Femtosecond Mathieu Beams for RapidControllable Fabrication of ComplexMicrocages and Application in TrappingMicroobjectsChaowei Wang,† Liang Yang,*,† Yanlei Hu,† Shenglong Rao,† Yulong Wang,† Deng Pan,†

Shengyun Ji,† Chenchu Zhang,‡ Yahui Su,§ Wulin Zhu,† Jiawen Li,† Dong Wu,*,† and Jiaru Chu†

†Hefei National Laboratory for Physical Sciences at the Microscale and CAS Key Laboratory of Mechanical Behavior and Design ofMaterials, Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China,Hefei 230026, China‡Institute of Industry and Equipment Technology, Hefei University of Technology, Hefei 230009, China§School of Electronics and Information Engineering, Anhui University, Hefei 230601, China

*S Supporting Information

ABSTRACT: Structured laser beam based microfabricationtechnology provides a rapid and flexible way to create somespecial microstructures. As an important member in thepropagation of invariant structured optical fields, Mathieubeams (MBs) exhibit regular intensity distribution and diversecontrollable parameters, which makes it extremely suitable forflexible fabrication of functional microstructures. In this study,MBs are generated by a phase-only spatial light modulator(SLM) and used for femtosecond laser two-photon polymer-ization (TPP) fabrication. Based on structured beams, adynamic holographic processing method for controllablethree-dimensional (3D) microcage fabrication has beenpresented. MBs with diverse intensity distributions are generated by controlling the phase factors imprinted on MBswith a SLM, including feature parity, ellipticity parameter q, and integer m. The focusing properties of MBs in a highnumerical aperture laser microfabrication system are theoretically and experimentally investigated. On this basis, complextwo-dimensional microstructures and functional 3D microcages are rapidly and flexibly fabricated by the controllablepatterned focus, which enhances the fabrication speed by 2 orders of magnitude compared with conventional single-pointTPP. The fabricated microcages act as a nontrivial tool for trapping and sorting microparticles with different sizes. Finally,culturing of budding yeasts is investigated with these microcages, which demonstrates its application as 3D cell culturescaffolds.KEYWORDS: two-photon polymerization, Mathieu beams, polymer microcages, dynamic holographic processing,microobject trapping

Trapping and holding microobjects has been a hotresearch focus in recent years, which has importantapplications in biomedical research and fundamental

studies of cell behavior. Optical tweezers,1−3 a simple androbust implementation for microobject manipulation, havebeen successfully used to manipulate microobjects from severalmicrometers to tens of nanometers. However, an opticaltweezer is usually generated by a tightly focused laser beam,which is harmful to living samples or chemical reactions.Therefore, to address these issues, some specifically designedmicrostructures were fabricated for microobject manipula-tion.4,5 As an example, hierarchical helical arrays realized by

capillary force assembly of micropillar arrays,5 which wasfabricated by the two-step soft transfer of a silicon templateprepared by UV lithography and plasma etching, were used totrap many particles rapidly and simultaneously. Miniaturizedself-folding grippers which are actuated by differential residualstress,6 temperature,7,8 magnetic force,9 and chemicals10,11 cantrap microparticles inside “cage-like” spaces. Moreover, corner

Received: January 31, 2019Accepted: March 13, 2019Published: March 13, 2019

Artic

lewww.acsnano.orgCite This: ACS Nano XXXX, XXX, XXX−XXX

© XXXX American Chemical Society A DOI: 10.1021/acsnano.9b00893ACS Nano XXXX, XXX, XXX−XXX

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lithography,12 which is a wafer-scale nanopatterning techniqueinvolving conformal deposition and selective isotropicthinning, can form arrays of nanowire pyramids in sharpconcave corners for microbeads and cell trapping. Although avariety of complex microstructures have been achieved, manyof them have distinct drawbacks of complicated fabricationprocesses or dependence on expensive apparatus and lowcontrollability. Therefore, it is still in high demand to develop asimple, rapid, and controllable method to fabricate desiredmicro/nanostructures for manipulating microobjects.The two-photon polymerization (TPP) technique13−16 is

extensively studied for fabricating complex functional 3Dmicro/nanodevices, owing to its simple operation, sub-100 nmresolution, and intrinsic three-dimensional (3D) processingability. However, the wide application of TPP is restricted bythe low fabrication speed due to the single-point scanningstrategy.17 In order to improve the efficiency, typical methods,such as multifoci parallel fabrication by microlens arrays,18

diffractive optical elements,19 or multibeam interference,20 aredeveloped. Nevertheless, the disadvantage of these methods isthat the positions of the foci are fixed by the optical elements.Moreover, these methods are only suitable for fabricatingmicrostructure arrays with the same morphology. It is a muchmore flexible way to fabricate complicated microstructures byusing a SLM.21−24 Until now, multifocal fabrication offunctional microstructures has been performed by adoptingSLM, such as microoptics25 and microfluidic structures.26

