CN104297925B - A kind of folding realizing femtosecond laser Diode laser spreads out the method for designing of hybrid element - Google Patents

Abstract

A kind of folding realizing femtosecond laser Diode laser spreads out the method for designing of hybrid element, relates to laser beam shaping field.The invention discloses a kind of folding that can realize 800nm femtosecond laser beam Diode laser to spread out hybrid element method for designing.This element is made up of planoconvex lens substrate and binary micro structure diffractive optical surfaces two parts, and structural representation is as it is shown in figure 1, (1) is planoconvex lens substrate, and (2) are binary micro structure diffractive optical surfaces.800nm femtosecond laser beam passes through element, and planoconvex lens undertakes the focal power of system, and micro structure diffractive optical surfaces is used for adjusting optical field distribution, may finally obtain the laser beam of Diode laser, little focal spot.The method is that the femtosecond laser parallel micromachining lens realizing Diode laser provide feasible design.

Description

A kind of folding realizing femtosecond laser Diode laser spreads out the method for designing of hybrid element

Technical field:

The present invention relates to laser field, be specially laser beam shaping field.

Background technology:

Since nineteen sixty laser instrument comes out, laser application in processing is constantly expanded, and has particularly played very important effect in laser boring, cutting, photoetching etc..In laser boring and cutting experiment, size and depth of focus after light beam focusing are the keys determining experiment accuracy and cutting accuracy.Compared to traditional processing method, femtosecond laser parallel micromachining has that adaptability for materials is wide, noncontact, pollution-free, in high precision, the advantage such as high efficiency, the high-quality for micro/nano-scale process, and it is a kind of significantly more efficient manufacturing process that femtosecond laser is processed.Therefore the Diode laser realizing femtosecond laser beam has great significance.

The method realizing Diode laser has a variety of, mainly has following six kinds of methods:

1. traditional method is to carry out extended focal depth by reduction numerical aperture, but the contradictory relation of lens depth of focus and focal spot size makes resolution be difficult to obtain lifting with working depth simultaneously, increases depth of focus and will necessarily cause the increase of focal spot size.

2. utilizing axial cone mirror to realize Diode laser, incident plane wave can be transformed to the light intensity conical wave along the axial cone linear distribution of mirror optical axis by axial cone mirror, and can propagate far distance without what spread.But the light intensity propagation distance linearly trend growth that the conical wave formed is on axle, and vibrate with fierceness.

3. Beams realizes laser Diode laser, and such as conscope method, unlimited narrow circule method etc., but these methods exist that focal depth range is wayward and on-axis intensity vibration severity in focal depth range, or the problem such as capacity usage ratio is low.

4. utilizing conservation of energy design logarithm light cone to realize Beams, the method effectively increases depth of focus, but the capacity usage ratio in focal depth range is too low.

5. along with the development of binary optical technique, utilize refraction/diffraction mixed optical element to realize Diode laser and become the focus of people's research, this method is as object function using on-axis intensity distribution, by adopting optimized algorithm to solve the PHASE DISTRIBUTION function of diffraction surfaces or intensity distribution function obtains Diode laser.

6. wavefront coding technology, the method is a kind of novel technical method expanding depth of focus optical technology combined with image procossing.At present, the method application in optical system also achieves considerable progress.

Summary of the invention:

The present invention utilizes the folding hybrid element that spreads out to realize 800nm femtosecond laser beam Diode laser, discloses this folding and spreads out the method for designing of hybrid element.

Roll over the design of the hybrid element that spreads out based on mature scalar diffraction theory.This element is made up of planoconvex lens substrate and binary micro structure diffractive optical surfaces two parts, and planoconvex lens undertakes the focal power of system, and micro structure diffractive optical surfaces is used for adjusting optical field distribution.

Design Diode laser rolls over the recovery problem that the hybrid element that spreads out is phase place.Therefore, the design procedure of the present invention is as follows:

(1) according to the parameter of laser instrument used and design depth of focus focal spot requirement determine folding spread out the material of hybrid element, element initial aperture value, diffraction surfaces initial aperture value, component thickness, incident field Energy distribution, emergent light field energy distribution.

