Nonlinear optical properties of detonation nanodiamond in the near infrared: Effects of concentration and size distribution

Diamond & Related Materials 32 (2013) 66–71

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Nonlinear optical properties of detonation nanodiamond in the near infrared: Effects of concentration and size distribution Sébastien Josset a, Olivier Muller b, Loïc Schmidlin a, Vincent Pichot a,⁎, Denis Spitzer a a NS3E “Nanomatériaux pour Systèmes Sous Sollicitations Extrêmes” UMR 3208 ISL/CNRS French-German Research Institute of Saint-Louis, French National Research Centre, 5 rue du Général Cassagnou, 68301, Saint-Louis cedex, France b Laboratory for Optronics and Laser Applications, French-German Research Institute of Saint-Louis, 5 rue du Général Cassagnou, 68301, Saint-Louis cedex, France

a r t i c l e

i n f o

Article history: Received 5 June 2012 Received in revised form 29 November 2012 Accepted 3 December 2012 Available online 8 December 2012 Keywords: Detonation nanodiamonds Optical power limiting Non linear transmission Size distribution

a b s t r a c t The present work investigates the nonlinear optical (NLO) properties of detonation nanodiamond (DND), focusing on their optical power limiting efficiency in optronics. Among the relatively numerous types of tested nanomaterials, the nanocarbonaceous ones are particularly promising. Here, we show that stable colloidal DND hydrosols are very efficient at blocking high energy beams (1064 nm), with very good linear transmittances over the whole visible and near infrared (Vis-NIR) range at low fluencies. Through the use of ultracentrifugation we could demonstrate that the power limiting efficiency of DND hydrosols is directly linked to the polydispersity. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Optronics, and more generally photonics, are considered to be the ongoing successors of electronics for some applications due to their enhanced performances which could overcome the approaching limits due to miniaturization. Many optronics applications rely on the nonlinear optical (NLO) properties of some materials. This new kind of optics was first studied in the 1960s and drastically impacted classical optics which was limited to their linear effects for centuries [1]. Among the very wide possibilities offered by NLO effects, one can emphasize on the possibility to produce operators, amplifiers, oscillators, modulators, etc. based on the photons frequencies which have numerous advantages over their classical pendants in electronics [2,3]. Besides, NLO properties can diminish at a given wavelength the transmittance through a given material with increasing fluence, forming a so-called optical limiter [1]. This limitation is related to two major mechanisms: the third-order nonlinear susceptibility χ(3) (responsible for the twophoton absorption and the Kerr effect), and the cumulative nonlinearities (accounting for thermal lensing, and other cumulative non-linear scattering). From a practical point of view, this can be used to produce ultrafast switches for telecommunications or more specifically optical filters to protect optical equipments from high energy irradiation [4]. This last application started to become important in the military research in the 1980s as a response to attacks perpetrated through lasers becoming

⁎ Corresponding author. Tel.: +33 389695071. E-mail address: [email protected] (V. Pichot). 0925-9635/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.diamond.2012.12.001

steadily more powerful and aiming at blinding the enemy observation systems (including the eyes). An ideal optical limiting device should be optically transparent for incident light of low fluences, allowing observations in the visible and near infrared domains (Vis-NIR), but able to block high energy beams at any wavelength. This last issue is the actual challenge since protections against known fixed wavelength are relatively easily done using interference filters or adequate material highly absorbing at this given wavelength. The nanomaterials development in the last two decades has attracted much interest in optics, but their potential in NLO is only relatively recent. Mostly gold, silver, copper and carbon based nanoparticles, like carbon nanotubes, fullerenes, and more recently graphene, have been widely studied and are the nowadays benchmark materials for NLO but there is a concrete need for new (nano)materials with enhanced NLO properties [5–8]. Moreover, besides the obvious practical applications, the development of NLO studies can give new insights into material sciences and chemistry, especially by providing a better understanding of the size effects. Besides owing the best thermal conductivity and an excellent chemical inertness, the attraction for diamond since millenia is mainly linked to its amazing optical properties. If the price of bulk diamond considerably limits its use, low-priced detonation nanodiamond (DND) particles have become a material of great interest these last years. Thanks to their unique physical and chemical properties, there are numerous applications for these small entities, the most cited focusing on biology, matrix reinforcement and seeding for CVD growth [9–11]. Nanodiamond is very interesting for nonlinear optical studies. Indeed, Trojanek et al. revealed that the nonlinear optical properties of nanocrystalline

