Femtosecond Optical Trap-Assisted Nanopatterning through

Article pubs.acs.org/JPCC

Femtosecond Optical Trap-Assisted Nanopatterning through Microspheres by a Single Ti:Sapphire Oscillator Aleksander M. Shakhov,†,‡ Artyom A. Astafiev,*,† Dmytro O. Plutenko,†,§ Oleg M. Sarkisov,† Anatoly I. Shushin,† and Viktor A. Nadtochenko†,∥,⊥ †

Semenov Institute of Chemical Physics RAS, Kosygina st. 4, Moscow 119991, Russian Federation Moscow Institute of Physics and Technology, Institutskiy lane 9, Dolgoprudny, Moscow Region 141700, Russian Federation § Institute of Physics of National Academy of Sciences of Ukraine, Prospekt Nauki 46, 03680, Kiev, Ukraine ∥ Department of Chemistry, Moscow State University, GSP-1, Leninskiye Gory 1-3, 119991 Moscow, Russian Federation ⊥ Institute of Problems of Chemical Physics RAS, Academician Semenov avenue 1, Chernogolovka, Moscow region 142432, Russian Federation ‡

S Supporting Information *

ABSTRACT: A new approach for fabricating a range of patterns using femtosecond optical trap-assisted nanopatterning is presented. We report how a single Gaussian laser beam from a 55 fs, 80 MHz, 780 nm Ti:sapphire oscillator trapping dielectric microspheres near surfaces can be used to enable near-field, direct-write, subwavelength ∼λ/6 (∼130 nm), two-dimensional nanopatterning of a polymer surface. We discuss the stability conditions for effective manipulation of the particle by the pulsed beam. Klein−Kramers and Brownian motion models were used to analyze the positional accuracy of femtosecond tweezers. We studied effects of the microsphere size, pulsed laser energy and light polarization, and spacing between objective focal plane and polymer surface on the pattern size experimentally and theoretically. Microspheres with a diameter of about 1 μm provide the smallest patterns. The experimental results are reasonably matched by generalized Lorentz−Mie theory.

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INTRODUCTION Femtosecond lasers have established themselves as excellent and universal tools for structuring solid materials by direct ablative writing.1−8 This technique allows fabrication of largearea patterns and high-quality microstructures with structure sizes between 1 and 100 μm. In particular, periodic microstructures such as nanoripples, nanoparticles, nanocones, and nanospikes can be produced in almost any material using femtosecond pulses directly and without the need for masks or chemical photoresists to relieve the environmental concerns; for examples, see the recent review.9 Because of the light diffraction limit, the minimal size of the domain in which the freely propagating light can be localized is about half wavelength. Various optical nanopatterning techniques can overcome the theoretical diffraction limit of conventional focusing optics to create smaller feature sizes. Widely used methods include multiphoton absorption10,11 and near-field effects.12−20 Near-field effects can also be harnessed by coating a surface with a self-assembled array of microspheres18,20,21 and subsequently illuminating this surface with a laser pulse. This allows large areas to be patterned in a single shot, but only random and hexagonally close-packed patterns have been demonstrated.15,18−20 Optical trap-assisted nanopatterning addresses the challenges encountered with existing techniques. © 2015 American Chemical Society

For precise positioning of individual microspheres, optical tweezers can be employed.22 Here, Bessel beam continuous wave (CW) optical trap23 provides precise positioning of the microsphere on a surface without active feedback. CW laser optical traps can produce the radiation force with an order of a few piconewtons to manipulate micron-sized particles when the laser beam has the power of a few milliwatts. Pulsed lasers can produce the large peak radiation force with an order of nanonewtons. Ambardekar et al.24 used a pulsed laser to generate a large gradient force (up to 0.1 nN) within a short duration (∼45 μs) for overcoming the adhesive interaction between the particles and the surface. Deng et al.25 theoretically pointed out that the axial pulsed radiation force overcomes the adhesive interaction between the stuck particles and the surface and results in optical levitation due to the axial displacement. Agate et al. reported a comparison between the femtosecond and the CW optical tweezers and have found that femtosecond optical tweezers are as effective as CW optical tweezers.26 The average laser power is an important parameter for optical trapping of micron-sized particles by using high-repetition-rate femtosecond pulsed light beams.27 Shane et al.28 reported Received: January 16, 2015 Revised: May 7, 2015 Published: May 7, 2015 12562

