CN209640611U - Multistage stablizes the generation device of transmission bessel beam on a kind of axis - Google Patents
Multistage stablizes the generation device of transmission bessel beam on a kind of axis Download PDFInfo
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Abstract
The utility model discloses the generation devices that multistage on a kind of axis stablizes transmission bessel beam, which includes: positive axis axicon lens；The refractive index of the material of the positive axis axicon lens is greater than the refractive index of exterior space medium；Amplitude diaphragm is provided on the bottom surface of the positive axis axicon lens；The annular region of M discrete gradual change amplitude modulations is provided on the amplitude diaphragm.The utility model generates bessel beam using positive axis axicon lens, and amplitude diaphragm is provided on the bottom surface of positive axis axicon lens, incident plane wave is acted on by the amplitude modulation of gradual change in multiple annular regions, make the bessel beam generated that there is the on-axis intensity distribution having good uniformity, and transmission can be stablized in the discrete region of the multistage on optical axis, there is critically important practical application meaning.
Description
Technical field
The utility model relates to optical technical field, the production that multistage on a kind of axis stablizes transmission bessel beam is particularly related to
Generating apparatus.
Background technique
Bessel beam is a kind of Beams, when it is propagated in free space, perpendicular to the direction of propagation
Any cross section on, light distribution remains unchanged.Since the light distribution of bessel beam is independent of position on axis, significantly
It reduces for experimental system in the requirement for precisely aligning aspect, improves the stability and accuracy of system, thus it is swashing
There is wide application prospect in light processing, interferometry, optical acquisition etc..
It is a kind of involved in Chinese patent application application No. is 201811346604.6 to stablize transmission shellfish plug for generating
The device of your light beam can generate the bessel beam for stablizing transmission.However the bessel beam that above scheme generates is only capable of
It is realized in one section of region on optical axis and stablizes transmission, will receive certain restrictions in practical applications.
Utility model content
In view of this, the purpose of this utility model is that proposing that multistage on a kind of axis stablizes the generation of transmission bessel beam
Device can generate the bessel beam for stablizing transmission in the multistage region on optical axis.
Based on above-mentioned purpose, the utility model provides the generation dress that multistage on a kind of axis stablizes transmission bessel beam
It sets, comprising: positive axis axicon lens；The refractive index of the material of the positive axis axicon lens is greater than the refractive index of exterior space medium；The positive axis
Amplitude diaphragm is provided on the bottom surface of axicon lens；M discrete annular transmission regions are provided on the amplitude diaphragm；Corresponding to institute
M annular transmission region is stated, the amplitude transmission coefficient of the amplitude diaphragm meets following formula:
Wherein, ρ is the radial position coordinate on the amplitude diaphragm；The radius of the annular transmission region meets: 0 < R1<
R2≤R3<R4≤R5…<R2M-1<R2M≤ R, R are the radius of the amplitude diaphragm.
In some embodiments, the amplitude transmission coefficient further satisfaction of the amplitude diaphragm: T1(ρ)×T2(ρ)；Its
In, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；N is smooth order, and the value of N is positive
Real number.
In some embodiments, the amplitude transmission coefficient further satisfaction of the amplitude diaphragm: T1(ρ)×T2(ρ)；Its
In, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MTable
Show the radius of annular region；N is smooth order, and wherein N is positive real number.
In some embodiments, the amplitude transmission coefficient further satisfaction of the amplitude diaphragm: T1(ρ)×T2(ρ)；Its
In, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MTable
Show the radius of annular region；N is smooth order, and wherein N is positive real number.
In some embodiments, the amplitude transmission coefficient further satisfaction of the amplitude diaphragm: T1(ρ)×T2(ρ)；Its
In, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MTable
Show the radius of annular region；N is smooth order, and wherein N is positive real number.
In some embodiments, the ε1、ε2、ε3、ε4、…、ε2M-1And ε2MValue it is identical, and its value range is
[0 0.5]。
In some embodiments, the ε1、ε2、ε3、ε4、…、ε2M-1And ε2MValue be 0.2.
In some embodiments, the base angle of the positive axis axicon lens is 3 °；The bottom surface radius of the positive axis axicon lens is 3 lis
Rice.
In some embodiments, the refractive index of the material of the positive axis axicon lens is 1.5146；The exterior space medium
Refractive index be 1.
On the other hand, the utility model additionally provides the production method that multistage on a kind of axis stablizes transmission bessel beam,
It include: to make incident plane wave through device described in any one as above；Wherein, the incident plane wave is perpendicular to the positive axis
The bottom surface of axicon lens is incident.
From the above it can be seen that multistage stablizes the generation dress of transmission bessel beam on axis provided by the utility model
It sets, bessel beam is generated by positive axis axicon lens, and be provided with amplitude diaphragm on the bottom surface of positive axis axicon lens, pass through gradual change amplitude
Multiple annular regions of modulation act on incident plane wave, and the bessel beam generated is made to have the on-axis intensity having good uniformity
Distribution, and transmission can be stablized in the multistage region on optical axis, there is critically important practical application meaning.
Detailed description of the invention
In order to illustrate the embodiment of the utility model or the technical proposal in the existing technology more clearly, below will be to embodiment
Or attached drawing needed to be used in the description of the prior art does simple introduction, it should be apparent that, the accompanying drawings in the following description is only
It is some embodiments of the utility model, for those of ordinary skill in the art, in the premise not made the creative labor
Under, it is also possible to obtain other drawings based on these drawings.