Besides the multifoci array, structured beams are capable offabricating specific microstructures with high efficiency.27,28

Mathieu beams,29−31 as a kind of special structured beams,have two interesting features: “diffraction-free”, that is,preserving their shape while propagating, and “self-healing”,that is, recovering to its original shape even if part of the beamis destroyed by a small obstacle. Due to these specific features,MBs have already been used for 3D optical trapping andmicromanipulation.32 However, adopting MBs in femtosecondlaser TPP processing for rapid fabrication of functional 3Dstructures has not been reported so far. The focusingproperties of MBs under high numerical aperture (NA) andthe impact of laser beam parameters on fabricated micro/nanostructures have not been quantitatively investigated.In this work, we present a dynamic holographic processing

method to fabricate 3D microcages. First, MBs are generatedby using a liquid-crystal phase-only SLM without any otheroptical elements. The focusing properties of MBs in a high NAlaser microfabrication system are investigated by Debyevectorial diffraction theory. The relationship between intensitydistribution of focused MBs and phase factors imprinted onMBs by SLM, including feature parity, ellipticity parameter q,and integer m, is theoretically and experimentally studied. Onthis basis, a simple method to fabricate 3D microcages byprecisely scanning the MBs and Bessel beams (BBs) along theZ direction in the photoresist is proposed and experimentallyverified. This strategy exhibits great flexibility because thepatterned focus can be dynamically controlled. The fabricationspeed can be increased by 2 orders of magnitude comparedwith conventional single-point direct laser writing. Finally,effective trapping/sorting (SiO2 particles) and trapping/culturing (in vivo culturing of yeast) using the resultant 3Dmicrocages are demonstrated, leading to applications inmicrofluidics and biomedical study.

RESULTS AND DISCUSSIONMathieu Beam Generation. The generation of MBs is

accomplished by displaying the phase of MBs on the SLM,behind which nondiffraction MBs are reconstructed on-axis.The phase masks we imprinted on SLM for even, odd, andhelical MB generation can be expressed, respectively, as33

φ η ξ

ξ η

=

= =

M q

C Je q ce q m

Im(log ( , , ))

Im(log( ( , ) ( , ))), 0, 1, 2, 3...me

me

m m m(1)

φ η ξ

ξ η

=

= =

M q

S Jo q se q m

Im(log ( , , ))

Im(log( ( , ) ( , ))), 1, 2, 3...mo

mo

m m m (2)

φ η ξ

η ξ η ξ

=

= ± =

M q

M q M q m

Im(log ( , , ))

Im(log( ( , , ) ( , , ))), 1, 2, 3...

mHM

mHM

me

mo

(3)

Here, Jem(ξ, q) and Jom(ξ, q) are the even and odd modifiedMathieu functions of order m, and cem(η, q) and sem(η, q) arethe even and odd ordinary Mathieu functions of order m, andCm and Sm are constant. The ellipticity parameter is defined asq = f 2kt

2/4, where kt is the transverse spatial frequency and f isthe semifocal distance. Elliptical coordinates (ξ, η) are given byCartesian coordinates (x, y) of SLM pixels through thetransformation x = f cosh ξ cos η; y = f sinh ξ sin η.Figure 1a illustrates the experimental setup of TPP

fabrication using MBs. The incident Gaussian beam ismodulated by a computer-generated hologram (CGH)displayed on the SLM. All the CGHs used in the experimentneed to be pretreated, as shown in Figure 1b. Handling CGHsin this way serves two purposes. First, due to the pixilationeffect of the SLM, blazed grating (BG) phase can separate thezero-order light away from the other modulated light. Thus,with an iris diaphragm, the effect of zero-order light on thefabricated microstructures can be effectively reduced. Second,because the cross section of Gaussian light incidents on theSLM is circular, the CGHs are also tailored to a circle to bettermatch the incident light. The phase distribution of BG isexpressed as 2πx/Δ, in which Δ represents the period of theBG (15 pixels), and the pixel pitch of SLM is 8 μm. So the finalphase distribution of the CGH loaded on SLM can beexpressed as Ph(x,y) = mod(φm(x, y) + φBG(x, y),2π), where“mod” is the remainder operation, φm(x, y) is the Mathieubeam phase, and φBG(x, y) is the BG phase.The intensity distribution of MBs along the propagation axis

