Generation of silver nanoparticles with controlled size and spatial distribution by pulsed laser irradiation of silver ion-doped glass Stefan Wackerow and Amin Abdolvand* School of Engineering, Physics & Mathematics, College of Art, Science & Engineering, University of Dundee, Dundee DD1 4HN, UK * [email protected]
Abstract: Silver ions were driven into glass by a direct current electric field-assisted ion exchange technique. The silver ion exchanged glass was then irradiated by laser pulses of 10 ns and 10 ps in length at 355 nm for comparison purposes. In both cases, laser irradiation led to the formation of a metallic-like film at the surface of the ion exchange glass. Scanning electron microscopy showed that the films consist of a very dense single layer of silver nanoparticles with similar particle sizes and separation. Irradiation with different laser parameters shows no significant difference in transmission spectra and modification width between ps- and ns-pulsed lasers. Particle sizes and separation at the surface are increasing with increasing laser power, and are larger for picosecond pulsed laser irradiation. It is also shown that the film formation is a thermal process. ©2014 Optical Society of America OCIS codes: (160.4670) Optical materials; (160.4236) Nanomaterials; (160.2750) Glass and other amorphous materials; (140.3390) Laser materials processing.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5076
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1. Introduction Glasses containing metal nanoparticles have generated significant interest due to their linear and nonlinear optical properties [1, 2], which are dominated by the surface plasmon resonances (SPRs) of the nanoparticles. The spectral position and shape of the SPRs depend on the composition of the host material and could also be designed by tuning the size, shape or spatial distribution of the nanoparticles. Silver nanoparticles are often generated inside glass by a combination of the ion exchange and reduction processes. Ion exchange is normally done from a salt melt by thermal diffusion or from a solid silver film by electric field-assisted ion exchange . In both cases anions located in the glass are replaced by silver ions. Afterwards, or simultaneously, reduction of the silver ions to atoms is achieved by thermal treatment. Often this is done in air, resulting in the reduction of silver by reducing agents present in the glass. It can also be done in a hydrogen atmosphere, resulting in a fast reduction reaction between silver and hydrogen. During thermal treatment silver atoms are agglomerating to form nanoparticles. It has been shown that particle formation can also be induced by laser irradiation. This allows localized generation of silver nanoparticles on a very short timescale. Recently, we demonstrated that this technique can be used to generate silver nanoparticles on the surface of glass with high concentrations of ions and upon nanosecond pulsed laser irradiation . This technique led to the formation of regular monolayers of high density and uniform silver nanoparticles. In this contribution, we are presenting an analysis of the effect of irradiation of a silver ion exchanged glass with different laser parameters and also present a comparison study of the results for nanosecond and picosecond pulsed laser irradiations. For low laser powers only nanoparticles inside the glass were generated, while with increasing the laser power stronger effects at the surface occur. It was found that the particle size and separation at the surface are increasing with increasing laser power. Producing nanoparticles at the glass surface opens up a wide range of new possible applications for Terahertz generation , surface enhanced Raman scattering (SERS) , plasmonic devices  and sensors , plasmonic chain waveguides [8, 9], chemical catalysis  and photochemistry . 2. Experimental methods As a starting material commercial crown glass B270 (composition in wt%: (69.2) SiO2, (9.8) Na2O, (9.5) CaO, (7.6) K2O, (2.8) BaO, (1.1) Al2O3) with a thickness of 1 mm was used. Silver ions were brought into the glass by direct current (dc) electric field-assisted ion exchange  in a dry process. For this the glass was coated with a silver film by applying a fast drying suspension of silver flakes (Sigma Aldrich, 10 µm, ≥99.9%) in isopropanol, #204304 - $15.00 USD (C) 2014 OSA
Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5077
