CN112946881B - Method for generating arbitrary pointing light needle three-dimensional array - Google Patents
Method for generating arbitrary pointing light needle three-dimensional array Download PDFInfo
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Abstract
The invention relates to a method for generating a three-dimensional array of arbitrarily-directed optical needles, which uses two arrays for convergenceHigh numerical aperture objective lens coaxial placement of incident field, establishing 4πAn optical focusing system; at 4πPlacing a virtual uniform line source antenna stereoscopic array in a focal area of an optical focusing system, calculating to obtain a radiation field generated by the virtual uniform line source antenna stereoscopic array, completely converging the radiation field of the virtual uniform line source antenna stereoscopic array by two objective lenses and collimating the radiation field to a pupil plane, and reversing the radiation field of the virtual uniform line source antenna stereoscopic array by a time reversal technology to obtain an incident field of the pupil plane; the incident field is incident from the pupil plane, via 4πThe optical focusing system propagates and converges in the focal zone, 4πThe focal area of the optical focusing system forms a three-dimensional array of optical needles with controllable pointing direction. The method is beneficial to flexibly customizing the optical needle three-dimensional array.
Description
Technical Field
The invention belongs to the technical field of optical needle focal field customization, and particularly relates to a method for generating an arbitrary pointing optical needle three-dimensional array.
Background
In recent years, by utilizing the non-uniform distribution of the polarization state of the vector optical field on the wave front, after the tight focusing of the focusing system, the optical focal field distribution of special forms such as optical needle, light pipe, optical chain, optical bubble, etc. can be formed. The specific optical focal field has great application potential in the aspects of particle acceleration, micro-nano processing, high-density optical storage, particle trapping and the like.
For the construction of the light needle focal field, researchers have published reports on related methods. For example, wang hf et al report for the first time a method of generating an optical needle focal field by tightly focusing a radially polarized vector beam with a combination of a binary optical element and a high numerical aperture lens; yuYZ et al propose a method for generating a multi-segment longitudinal collinear optical needle focal field by a virtual multi-element uniform line source.
In the method disclosed and reported above, the generated optical needle focal fields are all along the optical axis direction, the direction is single, the arrangement mode of the multiple sections of optical needles is simple, the method is not suitable for two-dimensional or three-dimensional optical operation, and a complex multi-parameter optimization process is required, so that the design process is lack of flexibility.
Disclosure of Invention
The invention aims to provide a method for generating an arbitrarily-pointed optical needle three-dimensional array, which is beneficial to flexibly customizing the optical needle three-dimensional array.
In order to achieve the purpose, the invention adopts the technical scheme that: a method for generating any-pointing optical needle three-dimensional array is characterized in that two high-numerical-aperture objective lenses for converging an incident field are coaxially arranged to establish a 4 pi optical focusing system; placing a virtual uniform line source antenna three-dimensional array in a focal area of a 4 pi optical focusing system, calculating to obtain a radiation field generated by the virtual uniform line source antenna three-dimensional array, completely converging the radiation field of the virtual uniform line source antenna three-dimensional array by two objective lenses and collimating the radiation field to a pupil plane, and reversing the radiation field of the virtual uniform line source antenna three-dimensional array through a time reversal technology to obtain an incident field of the pupil plane; and the incident field is incident from a pupil plane, is transmitted by the 4 pi optical focusing system and is converged in a focal area, and a directional controllable light needle three-dimensional array is formed in the focal area of the 4 pi optical focusing system.
Furthermore, the array elements of the virtual uniform line source antenna stereoscopic array are uniform line sources, the geometric length of the virtual uniform line source antenna stereoscopic array can be set, the spatial direction of the virtual uniform line source antenna stereoscopic array can be adjusted, and the spatial position of the virtual uniform line source antenna stereoscopic array can be adjusted.
Furthermore, the phase difference of the incident field of the pupil planes at two sides of the 4 pi optical focusing system is pi.
