Novel composite light vortex detection method based on computer-generated holography

Abstract

The invention discloses a novel composite optical vortex detection method based on computer-generated holography, and the method comprises the steps: enabling the polarization direction of laser emitted by a broadband polarization-maintaining laser to meet the requirements of a reflection-type phase spatial light modulator through a polarization controller, obtaining Gaussian light with a proper size through a beam expanding system, and projecting the Gaussian light to the spatial light modulator; a composite light vortex blazed fork-shaped phase diagram is loaded on one spatial light modulator, a positive first-stage composite light vortex is selected through a diaphragm and is divided into two beams through a beam splitter, one beam enters a CCD1, a generated composite light vortex light field is recorded, the other beam enters the other spatial light modulator, and the other beam enters the other spatial light modulator. A conjugate symmetric continuation Fourier computer-generated hologram is loaded on the spatial light modulator, an incident composite light vortex is detected, and a detected light field is recorded by using a CCD 2.

Description

Technical Field

[0001] The present invention relates to the field of optical technologies, and particularly to a novel method for detecting composite optical vortices based on computer-generated holography. Background Art

[0002] Optical vortices have a helical wavefront phase structure, and their phase factor is described as exp(ilθ), where l is the topological charge number, which can theoretically take any integer, and θ is the azimuth angle. Due to the existence of their phase singularities, the intensity of vortex light presents a doughnut structure with a dark hollow in the middle. In recent years, due to the unique properties of their orbital angular momentum, optical vortices have received extensive attention at home and abroad. Important achievements have been made in the fields of optical communication, microparticle manipulation, quantum communication, and quantum entanglement. However, the wide application of optical vortices is inseparable from the correct detection of their orbital angular momentum.

[0003] In existing detection methods, to detect vortex beams using the interference method, it is necessary to detect the topological charge number of optical vortices according to the interference fringes. Currently, there are many common detection methods for optical vortices (OAM), mainly including the interference method, the diffraction method, and the computer-generated hologram method. Among them, the common interference methods mainly include the Mach-Zehnder interference method, the Sagnac interferometer method, and the shear interferometer method; the diffraction methods include single-slit interference, double-slit interference, triangular aperture interference, etc.; the computer-generated hologram methods include the gradient grating method, the annular grating method, etc. These above methods mainly detect the topological charge number of optical vortices by the number of fringes in the light field. However, the above methods do not perform well for multi-composite optical vortices and optical vortices with large topological charges.

[0004] Determining the topological charge number by the number of fringes is not conducive to the detection of vortex beams with large topological charges and cannot directly detect composite vortex beams; when using the diffraction method to detect composite vortex beams, the detection range is limited by the diffraction rules of the diffraction grating at the detection end, and the detection efficiency is low, which limits the flexibility of encoding. Summary of the Invention

[0005] The technical problem solved by the present invention is to overcome the defects of the prior art and provide a novel method for detecting composite optical vortices based on computer-generated holography.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A novel method for detecting composite optical vortices based on computer-generated holography, a novel method for detecting composite optical vortices based on computer-generated holography, includes the following steps:

[0008] Step 1: The laser emitted by a broadband polarization-maintaining laser passes through a polarization controller so that its polarization direction meets the requirements of a reflective phase spatial light modulator, and Gaussian light with a suitable size is obtained through a beam expander system and projected onto the spatial light modulator;

[0009] Step 2: Load a composite optical vortex flashing fork-shaped phase pattern on the spatial light modulator, and select the positive first-order composite optical vortex through the aperture;

[0010] Step 3: The positive first-order composite optical vortex passes through the beam splitter and is divided into two beams. One beam is incident on CCD1 to record the generated composite optical vortex light field, and the other beam is incident on another spatial light modulator. A conjugate symmetric extended Fourier computer-generated hologram is loaded on this spatial light modulator to detect the incident composite optical vortex, and CCD2 is used to record the detected light field.

[0011] Preferably, in Step 2, the complex amplitude expression of the optical vortex is as follows:

[0012]

[0013] Where: represents the spot size at the propagation distance z, w0 is the beam waist radius, l is the topological charge number, k is the wave number, is the Gouy phase, z R is the Rayleigh length, and R represents the radius of curvature.

[0014] The expression of the composite optical vortex is:

[0015] Where l1 and l2 are different optical vortex topological charges.

