CN1800908B - Design method of refraction-diffraction mixed structure of laser beam axisymmetric shaping element - Google Patents

Abstract

A design method of a refraction-diffraction mixed structure of a laser beam axisymmetric shaping element is characterized by comprising the following steps: the method overcomes the defects of small refraction capacity, limited reshaping capacity and high processing difficulty of the single-sided multi-step diffraction optical element, and greatly reduces the processing difficulty of the diffraction surface while ensuring the reshaping effect of the element.

Description

A kind of design method for refraction and diffraction hybrid structure of laser beam axis symmetry shaping element

Technical field

The present invention relates to the method for designing of a kind of laser beam axis symmetry shaping element, the spread out laser beam axis symmetry shaping element of Mixed Design of particularly a kind of folding.

Background technology

In many laser beam were used, such as laser boring, illumination etc. need be specific shape with laser beam reshaping, used with convenient.In various shaping methods, the diffraction element of many ledge structures is a kind of important method, the modulation that it can provide any position to distribute mutually, and it is changeable to have a flexible design, characteristics of high efficiency.Yet, the step width of many ledge structures correspondence that tradition diffraction shaping method for designing provides is often very little, if its minimum step width is less than the manufacturing limit of binary optical process equipment, then can not process or must process by the employing high precision apparatus, thereby cost increases greatly, has limited the application of diffraction shaping element greatly.

Summary of the invention

Technology of the present invention is dealt with problems and is: at shaping requirement and input laser beam parameter, tradition diffraction shaping circuit elements design generally provides single face diffraction face structure, its step width may be very little, cause very difficulty of processing, a kind of design method for refraction and diffraction hybrid structure of laser beam axis symmetry shaping element is provided, and this method increases the step width of diffraction surfaces greatly when guaranteeing the element shaping effect, reduce difficulty of processing, thereby reduced the element cost of manufacture.

Technical solution of the present invention: a kind of design method for refraction and diffraction hybrid structure of laser beam axis symmetry shaping element, it is characterized in that: shaping element is a monolithic component, the two sides, front and back is respectively the axisymmetric plane of refraction and the axisymmetric diffraction surfaces of design, wherein the type of plane of refraction can be sphere or circular conical surface, diffraction surfaces is many steps embossment structure, specifically realizes by following steps:

(1) determining of plane of refraction shape type and parameter, promptly sphere curvature radius or circular conical surface inclination angle determines

Calculating utilizes sphere to approach the available residue face of shaping surface shape shape steepness minimum value and corresponding sphere curvature radius.Calculating utilizes circular conical surface to approach the available residue face of shaping surface shape shape steepness minimum value and corresponding conical surface inclination angle.Contrast the minimum steepness of residue face shape that two types of planes of refraction obtain, get the little plane of refraction type for final design of its numerical value, the face shape parameter is corresponding sphere curvature radius or conical surface inclination angle.(the shape steepness is defined as rotational symmetry face shape function to the maximal value of absolute value in the laser beam bore of coordinate first order derivative radially here.The structural plane shape that shaping surface shape needs for the beam shaping that calculates by the ray tracing method.)

(2) diffraction surfaces shape determines

Utilize the selected plane of refraction type and the residue face shape of calculation of parameter correspondence,, be and roll over the diffraction surfaces shape of mixing shaping element of spreading out its many steps embossment structure that is quantified as equal altitudes.

The present invention's advantage compared with prior art is: it is little to the present invention is directed to the diffraction structure step width that traditional one plane type diffraction element method for designing provides, and unmanageable shortcoming proposes the design method for refraction and diffraction hybrid structure of laser beam axis symmetry shaping element.This method combine plane of refraction shape (sphere and circular conical surface) easy to process, refractive power is big and many steps diffraction element face shape flexible design, characteristics that degree of freedom is big, select suitable plane of refraction type and parameter by calculating, make the step width of diffraction surfaces increase greatly, thereby reduce the difficulty of processing and relative mismachining tolerance of diffraction surfaces, reduce the element cost of manufacture, strengthened the laser shaping ability of diffraction element.

