CN106773030A - A kind of simple uniform laser accunputure focusing microstructures and method for designing - Google Patents
A kind of simple uniform laser accunputure focusing microstructures and method for designing Download PDFInfo
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Abstract
The invention discloses a kind of simple uniform laser accunputure focusing microstructures and method for designing, it is composited by the binary amplitude type Fresnel zone plate radii sequence of two groups of correspondence different focals, and micro-structural central area is blocked, its construction process is：Given illumination wavelengths and the first focal length, determine first group of girdle radius sequence { r1,n}；The focal length of primary election second obtains second group of girdle radius sequence { r2,m}；Appropriate selection { r2,mIn partial sequence section replace { r1,nIn partial sequence section form new micro-structural girdle radius sequence；Each annulus transmitance is defined as, and first sets central shielding circle, and to each annulus transmitance of outermost girdle radius by { 1,0 } alternate coded since central shielding radius of circle coordinate, and initial annulus transmitance is 1；Preferred structure parameter realizes uniform laser accunputure intensity field distribution；The method for designing is applied to various typical polarization laser beam illumination situations, and the micro-structural of design can be applied to the fields such as laser assisted microprocessing, high-resolution micro-imaging, optical control.
Description
Technical field
The invention belongs to micronano optical technical field, more particularly to a kind of simple uniformly laser accunputure focusing microstructures and design
Method.
Background technology
The diffraction of light causes to focus on light field with complicated three-dimensional structure, amplitude, phase and polarization state to illuminating bundle
Etc. the distribution being modulated will focusing light field changed.Since 2008, laser accunputure focuses on (or light pencil focusing) problem and causes science
The extensive concern on boundary, as one of international forward position focus research topic.Even and fine laser accunputure focousing field has important scientific research
Value, it is in laser direct-writing micro-lithography, optical storage of data, scanning optical nano microtechnic, atom opticses, optical control etc.
Field has important application.
At present, thin laser accunputure focus modulation method is broadly divided into three major types, is based respectively on dioptric system, reflection optics
System and diffraction optical system.Dioptric system focus method is illuminated with many annulus pupil filterings, vector beam, refractor
It is focused to represent (referring to document H.Wang, L.Shi, B.Lukyanchuk, C.Sheppard, C.T.Chong.Creation of
a needle of longitudinally polarized light in vacuum using binary
optics.Nature Photonics,2008,2:501-505), it is Engineering method before conventional wave, advantage is theoretical clear
Clear, flexible design, have the disadvantage that Focused Optical system is complicated, iris filter processing request is harsh, the limitation of light beam transversal width compared with
Greatly.Reflective optics focus method, main use pupil filtering and parabolic mirror combination (referring to document H.Dehez,
A.April,M.Piche.Needles of longitudinally polarized light:guidelines for
minimum spot size and tunable axial extent.Optics Express,2012,20:14891-
14905), advantage is easily to realize that limiting figure aperture (NA=1, in air) focuses in theory, has the disadvantage to focus at laser accunputure
In reflected light path, system realizes that difficulty depends on ultraprecise machining method for aspheric surface, high cost.3rd class method is based on plane
Diffraction optical system, be directly focused using single plane optical microstructures (referring to document T.Liu, J.Tan, J.Liu,
H.Wang.Modulation of a super-Gaussian optical needle by high-NA Fresnel zone
plate.Optics Letters,2013,38:2742-2745), this is a kind of without lens, multiple beam diffraction interference focusing system
System, outstanding advantages are simple system, light structure, with low cost, flexible design, and the subject matter for existing is due to standard phenanthrene alunite
You are illuminated in short wavelength zone plate and large-numerical aperture is assembled under situation, and outer ring annulus radial width is close and loop bandwidth is received in number
Rice proposes very harsh requirement to tens nanometer to existing micro Process etching technics.
Above-mentioned technical problem is the main difficulty for facing in even and fine laser accunputure focus modulation at present.
