the absorption of optical 
 energy by micro- and nanoparticles in 
 liquid , and the follow - up photothermal conversion and heating of the 
 surrounding liquid , induces vapor bubbles around such particles if 
 the incident optical fluence exceeds a specific threshold . the energy efficacy of vapor bubble generation increases when the 
 particle - to - liquid heat transfer is localized and the bulk heating 
 of liquid is minimized . this thermal confinement is usually achieved 
 by shortening the duration of the optical excitation to minimize thermal 
 diffusion . in the case of a nanoparticle , 
 the duration of the optical excitation shortens to the nano- and picosecond 
 range to prevent the bulk heating of the surrounding liquid . this , in turn , makes the generation of a transient vapor nanobubble 
 a highly nonstationary processes . the combination 
 of the nanosize of the optical absorber with the drastic increase 
 in the photothermal efficacy of plasmonic nanoparticles ( compared 
 to that of any molecular absorbers ) resulted in a new class of nanoevents , 
 plasmonic nanobubbles ( pnbs)vapor nanobubbles , generated via 
 the photothermal conversion around plasmonic nanoparticles . the physical properties of pnbs were shown to be different 
 from 
 both those of the stationary photothermal effects of plasmonic nanoparticles under continuous optical excitation and 
 of laser - induced vapor bubbles in liquid via the mechanisms of optical breakdown or homogeneous optical absorbance by liquid . the photothermal properties of nanoparticles under stationary excitation 
 are determined by their preset properties , such as optical absorbance , 
 which remain permanent during their optical excitation . in contrast , 
 an intense short pulsed excitation of metal nanoparticle during the 
 generation of a pnb results in a rapid dynamic modification of the 
 optical absorbance , size , structure , and phase state of the nanoparticle and results in entirely new optical , physical , and biomedical properties 
 of pnb compared to those of plasmonic nanoparticles . for example , compared to gold nanospheres with a broad excitation 
 visible spectrum , gold nanosphere - generated pnbs yield an ultranarrow 
 peak in near - infrared . the photothermal 
 generation of vapor bubbles in optically absorbing liquids involves 
 extensive bulk heating above the evaporation threshold temperature , 
 while the pnb , in contrast , thermally insulates the bulk liquid and 
 thus maintains its temperature close to the ambient level . the optical breakdown - induced vapor nanobubbles 
 do not require significant optical absorbance by the medium . however , 
 an optical breakdown involves high local pressures and temperatures , 
 and often shock waves , thus making it difficult to precisely control 
 the optical breakdown - generated vapor nanobubble . the relatively high threshold of laser fluence and intensity 
 for optical breakdown limits biomedical applications of breakdown - generated 
 nanobubbles . in contrast , pnbs demonstrated excellent biologic safety because of their localized mechanical , nonthermal impact , and low 
 threshold energies down to 515 mj cm , which match even the federal laser safety standards . the remote on - demand generation , precise control 
 of their mechanical impact , and easy optical and acoustic detection 
 result in promising biomedical applications of pnbs for diagnostics , 
 therapy , and theranostics and in various industrial applications . however , pnb applications are still 
 relatively limited compared 
 to those of plasmonic nanoparticles or laser - induced vapor bubbles 
 in liquids . this is largely caused by the lack of the universal methodology 
 of pnb generation in real conditions . a pnb is not a particle 
 but rather a transient nonstationary nanoevent that results 
 from several transient nanoscale processes at the sub - nanosecond time 
 scale ( figure 1 ) . under an excitation of plasmonic 
 nanoparticle with an ultrashort single laser , these processes include 
 photon - phonon - heat conversion , nanoparticle surface - to - liquid heat 
 transfer , liquid evaporation , and vapor bubble expansion and collapse . the nonstationary nature of these processes , coupled with the dynamically 
 changing optical and thermal properties of the nanoparticle under 
 high ( melting ) temperatures , seriously complicates the modeling of 
 pnbs , compared to the modeling of stationary or low temperature photothermal 
 effects . experimental studies of pnbs at the nanoscale usually describe 
 their properties under the specific duration of the excitation laser 
 pulse and for the specific nanoparticle system . such properties are 