(2) diffraction surfaces initial phase Jacobian matrix is calculated.Write folding to spread out the calculation procedure of hybrid element diffraction surfaces initial phase, take step 1 is determined incident field Energy distribution, the distribution of emergent light field energy as input and output light field, calculate and obtain diffraction surfaces initial phase Jacobian matrix.

(3) curve matching.Diffraction surfaces initial phase Jacobian matrix is fitted with the phase function expression formula of binary optical elements in optical design software Zemax, obtain the coefficient value of diffraction surfaces normalization radially aperture coordinate, and by the element material determined in the coefficient value obtained and step 1, element initial aperture value, diffraction surfaces initial aperture value, component thickness input Zemax software.

(4) optimum structural parameter.Propose the conservation of energy of a kind of improvement, writing according to this method tries out in the macro document of Zemax software, the coefficient value of the aperture value of element, diffraction surfaces aperture value, convex curvature, component thickness and the normalization of binary face radially aperture coordinate is optimized, obtains the end value of said elements parameter.

The conservation of energy main thought of described improvement is as follows:

If P_rR () is the incident illumination energy density at element surface, P_zZ () is for spreading out after hybrid element emergent light at depth of focus front focal plane and optical axes crosspoint d through folding₁To depth of focus back focal plane and optical axes crosspoint d₂Between energy density in each plane.After setting Gaussian beam incides phase place device surface, it is d that emanated energy all concentrates on profile height₁d₂, bottom surface radius be ω cylinder in, and light distribution is uniform in focal depth range.Below core formula is derived.

If input Light Energy is Gauss distribution, its energy density distribution function is

$P_r\left(r\right)={\mathrm{Pe}}^{-\frac{{2r}^2}{{{\mathrm{\ω}}_0}^2}}---\left(1\right)$

ω in formula₀For gauss light beam waist radius value；P is input Gaussian beam pulse maximum energy-density value；R is Gaussian beam radial coordinate value.

If output light field energy is flat-top distribution, its energy density is constant, i.e. P_zZ ()=C, for convenience of calculating, general value is 1.

Have according to conservation of energy principle

$2{\∫}_0^x{\mathrm{\πrPe}}^{-\frac{{2r}^2}{{{\mathrm{\ω}}_0}^2}}\mathrm{dr}={\∫}_{d_1}^z{\mathrm{C\π\ω}}^2\mathrm{zdz}---\left(2\right)$

In formula, ω is outgoing beam waist radius value, and z is light wave transmission range on optical axis.

Solve formula (2) and then can obtain the expression formula of z

$z=\sqrt{\frac{{{\mathrm{\ω}}_0}^{2}P}{{\mathrm{C\ω}}^2}(1-e^{-\frac{{2x}^2}{{{\mathrm{\ω}}_0}^2}})+d_1^2}---\left(3\right)$

Using expression formula (3) as core formula, incident beam is regarded as and is made up of a lot of bar light, every light position of intersecting point coordinate on optical axis after element outgoing is controlled.The macro document suitable in Zemax software is write according to this thinking.

First, initial value is set.The initial value writing macro document required input is set according to expression formula (3): input beam waist radius value ω₀, output beam waist radius value ω, depth of focus front focus position d on optical axis₁, input Gaussian beam pulse maximum energy-density value P.Owing to being regard as incident beam to be made up of a lot of bar light, every light position of intersecting point coordinate on optical axis after element outgoing is controlled.And the initial position of every light is represented by the vertical axial coordinate at incident beam beam waist diameter, i.e. x in expression formula (3).Therefore, in order to obtain the value of x, it is arranged on the sampling number of x in incident beam beam waist diameter, and in incident beam beam waist diameter, carries out equidistant sampling.

Then, expression formula (3) is write.

Finally, parameters optimization.After macro document being write according to above two steps, it is loaded in Zemax software, the coefficient value of the aperture value of element, diffraction surfaces aperture value, convex curvature, component thickness and the normalization of binary face radially aperture coordinate is optimized by the optimization function utilizing software self, thus obtaining the end value of each parameter of element.

This element can make outgoing beam depth of focus increase within the scope of 1mm～2mm, and focal spot radius size is maintained within 50 μm.