DOI: 10.1021/acs.jpcc.5b00478 J. Phys. Chem. C 2015, 119, 12562−12571

Article

The Journal of Physical Chemistry C

move the sample relative to the laser beam focus. Laser polarization is controlled by a quarter-wave plate (Thorlabs). Manipulation of Samples: Sample Cell, Polymer Films, Beads. Figure 1 shows the sample cell construction. The sample cell is made as a cover glass−scotch tape−cover glass sandwich. The cavity in the scotch tape is filled with a droplet of microsphere water solution. The second glass plate covered by a polymer film is put on the scotch tape in such manner that the polymer contacts water. Deionized water, 2−3 layers of Scotch Magic tape of 62.5 μm thickness, and cover glass of 150 μm thickness (Menzel-Gläzer) are used. Polyacrylate polymer films are formed from a mixture of ethoxylated bisphenol A diacrylate (CAS Registry 64401-02-1) with Darocuor 4265 photoinitiator in mass proportion 95:5. A droplet of mixture is spread by spin coating techniques on the cover glass. The film is polymerized under a low-pressure germicidal mercury lamp (9 W). Thickness of the polymer films produced is 75 ± 20 μm. Optical absorption spectra of the polymer film are detected by a Shimadzu UV-3600 spectrophotometer. Beads from Cospheric LLC made of silica (n = 1.457) or polystyrene (n = 1.58) with diameters in the range from 0.55 to 3.8 μm are used. Positioning of Focal Plane. Position of the objective focal plane is controlled by a Z-piezo stage. The intensity of the backward reflected Ti:sapphire femtosecond laser radiation is registered by the CCD camera (PI-MAX Roper Scientific). A spatial filter (pinhole) is installed between the microscope port and the CCD camera to restrict the visible area to the focal spot. We assume that the objective focal plane coincides with the sample surface when the intensity of registered backreflected light is maximal (see Supporting Information, section SI 1, Figure S1). AFM Measurements. The sample surface after optical trapassisted nanopatterning is scanned by tapping-mode atomic force microscopy (AFM) (NT-MDT) with the NSG11S semicontact cantilever. Samples are rinsed by acetone and distillated water before AFM measurements. Positional Accuracy Measurement. Positional accuracy is measured as a function of average trapping power. A 6× zoom telescope attached to the microscope side port is used to magnify the image and transfer it to the CMOS-camera sensor (Thorlabs DCC1645M, 1280 × 1024 pixels). The bead image on the camera represents an Airy pattern. Matched filter method is utilized to find the bead center position through calculation of cross-correlation function between the central peak of the Airy pattern and the Gaussian distribution. Correspondence between position of the bead center on the camera image and real bead coordinates is found through a special calibration procedure. It relies on movement of a bead over a known distance by the piezo-stage. Ad hoc program code performs capture of camera image and yields bead position statistics at 15 fps. Positioning accuracy is calculated as root-mean-square deviation for 1000 measurements in accordance with the following formula:

three-dimensional (3D) optical trapping by using a 12 fs pulsed laser with 80 MHz repetition rate and concluded that “the linear optical trapping using pulsed lasers is independent of the pulse’s duration or time profile”.29 Pan et al. realized the transverse two-dimensional (2D) optical trapping of CdTe quantum dots by a high-repetition-rate picosecond pulsed laser with an input power as low as 100 mW.30 De et al.31 demonstrated the stable optical trapping of latex nanoparticles (with diameter of about 100 nm) with ∼120 fs pulsed laser at power levels where CW lasers cannot lead to a stable optical trap. Optical trap-assisted nanopatterning involves many parameters that can be employed to meet requirements of different applications. In this work we vary the microsphere material and size, femtosecond laser average power and light polarization, and spacing between objective focal plane and sample surface. The main goal of the present work is studying optical trapassisted nanopatterning when a focused 80 MHz, 55 fs, 780 nm laser beam is simultaneously used as a Gaussian optical trap and a nanopatterning tool. We demonstrate arbitrary 2D surface structures created with the microsphere used as a lens focusing femtosecond laser radiation and individual features smaller than 200 nm, which is less than one-third the processing wavelength.

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METHODOLOGY Experimental Details. Laser Microscopy Setup. Figure 1 shows the optical scheme of laser microscopy setup. Femto-

Figure 1. Optical scheme of laser microscopy setup. Inset shows a microsphere trapped by the femtosecond tweezers near the polymer film.

second laser pulses are focused by a 60× 0.7 NA objective lens (Olympus) of the Olympus IX71 inverted microscope. A beamsplitter (Melles-Griot 50/50) or ultrabroadband laser mirror (Newport 10B20UF.25) is used for coupling of laser beam to the objective lens. A femtosecond Ti:sapphire oscillator (Spectra-Physics Tsunami) pumped by 532 nm radiation from a Coherent Verdi V8 CW laser generates femtosecond pulses with 80 MHz repetition rate at 780 nm with average power up to 300 mW. Laser power is attenuated with a rotating zero-order half-wave plate installed before the linear polarizer. An SF10 prism compressor is used for dispersion compensation. The time duration of the femtosecond pulse at the microscope focal plane is measured by the autocorrelator (AA-M Avesta) and is equal to 55 fs. The microscope is equipped with a CMOS camera (DCC1545 M Thorlabs). A 3D scanning piezo-stage (custom-made, NT MDT) positioned by LabVIEW program code is employed to

⎤1/2 ⎡1 ⟨r ⟩ = ⎢ (⟨x⟩2 + ⟨y⟩2 )⎥ ⎦ ⎣2

(1)

where ⟨x⟩ and ⟨y⟩ is mean square deviations along x and y axes, respectively. Accuracy of the method is measured as a root-mean-square deviation of an immobile microsphere placed on a cover glass and it is equal to 5 nm. 12563


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Figure 2. Crater and its section along minor axis: (a, c) without the microsphere and (b, d) with the 1.54 μm SiO2 bead. In panels a and c, exposure time is 16 s and average power is 40 mW. In panels b and d, exposure time is 20 s and average power is 22 mW. Laser pulses: 55 fs, 80 MHz, 780 nm.