Fig. 1 is that the structure of the device of the utility model embodiment and light propagate schematic diagram；
Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) are respectively to generate single hop on axis to stablize in the embodiment of transmission bessel beam, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Amplitude transmission coefficient in the case of three kinds of (ρ)；
Fig. 3 (a), Fig. 3 (b), Fig. 3 (c) are respectively to generate single hop on axis to stablize in the embodiment of transmission bessel beam, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
On-axis intensity distribution in the case of three kinds of (ρ)；
Fig. 4 (a), Fig. 4 (c), Fig. 4 (e) are respectively to generate single hop on axis to stablize in the embodiment of transmission bessel beam, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Light distribution in the case of three kinds of (ρ), chain lines, dotted line, dotted line and solid line respectively correspond zi=600mm, 700mm,
Perpendicular to the light distribution on the cross section of z-axis along x-axis at 800mm and 900mm (i=1,2,3,4)；
Fig. 4 (b), Fig. 4 (d), Fig. 4 (f) are respectively to generate single hop on axis to stablize in the embodiment of transmission bessel beam, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Light intensity deviation in the case of three kinds of (ρ), chain lines, dotted line, dotted line and solid line respectively correspond zi=600mm, 700mm,
Perpendicular to the light intensity deviation on the cross section of z-axis along x-axis at 800mm and 900mm (i=1,2,3,4)；
Fig. 5 is to generate single hop on axis to stablize in the embodiment of transmission bessel beam, the axis in the case of different smooth orders
Upper light distribution；
Fig. 6 (a), Fig. 6 (b), Fig. 6 (c) are respectively to generate to stablize in the embodiment for transmitting bessel beam for two sections on axis, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Amplitude transmission coefficient in the case of three kinds of (ρ)；
Fig. 7 (a), Fig. 7 (b), Fig. 7 (c) are respectively to generate to stablize in the embodiment for transmitting bessel beam for two sections on axis, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
On-axis intensity distribution in the case of three kinds of (ρ)；
Fig. 8 (a), Fig. 8 (c), Fig. 8 (e) are respectively to generate to stablize in the embodiment for transmitting bessel beam for two sections on axis, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Light distribution in the case of three kinds of (ρ), chain lines, dotted line, dotted line and solid line respectively correspond zi=500mm, 600mm,
Perpendicular to the light distribution on the cross section of z-axis along x-axis at 900mm and 1000mm (i=1,2,3,4)；
Fig. 8 (b), Fig. 8 (d), Fig. 8 (f) are respectively to generate to stablize in the embodiment for transmitting bessel beam for two sections on axis, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Light intensity deviation in the case of three kinds of (ρ), chain lines, dotted line, dotted line and solid line respectively correspond zi=500mm, 600mm,
Perpendicular to the light intensity deviation on the cross section of z-axis along x-axis at 900mm and 1000mm (i=1,2,3,4)；
Fig. 9 (a), Fig. 9 (b), Fig. 9 (c) are respectively to generate to stablize in the embodiment for transmitting bessel beam for three sections on axis, no
Amplitude diaphragm is set, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)×T2
Amplitude transmission coefficient in the case of three kinds of (ρ)；
Figure 10 (a), Figure 10 (b), Figure 10 (c) are respectively to generate to stablize the embodiment for transmitting bessel beam for three sections on axis
In, it is not provided with amplitude diaphragm, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)
×T2On-axis intensity distribution in the case of three kinds of (ρ)；
Figure 11 (a), Figure 11 (c), Figure 11 (e) are respectively to generate to stablize the embodiment for transmitting bessel beam for three sections on axis
In, it is not provided with amplitude diaphragm, the amplitude transmission coefficient of amplitude diaphragm is T1 (ρ) and the amplitude transmission coefficient of amplitude diaphragm is T1
(ρ)×T2Light distribution in the case of three kinds of (ρ), chain lines, dotted line, dotted line and solid line respectively correspond zi=400mm,
Perpendicular to the light distribution on the cross section of z-axis along x-axis at 625mm, 715mm and 960mm (i=1,2,3,4)；
Figure 11 (b), Figure 11 (d), Figure 11 (f) are respectively to generate to stablize the embodiment for transmitting bessel beam for three sections on axis
In, it is not provided with amplitude diaphragm, the amplitude transmission coefficient of amplitude diaphragm is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm is T1(ρ)
×T2Light intensity deviation in the case of three kinds of (ρ), chain lines, dotted line, dotted line and solid line respectively correspond zi=400mm, 625mm,
Perpendicular to the light intensity deviation on the cross section of z-axis along x-axis at 715mm and 960mm (i=1,2,3,4).
Specific embodiment
For the purpose of this utility model, technical solution and advantage is more clearly understood, below in conjunction with specific embodiment, and
Referring to attached drawing, the utility model is further described.
The utility model embodiment provides the generation device that multistage on a kind of axis stablizes transmission bessel beam, with reference to figure
1 comprising: positive axis axicon lens 1.The refractive index of the material of positive axis axicon lens 1 is greater than the refractive index of exterior space medium.Positive axis axicon lens 1
Bottom surface on be provided with amplitude diaphragm 2, the shape of amplitude diaphragm 2 is circle, identical as the bottom surface of positive axis axicon lens 1, and is projected
It is overlapped setting.Further, M annular transmission region is provided on amplitude diaphragm 2, specifically, by setting amplitude diaphragm 2
Amplitude transmission coefficient determine this M annular transmission region.
