CN111025664A - Control method and system for self-accelerating light beam - Google Patents
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Abstract
According to the control method and the system for the self-accelerating light beam, provided by the invention, the initial phase and the amplitude of the self-accelerating light beam are obtained by establishing the relationship between the light intensity distribution and the phase and the relationship between the light intensity distribution and the amplitude distribution, so that the phase and the amplitude of the initial light beam are modulated, the control on the track of the self-accelerating light beam is further realized, the higher accuracy of the whole control process is ensured, and the control efficiency is improved.
Description
Technical Field
The invention relates to the technical field of light beam control, in particular to a control method and a control system for self-accelerating light beams.
Background
Free-space beam self-acceleration has important applications in many areas, such as manipulation of microscopic particles, high resolution imaging, electron acceleration, and plasma generation and control.
However, in the prior art, generally, a geometrical optics principle is utilized, light rays are tangent to a motion track of an expected self-acceleration light beam, and then the wave front distribution of an initial light beam is determined according to the relation that the light ray transmission direction is perpendicular to a wave surface. The method only considers the transmission direction of the light beam when designing the wave front of the initial light beam, and can not quantitatively analyze the change process of the light intensity in the transmission process and the influence of the amplitude distribution of the initial light beam on the characteristics of the self-accelerating light beam.
Therefore, it is a technical problem to be solved in the art to find a light beam control method with high control accuracy and high control efficiency.
Disclosure of Invention
The invention aims to provide a control method and a control system for self-accelerating light beams, which have the characteristics of high control precision and high control efficiency.
In order to achieve the purpose, the invention provides the following scheme:
a method of controlling an auto-accelerating beam, comprising:
constructing the wigner transformation of the experimental light beam, and determining the relationship between the wigner transformation of the experimental light beam and the initial phase of the experimental light beam;
acquiring the light intensity distribution of the experimental light beam according to the relationship between the Wegener transformation of the obtained experimental light beam and the initial phase of the experimental light beam;
acquiring the relation between the light intensity distribution and the initial phase according to the light intensity distribution of the experimental light beam;
determining a wigner transformation for obtaining an initial amplitude according to the light field wigner function and the initial phase;
establishing a relation between the light intensity distribution and the initial amplitude according to the wigner transformation of the initial amplitude;
acquiring the light intensity distribution of the self-accelerating light beam;
acquiring an initial phase of the self-accelerating light beam according to the relation between the light intensity distribution and the initial phase, loading the initial phase of the self-accelerating light beam on a phase modulator, and modulating the phase of the self-accelerating light beam;
and acquiring the initial amplitude of the self-accelerating light beam according to the relation between the light intensity distribution and the amplitude, loading the initial amplitude of the self-accelerating light beam on an amplitude modulator, and modulating the amplitude of the self-accelerating light beam.
Optionally, the constructing wigner transformation of the experimental light beam and determining to obtain a wigner function of the light field in the free space includes:
acquiring the wigner transformation of the experimental light beam according to the initial amplitude of the experimental light beam;
and determining to obtain a Wegener function of the light field in the free space according to the Wegener transformation of the experimental light beam.
Optionally, the relationship between the light intensity distribution and the initial phase is:
wherein I (x, z) is light intensity distribution, z is transmission distance, k is wave number,
is the second partial derivative of the phase and,
is the third order partial derivative of the phase,
the first partial derivative of the phase.
Optionally, the initial phase of the self-accelerating light beam is:
where k is the wave number, a and n are constants, and x is used to indicate the direction of propagation of the light beam.
Optionally, the wigner function of the light field in the free space is:
wherein, Wz(x, u, z) is the wigner transform at z, z is the transmission distance, k is the wave number, w0Is the beam waist radius of the gaussian beam,
denotes the partial differential of x, u being a one-dimensional spatial frequency coordinate, x being used to denote the direction of transmission of the beam.
Optionally, the initial amplitude of the self-accelerating light beam is:
wherein, w0Is the radius of the waist of a gaussian beam and x is used to indicate the direction of travel of the beam.
