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Femtosecond laser direct generation of 3D-microfluidic channels inside bulk PMMA

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Abstract

We report on laser direct generation of 3D-microchannels for microfluidic applications inside PMMA bulk material by focused femtosecond pulses. Inner lying channels with cross sectional areas from 100 µm2 to 4400 µm2 are directly created in the volume of a PMMA substrate. Using the presented process, the channel length is fundamentally unlimited. Here we demonstrate a channel length of 6 meters inside a substrate with dimensions of 20 × 20 × 1.1 mm. The formation of the micro channels is based on nonlinear absorption around the focal volume that triggers a material modification. The modified volume can be selectively opened to form the channel by a subsequent annealing process. The cross section of the channel is strongly influenced by the energy distribution and illumination around the focal volume determined by the optical setup and process design. The 3D channel layout can easily be realized by moving the specimen using 3D motorized stage, allowing freely chosen complex shaped channel architectures. Within a comprehensive parameter study, varying laser power, number of multi-passes, writing speed and writing depths, we identify an optimized process in terms of attainable channel height, width and aspect ratio, as well as process stability and reproducibility. The proof of concept for an application in three dimensional microfluidic systems is provided by florescence microscopy using a dye rhodamine B solution in isopropanol.

© 2017 Optical Society of America

1. Introduction

Lab-on-chip (LOC) devices are revolutionizing various fields, both in basic research and in medical applications as a multi-functional low-cost diagnostic tool [1, 2]. Microchannels are one of the key components of a broad class of LOC devices designed for efficient analysis of small volumes of (bio)-chemical reagents and biological species. Established materials for LOC substrates are silicon, different kind of glass and polymers [3]. Recently, especially polymers gain respectable interest because of low material costs of only 1-10% of glass, adjustable physical properties and biocompatibility [4].

The fabrication of LOC devices of both, polymers and glass is mainly based on photo lithographic techniques [5], hot embossing [6] or rapid prototyping like laser ablation [7, 8] and micro-milling [9]. Although these processes are well established, they are inherently planar surface technologies, thus requiring multiple processing steps (stacking, bonding, sealing, etc.) to integrate photonic and microfluidic components into three dimensions [10]. Common bonding technologies such as gluing [11], thermal bonding [12] or laser bonding [13] have different disadvantages as, e.g., risk of a channel collapse, high thermal stress to sensitive components or leakage. Especially for polymers, these assembly technologies are also associated with a low precision, in turn limiting possibilities of complex polymer structures [4].

An alternative process to create microfluidic structures in glass is the three dimensional (3D) structuring by femtosecond laser irradiation followed by chemical etching, generally abbreviated by FLICE or referred to as selective laser-induced etching (SLE) [14, 15]. Femtosecond laser pulses are used in a multiphoton absorption process inside the bulk material to trigger a material modification or to create nanocracks and gratings around the focal volume [16]. Irradiated areas exhibit a higher etching rate in common etchants like KOH or HF as unprocessed areas, therefore enabling a selective etching [17]. The FLICE process is associated with high surface qualities but low processing speeds, long etching times, structural limitations due to etching selectivity and environmental challenges [14, 18].

Approaches to create 3D-microchannels in transparent polymers are based on the use of methylisobutylketon (MIBK) as a solvent for femtosecond modified regions inside polymethyl-methacrylate (PMMA) but are limited to small channel length on the order of hundred micrometers [19]. Watanabe et. al. [20] used comparable laser induced modifications as three dimensional waveguides in PMMA. Further 3D structuring processes as the use of high energy femtosecond pulses [21, 22] are associated with low channel qualities. In polydimethylsiloxane (PDMS) 3D-microfluidic structures can be created by embedding and casting objects inside the solved polymer [23].

A promising technology to create integrated 3D-channels in transparent polymers is presented by Day and Gu [24]. At a wavelength of 800 nm, 80 fs laser pulses are used to modify the density of the polymer matrix by nonlinear absorption in the focal region. Due to a pulse repetition rate of 80 MHz, heat accumulation is proposed as to modify the polymer. After annealing above the glass transition temperature of the polymer, the modified regions are transformed into microchannels. As shown by Day and Gu [24] and measured by Baum et al. [32] using a thermogravimetric analysis, femtosecond laser modified regions of PMMA exhibit a lower thermal stability as compared to the pristine material and start to degrade at around 200 °C. Gaseous degraded material expands and forms a microfluidic channel wider than the modified region inside the heated and thus softened material. Straight channels with nearly circular cross sections and cross sectional areas of 50 to 300 µm2 have been demonstrated over a length of, yet only, several hundreds of micrometers. In addition, the process is performed under water, hampering applicability since PMMA exhibits a significant water absorption which is unfavorable for possible integrated microoptical elements for LOC applications [25].