 difficult to extrapolate into other laser pulse durations and nanoparticle 
 systems . in addition , the majority of experimental models use nanoparticle 
 ensembles , multiple laser pulses , and indirect detection of pnbs through 
 their secondary cumulated effects . all these factors distort the understanding 
 of the pnb generation mechanism . as a result , the practical use of 
 pnbs remains rather challenging for a broad community . a temporal sequence of 
 processes involved into the photothermal 
 generation of plasmonic nanobubble ( pnb ) and the initial dynamics 
 of the vapor layer near the surface of plasmonic ( gold ) nanoparticle 
 ( gnp ) . here , we study the key factor 
 for a pnb , a duration of 
 optical excitation , in the range from picosecond to continuous 
 excitation . this study employs various nanoparticle systems  from 
 isolated nanoparticles to their suspensions and to large clusters 
 of aggregated nanoparticles . we used the basic and most available 
 type of plasmonic nanoparticles  solid gold nanospheres ( also 
 known as colloids)under resonant 
 and off - resonant single pulse excitation . individual pnbs were directly 
 detected and quantified to provide reliable and easy - to - interpret 
 data that can be extrapolated to various applications . solid gold 
 spherical nanoparticles 
 ( gnps ) ( vanpelt biosciences , llc , montgomery village , md and ted pella , 
 inc . , redding , ca ) were employed as a model because they showed the 
 widest applications of the plasmonic effect . it possesses all of the 
 optical and thermal properties of more complex recently engineered 
 gnps such as rods , shells , cages , and stars . we studied three typical 
 states of gnps in water : single isolated particles , isolated clusters 
 of 5100 tightly aggregated particles , and suspensions of isolated 
 particles . the isolated particles are considered 
 as the best model to study the pnb generation mechanism , while cluster 
 and suspensions represent typical states of gnps in the majority of 
 plasmonic np applications . gnp aggregation was achieved by adding 
 nacl and resuspending gnps in water after their aggregation . the optical 
 excitation of gnps was performed in sealed glass cuvettes with internal 
 lateral dimensions of 1020 mm and a height of 0.12 mm . the optical extinction spectroscopy was used to monitor the concentration 
 of gnp suspensions ( figure s1 , supporting information ) . the gnp size and shape were characterized with transmission electron 
 microscopy ( figure s2 , supporting information ) . the results obtained with 
 multipulse excitation can suffer from uncertainties related to the 
 laser - induced modification of gnps by subsequent laser pulses . in 
 order to avoid any cumulative effects due to gnp modification and 
 to achieve the maximum accuracy of the measurements , we applied individual laser pulses of a specific wavelength , 
 fluence , and duration . to study the resonant excitation of gnps , the 
 laser radiation was applied at a fixed wavelength of 532 nm , close 
 to that of the plasmon resonance peak for 60 nm solid gold spheres . off - resonant pulsed excitation was studied with the variable near - infrared 
 wavelength in the range of 700850 nm . five excitation duration 
 modes were realized with five lasers : 20 ps pulses ( pl 2143a/20/ss , ekspla , lithuania ) , 70 ps ( pl2250 - 1-sh - p100 , ekspla , 
 lithuania ) , 400 ps ( sta-01 , standa ltd , lithuania ) , 14 ns ( lotis tii , 
 belarus ) , and a continuous laser ( pgl - v - h-532 , extreme lasers ) . we 
 did not employ shorter pulses ( < 10 ps ) in order to avoid optical 
 breakdown and plasma formation because this regime of vapor bubble 
 generation is completely different from the photothermal mechanism 
 considered in the present study . tunable near - infrared wavelengths were obtained from the correspondent 
 optical parametric generator units of each of the above - mentioned 
 lasers . laser beams were spatially filtered and focused into a spot 
 of 20 m diameter with the gaussian spatial distribution of 
 laser intensity . the beam diameter at the working plan 
 was measured at the level of 1/e of the maximal fluence 
 using the laser beam image ( obtained with a ccd digital camera , luka 
 model , andor technology , northern ireland ) . the pulse energy was measured 
 with ophir meter ( ophir optronics , ltd . , were imaged 
 with the original time - resolved optical scattering method . briefly , a probe laser pulse ( 576 nm , 20 ps , 
 100 j cm ) was directed at the cuvette at 
 a small angle ( figure 2b ) . only the scattered 
 part of the probe laser pulse was collected by the microscope objective . 