Further, a rectangular coordinate system is established in a focal area of the 4 pi optical focusing system, wherein the optical axis direction of the two objective lenses is the Z-axis direction, an MXNxP virtual uniform line source antenna three-dimensional array is set, M, N, P are the number of antenna array elements of X, Y, Z axes respectively, and X, Y, Z axis coordinates of the array elements are x axes respectively 0 、x 1 、x 2 …x M-1 ，y 0 、y 1 、y 2 …y N-1 And z 0 、z 1 、z 2 …z P-1 ；
The length of the antenna array element is L, and the current is I 0 Arbitrarily spatially directed as
Wherein theta is 0 Is the included angle between the array element and the optical axis,
the included angle between the projection of the array elements on the XOY plane and the X axis is shown;
according to the antenna radiation theory, the radiation field of the antenna array element with the central point at the origin point
Comprises the following steps:
wherein
In the formula I 0 Is the magnitude of the current of the array element, L is the length of the array element, mu 0 Is the magnetic permeability, k is the wave number, w is the angular frequency, j is the imaginary unit,
is the polar coordinates of the array element radiation field,
and
is a polar coordinate unit direction vector, C is a coefficient irrelevant to the array element radiation pattern,
the array element is used as the array factor of the continuous line source,
and
are respectively array elements at
And
a direction primitive factor for a direction;
forming an M multiplied by N multiplied by P antenna solid array by the antenna array elements, and obtaining a space solid array factor according to an antenna array directional diagram product theorem:
the radiation field of any spatial directional uniform line source solid array is:
further, the radiation field of the virtual uniform line source antenna stereoscopic array is inverted and is transmitted backwards from the pupil plane to the focal area of the 4 pi optical focusing system by using relative pi phase shift;
on the normalized pupil plane, for generating the incident field required by the light needle stereo array
Calculated from equation (9):
wherein
T (θ) is the apodization function of the objective lens, which is the polar coordinate of the incident field on the pupil plane; if the objective lens satisfies the helmholtz condition, T (θ) is:
the incident field of the pupil plane
Comprises the following steps:
wherein
And
is the unit vector of the pupil plane X, Y direction; and calculating the incident field to form an arbitrary pointing light needle three-dimensional array after the incident field is tightly focused by a 4 pi optical focusing system by utilizing the Debye theory.
Compared with the prior art, the invention has the following beneficial effects: the invention arranges the virtual uniform line source antenna stereo array in the focal area of the optical focusing system, and combines the uniform line source antenna radiation theory, the array antenna comprehensive technology and the time reversal technology to invert the radiation field of the stereo array antenna at the entrance pupil plane, and can generate the arbitrary pointing light needle stereo array near the focal area after being focused by the optical system. The method provided by the invention does not need a complicated and lengthy optimization process, and is very flexible and convenient in customizing the light needle three-dimensional array with the preset characteristics.
Drawings
FIG. 1 is a schematic diagram of a 4 π optical focusing system in an embodiment of the invention.
FIG. 2 is a schematic diagram of a rectangular coordinate system established in a 4 π optical focusing system in an embodiment of the present invention.
Fig. 3 is a 3D view of an X-axis optical needle array according to an embodiment of the present invention.
Fig. 4 is a 3D diagram of a Y-axis optical needle array according to a second embodiment of the present invention.
FIG. 5 is an XY-plane side view in a second embodiment of the present invention.
FIG. 6 is a side view of the XZ plane in the second embodiment of the present invention.
FIG. 7 is a YZ plane side view of a second embodiment of the present invention.
Fig. 8 is a 3D diagram of a Z-axis optical needle array in the third embodiment of the present invention.
Fig. 9 is a 3D diagram of a lateral optical needle array according to a fourth embodiment of the present invention.
Fig. 10 is a 3D diagram of a five-dimensional array of spatial light needles according to an embodiment of the present invention.