In this study, we extent this approach to a process under ambient conditions and utilize repetition rates in the kilohertz regime of a femtosecond laser at 1028 nm. We highlight the generation of microchannels with unlimited length on a macroscopic scale. Fluidic functionality is demonstrated using fluorescence microscopy and a dye solution of rhodamine B.

2. Experimental

2.1. Laser system

We used an ultrashort pulse laser (Light Conversion, Pharos-10-600) with a fundamental wavelength of 1028 nm having an adjustable pulse duration from 220 fs to 15 ps and variable repetition rate up to 610 kHz. The laser beam is focused by a 20X objective with a numerical aperture of 0.5 and a working distance of 2.1 mm (Zeiss, EC Epiplan-Neofluar). Samples are positioned using a translation stage with an accuracy of 250 nm (Aerotech, ANT130-XY) and a repeatability of 75 nm. The focal height is controlled by a nanopositioning z-stage (Aerotech, ANT95-50-L-Z).

2.2. Materials

Commercially available bulk PMMA sheets (type ME303010) with a thickness of 1.1 mm are used in this study. A CO2 Laser is applied to cut the sheets into size of 20 × 20 mm for the specimens. The polymer exhibits a glass transition temperature of 105 °C. Further thermal properties at room temperature are a specific heat capacity of 1.1 kJ/kgK and a heat conductivity of 0.181 W/mK [26] to be used for the following heat simulations. The refractive index n of the material at the laser wavelength of 1028 nm is calculated to 1.4819 at room temperature by Sellmeier equation, to be used for the calculation of the focal enlargement. Based on transmission and reflection measurements, the linear absorption coefficient at the laser wavelength is determined to 10.53 m−1.

2.3. Methods and characterization

Microchannels in PMMA are created in a two-step process. Firstly, the specimens are irradiated by focused femtosecond pulses triggering a nonlinear absorption inside the focal volume. The focal spot is then translated in three dimensions inside the bulk to create an internal modified structure of freely chosen 3D geometry. Secondly, the specimen are placed on a hot plate on top of a glass substrate and are annealed at 200 °C for 30 seconds. The temperature distribution after annealing for 30 s is simulated and shown in Fig. 1 (a). Temperature dependencies of the heat capacity and heat conduction of PMMA are included in the simulation [26]. As a boundary condition for the simulation, the temperature 1 mm above the hot plate is measured to 62 °C. It turns out, that after 30 seconds the temperature distribution reaches a steady condition. In figure 1 (b) heating curves at different depths in the PMMA specimen as defined from the bottom of the specimen are shown. After a completed annealing step, a temperature gradient of 4.1 degrees between bottom and surface is determined. It is worthwhile to note, that prior annealing no microchannels are found, i.e. their formation is clearly linked to the annealing process. In order to characterize channel cross sections, the treated specimen are ground down to the created microchannels and polished. Debris from this process step is removed by an ultrasonic bath. Channel geometries are measured by using a reflection and transmission light microscope (Nikon, 70 Eclipse LVDIA-N) which is also used for fluorescence microscopy in combination with a broadband LED and a filter block (Nikon, G-2A). A rhodamine B/isopropanol solution is used as fluorescent agent. Overview pictures are taken by a swingable digital microscope (LEICA, DVM6). Figure 2 highlights the capability to directly generate 3D-microchannel structures of complex geometries including 3D crossing and stacking of multiple channel layers. Please note that the shown channel architecture consists of a single channel meander.

 figure: Fig. 1

Fig. 1 Cross section of the simulated thermal distribution after 30 s (a) and temperature distribution in several depths at a width of 10 mm during the annealing process (b).

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 figure: Fig. 2

Fig. 2 Tilted view on a single meander shaped channel written in six connected layers.

