CN102495472B - Bessel beam generator based on annular Dammann gratings - Google Patents

Abstract

A bessel beam generator based on an annular Dammann gratings is sequentially formed by the annular Dammam gratings sharing the same optical axis, a first lens, an amplitude type spatial filter, a second lens and a focusing objective lens. The first lens and the second lens are a confocal lens group, each annular Dammam grating is first-ordered and multi-cycle and has the two-value phase difference of pi, and the amplitude type spatial filter is located on a confocal plane of the first lens and the second lens. Diffraction-free light beams with micron dimension or submicron dimension crosswise facula and 10-102 wavelength of axial focal depth can be generated in a focusing backfield of the focusing objective lens. Switch efficiency is as high as 80%. By means of a spatial filtering mode, quality of generated bessel beams is further improved. The micron or submicron diffraction-free bessel beam can be widely used in the fields of optical micro-machining, optical storage, large focus depth imaging, laser grain capture and quickening, a self-focusing servo-system and the like.

Description

Bessel beam generator based on the annulus Darman raster

Technical field

The present invention relates to non-diffraction Bessel beam, particularly a kind of bessel beam generator based on the annulus Darman raster.Can produce the bessel beam that has simultaneously micron order focal beam spot and overlength depth of focus, in optics processing, optical storage, optical acquisition, large depth field imaging and auto-focusing servo system, important using value be arranged.

Background technology

As everyone knows, the focal spot lateral dimension of general laser beam focousing field and the numerical aperture of condenser lens are inversely proportional to.Expect hot spot or micron resolution characteristic down to sub-micron of high order focusing, just must adopt high-NA objective.On the other hand, focus on square being inversely proportional to of numerical aperture of the depth of focus of light field and condenser lens.In other words, when we adopted the method that improves numerical aperture to improve horizontal resolution characteristic or dwindle the transverse focusing hot spot, the depth of focus of corresponding focousing field sharply reduced, and that is to say, in actual applications, large depth of focus and little transverse focusing hot spot are a pair of implacable contradiction.With the method for diffraction optics, can be implemented in when not sacrificing horizontal resolving power, prolong the depth of focus " referring to prior art " laser cutting head of prolongation depth of focus " CN101797666A " that focuses on light field.Yet the prolongation of this depth of focus often can only reach 2～4 times of original depth of focus.And this scheme tends to bring the rapid increase of the secondary lobe of horizontal focal spot, and for some practical application, the impact of secondary lobe also is the factor of a key, for example optical storage technology.1987, the people such as Durnin have proposed a kind of Beams or have been called bessel beam " Phys.Rev.Lett.581499 (1987) ", the focusing light field of this bessel beam has little horizontal focal spot and the depth of focus of overlength simultaneously, receives very big concern.Nowadays, bessel beam has become a kind of Beams that is widely known by the people, and has been widely used in the occasions such as Laser Processing, optical storage, large depth field imaging, laser capture and particle acceleration.

The annulus Darman raster is a kind of Dammam phase coding thought to be incorporated in the Circular Ring Grating, to produce a series of equal strength ring-shaped light spots in Fourier transform plane.The people such as Zhou Changhe proposed annulus Darman raster concept " Optics Letters 28,2174 (2003) " first in 2003.Subsequently, the annulus Darman raster is further developed, and be extended to radially periodic structure by initial aperiodic structure, and the annulus Darman raster has been widely used in the fields such as various optical measurement and Image Coding.

In Laser Processing, optical storage, laser capture and auto-focusing servo system, the light beam that how to obtain to have vertical depth of focus of little horizontal focal spot and overlength is that people look forward to the technical matters that solves.

Summary of the invention

The object of the invention is to propose a kind of bessel beam generator based on the annulus Darman raster, to produce the bessel beam that has simultaneously micron order focal beam spot and overlength depth of focus.Thereby, in optics processing, optical storage, optical acquisition, large depth field imaging and auto-focusing servo system, important using value is arranged.

Technical solution of the present invention is as follows:

A kind of bessel beam generator based on the annulus Darman raster, comprise successively along the light beam working direction: the annulus Darman raster, first lens, the amplitude type spatial filter, the second lens and focusing objective len, described first lens and the second lens form confocal lens combination, be characterized in that described annulus Darman raster is single order, multicycle, the two-value phasic difference is the annulus Darman raster of π, described annulus Darman raster, first lens, the amplitude type spatial filter, the second lens and focusing objective len common optical axis, described amplitude type spatial filter is positioned on the confocal plane of described first lens and the second lens, this amplitude type spatial filter mainly comprises an annular transmission region, and the interior external radius of this annular transmission region is followed successively by r ₀-δ r and r ₀+ δ r, wherein r ₀=f ₁Tan θ, angle θ satisfy grating equation sin θ=λ/Λ, and λ is operation wavelength, and Λ is the cycle radially of described annulus Darman raster, f ₁Be the focal length of first lens, the range of adjustment of δ r is 1～2 millimeter.