FIG. 11 is a pupil plane incident field profile in an embodiment of the invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The embodiment provides a method for generating an arbitrary pointing optical needle three-dimensional array, which is characterized in that two high-numerical-aperture objective lenses for converging an incident field are coaxially arranged to establish a 4 pi optical focusing system; placing a virtual uniform line source antenna stereoscopic array in a focal area of a 4 pi optical focusing system, calculating to obtain a radiation field generated by the virtual uniform line source antenna stereoscopic array, completely converging the radiation field of the virtual uniform line source antenna stereoscopic array by two objective lenses and collimating the radiation field to a pupil plane, and reversing the radiation field of the virtual uniform line source antenna stereoscopic array by a time reversal technology to obtain an incident field of the pupil plane; and the incident field is incident from a pupil plane, is transmitted through the 4 pi optical focusing system and is converged in a focal area, and a directional controllable light needle three-dimensional array is formed in the focal area of the 4 pi optical focusing system.
And the phase difference of the incident field of the pupil planes at the two sides of the 4 pi optical focusing system is pi. The array elements of the virtual uniform line source antenna stereoscopic array are uniform line sources, the geometric length of the virtual uniform line source antenna stereoscopic array can be set, the spatial direction of the virtual uniform line source antenna stereoscopic array can be adjusted, and the spatial position of the virtual uniform line source antenna stereoscopic array can be adjusted.
The method comprises the following concrete implementation steps:
(1) Designing a 4 pi optical focusing system
Based on the radiation theory of the uniform line source antenna and the comprehensive technology of the array antenna, and in combination with the time reversal technology, an expected light needle three-dimensional array can be formed in a focal area of a focusing system by reversing the radiation field of the virtual uniform line source three-dimensional array.
In order to fully collect and converge the radiation field of the virtual antenna stereo array, a 4 pi optical focusing system as shown in fig. 1 is established. The two objective lenses of the system are identical high-numerical aperture objective lenses, the design mode is confocal placement, and the optical axes of the two objective lenses are on the same straight line.
(2) Three-dimensional array of line source antennas capable of arbitrarily pointing in design space
A rectangular coordinate system is established in a focal area of the 4 pi optical focusing system, wherein the optical axis direction of the two objective lenses is the Z-axis direction, the Y-axis direction is vertically upward, and an MXNxP virtual uniform line source antenna three-dimensional array is designed, as shown in FIG. 2.
Wherein "+" represents the array element of the three-dimensional array, M, N, P is the array element number of X, Y, Z axis respectively, and the X-axis coordinate of the array element is X 0 、x 1 、x 2 …x M-1 The Y-axis and Z-axis coordinates of the array elements are respectively Y 0 、y 1 、y 2 …y N-1 And z 0 、z 1 、z 2 …z P-1 。
In figure 2, the radiation fields of the virtual stereoscopic array of uniform line sources are fully collected by the 4 pi optical focusing system collimated into their pupil planes and inverted and propagated back from the pupil planes with a relative pi phase shift to near the focal region of the focusing system.
(3) Calculating the radiation field of the spatial arbitrary pointing uniform line source antenna stereo array
The array element of the three-dimensional array is a uniform line source antenna, the length of the line source antenna is L, and the current of the line source antenna is I 0 Arbitrarily spatially directed as
Wherein theta is 0 Is the included angle between the array element and the optical axis,
the included angle between the projection of the array element on the XOY plane and the X axis.
Deducing and calculating the radiation field of the array element with the central point at the origin by using the antenna radiation theory
Comprises the following steps:
wherein:
in the formula I 0 Is the magnitude of the current of the array element, L is the length of the array element, mu 0 To be guideMagnetic susceptibility, k is the wave number, w is the angular frequency, j is the imaginary unit,
is the polar coordinates of the array element radiation field,
and
is a polar coordinate unit direction vector, C is a coefficient irrelevant to the array element radiation pattern,
the array element is used as the array factor of the continuous line source,
and
are respectively array elements at
And
direction primitive factor of direction.
