CN112764214A - Diffraction simulation method for generating hollow light beam - Google Patents
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Abstract
The invention discloses a diffraction simulation method for generating a hollow light beam, which comprises the steps of obtaining light parameters of different positions of a Gaussian light beam to be simulated after the Gaussian light beam passes through a spiral phase plate, and calculating a corresponding phase difference to be simulated based on the light parameters; calculating the topological charge number of the corresponding vortex light beam based on the phase difference to be simulated; acquiring the number of rings of the Fresnel zone plate to be simulated as the number of rings to be simulated, and calculating the radius of a ring corresponding to the number of rings to be simulated; calculating the light spot intensity of the Gaussian beam to be simulated on the focal plane based on the radius of the number of rings to be simulated and the topological charge number of the vortex beam; the Gaussian beam to be simulated is simulated based on the spot intensity and the radius of the number of rings to be simulated to obtain a diffraction simulation spot, and the diffraction simulation spot can be seen.
Description
Technical Field
The invention belongs to the technical field of design of diffractive optical devices, and particularly relates to a diffraction simulation method for generating a hollow light beam.
Background
The inter-satellite laser communication generally uses a Cassegrain type optical antenna as a transmitting antenna, a parallel light beam emitted by a laser passes through a pre-collimation and beam expansion system and then is incident into the Cassegrain optical antenna, focused on an antenna ocular lens group, primarily reflected by a hyperboloid secondary lens, secondarily reflected by a paraboloid primary lens and transmitted out at a very small divergence angle. But due to the shielding of the secondary antenna mirror, part of the light beam at the center of the gaussian light beam cannot be emitted. The energy in the center of the gaussian beam is the largest, and if the gaussian beam cannot be emitted, the energy loss of the beam is huge.
Disclosure of Invention
The technical problem to be solved by the invention is that when a Gaussian beam is incident into a Cassegrain optical antenna, due to the central shielding, the energy of the beam center cannot be transmitted through the antenna, and huge beam energy loss is caused. Therefore, the invention provides a diffraction simulation method for generating a hollow light beam, which is used for converting an incident light beam into the hollow light beam so as to avoid energy loss caused by shielding of the center of a Cassegrain antenna; the invention can also control the size of the hollow light beam to adapt to the Cassegrain optical antenna with different shielding ratios by adjusting design parameters.
The invention is realized by the following technical scheme:
a diffraction simulation method for generating a hollow beam, comprising:
acquiring light parameters of Gaussian beams to be simulated at different positions after passing through a spiral phase plate, and calculating corresponding phase differences to be simulated based on the light parameters;
calculating the topological charge number of the corresponding vortex light beam based on the phase difference to be simulated;
acquiring the number of rings of a Fresnel zone plate to be simulated as the number of rings to be simulated, and calculating the radius of a ring corresponding to the number of rings to be simulated;
calculating the light spot intensity of the Gaussian beam to be simulated on the focal plane based on the radius of the number of the rings to be simulated and the topological charge number of the vortex beam;
and simulating the Gaussian beam to be simulated based on the light spot intensity and the radius of the number of rings to be simulated to obtain a diffraction simulation light spot.
Further, the light parameters include incident light wavelength, helical phase plate refractive index, air refractive index, helical phase plate azimuth angle, and helical phase plate step thickness;
the calculating a corresponding phase difference based on the ray parameters includes:
calculating the wavelength of incident light, the refractive index of the spiral phase plate, the refractive index of air, the azimuth angle of the spiral phase plate and the step thickness of the spiral phase plate by using a phase difference calculation formula to obtain a phase difference;
the phase difference calculation formula specifically includes:wherein τ represents a phase difference, n1Representing the refractive index of the spiral phase plate, n2Denotes the refractive index of air, h denotes the thickness at the step of the spiral phase plate, λ denotes the incident light wavelength of the gaussian beam, and θ denotes the azimuth angle of the spiral phase plate.
Further, the diffraction simulation method for generating the hollow beam further comprises the following steps:
calculating the thickness of the spiral phase plate at the step based on the topological charge number of the vortex light beam;
the formula for calculating the thickness of the step of the spiral phase plate is specifically as follows:wherein h represents the thickness of the step of the spiral phase plate, l represents the topological charge number of the vortex beam, lambda represents the incident light wavelength of the Gaussian beam, and n1Representing the refractive index of the spiral phase plate, n2Representing the refractive index of air.
