CN102103264A - Method for generating annular non-flat-topped beam by superposing modified multi-Gaussian beams - Google Patents

Abstract

The invention proposes a method for generating an annular non-flat-top beam by superposition of modulated multi-Gaussian beams, and its technical field relates to laser shaping and focusing. This method can solve the disadvantage that the light intensity of the existing annular beam is uniformly distributed within the width of the ring in the radial direction, which is not conducive to the reduction of the focus spot size. The characteristic of the light intensity distribution of the beam is that the closer to the edge, the stronger the light intensity. to a modulated non-flat-top annular beam. A mathematical model of the beam is designed. Through this model, the beam represented by the model can be generated using computational holography. And by adjusting the parameters of the model, non-flat-top annular beams with different modulation characteristics can be obtained. Using a microscope objective to focus a radially polarized non-flat-top annular beam can result in a smaller focused spot size. It has a wide range of applications in optical data storage, optical tweezers manipulation technology, and laser processing.

Description

A kind of method of utilizing the many Gaussian beam stacks of modulation to produce annular non-flat top beam

Technical field

The present invention relates to the stack problem of digital holography and light beam, thereby realize producing a kind of new annular beam.

Background technology

The light beam focus issues is a research focus always.A high order focusing, the hot spot that the full width at half maximum degree is very little is that tool has great advantage in a lot of laser application problems.For example, in laser processing technology, it is good more to focus on, and hot spot is more little, and machining precision is just high more; In optical storage of data, laser focusing is more little, and then the density of data storage is big more; In optical tweezer technology is used, the laser of same power, focal spot is more little, and the power of catching is then big more, and controlling particle size can be more little.

Verified, light beam when focusing on, the radial distribution of light intensity, the polarization state of laser, the numerical aperture size of focusing objective len has determined the size [Appl.Opt., Vol.43, No.22,4322,2004] of hot spot.Studies show that: when the laser incident of radial polarisation, numerical aperture is big more, and hot spot is more little.And when using annular aperture restriction incident laser, the spot size of acquisition can further be dwindled [Phys.Rev.Lett.Vol.91, No.23,233901,2003].But when being to use annular aperture restriction incoming laser beam, also can cause the inconvenience of a lot of practical applications, and the utilization factor of luminous energy is restricted also.In order to overcome the defective of annular aperture, the someone has designed binary pure phase position annular diffraction optical element.When the incident of radial polarisation laser, theoretical analysis shows: hot spot full width at half maximum degree can be less than half wavelength [Nature Photonics, Vol.2,501-505,2008].Recently, reported a kind of annular flat top beam [Chin.Opt.Lett.Vol.9, No.1,11402-11405,2010] that radially superposes and constitute by a plurality of Gaussian beams.The advantage of annular beam is not need annular aperture just can realize ring illumination, and the efficiency of light energy utilization is improved.Utilize the annular beam of radial polarisation, do not need annular aperture just can obtain the hot spot of high order focusing.The characteristics of this light beam are that in annular width, light distribution is that beam energy does not focus on the marginal portion in aperture to greatest extent uniformly, thereby spot size awaits further to improve behind the object lens focusing.

Summary of the invention

The present invention has proposed a kind of Gaussian beam stack by radial modulation and has produced the radially annular beam of light intensity non-uniform Distribution for addressing this problem.The mathematical model of its light beam is:

$E\left(r\right)={\left(\frac{r}{r_0}\right)}^m\underset{n=-N}{\overset{N}{\mathrm{\Σ}}}\exp (-{\left(\frac{r-r_c-{\mathrm{nw}}_0}{w_0}\right)}^2)---\left(1\right)$