When in use, incident plane wave is incident perpendicular to the bottom surface of positive axis axicon lens 1, based on amplitude transmission on amplitude diaphragm 2
The modulation of coefficient to change the optical field distribution in 1 right side transmission region of positive axis axicon lens, and then realizes the technology effect of the utility model
Fruit.
For the technical solution of the utility model is further described, the design and thoroughly of positive axis axicon lens is divided into aftermentioned content
Penetrate that the calculating of light field, single hop stablizes that the generation of transmission bessel beam, multistage stablizes the production of transmission bessel beam on axis on axis
Raw three steps, are progressively illustrated the optical principle of the embodiment of the utility model.
One, the design of positive axis axicon lens and the calculating of Transmission field
With reference to Fig. 1, the generation device that multistage stablizes transmission bessel beam on the axis of the present embodiment includes: positive axis axicon lens 1
With amplitude diaphragm 2.When on the plane wave of unit amplitude from left to right normal incidence to the bottom surface of positive axis axicon lens 1, in positive axis axicon lens 1
Bottom surface on, light reflects, but does not change direction；It on the exit facet of positive axis axicon lens 1, reflects again, by reflecting
Law, the deflection angle of emergent ray are as follows:
In formula (1), angle of the θ between emergent ray and optical axis, n1And n0Respectively positive axis axicon lens 1 and outside are empty
Between refractive index, α be orthopyamid mirror 1 base angle, as shown in Figure 1.
As shown in Figure 1, in z=0 plane, radius ρ0Position at phase are as follows:
In formula (2), λ is the wavelength of incident plane wave,Wherein x0Z=is respectively indicated with y0
Lateral position coordinate in 0 plane.Therefore, the optical field distribution in z=0 plane are as follows:
In formula (3), A (ρ0) indicate that radius is ρ in z=0 plane0Position at amplitude, j is imaginary unit.
It will be seen from figure 1 that being emitted in plane wave normal incidence to amplitude diaphragm 2 from axial cone mirror, will horizontally occur inclined
It moves.Radius is light incident at the position of ρ on amplitude diaphragm 2, the position of emergent ray corresponding half in z=0 plane
Diameter is ρ0, as shown in Figure 1.From the geometric relations:
ρ=ρ0+ρ×tan(α)×tan(θ) (4)
By mathematic(al) manipulation, formula (4) can be written as follow form:
Therefore, optical field distribution when on the plane wave incidence of unit amplitude to amplitude diaphragm 2, in z=0 plane are as follows:
In formula (6), ρ is provided by formula (5).In the case where unit amplitude plane wave incidence, when setting amplitude light
When door screen 2, A (ρ0)=T (ρ), wherein T (ρ) is the amplitude transmission coefficient of amplitude diaphragm 2；When being not provided with amplitude diaphragm 2, T (ρ)
=1.
After obtaining the optical field distribution in z=0 plane, stringent Rayleigh is recycled --- rope end Philippine side method can calculate
Optical field distribution in the transmission region on 1 right side of positive axis axicon lens at any point (x, y, z) out are as follows:
In formula (7), E0(x0, y0, z=0) indicate z=0 plane on optical field distribution；λ is the wave of incident plane wave
It is long；R indicates the source point (x in z=0 plane0, y0The distance between, 0) and point of observation (x, y, z), it may be assumed that
Two, single hop stablizes the generation for transmitting bessel beam on axis
The changing rule that oscillation rises is presented in the bessel beam generated by positive axis axicon lens 1, in the direction of the optical axis, light intensity.
For this purpose, the utility model patent proposes, amplitude diaphragm 2 is set on the bottom surface of positive axis axicon lens 1, as shown in Figure 1, to change just
Optical field distribution in 1 right side transmission region of axial cone mirror, it is expected that obtaining the bessel beam for stablizing transmission.
Firstly, realizing the single hop transmission range [z on optical axis by design amplitude diaphragm 21z2] the stable biography of the interior generation of range
Defeated bessel beam.In general, [z1z2] range determined by practical application request.
To solve the problems, such as that the bessel beam generated by positive axis axicon lens 1 is unstable in light on-axis intensity, it is divided into following two
Step.The first step is [R in radius to solve the problems, such as on-axis intensity monotone increasing1R2] annular region in introduce annular amplitude
Diaphragm.At this point, the amplitude transmission coefficient of amplitude diaphragm 2 are as follows:
In formula (9), ρ indicates the radial position coordinate on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)；R1And R2Respectively
For the internal diameter and outer diameter of annular region；The inside and outside radius of annular region meets: 0 < R1< R2≤ R, wherein R is amplitude diaphragm 2
Radius.According to theory of geometric optics, the transmission range z and the radial position ρ in z=0 plane of bessel beam0Between relationship
Are as follows: z=ρ0/ tan (θ) is according to formula (1) and formula (5), on amplitude diaphragm 2, the inside and outside radius point of annular transmission region
Not are as follows:
In formula (10), transmission range z on axisi(i=1,2) is determined by practical application request.It, can using formula (10)
Obtain the inside and outside radius R of annular transmission regioni(i=1,2) recycles formula (9) to design amplitude diaphragm 2.