Further, the diffraction simulation method for generating the hollow beam further comprises the following steps:
calculating the thickness of the spiral phase plate at the azimuth angle based on the thickness of the spiral phase plate at the step;
the formula for calculating the thickness of the spiral phase plate at the azimuth angle specifically comprises the following steps:wherein s represents a spiroThe thicknesses of the spiral phase plate at different azimuth angles are represented by theta, the thickness of the spiral phase plate at the step position is represented by h, the topological charge number of the vortex beam is represented by l, the incident light wavelength of the Gaussian beam is represented by lambda, and n1Representing the refractive index of the spiral phase plate, n2Representing the refractive index of air.
Further, the calculating the radius of the ring corresponding to the number of the rings to be simulated includes:
acquiring the number n of rings to be simulated and the focal length f of a Fresnel zone plate, and calculating the incident light wavelength lambda of a Gaussian beam, the number n of rings to be simulated and the focal length f of the Fresnel zone plate according to a Fresnel zone plate ring radius calculation formula to obtain the ring radius corresponding to the number of rings to be simulated;
the calculation formula of the annular radius of the Fresnel zone plate is specifically as follows:wherein r isnAnd representing the radius of the circular ring corresponding to the number n of the ring to be simulated.
Further, the calculating the spot intensity of the gaussian beam to be simulated on the focal plane includes:
by spot intensity calculation formulaCalculating the light spot intensity of the Gaussian beam to be simulated on a focal plane; wherein i represents the number of the ith ring to be simulated, A represents the amplitude intensity, lambda represents the incident light wavelength of the Gaussian beam, r represents the radius of the ring corresponding to the number of the ith ring to be simulated, k represents the incident light wave number of the Gaussian beam, l represents the topological charge number of the vortex beam, d represents the integral sign,representing the integral variable.
Further, the simulating the gaussian beam to be simulated based on the spot intensity and the radius of the number of rings to be simulated includes:
converting the radius of the number of the rings to be simulated according to a polar coordinate conversion formula to obtain a polar coordinate parameter;
performing simulation based on the polar coordinate parameters and the light panel strength;
the polar coordinate conversion formula specifically includes:
r=[(ρcosθ-r cosφ)2+(ρsinθ-r sinφ)2+z2]1/2。
further, the diffraction simulation method for generating the hollow beam further comprises the following steps:
and adjusting the size of the diffraction simulation light spot by adjusting the topological charge number corresponding to the Gaussian beam to be simulated and the number of rings to be simulated.
The invention provides a diffraction simulation method for generating a hollow light beam, which comprises the steps of obtaining light parameters of different positions of a Gaussian light beam to be simulated after the Gaussian light beam passes through a spiral phase plate, and calculating a corresponding phase difference to be simulated based on the light parameters; calculating the topological charge number of the corresponding vortex light beam based on the phase difference to be simulated; acquiring the number of rings of the Fresnel zone plate to be simulated as the number of rings to be simulated, and calculating the radius of a ring corresponding to the number of rings to be simulated; calculating the light spot intensity of the Gaussian beam to be simulated on the focal plane based on the radius of the number of rings to be simulated and the topological charge number of the vortex beam; the Gaussian beam to be simulated is simulated based on the spot intensity and the radius of the number of rings to be simulated to obtain a diffraction simulation spot, and the diffraction simulation spot can be seen.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart of a diffraction simulation method for generating a hollow beam according to the present invention.
Fig. 2 is a simulated diagram of spot diffraction according to an embodiment of the invention.
FIG. 3 is a simulated diffraction diagram of spots with different topological charge numbers according to one embodiment of the present invention.
Fig. 4 is a simulation diagram of spot diffraction for different numbers of rings to be simulated in an embodiment of the present invention.
Fig. 5 is another simulated diffraction pattern of a light spot according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1
As shown in fig. 1, the present invention provides a diffraction simulation method for generating a hollow beam, which specifically includes the following steps:
s10: and acquiring light parameters of the Gaussian beam to be simulated at different positions after the Gaussian beam passes through the spiral phase plate, and calculating the corresponding phase difference to be simulated based on the light parameters.