S. Josset et al. / Diamond & Related Materials 32 (2013) 66–71

diamond grown by CVD process are really close to the one of bulk diamond. A very interesting multiphoton absorption mechanism has been demonstrated by Glinka et al. for diamond nanoparticles depending on their size and the excitating wavelength [12,13]. Moreover, a promising nonlinear behaviour of DND and their cousins the nano-onions at 532 nm was observed, and the nonlinear scattering of a 30 g L −1 functionalized DND at 1064 nm was demonstrated [14,15]. Most of the applications of DND require well dispersed particles, but nanodiamonds obtained by detonation are often found to aggregate into clusters of hundred nanometers in size or even bigger. Different mechanical methods have been used in order to break the aggregates: milling, ultrasonic stirring and both of them simultaneously [16–20]. The most efficient one seems to be the one invented by Ozawa which uses wet milling with zirconia micro-beads coupled to high-power ultrasonication. But two main drawbacks can be identified depending on the purpose of the nanoparticles: the first one is that small amount of zirconium impurities coming from the erosion of the zirconia beads are found in the samples. The second one is the local heating due to the shocks between the diamonds and the beads which might induce the transformation of the sp3 surface of the nanodiamonds into sp 2 surface species. Hence, the optimization of both dispersion and particle sizing are the first issues for a better understanding of the size effects of the DND of their non-linear optical properties. Ultracentrifugation (UC) is often used in biology, e.g. for the separation of proteins, DNA. After the air-annealing of nanodiamonds Shenderova et al. used a multi-step ultracentrifugation process with increasing Relative Centrifugal Force (RCF) ranging from 1×103 g to 2×104 g [21]. This process led to the obtention of nanodiamond aggregates between 5 and 70 nm. Morita et al. applied this technique with RCF going up to 3.5×105 g on nanodiamonds produced by high pressure and high temperature process (HPHT) [22]. These nanodiamonds are bigger than detonation nanodiamonds and have a particle size distribution with a mean diameter of 30 nm. However, if very small HPHT nanodiamonds (4 nm) can be observed, Transmission Electron Microscopy observations in this study reveal that most of these small particles are bound by interparticulate carbonaceous phases, leading to very stable agglomerates. This work deals both with the use of ultracentrifugation to obtain well dispersed, size controlled, DND suspensions and the non-linear properties of those aqueous suspensions, with respect to their size distributions and weight concentrations. A fullerene suspension in toluene has been chosen as a comparative because of its high performances in NLO, C60 being for unexplained reasons more efficient for optical limitation than its “cousins” at 532 nm (C70, C76 and C84) and even more at 1064 nm [23]. The NLO properties of fullerenes, and those of onion-like carbons, are directly linked to their π-electrons densities which induce a high χ(3) susceptibility, leading in turn to increased third order nonlinear phenomena [24,25]. However, C60 is also more easily destructed at this wavelength and nano-onions are photobleached whereas DND hydrosols seems to be very stable [15,26]. In the case of DND, Rayleigh scattering appears to be the most contributing part of the optical limitation [7,26]. 2. Experimental section 2.1. Ultracentrifugation of the DND suspensions Nanodiamonds were synthesized at the French German Research Institute of Saint-Louis (ISL) by the detonation of hexogen/trinitrotoluene charges 30/70 [27]. The purification process used to recover the detonation nanodiamonds from the detonation soot leads to the formation of hydrophilic oxygenated groups on the surface of the nanodiamonds. The mean surface density of carboxyl groups is estimated to be about 0.80 “COOH”/nm2 [28]. Nanodiamonds suspension with a concentration of 1 g L−1 was prepared in ultrapure water (resistivity=18.2 MΩ) by a 1 h ultrasonication treatment. This concentration was used in order to