The content of the invention
In order to overcome the shortcoming of above-mentioned prior art, focused on it is an object of the invention to provide a kind of simple uniform laser accunputure
Micro-structural and method for designing, composite microstructure is constructed based on binary amplitude type Fresnel zone plate, is illuminated using laser beam, is led to
Cross uniform laser accunputure needed for a small amount of annulus is capable of achieving.
To achieve these goals, the technical solution adopted by the present invention is：
A kind of simple uniform laser accunputure focusing microstructures, by two groups of binary amplitude type Fresnels of correspondence different focal
Piece radii sequence is composited, and micro-structural central area is blocked.
First group of girdle radius sequenceN=0,1,2 ..., N1, second group of girdle radius
SequenceM=1,2 ..., N2, wherein, λ is medium optical wavelength where micro-structural, f1It is
The first given focal length, f2It is the second focal length, f2=f1+ △ f, △ f are burnt shifting amount, are an arithmetic number, N1It is first group of sequence
Annulus number, N2It is second group of sequence annulus number, N1And N2Take even number.
The girdle radius sequence of uniform laser accunputure focusing microstructures of the present inventionWherein, niIt is odd number, noIt is even
Number, meets 1≤ni<no≤N1, r2,iIt is even columnIn first be more thanNumber, r2,oIt is
Odd columnIn last be less thanNumber.
Each annulus transmitance isFrom radial direction radiusExtremelyAnnulus transmitance presses { 1,0 }
Alternate coded, is 0 when annulus is light tight, is 1 during printing opacity, and initial annulus transmitanceIt is described to micro-
Structure centre region is blocked, and refers to pair radius coordinateWithin all concentric rings band transmitance set to 0.
The method for designing of simple uniform laser accunputure focusing microstructures of the present invention, comprises the following steps：
Step one, gives medium optical wavelength λ and the first focal length f where micro-structural1, according toN=0,1,2 ..., N1Determine first group of girdle radius sequence { r1,n, N1It is first group of sequence
Annulus number, takes even number；
Step 2, primary election arithmetic number △ f, by the second focal length f2=f1+ △ f obtain second group of girdle radius sequenceM=1,2 ..., N2, N2It is second group of sequence annulus number, takes even number；
Step 3, primary election odd number niWith even number no, meet 1≤ni<no≤N1；
Step 4, by sequence { r2,mIt is divided into even columnAnd odd column
First is selected in P to be more thanSeveral r2,i, select last to be less than in QSeveral r2,o；
Step 5 the, using { r in second group of sequence2,i,r2,i+1,r2,i+2,...,r2,oReplace first group of sequence inForm new micro-structural girdle radius sequence
Step 6, each annulus transmitance is defined asFrom radial direction radiusExtremelyAnnulus transmitance
It is 0 when annulus is light tight by { 1,0 } alternate coded, is 1 during printing opacity, and initial annulus transmitance
Step 7, laser beam illumination micro-structural annulus is calculated using vector angular spectra theory and Fast Hankel Transform algorithm
Diffractive light field during piece thereafter；
Step 8, preferred parameter { ni,no, △ f } and obtain uniform laser accunputure intensity field distribution.
In the step one, illuminating bundle is linearly polarized light, circularly polarized light or radial polarisation light；Illumination wavelengths are from X-ray
Chosen near infrared band, take 1nm<λ<1000nm.
In the step 7, vector angular spectra theory refers to first pass around surface after a Fourier transformation obtains micro-structural to go out
The angular spectrum of light field is penetrated, each polarized component that Fourier transformation obtains light field is then again passed by, so as to be calculated laser
Optical field distribution during beam lighting micro-structural thereafter in any distance perpendicular plane.
In the step 7, Fast Hankel Transform algorithm refers in standard Hankel transform integral expression, to utilize
Nonlinear exponent function variable is replaced, and the unilateral Hankel transform of standard is expressed as into bilateral cross-correlation integral, so as to realize utilizing
Fourier transformation calculates a kind of fast, accurately computational methods of cross-correlation.
