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CN110879467B - Method for regulating and controlling longitudinal structure of light beam - Google Patents

Method for regulating and controlling longitudinal structure of light beam Download PDF

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CN110879467B
CN110879467B CN201811033511.8A CN201811033511A CN110879467B CN 110879467 B CN110879467 B CN 110879467B CN 201811033511 A CN201811033511 A CN 201811033511A CN 110879467 B CN110879467 B CN 110879467B
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light
light beam
dot matrix
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lattice
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朱时军
汪瑞
李振华
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0927—Systems for changing the beam intensity distribution, e.g. Gaussian to top-hat

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Abstract

The invention relates to a method for regulating and controlling a longitudinal structure of a light beam, which is technically characterized in that a light beam is focused for many times in the transmission process along an optical axis by regulating and controlling a related structure of the light beam on an initial source plane, an optical dot matrix or an optical needle is formed on a transmission shaft, and the position, the number and the length of the dot matrix can be accurately controlled; meanwhile, the light beam can also carry radial polarization distribution on the initial source plane, and the polarization structure is kept in the transmission process, so that the optical lattice or the optical needle can have radial polarization transverse light intensity distribution, namely, the central light intensity is zero. By the regulating method, the transverse intensity distribution of the light beam can be regulated while the longitudinal structure of the light beam is accurately regulated.