Description of drawings

Fig. 1 is a shaping element structural representation of the present invention;

Fig. 2 distribute according to incident light for the present invention and shaping after emergent light distribute, utilize the ray tracing method to obtain coordinate Mapping and concern;

Fig. 3 obtains aspheric surface figure for of the present invention according to the coordinate Mapping relation;

Fig. 4 is a shaping surface shape of utilizing the conical surface and sphere to fit initial design of the present invention;

Fig. 5 is folded into contour many steps diffraction surfaces shape for of the present invention with continuous residue face shape;

Fig. 6 is the plane of incidence and the exit facet coordinate Mapping relation of embodiments of the invention 1 correspondence;

Fig. 7 is the required initial face shape of the shaping of embodiments of the invention 1 correspondence;

Fig. 8 is the light distribution of the shaping front and back of embodiments of the invention 1 correspondence;

Fig. 9 obtains remaining the steepness of face shape for the circular conical surface match of the different face angles of usefulness of embodiments of the invention 1 correspondence;

Figure 10 obtains remaining the steepness of face shape for the sphere match of the usefulness different curvature radius of embodiments of the invention 1 correspondence;

Figure 11 is the shaping surface shape of embodiments of the invention 1 correspondence, plane of refraction shape and residue face shape;

Figure 12 is the diffraction surfaces shape that 8 steps of embodiments of the invention 1 correspondence quantize;

Figure 13 is the plane of incidence and the exit facet coordinate Mapping relation of embodiments of the invention 2 correspondences;

Figure 14 is the required initial face shape of the shaping of embodiments of the invention 2 correspondences;

Figure 15 is the light distribution of the shaping front and back of embodiments of the invention 2 correspondences;

Figure 16 obtains remaining the steepness of face shape for the circular conical surface match of the different face angles of usefulness of embodiments of the invention 2 correspondences;

Figure 17 obtains remaining the steepness of face shape for the sphere match of the usefulness different curvature radius of embodiments of the invention 2 correspondences;

Figure 18 is the shaping surface shape of embodiments of the invention 2 correspondences, plane of refraction shape and residue face shape;

Figure 19 is the diffraction surfaces shape that 8 steps of embodiments of the invention 2 correspondences quantize.

Embodiment

The refraction and diffraction hybrid structure of laser beam axis symmetry shaping element as shown in Figure 1.Element is an one chip, and the two sides, front and back is respectively axisymmetric plane of refraction and axisymmetric diffraction surfaces, and wherein the type of plane of refraction can be sphere or circular conical surface, and diffraction surfaces is many steps embossment structure.Its method for designing mainly contains following step and constitutes:

1. calculate the required face shape of laser beam axis symmetry shaping

A) utilize the method for ray tracing to obtain the coordinate Mapping that initial laser distributes between the laser distribution (exit facet) after (plane of incidence) and the shaping and concern ρ=Γ (r), as shown in Figure 2, promptly find the solution formula (1) and formula (2).

$\underset{0}{\overset{r}{\∫}}{I}_0\left(r\right)2\mathrm{\πrdr}=\underset{0}{\overset{\mathrm{\Γ}\left(r\right)}{\∫}}{I}_1\left(\mathrm{\ρ}\right)2\mathrm{\π\ρd\ρ}---\left(1\right)$

$\underset{0}{\overset{r_{\max }}{\∫}}{I}_0\left(r\right)2\mathrm{\πrdr}=\underset{0}{\overset{{\mathrm{\ρ}}_{\max }}{\∫}}{I}_1\left(\mathrm{\ρ}\right)2\mathrm{\π\ρd\ρ}---\left(2\right)$

Wherein, I ₀(r) and I ₁(ρ) be respectively light distribution under the radial coordinate before and after the shaping, ρ and r are respectively the radial coordinate of the plane of incidence and exit facet, ρ _MaxAnd r _MaxIt is respectively the maximum caliber of light beam after the maximum caliber of input beam and the shaping.In general, mapping Γ (r) can't resolve and find the solution, and needs numerical solution.