In the step 8, preferred parameter { ni,no, △ f } detailed process：
First, according to the first focal length f1The second focal length f is chosen with burnt shifting amount △ f2；
Second, adjusting parameter niAnd noIt is preliminary to focus on the light pencil for stretching occur；
3rd, fine setting △ f are adjusted to the uniformity of laser accunputure, and laser accunputure intensity field characteristic is uniformly distributed needed for producing.
Compared with prior art, the beneficial effects of the invention are as follows：
Present system is simple, light structure, realizes that girdle radius are by formula merely with single plane micro-structural annulus piece
Directly determine；It is to be capable of achieving using existing ripe micro fabrication, it is with low cost, can batch making；Method for designing flexibly, is fitted
For from X-ray to near-infrared laser wavelength, illuminating bundle can be linearly polarized light, circularly polarized light and radial polarisation light etc.；Light
Pin operating distance and micro-structural numerical aperture can be with arbitrarily devised.
Brief description of the drawings
Fig. 1 is the micro-structural schematic diagram in the present invention, and 1 is the corresponding annulus sequence of the first focal length in figure, and 2 is the second focal length
Corresponding annulus sequence, 3 represent central shielding circular portion.
Fig. 2 is micro-structural M of the present invention1Corresponding radial direction transmittance function figure.
Fig. 3 is micro-structural M of the present invention2Corresponding radial direction transmittance function figure.
Fig. 4 is micro-structural M of the present invention1Corresponding axially normalization focus strength design result strictly calculates knot with FDTD
Fruit compares figure.
Fig. 5 is micro-structural M of the present invention1The strict result of calculation figures of laser accunputure field intensity FDTD in corresponding X-Z plane.
Fig. 6 is micro-structural M of the present invention1The strict result of calculation figures of laser accunputure field intensity FDTD in corresponding Y-Z plane.
Fig. 7 is micro-structural M of the present invention2Corresponding axially normalization focus strength field pattern.
Specific embodiment
Describe embodiments of the present invention in detail with reference to the accompanying drawings and examples.
Uniform laser light beam is directly focused on using the micro-structural annulus piece shown in Fig. 1, surface is specific after rang ring strap
Area modulation produces uniform light pencil, and light is carried out using vector angular spectrum (Vectorial Angular Spectrum, VAS) theory
Propagate analysis in field.
(1) standard Fresnel zone plate
If the wavelength of laser illuminator light beam is λ0, work where Fresnel zone plate (Fresnel Zone Plate, FZP)
The refractive index of medium is η, then Light in Medium ripple wavelength is λ=λ0/ η, the girdle radius that can obtain standard Fresnel zone plate are
In formula, n is girdle radius ordinal number, and f is principal focal distance.For large-numerical aperture FZP, effective numerical aperture can be according to
Maximum divergence half-angle α definition, i.e. NA=η sin α meet tan α=rN/f；After numerical aperture definition, can be pushed away using formula (1)
Lead and obtain relationship below
Thus, focal length f is established and associated with numerical aperture NA, medium refraction index η, wavelength X, maximum loop band number N.Given f,
According to formula (2), the annulus number N met under the premise of design NA can be calculated, and then obtain FZP diameters
If N is even number, the amplitude transmittance function of FZP is represented with t (r), for binary amplitude type FZP, transmittance function
It is described as
In formula, m=0,1 ..., N/2-1；Above formula assumes that innermost ring is printing opacity situation.