is calculated by the Fresnel diffraction theory as the paraxialapproximation condition is satisfied. The intensity profiles inthe transverse direction, at distances of 0.4, 0.7, 1.0, 1.3, and1.6 m from the SLM, are calculated and experimentallymeasured (Figure S1). It can be seen that the intensity profileschange little both in theoretical prediction and in experimentalmeasurement, which demonstrates the propagation invariantproperty of MBs.Further, simulation of the transverse intensity distribution of

the reconstructed optical field at different planes is shown inFigure 1c. The intensity distribution from plane 1 to plane 4corresponds to the intensity distribution at the front plane ofLens1 (600 mm), focus of Lens1, back of Lens2 (200 mm),and the entrance pupil of the objective, respectively. It is foundthat the intensity distributions exhibit a main multifoci ring

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containing most of the energy and additional surroundingpattern containing much lower energy. An iris was placed atthe Fourier plane of Lens1 to filter out unwanted orders and letMBs pass through, as shown in Figure S2.Focusing Properties under High Numerical Aperture

Objective Lens with Different Focal Length Ratio LensGroup in a 4f System. It is well-known that the diffractionbehavior of light tightly focused by a high NA objective isdifferent from the scalar diffraction.34 In order to facilitate thevisualization of the field distribution at the focal region, weused Debye vectorial diffraction theory for optical fieldsimulation.35 The intensity distribution in the focal regioncan be rewritten as36

∫ ∫λθ θ θ φ

θ θ φ

θ φ θ φ

=

× [ +

+ ]

α πE x y z

iCP

ikn z x

y

( , , ) sin cos ( , )

exp ( cos sin cos

sin sin ) d d

1 1 1 10 0

2

1 1 1 1

0 1 1 1 1 1

1 1 1 1 1 (4)

where C is a constant; λ is the wavelength of incident light; n0is the refractive index of the immersion medium; α is themaximum focusing angle of the objective lens and can becalculated by α = arcsin(rNA/Rn0); r is the off-axis coordinateof the incident wave; R is the object lens pupil radius; θ1 is thefocusing angle of the objective lens, and φ1 is the azimuthal

angle of object plane. P(θ1, φ1) is the polarization state of theEM field in the focal region, which can be expressed as

θ φ θ φ

θ φ φ θ φ

= [ + − ]

+ [ − ] −

P i

j k

( , ) 1 (cos 1)cos

(cos 1)cos sin (sin cos )

1 1 12

1

1 1 1 1 1 (5)

for incidence with linear polarization in the X direction.In the TPP fabrication system, many factors will affect the

light field distribution, such as the focal length ratio of the lensin the 4f system. To show the effect of focal length ratio on thefocused light under high NA objective lens, theoreticalsimulations and experiments are conducted. According to eqs4 and 5, taking the even-MBs, for example, simulated opticalintensity distribution with the focal length ratio of lenses L1and L2 changed from 1:1 to 5:1, as shown in Figure 2. As thefocal length ratio of the lenses L1 and the L2 becomes larger,the diameter of the light field entering the pupil is reduced(Figure 2a) and the diameter of the focused light field (Figure2b) under the objective lens becomes larger (marked in awhite line) and the Z direction is stretched (Figure 2c). Thereason is that the numerical aperture of the objective lens isnot fully utilized due to the smaller diameter of the incidentbeam. The ratios of 1:1 and 3:1 were experimentally measured(shown in Figures S3 and S4), which is in agreement with thetheoretical prediction. It is found from the experimental lightfield in the X−Y plane along different Z positions that adiscrete intensity profile becomes a single-ring structuregradually. With this factor, it is possible to obtain focusedlight with different diameters and different Z direction lengthsby changing the ratio of the lens groups.

Optical Intensity Distributions and CorrespondingMicrostructures Fabricated by Mathieu Beams withDifferent Feature Parity and Integer m. Mathieu beamsare characterized by three parameters: the feature parity, theellipicity parameter q, and the integer m, which is termedtopological charge. We systematically studied the effects ofthese parameters on the intensity profile of MBs and the finalfabricated microstructures. On the basis of eqs 1−3, it can beseen that only in the case of even-MBs, the integer m beginsfrom 0 and the remaining two cases are from 1. Figure 3a is aseries of CGHs with different parameters for even-MBs, inwhich the bright and dark gray values correspond to a phase of0 and π, respectively. These CGHs have a similar feature parity(even) and ellipicity parameter q of 5 without the loss ofgenerality. The integer m changes from 0 to 6 successively.From the simulated results in Figure 3b, it can be seen thateven-MBs show multifoci arranged in a ring manner at thefocal plane. Around the focus ring, there is still a little straylight with weak intensity. Apparently, the number of focus Nm