Description

Method for regulating and controlling longitudinal structure of light beam
Technical Field
The invention relates to a light beam regulation and control technology, in particular to a method for regulating and controlling a longitudinal structure of a light beam.
Background
In the past decade, there has been much attention paid to how to design and regulate the correlation structure of partially coherent light, wherein the non-uniform correlation light beam has a lower scintillation property and a higher light intensity in random media such as atmospheric turbulence, ocean turbulence and the like due to its special self-focusing property, and is of interest. Unlike the uniformly associated beam, this non-uniform associated structure necessitates an optical system with a high order Fourier form transform of the beam, which can be modeled by a spatial light modulator [ Cui S, Chen Z, Zhang L, et al.
Because the periodic intensity distribution of the optical lattice is like a potential well which is distributed in one period, the optical lattice can be widely applied to researching ferromagnetic properties, antiferromagnetic properties and paramagnetic properties of the caged atoms, polarization gradient cooling and dynamics of the caging, Raman cooling and adiabatic cooling, wave packet dynamics, quantum transmission and tunnel effect, Bragg diffraction of light passing through the atomic optical lattice and the like. Meanwhile, the optical lattice can also be applied to the fields of high-density storage, material thermal processing, biology and the like. The wide application prospect of the optical lattice makes how to generate a proper optical lattice have high practical value, wherein, the accurate regulation and control of the optical lattice which is longitudinally distributed is always a difficult point.
Disclosure of Invention
The invention aims to provide a method for regulating and controlling a longitudinal structure of a light beam, which is used for accurately regulating and controlling the position, the period and the period number of a longitudinal optical dot matrix and preliminarily regulating and controlling the size of a light spot of a single dot matrix or accurately regulating and controlling the length of a light needle.
The technical scheme is as follows: a method for regulating and controlling a longitudinal structure of a light beam utilizes the self-focusing characteristic of high-order non-uniform correlation to generate a dot matrix or needle-shaped light field with intensity distribution along the transmission direction in the transmission process; first of all, generating a field having an associated property at the source field
Figure BDA0001790318930000011
The light beam with the associated structure can be self-focused in the free transmission process to generate a dot matrix or needle shape intensity; wherein r is1＝(x1,y1)，r2＝(x2,y2) Representing the position vectors of two points in the source plane, wcRepresenting the correlation width, k is the beam wavenumber, vnIs the multiple gaussian function offset position in the weighting function, and N is the number of gaussian functions.
After the light beam with the correlation characteristic is generated, the light beam can be directly transmitted through free space to generate a dot matrix or needle-shaped light intensity distribution; meanwhile, the light beam with the associated structure in the source field controls the transverse light distribution of the transmitted dot matrix or needle-shaped light beam by adding different initial light distribution and polarization distribution; v. ofnThe value of (A) controls the position of the lattice faculae in the transmission process, and N controls the number of the lattices; w is acControlling the longitudinal width of a single dot matrix light spot; when w iscThe smaller the value is, the longer the longitudinal width of a single dot matrix light spot is increased, so that the intensities of the dot matrix light spots at different positions are connected to form a light needle longitudinal light intensity structure; when w iscThe larger the value is, the larger the longitudinal width of a single dot matrix light spot is, the light intensity of the dot matrix light spots at different positions are separated from each other, and a light field forms a longitudinal dot matrix light intensity structure after transmission.
The position relation between the weight matrix Gaussian lattice offset position and the light field longitudinal lattice is as follows:
Figure BDA0001790318930000021
wherein z is0T is the initial position, the period interval, w of the target lattice0Is the light intensity width of the source field.
The Cross Spectral Density (CSD) expression of the modulated beam is:
Figure BDA0001790318930000022
compared with the prior art, the invention has the following remarkable advantages: (1) the invention controls the correlation width wcThe longitudinal width of a single light spot can be controlled, wcThe larger, the smaller the longitudinal width of the spot, wcThe smaller the light spot is, the larger the longitudinal width of the light spot is; n and vnThe number and the position of the lattice faculae can be accurately controlled; by regulating wcAnd vnThe intensity distributions of the lattice light spots at different positions can be connected into acicular longitudinal intensity distributions at different positions and lengths, or the intensity distributions of the lattice light spots at different positions can be separated from each other to form lattice intensity distributions at different positions and numbers; (2) the position of the optical needle is represented by z0The length is determined by T, N; in the formation of a lattice structure, z0T determines the position of the dot matrix, and N determines the number of the dot matrix light spots; (3) for the light beam with the original source plane of the Gaussian light intensity distribution of the scalar quantity, the longitudinal optical lattice and the light needle light intensity distribution are both solid; for the light beam with radial polarization Gaussian intensity distribution on the initial source plane, the longitudinal optical lattice and the light needle light intensity distribution are both hollow; these two beams can manipulate two different particles in terms of beam manipulation of the particles: particles with a refractive index greater than the surrounding environment and particles with a refractive index less than the surrounding environment, and coherence can also manipulate the spot size at the focus.
Drawings
FIG. 1 is a longitudinal schematic view of a Gaussian transverse intensity distribution optical lattice.
Fig. 2 is a longitudinal schematic view of a gaussian transverse intensity distribution light needle.
Fig. 3(a) and 3(b) are schematic diagrams of the lateral and longitudinal directions of a radial polarizing light needle, respectively.