A control system for self-accelerating a light beam, comprising:
the optical field Weigand function determining module is used for constructing Weigand transformation of the experimental light beam and determining the relationship between the Weigand transformation of the experimental light beam and the initial phase of the experimental light beam;
the first light intensity distribution acquisition module is used for acquiring the light intensity distribution of the experimental light beam according to the relationship between the Wegener transformation of the acquired experimental light beam and the initial phase of the experimental light beam;
the light intensity-phase relation acquisition module is used for acquiring the relation between the light intensity distribution and the initial phase according to the light intensity distribution of the experimental light beam;
the amplitude wigner transformation determining module is used for determining and obtaining wigner transformation of initial amplitude according to the light field wigner function and the initial phase;
the light intensity-amplitude relation establishing module is used for establishing the relation between the light intensity distribution and the initial amplitude according to the Weigner transformation of the initial amplitude;
the second light intensity distribution acquisition module is used for acquiring the light intensity distribution of the self-accelerating light beam;
the phase modulation module is used for acquiring the initial phase of the self-accelerating light beam according to the relation between the light intensity distribution and the initial phase, loading the initial phase of the self-accelerating light beam on the phase modulator and modulating the phase of the self-accelerating light beam;
and the amplitude modulation module is used for acquiring the initial amplitude of the self-accelerating light beam according to the relation between the light intensity distribution and the amplitude, loading the initial amplitude of the self-accelerating light beam on an amplitude modulator and modulating the amplitude of the self-accelerating light beam.
Optionally, the light field wigner function determining module includes:
the Weigand transformation unit is used for obtaining the Weigand transformation of the experimental light beam according to the initial amplitude of the experimental light beam;
and the light field wigner function determining unit is used for determining and obtaining the light field wigner function in the free space according to the wigner transformation of the experimental light beam.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: according to the control method and the system for the self-accelerating light beam, provided by the invention, the initial phase and the amplitude of the self-accelerating light beam are obtained by establishing the relationship between the light intensity distribution and the phase and the relationship between the light intensity distribution and the amplitude distribution, so that the phase and the amplitude of the initial light beam are modulated, the control on the track of the self-accelerating light beam is further realized, the higher accuracy of the whole control process is ensured, and the control efficiency is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method for controlling an auto-acceleration beam according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating optical field modulation and transmission according to an embodiment of the present invention;
FIG. 3a is a diagram of the movement trace of the self-accelerating light beam with a wavelength of 550 nm along the parabola when the radius of the Gaussian beam waist is 5mm by using the control method provided by the present invention;
FIG. 3b is a diagram showing the movement trajectory of the self-accelerating light beam with a wavelength of 550 nm along a parabola when the radius of the Gaussian beam waist is 2mm by using the control method provided by the present invention;
fig. 4 is a schematic structural diagram of an auto-acceleration beam control system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a control method and a control system for self-accelerating light beams, which have the characteristics of high control precision and high control efficiency.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of an auto-acceleration beam control method according to an embodiment of the present invention, and as shown in fig. 1, the method for controlling an auto-acceleration beam includes:
s100, constructing the Weiganan transformation of the experimental light beam, and determining the relationship between the Weiganan transformation of the experimental light beam and the initial phase of the experimental light beam.
S101, obtaining the light intensity distribution of the experimental light beam according to the relationship between the Weiganan transformation of the obtained experimental light beam and the initial phase of the experimental light beam.
And S102, acquiring the relation between the light intensity distribution and the initial phase according to the light intensity distribution of the experimental light beam.
S103, determining and obtaining the Weiganan transformation of the initial amplitude according to the Weiganan function of the light field and the initial phase.
S104, establishing the relation between the light intensity distribution and the initial amplitude according to the Weiganner transformation of the initial amplitude.
And S105, acquiring the light intensity distribution of the self-accelerating light beam.
S106, acquiring the initial phase of the self-accelerating light beam according to the relation between the light intensity distribution and the initial phase, loading the initial phase of the self-accelerating light beam on a phase modulator, and modulating the phase of the self-accelerating light beam.
S107, obtaining the initial amplitude of the self-accelerating light beam according to the relation between the light intensity distribution and the amplitude, loading the initial amplitude of the self-accelerating light beam on an amplitude modulator, and modulating the amplitude of the self-accelerating light beam.