e

in the ring is directly related to the integer m, which can beexpressed as Nm

e = (m + 1) × 2 (m = 0, 1, 2, 3) and Nme = m × 2

(m ≥ 4). The diameters of the rings remain unchanged. Themeasured results are consistent with the simulation (Figure3c). In the experiment, a focused optical field is projected intoa ∼8 μm thick SZ2080 photoresist sample, and complex 2Dmultifoci patterns can be fabricated by single exposure withoutsingle-point scanning. In order to ensure sufficient TPP allthrough the polymer, a longer focal length in the Z direction isneeded, then the focal length ratio of lenses L1 and L2 isselected as 3:1. All the microstructures are fabricated with alaser power of 110 mW, which is measured in front of theobjective, and an exposure time of 100 ms (Figure 3d). Similarresults for odd-MBs are shown in Figure 3e−h. Likewise, the

Figure 1. Dynamic holographic femtosecond laser processingsystem and the propagation properties of generated MBs. (a)Schematic diagram of an SLM-based fabrication system. HWP, halfwave plate; GTP, Glan laser beam splitter; Lcos-SLM, liquid-crystal-on-silicon spatial light modulator; M, mirror; L, lens.Femtosecond laser is modulated to MBs by the SLM, whichdisplays the designed holograms. (b) Illustration of the computer-generated hologram. (c) Simulated transverse intensity distribu-tion of MBs at different planes along the propagation direction inthe optical systems. Plane 1 to plane 5 correspond to front ofLens1, focus of Lens1, back of Lens2, front of objective, and focusof objective, respectively.

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measured intensity profile and fabricated microstructure agreewell with the simulation. It is worth noting that the relationshipbetween the number of focus Nm

o and the integer m is differentfrom the even-MBs, which can be expressed as Nm

o = m × 2.The results for helical MBs are shown in Figure S5, and therelationship between the number of focus Nm

H and the integerm is the same as the odd ones.We can find that the multifoci microstructures are not

perfectly homogeneously polymerized. This is caused by threeaspects. First, the optical system in the experiment was notperfect. For example, all lenses in the optical system are hardly100% completely coaxial, and it is difficult to completelyguarantee the laser beam focus perfectly vertically to thesample after passing through the microscope system. Thesenonideal hardware conditions may bring errors to thefabrication. Second, there is a refractive index mismatchbetween different materials behind the objective, which willbring aberrations. Finally, linear polarization incidences alsolead to an inhomogeneous intensity distribution after high NAfocusing. In order to enhance the resolution and uniformity offabricated final structures, the point spread function of thepatterned focus can be optimized by compensating theaberration of high NA fabrication systems.37−39

Optical Intensity Distributions and CorrespondingMicrostructures Fabricated by Mathieu Beams withDifferent Ellipicity Parameter q. From previous results, it isobvious that when the ellipicity parameter q is constant, thediameters of the microring structures are constant at differentintegers for all even, odd, and helical MBs. Here, we take theeven-MBs with integer 6 as an example to analyze the effect ofq on the diameter of the fabricated microstructure, without the

loss of generality. Figure 4a is a series of CGHs for thegeneration of even-MBs with the same integer m = 6 and a setof different ellipticity parameters. From the simulated results inFigure 4b, it can be seen that the diameter of the intensitypattern at the focal plane increases with the ellipticityparameter changing from q = 1 to q = 20. The measureddiameter change is consistent with theoretical simulation.Meanwhile, the smaller the ellipicity parameter became, themore evenly spaced the multifoci is. In Figure 4d, all of themicrostructures are fabricated by a single exposure with theintensity profile in Figure 4c in a ∼8 μm thickness SZ2080photoresist sample. When the ellipticity parameter is q = 1, thesingle exposure time is 80 ms with a laser power of 100 mW.When the ellipicity parameter is q = 15, the single exposuretime is 400 ms and a laser power of 140 mW is needed. As thediameter of the microstructure increases, the needed singleexposure time and laser power also increase. All processingparameters are displayed in Table 1 in the SupportingInformation. As mentioned in the above section, the focallength ratio of lenses L1 and L2 is selected as 3:1 to ensure thatTPP occurs all through the polymer. For the precise control ofmicrostructure diameter, a quantitative study between thediameter and ellipticity parameter q is conducted. The red linein Figure 4e represents the simulated results. When ellipticityparameter q changes from 1 to 20, the diameter ofmicrostructures varies from 4.3 to 21 μm. The black linerepresents the average of five measured microstructures underthe same experimental conditions. Correspondingly, theaverage diameters of microstructures vary from 4.1 to 20.2μm. In the simulation, the diameters are calculated accordingto the full width at half-height of the intensity distribution. It

Figure 2. Simulated optical intensity distribution at the pupil and the focal region of a 1.35 NA oil immersion objective for Mathieu beamswith different ratio between Lens1 and Lens2. (a) Intensity distribution at the pupil of the oil immersion objective. (b,c) Intensitydistributions at XZ and XY planes of focused Mathieu beams. The hologram for the simulation is even-MBs with integers m = 6 and q = 6,without the loss of generality.