followed by 20 min of sintering at 300°C. Afterwards the glass was subjected to a strong dc electric potential of 1 kV over 1 mm at a temperature of 300 °C. This led to the replacement of anions in the glass by silver ions due to ionic conduction. The sample was then divided into two identical pieces and the excess silver was gently removed from the surfaces using a bath of nitric acid [3, 12]. Each sample piece was irradiated at various laser fluences using laser pulse lengths of 10 ns and 10 ps, respectively. For these experiments two different laser systems operating at 355 nm were employed. The picosecond pulsed laser irradiation experiments were performed using a Coherent Talisker Ultra System while for the nanosecond a Laservall Violino UV laser was employed. In both cases the laser beam was focused to a spot 60 µm in diameter by a flatfield scanning lens system – a specialized lens system in which the focal plane of the deflected laser beam is a flat surface. In both cases, the laser beam was raster scanned at a scanning speed of 14 mm/s and a repetition rate of 80 kHz, which results in approximately 340 pulses per spot being fired onto the targets. The characterizations were performed using a JASCO V-670 UV/VIS/NIR spectrophotometer, KEYENCE Digital Microscope VHX-1000, and a Hitachi S-4700 field emission scanning electron microscope (SEM). 3. Results and discussion Line widths & threshold fluence: For a Gaussian beam profile the square of the width d of the beam - where the threshold fluence Fth is achieved - is given by [13–15] d 2 = 8w0 2 ln( F0 / Fth ).
Here F0 is the peak fluence and w0 is the radius at which the fluence decreases to F0/e2. A semi-logarithmic plot of the squared diameter of the modified area d2 versus fluence F will then produce a straight line if the modification is limited by the threshold fluence. The line intercepts the horizontal (fluence) axis at the threshold fluence, and the beam radius can then be determined from the slope. Lines were written into the samples with both lasers at different fluences, and modified line widths were measured both in transmission and reflection modes of the optical microscope. In transmission mode the total modified width was measured, including the area with color change due to the nanoparticle formation inside the glass volume. In reflection mode only the width associated with a changed surface structure was considered. The measured line widths are plotted as a function of fluence on a logarithmic scale in Fig. 1. Linear functions have been fitted to the measured widths, which are also shown in the plot. From these functions threshold fluences and beam radii were determined and are presented in Table 1. The modification widths are nearly similar for both the picosecond and nanosecond pulses, as are the fitted functions. The obtained beam radii are more than twice as large as the actual beam radii. This indicates that the assumption made in this calculation that modifications are solely determined by a threshold fluence do not entirely apply here. There must then exist a different additional mechanism determining the modification width observed here; it is not only determined by local laser fluence, but also by heat diffusion as will be discussed shortly. The function is however a good fit to the experimental data and is therefore suitable for comparing picosecond and nanosecond pulses, and also showing that the obtained threshold fluences are valid. Interestingly the line widths are nearly identical after irradiation with ps and ns pulses. This shows that the different irradiance does not affect this macroscopic property of the modification. Hence, the process must be driven mainly by linear absorption. The threshold fluence is higher for the surface modification than for the nanoparticle generation in the glass volume. From annealing experiments it is known that particle formation in the volume starts to occur at temperatures around the glass transition point . A modification similar to the observed surface changes could not be achieved in annealing
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5078
experiments, however because of the change of surface morphology this can be attributed to melting of the glass. Therefore the two processes have different threshold temperatures. Table 1. Fitting parameters for modification widths shown in Fig. 1. Threshold fluence [mJ/cm2]
Fitted beam radius [µm]
ps pulses, volume
85.8 ± 5.3
73.5 ± 2.9
ps pulses, surface
134.5 ± 6.7
71.8 ± 2.8
ns pulses, volume
81.9 ± 3.6
68.5 ± 1.8
ns pulses, surface
130.0 ± 4.8
72.3 ± 2.3
Pulse energy [µJ] 2
Volume particles Surface modification
(Width [µm]) ²
Fig. 1. Squared width of the laser-induced modifications versus fluence on a logarithmic scale for both ps (red) and ns (blue) pulsed lasers. Top axis shows laser pulse energies for comparison, the right axis shows the actual (non-squared) width values. The width of the area with particles in the volume (triangles) has been measured by transmission optical microscopy. Similarly the width of the area with surface modification (filled circles) was measured by reflection microscopy. Linear fits shown as red and blue lines define the threshold fluence at the fluence axis intercept.