(2) design of micro-structural
From standard Fresnel zone plate radius formula (1), by two kinds of Fresnel zone plate sequences of different focal
New micro-structural is compounded to form, specific design step is as follows：
Step one, setted wavelength λ and the first focal length f1, according to
Determine first group of FZP girdle radius sequences { r1,n, N1It is first group of sequence annulus number, takes even number；
Step 2, chooses arithmetic number △ f, by the second focal length
f2=f1+△f (5)
Obtain second group of FZP girdle radius sequence
N2It is second group of sequence annulus number, takes even number；
Step 3, primary election odd number niWith even number no, meet 1≤ni<no≤N1；
Step 4, by sequence { r2,mEven column is divided into according to subscript mAnd odd columnFirst is selected in P to be more thanSeveral r2,i, select last to be less than in Q's
Number r2,o；
Step 5 the, using { r in second group of sequence2,i,r2,i+1,r2,i+2,...,r2,oReplace first group of sequence inForm new micro-structural girdle radius sequence
Step 6, each annulus transmitance is defined as, central shielding circleFrom radial direction radiusExtremely
Each annulus transmitance presses { 1,0 } alternate coded, is 0 when annulus is light tight, is 1 during printing opacity, and first light penetrating ring band is located atI.e.Therefore the micro-structural transmittance function for being constructed is piecewise function, is expressed as t
(r)；
Step 7, laser beam illumination micro-structural annulus is calculated using vector angular spectra theory and Fast Hankel Transform algorithm
Diffractive light field during piece thereafter；
Step 8, preferred parameter { ni,no, △ f } and obtain uniform laser accunputure intensity field distribution.
By step one to step 6, the initial configuration of micro-structural annulus piece is constructed；Micro-structural is calculated by step 7
Corresponding focusing light field；By the last preferred parameter of step 8.During laser beam illumination large-numerical aperture micro-structural, it is necessary to consider
The vector polarization characteristic of electromagnetic wave, is completely illustrated using Vector Diffraction Theory, while for speed-up computation process, choosing fast
Fast Hankel transform algorithm accurately calculates optical field distribution.
(3) vector angular spectra theory light field is calculated
Assuming that along the linearly polarized light (LPB) of X-direction vibration along Z axis forward-propagating, vertical illumination micro-structural, through micro-structural
After annulus piece diffraction, according to vector angular spectra theory, in z>Any point in 0 perpendicular planeElectric field E at position
Orthogonal components are
In formula, Ex(r, z) represents x to component, Ey(r, z) represents y to component,Represent z to component, q (l)
=(1/ λ2-l2)1/2, l represents radial spatial frequency component；J0And J1It is respectively first kind zeroth order and first-order bessel function, j is
Imaginary unit；Space angular spectrum A0L () is expressed as：
In formula, t (r) represents the corresponding amplitude transmittance function of any round Symmetry Microstructure；G (r) represents that illuminating bundle exists
Optical field amplitude in micro-structural annulus plate plane, it is assumed here that uniform plane wave is illuminated, correspondence g (r)=1.Obtain micro- by formula (7)
Light distribution is after structure ring strap
When illuminating bundle is (left-handed) circularly polarized light (CPB), each component of electric field E is
In formula, A0L () is given by formula (8).Therefore, distribution of light intensity is distributed as I (r, z)=2 | Ex(r,z)|2+|Ez(r,z)
|2.Obviously for circularly polarized light, intensity distribution meets rotational symmetry, is different from linearly polarized light situation.
When can respectively be calculated linearly polarized light and circularly polarized light illumination micro-structural annulus piece using formula (7)~formula (9)
Thereafter the optical field distribution in any perpendicular plane, can also similarly calculate the distribution of light field under radial polarisation light illumination situations.
(4) quick preferably micro-structural
, it is necessary to zeroth order and single order Hankel transform is performed a plurality of times in the calculating process of formula (7)~formula (9), therefore Hunk
The computational efficiency and precision of your conversion are the keys of method for designing, and in order to accelerate computing, a kind of quick Hunk that of programming realization becomes
Scaling method is (referring to document A.E.Siegman.Quasi Fast Hankel Transform.Optics Letters, 1977,1:
13-15), the algorithm has a remarkable advantages such as fast, high precision, extremely low the Computer Storage requirement of calculating speed, general principle be
In standard Hankel transform integral expression, replaced using nonlinear exponent function variable, by the unilateral Hankel transform table of standard
Bilateral cross-correlation integral is shown as, by after such conversion cross-correlation can be calculated using Fourier transformation.