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should be noted that a wider range of diameters of themicrostructures could be obtained when an appropriate beamreducer and low magnification objective are used.The deviation between measured and calculated diameters

may come from two aspects. The first and the most importantreason is the shrinkage of the photoresist, especially when thelaser exposure dosage is close to the photoresist polymerizationthreshold. The second reason is that the simulation is based ona series of ideal experimental conditions. For example, theincident light we supposed is a uniform standard Gaussianbeam, and the optical system is idealized. Actually, errors willbe caused by the pixelization of holograms, the high NAobjective system, and the nonideality of the optical system.With this MB-based TPP processing, a complex 2D

microstructure can be easily fabricated combined with themovement of the sample anchored to the piezoelectricplatform. Figure 4f,g and Figure S5 are the SEM andfluorescence images of patterned microring array. Theprocessing parameters for each microring are the same as inFigure 4d.Dynamic Holographic Processing of Various Control-

lable 3D Microcages. Based on systematic study on TPPwith MBs, a method for rapid fabrication of 3D microcages byscanning patterned focus along the Z direction is proposed.Different from the conventional TPP process by single-point

scanning, this method can greatly reduce the processing time.Furthermore, by changing the tailored holograms during thescanning of patterned focus with evenly spaced, microcageswith variable cross section could be successfully produced.With this dynamic holographic processing method (DHP), wecan easily and rapidly fabricate different kinds of microcages.Figure 5a is the schematic illustration of the DHP method.Different layers are processed by MBs and BBs. Taking single-layer microcages as an example, the stretching speed of theplatform is 50 μm/s and the designed height of the bottompillars in the microcages is 15 μm. So the fabrication time is 0.3s, which means the hologram (Mathieu beam) is displayed for0.3 s. Meanwhile, the designed height of the junction in themicrocages is 3 μm, making the fabrication time 0.06 s, whichmeans the hologram (Bessel beam) is displayed for 0.06 s.Therefore, with the integrated control software, the dynamicholographic processing has been realized. We define theexposure time as the fabrication time. In the experiment, thethickness of photoresist is ∼500 μm, which ensures that thereis enough space to process the 3D microcages. For precise 3Dmicrofabrication, a higher Z direction resolution is required,and the focal length ratio of lenses L1 and L2 is selected as 1:1.Figure 5b is the SEM image of single-layer microcages witheight pillars at the bottom. The microcages have ∼18 μmheight and ∼10.5 μm diameter. The fabrication time for one

Figure 3. Numerical simulations, experimental measured intensity profile, and fabrication results of MBs with different feature parity andinteger. (a) Holograms for even-MBs with different integers from m = 0 to m = 6, while fixing q = 5, without the loss of generality. (b)Calculated and (c) measured intensity distribution in the X−Z plane at the focus plane. (d) SEM images of multifoci microstructures bysingle exposure of femtosecond MBs. All the microstructures are fabricated with a laser power of 110 mW and an exposure time of 100 ms.(e) Holograms for odd-MBs with different integers from m = 1 to m = 7, while fixing q = 5. (f) Calculated and (g) measured intensitydistribution in the X−Z plane at the focal plane. (h) SEM images of multispot microstructures by single exposure of femtosecond MBs. Theprocessing parameters are the same as mentioned in (d). All scale bars are 5 μm.

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single-layer microcage is 0.36 s, whereas it increases to 54 s forconventional single-point scanning (Figure 5c), which meansthat the fabrication time can be reduced by 2 orders ofmagnitude. Figure 5d is the SEM image of two-layermicrocages with eight pillars at the bottom layer and sixpillars at the top layer. The microcages have ∼36 μm heightand ∼10.5 μm diameter. The stretching speed for fabrication is50 μm/s, whereas the used power is 90 mW. Similarly, thefabrication time can reduce from 102 to 1.12 s (Figure 5e)compared with single-point TPP processing in theory. Figure5f is the SEM image of three-layer microcages with eight pillarsat the bottom, six pillars at the middle, and four pillars at top.The microcages are ∼54 μm in height, and the diameters arethe same as in Figure 5b,d. Compared to the single-pointscanning method, the fabrication time is 100 times less.Because the scanning strategy is moving the sample along

the Z direction, the height of the microcages could befabricated as long as the working distance of the oil immersionlens. Therefore, this processing method can fabricate highaspect ratio microcages (Figure 5h). These microcages have∼90 μm height, and the aspect ratio is 9:1 approximately.Further, the location of microcages can be well designed; forexample, a “USTC” pattern was designed by microcages withdifferent heights (Figure 5i). It is challenging for othertechniques to fabricate these 3D microcages, and thus ourapproach shows the distinct advantages in terms of 3D andcustomization capabilities.