B) utilize refraction principle calculate to realize the required rotational symmetry face shape distribution h (r) of coordinate Mapping Γ (r), as shown in Figure 3, i.e. calculating formula (3)

$h\left(r\right)=\frac{1}{n-1}\∫\frac{\mathrm{\Γ}\left(r\right)-r}{z}\mathrm{dr}---\left(3\right)$

Wherein, n is the material refractive index, and z is that the plane of incidence and shaping divide the distance between the cloth cover.

2. determine plane of refraction shape type and parameter

A) calculate sphere and approach the available residue face of shaping surface shape h (r) shape steepness minimum value and corresponding sphere curvature radius, as shown in Figure 4, promptly numerical solution R makes residue face shape distribute

The steepness minimum, steepness is defined as the absolute value of Δ h (r) to the single order inverse of r here At 0-r _MaxMaximal value in the scope, wherein R is sphere curvature radius (positive number is represented protruding sphere, and negative is represented concave spherical surface),

Be approximate sphere face shape.

B) calculate circular conical surface and approach the available residue face of shaping surface shape h (r) shape steepness minimum value and corresponding conical surface inclination angle, as shown in Figure 4, be meant that finding the solution θ makes residue face shape function Δ h (r)=h (r)-tan (θ) r steepness minimum.Here steepness is defined as the absolute value of Δ h (r) to the first order derivative of r

At 0-r _MaxMaximal value in the scope.Wherein, θ conical surface inclination angle (positive number is represented the conical surface of projection, the conical surface that the negative representative is recessed), tan (θ) r is corresponding circular conical surface face shape.

C) determine the type and the relevant parameters of plane of refraction

Contrast the minimum steepness of residue face shape that top two types of planes of refraction obtain, get the little plane of refraction type for final design of its numerical value, the face line parameter is corresponding sphere curvature radius R or conical surface inclination angle [theta].

3. calculate the structure of diffraction surfaces shape

A) utilize the selected plane of refraction type and the residue face shape Δ h (r) of calculation of parameter correspondence.

B) Δ h (r) equal altitudes is quantified as the diffraction relief surface shape of many steps, as shown in Figure 5.

Quantitative formula is

$h_{\mathrm{diff}}\left(r\right)=\frac{\mathrm{\λ}}{L(n-1)}\·\mathrm{int}\left\{\mathrm{mod}\right[\mathrm{\Δh}\left(r\right),\frac{\mathrm{\λ}}{(n-1)}]/\frac{\mathrm{\λ}}{L(n-1)}\}---\left(4\right)$

Wherein, λ is an optical maser wavelength, h _Diff(r) and Δ h (r) be respectively the residue face shape before quantizing and quantize after diffraction surfaces shape, L is for quantizing number of steps.Int is that decimal rounds, and mod is two remainders that numerical value is divided by of calculating, Be bench height.For convenience of the binary optical processing technology, L generally is taken as 2 ⁿ, n is a positive integer.

Can know by formula (4), be quantized the local corresponding step width minimum of function the first order derivative absolute value maximum of coordinate radially.If minimum step width is near the manufacturing limit of binary optical process equipment, then difficulty of processing is very big, and the error that processes in other words can be very big.But the sphere or the conical surface of the selection suitable parameters by step 2 approach shaping surface shape, and the steepness of residue face shape reduces greatly, thereby the step of the diffraction surfaces shape that quantizes is very wide, thereby greatly reduces difficulty of processing.

Embodiment 1

The incident beam parameter: wavelength 1.06um, bore Φ 40mm, gauss light beam waist half width 10mm, shaping is apart from 500mm, and shaping element is positioned at the gauss light beam waist place.Laser beam is that circular flat distributes bore 20mm after the shaping.Element material is for melting quartz, corresponding refractive index 1.45.

1, calculates the required rotational symmetry face shape of laser beam reshaping.

A) numerical solution formula (1) and formula (2) obtain the plane of incidence and exit facet radial coordinate mapping relations ρ=Γ (r) as shown in Figure 6.

B) according to the coordinate Mapping relation, find the solution formula (3) and obtain initial shaping surface shape distribution h (r) (Fig. 7).Fig. 8 has provided the radial distribution of shaping front and back light intensity.

2. determine plane of refraction shape type and parameter.

A) to approach the steepness minimum value of residue face shape in 0～20mm of shaping surface shape be 0.014 to the numerical solution sphere, and the radius-of-curvature of corresponding sphere is-667mm, as shown in Figure 9.

