CN104297925A - Design method of hybrid refractive-diffractive element for achieving femtosecond laser long focal depth - Google Patents

Abstract

The invention discloses a design method of a hybrid refractive-diffractive element for achieving femtosecond laser long focal depth and relates to the field of laser beam shaping. The design method of the hybrid refractive-diffractive element capable of achieving 800 nm femtosecond laser beam long focal depth. The element is composed of a plano-convex lens substrate and a binary microstructure diffraction optical surface. As is shown in a structural representation diagram 1, (1) represents the plano-convex lens substrate and (2) represents the binary microstructure diffraction optical surface. 800 nm femtosecond laser beams pass through the element, a plano-convex lens bears the focal power of a system, the microstructure diffraction optical surface is used for regulating optical field distribution, and finally, long-focal-depth and small-focal-spot laser beams can be obtained. The method provides a feasible design scheme for lenses for achieving long-focal-length femtosecond laser micro processing.

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 came out, the application of laser in processing is constantly expanded, and particularly in laser boring, cutting, photoetching etc., plays very important effect.In laser boring and cutting experiment, the size after light beam focuses on and depth of focus are the keys determining experiment accuracy and cutting accuracy.Compared to traditional job operation, the advantages such as femtosecond laser parallel micromachining has that adaptability for materials is wide, noncontact, pollution-free, high precision, high-level efficiency, the high-quality for micro/nano-scale process, and femtosecond laser processing is one more effectively manufacturing process.Therefore the Diode laser realizing femtosecond laser beam has great significance.

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

1. traditional method carrys out extended focal depth by reducing numerical aperture, but the contradictory relation of lens depth of focus and focal spot size makes resolution and working depth be difficult to obtain lifting simultaneously, increases the increase that depth of focus will inevitably cause focal spot size.

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

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

4. utilize conservation of energy to design logarithm light cone and 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 realize Diode laser become people research focus, this method is using on-axis intensity distribution as objective function, solves the PHASE DISTRIBUTION function of diffraction surfaces or intensity distribution function obtains Diode laser by adopting optimized algorithm.

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 application of the method 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 to spread 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 plano-convex lens substrate and binary microstructure diffractive optical surfaces two parts, and the focal power of system born by plano-convex lens, and microstructure diffractive optical surfaces is for adjusting optical field distribution.

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

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

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

(3) curve.The phase function expression formula of binary optical elements in diffraction surfaces initial phase Jacobian matrix and optical design software Zemax is carried out matching, obtain the coefficient value of the radial aperture coordinate of diffraction surfaces normalization, and the element material determined in the coefficient value obtained and step 1, element initial aperture value, diffraction surfaces initial aperture value, component thickness are inputted in Zemax software.

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

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

If P _r(r) for incident light is in the energy density of element surface, P _zz () is for the emergent light that to spread out through folding after hybrid element is at depth of focus front focal plane and optical axes crosspoint d ₁to depth of focus back focal plane and optical axes crosspoint d ₂between energy density in each plane.After setting Gaussian beam incides phase place device surface, it is d that emanated energy all concentrates on profile height ₁d ₂, bottom surface radius is in the right cylinder of ω, and light distribution is even in focal depth range.Below core formula is derived.

If input Light Energy is Gaussian 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 formula ₀for gauss light beam waist radius value; P is input Gaussian beam monopulse 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 the transmission range of light wave on optical axis.

Solve the expression formula that formula (2) then can obtain 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, the position of intersecting point coordinate of every bar light after element outgoing on optical axis is controlled.The macro document being applicable to 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 ω ₀, output beam waist radius value ω, the position d of depth of focus front focus on optical axis ₁, input Gaussian beam monopulse maximum energy-density value P.Owing to being incident beam is regarded as be made up of a lot of bar light, the position of intersecting point coordinate of every bar light after element outgoing on optical axis is controlled.And the initial position of every bar light is represented by the vertical axial coordinate at incident beam beam waist diameter, the x namely in expression formula (3).Therefore, in order to obtain the value of x, being arranged on the sampling number of x in incident beam beam waist diameter, and carrying out equidistant sampling in incident beam beam waist diameter.

Then, expression formula (3) is write.

Finally, Optimal Parameters.After macro document being write according to above two steps, be loaded in Zemax software, utilize the coefficient value of the radial aperture coordinate of the aperture value of optimizational function to element of software self, diffraction surfaces aperture value, convex curvature, component thickness and the normalization of binary face to be optimized, thus obtain the end value of each parameter of element.

This element can make outgoing beam depth of focus be increased within the scope of 1mm ~ 2mm, and focal spot radius size remains 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 initial configuration functional arrangement

The hot spot out of focus situation of Fig. 4 initial configuration

Hot spot out of focus situation after Fig. 5 optimizes

Spot energy distribution figure after Fig. 6 optimizes

Specific embodiments:

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

If r ₀for 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 correlation parameter

According to parameter shown in table 1, can determine that the material rolling over the hybrid element that spreads out adopts BK7 glass, 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 Gaussian distribution, and choose the input light field of Gaussian beam as GS algorithm, after propagation distance z, its expression formula is:

E(r ₀,z)＝A(r ₀,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 A ₀for amplitude constant; ω ₀for 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) for Gaussian beam cophasal surface radius-of-curvature, 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:

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

Require that emergent light spot energy be that flat-top distributes, therefore choose the output light field of super-Gaussian beam 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; J ₀for zero Bessel function; F is the Fresnel number relevant with light beam, and its expression formula is:

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

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

ω ₀＝3.5mm，A ₀＝1，ω＝50μm，N＝36，z＝200mm。

Therefore can determine that GS algorithm basic process is: Gaussian beam to be 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, keep phase invariant simultaneously, 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, keep phase invariant simultaneously, then fresnel diffraction integral transformation is done again ... circulation like this, until obtain satisfied result or reach abundant cycle index.For reaching the effect of Diode laser, during iteration, in target focal depth range, setting up multiple output face, after exporting to make each, affecting another output face subsequently.