[0016] Preferably, the cylindrical coordinate system in the complex amplitude expression of the optical vortex is changed to the rectangular coordinate system, that is to obtain the following formula:

[0017]

[0018] The 3×3 optical vortex array consists of nine parts. The central positions of each part are A(0, 0), B(a, 0), C(2a, 0), D(0, -a), E(a, -a), F(2a, -a), G(0, -2a), H(a, -2a), and I(2a, -2a) respectively;

[0019] The expression of the 3×3 optical vortex array in the rectangular coordinate system is as follows

[0020]

[0021] Preferably, in Step 3, the complex amplitude distribution f0(m, n) of the optical vortex array for generating the conjugate symmetric extended Fourier computer-generated hologram is expressed as

[0022]

[0023] Where A(m, n) is the amplitude of the optical vortex array, is the phase of the optical vortex array. Perform conjugate symmetric extension on f0(m, n):

[0024]

[0025] The superscript "*" represents the complex conjugate. Let the number of columns M and the number of rows N be both even, and make f(0, n) = f(m, 0) = f(M / 2, 0) = 0, and the symmetry center position is (M / 2, N / 2).

[0026] Preferably, perform a two-dimensional discrete Fourier transform on f(m, n):

[0027]

[0028] where μ and ν are the frequency domain sample numbers in the horizontal and vertical directions respectively. Substitute the simple representation formula of the complex amplitude distribution f0(m, n) of the optical vortex array and the formula for conjugate symmetric extension of f0(m, n) into the formula for the two-dimensional discrete Fourier transform of f(m, n) and after arrangement, we can get:

[0029]

[0030] The above contains the amplitude information A(m, n) of the object light wave and also contains the phase information of the object light wave is a real-valued function.

[0031] Compared with the prior art, the beneficial effects of the present invention are:

[0032] A novel method for detecting composite optical vortices based on computer-generated holography of the present invention simultaneously detects composite optical vortices based on conjugate symmetric extension Fourier computer-generated holograms, achieving a good detection effect. By using whether the position of the diffracted light field presents a Gaussian point to detect the topological charges of single optical vortices and composite optical vortices, it solves the problem of difficult detection of composite optical vortices and optical vortices with large topological charges. The detection method proposed in the present invention for detecting optical vortices based on the computer-generated holography method has a simple and easy experimental device, does not damage the characteristics of the optical vortex light field, and the detection result presents a Gaussian point, which is of great significance for further communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is the conjugate symmetric extension Fourier computer-generated hologram of the present invention;

[0034] Figure 2 is the experimental device diagram of the present invention;

[0035] Figure 3 is the single optical vortex detection diagram of the present invention;

[0036] Figure 4 is the generation diagram of the composite optical vortex of the present invention;

[0037] Figure 5 is the detection result diagram of the composite vortex beam of the present invention;

[0038] Figure 6 This is the topological charge composite vortex beam diagram of the present invention;

[0039] Figure 7 This is the detection array hologram of the present invention;

[0040] Figure 8 This is the measurement diagram of the multiplexed composite vortex beam and the large topological charge vortex beam of the present invention. Specific embodiments

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0042] Please refer to Figure 1-2 , the present invention provides a technical solution:

[0043] A novel composite optical vortex detection method based on computer-generated holography,

[0044] A novel composite optical vortex detection method based on computer-generated holography, a novel composite optical vortex detection method based on computer-generated holography, includes the following steps:

[0045] Step 1: The laser emitted by a broadband polarization-maintaining laser (λ = 1550 nm) passes through a polarization controller (Pol) to make its polarization direction suitable for the requirements of a reflective phase spatial light modulator (SLM1), and a Gaussian beam with a suitable size is obtained through a beam expansion system and projected onto the spatial light modulator;

[0046] Step 2: A Figure 2 composite optical vortex blazed fork phase diagram is loaded on the spatial light modulator, and the positive first-order composite optical vortex is selected through an aperture;

[0047] Step 3: The positive first-order composite optical vortex passes through a beam splitter and is divided into two beams. One beam is incident on CCD1 to record the generated composite optical vortex light field, and the other beam is incident on another spatial light modulator (SLM2). A conjugate symmetric extended Fourier computer-generated hologram is loaded on this spatial light modulator (SLM2) to detect the incident composite optical vortex, and CCD2 is used to record the detected light field. In step 2, the complex amplitude expression of the optical vortex is as follows:

[0048]

[0049] Where: represents the spot size at the propagation distance z, w0 is the beam waist radius, l is the topological charge number, k is the wave number, is the Gouy phase, zR is the Rayleigh length, and R represents the radius of curvature. where l1 and l2 are different optical vortex topological charges.