Accompanying drawing illustrates:

Fig. 1 rolls over the hybrid element face type schematic diagram that spreads out

The conservation of energy schematic diagram that Fig. 2 improves

Fig. 3 diffraction surfaces initiating structure functional arrangement

The hot spot out of focus situation of Fig. 4 initiating structure

Hot spot out of focus situation after Fig. 5 optimization

Spot energy distribution figure after Fig. 6 optimization

Specific embodiments:

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

If r₀For input light field spot radius coordinate, r_iFor output light field spot radius coordinate.

The present invention is directed to 800nm femto-second laser, this laser instrument parameters is as shown in table 1.

Table 1800nm femto-second laser relevant parameter

Parameter according to table 1, it may be determined that the material rolling over the hybrid element that spreads out adopts BK7 glass, and element initial aperture value is 20mm, and diffraction surfaces initial aperture value is 10mm, and component thickness is 2mm.The output facula energy of 800nm femto-second laser is Gauss distribution, chooses the Gaussian beam input light field as GS algorithm, and after propagation distance z, its expression formula is:

E(r₀, z)=A (r₀,z)exp(-ikz)(4)

$A(r_0,z)=\frac{A_0{\mathrm{\ω}}_0}{\mathrm{\ω}\left(z\right)}\exp [-\frac{{r_0}^2}{{\mathrm{\ω}}^2\left(z\right)}]\exp \{-i[\frac{{{\mathrm{kr}}_0}^2}{2R\left(z\right)}-\mathrm{\Ψ}\left]\right\}---\left(5\right)$

Wherein A₀For amplitude constant；ω₀For gauss light beam waist radius value；The beamwidth that ω (z) is Gaussian beam, its expression formula is:

$\mathrm{\ω}\left(z\right)={\mathrm{\ω}}_0\sqrt{1+{(z/Z_0)}^2}---\left(6\right)$

$Z_0=\frac{1}{2}k{\mathrm{\ω}}_0^2=\frac{\mathrm{\π}{\mathrm{\ω}}_0^2}{\mathrm{\λ}}---\left(7\right)$

R (z) is Gaussian beam equiphase surface radius of curvature, and expression formula is:

$R\left(z\right)=Z_0(\frac{z}{Z_0}+\frac{Z_0}{z})---\left(8\right)$

Ψ is Gaussian beam phase factor, and expression formula is:

$\mathrm{\Ψ}={\tan }^{-1}\frac{z}{Z_0}---\left(9\right)$

Requiring that emergent light spot energy is flat-top distribution, therefore choose the super-Gaussian beam output light field as GS algorithm, its propagation in free space can be described by Collins Formula, by the transmission formula after distance z is:

E(r_i, z)=U (r_i,z)exp{i[kz+Φ(r_i,z)]}(10)

Wherein

$U(r_i,z)=2\mathrm{\πF}{\∫}_0^{+\∞}\exp \left({-\mathrm{\υ}}^N\right)J_0\left(2\mathrm{\πF\υ}\frac{r_i}{\mathrm{\ω}}\right)\exp \left({\mathrm{i\πF\υ}}^2\right)\mathrm{\υd\υ}---\left(11\right)$

$\mathrm{\Φ}(r_i,z)=\frac{{{\mathrm{kr}}_i}^2}{2z}+\arg \left\{{\∫}_0^{+\∞}\exp \left({-\mathrm{\υ}}^N\right)J_0\left(2\mathrm{\πF\υ}\frac{r_i}{\mathrm{\ω}}\right)\exp \left({\mathrm{i\πF\υ}}^2\right)\mathrm{\υd\υ}\right\}---\left(12\right)$

In formula, k is wave number；ω is super-Gaussian beam waist radius value；N is the exponent number of super-Gaussian beam；J₀For zero Bessel function；F is the Fresnel number relevant with light beam, and its expression formula is:

$F=\frac{{\mathrm{\ω}}^2}{\mathrm{\λz}}---\left(13\right)$

According to designing requirement and laser instrument basic parameter shown in table 1, in above-mentioned formula and expression formula, parameter value is as follows:

ω₀=3.5mm, A₀=1, ω=50 μm, N=36, z=200mm.