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have enough particles concentration to obtain reliable results with Dynamic Light Scattering (DLS). The supernatant SA obtained from this suspension after 48 h of sedimentation (0.18 g L−1) was submitted to ultracentrifugation for different RCF (from 9.5×103 g to 3.4×105 g) and durations (from 5 min to 4 h). The ultracentrifuge used is the Optima Max from Beckman Coulter with two different rotors with constant angles of 26°: the MLA 55 and the MLA 80 allowing respectively RCF up to 2.9×105 g and 4.4×105 g. 2.2. Size distributions analyses After ultracentrifugation, the size distributions of the DND present in the supernatant of the resulting suspensions were analyzed by DLS (Malvern zetasizer NanoZS). It is noteworthy to emphasize that the sphericity of the synthesized particles is very close to the unity, so that it can be assumed that their real diameters can be relatively well approximated with their Hydrodynamic Equivalent Diameters (HED). To confirm this assumption, Atomic Force Microscopy (AFM) observations were realized by deposing 10 μL droplets of the supernatant obtained after 5 min ultracentrifugation of SA at 1.5×105 g. Mica is an atomically flat support (Veeco™) and its high hydrophilic nature lets the droplet instantaneously spread over the whole surface, allowing particle size characterizations. AFM characterizations were achieved in the Tapping Mode® with a Nanoscope IV multimode AFM (Digital Instruments, Santa Barbara, USA). The probe used was a “FESP” (Force Etched Silicon Probe) produced by NanoWorld Ltd. Co with a radius of curvature about 8 nm. 2.3. Preparation of the nanocarbonaceous suspensions To determine the influence of the DND concentration onto their optical properties, two aqueous sets of serial dilutions (1/2nd and 1/10th) were prepared from the supernatant SA (0.18 g L − 1) as described above. The first more concentrated set with weight concentrations ranging from 1.8 × 10 − 1 g L − 1 to 2.0 × 10 − 2 g L − 1 was dedicated to the Vis-NIR linear transmission measurements, whereas the second set (1.8 × 10 − 1 g L − 1 to 1.8 × 10 − 4 g L − 1) was used for the NLO characterizations. For the C60, a solution with a concentration of 1.2 10 3 mg L −1 in toluene was prepared to obtain similar NLO properties as for the SA suspension at 1064 nm. 2.4. Preparation of the nanocarbonaceous suspensions with identical weight concentrations To determine the influence of the size distribution over the NLO properties, four suspensions were prepared from SA. The first one (SB−) was achieved by submitting SA to UC (5.9×104 g for 10 min). Note that these conditions were chosen to obtain an overall concentration compatible with DLS measurements, i.e. not too low, with a relatively low polydispersity index (PDI: square of the normalized standard deviation of a distribution). For the second suspension (SB+), a 5 mL aliquot of SB− was completely dried and then resuspended in 5 mL UHQ water. Thanks to this procedure, only the particle size distribution is modified through aggregates formation, but not the overall concentration. The third suspension (SB=) was prepared from an equivolumic mix of SB− and SB+. The size distribution profiles were determined by DLS according to the same procedure than described above. The weight concentration of these suspensions was estimated by drying 100 mL of SB− and burn the DND residue under a 50 mL min−1 flux of 80:20 N2:O2 (CO2 free). The exhaust gas was bubbled into a 100 mL vigorously agitated, concentrated (2.0× 10−2 M), Ca(OH)2 solution freshly prepared and HCl titrated. This procedure precipitates the gaseous CO2 formed during the DND combustion into insoluble CaCO3 in concentrated alkali Ca2+ solution (dissociation constant of CaCO3 in pure water at 298 K: 4.9× 10−9). Conductivity measurements of the bubbling solution before and after combustion were used to