Forming an M multiplied by N multiplied by P antenna solid array by the array elements, and obtaining a space solid array factor according to an antenna array directional diagram product theorem:
the radiation field of the uniform line source three-dimensional array pointing at any space can be obtained:
(4) Calculating the incident field of the pupil plane of a 4 pi optical focusing system
The radiation field of the solid array of uniform line source antennas shown in figure 2 is completely collected by two identical high numerical aperture objectives and collimated to the pupil planes of both objectives. By utilizing a time reversal technology, the radiation field is reversed and is transmitted backwards from the pupil plane to the focal area of the focusing system by using relative pi phase shift, and an arbitrary pointing optical needle three-dimensional array can be formed. On the normalized pupil plane, for generating the incident field required by the light needle stereo array
Calculated from equation (9):
wherein
T (θ) is the apodization function of the objective lens, which is the polar coordinate of the incident field in the pupil plane. If the objective lens satisfies the helmholtz condition, T (θ) is:
the incident field of the pupil plane
Comprises the following steps:
wherein
And
is the pupil plane X, Y direction unit vector. Calculating tight focusing of the incident field by 4 pi optical focusing system by Debye theoryAfter being focused, the optical needle three-dimensional array with any direction can be formed.
(5) Specific examples
The following examples demonstrate the effectiveness and flexibility of the above-described method. To simplify the calculation, the example normalizes the parameter C independent of the shape of the light Jiao Changxing, and the currents of the three-dimensional array elements are all equal, and takes I m ＝I n ＝I p ＝1。
(5.1) Generation of optical needle stereoscopic array in coordinate Axis Direction
1.X axial optical needle stereo focal field
At this time, the array element orientation theta 0 ＝90°，
Then:
when L =2 λ, M =3, N =2, P =2, x 0 ＝-3λ、x 1 ＝0、x 2 ＝3λ、y 0 ＝-λ、y 1 ＝λ、z 0 ＝-λ、z 1 When = λ, a 3D pattern of a 3 × 2 × 2 stereoscopic array of X-axis optical needles is obtained as shown in fig. 3.
2.Y axial optical needle stereo array
At the moment, the array element is in the direction of theta 0 ＝90°，
Then the
When L =1.5 lambda, M =2, N =3, P =2, x 0 ＝-λ、x 1 ＝λ、y 0 ＝-3.5λ、y 1 ＝0、y 2 ＝3.5λ、z 0 ＝-λ、z 1 When = λ, the 3D pattern for obtaining a 2 × 3 × 2 stereoscopic array of Y-axis optical needles is shown in fig. 4, and fig. 5, 6, and 7 are XY, XZ, and YZ side views of the focal field of the array, respectively.
3.Z axial optical needle stereo array generation
At the moment, the array element is in the direction of theta 0 =0 °, then:
when L =2.5 λ, M =2, N =2, P =3, x 0 ＝-λ、x 1 ＝λ、y 0 ＝-λ、y 1 ＝λ、z 0 ＝-4λ、z 1 ＝0、z 2 Fig. 8 shows a 3D pattern for obtaining a 2 × 2 × 3 stereoscopic array of Z-axis optical needles when =4 λ.
(4.2) Generation of a three-dimensional array of transverse light needles in directions other than the coordinate axes
At the moment, the orientation of the array element is theta 0 ＝90°，
Then
Taking a transverse 2 × 2 × 2 stereo array as an example, when L =3 λ,
M＝N＝P＝2、x 0 ＝-3λ、x 1 ＝3λ、y 0 ＝-3λ、y 1 ＝3λ、z 0 ＝-2λ、z 1 =2 λ, and a 3D pattern resulting in a 2 × 2 × 2 stereoscopic array of transverse optical needles is shown in fig. 9.
(4.3) customization of other arbitrarily-directed stereoarrays of optical needles
With array element length L =3 λ and azimuth angle θ 0 ＝45°、
For illustration, the parameters M = N = P =2, x 0 ＝-1.75λ、x 1 ＝1.75λ、y 0 ＝-1.75λ、y 1 ＝1.75λ、z 0 ＝-2.5λ、z 1 Fig. 10 shows a 3D pattern for obtaining a spatial optical needle 2 × 2 × 2 stereoscopic array by using =2.5 λ.