S100 specifically comprises:
and acquiring the wigner transformation of the experimental light beam according to the initial amplitude of the experimental light beam.
And determining to obtain a Wegener function of the light field in the free space according to the Wegener transformation of the experimental light beam.
Wherein the relationship between the light intensity distribution and the initial phase is:
wherein I (x, z) is a light intensity distribution, z is a transmission distance, k is a wave number,
is the second partial derivative of the phase and,
is the third order partial derivative of the phase,
the first partial derivative of the phase.
The initial phase of the self-accelerating light beam is as follows:
in the formula, a and n are both constants.
The wigner function of the light field in the free space is:
wherein, Wz(x, u, z) is the wigner transformation at z, w0Is the beam waist radius of the gaussian beam,
representing the partial differential of x.
The initial amplitude of the self-accelerating beam is:
as another embodiment of the invention, the invention can utilize the Wegener transform to establish the relationship between the beam propagation trajectory and the phase and amplitude of the initial beam. The method specifically comprises the following steps:
the light field of an arbitrary beam can be represented as
Where A (x, y) is the amplitude of the beam,
the phase of the beam, (x, y) is the spatial cross-sectional coordinate, and i is the imaginary unit.
From the nature of the wigner transform, it can be seen that the wigner transform of a beam can be expressed as a convolution of the phase wigner transform and the amplitude wigner transform.
The wigner transformation of the phase can be obtained by the definition of wigner transformation:
herein, the
Is one-dimensional wigner transformation of phase (x, x)1) U is a one-dimensional spatial frequency coordinate, and x is used to indicate the transmission direction of the light beam. For convenience of presentation, only written out hereIn the case of one dimension (the same applies hereinafter), two dimensions can be directly obtained by one-dimensional expansion.
As can be seen from the taylor expansion, the equation (1) can be expressed under geometrical-optical approximation:
wherein
Denotes a partial differential value of x, δ [, ]]Is a Dirac delta function.
If the amplitude of the beam is known, the wigner transform of the amplitude can be found using the properties of the wigner transform.
The wigner transformation of the light beam is equal to the convolution of amplitude wigner transformation and phase wigner transformation, and then the wigner transformation of the light beam can be solved by the wigner transformation with the amplitude and the phase according to the convolution property of the Dirac delta function. The specific solving process can be solved according to the definition of convolution, and the method which can not be analyzed and solved and can be used for solving by using a numerical method according to the definition of the volume is solved. If the initial amplitude is gaussian, it can be expressed for the one-dimensional case as:
w herein0For the waist radius of a gaussian beam, its wigner transform is:
from formula (3), the Weiganan transform formula of the light beam transmission in free space
The Wegener function of the light field at any position of the free space can be solved, namely:
w hereinz(x, u, z) is the wigner transform at z, z is the transmission distance, and k is the wavenumber.
The light intensity is equal to the integral of the Wegener function in the frequency domain, so that the light intensity distribution at any position can be obtained. Adding the initial light beam as a plane wave, then:
herein, the
And
respectively representing the 3 rd, 2 nd and 1 st partial derivatives of the phase.
(5) Using the distribution and initial phase of the light intensity of formula (5)
The transmission path of the light beam can be controlled by modulating the distribution of the initial phase. If the transmission trajectory of the light beam is: x is aznSince a is a constant and n is an arbitrary constant and the initial phase is independent of z, it can be seen from the formula (5)
The integration can be obtained:
thereby completing the design of the initial phase.
Substituting the formula (7) into the formula (4) can obtain the Weiganan transformation with Gaussian amplitude modulation, and then integrating the frequency to obtain the light intensity distribution, thereby establishing the relationship between the light intensity distribution function and the Gaussian amplitude modulation. And finally, solving the light intensity distribution of the initial light beam according to the relation between the light intensity distribution at any position and the amplitude of the initial light beam, and realizing the amplitude design of the initial light beam.
The trajectory of the self-accelerating light beam is used for describing the position change of the light intensity of the light beam in the transmission process, and since the initial phase is independent of the transmission distance, by combining the formula (5) and utilizing dimension analysis, according to the trajectory of the self-accelerating light beam, the initial phase can be designed by the relation between the light beam transmission trajectory and the initial light beam phase, and the designed phase is loaded on a phase modulation device, such as: the phase modulation device is used for modulating the phase of the light beam.