Computational Details. Numerical modeling is performed by generalized Lorentz−Mie (GLM) theory.32 The traditional method used in scattering calculations is to assume that the actual incident field is equal to the paraxial field on the surface of the scatterer. Laser beams present some serious theoretical difficulties. These problems are due to the fact that standard representations of laser beams are not radiation fields. Their standard mathematical forms are not solutions of the vector Helmholtz equation but are solutions of the paraxial scalar wave equation, and higher-order corrections can be used to improve the accuracy as reality becomes less paraxial.33 Such pseudofields are only approximate solutions of the vector wave equation. The deviation from correctness increases as the beam is more strongly focused.34−36 As a result, an artificial dependence on particle position and size is introduced into scattering calculations because the differing multipole expansions correspond to different beams. This is obviously undesirable. In the present study, generalized scattering Lorenz−Mie theory is used for the calculation of electromagnetic near field for homogeneous isotropic sphere in a uniform isotropic medium.37,38 Incident Ei, scattered field Es and field inside a sphere El are represented as the sum of spherical harmonics: Ei =

∑

E =

∑

i i i i anm M nm + bnm Nnm s s s s anm M nm + bnm N nm

|m|≤ n > 0 l

E =

∑ |m|≤ n > 0

− μ ψn′(ηx)ψn(x)

1

l anm =

ξn(x)ψ ′(x) 1 ψ ′(ηx)ξn(x) μ n

− ξn′(x)ψn(x)

s bnm

=

1 ψ (x)ψn′(ηx) η n 1 ξ ′(x)ψn(ηx) μ n

l = bnm

ψn(x)ξn′(x) 1 ξ ′(x)ψn(ηx) μ n

1

− η ψn(ηx)ξn′(x)

−

i anm

i anm 1 ψ (ηx)ξn′(x) η n

1

− μ ψn′(x)ψn(ηx) 1

− η ξn(x)ψn′(ηx) − ψn′(x)ξn(x) 1

− η ξn(x)ψn′(ηx)

i bnm

i bnm

(3)

where η = nsph/nmed is the relative refractive index and μ = μsph/ μmed is the relative magnetic permeability. ψn(ρ) = ρjn(ρ) and ξn(ρ) = ρh(1) n (ρ) are Riccati−Bessel functions, and jn(ρ) and h(1) n (ρ) are spherical Bessel functions. Incident light is linearly or circular polarized, and the wavelength is 780 nm. The finite spectral width (20 nm full width at half-maximum (fwhm)) of the 55 fs pulse is not taken into account. Expansion coefficients for incident wave field can be determined by the far-field matching method.39 In the present work expansion coefficients are calculated by numerical integration carried out in a manner similar to that used by Barton.40 In contrast to Barton,40 in our work the integration is done over a sphere at infinity.41 It is assumed the angular intensity distribution of a modeled beam in the far field is Gaussian. The modeled beam overfills an objective lens input aperture as only the central part at fwhm overpasses the trough aperture and is focused in a sample plane. In all calculations, we use a limited number of spherical harmonics (5000). Near-field intensity distribution is strongly affected by the refractive index of the surrounding media.8 We assume the media to be uniform, with the refractive index equal to 1.33 (refractive index of water).

|m|≤ n > 0 s

=

1 ψ (ηx)ψn′(x) η n 1 ψ ′(ηx)ξn(x) μ n

s anm

l l l l anm M nm + bnm Nnm

(2)

Mnm and Nnm are vector spherical harmonics. The expansion coefficients for an incident wave electric field, a scattered wave electric field, and electric field inside a sphere are bounded as follows: 12564


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Figure 3. Crater depth (a) and width (b) versus the incident average laser power ⟨P⟩ when optical trap-assisted nanopatterning is performed with and without a 1.54 μm silica bead. ⟨I⟩ is the average intensity of the incident light. Exposure time is 20 s, and data is averaged by 8−10 craters. In panel a, data are fitted with a power function ⟨P⟩n, where n is 3 for curve 1 (with bead) and 3.5 for curve 2 (no bead). In panel b, red circles and black squares are fwhm of craters produced with bead along and perpendicular to the polarization, respectively; brown diamonds and blue triangles are respective fwhm of craters produced without bead. Laser pulses: 55 fs, 80 MHz, 780 nm.

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Light Intensity Distribution Calculated by GLM Approach. Figure 4 shows the light intensity distribution calculated by GLM approach without and with a 1 μm silica or polystyrene bead in water medium near the focal point of the microscope objective for linearly polarized focused CW radiation at 780 nm. In this work the bead is typically pressed

RESULTS AND DISCUSSIONS Morphology of Femtosecond Optical Trap-Assisted Nanopatterning: Fixed Optical Trap. Figure 2 demonstrates a typical crater formed without beads and a crater produced using the bead as a lens to focus the processing femtosecond laser beam when the bead is optically trapped by the same femtosecond laser beam. For linearly polarized light, the crater has an elliptical shape. The crater shape is close to circular without the bead. Figure 2 depicts an increase of the crater aspect ratio that is determined as the ratio d/(a + b),42 where a and b are the semimajor and semiminor axis of the ellipse, respectively, and d is crater depth. Major and minor axis are measured as full width at half-maximum of crater depth. We have a crater aspect ratio of 0.2 without the bead (Figure 2a,c) and 0.5 with the bead (Figure 2b,d). When circularly polarized light is used for nanopatterning with the bead, the crater shape is close to the circle. The crater depth almost does not depend on the light polarization (see Figure S2 in the Supporting Information). Role of Multiphoton Absorption in Nanopatterning of Polymer. Figure 3 shows the measured crater size versus the incident laser power when no bead is used and when nanopatterning is performed with a silica bead. Figure 3a indicates that about a 2-fold lower incident laser power is required to ablate the same depth crater with a bead. The dependence of the crater depth on laser power is approximated by ∼⟨P⟩3 where ⟨P⟩ is an average femtosecond laser power. The cubic dependence of the crater depth on incident laser power can be explained by the three-photon absorption in the polymer. Three-photon absorption of 780 nm femtosecond pulse corresponds to 260 nm (4.77 eV) wavelength, which falls within the polymer absorption band (see Supporting Information, section SI 3, Figure S4). At the same time, for trap-assisted nanopatterning, the crater width decreases slightly with increasing laser power (Figure 3b). This dependence suggests the increase of the trap stiffness at higher laser power. For small laser power, uniformity in crater width is tens of nanometers, but with increasing power, nanopatterning uniformity reaches the value of 15 nm or less than 10% of the crater size. At lower laser power, craters have depth comparable with the AFM measurement error and consequently their width is measured less accurately. We suggest that higher uniformity of crater sizes at high laser power might be explained by this reason.