Second step solves the oscillation problem of on-axis intensity.For inhibit on-axis intensity oscillation, the two of annular transmission region
A boundary introduces the smooth diaphragm of amplitude, and the amplitude transmission coefficient of the smooth diaphragm of amplitude is no longer mutated by 1 to 0, but by one
The function of consecutive variations provides.The amplitude transmission coefficient further satisfaction of amplitude diaphragm 2 in the present embodiment: T1(ρ)×T2(ρ)；
Wherein, T2The expression formula of (ρ) are as follows:
In formula (11), ρ indicates the radial position coordinate on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)；ε1And ε2For
Smooth length proportionality coefficient；N is smooth order, and wherein N is positive real number.
In the present embodiment, amplitude diaphragm 2 forms gradual change amplitude diaphragm.Therefore, the amplitude transmission coefficient of gradual change amplitude diaphragm
Are as follows:
T (ρ)=T1(ρ)×T2(ρ) (12)
In formula (12), T1(ρ) and T2(ρ) is provided by formula (9) and (11) respectively.
In contrast thereto, in the case where being not provided with amplitude diaphragm 2, amplitude transmission coefficient are as follows:
In formula (13), R is the radius of orthopyamid mirror 1.
Next, simulation calculating will be carried out to generated bessel beam, its light distribution is obtained.In order on optical axis
The bessel beam that single hop stablizes transmission is generated, parameter is selected as follows: the radius of positive axis axicon lens 1 is R=3cm；Positive axis axicon lens 1
Base angle is α=3 °；The wavelength of incident plane wave is λ=632.8nm；Positive axis axicon lens 1 selects K9 glass, selectes the corresponding folding of wavelength
Penetrating rate is n1=1.5146；Exterior space is air, refractive index n0=1.0；The transmission range model of bessel beam on optical axis
Enclose setting are as follows: [4001100] mm；According to formula (10), on annular amplitude diaphragm and the smooth diaphragm of amplitude, annular transmission region
Inside and outside radius be respectively R1=1.08cm and R2=2.97cm；Smooth length proportionality coefficient are as follows: ε1=ε2=0.1, smooth rank
Number is N=2.
According to parameter selected above, it is calculated and is not provided with amplitude diaphragm 2, the amplitude transmission coefficient of amplitude diaphragm 2 is
T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2Amplitude transmission coefficient such as Fig. 2 (a) in the case of three kinds of (ρ), 2
(b) and shown in 2 (c).
Based on scalar diffraction theory and complete Rayleigh --- rope end Philippine side method, using formula (7), simulation is calculated just
On-axis intensity distribution in the transmission region on 1 right side of axial cone mirror.Fig. 3 (a), 3 (b) and 3 (c) respectively correspond be not provided with amplitude diaphragm 2,
The amplitude transmission coefficient of amplitude diaphragm 2 is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2(ρ) three kinds of situations
Under on-axis intensity distribution.As can be seen that the changing rule that oscillation rises is presented in on-axis intensity when being not provided with amplitude diaphragm 2,
As shown in Fig. 3 (a)；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1When (ρ), the ascendant trend of on-axis intensity is effectively suppressed,
But there are still violent oscillation effects for on-axis intensity, as shown in Fig. 3 (b)；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1(ρ)
×T2When (ρ), the oscillation effect of on-axis intensity is effectively suppressed, and the bessel beam for stablizing transmission is obtained, such as Fig. 3 (c) institute
Show.
For the stability of quantitatively characterizing on-axis intensity, the relative error of on-axis intensity is defined are as follows:Wherein IzIndicate the light intensity on optical axis at certain point,Indicate being averaged in certain section of region on optical axis
Light intensity.Numerical result in Fig. 3 shows that transmission range is to be not provided with amplitude within the scope of [600900] mm on optical axis
Diaphragm 2, amplitude diaphragm 2 amplitude transmission coefficient be T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2(ρ) three
In the case of kind, the maximum relative error of on-axis intensity is respectively as follows: 26.13%, 5.94% and 0.01%, this shows using designed
Amplitude diaphragm 2, obtained on optical axis single hop stablize transmission bessel beam.
For characterize caused by bessel beam performance, in zi=600mm, 700mm, 800mm and 900mm (i=1,2,
3,4) on four cross sections, simulation calculates light distribution along x-axis, respectively as in Fig. 4 chain lines, dotted line, dotted line and
It is shown in solid.Fig. 4 (a), 4 (c) and 4 (e) respectively correspond and are not provided with amplitude diaphragm 2, the amplitude transmission coefficient of amplitude diaphragm 2 is T1
The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2It is distributed in the case of three kinds of (ρ) along the actual light intensity of x-axis.From Fig. 4
(a), 4 (c) and 4 (e) as can be seen that the actual light intensity on four cross sections is widely different when being not provided with amplitude diaphragm 2；When
The amplitude transmission coefficient of amplitude diaphragm 2 is T1When (ρ), the actual light intensity deviation on four cross sections is smaller；When amplitude diaphragm 2
Amplitude transmission coefficient is T1(ρ)×T2When (ρ), the actual light intensity distribution on four cross sections is almost overlapped.Simulate calculated result also
Show all to obtain high-resolution bessel beam on all cross sections, spot radius is 8.97 μm, this with according to several
The spot radius what optical theory obtainsIt is completely the same.