The light parameters comprise incident light wavelength, spiral phase plate refractive index, air refractive index, spiral phase plate azimuth angle and spiral phase plate step thickness.
Specifically, the wavelength of incident light, the refractive index of the spiral phase plate, the refractive index of air, the azimuth angle of the spiral phase plate and the step thickness of the spiral phase plate at different positions of the Gaussian beam to be simulated after passing through the spiral phase plate are obtained, and the phase difference is obtained by calculating through a phase difference calculation formula.
The phase difference calculation formula specifically comprises:wherein τ represents a phase difference, n1Representing the refractive index of the spiral phase plate, n2Denotes the refractive index of air, h denotes the thickness at the step of the spiral phase plate, λ denotes the incident light wavelength of the gaussian beam, and θ denotes the azimuth angle of the spiral phase plate.
S20: and calculating the topological charge number of the corresponding vortex light beam based on the phase difference to be simulated.
Specifically, the helical phase plate converts a gaussian beam to be simulated into a vortex beam, converts a phase difference to be simulated into an integral multiple of 2 pi, and records the integral multiple as 2 pi l, wherein l is called the topological charge number of the vortex beam.
S30: and acquiring the number of rings of the Fresnel zone plate to be simulated as the number of rings to be simulated, and calculating the radius of the ring corresponding to the number of rings to be simulated.
Specifically, the number n of rings to be simulated is obtained, the focal length f of the Fresnel zone plate is obtained, and the incident light wavelength lambda of the Gaussian beam, the number n of rings to be simulated and the focal length f of the Fresnel zone plate are calculated according to a Fresnel zone plate ring radius calculation formula to obtain the ring radius corresponding to the number of rings to be simulated.
The calculation formula of the circular ring radius of the Fresnel zone plate is as follows:wherein r isnAnd representing the radius of the circular ring corresponding to the number n of the ring to be simulated.
S40: and calculating the light spot intensity of the Gaussian beam to be simulated on the focal plane based on the radius of the number of rings to be simulated and the topological charge number of the vortex beam.
Specifically, the radius of the number of rings to be simulated and the topological charge number of the vortex beam are calculated through a light spot intensity calculation formula, so that the light spot intensity of the Gaussian beam to be simulated on the focal plane is obtained.
The spot intensity calculation formula specifically includes:
wherein i represents the number of the ith ring to be simulated, A represents the amplitude intensity, lambda represents the incident light wavelength of the Gaussian beam, r represents the radius of the ring corresponding to the number of the ith ring to be simulated, k represents the incident light wave number of the Gaussian beam, l represents the topological charge number of the vortex beam, d represents the integral sign,representing the integral variable.
S50: and simulating the Gaussian beam to be simulated based on the light spot intensity and the radius of the number of rings to be simulated to obtain the diffraction simulation light spot.
Specifically, the radius of the number of rings to be simulated is converted according to a polar coordinate conversion formula to obtain a polar coordinate parameter, and then the Gaussian beam to be simulated is simulated according to the polar coordinate parameter and the radius of the number of rings to be simulated to obtain the diffraction simulation facula.
The polar coordinate conversion formula is specifically as follows:
r=[(ρcosθ-r cosφ)2+(ρsinθ-r sinφ)2+z2]1/2。
further, a diffraction simulation method for generating a hollow beam further comprises:
and calculating the thickness of the spiral phase plate at the step based on the topological charge number of the vortex beam.
The formula for calculating the thickness of the step of the spiral phase plate is specifically as follows:wherein h represents the thickness of the step of the spiral phase plate, l represents the topological charge number of the vortex beam, lambda represents the incident light wavelength of the Gaussian beam, and n1Representing the refractive index of the spiral phase plate, n2Representing the refractive index of air.
To further prove the accuracy of the simulation method of the present invention, as shown in fig. 2, the wavelength λ of the gaussian beam to be simulated is 633nm, the focal length f of the fresnel zone plate is 0.5m, the number N of rings to be simulated is 100, the topological load number l is 1, the number of rings to be simulated corresponds to the fresnel zone plate with the radius of 5.6mm, and a light spot diffraction simulation diagram is obtained on the focal plane. Wherein, (a) represents a focal plane speckle pattern; (b) representing a three-dimensional intensity pattern of the light spot; (c) representing the spot intensity profile.