B) to approach the steepness minimum value of residue face shape in 0-20mm of shaping surface shape be 0.025 to the numerical solution circular conical surface, and corresponding conical surface inclination angle is-1.11 degree, as shown in figure 10.

C) two kinds of face shapes of contrast obtain minimum steepness, and the sphere face shape that numerical value is little is final plane of refraction shape, and sphere curvature radius is-667mm.

3. calculate the structure of diffraction surfaces shape.

A) utilize selected sphere and radius-of-curvature to calculate corresponding residue face shape, as shown in figure 11.

B) utilize formula (4) will remain face shape and be quantified as 8 step surface shapes, as shown in figure 12.

The minimum step width of the diffraction surfaces shape of embodiment 1 design is 20.3um.If directly equal altitudes quantizes initial shaping surface shape h (r), the minimum step width after it quantizes is 6.63um.As can be seen, roll over the difficulty of processing that the Mixed Design of spreading out greatly reduces diffraction surfaces.

Embodiment 2

Incident beam parameter: wavelength 1.06um, bore Φ 40mm, gauss light beam waist half width 10mm.Shaping distance: 500mm, shaping element are positioned at the gauss light beam waist place.Laser beam is that annular flat-top distributes internal diameter 30mm, external diameter 50mm after the shaping.Element material is for melting quartz, corresponding refractive index 1.45.

Concrete steps:

1. calculate the required rotational symmetry face shape of laser beam reshaping.

A) numerical solution formula (1) and formula (2) obtain the radial coordinate mapping relations ρ=Γ (r) of the plane of incidence and exit facet, as shown in figure 13.

B) according to the coordinate Mapping relation, find the solution formula (3) and obtain initial shaping surface shape distribution h (r), as shown in figure 14, Figure 15 has provided the radial distribution of shaping front and back light intensity.

2. determine plane of refraction shape type and parameter.

A) to approach the steepness minimum value of residue face shape in 0～20mm of h (r) be 0.067 to the sphere of numerical solution, and the radius-of-curvature of corresponding sphere is-561mm, as shown in figure 16.

B) to approach the steepness minimum value of residue face shape in 0～20mm of h (r) be 0.0445 to the numerical solution circular conical surface, and corresponding conical surface inclination angle is 2.55 degree, as shown in figure 17.

C) two kinds of face shapes of contrast obtain minimum steepness, and the circular conical surface that numerical value is little is final plane of refraction shape, and conical surface inclination angle is 2.55 degree.

3. calculate the structure of diffraction surfaces shape

A) the residue face shape Δ h (r) that utilizes selected circular conical surface and conical surface inclinometer to get it right and answer is as Figure 18.

B) utilize formula (4) will remain face shape and be quantified as 8 step surface shapes, as shown in figure 19.

The minimum step width of the diffraction surfaces shape of embodiment 2 designs is 13.12um.If directly equal altitudes quantizes initial shaping surface shape, the minimum step width after it quantizes is 4.39um.As can be seen, roll over the difficulty of processing that the Mixed Design of spreading out greatly reduces diffraction surfaces.

In a word, the present invention is converted to the monolithic two plane type with traditional many ledge structures of monolithic one plane type diffraction shaping element, the two sides is respectively the diffraction surfaces of plane of refraction and many ledge structures, select suitable plane of refraction type (sphere or circular conical surface) and parameter (sphere curvature radius or circular conical surface inclination angle) by calculating, the step width of the diffraction surfaces of designing can be widened greatly, it is little that this method has overcome many steps of single face diffraction optical element refractive power, shaping capability is limited, the defective that difficulty of processing is big, when guaranteeing the element shaping effect, greatly reduce the difficulty of processing of diffraction surfaces.