 in order to image transient pnbs , the probe pulse was delayed with 
 respect to the excitation pulse by 10 ns . since the intensity of the 
 scattered light correlates with the size of the scattering object , the image pixel amplitude was used as a metric of the gnp cluster 
 size . in order to estimate the pnb maximum diameter , we used another 
 scattering technique with a low - power continuous probe laser ( 633 
 nm ) ( figure 2c ) . this continuous probe laser 
 was focused on the object collinearly with the excitation pulse , and 
 the axial intensity of the probe laser was monitored . an expanding 
 and collapsing pnb scatters the probe laser beam and , thus , reduces 
 its axial intensity when the pnb expands and restores it to the baseline 
 level when the pnb collapses , thus producing the signal of the pnb - specific 
 time - shape . the duration of the pnb - specific 
 time - response was measured at the half - maximum level as a pnb lifetime . this lifetime correlates to the maximum diameter of the pnb and therefore was used as the major pnb metric . ( a ) the gnp is exposed to a focused collinear single 
 excitation laser pulse with tunable wavelength and fluence , and to 
 a continuous probe laser beam ( 633 nm ) . ( b ) the optical scattering 
 effect of the expanding and collapsing vapor nanobubble reduces the 
 axial intensity of the continuous probe laser beam and thus delivers 
 the nanobubble - specific time - response of the photodetector . ( c ) optical 
 scattering imaging of pnb with a pulsed probe laser . in order to theoretically estimate 
 the threshold fluence that corresponds to the heating of the gnp in 
 water up to the critical water temperature and to calculate some other 
 parameters of gnp heating , we used a model adopted from our previous 
 work . this model couples an equation 
 with respect to the temperature of the gnp with the navier  stokes 
 equations and describes the temperature and pressure distribution 
 in the surrounding water . for the range of pulse duration under consideration , tl  20 ps , the effects of the electron - lattice 
 nonequilibrium in the gnp material and thermal expansion of the gnp 
 are relatively small and are neglected in the present model . then 
 the homogeneous gnp temperature , tp(t ) , is determined by an equation accounting for the laser 
 heating of the gnp and its conductive cooling by the surrounding water:1where rp , mp = ( 4/3)rp3p , and a are the particle radius , mass , and absorption 
 cross section ( a = 7000 nm for gnp of rp = 30 nm at the laser wavelength 532 nm ) , p = 19300 kg m and cp = 143.6 j kgk are the density and specific heat of the particle material ( gold ) , t is the time , il(t ) is the laser intensity , and q is the conductive 
 heat flux density at the particle surface . the heat flux density is 
 calculated based on the fourier law , qf = ftf/r , at r = rp , where r is the radial distance counted 
 from the gnp center , tf(t , r ) is the unsteady distribution of temperature 
 in the surrounding fluid , and f is the thermal conductivity 
 of the fluid . in order to calculate tf(t , r ) and q , eq 1 is solved together with the unsteady one - dimensional 
 navier  stokes equations for compressible fluid as described 
 in our previous work . since the purpose 
 of the simulations is to estimate only the initial stage of gnp heating , 
 when the vapor bubble is not formed yet , the navier stokes 
 equations are solved with the single - phase equation of state for liquid 
 water recommended for general and scientific use by the international 
 association for the properties of water and steam ( iapws ) . it is worth noting that recent molecular dynamics 
 simulations also showed that the surface tension pressure around a 
 60 nm sphere can inhibit the boiling of water and thus can support 
 further heating of the gnps up to the bulk melting temperature of 
 gold ( 1337 k ) without the active expansion of a vapor bubble . the temperature - dependent thermal conductivity and viscosity of 
 liquid water are calculated based on tabulated data from recent iapws 
 releases . in the model combining 
 eq 1 for a gnp with the navier stokes 
 equations for the surrounding water , it is assumed that the water 
 temperature at the gnp surface is equal to tpand , thus , the effect of the finite thermal boundary resistance 
 of the gnp / water interface is not taken into account . the problem is solved numerically with a splitting 
 method that ensures the total second order of approximation in time 
 and space . in particular , the convective part of the navier  stokes 
 equations is solved with the richtmayer scheme , and the diffusion 
 part is solved by the central difference scheme . in calculations of the pulsed laser heating , the 
 temporal profile 
 of the laser intensity is assumed to be gaussian , il(t ) = fl exp([t  3t]/[2t])/((2t ) ) , t = tl/(2(2 ln 2 ) ) , where fl and tl are the incident laser 
 fluence and the laser pulse duration ( full width at half - maximum ) , 
 respectively . in calculations 
 of continuous 
 wave ( c.w . ) laser heating , where the laser intensity is constant , il = fl/t ( t is the laser exposure time ) , 
 and the pressure waves are assumed to be weak and do not affect the 
 temperature distribution in water , so that eq 1 is coupled with the one - dimensional heat conduction equation instead 
 of full navier  stokes equations . in order to reveal the effects 
 of unsteadiness during c.w . laser excitations , the computational results 
 obtained with this model at the constant thermal conductivity of water 
 ( f = 0.6 w mk ) were compared with results obtained with a 
 quasi - steady - state model based on eq 1 , where 
 the fourier heat flux is calculated in the form qf = 2rpkfnu(tp  t ) , where nu is the nusselt number , and t is the ambient fluid temperature . the solution of the steady - state 
 heat transfer problem for a spherical body in a fluid with constant 
 thermal conductivity results in nu = 2 . with the assumption of nu = 
 2 , the solution of eq 1 takes the form : the comparison of this solution with 