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S. Josset et al. / Diamond & Related Materials 32 (2013) 66–71

determine that the amount of carbon from the DND in those suspensions is 7.5 × 10−3 g L −1. Hence, a fourth suspension (SC) was prepared by diluting SA to this concentration. 2.5. Linear and non-linear optical measurements The linear transmittance measurements were classically realized with a UV-Vis-NIR spectrophotometer (CARY5E, Varian) scanning with wavelengths ranging from 400 nm to 1100 nm. These linear transmittance results are corrected by the transmittance of both solvent (water or toluene) and cuvette (polystyrene). For the NLO characterizations, an Nd:YAG laser system (Spectron) was used as a laser source for nanosecond laser pulses. The output energy of the laser system extents up to 400 mJ with a wavelength of 1064 nm with pulse durations of about 7 ns at 5 Hz (20 pulses per fluence level). The laser beam first passes through an optical isolator in order to protect the laser source from reflected radiation (Fig. 1). Then, using a Galilean telescope, the laser beam is expanded by a factor of 6.7 to a beam diameter of approximately 33 mm in order to produce far field conditions (plane waves). Using a beam splitter, the laser beam is split into a reference beam and a signal beam. The energy of the laser pulse is assessed by the means of the reference beam. The incident radiation intensity on the reference photodiode (Thorlabs DET36A/M) remains so far constant throughout the measurement of a protective filter, apart from unavoidable fluctuations in the intensity of the laser system which are recorded by the reference beam. The initially expanded beam is brought to a diameter of 12 mm after passing the aperture A1. The beam then passes through a Keplerian telescope, consisting of lens L1 (focal length f=60 mm) and lens L2 (focal length f=100 mm). The A2 aperture, with a diameter of 20 mm is positioned behind lens L2. By means of A1 and A2, a f/5 optical system is achieved. The sample to be examined is placed in the focal plane of the telescope. The waist of the laser beam in the focus is approximately 10 μm at a wavelength of 1064 nm. The laser beam transmitted through the sample is further focused through lens L3 (focal length 400 mm) to measure the pulsed energy on a photodiode (Thorlabs DET36A/M), whereby the photodiode signal is recorded by means of an oscilloscope for later evaluation (Lecroy 3 GHz). In addition, a pinhole aperture with an opening diameter of 600 μm is positioned at the focal point of lens L3 toward the photodiode. Together with the focal length of lens L3, its diameter defines a field of view of 1.5 mrad, which corresponds to the smallest critical angle αmin of the human eye (as per DIN EN 60825-1). If light is emitted from an angle field of less than αmin, the source of radiation is seen as