3D Microcages for Trapping Microobjects. The abilityto manipulate microobjects is highly desirable in biologicaldevices and chemical analysis and has drawn great attention.Although entirely new perspectives are provided by thecomplex patterning of light fields in advanced optical tweezermicromanipulation,40 substantial 3D microstructures are stilldesired to be fabricated so that the energy beam does not causeharm to living samples or chemical reactions. In this work, wedemonstrate the feasibility of 3D microcages fabricated byDHP for trapping particles, as illustrated in Figure 6a. Adeionized water solution containing 5 μm diameter SiO2

particles is dropped on the sample, which is fabricated on aglass slide. Part of particles are trapped in the microcages bygravity and hydrodynamic forces. Then, the sample is cleanedby deionized water and shaken slightly to flush the nontrappedparticles away. The trapped particles are confined in themicrocages (Figures 6b−d). Trapping efficiency is animportant factor to evaluate the trapping capability. We definethe trapping efficiency as the ratio of the microcages that trapSiO2 particles with success to the total number of microcages.In our experiments, the trapping efficiency can reach morethan ∼90% (Figure 6a and Figure S7) when the number ofrepeating cycles exceeds 5. After we repeated the trappingexperiments for several times (>5), the microcages can trapmicroparticles in every experiment and have no obviousdeformation.

Figure 4. Controlling the diameter of fabricated microstructures by tuning the ellipticity parameter of MBs. (a) Holograms for even-MBswith different ellipticity parameter from q = 1 to q = 20, while fixing m = 6. (b) Calculated and (c) measured intensity distribution in the X−Z plane at the focus plane. (d) SEM images of multifoci microstructure fabricated by a single exposure of femtosecond MBs with differentdiameters from 4.1 to 20.2 μm. (e) Dependence of the diameter of the polymerized microring on ellipticity parameter q. The inset shows themeasured diameter. (f) SEM and (g) fluorescence images of a “microring array” pattern. All scale bars are 10 μm.

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In recent years, microobject sorting has been important toenrich or purify biosamples into well-defined groups for plentyof applications. A variety of microfluidic sorting methods basedon 2D substrates have been developed to separate micro-particles based on size.41,42 Here, we show that our 3Dmicrocages can separate particles of different diameters bychanging the number of pillars at the bottom, similar to theprocess in Figure 6a. A deionized water solution containingdifferent SiO2 particles with various diameters (e.g., 2, 3, 4, 5, 6,and 7 μm) is dropped on the samples fabricated on the slide.There are two types of microcages. One is single-layermicrocages with four pillars at the bottom (Figure 6e), andthe other is single-layer microcages with eight pillars at thebottom (Figure 6h). Due to different number of pillars, thedistance between the pillars is different. For four pillarsmicrocages, small particles (2 and 3 μm) will be washed outfrom the gap (∼4.3 μm) between two adjacent pillars, whilelarge particles (5 and 6 μm) remain inside the microcages(Figure 6f,g). In contrast, both small and large particles remaininside the microcages with eight pillars (Figure 6i,j), due tosmaller pillar gap (∼1.2 μm). Therefore, particle sorting isachieved by these microcages with different shapes.In general, the growth environment of cells in vivo is mainly

3D microenvironments, in which cell behaviors are differentfrom that in 2D substrates. Here, the microcages can act asfunctional 3D cell culture scaffolds for cell trapping andculturing. As shown in Figure 7, yeast cells (Angel Yeast Co.,Ltd.) are trapped and then subsequently cultured in liquidculture medium. The trapping of yeast is realized by droppinga few drops of high concentration yeast culture medium on the

microcages. A part of the yeast are trapped in the microcagesby gravity and hydrodynamic forces, after which the sample iscleaned by the culture medium. Finally, the growth anddividing process of trapped yeast is observed in situ with abright-field microscope for 3 h in 20 mL of culture medium.The 3 h culturing of yeast in the microcage can be divided

into two steps. The first step is the growth of the primarygeneration of yeast (Figure 7a−c). The second step is thebudding process and the growth of the first generation of yeast(Figure 7d−f). The dependence of the diameter of the yeast onculture time is shown in Figure 7g. With the increasing ofculture time, the diameter of the primary generation of yeastincreases obviously in the first step (blue area) but enlargeslittle when the budding process starts (gray area). After 0.5 h ofculture, the first generation of yeast grows to a normal volume.The SEM images of the 3D microcage with the cultured yeastare shown in Figure 7h. This method provides a valid solutionfor observing cellular behaviors in the 3D microenvironment.