Further, a diffraction simulation method for generating a hollow beam further comprises:
and calculating the thickness of the spiral phase plate at the azimuth angle based on the thickness of the step of the spiral phase plate.
The formula for calculating the thickness of the spiral phase plate at the azimuth angle specifically comprises the following steps:wherein s represents the thickness of the spiral phase plate at different azimuth angles, and theta representsAzimuth angle of the spiral phase plate, h represents thickness of the spiral phase plate at step, l represents topological charge number of vortex beam, lambda represents incident light wavelength of Gaussian beam, and n1Representing the refractive index of the spiral phase plate, n2Representing the refractive index of air.
Further, a diffraction simulation method for generating a hollow beam further comprises:
and adjusting the size of the diffraction simulation light spot by adjusting the topological charge number corresponding to the Gaussian beam to be simulated and the number of rings to be simulated.
Fig. 3 is a light spot diffraction simulation diagram corresponding to different topological charge l values under the conditions that the wavelength λ of the gaussian beam to be simulated is 633nm, the focal length f of the fresnel zone plate is 0.5m, and the number N of rings to be simulated is 100.
The method comprises the steps of (a) representing a spot diffraction pattern of a Fresnel zone plate with the topological charge number l being 1 on a focal plane, and (d) representing an intensity distribution graph of corresponding spots. (b) The spot diffraction pattern of the Fresnel zone plate with the topological charge number l being 2 on the focal plane is shown, and (e) the intensity distribution graph of the corresponding spot is shown. (c) The light spot diffraction pattern of the Fresnel zone plate with the topological charge number l being 3 on the focal plane is shown, and (f) the intensity distribution graph of the corresponding light spots is shown.
As can be seen from fig. 3, the outer diameter and the hollow radius of the spot in the focal plane increase with increasing value of/.
Fig. 4 is a light spot diffraction simulation diagram corresponding to different ring numbers N to be simulated, where the wavelength λ of the gaussian beam to be simulated is 633nm, the focal length f of the fresnel zone plate is 0.5m, and the topological charge number l is 3.
The method comprises the steps of (a) representing a light spot diffraction pattern of a Fresnel zone plate with the ring number N to be simulated being 60 on a focal plane, and (d) representing an intensity distribution diagram of corresponding light spots. (b) The light spot diffraction pattern of the Fresnel zone plate with the number N of rings to be simulated being 100 on the focal plane is shown, and (e) the intensity distribution graph of the corresponding light spots is shown. (c) The light spot diffraction pattern of the Fresnel zone plate with the number N of rings to be simulated being 140 on the focal plane is shown, and (f) the intensity distribution graph of the corresponding light spots is shown.
As can be seen from fig. 4, the outer diameter and the hollow radius of the light spot on the focal plane are both reduced as the value of N is increased.
From fig. 3 and 4, the effect of the values of l and N on the spot can be seen. When the optical fiber is applied to a Cassegrain optical antenna system, the ratio of the hollow part to the whole light spot is more required to be related, and the ratio is consistent with the shading ratio of the Cassegrain optical antenna. Therefore, 1/e of the maximum light intensity of the annular Gaussian beam is taken2The radial dimension of the ring beam is used as the inner and outer diameters of the ring beam, and the relationship between the hollow ratio of the ring beam and the values of l and N is obtained by performing simulation by the diffraction simulation method for generating the hollow beam as shown in fig. 5.
The above embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, it should be understood that the above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A diffraction simulation method for generating a hollow beam, comprising:
acquiring light parameters of Gaussian beams to be simulated at different positions after passing through a spiral phase plate, and calculating corresponding phase differences to be simulated based on the light parameters;
calculating the topological charge number of the corresponding vortex light beam based on the phase difference to be simulated;
acquiring the number of rings of a Fresnel zone plate to be simulated as the number of rings to be simulated, and calculating the radius of a ring corresponding to the number of rings to be simulated;
calculating the light spot intensity of the Gaussian beam to be simulated on the focal plane based on the radius of the number of the rings to be simulated and the topological charge number of the vortex beam;
and simulating the Gaussian beam to be simulated based on the light spot intensity and the radius of the number of rings to be simulated to obtain a diffraction simulation light spot.