a point. The MPE (maximum permissible exposure) and AEL (accessible emission limit) are independent of the size of the radiation source in this case. This represents the worst case and is thus realized in the experiment. If radiation is emitted from a larger angle range than αmin, the light source is regarded as an extented source. Higher limits are permitted for extented sources. The incident pulse energy on the sample can be varied by means of neutral density filters in front of the Keplerian telescope. Input energy during the experiment is usually in the range of nanojoules up to tenth of milijoules. The neutral density filters after the telescope serve to protect the photodiode from excessively high light intensities and also ensure that the photodiode together with the preamplifier always operate in the linear range. The optical path of the beams through the suspensions is equal in both linear and nonlinear characterizations to 10 mm. 3. Results and discussion 3.1. DND sorting by size through UC The influence of the RCF and the duration applied during the ultracentrifugation on the size of aggregates and particles still present in the suspension after these solicitations have been investigated. The ultracentrifugation was used in order to select the particle sizes, it is noteworthy to emphasize that the ultracentrifugation does not allow the disaggregation of the nanodiamond particles. The hydrodynamical equivalent diameter (HED) of the diffracting entities (aggregates and/ or particles) were determined from the “Z-average” values calculated from the intensity signal (the Z-average is sometimes called “cumulant average”). As expected, when the duration of the UC and/or the applied force increase, the HED of the particles in the resulting suspensions becomes smaller, but the overall concentration in the suspension also drastically decreases. The HEDs can be very satisfyingly correlated to both RCF and duration using a four parameters empirical equation (Eq. 1, number of experiments: 29, degree of Freedom adjusted coefficient of correlation: 0.984; Fig. 2a). This can considerably facilitate the preparation of calibrated DND suspensions. The polydispersity indexes (PDI) of the different suspensions were found to be between 0.18 and 0.29 indicating a relatively large distribution directly linked to the starting size distribution (PDI = 0.30). However, for a given HED, a smaller PDI can be obtained with a longer centrifugation time at lower CF as shown on Fig. 2b). This can be explained by the much weaker wake effects at low velocities of the

Fig. 1. Optical setup for the NLO experiments. A1, A2: apertures, L1, L2, L3: Lens, NDf: Neutral Density filters, B/S: Beam Splitter.

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Eq. 1. Empirical relationship between HED (nm), RCF (g) applied and duration t (s) of the ultracentrifugation. a = 11, b = 0.03, c = 0.62, d = 2.4 × 107.

a

Hydrodynamical Equivalent Diameter (nm) 70 60

105

Rel. Freq. by intensity

0.15

SA & SC Smin B Smix B

0.1

Smax B

0.05

CF(g)

50

0 0 10

40

101

30

102

103

104

d(nm)

20 10

10

Fig. 4. Size distributions of SA, SB−, SB+, SB = and SC (identical to SA) determined by DLS.

4

103

104

t (s)

Polydispersity index

b

0.28

0.26

105

CF(g)

0.24

0.22

0.20

104

103

t (s)

104

Fig. 2. a) HED (nm) vs. RCF (g) applied and duration t (s) of the ultracentrifugation. b) Polydispersity index vs. RCF (g) applied and duration t (s) of the ultracentrifugation.

larger particles onto the smaller ones, leading to a more effective size separation. The UC operational parameters were chosen according to these results for the study of the effect of the size distribution on the NLO properties. The AFM micrographs at different places of the supernatant obtained after ultracentrifugation of SA (5 min at 1.5×105 g) are homogeneous and visually in a good agreement with the DLS results in terms of number AFM (height) DLS (number)

of diffractive particles. In order to confirm this point, an AFM micrograph was analyzed with the freeware ImageJ to determine the local maxima and obtain their distribution. The noise tolerance was set to 10 leading to about 4800 maxima on a 5 μm by 5 μm surface. The good agreement between the distributions obtained by AFM and by DLS confirms the assumption that the DLS size measurements can be used as an acceptable approximation of the actual sizes, at least for well disaggregated particles suspensions (Fig. 3). The size distributions of SA, the same as SC, and those of the three isocratic suspensions SB−, SB=, SB+ determined by DLS are depicted on Fig. 4 (respective Z-average values: 168 nm, 34 nm, 78 nm and 99 nm; respective polydispersity index: 0.250, 0.173, 0.186 and 0.155). These distributions were measured before and after the optical measurements showing neither precipitation nor deviations in their distributions. 3.2. Nonlinear optics Fig. 5 shows the nonlinear transmissions of SA and of a C60 solution in toluene for which it was necessary to add up to 1200 mg L −1 to obtain similar optical limiting. It is interesting to point out that both types of materials show the same onset of non-linear transmission. It is well accepted that the main non-linear mechanism occurring in C60 is reverse saturable absorption, mostly attributed to triplet-triplet absorption [29]. Considering the DND suspension, the reasons for this effect are more unclear. Dynamic light scattering, especially Rayleigh–Mie scattering, as pointed out by Mikheev et al. contributes to the mechanisms routing to the optical limiting phenomenon [26]. Moreover, the existence of other effects like non-linear scattering and excited states

Rel. Freq.