Adjusting parameter { ni,no, △ f } detailed process：
First, according to the first focal length f1The second focal length f is chosen with burnt shifting amount △ f2；
Secondly, adjusting parameter niAnd noIt is preliminary to focus on the light pencil for stretching occur；
Finally, fine setting △ f are adjusted to the uniformity of laser accunputure, and light pencil intensity field spy is uniformly distributed needed for producing
Property.
(5) specific embodiment
Using 633nm linearly polarized laser beam lightings, air dielectric (η=1) devises respectively D=19.05 μm of diameter
Two kinds of typical microstructures with 44.88 μm, design parameter is shown in Table 1 to table 3.
tiThe transmitance of each ring is represented, is 0 or 1, NtIt is light penetrating ring band number；Represent horizontal using FWHM (half extreme value overall with)
To the yardstick with axial focusing light beam；zwdIt is the average value along axle light field maximum intensity half coordinate (both sides), represents light pencil
Leave the distance of micro-structural piece, referred to as operating distance.
The microstructure parameters of table 1 and focus characteristics
The M of table 21Structural parameters (unit：μm)
The M of table 32Structural parameters (unit：μm)
In table 1, M1D=19.05 μm of diameter, be made up of (radial coordinate is shown in Table 2) 20 annulus, each ring transmitance tiSee
Table 1, altogether containing 7 light penetrating ring bands, M1Corresponding radial direction transmittance function is as shown in Figure 2.M1Operating distance is 4.920 μm, numerical aperture
Footpath is NA=0.97, and laser accunputure axial length (depth of focus DOF) is 6.39 λ.Illuminated using X-direction linearly polarized light, therefore in X-Y plane
Focal beam spot it is asymmetric, it is narrower along Y-direction hot spot.Fig. 4 show M1Corresponding axially normalization focus strength distribution results
With strict electromagnetism computer sim- ulation (Finite-Difference Time-Domain Method, FDTD) results contrast figure, as seen from the figure, the method for the invention is just
True property；Fig. 5 and Fig. 6 are respectively M1The strict result of calculation figures of laser accunputure field intensity FDTD in corresponding X-Z plane and Y-Z plane.
In table 1, M2D=44.88 μm of diameter, be made up of (radial coordinate is shown in Table 3) 48 annulus, each ring transmitance tiSee
Table 1, altogether containing 17 light penetrating ring bands, M2Corresponding radial direction transmittance function is as shown in Figure 3.M2Operating distance is 8.155 μm, numerical value
Aperture is NA=0.94, and laser accunputure is along the λ of shaft length 5.77.In z=zwdPerpendicular plane in, the spot width of Y-direction is only 0.39
λ.Fig. 7 is M2Corresponding axially normalization focus strength field pattern.
Specific embodiment of the invention is described above in association with accompanying drawing, but these explanations can not be understood to limitation
The scope of the present invention, protection scope of the present invention is limited by appended claims, any in the claims in the present invention base
Change on plinth is all protection scope of the present invention.
Claims (9)
1. a kind of simple uniform laser accunputure focusing microstructures, it is characterised in that by two groups of binary amplitude types of correspondence different focal
Fresnel zone plate radii sequence is composited, and micro-structural central area is blocked.
2. simple uniform laser accunputure focusing microstructures according to claim 1, it is characterised in that first group of girdle radius sequenceN=0,1,2 ..., N1, second group of girdle radius sequence
M=1,2 ..., N2, wherein, λ is medium optical wavelength where given micro-structural, f1It is the first given focal length, f2It is second
Focal length, f2=f1+ △ f, △ f are burnt shifting amount, are an arithmetic number, N1It is first group of sequence annulus number, N2It is second group of sequence ring
Band number, N1And N2Take even number.