 the numerical solution of eq 1 coupled with 
 the unsteady heat conduction equation for water showed that the quasi - steady - state 
 approximation ( nu = 2 ) accurately predicts the maximum 
 increase in temperature t , but substantially , 
 in two orders of magnitude , underestimates the characteristic heating 
 time . to estimate how fast a vapor may develop 
 at the surface of a gnp ( 60 nm solid gold nanosphere ) , we simulated 
 the gnp surface temperature dynamics in water in response to a single 
 laser pulse . in simulations , the laser fluence was fixed at the level 
 of 66 mj cm , which is well above the pnb generation 
 threshold . in this model , and for the initial stage of the gnp heating , 
 we considered that the level of the optical absorbance cross - section 
 of the gnp remains constant during its interaction with the laser 
 pulse ( although at later stages it changes drastically due to the 
 gnp heating and melting ) . this relatively high threshold 
 ensures the onset of vapor near the gnp surface under any conditions . after this temperature level was achieved , we did not model the follow - up 
 temperature dynamics because the laser - induced temperatures rapidly 
 reach the gnp surface melting conditions , and thus the gnp optical 
 absorbance , structure , and size undergo radical dynamic changes . we defined the vapor onset time tpnb ( figure 3a ) as the time interval 
 from the beginning of the laser pulse ( at the laser intensity level 
 1/e ) to the time point when the gnp surface temperature 
 reaches the vapor onset threshold . naturally , the vapor onset time 
 can not be shorter than the gnp thermalization time which has been 
 approximated by 5 ps . the vapor onset time was analyzed as a function 
 of the laser pulse duration from 20 ps to 14 ns ( black curve in figure 3b ) . ( a ) the calculated time - course of the temperature of gold 
 60 nm 
 nanospheres in water ( red curve ) during the absorption of a single 
 laser pulse at 532 nm ( pulse duration 20 ps ) with a gaussian temporal 
 profile ( black curve ) with the fluence of 66 mj cm . ( b ) the calculated vapor onset time ( black curve ) and the portion 
 of the laser pulse energy ( red curve ) which corresponds to the portion 
 of the pulse after the vapor onset as a function of the laser pulse 
 duration at 532 nm wavelength and fluence of 66 mj cm . ( c ) the calculated pnb generation threshold fluence as a function 
 of laser pulse duration at 532 nm wavelength . we also considered continuous excitation as a separate case 
 ( see 
 below ) . formally , their values were even lower than the gnp thermalization 
 time and were therefore approximated the vapor onset time by the longer 
 gnp thermalization time ( figure 3b ) . we further defined 
  the pnb energy  of the laser pulse as the percentage 
 of the laser pulse energy , which corresponds to the time interval 
 from the vapor onset to the end of the laser pulse ( figure 3a ) . pnb energy  indicates the 
 incident optical energy that can be utilized by a pnb . we analyzed 
 this pnb energy as a function of the pulse duration ( red curve in 
 figure 3b ) . for picosecond pulses , the vapor 
 onset time is only a small fraction of the whole pulse duration , and 
 hence the level of pnb energy was relatively high . longer pulses show 
 a decrease in the pnb energy due to the increased thermal losses for 
 the bulk heating of the surrounding water . finally , we estimated the 
 vapor onset threshold fluence which was defined as the fluence required 
 to achieve the vapor onset temperature of the gnp surface ( figure 3c ) . the pnb threshold fluence increases with the 
 pulse duration , mainly due to the increasing energy losses to the 
 bulk heating of water . thus , the modeled vapor onset time and the 
 laser threshold fluence are the lowest for the shortest pulses . in 
 particular , for the picosecond pulses the pulse energy is almost totally 
 utilized to generate the pnb . to 
 study the influence of the excitation pulse duration on pnb generation , 
 we employed isolated gnps in water and single laser pulses at 532 
 nm , which is close to the wavelength of plasmon resonance in 60 nm 
 gnps . individual gnps and pnbs were imaged via our time - resolved optical 
 scattering method ( figure 4a , b ) . the maximal diameter of the expanding and collapsing 
 individual pnb was quantified through the duration of its optical 
 scattering time - response ( figure 4c ) . this pnb metric was applied to characterize 
 the energy efficacy of pnb generation for a specific laser fluence . 
 under the fixed laser fluence applied ( 66 mj cm ) , pnbs were observed for all three picosecond pulse durations from 
 20 to 400 ps but were not observed for the nanosecond pulses ( figure 4d ) . the maximum pnb lifetime ( and hence the maximum 
 energy efficacy of pnb generation ) was observed for the shortest pulse 
 of 20 ps . apparently , the fluence applied , 66 mj cm , was above the pnb generation threshold for 20 and 70 ps pulses , 
 close to the threshold for the 400 ps pulse and below the threshold 
 for the 14 ns pulse ( figure 4d ) . we next measured 
 the pnb generation threshold fluence as a function of the laser pulse 
 duration ( red curve in figure 4d ) . optical scattering 
 time - resolved images of an individual gold 60 nm sphere in water ( a ) 
 and of pnb ( b ) generated around the same sphere in single 20 ps pulse 
 excitation at 532 nm . ( c ) time - response of 
 the same pnb as shown at ( b ) was obtained with the ( continuous wave ) 
 c.w . the lifetime is measured as the duration 
 at the level of 0.5 of the maximum amplitude of the pnb - specific signal . ( d ) dependences of the pnb lifetime ( black curve ) under specific excitation 
 wavelength of 532 nm and fluence of 66 mj cm and 
 dependence of the pnb generation threshold fluence ( red curve ) at 
 the excitation wavelength of 532 nm upon the excitation duration . the minimum threshold , which is 
 less than 18 mj cm , was observed for the shortest , 
 20 ps pulse . the 20-fold increase 