0.2

0.15

0.1

0.05

0 100

101

102

103

104

d (nm) Fig. 3. Size distributions obtained by DLS and AFM of the DND present in the supernatant of an aliquot of SA after ultracentrifugation (5 min at 1.5 × 105 g). The analyzed image is superposed.

Nonlinear Transmittance at 1064 nm

0.25 100

10-1

SA 180 mg/L C60 1200 mg/L -2

10

10-4

10-2

100

102

EIN (µJ) Fig. 5. Nonlinear transmissions of SA and of a C60 solution in toluene.

104

70

S. Josset et al. / Diamond & Related Materials 32 (2013) 66–71

Linear Transmittance

1

0.8

0.6

0

SA/2

1

SA/2

0.4

2

Eq. 2. Merit function.

SA/2

3

0.2

SA/2

C60 1200 mg/L 0 400

500

600

700

800

900

1000

1100

Wavelength (nm) Fig. 6. Linear transmissions of SA, its serial dilutions and a C60 solution in toluene.

absorption are to be taken into account. However, the measurements with the fullerene were stopped at 600 μJ because its limiting properties were no longer sufficient to protect the optical setup at higher fluencies, on the contrary to the DND suspension which was efficiently acting at fluencies starting from about 90 μJ up to 8900 μJ. One might suppose that the behavior of the C60 solution at higher fluencies is linked whether to their destruction or to the so-called plasmon bleaching effect, whereas the DND suspensions are remarkably stable [7]. Secondly, an ideal limiting system should protect at high energy inputs, but should obviously allow observations in the Vis-NIR range at lower fluencies. The linear transmission properties between 400 nm and 1100 nm at low fluences of DND suspensions at various concentrations and that of the C60 solution are depicted in Fig. 6. This clearly shows that the concentrated C60 solution does not enable observations between 400 nm and 700 nm, i.e. in almost all the visible range. On the contrary, the DND suspensions used have relatively high linear transmissions over the whole Vis-NIR range. Since they are under a critical weight concentration, these colloidal aqueous suspensions are stable over years without any modifications, even by heating with constant volume. The work realized by Mikheev et al. gives very interesting insight into the phenomena implicated in the nonlinear scattering of DND, showing the predominance of Rayleigh scaterring at higher fluencies. However, the 30 g L −1 DND suspensions of 50 nm aggregates exhibits only 60% transmission at 1064 nm, whereas the most concentrated DND suspension in our work (SA) let

95% of the photon flux passes through at low fluence. It can be assumed that a 30 g L −1 DND suspension is almost completely opaque in the visible range, which might be redhibitory for many applications. The influence of the DND concentration on the optical limiting properties is depicted in Fig. 7. The most concentrated suspension SA blocks 97% of the incident beam at 8900 μJ. Diluting SA by a factor of ten and hundred leads respectively to 90% and 85% optical limitations at 8900 μJ, with interesting transparencies in the Vis-NIR range. The most diluted suspension tested (1.8 × 10−1 mg L −1) does not enable measurements at the highest energy input because it is no longer efficient enough regarding the limiting properties. In order to compare the efficiencies of different materials, we defined a dimensionless criterion, Ω, which is equal to the ratio of the average linear transmission in the Vis-NIR range to the average value of the nonlinear transmission at 1064 nm over the range of tested fluencies (Eq. 2). Hence, it takes in account both the required transparency for observations and the limiting properties. Obviously, the wavelengths range can be adapted if only a part of this spectrum is used, e.g. for infrared sensors. The average linear transmissions of the diluted suspensions are assumed to be equal to the unity when the weight concentration is below 0.225 mg L −1 (Fig. 6). Hence, the Ω for SA, its serial dilutions to the tenth (1/10, 1/100 and 1/1000), and the C60 solution are respectively: ΩSA = 6.75, ΩSA/10 = 4.20, ΩSA/100 = 2.77, ΩSA/1000 = 1.86 and ΩC60 = 0.84. This confirms numerically the visual conclusion that even the most diluted DND suspension is more efficient, according to the Ω criteria, than the fullerene suspension. The four isocratic suspensions (i.e. same weight concentration of DND but different size distributions) have characteristics and merit criteria summarized in Table 1. Through the aliasing of the weight concentration effects, it clearly appears, as expected, that the size distribution has a drastic effect on

