processing, and optical communication. Brief Description of the Drawings

[0016] Figure 1 is a flowchart of a method for generating a switchable optical ring lattice according to an embodiment of the present invention;

[0017] Figure 2 is an experimental apparatus used in a method for generating a switchable optical ring lattice according to an embodiment of the present invention;

[0018] Figure 3 is a schematic diagram of an optical ring bright-field lattice obtained according to an embodiment of the present invention;

[0019] Figure 4 is a schematic diagram of an optical ring dark-field lattice obtained according to an embodiment of the present invention;

[0020] Figure 5 is a schematic diagram of the switching of the optical ring dark-field - bright-field - multi-layer lattice at a fixed plane according to an embodiment of the present invention;

[0021] Figure 6 is a schematic diagram of the switching of the optical ring bright-field - dark-field - multi-layer lattice at a fixed plane according to an embodiment of the present invention. Detailed Description of the Embodiment

[0022] To enable those skilled in the art to better understand the solution of the present invention, the exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments or examples obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0023] According to an embodiment of the present invention, a method for generating a switchable optical ring lattice is provided, and the method includes: preloading a preset complex amplitude mask onto a phase-type spatial light modulator, where the complex amplitude mask is a complex amplitude mask corresponding to a superposed circular Airy vortex beam carrying the same chirality and different topological charges; wherein, multiple parameters of the complex amplitude mask are adjustable in real time; making a plane light wave incident on the spatial light modulator, and performing an inverse Fourier transform on the light output from the spatial light modulator to obtain an optical ring lattice with a chiral radial structure.

[0024] Figure 1 The flowchart of the above method for generating a switchable optical ring lattice is shown.

[0025] As Figure 1 shown, in step S110, a preset complex amplitude mask is preloaded onto a phase-type spatial light modulator.

[0026] Among them, the complex amplitude mask is a complex amplitude mask corresponding to a superposed circular Airy vortex beam carrying the same chirality and different topological charges.

[0027] "Superposed circular Airy vortex beam carrying the same chirality and different topological charges" refers to the target light field obtained by superposing two circular Airy vortex beams carrying the same chirality and different topological charges.

[0028] In the embodiment of the present invention, multiple parameters of the complex amplitude mask are adjustable in real time.

[0029] As an example, multiple adjustable parameters include, for example, one or more of the following parameters: the propagation distance of the target light field; the respective initial emission angle parameters of the two circular Airy vortex beams; the respective topological charges of the two circular Airy vortex beams; wherein, the target light field is the light field corresponding to the superposed circular Airy vortex beam.

[0030] It should be understood that the number of preset values corresponding to each adjustable parameter can be a finite number or an infinite number. That is to say, for any adjustable parameter, for example, several different preset values can be set for this parameter, so that the parameter can be switched between these multiple preset values; or, for this adjustable parameter, its value can also be changed infinitely by means of experiments to adjust, so as to switch the finally obtained optical ring lattice.

[0031] In one example, the step of preloading a preset complex amplitude mask onto the phase-type spatial light modulator in step S110 can be achieved through the following process: superimpose two circular Airy vortex beams with the same chirality and different topological charges, and use complex amplitude modulation technology and digital propagation technology based on the angular spectrum theory to obtain the Fourier spectral hologram of the superimposed circular Airy beam at a fixed plane, and encode it on the spatial light modulator.

[0032] In step S120, make a plane light wave incident on the spatial light modulator, perform an inverse Fourier transform on the light exiting the spatial light modulator, and obtain an optical ring lattice with a chiral radial structure.

[0033] In one example, the step of performing an inverse Fourier transform on the light exiting the spatial light modulator can be achieved in the following manner: place the spatial light modulator at the front focal plane of a lens, so that the light exiting the spatial light modulator undergoes an inverse Fourier transform by the lens to obtain the target superimposed circular Airy vortex beam (i.e., the target light field) on the rear focal plane of the lens.

[0034] As an example, the optical ring lattice obtained in step S120 can be an optical ring bright field lattice or an optical ring dark field lattice.

[0035] As an example, the expression of the complex amplitude mask loaded onto the spatial light modulator is, for example:

[0036]

[0037] Among them, represents the corresponding complex amplitude mask, represents the phase after the Fourier transform of the superimposed circular Airy vortex beam, represents the frequency domain coordinates of the superimposed circular Airy vortex beam, is the phase of the blazed grating, and mod is the modulo operator, is the phase depth of the blazed grating.

[0038] In addition, as an example, multiple parameters are used as multiple adjustable parameters of the complex amplitude mask, and each adjustable parameter corresponds to multiple preset values. The above method may further include Figure 1 the step S130 shown in Figure 1 The step S130 shown in

[0039] is optional and not an essential step.