The principal plane of described focusing objective len satisfies relational expression apart from the distance at the center of the second lens:

$d\&le;({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+f_2)\frac{f_2}{f_1}\frac{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\tan \mathrm{\&theta;}-\mathrm{<figure-callout\; id="1"\; label="R\; f"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">R</figure-callout>}}{f_{}},$

Wherein: f ₂Be the focal length of the second lens (22), R is the incident beam radius.

Technique effect of the present invention is as follows:

The present invention is in conjunction with annulus Darman raster and a confocal lens combination, produces a kind of horizontal hot spot in micron or sub-micrometer scale, axially depth of focus is 10～10 in the back focal plane of focusing objective len ²The Beams of wavelength.The conversion efficiency that the present invention can produce at the focusing back court of focusing objective len this non-diffraction Bessel beam generator can be higher than 80%.Simultaneously, by the mode of spatial filtering, the bessel beam quality that produces can further improve.The non-diffraction Bessel beam of this micron or sub-micron can be widely used in the little processing of optics, optical storage, large depth field imaging, laser particle is caught and the occasions such as acceleration and auto-focusing servo system.

Description of drawings

Fig. 1 is the synoptic diagram that the present invention is based on the bessel beam generator of annulus Darman raster.

1-annulus Darman raster; 21 and the confocal lens combination of 22-; 23-amplitude type spatial filter; The 3-focusing objective len.

Fig. 2 is the bessel beam physical model that focuses on.

Fig. 3 is the light field theoretical modeling figure (single order, 50 cycles, two-value position phase annulus Darman raster) of the bessel beam of focusing.

Fig. 4 is the axial intensity distribution of the bessel beam of focusing.

Fig. 5 is the transverse intensity distribution (axial location is z=-50 λ) of the bessel beam of focusing.

Embodiment

The invention will be further described below in conjunction with embodiment and accompanying drawing, but should not limit protection scope of the present invention with this.

One, Theoretical Design

Shown in Figure 1 is a typical bessel beam generator based on the annulus Darman raster, from left to right comprises successively: annulus Darman raster 1, confocal lens combination, amplitude type spatial filter 23 and focusing objective len 3 that first lens 21 and the second lens 22 consist of.Take the focus of condenser lens 3 as initial point, set up rectangular coordinate system.We know that the transmittance function of annulus Darman raster can be write as the form " referring to Optics Letters 31,2387 (2006) " of the sum of series of a series of round sine or cosine function, namely

$T\left(r\right)=\underset{q=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{C}_q\cos (2\mathrm{\&pi;qr}/\mathrm{\&Lambda;})---\left(1\right)$

Wherein: r is radial coordinate, and Λ is the cycle radially.For convenient, here clear aperature is normalized to 1, and then periodicity is N=1/ Λ in the aperture.C _qBe q corresponding order of diffraction ordered coefficients, it is by normalization position phase turning point { r _mDecision, wherein r ₀=0, r _M=1, M is the sum of total position phase turning point.Q the order of diffraction time q corresponding diffraction ring.In fact, q the order of diffraction time corresponding item also can be decomposed into a pair of light cone, namely

$\cos (2\mathrm{\&pi;qr}/\mathrm{\&Lambda;})=\frac{1}{2}[e^{i2\mathrm{\&pi;qr}/\mathrm{\&Lambda;}}+e^{-\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;qr}/\mathrm{\&Lambda;}}]---\left(2\right)$

And each light cone can be write as exp (± i2 π qr/ Λ)=exp (ik β _qR), i.e. the transmittance function of circular cone prism, wherein β _q=mq λ/Λ=mqN λ, k=2 π/λ are corresponding wave number.Therefore, formula (2) can be regarded a pair of circular cone prism as, and wherein positive that correspondence is born circular cone prism, and that negative corresponding normal cone prism.Like this, the diffractive light field of annulus Darman raster can be seen the stack of the diffractive light field of a series of positive and negative circular cone prism as, namely a series of bessel beams and.Q can be expressed as the diffractive light field after object lens focus on of positive and negative circular cone prism:

Wherein,

Maximum aperture angle α=arcsin (NA/n ₀), n wherein _oRefractive index for the object lens back court.

Relevant with the polarization state of incident field, it can be expressed as

Wherein:

Be polarization factor, it can be write as the form of Jones matrix.For x line polarisation,

For y line polarisation

L (θ) is shape factor, and for uniform plane wave, it can be write as L (θ)=1.The focusing light field of annulus Darman raster just can be regarded the bessel beam sum of a series of focusing as.By modulation normalization position phase turning point { r _m, we can realize main diffraction energy concentrate on appointment the level time on.For single order annulus Darman raster, main energy (greater than 80%) concentrates on first order of diffraction time, namely on the first pair of light cone.