CONCLUSION

In summary, a rapid and flexible 3D microcage fabricationmethod based on dynamic holographic processing isdeveloped. The focusing properties of MBs generated byphase modulation are theoretically and experimentallyinvestigated. The 2D circle microstructures with multifoci arefabricated by single exposure of focused MBs. Moreover, 3Dmicrocages with various geometries are fabricated bydynamically controlling the different patterned focuses.Compared with the traditional single-point scanning directlaser writing, the fabrication speed can be increased by 2 orders

Figure 5. Various kinds of 3D microcage fabrication with the dynamic holographic processing technique. (a) Illustration of the fabricationprocess of a three-layer microcage. Different layers are processed by MBs and BBs. The scanning speed is 50 μm/s, whereas the used poweris 90 mW. (b,d,f) SEM images of different kinds of microcages. (c,d,f) Quantification of single structure processing time. The black columnrepresents dynamic holographic femtosecond laser processing, and the red column represents single-point scanning. (h) SEM image for highaspect ratio microcages (height: ∼90 μm). (i) 3D microcage array with two different heights distributed in the “USTC” pattern. All scalebars are 10 μm.

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of magnitude. These 3D microcages are demonstrated to havefine ability in trapping SiO2 particles with a high trapping ratioand sorting microparticles with different shapes. Finally, the3D microcages are used as cell culture scaffolds for theobservation of growth and budding of yeast. We believe thesecontrollable 3D microcages can act as a capture−hold−analyzesystem for a broad applications such as microfluidics andbiological research.

METHODSNumerical Simulation of the Intensity Distribution in the

Focal Region under a High NA Objective. It is crucial toinvestigate the focusing properties of the MBs. Because the paraxialapproximation does not consider the vectorial nature, in this work, weuse Debye vectorial diffraction theory, which describes thedepolarization effect of a high NA object by calculating the threeorthogonal field components Ex, Ey, and Ez.Hologram Generation. In this work, we use Matlab software to

generate and compute holograms (BG’s hologram and Mathieubeam’s hologram). All the holograms are designed to be matrixes withthe same dimension (1080 × 1080 in our experiments) correspondingto the modulated liquid crystal panel pixels of SLM. Every elementvalue in the matrixes is the phase to be modulated. As is known, theincident wavefront can be expressed as E(x,y) = A(x,y)eiφa(x,y). When it

propagate through a pure phase plate ϕ(x,y) = eiφb(x,y), the modulatedoutput beam can be expressed as Eout(x,y) = E(x,y) × ϕ(x,y) = A(x,y)ei[φa(x,y) + φb(x,y)]. In our experiment, we can modulate the incidentGaussian beam by the Mathieu beam’s hologram phase φm(x, y) andthe BG’s hologram phase φBG(x, y), so we just need to add twomatrixes together numerically. The final phase distribution should beloaded on the SLM is Ph(x, y) = mod(φm(x, y) + φBG(x, y),2π),where “mod” is a remainder operation.

Materials and Equipment. A commercially available zirconium−silicon hybrid sol−gel material doped with 4,4′-bis(diethylamino)-benzophenone photoinitiator at 1 wt % (SZ2080, IESLFORTH) wasused for photopolymerization in our experiment. Before micro-structure processing, the SZ2080 was placed on a thermal platform setto be 100 °C for 1 h to evaporate the solvent. The femtosecond lasersource is a mode-locked Ti:sapphire ultrafast oscillator (Coherent,Chamleon Vision-S) with central wavelength at 800 nm, pulseduration of 75 fs, and repetition rate at 80 MHz. The laser power ismodulated with a half-wave plate and a Glan laser beam splitter. Afterexpansion, the laser beam illuminates a phase-only SLM (Pluto NIRII,Holoeye, 1920 × 1080 pixels, 256 gray levels, and pixel pitch of 8μm). The modulated beam is relayed to a 4f system and focused by ahigh NA object lens (60×, NA = 1.35, Olympus) into the photoresist,which is mounted on a piezoelectric platform (E545, from PhysikInstrumente GmbH & Co. KG, Germany) with nanometer resolutionand a 200 μm × 200 μm × 200 μm moving range. After