Optical transmission spectra: After writing lines, nine squares have been written on to each sample, with the same fluences and laser parameters as for the lines, to enable measurement of optical transmission spectra. Images of the produced squares are shown in Fig. 2, with the ps-pulsed irradiated areas shown in image (a) and the ns-irradiated areas in images (b) and (c). All three images were taken with the microscope working in reflection mode. Images (a) and (b) were taken with a white background behind the sample while image (c) was taken with a black background, showing the strong surface reflection. In this configuration images show both surface reflections and transmitted light. For areas where the nanoparticles are inside the glass a reddish color is observed, while the image also shows the metallic look resulting from the surface particles in other areas. The squares were written line by line, filling the area nearly homogeneously. The line distance had to be varied for different fluences since the modification width varies – as explained earlier. A constant line distance would either result in unmodified spaces between the lines for low fluences or multiply overlapping lines for high fluences. Therefore the line distance was always set to 90% of the surface modification width measured for single lines written with the same fluence. For fluences below 130 mJ/cm2 the line width was set to 90% of the volume modification width since no surface modification was observed for these fluences.
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As seen in Fig. 2, the ps-irradiated areas show only volume particles for up to 4µJ. At 5µJ a reflective film was formed, which reflected more strongly for the squares written with higher pulse energies. At 6µJ the surface becomes rough in parts of the square, while the whole squares turn rough for higher powers. This roughening coincides with the formation of bubbles inside the glass. The threshold of this process was found to be very sensitive to small fluence variations, which explains the inhomogeneity of the square written with pulse energies ≥ 6µJ.
Fig. 2. Images of laser-irradiated areas. (a): ps-irradiated squares. Energies were, from left to right, in the top row: 2, 3, 4 µJ, middle row: 5, 6, 8 µJ, bottom row: 10, 12, 14 µJ. (b): nsirradiated squares. Top row: 2.4, 2.9, 3.3 µJ, middle: 4.0, 5.5, 6.5µJ, bottom: 7.5, 10, 12µJ. These two images were taken with a microscope in reflection mode using a white background. Image (c) also shows the squares made by ns irradiation (same as (b)), but with a black background. This reduces the effect of light transmitted through the glass, reducing the effect of particles inside the glass, and therefore enhancing visibility of surface reflection.
Optical transmission spectra of the irradiated areas are shown in Fig. 3. Spectra are measured as extinction, which is the negative natural logarithm of transmission. Plots also show the extinction of the original ion-exchanged glass for comparison. At the laser wavelength of 355 nm this shows an extinction of 1.07, equivalent to a transmission of approximately 34.3%. For low pulse energies the spectra exhibit a distinct plasmon band growing markedly with increasing pulse energy. At 4 µJ a broadband extinction over the whole wavelength range occurs. This broadband extinction results from electromagnetic coupling of the nanoparticles in the surface layer . The surface roughness and scattering at bubbles and parallel written lines (as the laser fluence increases) are also contributing to the broadband background. Electron microscopy, particle size analysis: An image from the center of the line written with 12µJ and ps pulses is shown in Fig. 4(a), and the one written with ns pulses in Fig. 4(b). Mostly particles have similar sizes in the bright areas and smaller sizes in some dark areas. These particles are located in a single layer at the glass surface, which was shown in a previous publication  by imaging the cross section. Images were taken from the center of all laser-written lines. It was observed that these areas are larger and darker for lower laser power. Particle diameters (sizes) and separations were determined for different laser parameters and are plotted in Fig. 5. The mean values are plotted as data points, and the standard deviation of size and separation distributions as error bars. The data shows a strong correlation between particle separations and sizes, the separations are always only slightly larger than the sizes. With decreasing pulse energy measured values become smaller. The ns irradiation produces considerably smaller particles than the ps irradiation.