[0050] Preferably, the cylindrical coordinate system in the complex amplitude expression of the optical vortex is changed to the Cartesian coordinate system, that is to obtain the following formula:

[0051]

[0052] The 3×3 optical vortex array consists of nine parts. A(0,0), B(a,0), C(2a,0), D(0, -a), E(a, -a), F(2a, -a), G(0, -2a), H(a, -2a), and I(2a, -2a) are the central positions of each part respectively;

[0053] The expression of the 3×3 optical vortex array in the Cartesian coordinate system is as follows

[0054]

[0055] In step three, the complex amplitude distribution f0(m, n) of the optical vortex array in conjugate symmetric extended Fourier computer-generated hologram is simply expressed as

[0056]

[0057] where A(m, n) is the amplitude of the optical vortex array, is the phase of the optical vortex array. Perform conjugate symmetric extension on f0(m, n):

[0058]

[0059] The superscript "*" represents complex conjugate. Let the number of columns M and the number of rows N be both even, and make f(0, n) = f(m, 0) = f(M / 2, 0) = 0, and the symmetric center position is (M / 2, N / 2).

[0060] Perform two-dimensional discrete Fourier transform on f(m, n):

[0061]

[0062] where μ and ν are the frequency domain sample numbers in the horizontal and vertical directions respectively. Substitute the simple expression formula of the complex amplitude distribution f0(m, n) of the optical vortex array and the formula of conjugate symmetric extension of f0(m, n) into the two-dimensional discrete Fourier transform formula of f(m, n) and organize to obtain:

[0063]

[0064] The above contains the amplitude information A(m, n) of the object light wave and also contains the phase information of the object light wave is a real-valued function. Encoding this real-valued function into a grayscale image with values ranging from 0 to 255 is Figure 1 the computer-generated hologram shown in (c), Figure 1 where (a) is a schematic diagram of the plane, (b) is a simulation diagram of the light array, and (c) is the conjugate-symmetric extended computer-generated hologram;

[0065] When the incident light field is a composite optical vortex, and the computer-generated hologram made of a 3×3 optical vortex array is used at the detection end, then:

[0066]

[0067] When the topological charges (l1, l2) of the incident composite optical vortex are contained in the 3×3 optical vortex array, a Gaussian point (E0) will be generated at the corresponding position. Therefore, by judging the position of the Gaussian point of the light field, the topological charges contained in the incident light field can be inferred.

[0068] This detection method uses the conjugate-symmetric extended Fourier computer-generated holography technology. Its essence is to utilize the characteristic that the Fourier transform of a conjugate-symmetric complex function is a real-valued function. The 3×3 optical vortex array (topological charges from -1 to -9), such as the above-mentioned Figure 1 (b) is used as the complex amplitude of the object light wave, and after conjugate-symmetric extension and Fourier transform, the obtained real-valued function contains both the amplitude information and the phase information of the object light wave. Finally, appropriate encoding is performed to generate a hologram. Loading this computer-generated hologram onto a spatial light modulator (SLM), when the incident light is Gaussian light, the original object light wave, that is, the 3×3 optical vortex array, can be reproduced. When the incident light is an optical vortex or a composite optical vortex, the orbital angular momentum contained in the incident light field can be detected at the corresponding position. Judging the orbital angular momentum of the incident light field by whether a Gaussian point appears at the position is more accurate and intuitive compared to observing the number of fringes in the diffraction light field in the past. Therefore, it is more effective for the detection of optical vortices with large topological charges. If the topological charges contained in the incident light field are greater than 9, simply switch the hologram loaded on the SLM to correctly detect. The computer-generated hologram of the 3×3 optical vortex array can correctly detect 9 types of topological charge optical vortices.

[0069] This detection method uses a computer-generated hologram encoded by conjugate-symmetric extension of a 3×3 optical vortex array (l = -1 to -9) and can simultaneously detect 9 different optical vortices. When the single optical vortex blazed fork-shaped phase diagram is loaded on SLM1, CCD1 records the generated optical vortex. When a specific computer-generated hologram is loaded on SLM2, the orbital angular momentum of the incident single optical vortex can be detected.