Therefore can determine that GS algorithm basic process is: Gaussian beam is spread out hybrid element through folding, carry out a fresnel diffraction integral transformation, obtain output plane optical field distribution, now replace the distribution of former optical field amplitude with the distribution of amplitudes of super-Gaussian beam, it is maintained with phase invariant, then do Fresnel to convert against diffraction integral, obtain input plane optical field distribution, the distribution of former optical field amplitude is replaced with Gaussian beam distribution of amplitudes at input plane, it is maintained with phase invariant, then fresnel diffraction integral transformation is done again ... so circulate, until obtaining satisfied result or reaching abundant cycle-index.For reaching the effect of Diode laser, in target focal depth range, during iteration, set up multiple output face, so that affecting another output face subsequently after each output.

The following initial value of GS algorithm picks: x, y-coordinate are equidistant between-50mm to 50mm respectively takes 500 numerical value；Equidistant in focal depth range 2mm take 200 output faces；Circulate 500 times；The component structure cycle is 10mm.

In order to accelerate the speed of iterative computation, when carrying out fresnel diffraction integration and inverse diffraction integral, adopting the expression formula of Fourier transformation form, the fresnel diffraction formula of Fourier transformation form is:

The Fresnel of Fourier transformation form against diffraction integral formula is:

In above-mentioned two formulas, λ is element manipulation wavelength, takes 800nm；K is wave number；Z is that light field output face is to the distance of input face when fresnel diffraction conversion and inverse Diffraction Transformation, and value is 2mm.

The diffraction surfaces type initial phase Jacobian matrix of one 500 × 500 is obtained, as shown in Figure 3 by above GS algorithmic procedure.Again through the Curve Fitting Toolbox in Matlab, the formula of binary optical face phase place described in this matrix and Zemax is fitted.

In Zemax software, phase place is added on light according to following multinomial by binary optical face 2 (binary2):

$\mathrm{\φ}=M{\mathrm{\Σ}}_{i=1}^N{A}_i{\mathrm{\ρ}}^{2i}---\left(16\right)$

In formula, N is the sequence number of multinomial coefficient in progression, and M is the order of diffraction time, makes it be equal to 1, A_iBeing the coefficient of the 2i power of ρ, ρ is normalized radial direction aperture coordinate, namely

$\mathrm{\ρ}=\frac{\sqrt{(x^2+y^2)}}{{\mathrm{\ρ}}_N}---\left(17\right)$

Wherein, ρ_NFor normalization radius.

The initial phase Jacobian matrix obtained by GS algorithm is fitted according to formula (16), takes the first five items of expression formula, obtains fitting expression as follows:

φ=-163.6 ρ²+496.4ρ⁴-628.6ρ⁶+350.6ρ⁸-71.09ρ¹⁰(18)

By five coefficients-163.6,496.4 ,-628.6,350.6 ,-71.09 it is separately input in the excessive data editing machine (ExtraDataEditor) of Zemax software, in Analysis SpotsDiagrams ThroughFocus, checks out of focus situation as shown in Figure 4.

Gaussian beam is after designed lens as seen from Figure 4, disperses and slows down to some extent, and depth of focus increases to about 1.5mm, and root mean square radii is at about 36.48 μm.

In order to reduce the root mean square radii of focal spot, conservation of energy according to proposed improvement tries to achieve the expression formula (3) of light wave propagation distance z on optical axis, by control outgoing beam position of intersecting point on optical axis realize reach the little focal spot effect of Diode laser be maintained with outgoing light field focal depth range self-energy be flat-top be distributed.Write in Zemax the macro document for optimizing according to expression formula (3), take ω₀=3.5mm；ω=50 μm；C=1；P=0.091；d₁=200mm；Use operand REAZ, and to arrange its weight be 1；Taking 100 sample points in incident beam beam waist diameter, namely x is equidistant in incident beam beam waist diameter takes 100 values.

Being loaded in Zemax software by the macro document write, the structure of lens plane of refraction and diffraction surfaces is optimized, after optimizing, 5 parameters become respectively :-377.35,355.12 ,-1174.46,544.83 ,-130.27.The output of other parameters of element is as shown in table 2.

The basic parameter of element after table 2 optimization

As seen from Figure 5, the folding the finally given hybrid element that spreads out can make the depth of focus of femtosecond laser beam increase to 1.5mm in theory, and hot spot root mean square radii is about 13.16 μm, it is achieved that the Diode laser of outgoing beam and little focal spot.