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3. Results and discussion

Femtosecond direct generation of microchannels in PMMA is achieved by scanning the laser along the targeted channel trajectory multiple times (multi pass process). Prior to annealing a refractive index modification can be observed in the laser irradiated regions. Cross-sections and top views of these regions appear as waveguide structures similar as being reported in PMMA by Paetzold et al. [27]. In addition, inside the modified area non-periodic bubble like disruptions are observed. In accordance to Kelb et al. [28] these initial modification lead to a refocusing of the impinging laser beam, which in turn creates a second modification below the original focal spot and thus to a double modified cross section. After annealing these cascaded foci modifications merge and create a single homogeneous continuous channel. Femtosecond laser exposed PMMA degenerates at high intensities around the focal volume. The degradation process consists of a direct cleavage of the polymer backbone under formation of monomers which indicates the scission of the polymer backbone [29]. Based on chemical analysis of the volatiles released during irradiation and an increased UV-Absorption by the C=C double bonds, Baum et al. suggest a combined process of randomly cleaved polymer chains and unzipping towards monomer (methyl methacrylate) [30, 31]. Changes of such chemical structures of modified areas can be observed using fluorescence microscopy as shown by Kallepalli et al. [21] and are also observable for our processed specimen. Modified regions exhibit a lower thermal stability as compared to the pristine material and start to degrade around 200 °C transferring material to the gaseous state. As measured by Baum et al. [32] using a thermogravimetric analysis femtosecond laser modified PMMA shows an increased weight loss due to decomposition between 175 and 375 °C as compared to pristine material. Degradation below 250 °C is attributed to more unsaturated endgroups. In the studied process gaseous degraded material creates a pressure inside the fully sealed channel network and expands into the heated and thus softened material. Furthermore cascaded foci merge to a single microchannel. Therefore channel cross-sections are larger than focal volumes. Channel enlargement can be inhibited by opening a modified area before annealing. For the parameter study presented here, horizontal microchannels with a minimal length of 15 mm are created in different depths below the surface.

3.1. Influence of processing parameters

In this study, the influences of the process parameters laser power, scanning repetitions, scanning speed and writing depth on the channel characteristics height, width and aspect ratio (def. height/width) are examined. Experiments are performed using a pulse duration of 220 fs and a pulse repetition rate of 61 kHz. The objective is illuminated by a raw beam diameter of 5 mm measured at 1/e2 (50 % aperture illumination). These process parameters have been identified as suitable in pre-experiments.

Channel geometries (i.e. height, width and aspect ratio) using different laser powers from 4 mW to 60 mW are summarized in Fig. 3. Each structure is scanned 4 times at a writing speed of 5 mm/s. Apparently, at higher laser power channel height and width are increasing, yet with a decreasing aspect ratio due to a stronger raise of the width as compared to the height. Channels with a cross sectional area ranging from 22 µm to 118 µm in height and 6 µm to 47 µm in width can be created by adjusting the laser power. Figure 4 exemplary shows cross sections of microchannels generated with different laser powers and at different depths, demonstrating the elliptical shape of the channels. These dimensions are larger and thus preferable for fluidic applications than those reported by Day et al. [24]. For a laser power above 60 mW, surrounding material is damaged and below 4 mW no sufficient modification to form a microchannel after annealing is triggered.

 figure: Fig. 3

Fig. 3 Height and width of microchannels generated at different laser powers and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.

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 figure: Fig. 4

Fig. 4 Elliptical cross section of microfluidic channels (a) produced at two different power levels (P1, P2) with Δ= 6 mW resulting in an expansion in height of 9 µm and in width of 4 µm and (b) in two different depths with Δ = 105 µm.

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Beside laser power, the number of scanning repetitions has a significant influence on the size and the aspect ratio of the microchannel. In Fig. 5 dimensions of microchannels created with different scanning repetitions are shown. Further processing parameters are a laser power of 35 mW and a writing speed of 5 mm/s. With the used process setup a minimum aspect ratio of 2.1 can be achieved. Corresponding channel height and width are 100 µm and 47 µm, respectively. It is worthwhile to highlight that the effect of decreasing aspect ratio by increasing scanning repetitions saturates beyond 10 repetitions.

 figure: Fig. 5

Fig. 5 Height and width of microchannels generated with different number of scanning repetitions and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.