[0040] As an example, when the main ring radius and the main ring width of two circular Airy vortex beams are the same, the obtained optical ring lattice is an optical ring bright-field lattice; when the main ring radii of two circular Airy vortex beams are different but the main ring widths are the same, the obtained optical ring lattice is an optical ring dark-field lattice.

[0041] As mentioned above, for the optical ring lattices generated by the structured light fields in the past, since the interfering light waves may diverge during propagation, the lattice patterns cannot be stably propagated at long distances. In this invention, two circular Airy vortex beams carrying different topological charges are used for interference. Since this kind of beam propagates in a rotating self-focusing manner, compared with the superimposed Laguerre and Bessel beams, it has a higher angular velocity and can generate a richer lattice structure. By using digital propagation technology, at a fixed operation plane, by changing the artificial propagation distance, it is possible to switch in real time between bright-field lattices, dark-field lattices with chiral radial structures, and multi-layer complex structure lattices without changing the beam settings. It has important value in the fields of holographic optical tweezers, laser processing, and optical communication.

[0042] In summary, the present invention proposes a method for generating switchable optical ring lattices. Based on the complex amplitude modulation technology, a hologram of superimposed circular Airy vortex beams carrying the same chirality and different topological charges is loaded on a spatial light modulator. By using digital propagation technology, the function of real-time switching of the required lattices at a fixed plane is realized, which has the advantages of simple device, independent manipulation, and dynamically adjustable lattice structure.

[0043] Preferred Embodiment

[0044] First, the complex amplitude expression of the circular Airy vortex beam in the initial plane in the cylindrical coordinate system is given as:

[0045]

[0046] In the formula, Ai represents the Airy function, r, are the radial and angular coordinates in the polar coordinate system respectively, a is the attenuation coefficient, β n =(r n -r) / w n , where r n is the size of the main ring radius, w n is the main ring width, m n is the azimuthal index of the helical phase (i.e., the topological charge), v n is the parameter determining the initial emission angle (i.e., the initial emission angle parameter), satisfying θ = v n / (kx0), k is the wave number, x0 is the transverse coordinate scale, and θ represents the initial emission angle. The i in formula (1) represents the imaginary unit. z is the propagation distance in the propagation direction. z0 represents the initial position of propagation.

[0047] The target optical field is the superposition of two circular Airy vortex beams, and its complex amplitude can be expressed as:

[0048]

[0049] In formula (2), and respectively represent the complex amplitudes of the two circular Airy vortex beams.

[0050] n is the ordinal number of the superimposed circular Airy vortex beams. In the embodiments of the present invention, n takes the value of 1 or 2. n = 1 corresponds to the first circular Airy vortex beam, and n = 2 corresponds to the second circular Airy vortex beam.

[0051] When r1 = r2 = r0 and w1 = w2 = w0, formula (2) can be expressed as:

[0052]

[0053] where C = Ai(β0)exp(aβ0), and β0 = (r0 - r) / w0.

[0054] Among them, r1 represents the main ring radius of the first circular Airy vortex beam, r2 represents the main ring radius of the second circular Airy vortex beam, r1 = r2 = r0 means that the values of the main ring radii of the first and second circular Airy vortex beams are both equal to r0, and r0 is a preset radius value.

[0055] In addition, w1 represents the main ring width of the first circular Airy vortex beam, w2 represents the main ring width of the second circular Airy vortex beam, w1 = w2 = w0 means that the main ring widths of the first and second circular Airy vortex beams are both equal to w0, and w0 is a preset main ring width value.

[0056] m1 represents the topological charge of the first circular Airy vortex beam, and m2 represents the topological charge of the second circular Airy vortex beam.

[0057] v1 represents the initial emission angle parameter of the first circular Airy vortex beam, and v2 represents the initial emission angle parameter of the second circular Airy vortex beam.

[0058] In addition, when n = 1, β1 = (r1 - r) / w1; when n = 2, β2 = (r2 - r) / w2. Let β1 and β2 both be equal to β0, that is, β1 = β2 = β0.

[0059] The light intensity of the target optical field can be expressed as:

[0060]

[0061] where \(N = |m_1 - m_2|\) represents the number of main lobes of the annular lattice, and \(|v_1 - v_2|\) is related to the overlap of the propagation trajectories of the two circular Airy vortex beams. By changing the topological charge parameter \(m\) of the two circular Airy vortex beams n , and the main ring radius parameter \(r\) n , the light intensity profile presents an optical annular lattice.