[0070] Such as Figure 3As shown, when the blazed fork-shaped phase diagrams with topological charges from 1 to 9 are respectively loaded on SLM1, 9 optical field diagrams are respectively recorded on CCD2. When the topological charge of the incident optical vortex is 1, a Gaussian point is generated at position 1. When the topological charge of the incident optical vortex is 2, a Gaussian point is generated at position 2, and so on. We can judge the optical vortex components contained in the incident optical field from whether there are Gaussian points at each position.

[0071] The above experiments have achieved good results in the detection of single optical vortices. The proposed conjugate symmetric extension Fourier computer-generated holography-based detection method not only has good effects on the detection of single optical vortices, but also has good performance in the detection of composite optical vortices. By loading a composite phase diagram on SLM1, a composite optical vortex can be generated. This detection method blazes on the composite phase to improve the efficiency of generating composite optical vortices and achieve good composite optical vortex generation effects.

[0072] As Figure 4 , three different composite blazed fork-shaped phase diagrams (original phase diagrams) are respectively loaded on SLM1, and the corresponding three composite optical vortex optical field diagrams recorded by CCD1. The correct generation of composite optical vortices can be judged from the optical field recorded by CCD1. The Fourier computer-generated hologram is loaded on SLM2, and the optical field diagram recorded on CCD2 is as shown in Figure 5. When the incident light is a composite optical vortex composed of 2 and 7, Gaussian points appear at the positions of 2 and 7 in the detected optical field, indicating that this composite optical vortex is composed of optical vortices with topological charges of 2 and 7. Experiments show that the proposed detection method is effective and feasible for the detection of composite optical vortices.

[0073] Figure 4 The detection results of the composite vortex beam in (a) where l1 = 2, l2 = 7, (b) where l1 = 3, l2 = 8, and (c) where l1 = 2, l2 = 9.

[0074] The composite vortex beam to be detected is expanded to a three-way composite vortex beam, and the topological charge numbers of the composite vortex beam can be arbitrarily selected. In the experiment, a composite vortex beam with a combination of topological charges of 3, 11, and 25 is selected as the beam to be detected, and its optical field distribution is as Figure 6 (a) shown. A blazed fork grating hologram capable of generating the composite vortex beam shown in Figure 6 (a) is loaded on SLM1, as Figure 6 (b) shown. After the light source beam passing through polarization modulation and beam expansion is incident on SLM1, the optical field to be detected is generated through diffraction. CCD1 records the intensity distribution of the composite vortex beam to be detected. From Figure 6It can be seen from (c) that the light field distribution of the three-way composite vortex beam containing large topological charge is more complex. In the experiment, the peripheral light intensity of the composite vortex beam becomes weaker, and the boundary distribution of the dark petals of each layer becomes more blurred, which increases the difficulty of pattern detection of the composite vortex beam.

[0075] Figure 6 (a) Simulated light intensity distribution of multi-channel composite vortex beam with l=3, 11, and 25, (b) Blazed fork grating loaded on SLM1, (c) Experimental light intensity distribution of multi-channel composite vortex beam with l=3, 11, and 25.

[0076] A 3×3 detection array is constructed based on the topological charge combination of the incident composite vortex beam. The topological charges at each position in the array are set to -3, -6, -9, -11, -14, -17, -20, -22, and -25 from left to right and from top to bottom. The light field distribution of the detection array is shown in the figure. Figure 7 (a) shows that the hologram of the detection array is generated using the conjugate symmetric extension Fourier computational holography algorithm, as shown in Figure 7 (b) As shown in Figure 2, most of the information in the hologram is still concentrated in the central area, as shown in Figure 2. Figure 7 (c) is shown. Load the SLM2 as Figure 7 The CGH shown in (b) detects the incident composite vortex beam.

[0077] Figure 7 (a) Detection array light intensity distribution, (b) detection array hologram, (c) center encoding information.

[0078] When the composite vortex beam to be measured is generated after passing through SLM1 and enters SLM2, the camera CCD2 is used to record the light field after passing through SLM2. The recording results are as follows: Figure 8 As shown in the figure, the recorded light field distribution shows that Gaussian spots appear at positions corresponding to topological charges of -3, -11, and -25 in the vortex array, indicating that the incident composite vortex beam contains orbital angular momentum modes with topological charges of 3, 11, and 25. Experiments demonstrate that the proposed detection method also has good detection efficiency for large topological charges and three-way composite vortex beams.