Figure 4. Calculated intensity distribution Ipeak(x, y, z) near the focal point of the objective lens from left to right: (a) uniform medium (water), (b) silica microsphere in water, (c) polystyrene microsphere in water. x, y, z are coordinates measured from the bead center. White dashed lines indicate center of the bead and the focal point. Positions of the beads relative to the focal point correspond to the maximal intensity enhancement. The left graph shows intensity distribution along the z-axis in the y-plane for silica (blue curve) and polystyrene (red curve). The bottom graph shows intensity distribution along the x-axis (solid line) and y-axis (dashed line) for silica (3 and 4, blue curves) and polystyrene (1 and 2, red curves), respectively. Microsphere diameter is 1 μm, and the laser beam is focused by a 0.7 NA objective lens. Shift of the focal spot from the bead center corresponding to the maximal enhancement is 710 nm. 12565


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The Journal of Physical Chemistry C by optical forces to the sample surface. As a result, because of additional forces from the sample, the bead takes a position relative to the focal point different from the one in the uniform medium. We can shift focal point relative to the bead center to the position in which maximum intensity enhancement is achieved. The light distribution depends on the position of the bead center relative to the focal plane of the microscope. This effect will be considered below. Figure 4 shows light intensity distribution, Ipeak(x, y, z), when the bead position corresponds to the highest intensity enhancement in the near field. For comparison, the light intensity distribution when the optically trapped bead is in the equilibrium position is presented in the Supporting Information (Figure S5). The laser spot of a 780 nm Gaussian beam focused by a 0.7 NA microscope objective is characterized by the following parameters: waist size along the x-axis of 0.623 μm and waist size along the y-axis of 0.586 μm. The near field of the SiO2 bead has dimensions 0.488 μm along the x-axis, 0.396 μm along the y-axis, and 1.01 μm along the zaxis. The enhancement factor, defined as a ratio of the Fenh = Ispot/I0, is 1.8. For a polystyrene bead, the same parameters are 0.448 μm along the x-axis, 0.313 μm along the y-axis, and 0.541 μm along the z-axis. The field enhancement factor is FE field = 2.62. The near-field spot is localized near the surface of the bead. The GLM modeling predicts an elliptical near-field zone shape that is in agreement with experimental observation of an elliptical shape of the crater. Spacing of Objective Focal Plane and Position of the Bead Relative to Polymer Substrate. As discussed above, light enhancement in the near-field zone of the bead depends on its position relative to the objective focal plane. Hence, bead-assisted nanopatterning is strongly affected by precise positioning of the objective lens focus. Figure 5 shows the measured dependence of the crater depth as a function of the position of the focal plane of the microscope objective relative to the sample surface for craters produced with a 1.15 μm silica bead (see Supportin Information, section SI 1 for method of position measurement). Z = 0 corresponds to the microscope objective position when the focal plane coincides with the polymer surface. Positive Z values mean the position of the focal plane is inside the polymer film, and Z < 0 signifies the focal plane position is inside water. Figure 5a depicts the crater depth versus Z value. The depth is maximal at Z = 0.4 μm; assuming that the bead directly contacts the polymer surface, that means there is ∼1 μm of separation between the bead center and the objective focal point. This result can be understood through dependence of intensity enhancement in the near-field spot on bead−focal point spacing. We know that the ablation rate follows the I3 law (Figure 3a), so the same graph shows the dependence of the third power of the intensity enhancement factor Fenh = Ispot/I0 on Z. Fenh was calculated by GLM modeling, and Z is taken to be equal to the bead−focal point distance minus the bead radius (0.57 μm). Figure 5a shows good agreement between experimental measurements and simulations; in particular, Z corresponding to the maximal ablation rate is the same. These results can be considered as an additional confirmation of the third order of the multiphoton process of polymer ablation. At the same time, these measurements demonstrate that the highest ablation rate is achieved when the laser beam pushes the bead to the polymer surface and the focal plane of the objective lens is positioned inside the polymer. Figure 5b demonstrates the experimental dependence of the major and minor axes of the elliptic crater (left axis) on Z. For comparison, the near-field spot size

Figure 5. Crater depth (a) and crater width along major and minor axis (b) versus position of focal plane relative to the polymer surface (left scale). Z = 0 corresponds to the polymer surface; Z > 0 stands for focal plane inside the polymer; Z < 0 for focal plane inside water. Bead is 1.15 μm SiO2. Exposure time, 20 s; average laser power, 12 mW. Panel a also shows simulated Fenh3 versus Z (black squares, right scale). Panel b shows simulated near-field width fwhm (empty circles and triangles, right scale) versus Z. Red and blue curves designate near-field width along and perpendicular to the polarization, respectively.