 in the pulse duration from 20 to 400 ps increases the threshold fluence 
 6.4-fold to 115 mj cm , while for the nanosecond 
 pulse , the pnb generation threshold fluence increases by almost two 
 orders of magnitude ( red curve in figure 4d ) . thus , the laser pulse duration radically influences both the energy 
 efficacy and the threshold fluence of pnb generation . quantitatively , the experimentally observed pnb generation thresholds 
 are higher than the estimated values . this disagreement may be caused 
 by several factors that are not taken into account in the theoretical 
 model but reduce the efficiency of pnb generation . namely , our model 
 does not account for additional energy required ( 1 ) to overcome the 
 surface tension pressure ( which is very high for isolated 60 nm gnps ) , 
 ( 2 ) to evaporate a specific volume of liquid for the formation of 
 a pnb , and ( 3 ) to compensate a substantial dynamic decrease in the 
 optical absorbance of a gnp during its interaction with the laser 
 pulse . the latter effect is caused by ( i ) vapor around the gnp that 
 significantly changes the dielectric functions of gold and , hence , 
 reduces optical absorbance at the resonance wavelength , ( ii ) extensive heating , melting , and size reduction 
 of the gnp , and ( iii ) additional scattering of the incident excitation laser 
 beam by the vapor all these factors are not taken into account in our model and explain 
 the almost one order of magnitude difference between the theoretical 
 and experimental pnb generation threshold fluences . a more accurate 
 theoretical prediction of the threshold fluences requires a fairly 
 complex computational methodology that is capable , in particular , 
 of connecting the heat and mass transfer processes in and around a 
 gnp with the dynamic variation of its optical absorbance . in addition , the individual pnb detection 
 limit in our experiments might have been relatively high , above 200 
 nm , and thus the smallest pnbs ( generated under the lower fluences ) 
 might have been missed . nevertheless , the above experimental data 
 are based on the direct detection of individual pnbs , and therefore 
 they correctly describe the influence of the laser pulse duration 
 on the pnb generation threshold and energy efficacy . to summarize , 
 short picosecond pulses provide the best energy efficacy of photothermal 
 pnb generation , while the use of popular nanosecond lasers may require 
 a 100-fold increase in the laser energy . the isolated gnps 
 studied above are not typical for real - world photothermal applications , 
 where gnps are used in the form of suspensions or / and aggregated clusters . 
 for example , active biotargeting of gnps results in their intracellular 
 clustering . we therefore studied the pnb 
 lifetimes ( a metric of the energy efficacy of pnb generation ) as a 
 function of the cluster size for isolated gnp clusters ( figure 5 ) and the concentration for gnp suspension ( figure 6 ) under a specific level of the laser fluence , 66 
 mj cm , above pnb generation threshold fluence . the excitation wavelength of 532 nm was close to that of the plasmon 
 resonance for the 60 nm solid spheres employed . on the basis of our 
 previous results , we used the most efficient 20 ps pulse . gnp clusters 
 in water were formed via the salt - driven aggregation of gnps . the 
 relative size of each individual gnp cluster was quantified via the 
 pixel amplitude of its optical scattering image ( figure 5a ) . the pnb lifetime was measured for individual clusters 
 in response to a single laser pulse ( figure 5b ) . the pnb lifetime increases with the gnp cluster size almost linearly 
 and exceeds that of a single gnp by approximately five - fold ( black 
 curve in figure 5c ) . this significant increase 
 in pnb generation efficacy of the cluster vs isolated gnp under identical 
 laser fluence can be explained by ( 1 ) the enhancement of plasmonic 
 properties and the increased optical absorbance of the cluster , ( 2 ) the coalescence of the initial vapors around 
 gnps into the joint vapor blanket around the whole cluster , which 
 increases the bubble radius and hence reduces the surface tension 
 pressure . the clustering of gnps also 
 results in an almost four - fold decrease in the pnb threshold fluence 
 compared to that for an isolated single gnp , from 18 mj cm to 5 mj cm ( red curve in figure 5c ) . this effect provides a unique opportunity to selectively 
 generate pnbs only around the largest gnp clusters at the minimum 
 laser fluence and without generating pnbs around single unclustered 
 gnps or their small clusters . in biomedical applications , this cluster 
 size effect allows a dramatic improvement in the target cell specificity 
 of pnbs compared to that of gnps . generation 
 of pnbs around isolated gnp clusters in water under 
 resonant excitation with 20 ps laser pulse at 532 nm . optical scattering 
 time - resolved images of an gnp cluster in water ( a ) and of pnb ( b ) 
 generated around the same cluster in single 20 ps pulse excitation 
 at 532 nm . ( c ) the energy efficacy of pnb generation ( measured via 
 the lifetime of individual pnbs at 66 mj cm , black 
 curve ) and the pnb generation threshold fluence ( red curve ) as functions 
 of the gnp cluster size ( quantified via the pixel amplitude of the 
 optical scattering image of a gnp cluster ) . for water suspensions of unclustered single gnps , we observed 
 multiple 
 pnbs under a single pulse excitation ( figure 6a ) . these multiple pnbs were generated synchronously and were analyzed 
 through an integrated optical scattering time a pnb lifetime has been averaged over 10 responses 
 obtained from 10 different areas of the suspension . an increase in 
 the gnp concentration by four orders of magnitude increases the pnb 
 lifetime from 4 to 280 ns ( black curve in figure 6c ) and at the same time causes an almost four - fold decrease 
 in the pnb threshold fluence ( red curve in figure 6c ) . even at the maximum gnp concentration , the pnb generation 
 threshold in suspension ( 20 mj cm ) is significantly 