3. simple uniform laser accunputure focusing microstructures according to claim 2, it is characterised in that the annulus of the micro-structural half
Footpath sequenceWherein, niIt is odd number,
noIt is even number, meets 1≤ni<no≤N1, r2,iIt is even columnIn first be more thanNumber,
r2, oIt is odd columnIn last be less thanNumber.
4. simple uniform laser accunputure focusing microstructures according to claim 3, it is characterised in that each annulus transmitance isFrom radial direction radiusExtremelyEach annulus transmitance presses { 1,0 } alternate coded, is when annulus is light tight
0, it is 1 during printing opacity, and initial annulus transmitanceIt is described that micro-structural central area is blocked, be
Refer to pair radius coordinateWithin all concentric rings band transmitance set to 0.
5. the method for designing of simple uniform laser accunputure focusing microstructures described in claim 1, it is characterised in that including following step
Suddenly：
Step one, gives medium optical wavelength λ and the first focal length f where micro-structural1, according ton
=0,1,2 ..., N1Determine first group of girdle radius sequence { r1,n, N1It is first group of sequence annulus number, takes even number；
Step 2, primary election arithmetic number △ f, by the second focal length f2=f1+ △ f obtain second group of girdle radius sequenceM=1,2 ..., N2, N2It is second group of sequence annulus number, takes even number；
Step 3, primary election odd number niWith even number no, meet 1≤ni<no≤N1；
Step 4, by sequence { r2,mIt is divided into even columnAnd odd column
First is selected in P to be more thanSeveral r2,i, select last to be less than in QSeveral r2,o；
Step 5 the, using { r in second group of sequence2,i,r2,i+1,r2,i+2,...,r2,oReplace first group of sequence in
Form new micro-structural girdle radius sequence
Step 6, each annulus transmitance is defined asFrom radial direction radiusExtremelyAnnulus transmitance by 1,
0 } alternate coded, is 0 when annulus is light tight, is 1 during printing opacity, and initial annulus transmitance
Step 7, when calculating laser beam illumination micro-structural annulus piece using vector angular spectra theory and Fast Hankel Transform algorithm
Thereafter diffractive light field；
Step 8, preferred parameter { ni,no, △ f } and obtain uniform laser accunputure intensity field distribution.
6. the method for designing of simple uniform laser accunputure focusing microstructures according to claim 5, it is characterised in that the step
In one, illuminating bundle is linearly polarized light, circularly polarized light or radial polarisation light；Illumination wavelengths from X-ray near infrared band in select
Take, take 1nm<λ<1000nm.
7. the method for designing of simple uniform laser accunputure focusing microstructures according to claim 5, it is characterised in that the step
In seven, vector angular spectra theory refers to first pass around the angular spectrum that a Fourier transformation obtains outgoing light field in surface after micro-structural, so
Each polarized component that Fourier transformation obtains light field is again passed by afterwards, so as to be calculated during laser beam illumination micro-structural
Thereafter the optical field distribution in any distance perpendicular plane.
8. the method for designing of simple uniform laser accunputure focusing microstructures according to claim 5, it is characterised in that the step
In seven, Fast Hankel Transform algorithm refers in standard Hankel transform integral expression, to be become using nonlinear exponent function
Amount is replaced, and the unilateral Hankel transform of standard is expressed as into bilateral cross-correlation integral, so as to realize calculating mutual using Fourier transformation
A kind of related fast, accurately computational methods.
9. the method for designing of simple uniform laser accunputure focusing microstructures according to claim 5, it is characterised in that the step
In eight, preferred parameter { ni,no, △ f } detailed process：
First, according to the first focal length f1The second focal length f is chosen with burnt shifting amount △ f2；
Second, adjusting parameter niAnd noIt is preliminary to focus on the light pencil for stretching occur；
3rd, fine setting △ f are adjusted to the uniformity of laser accunputure, and laser accunputure intensity field characteristic is uniformly distributed needed for producing.
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