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The channel dimensions are also influenced by the number of pulses applied per point, which is, in this study, controlled by the writing speed at a fixed pulse repetition rate. Figure 6 depicts the dimensions of microchannels created with a writing speed in the range between 0.5 mm/s to 10 mm/s (laser power 35 mW and 4 scanning repetitions). For writing speeds below 2 mm/s, significant channel enlargements at a low aspect ratio are found, whereas for writing speeds above 6 mm/s channel dimensions are associated with an increased standard deviation. Taking into account a spot diameter of 2.7 µm the number of pulses per point decrease from 1317 at 0.5 mm/s to 66 at 10 mm/s per scan. Thus, we attribute the channel enlargement at low speeds to a heat accumulation and the stronger deviating dimensions at higher speeds to an insufficient energy deposition.

 figure: Fig. 6

Fig. 6 Height and width of microchannels written with different speeds and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.

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Beside these adjustable process parameters, the depth at which the channel is written turns out to be an influencing factor as well. In Fig. 7 height, width and aspect ratio are shown for channels generated in different depths. Further process parameters are laser power 35 mW, writing speed 5 mm/s and 4 scanning repetitions. By altering the focal position inside the specimen the channel height increases from 83.3 µm at a depth of 100 µm to 97.1 µm at a depth of 900 µm. This increase can be attributed to a focal extension due to spherical aberrations introduced by different refractive indices between air and PMMA. Sun et al. [33] developed a simple model (1) based on geometrical optics to describe the increase of the foci range Δ in a focusing depth fd. In accordance to Wiersma et al. [34], this geometrical model can be applied to estimate the enlargement of the focal area in beam propagation.

Δ=fdn(n2NA21NA2n)
Using (1) we find an increase of the foci range of 14.3 µm, which agrees well with the experimentally determined enlargement of the channel height of 13.8±1.55 µm from a focusing depth of 100 µm to 900 µm.

 figure: Fig. 7

Fig. 7 Height and width of microchannels generated in different depths and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.

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In order to exclude the temperature gradient during the annealing process being accountable for the channel enlargement, irradiated reference specimen were annealed upside down yielding comparable results with respect to the channel dimensions.

From an application point of view, it is worthwhile to mention that the process parameters laser power, writing speed or number of repetitions can be used to compensate the writing depth induced variations of channel dimensions, in turn allowing the generation of microchannel with uniform shape and dimensions in a complex multilayer 3D-microfluidic chip.

3.2. Microfluidic demonstration

To highlight the functionality of the laser direct generated microfluidic channels, fluorescence microscopy (central excitation wavelength: 535 nm, bandwidth: 50 nm) is applied to track the flow of rhodamine B/isopropanol solution through the microchannel. In Fig. 8 (middle) an overview picture of the examined microfluidic network including several crosses and turnarounds without dye is shown. Detailed views show fluid filled channels and corresponding fluorescence pictures of rhodamine solution inside the channel at two different locations of the microfluidic network. On the left hand side completely filled crossed channels can be observed. Precise fluid filled turnarounds of microchannels are demonstrated on the right hand side.

 figure: Fig. 8

Fig. 8 Top view on an unfilled microfluidic network (middle) and detailed view on corresponding fluid filled channels (left and right).

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4. Conclusion

In this study femtosecond laser direct generation of 3D-microchannels in PMMA with basically unlimited length and no etching ratio limitations is reported. The formation of microchannels is based on nonlinear absorption around the focal volume triggering a material modification. The modified volume is selectively opened to form the channel by a subsequent annealing process with the channel cross section being orders of magnitude larger than the focal volume. Microchannel dimensions such as height, width and aspect ratio are adjustable by controlling laser power, writing speed and scanning repetitions. Variations in channel height due to focal enlargement in different writing depths can be compensated by adjusting the process parameters. The femtosecond laser direct generation process is compatible to rapid prototyping and enables the direct fabrication of complex integrated structures.

References and links

1. E. K. Sackmann, A. L. Fulton, and D. J. Beebe, “The present and future role of microfluidics in biomedical research,” Nature 507, 181–189 (2014). [CrossRef]   [PubMed]  

2. G. M. Whitesides, “The origins and the future of microfluidics,” Nature 442, 368–373 (2006). [CrossRef]   [PubMed]  

3. E. Roy, A. Pallandre, B. Zribi, M.-C. Horny, F. D. Delapierre, A. Cattoni, J. Gamby, and A.-M. Haghiri-Gosnet, “Overview of Materials for Microfluidic Applications,” in Advances in Microfluidics - New Applications in Biology, Energy, and Materials Sciences (INTECH, 2016). [CrossRef]  

4. P. Abgrall and A. Gue, “Lab-on-chip technologies: making a microfluidic network and coupling it into a complete microsystem-a review,” J. Micromech. Microeng. 17, R15 (2007). [CrossRef]  

5. J. Vieillard, R. Mazurczyk, L.-L. Boum, A. Bouchard, Y. Chevolot, P. Cremillieu, B. Hannes, and S. Krawczyk, “Integrated microfluidic-microoptical systems fabricated by dry etching of soda-lime glass,” Appl. Surf. Sci. 85, 465–469 (2008).