[0062] To experimentally prepare the required optical annular lattice, first perform a Fourier transform on the superposed circular Airy vortex beams to obtain the complex amplitude distribution in their spectral space (i.e., ):

[0063]

[0064] where (i.e., ) represents the Fourier transform of \(U\) (i.e., ), \(U\) represents the complex amplitude of the target light field, represents the frequency domain coordinates of the superposed circular Airy vortex beams, represents the spatial domain coordinates of the superposed circular Airy vortex beams. Combining the digital propagation phase, the frequency domain complex amplitude distribution of the two superposed circular Airy vortex beams at the propagation distance \(z\) can be obtained:

[0065]

[0066] where, \(\exp(ik z z)\) represents the phase factor propagating along the \(z\) direction, \(k z =(4\pi 2 / \lambda 2 -k x 2 -k y 2 ) 1 / 2 is the wave vector in the \(z\) direction, and \(k = [k x ,k y ,k z , \(k x is the wave vector in the \(x\) direction, \(k y is the wave vector in the \(y\) direction.

[0067] Take the frequency domain complex amplitude distribution of the superposed circular Airy vortex beams at the propagation distance \(z\) calculated by equation (5) as the target light field for complex amplitude modulation. In the experiment, a phase-type spatial light modulator is used. The phase information of the target light field can be directly modulated, and the complex amplitude information needs to be modulated by making an intensity mask.

[0068] When the incident light is a plane wave, the intensity mask can be obtained by loading a blazed grating. The diffraction efficiency of the blazed grating is related to the normalized light intensity of the superposed circular Airy vortex beams after Fourier transform Equal (I fourier That is Therefore, the phase depth of the blazed grating can be expressed as:

[0069]

[0070] Loading the phase depth factor of the blazed grating on the pure phase mask of the spatial light modulator the corresponding complex amplitude mask can be obtained

[0071]

[0072] wherein, represents the phase after the Fourier transform of the superposed circular Airy vortex beam, is the phase of the blazed grating, and mod is the modulo operator. are polar coordinates, and z is the propagation direction.

[0073] Loading the complex amplitude mask obtained from equation (8) on the spatial light modulator, after the plane wave is incident on the spatial light modulator for complex amplitude modulation, and then performing the inverse Fourier transform using a lens, with the spatial light modulator located at the front focal plane of the lens, the target superposed circular Airy vortex beam can be obtained on the rear focal plane of the lens.

[0074] Finally, by changing the complex amplitude mask loaded on the spatial light modulator, the optical annular bright field lattice, dark field lattice, and multi-layer complex structure lattice with chiral radial structures can be obtained.

[0075] See Figure 2 , first, the plane wave is reflected by mirror 1 to the surface of the phase-type spatial light modulator 2, and device 2 loads different complex amplitude masks of the superposed circular Airy vortex beam. The light field reflected from the surface of the spatial light modulator is reflected by mirror 3, and after passing through lens 4 for inverse Fourier transform, a CCD 5 is placed at the rear focal plane of the lens after diffraction, and the output image is the optically switchable optical annular lattice at a fixed position generated.

[0076] Assume that the target light fields are two circular Airy vortex beams carrying topological charges of 1 and 7 respectively. When the main ring radii and widths of the two vortex beams are the same, an annular bright field lattice can be obtained, that is, 6 bright spots are generated, as Figure 3 shown; when the main ring radii of the two vortex beams are different, adjusting the main ring radius of one beam to the sum obtained by adding 1.58 times the main ring width to the main ring radius of the other beam, that is, making r2 = r1 + 1.58w0, a dark field lattice with 6 vortex dark cores can be generated, as Figure 4 shown. Wherein, w0 is the preset main ring width value mentioned above.

[0077] Figure 3 and Figure 4 The generated annular lattice is the lattice at the initial plane z = 0. By using digital propagation technology and changing the propagation distance z, the switching between the dark-field lattice and the bright-field lattice can be realized at a fixed plane. As Figure 5 shown, when z = 100 mm, the dark-field lattice has been converted into a bright-field lattice. At z = 250 mm, it has been converted into a multi-layer complex structure. Moreover, this lattice has a rich radial structure and a certain rotation direction, forming a chiral lattice. Similarly, the bright-field lattice can also be switched to the dark-field lattice, as Figure 6 shown. At this time, the topological charges of the two circular Airy vortex beams are 2 and 12 respectively. When the main ring radius and width are the same, a bright-field lattice with 10 bright spots can be obtained at the z = 0 plane. As the propagation lattice rotates clockwise, at z = 60 mm, it is switched to the dark-field lattice, and at z = 250 mm, it is switched to a more complex multi-layer lattice. The experimental results are in good agreement with the theoretical calculation results. The above lattice generation and switching are unique to the superposition of such self-focusing beams as circular Airy vortex beams, and its physical mechanism is related to the symmetry breaking of the topological energy flow distribution of the beam and the inter-mode interference.