Detailed Description
The invention provides a method for regulating and controlling a longitudinal structure of a light beam, which comprises the following steps of firstly constructing a weight function (probability density function) with a transverse Gaussian lattice, wherein the expression is as follows:
Figure BDA0001790318930000031
wherein C is0Represents a normalized coefficient;
the transmission kernel function expression is:
Figure BDA0001790318930000032
the cross-spectral density (CSD) expression of the light field generated on the source plane by the weights and the transmission kernel is:
Figure BDA0001790318930000033
wherein r is1＝(x1,y1)，r2＝(x2,y2) Representing the position vectors of two points in the source plane, w0Indicates the width of light intensity, vnIndicates the correlation width, wcIs the wave number of the beam, vnIs the offset position of the weight function, and N is the number of gaussian functions.
For a vector beam with a polarization structure, the initial light field carries a beam with a radial polarization structure, and the weighting function and the transmission kernel function are as follows:
Figure BDA0001790318930000041
Figure BDA0001790318930000042
Figure BDA0001790318930000043
wherein Hx(r, v) and Hy(r, v) represent the x and y polarization direction transfer kernel functions, respectively.
The CSD cells of the initial source plane are:
Figure BDA0001790318930000044
Figure BDA0001790318930000045
Figure BDA0001790318930000046
Figure BDA0001790318930000047
the position relationship between the weight matrix Gaussian lattice offset position and the light field longitudinal lattice is as follows:
Figure BDA0001790318930000048
where z is0T is the target lattice initial position and the period pitch, respectively, and N is 1, …, N. The longitudinal structure of the light beam is accurately regulated and controlled through the relation.
The present invention will be described in detail with reference to examples.
Examples
Firstly, a plane beam emitted by a He-Ne laser passes through a linear polarizer to form a completely coherent linearly polarized light beam, the size of a light spot is controlled by a beam expander, then the beam is subjected to phase modulation by a spatial light modulator to obtain a required associated structure, and finally a Gaussian intensity distribution initial source field is obtained by a Gaussian filter; for the Gaussian beam with the radial polarization initial source field, the structure of the optical path is not changed, and a radial polarization converter is arranged between the spatial light modulator and the Gaussian filter.
The core of the method is that the initial light beam correlation structure is given as follows:
Figure BDA0001790318930000049
and the correlation structure in the formula (1) is obtained by modulating the random phase of the light beam by the spatial light modulator, and the expression of the random phase modulation is as follows:
ψ(r,v)＝exp(ikr2v) (2)
where v denotes a random variable, and v takes the value of a probabilistic random distribution, where the probability distribution is expressed as:
Figure BDA0001790318930000051
wherein
Figure BDA0001790318930000052
Is a normalized coefficient.
The correlation structure expression of the light beam is as follows through the phase modulation of the spatial light modulator by the formulas (2) and (3):
Figure BDA0001790318930000053
neglecting the constant of (4)
Figure BDA0001790318930000054
It is the same as formula (1).
For an initial light beam with a Gaussian intensity distribution scalar, after obtaining a correlation structure in the formula (1) through phase modulation, directly obtaining the correlation structure through a Gaussian filter, wherein a CSD expression of the modulated light beam is as follows:
Figure BDA0001790318930000055
in summary, the overall process of generating the beam of formula (5) can be described by the following expression:
w(r1,r2)＝∫pco(v)H*(r1,v)H(r2,v)dv (6)
wherein
Figure BDA0001790318930000056
Figure BDA0001790318930000057
The intensity distribution of the light beam described by the formula (5) after passing through an ABCD optical system is expressed as:
s(ρ,z)＝∫pco(v)|H(ρ,v,z)|2dv (8)
wherein
Figure BDA0001790318930000061
Where ρ is (ρ)x,ρy) Is the position vector on the receiving surface.
For a gaussian beam with an initial source field being radial polarization, after passing through a spatial light modulator, a linear polarization converter is required to convert a linear polarization beam into a radial polarization beam, and finally intensity modulation is performed through a gaussian filter, so as to obtain an initial source plane beam 2 × 2CSD expression as follows:
Figure BDA0001790318930000062
like equation (5), equation (10) can also be decomposed into the form of equation (6), as follows:
Figure BDA0001790318930000063
wherein α, β ═ x, y, and
Figure BDA0001790318930000064
the intensity distribution of the light beam after passing through an ABCD optical system is expressed as follows:
sα(ρ,z)＝∫pco(v)|Hα(ρ,v,z)|2dv (13)
wherein
Figure BDA0001790318930000065
When the optical system through which the initial light beam passes is free space, the intensity distribution of the light beam during transmission can be numerically calculated by equations (8) and (13).
The present invention will be described in detail with reference to examples.
Examples
In this embodiment, the following parameters are taken: k 2 pi/λ, λ 632.8nm, w0＝2mm，z0＝19mm，
Figure BDA0001790318930000071
When w is shown in FIG. 1cWhen the length of the longitudinal structure of the Gaussian intensity distribution in the beam transmission process is 2mm, the beam intensity distribution is observed to present 16 light spot lattices along the transmission axis, and the position and the period are accurately controlled as expected; FIG. 2 is wcThe longitudinal structure of the light beam with 1 mm-long Gaussian intensity distribution in the transmission process can be seen, a plurality of lattice light spots are connected together to form a light needle, and the length of the light needle is accurately controlled; FIG. 3(a) and FIG. 3(b) are wcThe cross-sectional intensity distribution and the longitudinal intensity structure of the initial beam of the radially polarized gaussian after the transmission through free space at 1mm can be seen, while the length of the optical needle is precisely controlled as in fig. 2, fig. 3(a) is a transverse cross-sectional intensity diagram of the radially polarized optical needle at z 21mm, and fig. 3(b) is a longitudinal cross-sectional view of the radially polarized optical needleIt can be seen that the optical needle is of a "hollow" construction. The explanation shows that the light beam longitudinal structure can be accurately regulated and controlled by the light beam regulation and control method, and meanwhile, the light beam transverse intensity distribution can be regulated and controlled.