Wherein r is a radial coordinate, w ₀Wide for the waist of single non-modulation Gaussian beam, m is an integer, and the size of m has determined the degree of radial light modulation.Constant r _cDetermined the radial position of full annular light beam, r ₀Be a constant, can select usually promptly to select r than the little numerical value that waist of Gaussian beam is wide of maximum radius near focusing objective len aperture maximum radius ₀=r _Max-w ₀The size of N depends on the wide w of waist of single non-modulation Gaussian beam ₀Common w ₀More little, N just can be big more.When the not modulated waist of 2N+1 is wide is w ₀, also be the wide w of waist just apart radially ₀Gaussian beam (as summation aft section in the formula (1)), when the width of the unmodulated annular beam of stack generation is W, w ₀Determine by following equation with the relation of N:

$w_0=\frac{W}{N+{\{1-\ln [\underset{n=-N}{\overset{N}{\mathrm{\Σ}}}\exp (-n^2)\left]\right\}}^{1/2}}---\left(2\right)$

Fig. 1 has represented the intensity distributions of (2N+1) individual Gaussian beam after modulated, and the one dimension radial distribution of the annular beam of the intensity non-uniform Distribution that produces of their stacks.Can see that the feature of the intensity distributions of the light beam after the modulation is: strong more the closer to the aperture edge light intensity.Such light beam, the spot size after helping more reducing to focus on.Realize the light beam of such feature, only need be with the represented object beam of this light beam expression formula (1), with the interference of oblique incidence plane reference beams, produce interferogram by computing machine, and be added on the LCD space light modulator, with the irradiation of collimated laser light bundle, can produce the non-flat top beam of needed annular again.Fig. 2 utilizes computing machine to produce the index path that the hologram method obtains needed light beam

Description of drawings

Fig. 1 is the intensity distributions of (2N+1) individual modulated Gaussian beam, and the one dimension radial distribution curve of the annular beam of the intensity non-uniform Distribution that produces of their stacks, wherein r _Max=1.4, w ₀=0.030, N=20, m=10, r ₀=1.37, r _c=0.75.

Fig. 2 utilizes computing machine to produce the index path that the hologram method obtains needed light beam.The light beam represented with formula (1) is object beam, is that reference light wave interferes the interferogram that is produced to obtain interference fringe picture by computing machine by the Matlab programming with the plane wave, this figure is added on the spatial light modulator again.Utilize collimated laser light bundle incident spatial light modulator can obtain the represented annular non-flat top beam of formula (1).

Embodiment

Below with specific embodiment embodiments of the present invention are described.

Set the parameter of the mathematical model of representing light beam earlier.Formula (1) is a mathematical model, and its parameter can be set to: r _Max=1.4, w ₀=0.03, N=20, m=10, r ₀=1.37, r _c=0.75.As the Plane Electromagnetic Wave in Oblique of reference light wave, its direction cosine are set at 0.05.With Matlab programming, obtain interference fringe picture, and to check that the bitmap mode opens.The pixel setting is consistent with the pixel resolution of spatial light modulator during programming.The pixel of the spatial light modulator that we use is 1024 * 768.Each Pixel Dimensions is 14 μ m * 14 μ m.Use helium-neon gas laser as light source, its wavelength is 0.633 μ m.With the GC0-2501 continuous zoom expander lens that China DaHeng photoelectricity company limited produces the liquid crystal display that is full of whole spatial light modulator to diameter is restrainted in the laser beam expansion.Also can show the speck mirror with 10 earlier and focus on, use aperture filtering again, with convergent mirror it is transformed to the liquid crystal display of parallel light-wave irradiation spatial light modulator then.At this moment, can see the non-flat apical ring shaped light beam of radial modulation with white screen in the suitable distance in liquid crystal display back.

Claims (3)

1. A circularly symmetrical annular non-flat-top beam is characterized in that the radial direction is produced by superposition of (2N+1) modulated Gaussian beams, which can be represented by the following mathematical expression: $\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; N</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; nw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$ 2. According to claim 1, the single modulated Gaussian beam is: ${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; nw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$ Its characteristic is that the Gaussian beam intensity distribution is asymmetric along the radial direction. 3. According to claim 1, each modulated Gaussian beam is staggered from each other in the radial direction, and it is characterized in that the radial distance between the intensity peaks of every two adjacent modulated Gaussian beams is a single unmodulated The waist width of the Gaussian beam.

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