100

2.8

2.6

Ω

Nonlinear Transmittance at 1064 nm

3.0

10-1

0

SA/10

2.4

1

SA/10

2

2.2

SA/10

3

-2

10 10-4

SA/10

10-2

100

102

EIN (µJ) Fig. 7. Nonlinear transmissions of SA and its serial dilutions.

104

2.0

0.16

0.18

0.20

0.22

Polydispersity Index Fig. 8. Relationship between Ω and the polydispersity index.

0.24

S. Josset et al. / Diamond & Related Materials 32 (2013) 66–71

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Prime novelty statement

Table 1 Polydispersity indexes PDI, Z-average values, and Ω of SB−, SB=, SB+ and SC. Suspension

PDI

Z-average (nm)

Ω

SB− SB= SB+ SC

0.155 0.186 0.173 0.250

98.6 78.1 34.2 168.0

2.20 2.46 2.33 2.81

the limiting potential of DND suspensions. Very interestingly, there is a significant positive linear correlation between the Ω criterion and the PDI of the different suspensions (Ω = 6.3 PDI + 1.2; r 2 adjusted: 0.982, Fischer ratio: 167.3) (Fig. 8), but this is not the case with the Z-average values. It is noteworthy to emphasize that in those cases, the mean linear transmittance is equal to 100%, so that the merit function is only depending on the nonlinear properties of the isocratic suspensions. Usually, polydispersity and more generally disorder in optics are linked with problems, especially noise. Here, we show that polydispersity is, in this case advantageous since the main objective of optical limitation is to disperse the incident energy as well as possible. Mikheev et al. proved that the main nonlinear limiting effect of DND hydrosols is Rayleigh scattering [15]. This is in good agreement with our observation that the nonlinear transmission efficiencies are correlated with the PDI of DLS measurements which are based on Rayleigh diffusion too. Hence, a much more efficient dispersion of light can be achieved by a polydisperse DND suspension. Of course, the smallest the particles are, the better the linear transmission is, so that there is a compromise to find between PDI and Z-average. 4. Conclusions Here we show that DND hydrosols have extremely interesting nonlinear optical properties, which are better at 1064 nm than the more classical C60 based solutions. Moreover, their unique properties, especially the high thermal conductivity and the chemical inertness, might confer them a very good resistance to high energy pulses so that DND based materials should be further investigated in terms of NLO [15]. Especially, the causes routing to the observed drop in transmission at high laser fluences have to be further investigated in terms of light scattering on the one hand and in terms of excited state absorption due to the occurrence of plasmas on the other hand. Through AFM measurements, we could unambiguously prove the very good agreement between the sizes obtained by DLS measurements and the real particle sizes. Hence, the use of ultracentrifugation allows the preparation of DND suspensions which are well calibrated in both sizes and dispersities (DLS characterization). The definition of a merit function Ω allows the objective comparison between materials and takes in account both transparency and optical limitation. We could show that, at a constant weight concentration, there is a direct positive relationship between this criterion Ω and the polydispersity index which shows that different sizes act in a synergistic way to limit high fluencies beams. Finally, this work emphasizes on the fact that the comparisons between particles based materials dedicated to nonlinear applications require accurate and complete size distribution characterizations.

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