Claims (1)

1. A method for regulating and controlling a longitudinal structure of a light beam is characterized in that a self-focusing characteristic of high-order non-uniform correlation is utilized, and a lattice or needle-shaped light field with intensity distribution is generated along a transmission direction in a transmission process; first of all, generating a field having an associated property at the source field
Figure FDA0003258270540000011
The light beam with the correlation structure can be self-focused in the free transmission process to generate a dot matrix or needle-shaped intensity distribution; wherein r is1＝(x1,y1)，r2＝(x2,y2) Representing the position vectors of two points in the source plane, wcRepresenting the correlation width, k is the beam wavenumber, vnIs the offset position of multiple Gaussian functions in the weight function, and N is the number of Gaussian functions;
after the light beam with the correlation characteristic is generated, the light beam is directly transmitted through free space to generate a dot matrix or needle-shaped light intensity distribution; meanwhile, the light beam with the associated structure at the source field controls the transverse light distribution of the transmitted dot matrix or needle-shaped light beam by adding different initial light distribution and polarization distribution; v. ofnThe value of (A) controls the position of the lattice faculae in the transmission process, and N controls the number of the lattices; w is acControlling the longitudinal width of a single dot matrix light spot; when w iscThe smaller the value is, the longer the longitudinal width of a single dot matrix light spot is increased, so that the intensities of the dot matrix light spots at different positions are connected to form a light needle longitudinal light intensity structure; when w iscThe larger the value is, the longitudinal width of a single dot matrix light spot is shrunk, the light intensities of the dot matrix light spots at different positions are mutually separated, and a longitudinal dot matrix light intensity structure is formed after the light field is transmitted;
the position relation between the weight matrix Gaussian lattice offset position and the light field longitudinal lattice is as follows:
Figure FDA0003258270540000012
wherein z is0T is the initial position, the period interval, w of the target lattice0Is the light intensity width of the source field;
the cross-spectral density expression of the modulated beam is as follows:
Figure FDA0003258270540000013
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0460625A2 (en) * 1990-06-05 1991-12-11 Matsushita Electric Industrial Co., Ltd. Optical information processing apparatus and method using computer generated hologram
CN101178484A (en) * 2007-12-07 2008-05-14 南京大学 Generation device of random polarization distributing vector light beam
CN101794024A (en) * 2010-04-02 2010-08-04 上海理工大学 Device and method for generating column vector beams
CN105589203A (en) * 2016-03-13 2016-05-18 南京理工大学 Method and device for generating radial polarized array beam
CN105607275A (en) * 2016-03-13 2016-05-25 南京理工大学 Method and apparatus for generation of radial polarized cosine Gaussian Shell Model (GSM) light beam

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0460625A2 (en) * 1990-06-05 1991-12-11 Matsushita Electric Industrial Co., Ltd. Optical information processing apparatus and method using computer generated hologram
CN101178484A (en) * 2007-12-07 2008-05-14 南京大学 Generation device of random polarization distributing vector light beam
CN101794024A (en) * 2010-04-02 2010-08-04 上海理工大学 Device and method for generating column vector beams
CN105589203A (en) * 2016-03-13 2016-05-18 南京理工大学 Method and device for generating radial polarized array beam
CN105607275A (en) * 2016-03-13 2016-05-25 南京理工大学 Method and apparatus for generation of radial polarized cosine Gaussian Shell Model (GSM) light beam

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