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5080
14µJ 12µJ 10µJ 8µJ 6µJ
4.0µJ 3.3µJ 2.9µJ 2.4µJ original
5µJ 4µJ 3µJ 2µJ original
12.0µJ 10.0µJ 7.5µJ 6.5µJ 5.5µJ
Fig. 3. Extinction spectra from areas irradiated with ps pulses (a) and ns pulses (b). There is a plasmon band showing for all irradiated squares, centered at 450nm - typical for silver nanoparticles. There is also a nearly constant background, which is measured for irradiation with energy per pulse from 4 µJ upwards. It also becomes stronger with increasing pulse energy.
Fig. 4. Highly magnified SEM images of the centers of lines, both written with pulse energies of 12 µJ, with ps (a) and ns (b) pulses. The particle diameters are ~100 nm for ps, and 60 nm for ns irradiations, with a small variation in particle sizes and separation.
Thermal considerations: A number of our observations are related to the heating of samples. For instance, particle formation inside a similar ion-exchanged glass has been observed for annealing at 400°C or more . Here, for ps pulses, formation of a distinct amount of particles inside the glass is observed for pulse energies of 3 µJ and more. Laser irradiation occurs on a much shorter timescale than thermal annealing. Bubble formation, together with the surface roughening, was observed for pulse energies higher than 6 µJ. The important thermal characteristics of B270 glass are its transformation temperature of 533°C and softening temperature of 708°C. It was not possible to find any reports on the vaporization temperature of B270 in the literature. For fused silica the vaporization temperature is 2430°C , which we would consider as a reasonable first-order approximation.
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5081
Diameter, distance [nm]
ps distance ps diameter
ns distance ns diameter 100
Pulse energy [µJ]
Fig. 5. Plot of particle diameters and inter-particle distances (from center to center) determined for different laser parameters.
Important characteristics of a laser heating process are the absorption length la and the time-dependent heat diffusion length l(t): l (t ) = (kt / ρ c p )1/2 = ( Dt )1/2 ,
where k - thermal conductivity, ρ - density, cp - heat capacity, and D is the thermal diffusivity. The heat diffusion length is a measure for the volume that is affected by heat diffusion, while the absorption length determines the size of the volume heated directly by laser irradiation. If l(t) < la then heat diffusion has only a small effect on the final temperature distribution, and can be neglected. Absorption in the ion-exchanged layer is induced by silver ions. They show an absorption band in glass centered at ~240 nm, which is caused by electrons being excited from 4f to 5s level. This band follows a Lorentz distribution and its area is proportional to the amount of silver ions in the glass. The center of the absorption band lies within the glass absorption band, which is caused by oxygen ions. The glass absorption of B270 at 355 nm is low, inducing an extinction of 0.13 for a slice of 1 mm thickness. After ion exchange extinction at 355 nm increases to 1.07 due to a homogeneous layer of silver ions, which has a thickness of ~40 µm. From these values the absorption length of la = 43 µm is obtained. The values for the material constants for B270 are D = 5.2 × 10−7 m2.s−1, ρ = 2500 kg.m-3 and cp = 860 J.kg−1.K−1. The thermal diffusivity of glass is temperature-dependent . To simplify the calculations it is kept constant and approximated by a temperature-averaged value. With these values the thermal diffusion length can be calculated for different diffusion times. It becomes equal to la for non-irradiated material after 3 ms, which is 240 times longer than the time between two laser pulses in our case. Therefore, the pulsed nature of the laser can be neglected under these conditions. It is shorter than the time of total irradiation of each spot for 340 pulses/spot used in the experiments, so heat conduction has a considerable influence on final temperatures. Also thermal diffusion length on the timescale of irradiation is considerably larger than the beam radius of 30 µm, and hence it would not be sufficient to calculate heat diffusion in only one dimension. The absorption length is decreasing during the process. There are silver nanoparticles forming in the glass, which induce absorption due to their plasmon band. Due to this effect, for irradiation with 3 µJ ps pulses, the extinction at 355 nm increases to 4 after the process, which is equivalent to an absorption length of 10 µm. Irradiation with 5 µJ pulses results in an extinction of 7 at 355 nm, leading to an absorption length of 5.7 µm.