calculated as a function of Z value is plotted on the same graph. Figure 5b shows good agreement between the measured sizes of craters in the polymer film and the calculated values of the near-field spot. Trap Stiffness and Stability of Femtosecond Optical Trapping during Nanopatterning. The process of nanopatterning is affected by optical trapping positional accuracy related to the bead Brownian motion. Figure 6 demonstrates the experimentally measured dependence of the root-meansquare displacement of 1.23 μm SiO2 bead, ⟨r⟩, versus average femtosecond laser power. The mean square of the displacement ⟨r⟩ as a function of the average power ⟨P⟩ is approximated by the ⟨P⟩−1/2 law. It is a consequence of the relation43 between the mean square of the displacement ⟨r⟩ and the trap stiffness, K: ⎡ πkT ⎤1/2 ⟨r ⟩ = ⎢ ⎣ 2K ⎥⎦

(4)

The stiffness, K, is directly proportional to the power, P, and because of this, ⟨r⟩ ∼ ⟨P⟩−1/2. For comparison the blue line on Figure 6 represents calculated bead’s square mean deviation versus power. Calculations were performed using MathLab code for CW laser radiation;44 mean displacement was found from the calculated trap stiffness using eq 4. As can be seen in Figure 6, experimental and simulated plots are qualitatively similar. There is a certain numerical difference which is probably caused by measurement of positional accuracy near 12566


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Effects of the Bead Size. The critical parameter for femtosecond optical trap-assisted nanopatterning is the size of the microsphere. Figure 8a demonstrates the dependence of the major and minor width of the crater on the bead diameter. The minimal crater size is observed for a 1 μm bead. The ratio of the major axis to the minor axis is close to 1.5 for beads with diameter more than 1 μm, and for 0.5 μm beads, the axis ratio is about 1.2. Experimentally it was found that major and minor width of the crater grows with the increase of the bead diameter when D > 1 μm. This result does not agree with GLM modeling results (Figure 8b). The GLM modeling predicts almost constant minor width value for beads larger than 1.2 μm. We surmise microspheres with diameter smaller than 1 μm undergo stronger Brownian motion, which worsens positional accuracy and causes larger structure sizes. However, crater size growth for beads larger than 1 μm cannot be explained by our theoretical calculation. This fact is assumed to take place because of bead−surface interaction which is not considered in the GLM-based simulation. Figure 8c shows the dependence of the intensity enhancement factor, Fenh, versus bead diameter. For experimental conditions used in the present work, the Fenh value grows not more than 15% when the diameter is increased from 1 to 4 μm. McLeod and Arnold22 found that the optimal experimental results are for 0.76 μm beads at 355 nm structuring laser wavelength and at 1064 nm trapping laser. We have optimal bead size of 1 μm, probably because a different wavelength (780 nm) is used both for structuring and for trapping. Peak Optical Trapping Forces. Wang and Chai have analytically derived the expressions for both the particle’s velocity and displacement under the action of the pulsed radiation force within the pulse duration for the Rayleigh dielectric particles.45 For particles whose linear dimensions approach or are equal to the optical wavelength, classical electrodynamics can be used to apply the conservation law for linear momentum in an optical field. Here, the net optical force exerted on an arbitrary object is completely determined by Maxwell’s stress tensor T(r,t).29,46−48 The traditional Minkowski form of Maxwell’s stress tensor defines the influx of optical momentum per unit of time49

Figure 6. Mean deviation versus average laser power measured for a 1.23 μm SiO2 microsphere trapped by the femtosecond laser beam focused by the 60× 0.7 NA objective lens (black squares). The microsphere was held in contact with the sample surface. Curve 1 (red) is a fitting of experimental data with ⟨r⟩ ∼ ⟨P⟩−1/2 relation. Curve 2 (blue) is simulated deviations for optical trapping with CW radiation.

the sample surface in the experiment, while in the simulations the bead was assumed to be in the uniform medium. Figure 6 also demonstrates that for power, ⟨P⟩, exceeding a few milliwatts, the ⟨r⟩ value is close to ∼10 nm, and this value is more than 10 times smaller than the size of the near-field spot. These results suggest that at the trapping power of several milliwatts, the 80 MHz femtosecond laser trap provides enough positional accuracy and it does not limit the spatial resolution of the nanopatterning. Temporal Stability of the Femtosecond Optical TrapAssisted Nanopatterning. Figure 7 shows the dependence of the crater depth and crater width as a function of the time exposure. The crater depth increases monotonically with time duration. The growth of the crater depth slows with an increase of the exposure time. This nonlinearity can be understood in the following way: as long as the crater grows, the effective intensity at the crater’s bottom is decreasing because of increasing distance to the bead surface (see the light intensity distribution along the z-axis presented in Figure 4). At the same time the crater width remains practically unchanged with time within the limit of experimental error. This result is evidence that the 80 MHz femtosecond trap is quite stable for nanopatterning, which means the bead position remains the same during nanopatterning within an accuracy of tens of nanometers.