For the stabilization transmission characteristic for clearly illustrating that bessel beam on varying cross-section, the light intensity on cross section is defined
Deviation are as follows: Δ Ix=| Ix-I0|, wherein IxIndicate the light distribution on cross section along x-axis,Indicate four
Along the average intensity of x-axis on cross section.Fig. 4 (b), 4 (d) and 4 (f), which are set forth, is not provided with amplitude diaphragm 2, amplitude diaphragm 2
Amplitude transmission coefficient be T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2Along x-axis in the case of three kinds of (ρ)
Light intensity deviation.Simulation calculated result show the largest light intensity deviation at above-mentioned three kinds, on cross section be respectively as follows: 6649,
477 and 0.39.Further, it can define the maximum relative light intensity deviation on cross section are as follows:
At above-mentioned three kinds, the maximum relative light intensity deviation on cross section is respectively as follows: 20.01%, 2.59% and 0.002%.
In addition, keeping other parameters constant by the smooth order for changing amplitude diaphragm 2, calculating bessel beam
On-axis intensity distribution, as shown in Figure 5.From fig. 5, it can be seen that all obtaining and stablizing on axis in the case where different smooth orders
The bessel beam of transmission.It simulates calculated result to show when N is respectively 0.5,1,2,4 and 8, the transmission range on axis
[600900] within the scope of mm, the maximum relative error of on-axis intensity is respectively as follows: 0.57%, 0.08%, 0.01%, 0.01% and
0.03%.
It should be noted that in the above-described embodiments, to obtain stablizing the bessel beam of transmission, T on axis2(ρ) is used
[sin(x)]NForm, provided by formula (11).However, in practical applications, for the technical effect for realizing the utility model, T2
(ρ) can be provided by the function of any one consecutive variations.
In other embodiments, T2(ρ) can also be indicated by following form:
1)
In formula (14),ρ indicates the diameter on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)
To position coordinates；ε1And ε2For smooth length proportionality coefficient；N is smooth order, and wherein N is positive real number.
2)
In formula (15), J0For zero Bessel function；ρ indicates the diameter on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)
To position coordinates；ε1And ε2For smooth length proportionality coefficient；N is smooth order, and wherein N is positive real number.
3)
In formula (16), J1For first-order bessel function；ρ indicates the diameter on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)
To position coordinates；ε1And ε2For smooth length proportionality coefficient；N is smooth order, and wherein N is positive real number.
Three, multistage stablizes the generation for transmitting bessel beam on axis
Stablize the generation of transmission bessel beam based on single hop in aforementioned axis, further, provides more on a kind of generation axis
Duan Wending transmits the embodiment of bessel beam, to enhance the effect of practical application.In the present embodiment, it is set on amplitude diaphragm 2
It is equipped with M annular transmission region.I.e. if it is desired on optical axis M sections of separate areas [z1z2]、[z3z4]、[z5z6] ... and
[z2M-1z2M] in generate the bessel beam for stablizing transmission, then need M on amplitude diaphragm 2 discrete annular transmission regions
[R1R2]、[R3R4]、[R5R6] ... and [R2M-1R2M] in introduce annular amplitude diaphragm.At this point, the amplitude transmission system of amplitude diaphragm 2
Number are as follows:
In formula (17), ρ indicates the radial position coordinate on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)；M annular
The radius of transmission region meets: 0 < R1< R2≤R3< R4≤R5... < R2M-1< R2M≤ R, wherein R is the half of amplitude diaphragm 2
Diameter.By theory of geometric optics, formula (10) are analogous to, on amplitude diaphragm 2, the radius R of M annular transmission region1, R2, R3,
R4..., R2MWith transmission range z on axis1, z2, z3, z4..., z2MBetween meet following relationship:
In formula (18), transmission range z on axisi(i=1,2,3,4 ..., 2M) is determined by practical application request.It utilizes
The radius R of M annular transmission region can be obtained in formula (18)i(i=1,2,3,4 ..., 2M) recycles formula (17) design
Amplitude diaphragm 2 out.
To obtain the bessel beam for stablizing transmission on axis, it is analogous to previous embodiment, in M discrete annular transparent areas
The boundary in domain introduces the smooth diaphragm of amplitude, and the amplitude transmission coefficient of the smooth diaphragm of amplitude is no longer mutated by 1 to 0, but by one
The function of a consecutive variations provides.The amplitude transmission coefficient further satisfaction of amplitude diaphragm 2 in the present embodiment: T1(ρ)×T2
(ρ)；Wherein, T2The expression formula of (ρ) are as follows:
In formula (19), ρ indicates the radial position coordinate on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)；ε1、ε2、ε3、
ε4、...、ε2M-1And ε2MFor smooth length proportionality coefficient；N is smooth order, and wherein N is positive real number.
In the present embodiment, amplitude diaphragm 2 forms gradual change amplitude diaphragm.Therefore, the amplitude transmission coefficient of gradual change amplitude diaphragm
Are as follows:
T (ρ)=T1(ρ)×T2(ρ) (20)
In formula (20), T1(ρ) and T2(ρ) is provided by formula (17) and (19) respectively.
Next, providing two embodiments, respectively corresponds and stablize transmission bessel beam with three sections on axis for two sections on axis
It generates, to be further illustrated.