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5082
The thermal diffusion length for the 10 ns laser pulse length is 72 nm, while for 10 ps it is only 2.3 nm. This is much smaller than the absorption length of non-irradiated particlecontaining glass, which explains why experimental results for the two different pulse lengths are macroscopically nearly identical. However SEM images show smaller particle sizes for ns-pulsed irradiation than for ps-pulsed irradiation for the same laser fluence. This indicates a different behavior for both pulse lengths when the surface particle film is formed. This can be explained by the reduction of the absorption length below the thermal diffusion length for 10 ns. Nonlinear absorption effect in the metallic surface layer could also contribute to this. The time-dependent temperature distribution in the glass during the process T(x,y,z,t) can be described by the heat diffusion equation: ∂T ( x, y , z, t ) 1 ∂Q ( x, y , z, t ) = ∇[ D∇T ( x, y , z, t )] + , ∂t ∂t ρcp
where Q(x,y,z,t) is the generated heat density. Its time derivative is equal to the temperature increase due to the absorption of laser radiation. For a pulsed Gaussian laser beam with a repetition rate f it can be written as: ∂Q ( x, y , z, t ) N −1 n ( x − vn / f )2 + y 2 z = Q0δ (t − ) exp[− − ], ∂t f w0 2 la n =0
where Q0 is the maximum heat density at the focus generated by a single pulse and δ(t) is the Dirac delta function describing infinitely short pulses. The Gaussian beam, with a beam radius of w0, is aligned parallel to the z-axis and irradiating the sample surface which is located at z = 0. The beam is scanning over the sample surface in the x-direction with speed v. Absorption is described by the absorption length la. Assuming a constant diffusivity the heat equation becomes a linear differential equation. Then the temperature distribution after N-th laser pulse can be written as a sum of the temperature changes caused by the individual pulses : T (t , x, y , z ) = n =0 ΔT1 (t − n / f , x − vn / f , y , z ) + T0 , N −1
where ΔT1 is the temperature change induced by a single pulse. Using the Green’s function method  the solution for the temperature change induced by a single pulse can be found: ΔT1 (t ', x ', y , z ) =
− x '2 − y 2 exp [ f ( z, t ') + f z ( − z, t ') ] . ρ c pπ ( w0 2 + 4 Dt ') w0 2 + 4 Dt ' z Ep
Here Ep is the laser pulse energy and z + Dt '/ la 1 z + 2 Dt '/ la (7) exp erfc . 2 la l 2 Dt ' a Temperature distributions have been simulated for the employed experimental conditions for pulse energies of 3µJ and 6µJ. These two energy values are most interesting because particle formation in the volume occurs for 3µJ and more, and 6µJ is the threshold for both bubble formation and surface particle formation. Simulations were run for different absorption lengths since absorption lengths are changing during the experiment and are not exactly known. Up to 10000 laser pulses were simulated, and the maximum temperature increase in the glass was obtained for each simulation. The maximum temperature increase by a single laser pulse for different absorption lengths was also calculated for comparison. The results of this simulation are shown in Fig. 6. f z ( z, t ') =
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5083
Max. temperature increase [K]
This simulation shows an increasing maximum temperature for shorter absorption lengths due to the smaller size of the heated volume, and hence the observation of smaller particle sizes for ns-pulsed irradiation than for the ps-pulsed irradiation with the same laser fluence. For irradiation with 3µJ pulses of original ion-exchanged glass with an absorption length of 43 µm a maximum temperature increase of 650 K is obtained. Therefore, the temperature of the glass exceeds the transition temperature and is clearly within the range known to cause particle formation. This fits well to the experimental result for these parameters shown in Fig. 2.