[0079] In addition, due to the object-oriented characteristics of conjugate symmetric extended Fourier computer-generated holography, the specifications of the generated vortex beam array can be further expanded according to the requirements of the composite vortex beam to be measured, such as generating 5×5 and 10×10 vortex beam arrays, further improving the detection efficiency of the composite vortex beam.

[0080] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the present invention.

[0081] In addition, the terms "first" and "second" are only used for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0082] In the present invention, unless otherwise clearly specified and defined, the terms "mounted", "connected", "coupled", "fixed", etc. should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the internal communication of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0083] In the present invention, unless otherwise clearly specified and defined, the first feature being "on" or "under" the second feature may be that the first and second features are in direct contact, or the first and second features are indirectly in contact through an intermediate medium. Moreover, the first feature being "above", "over" and "on top of" the second feature may be that the first feature is directly above or obliquely above the second feature, or merely indicates that the first feature has a higher horizontal height than the second feature. The first feature being "under", "beneath" and "underneath" the second feature may be that the first feature is directly below or obliquely below the second feature, or merely indicates that the first feature has a lower horizontal height than the second feature.

[0084] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0085] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A novel composite optical vortex detection method based on computer-generated hologram, characterized in that, It includes the following steps: Step 1: The laser emitted by the broadband polarization-maintaining laser passes through a polarization controller to make its polarization direction meet the requirements of the reflective phase spatial light modulator, and a Gaussian beam with a suitable size is obtained through a beam expander system and projected onto the spatial light modulator. Step 2: A composite optical vortex flashing fork-shaped phase pattern is loaded on the spatial light modulator, and the positive first-order composite optical vortex is selected through an aperture. Step 3: The positive first-order composite optical vortex passes through a beam splitter and is divided into two beams. One beam is incident on CCD1 to record the generated composite optical vortex light field, and the other beam is incident on another spatial light modulator. A conjugate symmetric extended Fourier computer-generated hologram is loaded on this spatial light modulator to detect the incident composite optical vortex, and CCD2 is used to record the detected light field.

2. A novel composite optical vortex detection method based on computer-generated holography according to claim 1, characterized in that, In Step 2, the complex amplitude expression of a single optical vortex is as follows: Wherein: represents the spot size at the propagation distance z, w0 is the beam waist radius, l is the topological charge number, k is the wave number, is the Gouy phase, z R is the Rayleigh length, R represents the radius of curvature, and the composite optical vortex is expressed as: where l1 and l2 are different optical vortex topological charges.

3. A novel composite optical vortex detection method based on computer-generated holography according to claim 2, characterized in that: Changing the cylindrical coordinate system in the complex amplitude expression of the optical vortex to a rectangular coordinate system gives the following formula: The 3×3 optical vortex array consists of nine parts. The central positions of each part are A(0, 0), B(a, 0), C(2a, 0), D(0, -a), E(a, -a), F(2a, -a), G(0, -2a), H(a, -2a), and I(2a, -2a) respectively. The expression of the 3×3 optical vortex array in the rectangular coordinate system is as follows 4. A novel composite optical vortex detection method based on computer-generated holography according to claim 1, characterized in that: In Step 3, the complex amplitude distribution f0(m, n) of the optical vortex array used to generate the conjugate symmetric extended Fourier computer-generated hologram is expressed as where A(m, n) is the amplitude of the optical vortex array, is the phase of the optical vortex array, and conjugate symmetric extension is performed on f0(m, n): The superscript "*" represents the complex conjugate. Let the number of columns M and the number of rows N be both even, and make f(0, n) = f(m, 0) = f(M / 2, 0) = 0, and the symmetric center position is (M / 2, N / 2).

5. A novel composite optical vortex detection method based on computer-generated hologram according to claim 4, wherein: Perform a two-dimensional discrete Fourier transform on f(m, n): where μ and ν are the frequency domain sample numbers in the horizontal and vertical directions respectively. Substitute the simple expression formula of the complex amplitude distribution f0(m, n) of the optical vortex array and the formula for conjugate symmetric extension of f0(m, n) into the two-dimensional discrete Fourier transform formula of f(m, n) and simplify to obtain: The above contains the amplitude information A(m, n) of the object wave and also contains the phase information of the object wave is a real-valued function.

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