Tij = EiDj + HiBj −

1 δij(HkDk + HkBk ) 2

(5)

where Di = εrε0·Ei is electric displacement, Bi = μrμ0·Hi magnetic flux, εr the relative dielectric constant, ε0 the permittivity of free space, μr the relative permeability, and μ0

Figure 7. Crater depth and width (fwhm) along major (red circles) and minor (black squares) axis versus exposure time for 1.54 μm SiO2 bead. Average power was 10.5 mW. Data was averaged by six craters. 12567


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Figure 8. Crater width along minor and major axis (red circles and black squares, respectively) (a), near-field width parallel and perpendicular to light polarization (red circles and blue triangles, respectively) (b), and enhancement factor Fenh (c) versus microsphere size, D. Crater fwhmx and fwhmy are experimental results with exposure time of 20 s. Near-field sizes and Fenh are calculated for 0.7 NA objective lens with focus shift toward light propagation which is equal to the bead diameter. In simulations, bead material is polystyrene with n = 1.58.

the permeability of free space. The net optical force exerted on an arbitrary object is completely determined by Maxwell’s stress tensor Fopt =

⎡

⎤

∫S Tij ds = ∫S ⎢⎣EiDj + HiBj − 12 δij(HkDk + HkBk )⎥⎦ ds (6)

The motion of the bead in the fluid can be described by the standard Langevin equation50,51

mv̇ = f fr + fext + f rand

(7)

where v = ṙ is the velocity of the particle; ffr the friction force; fext the sum of external forces including the buoyant force, gravitational force, and the pulsed radiation force (fopt); and frand the stochastic force. Naturally, the force frand essentially determines stochastic properties of the bead trajectory. Apart from frand, however, two other (regular) forces, ffr and fopt, can also significantly manifest themselves in the trajectory. The friction force, ffr, is described in the simple hydrodynamic Stokes approximation predicting ffr = −mγv, where γ = 6πηa/m is the friction coefficient (or the velocity relaxation rate), proportional to the liquid viscosity η (for water, η = 10−3 Pa·s) and the bead radius, a. fopt is a potential force determined by the time-modulated trapping potential well U(r, t), i.e., Fopt(r, t) = −∇rU(r, t), where ∇r is the gradient operator. Figure 9 demonstrates the optical trapping forces, Fopt, acting upon the polystyrene and SiO2 beads and pseudopotential, U. The potential well is symmetrical for x and y axes, and it has a lower barrier for the z axis in the direction of the light propagation. This fact is not very critical for the trapping of the bead when it is in contact with the polymer surface because the polymer surface restricts the bead motion in the light propagation direction. Fopt and U values in Figure 9 are normalized to the incident laser power, P. The forces acting on the polystyrene beads are about 1.3−1.5 times higher than that for the SiO2 bead. For 100 mW average power and 80 MHz repetition rate, the peak power of the 55 fs laser pulse is equal to ∼23 kW. The peak trapping force is estimated to be ∼9.2 μN (Figure 9a−c). We can estimate the velocity of the particle using basic formulas of mechanics: Vp ∼ (Foptτs)/m, which yields a speed of 360 μm/s, where τs is pulse time duration and m is the particle mass. The momentum relaxation time of the particle is τr = m/γ. It is equal to τr ∼ 147 ns for SiO2 microsphere of 1 μm. For a short time t < τr, the motion of the free particle becomes ballistic.50,51 The period of the pulse sequence τp =12.5 ns is shorter than the relaxation time, τr. This

Figure 9. GLM model of the pseudopotential, U, and optical trapping forces, F, acting on a 1 μm polystyrene (red line, n = 1.58) or SiO2 (blue line, n = 1.47) sphere in water (n = 1.33) when 780 nm pulse is focused by 0.7 NA objective lens: (a−c) optical trapping forces for x, y, and z axes; (d−f) pseudopotential for x, y, and z axes. Potential and optical trapping forces are normalized to the power, P, of the incident light.

result suggests theoretical analysis of the averaging procedure for optical trapping effect of femtosecond pulses. Averaging of Optical Trapping Forces. Stochastic Langevin eq 7 completely describes the optical trapping phenomenon.50,51 However, eq 7 is not quite suitable for the theoretical analysis. The problem can be much more conveniently analyzed with the use of the Klein−Kramers equation for the distribution function ρ(r,v|t) of the bead in the 12568


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Figure 10. 2D-predefined patterns: (1, 2) linear groove and its cross-section, scale size is 400 nm; (3) “ICP”; and (4) craters massive, scale size is 1 μm for both. The central panel shows writing of 15 μm circular groove on the polymer surface. The bead on panels 1 and 2 is 1 μm polystyrene, and on other panels the bead is 1.23 μm silica. Stage velocity is 5 μm/s.

L̂ (t ) = −v∇x + m−1∇x U̅ ∇v + γ ∇v (v + ∇v ⟨v 2⟩)

phase space. For simplicity, we will consider the case of onedimensional motion, in which the equation in the phase space (x, v) is written as

In these equations, time-averaged functions are defined by the formula

∂ρ /∂t = L̂(t )ρ with L̂(t ) = − v∇x + m−1∇x U ∇v + γ ∇v (v + ∇v ⟨v 2⟩)

X̅ (t ) = (2ta)

(8)

n

1/2

lb = ⟨v ⟩ τp = (kBT /m)

τp

(9)

∂ρ ̅ /∂t = [−v∇x + m−1∇x U̅ ∇v + γ ∇v (v + ∇v ⟨v 2⟩)]ρ ̅

(14)

with U̅ (x) = (2ta)

(10)

ta

∫−t

dτ U (x , t + τ ) ≈ (τs/τp)U0(x)

a

In particular, the bead displacement is lb ≈ 0.97 Å for 0.5 μm polystyrene and 0.028 Å for 4 μm glass beads. The typical values of lb are much smaller than the characteristic width, lw, of the trapping potential well U0(x), which is estimated to be lw ≈ 5 w0.52 The diffraction-limited “spot size” is given as 2w0 = 1.22λ/NA, where w0 is the transverse waist at z = 0 . The waist, w0, is 0.68 μm for the objective with 0.7 NA. In this case (i.e., when lb ≪ lw), at intermediate times in the region τp ≪ t ≪ τw = lw/⟨v2⟩1/2 one can neglect the effect of motion and describe the space−time evolution of the bead by the time-averaged distribution function ρ̅(x, v|t), satisfying an equation of the type in eq 8, but with time-averaged trapping potential, U̅ (x). The average form of this equation can easily be derived starting with the difference formulation of eq 8: [ρ ̅ (t + Δt ) − ρ ̅ (t )]/(Δt ) ≈ L̂(t )ρ(t ) ≈ L̂ (t )ρ ̅ (t ) in which