Designing an initial amplitude according to the amplitude distribution requirement of the self-accelerating light beam by the relation between the amplitude distribution of the light beam transmission track and the initial light beam amplitude, and loading the designed initial amplitude distribution on an amplitude modulation device, such as: the amplitude type spatial light modulator, the diaphragm and the like, and then the light beam passes through the modulation device to realize the modulation of the light beam amplitude.
After the light beam is modulated by the amplitude and the phase, the light beam is transmitted according to the designed track, and can meet the specific amplitude distribution, thereby completing the control of the self-accelerating light beam transmission of any track.
The whole optical field modulation and transmission process using the method provided by the present invention is shown in fig. 2. And the method provided by the invention is adopted to make the self-accelerating light beam with the wavelength of 550 nanometers move along the parabola according to the specific motion track and effect when the radius of the Gaussian beam waist is 5mm and 2mm respectively, as shown in fig. 3a and fig. 3 b.
In addition, the present invention also provides a control system for self-accelerating a light beam, as shown in fig. 4, the system comprising: the device comprises a light field wigner function determining module 1, a first light intensity distribution obtaining module 2, a light intensity-phase relation obtaining module 3, an amplitude wigner transformation determining module 4, a light intensity-amplitude relation establishing module 5, a second light intensity distribution obtaining module 6, a phase modulation module 7 and an amplitude modulation module 8.
The light field wigner function determining module 1 is used for constructing wigner transformation of the experimental light beam and determining the relationship between the wigner transformation of the experimental light beam and the initial phase of the experimental light beam.
The first light intensity distribution obtaining module 2 is configured to obtain the light intensity distribution of the experimental light beam according to a relationship between wigner transformation of the obtained experimental light beam and an initial phase of the experimental light beam.
The light intensity-phase relation obtaining module 3 is used for obtaining the relation between the light intensity distribution and the initial phase according to the light intensity distribution of the experimental light beam.
The amplitude wigner transform determining module 4 is configured to determine a wigner transform that obtains an initial amplitude from the light field wigner function and the initial phase.
The light intensity-amplitude relationship establishing module 5 establishes a relationship between the light intensity distribution and the initial amplitude according to the wigner transformation of the initial amplitude.
The second light intensity distribution obtaining module 6 is used for obtaining the light intensity distribution of the self-accelerating light beam.
The phase modulation module 7 is configured to obtain an initial phase of the self-accelerating light beam according to a relationship between the light intensity distribution and the initial phase, load the initial phase of the self-accelerating light beam on the phase modulator, and modulate the phase of the self-accelerating light beam.
The amplitude modulation module 8 is configured to obtain an initial amplitude of the self-accelerating light beam according to the relationship between the light intensity distribution and the amplitude, load the initial amplitude of the self-accelerating light beam on an amplitude modulator, and modulate the amplitude of the self-accelerating light beam.
The light field wigner function determining module 1 may further include: the device comprises a Weiganan conversion unit and a light field Weiganan function determination unit.
The Weiganan conversion unit is used for obtaining the Weiganan conversion of the experiment light beam according to the initial amplitude of the experiment light beam. And the light field wigner function determining unit is used for determining and obtaining the light field wigner function in the free space according to the wigner transformation of the experimental light beam.
Compared with the prior art, the invention has the following characteristics:
1. determining a transmission path of the self-accelerating light beam according to actual needs;
2. according to the specific parameters of the transmission path, determining the phase distribution of the initial light field by the formula of the invention;
3. quantitatively analyzing the change of the spot size and the attenuation rule of the light intensity in the light beam transmission process by changing the amplitude distribution of the initial light beam;
4. the phase and amplitude distribution of the initial light field is determined in conjunction with the actual need.