1) two sections of stable generations for transmitting bessel beam on axis
The generation embodiment for stablizing transmission bessel beam according to aforementioned multistage is realized on optical axis by amplitude diaphragm 2
Two sections of discrete region [z1z2] and [z3z4] in generate stablize transmission bessel beam.For this purpose, needing to set on amplitude diaphragm 2
Fixed two discrete annular transmission region [R1R2] and [R3R4].Therefore, the amplitude transmission coefficient of amplitude diaphragm 2 are as follows:
T (ρ)=T1(ρ)×T2(ρ) (21)
Wherein,
In the present embodiment, in order to which the bessel beam for stablizing transmission, parameter choosing are generated in two sections of separate areas on optical axis
Fixed as follows: the radius of positive axis axicon lens 1 is R=3cm；The base angle of positive axis axicon lens 1 is α=3 °；The wavelength of incident plane wave be λ=
632.8nm；Positive axis axicon lens 1 selects K9 glass, and selecting the corresponding refractive index of wavelength is n1=1.5146；Exterior space is air,
Refractive index is n0=1.0；The distance range that two sections of discrete bessel beams stablize transmission on optical axis is set separately are as follows: [400
700] mm and [800 1100] mm；According to formula (18), the radius that annular transmission region can be calculated is respectively R1=
1.08cm、R2=1.89cm, R3=2.16cm and R4=2.97cm；Smooth length proportionality coefficient are as follows: ε1=ε2=ε3=ε4=
0.2, smooth order is N=2.It should be noted that the value of each smooth length proportionality coefficient is identical in the present embodiment；And at it
In his embodiment, the value of each smooth length proportionality coefficient may be set to be it is not identical, specific value can according to implement needs
Flexible setting.
According to parameter selected above, it is calculated and is not provided with amplitude diaphragm 2, the amplitude transmission coefficient of amplitude diaphragm 2 is
T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2Amplitude transmission coefficient in the case of three kinds of (ρ) is respectively such as Fig. 6
(a), shown in 6 (b) and 6 (c).
Based on scalar diffraction theory and complete Rayleigh --- rope end Philippine side method, using formula (7), simulation is calculated just
On-axis intensity distribution in the transmission region on 1 right side of axial cone mirror.Fig. 7 (a), 7 (b) and 7 (c) respectively correspond be not provided with amplitude diaphragm 2,
The amplitude transmission coefficient of amplitude diaphragm 2 is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2(ρ) three kinds of situations
Under on-axis intensity distribution.When being not provided with amplitude diaphragm 2, the changing rule that oscillation rises is presented in on-axis intensity, such as Fig. 7 (a)
It is shown；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1When (ρ), on axis within the scope of two sections of discrete transmission ranges, axis glazing
Strong ascendant trend is effectively suppressed, but there are still violent oscillation effects, such as Fig. 7 for on-axis intensity in two sections of separate areas
(b) shown in；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1(ρ)×T2When (ρ), the oscillation effect of on-axis intensity is effectively pressed down
System obtains the bessel beam for stablizing transmission, as shown in Fig. 7 (c) on optical axis in two sections of separate areas.
For the light stability of bessel beam in two sections of separate areas on characterization optical axis, defines the opposite of on-axis intensity and miss
Difference are as follows:Wherein IzIndicate the light intensity on optical axis at certain point,It indicates on optical axis in two sections of regions
Average intensity.Simulation calculated result in Fig. 7 (a), 7 (b) and 7 (c) shows that transmission range is [500 600] mm on optical axis
Within the scope of [900 1000] mm, at above-mentioned three kinds, the maximum relative error of on-axis intensity is respectively as follows: 45.27%,
15.64% and 0.36%, this shows to obtain stabilization in two sections of separate areas on optical axis using designed amplitude diaphragm 2
The bessel beam of transmission.
For characterize caused by bessel beam performance, in zi=500mm, 600mm, 900mm and 1000mm (i=1,
2,3,4) on four cross sections, simulation calculates light distribution along x-axis, respectively as in Fig. 8 chain-dotted line, dotted line, dotted line and
It is shown in solid.Fig. 8 (a), 8 (c) and 8 (e) respectively correspond and are not provided with amplitude diaphragm 2, the amplitude transmission coefficient of amplitude diaphragm 2 is T1
The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2It is distributed in the case of three kinds of (ρ) along the actual light intensity of x-axis.From Fig. 8
(a), 8 (c) and 8 (e) as can be seen that the actual light intensity difference on four cross sections is very in the case where being not provided with amplitude diaphragm 2
Greatly；It is T in the amplitude transmission coefficient of amplitude diaphragm 21In the case where (ρ), the actual light intensity deviation on four cross sections is smaller；In
The amplitude transmission coefficient of amplitude diaphragm 2 is T1(ρ)×T2In the case where (ρ), the actual light intensity distribution on four cross sections is almost weighed
It closes.Simulation calculated result, which is also shown that on all cross sections, all obtains high-resolution bessel beam, and spot radius is
8.97 μm, this and the spot radius obtained according to theory of geometric opticsIt is completely the same.
For the transmission stability for clearly illustrating that bessel beam on varying cross-section, Fig. 8 (b), 8 (d) and 8 (f) point
Along the light intensity deviation of x-axis in the case of not giving above-mentioned three kinds.Simulation calculated result shows at above-mentioned three kinds, transversal
Largest light intensity deviation on face is respectively as follows: 10064,904 and 37.64；Maximum relative light intensity deviation on cross section is respectively as follows:
30.73%, 4.60% and 0.21%.