 higher than that for individual gnp clusters ( 5 mj cm ) . therefore , gnp clusters provide higher energy efficacy of the 
 pnb generation compared to that for gnp suspensions . generation of pnbs in 
 water suspension of single gnps under resonant 
 excitation with 20 ps laser pulse at 532 nm . ( a ) optical scattering 
 time - resolved image of pnbs generated at laser fluence of 66 mj cm . response 
 of the same pnbs as shown at ( a ) was obtained with the ( continuous 
 wave ) c.w . ( c ) the energy efficacy of pnb generation 
 ( measured via the lifetime of individual pnbs at 66 mj / cm , black curve ) and the pnb generation threshold fluence ( red curve ) 
 as functions of the gnp concentration in the suspension . first , in experiments with gnp suspension , the maximum 
 gnp concentration studied corresponds to the averaged distance between 
 individual gnps on the order of 1 m . this distance is comparable 
 with the maximum size of pnbs and may cause a coalescence of several 
 pnbs in a larger one with a longer lifetime . second , an increase in 
 gnp concentration increases the probability of a single gnp being 
 exposed to a laser pulse . in our conditions , the probability of pnb 
 generation in suspension at the low concentration was less than 1 . this influenced the averaging of the pnb lifetime over 10 pulses that 
 were applied to the different areas of the suspension . the increase 
 in the gnp concentration increased the pnb generation probability 
 and , accordingly , the average lifetime . third , at high gnp concentrations 
 the pnb generation probability becomes equal to 1 and a further increase 
 in the pnb lifetime is caused by the increase in the number of simultaneously 
 generated pnbs whose integrated optical scattering effect is detected 
 as a single time response of a longer duration compared to 
 that from a single pnb ( in addition to the mentioned above effect 
 of coalescence of several small pnbs into one large pnb at high gnp 
 concentration ) . these three effects explain the influence of the gnp 
 concentration upon the pnb generation energy efficacy and threshold . therefore , the gnp suspension does not correctly describe the pnb 
 generation mechanism for individual gnps . among three gnp systems studied , single gnps , suspensions of gnps , and clusters of tightly 
 aggregated gnps , the latter show the highest pnb generation efficacy . to model the pnb generation 
 under continuous optical excitation , we estimated the thermal response 
 of an isolated gnp to continuous wave ( c.w . ) laser excitation at 532 
 nm under the same optical dose ( fluence ) as employed above for the 
 pulsed excitation . under the same optical dose ( fluence ) as employed 
 above for the pulsed excitation , the pnb threshold temperature could 
 not be achieved due to intense thermal losses . in this model , the 
 duration of optical excitation was 1 s. the estimated threshold fluence 
 turned out to be 9 orders of magnitude higher , 2  10 mj cm . experimental studies of isolated gnps 
 in water under these conditions , which are identical to those described 
 in second section for the pulsed excitation , resulted in no detectible 
 pnbs in the range of the laser intensities below 2 mw cm and the duration of excitation up to 20 s ( fluences of up to 4  
 10 j cm ) . the gnp suspensions 
 at the highest concentration of 10 gnp per milliliter 
 also did not return any detectable pnbs under the c.w . excitation 
 at this laser intensity and duration as long as 60 s. when the gnp 
 suspension was replaced by individual large ( microscopically visible ) 
 gnp clusters ( figure 7a ) , a microscopic pnb 
 was detected after 30 seconds of excitation at laser intensity of 
 2 mw cm ( figure 7b ) . as 
 the excitation was continued , pnbs grew from micro to almost macro 
 size almost linearly with the time ( figure 7c ) . for isolated gnp clusters , the pnb generation threshold fluence 
 decreased with the cluster size ( figure 7d ) , 
 which was similar to what was observed under pulsed excitation ( figure 5c ) . continuous excitation of pnbs . optical scattering time - resolved 
 image of a gnp cluster ( a ) and pnb ( b ) generated around gnp cluster 
 at the c.w . ( c ) dependence of the pnb diameter upon continuous 
 excitation time ( 532 nm ) , the change in the slope occurs when the 
 bubble diameter reaches 0.12 mm , the height of the cuvette , after 
 that , the bubble growth is basically two - dimensional . ( d ) pnb generation 
 threshold fluence at continuous excitation of pnb upon the gnp cluster 
 size quantified via the pixel image amplitude of the optical absorbance 
 of a gnp cluster . generation of pnbs requires 
 multiorder increase in optical fluence compared to the pulsed excitation 
 and in many cases can not be achieved at all . the vapor onset times 
 under continuous excitation are associated with a thermal diffusion 
 radius of 12 mm ( for thermal diffusion from a spherical gnp ) , which is four orders of magnitude larger than 
 the maximum size of a gnp cluster and more than five orders of magnitude 
 larger than the size of an individual gnp . this spatial scale characterizes 
 the size of the water volume heated by a gnp and clearly indicates 
 that the c.w . in contrast , the pnb generation under short pulse excitation involves 
 heating and evaporation of the water within several nanometers from 
 gnp surface and does not affect the bulk water temperature as we observed 
 previously . the pnb generation under 
 c.w . laser excitation , therefore , is achieved through a bulk thermal 
 impact on the surrounding media , while the pulsed nonstationary excitation 
 results in the localized mechanical , nonthermal impact of a rapidly 
 expanding and collapsing pnb which , in addition , thermally insulates 
 the bulk media from the laser - heated gnp . generation of pnbs similar to the 
 laser - induced generation of vapor bubbles in optically absorbing homogeneous 
 liquid . therefore , the advantage of plasmonic nanoparticles over optically 
 absorbing liquids is achieved only under a short pulse excitation . 