6. S. Qi, X. Liu, S. Ford, J. Barrows, G. Thomas, K. Kelly, A. McCandless, K. Lian, J. Goettert, and S. A. Soper, “Microfluidic devices fabricated in poly (methyl methacrylate) using hot-embossing with integrated sampling capillary and fiber optics for fluorescence detection,” Lab Chip 2, 88–95 (2002). [CrossRef]  

7. R. Suriano, A. Kuznetsov, S. M. Eaton, R. Kiyan, G. Cerullo, R. Osellame, B. N. Chichkov, M. Levi, and S. Turri, “Femtosecond laser ablation of polymeric substrates for the fabrication of microfluidic channels,” Appl. Surf. Sci. 257, 6243–6250 (2011). [CrossRef]  

8. L. Romoli, G. Tantussi, and G. Dini, “Experimental approach to the laser machining of PMMA substrates for the fabrication of microfluidic devices,” Opt. Lasers Eng. 49, 419–427 (2011). [CrossRef]  

9. F. Bundgaard, G. Perozziello, and O. Geschke, “Rapid prototyping tools and methods for all-COC/Topas® fluidic microsystems,” J. Mech. Eng. Sci. 220, 1625–1632 (2006). [CrossRef]  

10. S. Sivashankar, S. Agambayev, Y. Mashraei, E. Q. Li, S. T. Thoroddsen, and K. N. Salama, “A “twisted” microfluidic mixer suitable for a wide range of flow rate applications,” Biomicrofluidics 10, 34120 (2016). [CrossRef]  

11. R. J. Jackman, T. M. Floyd, R. Ghodssi, M. A. Schmidt, and K. F. Jensen, “Microfluidic systems with on-line UV detection fabricated in photodefinable epoxy,” J. Micromech. Microeng. 11, 263 (2001). [CrossRef]  

12. C.W. Tsao and D. L. DeVoe, “Bonding of thermoplastic polymer microfluidics,” Microfluid. Nanofluid. 6, 1–16 (2009). [CrossRef]  

13. X. Jiang, S. Chandrasekar, and C. Wang, “A laser microwelding method for assembly of polymer based microfluidic devices,” Opt. Lasers Eng. 66, 98–104 (2015). [CrossRef]  

14. Y. Bellouard, A. Said, M. Dugan, and P. Bado, “Fabrication of high-aspect ratio, micro-fluidic channels and tunnels using femtosecond laser pulses and chemical etching,” Opt. Express 12, 2120–2129 (2004). [CrossRef]   [PubMed]  

15. M. Hermans, J. Gottmann, and F. Riedel, “Selective, laser-induced etching of fused silica at high scan-speeds using KOH,” J. Laser Micro-Nanoeng. 9, 126 (2014). [CrossRef]  

16. C. Hnatovsky, R. S. Taylor, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Polarization-selective etching in femtosecond laser-assisted microfluidic channel fabrication in fused silica,” Opt. Lett. 30, 1867 (2005). [CrossRef]   [PubMed]  

17. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photon. 2, 219–225 (2008). [CrossRef]  

18. C. Hnatovsky, R. S. Taylor, E. Simova, P. P. Rajeev, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys. A 84, 47–61 (2006). [CrossRef]  

19. K. Yamasaki, S. Juodkazis, S. Matsuo, and H. Misawa, “Three-dimensional micro-channels in polymers: One-step fabrication,” Appl. Phys. A 77, 371–373 (2003). [CrossRef]  

20. W. Watanabe, S. Sowa, T. Tamaki, K. Itoh, and J. Nishii, “Three-dimensional waveguides fabricated in poly (methyl methacrylate) by a femtosecond laser,” Jpn. J. Appl. Phys. 45, L765 (2006). [CrossRef]  

21. L. N. D. Kallepalli, V. R. Soma, and N. R. Desai, “Femtosecond-laser direct writing in polymers and potential applications in microfluidics and memory devices,” Opt. Eng. 51, 073402 (2012). [CrossRef]  