By confocal lens combination 21 and 22 shown in Figure 1, we can realize the ability on so a pair of light cone is transferred on one of them light cone easily, namely on the light cone of the corresponding normal cone prism of shown in Figure 2 that.At this moment, the principal plane of focusing objective len 3 satisfies following relational expression from the second lens 22 centers apart from d:

$d\&le;({\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1+f_2)\frac{f_2}{f_1}\frac{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\tan \mathrm{\&theta;}-\mathrm{<figure-callout\; id="1"\; label="R\; f"\; filenames="HDA0000113831320000021.png,HDA0000113831320000031.png"\; state="\{\{state\}\}">R</figure-callout>}}{f_{}}---\left(5\right)$

In the formula, θ is the angle between the adjacent level time, and it satisfies grating equation sin θ=λ/Λ, and wherein, λ is operation wavelength, and Λ is the single order annulus Darman raster that adopts corresponding cycle diametrically.In addition, by the amplitude type spatial filter of an annular, we can well filter senior time and zero level.Like this, just can produce one at the back focal plane of focusing objective len 3 more perfectly without diffraction Bezier light field.External radius is followed successively by r in the annular transmission region of this amplitude type spatial filter 23 ₀-δ r and r ₀+ δ r, wherein r ₀=f ₁Tan θ, δ r can suitably regulate according to actual conditions in 1～2 millimeter scope.f ₁Focal length for first lens 21.

Two, embodiment

Below take NA=0.9 focusing objective len 3, circular polarization uniform strength distribution plane wave, fused silica glass substrate as example, for its operation wavelength (405nm), a kind of specific embodiments of the bessel beam generator based on the annulus Darman raster is proposed.The annulus Darman raster 1 that adopts is single order, two-value π position phase, multicycle annulus Darman raster.Fused silica glass is at the refractive index n of 405nm ₀=1.468), corresponding phase depth is h=0.405/ (2 * (1.468-1))=0.433 μ m.The position phase turning point that multicycle single order annulus Darman raster is corresponding is r ₁=0.5 " Optics Letters 31,2387 (2006) ".If the clear aperature of used focusing objective len 3 is 6mm, numerical aperture is 0.9, and the periodicity in the clear aperature is 50, and the cycle is 60 microns, and then the angle between the adjacent diffraction orders time is θ=arcsin (0.405/60)=0.39 °.The minimum feature of annulus Darman raster 1 correspondence is 30 microns, and this can adopt ripe photoetching technique and plasma etching technology to process the pure position of this binary annulus Darman raster mutually.The focal length of first lens 21 and the second lens 22 is followed successively by f ₁=50cm and f ₂=10cm, then the inner and outer ring radius of amplitude type spatial filter 23 is followed successively by 2.4mm and 4.4mm.(getting δ r=1mm).The radius of the launching spot after the collimator and extender is R=3mm, and then focusing objective len 3 principal planes are less than 14.2mm from the distance at lens 22 centers.

Fig. 3 has provided the numerical simulation circle of equal altitudes of the non-diffraction Bessel beam that under these conditions the bessel beam generator based on the annulus Darman raster produces.Therefrom we can find out, the lateral light spot size of this non-diffraction Bessel beam is a wavelength magnitude, and vertical depth of focus is greater than 20 λ.Fig. 4 has provided the axial intensity distribution of this bessel beam, and therefrom we can clearly find out, the axial depth of focus (full width at half maximum) of this Beams is 49.8 λ.Fig. 5 has provided the horizontal hot spot intensity distribution corresponding at z=-50 λ place, and therefrom we can find out, laterally the size of hot spot is 0.33 * 2=0.66 λ.And therefrom we it can also be seen that, laterally the secondary lobe of hot spot is less than 20%.For the operation wavelength of 405nm, laterally focal spot is about 267nm, and axially depth of focus is 20.2 microns.Thereby there is important application prospect the aspects such as this sub-micrometer scale Beams is caught at the little processing of optics, laser particle, large depth field imaging.

In sum, the present invention proposes a kind of specific design method and embodiment of the bessel beam generator based on the annulus Darman raster, and take NA=0.9 focusing objective len, circular polarization uniform strength distribution plane wave, fused silica glass substrate as example, for its operation wavelength (405nm), the feasible making Processing Routes of a kind of single order, two-value position phase, multicycle annulus Darman raster is proposed.

Claims (1)

1. bessel beam generator based on the annulus Darman raster, comprise successively along the light beam working direction: annulus Darman raster (1), first lens (21), amplitude type spatial filter (23), the second lens (22) and focusing objective len (3), described first lens (21) and the second lens (22) form confocal lens combination, it is characterized in that described annulus Darman raster (1) is single order, multicycle, the two-value phasic difference is the annulus Darman raster of π, described annulus Darman raster (1), first lens (21), amplitude type spatial filter (23), the second lens (22) and focusing objective len (3) common optical axis, described amplitude type spatial filter (23) is positioned on the confocal plane of described first lens (21) and the second lens (22), this amplitude type spatial filter (23) mainly comprises an annular transmission region, and the interior external radius of this annular transmission region is followed successively by r ₀-δ r and r ₀+ δ r, wherein r ₀=f ₁Tan θ, angle θ satisfy grating equation sin θ=λ/Λ, and λ is operation wavelength, and Λ is the cycle radially of described annulus Darman raster (1), f ₁Be the focal length of first lens (21), the range of adjustment of δ r is 1～2 millimeter;

The principal plane of described focusing objective len (3) satisfies relational expression apart from the distance at the center of the second lens (22):

F wherein ₂Be the focal length of the second lens (22), R is the incident beam radius.

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