Claims (1)

1. the design method for refraction and diffraction hybrid structure of laser beam axis symmetry shaping element, it is characterized in that: shaping element is a monolithic component, the two sides, front and back is respectively the axisymmetric plane of refraction and the axisymmetric diffraction surfaces of design, wherein the type of plane of refraction is sphere or circular conical surface, diffraction surfaces is many steps embossment structure, specifically realizes by following steps:

(1) determines the required face shape of laser beam axis symmetry shaping

A. utilize the method for ray tracing to obtain the initial laser distribution, promptly the laser after the plane of incidence and the shaping distributes, and promptly the coordinate Mapping between the exit facet concerns ρ=Γ (r), promptly finds the solution formula (1) and formula (2),

$\underset{0}{\overset{r}{\∫}}{I}_0\left(r\right)2\mathrm{\πrdr}=\underset{0}{\overset{\mathrm{\Γ}\left(r\right)}{\∫}}{I}_1\left(\mathrm{\ρ}\right)2\mathrm{\π\ρd\ρ}---\left(1\right)$

$\underset{0}{\overset{r_{\max }}{\∫}}{I}_0\left(r\right)2\mathrm{\πrdr}=\underset{0}{\overset{{\mathrm{\ρ}}_{\max }}{\∫}}{I}_1\left(\mathrm{\ρ}\right)2\mathrm{\π\ρd\ρ}---\left(2\right)$

Wherein, I ₀(r) and I ₁(ρ) be respectively light distribution under the radial coordinate before and after the shaping, ρ and r are respectively the radial coordinate of the plane of incidence and exit facet, ρ _MaxAnd r _MaxIt is respectively the maximum caliber of light beam after the maximum caliber of input beam and the shaping;

B. utilize refraction principle to calculate and realize the required rotational symmetry face shape distribution h (r) of coordinate Mapping Γ (r), i.e. calculating formula (3)

$h\left(r\right)=\frac{1}{n-1}\∫\frac{\mathrm{\Γ}\left(r\right)-r}{z}\mathrm{dr}---\left(3\right)$

Wherein, n is the material refractive index, and z is the distance between the plane of incidence and the exit facet;

(2) determine plane of refraction shape type and parameter

A. utilize sphere face shape to approach rotational symmetry face shape distribution h (r), residue face shape steepness minimum value that obtains and corresponding sphere curvature radius, promptly numerical solution R makes residue face shape distribute

The steepness minimum, steepness is defined as the absolute value of Δ h (r) to the first order derivative of r here

At 0～r _MaxMaximal value in the scope, wherein R is a sphere curvature radius, and positive number is represented protruding sphere, and negative is represented concave spherical surface,

Be approximate sphere face shape;

B. utilize circular conical surface face shape to approach rotational symmetry face shape distribution h (r), residue face shape steepness minimum value that obtains and corresponding conical surface inclination angle, promptly find the solution θ and make residue face shape function Δ h (r)=h (r)-tan (θ) r steepness minimum, steepness is defined as the absolute value of Δ h (r) to the first order derivative of r here

At 0～r _MaxMaximal value in the scope, wherein, θ is conical surface inclination angle, positive number is represented the conical surface of projection, the conical surface that the negative representative is recessed, tan (θ) r is corresponding circular conical surface face shape;

C. determine the type and the relevant parameters of plane of refraction

Contrast the minimum steepness of residue face shape that top two types of planes of refraction obtain, get the little plane of refraction type for final design of its numerical value, the face shape parameter is corresponding sphere curvature radius R or conical surface inclination angle [theta];

(3) structure of calculating diffraction surfaces shape

A. utilize the selected plane of refraction type and the residue face shape Δ h (r) of calculation of parameter correspondence;

B. Δ h (r) equal altitudes is quantified as the diffraction relief surface shape of many steps, quantitative formula is:

$h_{\mathrm{diff}}\left(r\right)=\frac{\mathrm{\λ}}{L(n-1)}\·\mathrm{int}\left\{\mathrm{mod}\right[\mathrm{\Δh}\left(r\right),\frac{\mathrm{\λ}}{(n-1)}]/\frac{\mathrm{\λ}}{L(n-1)}\}---\left(4\right)$

Wherein, λ is an optical maser wavelength, h _Diff(r) and Δ h (r) be respectively the residue face shape before quantizing and quantize after diffraction surfaces shape, L is for quantizing number of steps, int is that decimal rounds, mod is for calculating two remainders that numerical value is divided by,

Be bench height, n is a positive integer.

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