 in this case , the high optical absorbance of plasmonic nanoparticles 
 efficiently supports the localized heating of the surrounding liquid 
 above the vaporization threshold . longer , especially continuous , optical 
 excitation of plasmonic nanoparticles in three - dimensional liquid 
 delocalizes their heating to macroscale . in this case , any advantage 
 of the nanosize of optical absorbers as well as the energy efficacy , 
 is lost , and the suspension of plasmonic nanoparticles in transparent 
 liquid becomes almost equal to the homogeneous solution of optically 
 absorbing liquid . in a case of planar and thermally - isolated surface , the continuous excitation of plasmonic nanoparticles still may provide some localization of thermal effect . however , it can not be a case for a pnb which is basically a three - dimensional 
 phenomenon . in addition to the generation 
 of pnbs at the wavelength near the peak of plasmon resonance , we studied 
 pnb generation at off - resonant near - infrared wavelengths in the range 
 of 700800 nm , far from a stationary plasmon resonance . colloidal 
 gold is considered to have poor optical absorbance in this spectral 
 range , about 1% of that at the resonance wavelength at 530540 
 nm . the off - resonant excitation of isolated 
 gnps with a 20 ps pulse revealed an ultranarrow , just 3 nm wide , peak 
 at 782 nm ( figure 8a ) . for gold colloids used 
 in this experiment , the spectral width of the optical absorption spectrum 
 is about 100 nm . under identical laser fluence , the pnb lifetimes 
 at 782 and 532 nm were close , thus implying that the levels of optical 
 absorbance of gnps at 532 and 782 nm are similar . this effect is very unusual for gold colloids and has never 
 been observed under c.w . we therefore 
 studied how this off - resonant effect depends upon the duration of 
 the near - infrared laser pulse ( figure 8b ) . 
 at a fixed laser fluence , 66 mj cm , the pnb lifetime 
 rapidly dropped with the pulse length , and no pnbs were observed for 
 400 ps and 14 ns pulses . compared to resonant excitation ( figure 4d ) , it was impossible to induce pnbs 
 with pulses longer than 70 ps under laser fluences up to 300 mj cm . off - resonant generation of pnbs around isolated individual 
 gnps 
 in water obtained for 60 nm gold spheres irradiated by the 20 ps laser 
 pulse at fluence 66 mj cm . ( b ) experimentally measured pnb lifetime ( black curve ) and theoretically 
 calculated off - resonant pnb energy ( red curve ) as functions of the 
 duration of the excitation laser pulse at 782 nm . ( c ) the calculated 
 time - course of the gnp surface temperature of ( red curve ) during the 
 absorption of a single 20 ps laser pulse at 782 nm with a gaussian 
 temporal profile ( black curve ) . the shaded area of the pulse shows 
 the time window that determines the fraction of the laser pulse defined 
 as an  off - resonant pnb energy  . we further theoretically estimated the gnp surface temperature 
 dynamics at 780 nm and determined the vapor onset times using the 
 similar simulation approach as described above for the resonant excitation 
 ( figure 8c ) . next , based on the published data 
 for similar gnps , we estimated 
 that the actual expansion of a pnb does not begin simultaneously with 
 the onset of the laser pulse ( figure 1 ) and 
 may be delayed by at least 50 ps . we therefore used the time window 
 from the vapor onset to the beginning of the active expansion of the 
 pnb to estimate the percentage of the pulse energy that corresponds 
 to this off - resonant pnb and determined the  off - resonant pnb 
 energy  ( figure 8c ) . upon the basis 
 of similar calculations , this off - resonant pnb energy exceeds zero 
 only for the short picosecond pulses of 20 and 70 ps ( red curve in 
 figure 8b ) . interestingly , the pulse duration 
 functions of the estimated off - resonant pnb energy and the experimentally 
 measured pnb lifetime are very close ( figure 8b ) . to explain this high off - resonant photothermal efficacy of gold 
 colloids under short pulse excitation , we hypothesized earlier that 
 a new transient plasmonic structure may emerge and exist during this 
 short time window , and this structure transiently develops a high 
 and narrow peak of optical absorbance at 782 nm . this hypothetical transient plasmonic structure may 
 include hot 
 melted gold droplets in a vapor near the surface of the parent gnp . the system of metal droplets , vapor , and the parent gnp surface may 
 have a high optical absorbance similar to a plasmonic grating and 
 thus efficiently convert the near - infrared pulse into a pnb . the 