(13)

where ta satisfies the inequality τp ≪ ta ≪ τw. As for the increment Δt, it should be taken fairly large: Δt > ta. In the derivation of eq 11, we have applied the relation L̂(t )ρ(t ) ≈ L̂ (t) ρ̅(t), which is valid for the considered relation between times τp ≪ ta < Δt ≪ τw, which ensures smallness of the displacement of the bead particle during time intervalsta and Δt. Another manifestation of this smallness is the weak change Δρ(t) = ρ̅(t + Δt) − ρ̅(t) (for considered small values of Δt), resulting in high accuracy of the relation [ρ̅(t + Δt) − ρ̅(t)]/ (Δt) ≈ ρ ̇ . Taking into account the above-mentioned definitions and relations, one can rewrite the difference equation (eq 11) in the form of the differential equation

Here U0(x) is a peak value of the trapping potential. Equation 8 is rather complicated for qualitative analysis of bead trapping. For typical parameters values of systems under study this problem can significantly be simplified because of the small value of the bead displacement lb during the time τp = 12.5 ns between pulses: 2 1/2

ta

∫−t dτ X(t + τ) a

In this equation, ∇z = ∂/∂z for any variable z(z = x,v), ⟨v2⟩ = kBT/m is the mean square of velocity, and the time-modulated optical trapping potential is U(x, t). This potential will be represented in the form of a periodic sequence of highly localized pulses, whose shape is described by the dimensionless bell-shaped function S(t) with maximum value S(t = 0) = 1 and pulse duration τs = ∫ ∞ −∞ dt S(t) much smaller than the period of the sequence τp (τs ≪ τp): U (x , t ) = U0(x) ∑ S(t − nτp)

(12)

(15)

Equation 14 describes the space−time evolution of the bead for any value of the velocity relaxation time. In the limit of fast relaxation, in which lp ≪ ⟨v2⟩1/2τp < lw, where lp = vpτp and vp is maximal bead velocity under action of the trapping force, the averaged Klein−Kramers eq 14 is known to reduce to the Smoluchowski equation for the distribution in the coordinate space ρ̅S(x|t) = ∫ dv ρ̅(x, v|t): ∂ρS̅ /∂t = D∇x [∇x ρS̅ + (kBT ) −1∇x U̅ ρS̅ ]

(16)

where D = (kBT)/(mγ) is the diffusion coefficient. In principle, this equation is more simple and suitable for the analysis of optical trapping kinetics than is eq 14. For instance, maximal trapping force (Figure 9) for a 1 μm SiO2 bead is 9.2 μN for 100 mW average power femtosecond optical trap, lp is equal to 0.045 Å, and lb from eq 10 is equal 0.22 Å. For calculated values, we can conclude lp ≪ lb < lw and the diffusion approximation is applicable for the system under consideration. Experimental results closely match simulation data (Figure 6);

(11)

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The Journal of Physical Chemistry C therefore, femtosecond optical trapping can be considered using the averaging procedure.26 Femtosecond Optical Trap-Assisted Nanopatterning with Moving Optical Trap. The possibility of producing complex profiles with one femtosecond laser beam on the subdiffraction limit can be important for practical applications. Figure 10 shows different 2D predefined nanopatterns written on the polymer surface. This experiment demonstrates that an 80 MHz femtosecond laser beam can provide stable trapping and movement of the bead suitable for nanopatterning. The stage movement is either continuous or point-to-point with exposure time at machined points equal to 5 s and the speed between points as high as 5 μm/s. When the speed is about 15 μm/s, beads are pushed from the optical trap or there is a large displacement from the optical trap center along the direction of movement due to the friction force. We could use average power up to 20 mW with polystyrene microspheres and at least 2 times larger with silica microspheres. At higher powers, usually no damage of the bead was observed; instead, it was used to adhere to the polymer surface.