22. D. L. N. Kallepalli, N. R. Desai, and V. R. Soma, “Fabrication and optical characterization of microstructures in poly (methylmethacrylate) and poly (dimethylsiloxane) using femtosecond pulses for photonic and microfluidic applications,” Appl. Opt. 49, 2475–2489 (2010). [CrossRef]  

23. G. B. Salieb-Beugelaar, D. Gonçalves, M. P. Wolf, and P. Hunziker, “Microfluidic 3D Helix Mixers,” Micromachines 7, 189 (2016). [CrossRef]  

24. D. Day and M. Gu, “Microchannel fabrication in PMMA based on localized heating by nanojoule high repetition rate femtosecond pulses,” Opt. Express 13, 5939 (2005). [CrossRef]   [PubMed]  

25. M. Rosenberger, G. Koller, S. Belle, B. Schmauss, and R. Hellmann, “Planar Bragg grating in bulk polymethyl-methacrylate,” Opt. Express 20, 27288–27296 (2012). [CrossRef]   [PubMed]  

26. C. Bonten, Kunststofftechnik (Carl Hanser Verlag GmbH Co KG, 2016). [CrossRef]  

27. W. M. Paetzold, C. Reinhardt, A. Demircan, and U. Morgner, “Cascaded-focus laser writing of low-loss waveguides in polymers,” Opt. Lett. 41, 1269–1272 (2016). [CrossRef]  

28. C. Kelb, W. M. Pätzold, U. Morgner, M. Rahlves, E. Reithmeier, and B. Roth, “Characterization of femtosecond laser written gratings in PMMA using a phase-retrieval approach,” Opt. Mater. Express 6, 3202 (2016). [CrossRef]  

29. A. Baum, P. J. Scully, M. Basanta, C. P. Thomas, P. R. Fielden, N. J. Goddard, W. Perrie, and P. R. Chalker, “Photochemistry of refractive index structures in poly (methyl methacrylate) by femtosecond laser irradiation,” Opt. Lett. 32, 190–192 (2007). [CrossRef]  

30. A. Baum, P. J. Scully, W. Perrie, M. Sharp, K. G. Watkins, D. Jones, R. Issac, and D. A. Jaroszynski, “NUV and NIR femtosecond laser modification of PMMA,” Proc. of LPM 2007, University of Vienna (2007).

31. A. Baum, P. J. Scully, W. Perrie, D. Jones, R. Issac, and D. A. Jaroszynski, “Pulse-duration dependency of femtosecond laser refractive index modification in poly (methyl methacrylate),” Opt. Lett. 33, 651–653 (2008). [CrossRef]   [PubMed]  

32. A. Baum, P. J. Scully, W. Perrie, D. Liu, and V. Lucarini, “Mechanisms of femtosecond laser-induced refractive index modification of poly (methyl methacrylate),” J. Opt. Soc. Am. B 27, 107–111 (2010). [CrossRef]  

33. Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Effect of spherical aberration on the propagation of a tightly focused femtosecond laser pulse inside fused silica,” J. Opt. A 7 (11), 655 (2005) [CrossRef]  

34. S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14 (7), 1482 (1997). [CrossRef]  

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Figures (8)

Fig. 1
Fig. 1 Cross section of the simulated thermal distribution after 30 s (a) and temperature distribution in several depths at a width of 10 mm during the annealing process (b).
Fig. 2
Fig. 2 Tilted view on a single meander shaped channel written in six connected layers.
Fig. 3
Fig. 3 Height and width of microchannels generated at different laser powers and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.
Fig. 4
Fig. 4 Elliptical cross section of microfluidic channels (a) produced at two different power levels (P1, P2) with Δ= 6 mW resulting in an expansion in height of 9 µm and in width of 4 µm and (b) in two different depths with Δ = 105 µm.
Fig. 5
Fig. 5 Height and width of microchannels generated with different number of scanning repetitions and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.
Fig. 6
Fig. 6 Height and width of microchannels written with different speeds and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.
Fig. 7
Fig. 7 Height and width of microchannels generated in different depths and calculated aspect ratios (secondary axis). Error bars include the standard deviation of 5 generated microchannels. Lines are given as a guide to the eye.
Fig. 8
Fig. 8 Top view on an unfilled microfluidic network (middle) and detailed view on corresponding fluid filled channels (left and right).

Equations (1)

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Δ = f d n ( n 2 NA 2 1 NA 2 n )
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