2) three sections of stable generations for transmitting bessel beam on axis
The generation embodiment for stablizing transmission bessel beam according to aforementioned multistage is realized on optical axis by amplitude diaphragm 2
Three sections of discrete region [z1 z2]、[z3 z4] and [z5 z6] in generate stablize transmission bessel beam.For this purpose, in amplitude light
Need to set three discrete annular transmission region [R on door screen 21 R2]、[R3 R4] and [R5 R6].Therefore, the vibration of amplitude diaphragm 2
Width transmission coefficient are as follows:
T (ρ)=T1(ρ)×T2(ρ) (24)
Wherein,
In the present embodiment, in order to which the bessel beam for stablizing transmission, parameter choosing are generated in three sections of separate areas on optical axis
Fixed as follows: the radius of positive axis axicon lens 1 is R=3cm；The base angle of positive axis axicon lens 1 is α=3 °；The wavelength of incident plane wave be λ=
632.8nm；Positive axis axicon lens 1 selects K9 glass, and selecting the corresponding refractive index of wavelength is n1=1.5146；Exterior space is air,
Refractive index is n0=1.0；The distance range that three sections of discrete bessel beams stablize transmission on optical axis is set separately are as follows: [280
520] mm, [540 800] mm and [820 1100] mm；According to formula (18), the radius of annular transmission region can be calculated
Respectively R1=0.76cm, R2=1.41cm, R3=1.46cm, R4=2.16cm, R5=2.22cm and R6=2.97cm；It is smooth long
Spend proportionality coefficient are as follows: ε1=ε2=ε3=ε4=ε5=ε6=0.2, smooth order is N=2.
According to parameter selected above, it is calculated and is not provided with amplitude diaphragm 2, the amplitude transmission coefficient of amplitude diaphragm 2 is
T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2Amplitude transmission coefficient in the case of three kinds of (ρ) is respectively such as Fig. 9
(a), shown in 9 (b) and 9 (c).
Based on scalar diffraction theory and complete Rayleigh --- rope end Philippine side method, using formula (7), simulation is calculated just
On-axis intensity distribution in the transmission region on 1 right side of axial cone mirror.Figure 10 (a), 10 (b) and 10 (c), which respectively correspond, is not provided with amplitude light
Late 2, the amplitude transmission coefficient of amplitude diaphragm 2 is T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2Three kinds of (ρ)
In the case of on-axis intensity distribution.When being not provided with amplitude diaphragm 2, the changing rule that oscillation rises is presented in on-axis intensity, is such as schemed
Shown in 10 (a)；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1When (ρ), on axis within the scope of three sections of discrete transmission ranges,
The ascendant trend of on-axis intensity is effectively suppressed, but in three sections of separate areas on-axis intensity there are still violent oscillation effect,
As shown in Figure 10 (b)；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1(ρ)×T2When (ρ), the oscillation effect of on-axis intensity is had
Effect inhibits, and the bessel beam for stablizing transmission is obtained in three sections of separate areas on optical axis, as shown in Figure 10 (c).
For the light stability of bessel beam in three sections of separate areas on characterization optical axis, defines the opposite of on-axis intensity and miss
Difference are as follows:Wherein IzIndicate the light intensity on optical axis at certain point,It indicates on optical axis in three sections of regions
Average intensity.Simulation calculated result in Figure 10 show on optical axis transmission range be [350 450] mm, [620 720] mm and
Within the scope of [900 1000] mm, at above-mentioned three kinds, the maximum relative error of on-axis intensity is respectively as follows: 61.82%,
24.46% and 0.35%, this shows to produce stabilization in three sections of separate areas on optical axis using designed amplitude diaphragm 2
The bessel beam of transmission.
For characterize caused by bessel beam performance, in zi=400mm, 625mm, 715mm and 960mm (i=1,2,
3,4) on four cross sections, simulation calculates the light distribution along x-axis, respectively such as chain-dotted line, dotted line, dotted line and the reality in Figure 11
Shown in line.Figure 11 (a), 11 (c) and 11 (e) respectively correspond and are not provided with amplitude diaphragm 2, the amplitude transmission coefficient of amplitude diaphragm 2 is
T1The amplitude transmission coefficient of (ρ) and amplitude diaphragm 2 is T1(ρ)×T2It is distributed in the case of three kinds of (ρ) along the actual light intensity of x-axis.From figure
11 (a), 11 (c) and 11 (e) as can be seen that the actual light intensity difference on four cross sections is very when being not provided with amplitude diaphragm 2
Greatly；When the amplitude transmission coefficient of amplitude diaphragm 2 is T1When (ρ), the actual light intensity deviation on four cross sections is smaller；When amplitude light
The amplitude transmission coefficient of door screen 2 is T1(ρ)×T2When (ρ), the actual light intensity distribution on four cross sections is almost overlapped.Simulation calculates
As a result it is also shown that all obtaining high-resolution bessel beam on all cross sections, spot radius is 8.97 μm, this with
The spot radius obtained according to theory of geometric opticsIt is completely the same.
For the stabilization transmission characteristic for clearly illustrating that bessel beam on varying cross-section, Figure 11 (b), 11 (d) and 11
(f) along the light intensity deviation of x-axis in the case of being set forth above-mentioned three kinds.Calculated result is simulated to show at above-mentioned three kinds,
Largest light intensity deviation on cross section is respectively as follows: 15286,1894 and 19.32；Maximum relative light intensity deviation difference on cross section
Are as follows: 48.66%, 15.29% and 0.15%.