2. The diffraction simulation method for generating a hollow core beam according to claim 1, wherein the optical parameters include wavelength of incident light, refractive index of the spiral phase plate, refractive index of air, azimuth angle of the spiral phase plate, and step thickness of the spiral phase plate;
the calculating a corresponding phase difference based on the ray parameters includes:
calculating the wavelength of incident light, the refractive index of the spiral phase plate, the refractive index of air, the azimuth angle of the spiral phase plate and the step thickness of the spiral phase plate by using a phase difference calculation formula to obtain a phase difference;
the phase difference calculation formula specifically includes:wherein τ represents a phase difference, n1Representing the refractive index of the spiral phase plate, n2Denotes the refractive index of air, h denotes the thickness at the step of the spiral phase plate, λ denotes the incident light wavelength of the gaussian beam, and θ denotes the azimuth angle of the spiral phase plate.
3. The method of claim 2, wherein the method further comprises:
calculating the thickness of the spiral phase plate at the step based on the topological charge number of the vortex light beam;
the formula for calculating the thickness of the step of the spiral phase plate is specifically as follows:
wherein h represents the thickness of the step of the spiral phase plate, l represents the topological charge number of the vortex beam, lambda represents the incident light wavelength of the Gaussian beam, and n1Representing the refractive index of the spiral phase plate, n2Representing the refractive index of air.
4. The method of claim 3, wherein the method further comprises:
calculating the thickness of the spiral phase plate at the azimuth angle based on the thickness of the spiral phase plate at the step;
the formula for calculating the thickness of the spiral phase plate at the azimuth angle specifically comprises the following steps:wherein s represents the thickness of the spiral phase plate at different azimuth angles, theta represents the azimuth angle of the spiral phase plate, h represents the thickness of the step of the spiral phase plate, l represents the topological charge number of the vortex beam, lambda represents the incident light wavelength of the Gaussian beam, and n represents the thickness of the spiral phase plate at the step of the spiral phase plate1Representing the refractive index of the spiral phase plate, n2Representing the refractive index of air.
5. The diffraction simulation method for generating a hollow beam according to claim 1, wherein the calculating the radius of the ring corresponding to the number of the rings to be simulated comprises:
acquiring the number n of rings to be simulated and the focal length f of a Fresnel zone plate, and calculating the incident light wavelength lambda of a Gaussian beam, the number n of rings to be simulated and the focal length f of the Fresnel zone plate according to a Fresnel zone plate ring radius calculation formula to obtain the ring radius corresponding to the number of rings to be simulated;
6. The diffraction simulation method for generating a hollow beam according to claim 1, wherein the calculating the spot intensity of the gaussian beam to be simulated on the focal plane comprises:
by spot intensity calculation formulaCalculating the light spot intensity of the Gaussian beam to be simulated on a focal plane; wherein i represents the i-thThe number of rings to be simulated, A represents the amplitude intensity, lambda represents the incident light wavelength of the Gaussian beam, r represents the radius of the ring corresponding to the ith number of rings to be simulated, k represents the incident light wave number of the Gaussian beam, l represents the topological charge number of the vortex beam, d represents an integral sign,representing the integral variable.
7. The diffraction simulation method for generating a hollow light beam according to claim 1, wherein the simulating the Gaussian beam to be simulated based on the spot intensity and the radius of the number of rings to be simulated comprises:
converting the radius of the number of the rings to be simulated according to a polar coordinate conversion formula to obtain a polar coordinate parameter;
performing simulation based on the polar coordinate parameters and the light panel strength;
the polar coordinate conversion formula specifically includes:
r=[(ρ cosθ-r cosφ)2+(ρ sinθ-r sinφ)2+z2]1/2。
8. the method of claim 1, wherein the method further comprises:
and adjusting the size of the diffraction simulation light spot by adjusting the topological charge number corresponding to the Gaussian beam to be simulated and the number of rings to be simulated.
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