The following initial value of GS algorithm picks: x, y coordinate is equidistant between-50mm to 50mm respectively gets 500 numerical value; Equidistantly in focal depth range 2mm get 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 anomalous integral against diffraction integral, adopt the expression formula of Fourier transform form, the fresnel diffraction formula of Fourier transform form is:

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

In above-mentioned two formulas, λ is element manipulation wavelength, gets 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.By the Curve Fitting Toolbox in Matlab, the formula describing binary optical face phase place in this matrix and Zemax is carried out matching again.

Phase place is added on light by the polynomial expression in Zemax software below the basis of 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 equal 1, A _ibe the coefficient of the 2i power of ρ, ρ is normalized radial 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 carries out matching according to formula (16), gets the first five items of expression formula, obtains fitting expression as follows:

φ＝-163.6ρ ²+496.4ρ ⁴-628.6ρ ⁶+350.6ρ ⁸-71.09ρ ¹⁰ (18)

Five coefficients-163.6,496.4 ,-628.6,350.6 ,-71.09 are input in the excessive data editing machine (Extra Data Editor) of Zemax software respectively, in Analysis-Spots Diagrams-Through Focus, check out of focus situation as shown in Figure 4.

Gaussian beam is after designed lens as seen from Figure 4, and disperse and slow down to some extent, depth of focus is increased 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, trying to achieve the expression formula (3) of the propagation distance z of light wave on optical axis according to the conservation of energy of proposed improvement, realizing keeping outgoing light field be that flat-top distributes in focal depth range self-energy while reaching the little focal spot effect of Diode laser by controlling the position of intersecting point of outgoing beam on optical axis.Writing the macro document for optimizing in Zemax according to expression formula (3), getting ω ₀=3.5mm; ω=50 μm; C=1; P=0.091; d ₁=200mm; Use operand REAZ, and to arrange its weight be 1; In incident beam beam waist diameter, get 100 sample points, namely x is equidistant in incident beam beam waist diameter gets 100 values.

Be loaded into by the macro document write in Zemax software, be optimized the structure of lens reflection face and diffraction surfaces, after optimizing, 5 parameters become respectively :-377.35,355.12 ,-1174.46,544.83 ,-130.27.Other parameters of element export as shown in table 2.

The basic parameter of rear element optimized by table 2

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

As shown in Figure 6, can find out the flat-top distribution that emergent light spot energy is tapered, effect is more satisfactory for emergent light spot energy.

Based on concrete displaying and the introduction of the embodiment in the present invention, those skilled in the art, not making the every other embodiment obtained under innovative labor prerequisite, are 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 characterized in that step is as follows:

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

(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, get determine in step (1) incident field energy distribution, emergent light field energy distribution as input and output light field, calculate diffraction surfaces initial phase Jacobian matrix;

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

(4) optimum structural parameter; If P _r(r) for incident light is in the energy density of element surface, P _zz () is for the emergent light that to spread out through folding after hybrid element is at depth of focus front focal plane and optical axes crosspoint d ₁to depth of focus back focal plane and optical axes crosspoint d ₂between energy density in each plane; After setting Gaussian beam incides phase place device surface, it is d that emanated energy all concentrates on profile height ₁d ₂, bottom surface radius is in the right cylinder of ω, and light distribution is even in focal depth range;

Below core formula is derived:

If input Light Energy is Gaussian 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 formula ₀for gauss light beam waist radius value; P is input Gaussian beam monopulse 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 _z(z)=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 the transmission range of light wave on optical axis;

Solve the expression formula that formula (2) then can obtain 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 being applicable to 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 ω ₀, output beam waist radius value ω, the position d of depth of focus front focus on optical axis ₁, input Gaussian beam monopulse maximum energy-density value P; Owing to being incident beam is regarded as be made up of a lot of bar light, the position of intersecting point coordinate of every bar light after element outgoing on optical axis is controlled; And the initial position of every bar light is represented by the vertical axial coordinate at incident beam beam waist diameter, the x namely in expression formula (3); Therefore, in order to obtain the value of x, being arranged on the sampling number of x in incident beam beam waist diameter, and carrying out equidistant sampling in incident beam beam waist diameter;

Then, expression formula (3) is write;

Finally, Optimal Parameters: after macro document being write according to above two steps, be loaded in Zemax software, utilize the coefficient value of the radial aperture coordinate of the aperture value of optimizational function to element of software self, diffraction surfaces aperture value, convex curvature, component thickness and the normalization of binary face to be optimized, thus obtain the end value of each parameter of element.