2500 2000 Pulse train:
Single pulse: 6µJ
Absorption length [µm] Fig. 6. Simulated heating of ion exchanged glass for conditions used in the experiments. The vertical dotted black line marks the absorption length of non-irradiated glass of 43 µm. The dashed blue curve shows the maximum temperature increase for irradiation with 3 µJ pulses. Solid black curve shows maximum temperature increase for irradiation with 6 µJ pulses. Dotted red curve shows the maximum effect on temperature caused by a single pulse of 6 µJ. Notable is the 650 K temperature increase for 3 µJ irradiation at an absorption length of 43 µm. This is adequate to explain the observed generation of nanoparticles inside the glass. For laser pulse energy of 6 µJ bubble formation is observed. This requires heating over the boiling point at about 2400 °C. Such temperatures would be achieved with a constant absorption length of 10 µm. In the actual experiment larger and smaller absorption lengths occur.
For 6 µJ it has to be taken into account that the absorption length is reducing considerably during the process, not only due to the generation of particles in the volume of the glass, but also the temperature increase induces a shift of the absorption edge to longer wavelengths  as well as a shift of the Ag+ absorption band . In fused silica the glass absorption band is shifting by about 1 eV per 1000 K of temperature change. This can induce a strong decrease in absorption length since the irradiation wavelength lies on the flank of these absorption bands. It should be noted that lines within the squares were written with an overlap to produce a homogeneous area with surface particles, decreasing the initial absorption length. The line distance was 61 µm, while the width of the region with particles in the volume of the glass was 90 µm. In the experiment bubble formation occurs for pulse energies exceeding 6 µJ. This indicates that the glass was heated over the boiling point, which is at about 2400 °C. In the simulation this temperature occurs for absorption length of 10 µm. Particle formation in the volume of the glass is sufficient to explain this absorption length. When boiling temperatures are reached further heating leads to the evaporation of material. This is observed in the form of ablation of material from the surface and of evaporation within the material, resulting in bubble formation. The latter can result from the formation of a subsurface heated layer  which can form in weakly absorbing materials due to heat loss at the surface. Ablation of an
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5084
initially larger amount of metallic silver from the surface can result in regular patterns, which have been observed previously on a smaller scale, when evaporating single nanoparticles on a surface . 4. Conclusion Silver ion exchanged glasses were irradiated with picosecond and nanosecond laser pulses. This resulted in the formation a metallic-looking film at the glass surface. An optical transmission analysis showed surface plasmon absorption bands typical for silver nanoparticles, and a broadband extinction over the whole wavelength range - both becoming stronger with increasing pulse energies. The observations and measurements proved to be very similar for both ps- and ns-pulse laser irradiation. Scanning electron microscopy showed that the irradiation resulted in the formation of silver nanoparticles at the surface of the glass. These particles are located in a single layer with only small variations in particle sizes and separations. Both properties are increasing with increasing pulse energy, and are larger for ps pulses than for ns pulses. This allows for the production of samples with different particle sizes. Thermal analysis attributes the macroscopically similar results of ps and ns pulses to a similar temperature distribution, resulting from a long absorption length and small thermal diffusion length. The absorption length is decreasing with increasing temperatures. At the threshold of surface particle formation the boiling point of the glass is reached. This indicates that ablation is needed for this process, and the different results for ps and ns pulses indicate a very short absorption length at the surface absorption at this stage of the process. The presented process allows fast and localized fabrication of a single layer of silver nanoparticles on a glass surface. The size and separation of these nanoparticles can be controlled by the laser parameters. The produced structures represent a promising base material for applications in optoelectronics, sensing technologies and chemistry. Acknowledgments This work was conducted under the aegis of the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom (EP/I004173/1). The authors would like to thank Dr A. C. Hourd for proof reading the manuscript. AA is currently an EPSRC Career Acceleration Fellow at the University of Dundee.
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Received 6 Jan 2014; revised 12 Feb 2014; accepted 16 Feb 2014; published 25 Feb 2014 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.005076 | OPTICS EXPRESS 5085