5. After the light beam is modulated according to the designed amplitude and phase, the light beam is transmitted according to the designed track, and the control of the transmission of the self-accelerating light beam on any track is completed.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A method of controlling an auto-accelerating beam, comprising:
constructing the wigner transformation of the experimental light beam, and determining the relationship between the wigner transformation of the experimental light beam and the initial phase of the experimental light beam;
acquiring the light intensity distribution of the experimental light beam according to the relationship between the Wegener transformation of the obtained experimental light beam and the initial phase of the experimental light beam;
acquiring the relation between the light intensity distribution and the initial phase according to the light intensity distribution of the experimental light beam;
determining a wigner transformation for obtaining an initial amplitude according to the light field wigner function and the initial phase;
establishing a relation between the light intensity distribution and the initial amplitude according to the wigner transformation of the initial amplitude;
acquiring the light intensity distribution of the self-accelerating light beam;
acquiring an initial phase of the self-accelerating light beam according to the relation between the light intensity distribution and the initial phase, loading the initial phase of the self-accelerating light beam on a phase modulator, and modulating the phase of the self-accelerating light beam;
and acquiring the initial amplitude of the self-accelerating light beam according to the relation between the light intensity distribution and the amplitude, loading the initial amplitude of the self-accelerating light beam on an amplitude modulator, and modulating the amplitude of the self-accelerating light beam.
2. The method for controlling the self-accelerating light beam according to claim 1, wherein the constructing the wigner transformation of the experimental light beam and determining the wigner function of the light field in the free space comprises:
acquiring the wigner transformation of the experimental light beam according to the initial amplitude of the experimental light beam;
and determining to obtain a Wegener function of the light field in the free space according to the Wegener transformation of the experimental light beam.
3. The method as claimed in claim 1, wherein the relationship between the light intensity distribution and the initial phase is:
wherein I (x, z) is light intensity distribution, z is transmission distance, k is wave number,
is the second partial derivative of the phase and,
is the third order partial derivative of the phase,
the first partial derivative of the phase.
4. The method as claimed in claim 1, wherein the initial phase of the self-accelerating light beam is:
where k is the wave number, a and n are constants, and x is used to indicate the direction of propagation of the light beam.
5. The method as claimed in claim 1, wherein the wigner function of the light field in the free space is:
wherein, Wz(x, u, z) is the wigner transform at z, z is the transmission distance, k is the wave number, w0Is the beam waist radius of the gaussian beam,
denotes the partial differential of x, u being a one-dimensional spatial frequency coordinate, x being used to denote the direction of transmission of the beam.
6. The method as claimed in claim 1, wherein the initial amplitude of the self-accelerating beam is:
wherein, w0Is the radius of the waist of a gaussian beam and x is used to indicate the direction of travel of the beam.
7. A control system for self-accelerating a light beam, comprising:
the optical field Weigand function determining module is used for constructing Weigand transformation of the experimental light beam and determining the relationship between the Weigand transformation of the experimental light beam and the initial phase of the experimental light beam;
the first light intensity distribution acquisition module is used for acquiring the light intensity distribution of the experimental light beam according to the relationship between the Wegener transformation of the acquired experimental light beam and the initial phase of the experimental light beam;
the light intensity-phase relation acquisition module is used for acquiring the relation between the light intensity distribution and the initial phase according to the light intensity distribution of the experimental light beam;
the amplitude wigner transformation determining module is used for determining and obtaining wigner transformation of initial amplitude according to the light field wigner function and the initial phase;
the light intensity-amplitude relation establishing module is used for establishing the relation between the light intensity distribution and the initial amplitude according to the Weigner transformation of the initial amplitude;
the second light intensity distribution acquisition module is used for acquiring the light intensity distribution of the self-accelerating light beam;
the phase modulation module is used for acquiring the initial phase of the self-accelerating light beam according to the relation between the light intensity distribution and the initial phase, loading the initial phase of the self-accelerating light beam on the phase modulator and modulating the phase of the self-accelerating light beam;
and the amplitude modulation module is used for acquiring the initial amplitude of the self-accelerating light beam according to the relation between the light intensity distribution and the amplitude, loading the initial amplitude of the self-accelerating light beam on an amplitude modulator and modulating the amplitude of the self-accelerating light beam.
8. The system of claim 7, wherein the light field wigner function determining module comprises:
the Weigand transformation unit is used for obtaining the Weigand transformation of the experimental light beam according to the initial amplitude of the experimental light beam;
and the light field wigner function determining unit is used for determining and obtaining the light field wigner function in the free space according to the wigner transformation of the experimental light beam.
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