 coincidence of the experimental and theoretical data in figure 8b supports the transient nature of such plasmonic 
 structure . its ultranarrow , 3 nm wide , peak of optical absorbance 
 has never been reported for any isolated plasmonic structures . furthermore , 
 this peak is practically forbidden by electrodynamic theory , which 
 allows for narrow spectral peaks in optical absorbance only for regular 
 arrays and layers of plasmonic materials . nevertheless , it opens new 
 opportunities for practical applications of plasmonic nanoparticles 
 under  nonstationary plasmonics  and radically improves 
 the spectral selectivity and photothermal efficacy of gold colloids 
 at wavelength where such properties can not be achieved under stationary 
 plasmonic conversion . in this study , we observed 
 a nine orders of magnitude difference 
 in the energy efficacy and threshold of the pnb generation with the 
 variation of the duration of the optical excitation of plasmonic nanoparticles 
 from picosecond pulses to continuous excitation . in addition , we observed 
 a strong dependence of the pnb generation parameters upon the nanoparticle 
 state : isolated , suspension , or clustered . finally , we observed the 
 unique for pnbs opportunity for the nonstationary off - resonant excitation 
 of plasmonic nanoparticles at the wavelengths where the stationary 
 optical properties of plasmonic nanoparticles formally exclude any 
 efficient photothermal response . the influence of the gnp 
 size on the pnb generation was extensively analyzed by us previously . 
 generally , the solid spheres of a smaller size or larger than 200 
 nm would require more fluence to generate identical pnbs under the 
 resonant excitation . the results obtained 
 here for 60 nm gold colloids are fairly representative because the 
 variation of the nanoparticle size in a wide range from 10 to 250 
 nm results in less than one order of magnitude variation in the pnb 
 generation energy efficacy and threshold . the shape and structure of the gnps of similar size also influence 
 the pnb generation energy efficacy and threshold fluence by less than 
 one order of magnitude . therefore , the duration of the optical excitation appears to be 
 the most critical factor in the photothermal generation of pnb compared 
 to the gnp properties . pnb generation follows several universal rules : ( i ) a pnb can be generated around a plasmonic nanoparticle using 
 both pulsed nonstationary and continuous stationary optical excitation . ( ii ) the maximum energy efficacy of the photothermal generation 
 of pnb is achieved with picosecond laser pulses , while the minimum 
 energy efficacy is associated with continuous optical excitation , 
 which requires up to nine orders of magnitude more energy to generate 
 plasmonic nanobubble , compared to picosecond laser pulses . ( iii ) 
 the clusters of aggregated nanoparticles provide the maximal 
 energy efficacy of pnb generation compared to isolated nanoparticles 
 or their suspensions . ( iv ) for short laser pulses , generation 
 of pnbs does not cause 
 bulk heating of surrounding liquid , while continuous optical excitation 
 of plasmonic nanoparticles results in an opposite effect of significant 
 bulk heating of surrounding liquid . ( v ) short picosecond off - resonant 
 near - infrared optical excitation 
 of gold colloids results in efficient generation of plasmonic nanobubbles 
 at a specific wavelength and in a very narrow , nanometers - wide , spectral 
 interval around 780 nm .
plasmonic 
 nanobubbles ( pnbs ) are transient vapor nanobubbles generated 
 in liquid around laser - overheated plasmonic nanoparticles . unlike 
 plasmonic nanoparticles , pnbs properties are still largely 
 unknown due to their highly nonstationary nature . here 
 we show the 
 influence of the duration of the optical excitation on the energy 
 efficacy and threshold of pnb generation . 
 the combination of picosecond 
 pulsed excitation with the nanoparticle clustering provides the highest 
 energy efficacy and the lowest threshold fluence , around 5 mj cm2 , of pnb generation . 
 in contrast , long excitation 
 pulses reduce the energy efficacy of pnb generation by several orders 
 of magnitude . ultimately , the continuous excitation has the minimal 
 energy efficacy , nine orders of magnitude lower than that for the 
 picosecond excitation . 
 thus , the duration of the optical excitation 
 of plasmonic nanoparticles can have a stronger effect on the pnb generation 
 than the excitation wavelength , nanoparticle size , shape , or other 
  stationary  properties of plasmonic nanoparticles .