(4.4) the pupil plane incident field distributions required for customizing different stereoscopic arrays of optical pins are different, and taking a stereoscopic array of optical pins 2 × 2 × 2 in the Z-axis direction with L =3 λ as an example, the required pupil plane incident field distribution is shown in fig. 11.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (3)
1. A method for generating an arbitrarily-pointed optical needle three-dimensional array is characterized in that two high-numerical-aperture objective lenses for converging an incident field are coaxially arranged to establish a 4 pi optical focusing system; placing a virtual uniform line source antenna stereoscopic array in a focal area of a 4 pi optical focusing system, calculating to obtain a radiation field generated by the virtual uniform line source antenna stereoscopic array, completely converging the radiation field of the virtual uniform line source antenna stereoscopic array by two objective lenses and collimating the radiation field to a pupil plane, and reversing the radiation field of the virtual uniform line source antenna stereoscopic array by a time reversal technology to obtain an incident field of the pupil plane; the incident field is incident from a pupil plane, is transmitted through the 4 pi optical focusing system and is converged in a focal region, and a directional controllable light needle three-dimensional array is formed in the focal region of the 4 pi optical focusing system;
a rectangular coordinate system is established in a focal area of a 4 pi optical focusing system, wherein the optical axis direction of two objective lenses is the Z-axis direction, an MxNxP virtual uniform line source antenna stereo array is arranged, M, N, P are the number of antenna array elements of X, Y, Z axes respectively, and X, Y, Z axis coordinates of the array elements are x axes respectively 0 、x 1 、x 2 …x M-1 ，y 0 、y 1 、y 2 …y N-1 And z 0 、Z 1 、Z 2 …z P-1 ；
The length of the antenna array element is L, and the current is I 0 Arbitrarily spatially directed as
Wherein theta is 0 Is the included angle between the array element and the optical axis,
is the included angle between the projection of the array element on the XOY plane and the X axis;
according to the antenna radiation theory, the radiation field of the antenna array element with the central point at the origin point
Comprises the following steps:
wherein
In the formula I 0 Is the magnitude of the current of the array element, L is the length of the array element, mu 0 Is the magnetic permeability, k is the wave number, W is the angular frequency, j is the imaginary unit,
is the polar coordinates of the array element radiation field,
and
is a polar coordinate unit direction vector, C is a coefficient irrelevant to the array element radiation pattern,
the array element is used as the array factor of the continuous line source,
and
are respectively array elements at
And
a direction primitive factor for a direction;
forming an M multiplied by N multiplied by P antenna stereo array by the antenna array elements, and obtaining a spatial stereo array factor according to an antenna array pattern product theorem:
the radiation field of any spatial directional uniform line source stereo array is:
inverting the radiation field of the virtual uniform line source antenna stereoscopic array and transmitting the radiation field from the pupil plane to the focal area of the 4 pi optical focusing system by using relative pi phase shift;
on the normalized pupil plane, for generating the incident field required by the light needle stereo array
Calculated from equation (9):
wherein
T (θ) is the apodization function of the objective lens, in polar coordinates of the incident field in the pupil plane; if the objective lens satisfies the helmholtz condition, T (θ) is:
the incident field of the pupil plane
Comprises the following steps:
wherein
And
is the unit vector of the pupil plane X, Y direction; and calculating the incident field to form an arbitrary pointing light needle three-dimensional array after the incident field is tightly focused by a 4 pi optical focusing system by utilizing the Debye theory.
2. The method for generating the arbitrary pointing optical needle stereo array according to claim 1, wherein the array elements of the virtual uniform line source antenna stereo array are uniform line sources, the geometric length of the array elements can be set, the spatial orientation of the array elements can be adjusted, and the spatial position of the antenna stereo array can be adjusted.
3. The method of claim 1, wherein the phase of the incident field of the pupil planes at the two sides of the 4 pi optical focusing system is different by pi.
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| CN109188687A (en) * | 2018-10-24 | 2019-01-11 | 泉州师范学院 | A method of the same focal spot array of two dimension is generated using the radiation field of planar array antenna |
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