Figure 6. Microparticle trapping and sorting by microcages with different pillar numbers. (a) Schematic procedure for the trapping of SiO2particles. Deionized water solution containing 5 μm diameter SiO2 particles is dropped on the sample. Then, the sample is put in a Petri dishwith deionized water and shaken slightly to flush away free particles. At last, almost all microcages are filled with particles after repeating thisprocess several times. (b) SEM image of the sample after trapping SiO2 particles. (c) Tilted view (45°). (d) Magnified view. (e,h) Schematicdiagram for separating particles of different diameters using two different kinds of microcages. (f,g,i,j) SEM images of the separating resultswith top view and tilted view (45°). It is obvious that the microcages with four pillars (gap: ∼4.3 μm) at the bottom can only trap largediameter particles (5 and 6 μm) and small particles (2 and 3 μm) are washed out from the gap (∼4.3 μm) between two adjacent pillars,whereas the microcages with eight pillars (gap: ∼1.2 μm) at the bottom can trap particles with different diameters. All scale bars are 10 μm.

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polymerization, the sample was developed in 1-propanol for 1 h untilall of the unpolymerized parts were washed away.Manipulation of Microparticles. SiO2 microparticles with

different diameters synthesized by Wakely Scientific Corp. Inc. weremixed in deionized water solution with a concentration of 10−3 gmL−1. In order to make the SiO2 particles evenly distributed in thedeionized water solution, the container was shaken gently. The samplewas horizontally placed on the stage of an optical microscope (LeicaDMI3000B). The solution was dropped on the sample by a pipet, andmost particles sank to the bottom after 10 min. In this process, a partof particles were trapped within the microcages. Then, the samplewith trapped particles was transferred to a Petri dish with deionizedwater to wash untrapped particles away. Finally, the sample wasmounted on the stage for a few minutes for the evaporation of the restof the deionized water. This process is repeated for several times inorder to achieve a high trapping ratio.Yeast Culture. A kind of Saccharomyces cerevisiae (Angel Yeast

Co., Ltd.) was used in the culture experiment. The liquid culturemedium was produced by sterilizing the mixture of solid granularSabouraud’s glucose broth medium (10.0 g L−1 peptone, 40 g L−1

glucose, pH 5.6 ± 0.2 at 25 °C, QingDao Hope Biotechnology CO.,Ltd.) and distilled water with a concentration of 50 g L−1 at 120 °Cfor 20 min. The high concentration yeast medium was produced bydissolving 0.1 g of dry yeast uniformly into 15 mL of liquid culturemedium.Imaging Characterization. The SEM images were taken with a

secondary electron scanning electron microscope (ZEISS EVO18)operated at an accelerating voltage of 10 keV, after the samples weresputter coated with gold. The gold vaporization time is 80 s, and thegold thickness is ∼10 nm.

ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acsnano.9b00893.

More details about numerical simulation, experimentalresults, and discussions (PDF)

AUTHOR INFORMATIONCorresponding Authors*E-mail: ygliang@ustc.edu.cn.*E-mail: dongwu@ustc.edu.cn.ORCIDLiang Yang: 0000-0001-6103-6451Yanlei Hu: 0000-0003-1964-0043Jiawen Li: 0000-0003-3950-6212Dong Wu: 0000-0003-0623-1515Jiaru Chu: 0000-0001-6472-8103NotesThe authors declare no competing financial interest.

ACKNOWLEDGMENTSThis work was supported by the National Natural ScienceFoundation of China (Nos. 61475149, 51675503, 51875544,61805230, 11801126), the Fundamental Research Funds forthe Central Universities (WK2090090012, WK2090000013,WK2480000002, 2192017bhzx0003), Youth Innovation Pro-motion Association CAS (2017495), and National Key R&DProgram of China (2018YFB1105400). We acknowledge theExperimental Center of Engineering and Material Sciences atUSTC for the fabrication and measuring of samples. This workwas partly carried out at the USTC Center for Micro andNanoscale Research and Fabrication.

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Figure 7. Microcage as 3D culture scaffold for yeast trapping and culturing. (a) Yeast is trapped by a 3D microcage for culturing. Thediameter of the primary yeast is 4.2 μm. (b) After 1.0 h of culture, the diameter increases to 5.5 μm. (c) After 2.0 h of culture, the diameterincreases to 6.5 μm. (d) Diameter of the primary yeast changed little after 2 h of culturing. Afterward, it begins to bud at ∼2.3 h; thediameter of the first generation of yeast is 0.5 μm at 2.5 h, 2.6 μm at 2.7 h (e), and 4.5 μm at 3 h (f). (g) Dependence of the diameter of theyeast on culturing time. (h) SEM images of the 3D microcage with the cultured yeast. All scale bars are 5 μm.

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