It should be noted that multistage is stablized in transmission bessel beam embodiment on above-mentioned generation axis, to obtain on axis
Transmit stable bessel beam, T2(ρ) uses [sin (x)]NForm, provided by formula (19).However, in practical application
In, for the technical effect for realizing the utility model, T2(ρ) can be provided by the function of any one consecutive variations.
In other embodiments, T2(ρ) can also be indicated by following form:
1)
In formula (27),ρ indicates the diameter on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)
To position coordinates；ε1、ε2、ε3、ε4、...、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、...、R2M-1And R2MTable
Show the radius of annular region；N is smooth order, and wherein N is positive real number.
2)
In formula (28), J0For zero Bessel function；ρ indicates the diameter on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)
To position coordinates；ε1、ε2、ε3、ε4、...、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、...、R2M-1And R2MTable
Show the radius of annular region；N is smooth order, and wherein N is positive real number.
3)
In formula (29), J1For first-order bessel function；ρ indicates the diameter on amplitude diaphragm 2 (or 1 bottom surface of positive axis axicon lens)
To position coordinates；ε1、ε2、ε3、ε4、...、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、...、R2M-1And R2MTable
Show the radius of annular region；N is smooth order, and wherein N is positive real number.
Conceived based on same utility model, the utility model embodiment additionally provides multistage on a kind of axis and stablizes transmission shellfish plug
The production method of your light beam, this method comprises: making incident plane wave through multistage on axis described in any one embodiment as above
Stablize the generation device of transmission bessel beam；Wherein, the incident plane wave is incident perpendicular to the bottom surface of the positive axis axicon lens.
It should be understood by those ordinary skilled in the art that: the discussion of any of the above embodiment is exemplary only, not
It is intended to imply that the scope of the present disclosure (including claim) is limited to these examples；Under the thinking of the utility model, the above reality
Applying can also be combined between the technical characteristic in example or different embodiments, and step can be realized with random order, and be deposited
In many other variations of the different aspect of the utility model as described above, for simplicity, they are not provided in details.
The embodiments of the present invention are intended to cover fall into all such within the broad range of appended claims
Replacement, modifications and variations.Therefore, within the spirit and principle of the utility model, any omission for being made, modification, equivalent
Replacement, improvement etc., should be included within the scope of protection of this utility model.
Claims (9)
1. multistage stablizes the generation device of transmission bessel beam on a kind of axis characterized by comprising positive axis axicon lens；It is described
The refractive index of the material of positive axis axicon lens is greater than the refractive index of exterior space medium；Amplitude is provided on the bottom surface of the positive axis axicon lens
Diaphragm；M discrete annular transmission regions are provided on the amplitude diaphragm；It is described corresponding to described M annular transmission region
The amplitude transmission coefficient of amplitude diaphragm meets following formula:
Wherein, ρ is the radial position coordinate on the amplitude diaphragm；The radius of described M annular transmission region meets: 0 < R1<R2
≤R3<R4≤R5…<R2M-1<R2M≤ R, R are the radius of the amplitude diaphragm.
2. multistage stablizes the generation device of transmission bessel beam on axis according to claim 1, which is characterized in that described
The amplitude transmission coefficient further satisfaction of amplitude diaphragm: T1(ρ)×T2(ρ)；Wherein, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MIndicate M
The radius of a annular region；N is smooth order, and the value of N is positive real number.
3. multistage stablizes the generation device of transmission bessel beam on axis according to claim 1, which is characterized in that described
The amplitude transmission coefficient further satisfaction of amplitude diaphragm: T1(ρ)×T2(ρ)；Wherein, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MIndicate M
The radius of a annular region；N is smooth order, and wherein N is positive real number.
4. multistage stablizes the generation device of transmission bessel beam on axis according to claim 1, which is characterized in that described
The amplitude transmission coefficient further satisfaction of amplitude diaphragm: T1(ρ)×T2(ρ)；Wherein, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MIndicate ring
The radius in shape region；N is smooth order, and wherein N is positive real number.
5. multistage stablizes the generation device of transmission bessel beam on axis according to claim 1, which is characterized in that described
The amplitude transmission coefficient further satisfaction of amplitude diaphragm: T1(ρ)×T2(ρ)；Wherein, T2The expression formula of (ρ) are as follows:
Wherein, ε1、ε2、ε3、ε4、…、ε2M-1And ε2MFor smooth length proportionality coefficient；R1、R2、R3、R4、…、R2M-1And R2MIndicate ring
The radius in shape region；N is smooth order, and wherein N is positive real number.
6. stablize the generation device of transmission bessel beam according to multistage on axis described in claim 2 to 5 any one, it is special
Sign is, the ε1、ε2、ε3、ε4、…、ε2M-1And ε2MValue it is identical, and its value range be [0 0.5].
7. multistage stablizes the generation device of transmission bessel beam on axis according to claim 6, which is characterized in that described
ε1、ε2、ε3、ε4、…、ε2M-1And ε2MValue be 0.2.
8. stablize the generation device of transmission bessel beam to multistage on axis described in 5 any one according to claim 1, it is special
Sign is that the base angle of the positive axis axicon lens is 3 °；The bottom surface radius of the positive axis axicon lens is 3 centimetres.
9. stablize the generation device of transmission bessel beam to multistage on axis described in 5 any one according to claim 1, it is special
Sign is that the refractive index of the material of the positive axis axicon lens is 1.5146；The refractive index of the exterior space medium is 1.
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