[0078] An embodiment of the present invention provides a method for generating a switchable optical annular lattice. This method superimposes two circular Airy vortex beams with the same chirality and different topological charges, and uses complex amplitude modulation technology and digital propagation technology based on the angular spectrum theory to obtain the Fourier spectral hologram of the superimposed circular Airy beam at a fixed plane, and encodes it on a spatial light modulator. A plane light wave is incident on the spatial light modulator and undergoes an inverse Fourier transform through a lens, and a switchable optical annular lattice at a fixed plane can be obtained.

[0079] The present invention makes two circular Airy vortex beams with the same chirality and different topological charges interfere to form a target light field, and obtains the Fourier spectrum of the target light field after performing a Fourier transform on it. Then, using digital propagation technology based on the diffraction angular spectrum theory, the Fourier spectrum of the target light field is combined with the digital propagation phase to generate a phase hologram of the target light field at a fixed position, which is loaded on a spatial light modulator. After a plane wave is incident on the spatial light modulator and then undergoes an inverse Fourier transform, an optical annular lattice is obtained. By adjusting the topological charge and propagation distance of the target light field, a switchable optical bright-field lattice, dark-field lattice, and multi-layer annular lattice can be obtained.

[0080] Although the present invention has been described based on a limited number of embodiments, those skilled in the art in this technical field understand that, within the scope of the present invention thus described, other embodiments can be envisioned. For the scope of the present invention, the disclosure of the present invention is illustrative rather than restrictive, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for generating a switchable optical ring lattice, characterized in that, The method includes: Preloading a preset complex amplitude mask onto a phase-type spatial light modulator, where the complex amplitude mask is the complex amplitude mask corresponding to the superimposed circular Airy vortex beams with the same chirality and different topological charges; wherein, multiple parameters of the complex amplitude mask are adjustable in real time; The step of preloading the preset complex amplitude mask onto the phase-type spatial light modulator includes: superimposing two circular Airy vortex beams with the same chirality and different topological charges, and using complex amplitude modulation technology and digital propagation technology based on the angular spectrum theory to obtain the Fourier spectral hologram of the superimposed circular Airy beam at a fixed plane, and encoding it on the spatial light modulator; Making a plane light wave incident on the spatial light modulator, and performing an inverse Fourier transform on the light exiting the spatial light modulator to obtain an optical ring lattice with a chiral radial structure.

2. The method for generating a switchable optical ring lattice according to claim 1, characterized in that, The multiple parameters are used as the multiple adjustable parameters of the complex amplitude mask, wherein each adjustable parameter corresponds to multiple preset values; The method further includes: Selecting one or more of the multiple adjustable parameters of the complex amplitude mask as the parameters to be adjusted, and adjusting the parameters to be adjusted from the current values to their respective target values to achieve the switching between the currently obtained optical ring lattice and the target optical ring lattice.

3. The method for generating a switchable optical ring lattice according to claim 1 or 2, characterized in that, The optical ring lattice obtained by the method is an optical ring bright-field lattice or an optical ring dark-field lattice.

4. The method for generating a switchable optical ring lattice according to claim 1 or 2, characterized in that, The multiple adjustable parameters include at least one of the following parameters: The propagation distance of the target light field; the respective initial emission angle parameters of the two circular Airy vortex beams; the respective topological charges of the two circular Airy vortex beams; Wherein, the target light field is the light field corresponding to the superimposed circular Airy vortex beams.

5. The method for generating a switchable optical ring lattice according to claim 1 or 2, characterized in that, The expression of the complex amplitude mask loaded onto the spatial light modulator is: ； Among them, represents the corresponding complex amplitude mask, represents the phase after Fourier transform of the superposed circular Airy vortex beam, is the phase of the blazed grating, and mod is the modulo operator, is the phase depth of the blazed grating.

6. The method for generating a switchable optical ring lattice according to claim 1 or 2, characterized in that, The step of performing an inverse Fourier transform on the light exiting the spatial light modulator includes: Placing the spatial light modulator at the front focal plane of a lens, such that the light exiting the spatial light modulator undergoes an inverse Fourier transform through the lens to obtain a target superimposed circular Airy vortex beam on the rear focal plane of the lens.

7. The method for generating a switchable optical ring lattice according to claim 3, wherein: When the main ring radii and main ring widths of the two circular Airy vortex beams are the same, the obtained optical ring lattice is an optical ring bright-field lattice; When the main ring radii of the two circular Airy vortex beams are different but the main ring widths are the same, the obtained optical ring lattice is an optical ring dark-field lattice.

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