Emergent light spot energy is as shown in Figure 6, it can be seen that the flat-top distribution that emergent light spot energy is tapered, effect is more satisfactory.

Concrete based on the embodiment in the present invention is shown and introduces, the every other embodiment that those skilled in the art obtain under not making innovative labor premise, is protection scope of the present invention.

Claims (1)

1. the folding realizing femtosecond laser beam Diode laser spreads out the method for designing of hybrid element, it is characterised in that step is as follows:

(1) according to the parameter of laser instrument used and design depth of focus focal spot requirement determine folding spread out the material of hybrid element, element initial aperture value, diffraction surfaces initial aperture value, component thickness, incident field Energy distribution, emergent light field energy distribution；

(2) diffraction surfaces initial phase Jacobian matrix is calculated: write the calculation procedure rolling over the hybrid element diffraction surfaces initial phase that spreads out, take step (1) is determined incident field Energy distribution, the distribution of emergent light field energy as input and output light field, calculate and obtain diffraction surfaces initial phase Jacobian matrix；

(3) curve matching: diffraction surfaces initial phase Jacobian matrix is fitted with the phase function expression formula of binary optical elements in optical design software Zemax, obtain the coefficient value of diffraction surfaces normalization radially aperture coordinate, and by the element material determined in the coefficient value obtained and step (1), element initial aperture value, diffraction surfaces initial aperture value, component thickness input Zemax software；

(4) optimum structural parameter；If P_rR () is the incident illumination energy density at element surface, P_zZ () is for spreading out after hybrid element emergent light at depth of focus front focal plane and optical axes crosspoint d through folding₁To depth of focus back focal plane and optical axes crosspoint d₂Between energy density in each plane；After setting Gaussian beam incides phase place device surface, it is d that emanated energy all concentrates on profile height₁d₂, bottom surface radius be ω cylinder in, and light distribution is uniform in focal depth range；

Below core formula is derived:

If input Light Energy is Gauss distribution, its energy density distribution function is

$P_r\left(r\right)={\mathrm{Pe}}^{-\frac{2r^2}{{{\mathrm{\ω}}_0}^2}}---\left(1\right)$

ω in formula₀For gauss light beam waist radius value；P is input Gaussian beam pulse maximum energy-density value；R is Gaussian beam radial coordinate value；

If output light field energy is flat-top distribution, its energy density is constant, i.e. P_zZ ()=C, for convenience of calculating, C value is 1；

Have according to conservation of energy principle

$2{\∫}_0^x\mathrm{\πrP}{e}^{-\frac{2r^2}{{{\mathrm{\ω}}_0}^2}}\mathrm{dr}={\∫}_{d_1}^z\mathrm{C\π}{\mathrm{\ω}}^2\mathrm{zdz}---\left(2\right)$

In formula, ω is outgoing beam waist radius value, and z is light wave transmission range on optical axis；

Solve formula (2) and then can obtain the expression formula of z

$z=\sqrt{\frac{{{\mathrm{\ω}}_0}^{2}P}{C{\mathrm{\ω}}^2}(1-e^{-\frac{2x^2}{{{\mathrm{\ω}}_0}^2}})+d_1^2}---\left(3\right)$

Write the macro document suitable in Zemax software, specific as follows:

First, initial value is set: the initial value writing macro document required input is set according to expression formula (3): input beam waist radius value ω₀, output beam waist radius value ω, depth of focus front focus position d on optical axis₁, input Gaussian beam pulse maximum energy-density value P；Owing to being regard as incident beam to be made up of a lot of bar light, every light position of intersecting point coordinate on optical axis after element outgoing is controlled；And the initial position of every light is represented by the vertical axial coordinate at incident beam beam waist diameter, i.e. x in expression formula (3)；Therefore, in order to obtain the value of x, it is arranged on the sampling number of x in incident beam beam waist diameter, and in incident beam beam waist diameter, carries out equidistant sampling；

Then, expression formula (3) is write；

Finally, parameters optimization: after macro document being write according to above two steps, it is loaded in Zemax software, the coefficient value of the aperture value of element, diffraction surfaces aperture value, convex curvature, component thickness and the normalization of binary face radially aperture coordinate is optimized by the optimization function utilizing software self, thus obtaining the end value of each parameter of element.