ACKNOWLEDGMENTS

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REFERENCES

(1) Ben-Yakar, A.; Byer, R. L. Femtosecond Laser Ablation Properties of Borosilicate Glass. J. Appl. Phys. 2004, 96, 5316−5323. (2) Kautek, W.; Kruger, J.; Lenzner, M.; Sartania, S.; Spielmann, C.; Krausz, F. Laser Ablation of Dielectrics with Pulse Durations between 20 fs and 3 ps. Appl. Phys. Lett. 1996, 69, 3146−3148. (3) Korte, F.; Serbin, J.; Koch, J.; Egbert, A.; Fallnich, C.; Ostendorf, A.; Chichkov, B. N. Towards Nanostructuring with Femtosecond Laser Pulses. Appl. Phys. A: Mater. Sci. Process. 2003, 77, 229−235. (4) Nolte, S.; Momma, C.; Jacobs, H.; Tunnermann, A.; Chichkov, B. N.; Wellegehausen, B.; Welling, H. Ablation of Metals by Ultrashort Laser Pulses. J. Opt. Soc. Am. B 1997, 14, 2716−2722. (5) Simon, P.; Ihlemann, J. Machining of Submicron Structures on Metals and Semiconductors by Ultrashort UV-Laser Pulses. Appl. Phys. A: Mater. Sci. Process. 1996, 63, 505−508. (6) Stuart, B. C.; Feit, M. D.; Herman, S.; Rubenchik, A. M.; Shore, B. W.; Perry, M. D. Optical Ablation by High-Power Short-Pulse Lasers. J. Opt. Soc. Am. B 1996, 13, 459−468. (7) Stuart, B. C.; Feit, M. D.; Rubenchik, A. M.; Shore, B. W.; Perry, M. D. Laser-Induced Damage in Dielectrics with Nanosecond to Subpicosecond Pulses. Phys. Rev. Lett. 1995, 74, 2248−2251. (8) Wang, Z. B.; Guo, W.; Pena, A.; Whitehead, D. J.; Luk’yanchuk, B. S.; Li, L.; Liu, Z.; Zhou, Y.; Hong, M. H. Laser Micro/Nano Fabrication in Glass with Tunable-Focus Particle Lens Array. Opt. Express 2008, 16, 19706−19711. (9) Luo, C. W. Nanoparticles and Nanostructures Fabricated Using Femtosecond Laser Pulses. In Lasers - Applications in Science and Industry; Jakubczak, K., Ed.; InTech, 2011; p 276. (10) Aeschlimann, M.; Bauer, M.; Bayer, D.; Brixner, T.; Garcia de Abajo, F. J.; Pfeiffer, W.; Rohmer, M.; Spindler, C.; Steeb, F. Adaptive Subwavelength Control of Nano-Optical Fields. Nature 2007, 446, 301−304. (11) Kawata, S.; Sun, H. B.; Tanaka, T.; Takada, K. Finer Features for Functional Microdevices - Micromachines Can Be Created with Higher Resolution Using Two-Photon Absorption. Nature 2001, 412, 697−698. (12) Betzig, E.; Trautman, J. K. Near-Field Optics: Microscopy, Spectroscopy, and Surface Modification Beyond the Diffraction Limit. Science (Washington, DC, U.S.) 1992, 257, 189−195. (13) Chimmalgi, A.; Grigoropoulos, C. P.; Komvopoulos, K. Surface Nanostructuring by Nano-/Femtosecond Laser-Assisted Scanning Force Microscopy. J. Appl. Phys. 2005, 97. (14) Hwang, D. J.; Chimmalgi, A.; Grigoropoulos, C. P. Ablation of Thin Metal Films by Short-Pulsed Lasers Coupled through Near-Field Scanning Optical Microscopy Probes. J. Appl. Phys. 2006, 99. (15) Luk’Yanchuk, B. S.; Wang, Z. B.; Song, W. D.; Hong, M. H. Particle on Surface: 3D-Effects in Dry Laser Cleaning. Appl. Phys. A: Mater. Sci. Process. 2004, 79, 747−751. (16) Novotny, L.; Hecht, B. Principles of Nano-Optics; Cambridge University Press: Cambridge, U.K., 2012. (17) Ohtsu, M.; Kobayashi, K.; Ito, H.; Lee, G. H. Nanofabrication and Atom Manipulation by Optical Near-Field and Relevant Quantum Optical Theory. Proc. IEEE 2000, 88, 1499−1518. (18) Piglmayer, K.; Denk, R.; Bauerle, D. Laser-Induced Surface Patterning by Means of Microspheres. Appl. Phys. Lett. 2002, 80, 4693−4695.

CONCLUSIONS We have demonstrated optical trap-assisted nanopatterning by a single Ti:sapphire laser where both optical trapping and structuring are performed by a 55 fs pulse train from a laser oscillator focused by a microscope objective lens. Arbitrary 2D structures on a sample surface can be produced with this method. Precise measurement of bead position with ad hoc software and a video camera has allowed us to estimate bead positioning accuracy and deviation due to combination of Brownian motion and mechanical vibrations. We have produced features with sizes down to 130 nm, or λ/6, provided that the bead has an optimal diameter and the trapping power is high enough to allow for precise bead positioning. It has been shown that the root-mean-square deviation of the bead from the trap center can be made as low as 10 nm. Also, feature size is highly uniform for high working powers (down to 15 nm) and probably can be improved by damping of mechanical vibration and by more strict z-axis positional accuracy. We have shown that position of the laser beam convergence point relative to bead center is an important parameter that affects both ablation speed and the size of features produced through ablation and proposed a simple method to precisely control this position based on registration of back-reflected laser light. ASSOCIATED CONTENT

S Supporting Information *

Positioning of the focal plane of microscope objective relative to the sample surface (SI 1); effect of the femtosecond pulse polarization on the crater shape (SI 2); absorption of polymer film (SI 3); near-field distribution in the point of equilibrium in an optical trap (SI 4). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b00478.

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This work has been initiated by Professor Oleg M. Sarkisov and is dedicated to him. The work has financial support from the Russian Foundation for basic research in the part of theoretical studies and experimental measurements 14-03-00546 a, 13-0300388 a, 13-02-12433 (ofi_m2), 12-03-91056 (NC_a). Young scientists A. Astafiev and A. Shakhov had financial support from the Russian President’s grant MK-5486.2014.2. The experimental setup was prepared with partial support from the Russian Foundation for basic research Grant 14-33-00017.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: astafi[email protected]. Phone: 7 495 939 73 47. Notes

The authors declare no competing financial interest. 12570


Article

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Femtosecond Optical Trap-Assisted Nanopatterning through

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