# Plasmonic and Thermooptical Properties of Spherical Metallic Nanoparticles for Their Thermoplasmonic and Photonic Applications

Authors: Victor K. Pustovalov; Liudmila G. Astafyeva; Wolfgang Fritzsche
Journal: Journal of Nanoparticles
 (2014)

---

## Abstract

Investigations and use of nanoparticles (NPs) as photothermal (PT) agents in laser and optical nanotechnology are fast growing areas of research and applications. The potential benefits of NPs applications include possibility for thermal imaging and treatment of materials containing of NPs, applications of NPs for light-to-thermal energy conversion, in catalysis, laser nanomedicine, and chemistry. Efficiency of applications of metallic NPs for laser and optical nanotechnology depends on plasmonic and thermophysical properties of NPs, characteristics of radiation, and surrounding medium. Here we present the results of comparative analysis of NP properties (plasmonic, thermooptical, and others) allowing selecting their parameters for thermoplasmonic and photonic applications. Plasmonic and thermooptical properties of several metallic (aurum, silver, platinum, cobalt, zinc, nickel, titanium, cuprum, aluminum, molybdenum, vanadium, and palladium) NPs are theoretically investigated and analysis of them is carried out. Investigation of the influence of NPs parameters (type of metal, radii, optical indexes, density, and heat capacity of NP material), characteristics of radiation (wavelength and pulse duration), and ambient parameters on plasmonic and thermophysical properties of NPs has been carried out. It was established that maximum value of thermooptical parameter (maximum NP temperature) can be achieved with the use of absorption efficiency factor of NP smaller than its maximum value.


---

## Body

## 1. Introduction

Recent advances in photothermal nanotechnology based on the use of nanoparticles (NPs) and optical (laser) radiation have been demonstrated for their great potential. In recent years, the laser-NP interaction, absorption, and scattering of radiation energy by NP have become of great interest and an increasingly important for topic in photonic and laser nanotechnology [1–27] (also see the references in these papers). There are many reasons for this interest including application of NPs in different fields, such as catalysis [1, 2], laser nanobiomedicine [3–11], nanooptics and nanoelectronics [12–15], laser processing of metallic NPs in nanotechnology [16–23], and light-to-heat conversion [24–27].Most of these technologies rely on the position and strength of the surface plasmon on a nanosphere and the fact that NP will absorb and scatter radiation energy well at resonance wavelength. Successful applications of NPs in photonics and thermoplasmonics are based on appropriate plasmonic and optical properties of NPs. High absorption of radiation by NPs can be used for conversion of absorbed energy into NP thermal energy, heating of NP itself and ambient medium, and following photothermal phenomena in laser and optical nanotechnology and nanomedicine. High scattering of radiation is essential for optical diagnostics and imaging applications based on light scattering.Metallic NPs are mostly interesting for different nanotechnologies among other NPs. First investigations of optical properties of metallic NPs were carried out in [28, 29]. The attempts to search for the “ideal” plasmonic NPs were carried out in many papers. Optical absorption efficiency of some metallic NPs was investigated in [28–33]. Thermooptical analysis and selection of the properties of gold NPs for laser applications in nanotechnology were carried out in [8, 26, 34]. Searching for better plasmonic materials (metals) was carried out in [13, 32, 35, 36] based on investigations of quality factors of each metal. Different metallic NPs (gold, silver, platinum, zinc, etc.) were used in [1–36]. Gold and silver NPs were considered as the most appropriate ones and widely used in experiments. Methods of chemical synthesis of metallic NPs have been developed and presented in [37–39].On the other side, a comparative analysis of optimal parameters of different metallic NPs for using them as PT agents in thermoplasmonics and laser nanotechnology is still missing. Here we propose the results for analysis of the NP properties for their photonic and thermoplasmonic applications.Plasmonic and thermooptical properties of metallic NPs were theoretically investigated and compared in this paper based on computer modeling. We carry out complex investigation of the plasmonic and thermooptical properties of spherical metallic NPs for their interaction with optical (laser) radiation placed (embedded) in some ambient medium. We investigated the influence of the parameters of radiation, NP, and ambient medium on the properties of this interaction.


## 2. Plasmonic and Thermooptical Parameters of Nanoparticles

Among different characteristics of NPs, laser radiation, and ambient medium that will determine NP plasmonic and thermooptical properties we can note the following ones:(1)
laser (optical) radiation—(a) pulse durationt
P, (b) wavelength λ, and (c) radiation (laser) exposure (energy density) E
0, intensity I
0
=
E
0
/
t
P;
(2)
spherical nanoparticle—(a) type of NP metal with its values of densityρ
0, heat capacity c
0, optical indexes of refraction n
0
λ, and absorption χ
0
λ of NP metal and (b) NP radius r
0;
(3)
nonabsorbing surrounding medium—(a) coefficient of thermal conductivityk
∞ = const and (b) optical indexes of refraction n
λ.Consider the parameters that characterize the transformation of radiation energy in the processes of NP-radiation interaction.Efficiency factors of absorptionK
abs, scattering K
sca, and extinction K
ext of radiation by NP [29] determine the optical properties of NP.ParameterP
1 describes the correlation between absorption and scattering of radiation by NP. Parameter P
1 characterizes the contribution of the processes of absorption and scattering to the general energy balance of the NP:
(1)
P
1
=
K
abs
K
sca
.
The efficiency factor of absorption of laser radiation by NPs K
abs can be greater or smaller than the factor of scattering of radiation by NP K
sca in the cases of predominant role of absorption or scattering in the process of radiation interaction with NP:(2a)
K
abs
>
K
sca
,
P
1
>
1
,
(2b)
K
abs
<
K
sca
,
P
1
<
1
.The parameterΔ
T
0
/
E
0 [6–8] can be used for determination of thermooptical properties of NPs
(3)
Δ
T
0
E
0
=
K
abs
r
0
4
k
∞
t
P
[
1
-
exp
⁡
(
-
t
P
τ
0
)
]
,
τ
0
=
ρ
0
c
0
r
0
2
/
3
k
∞—characteristic time for heating and cooling of NP. This parameter determines the increase of NP temperature Δ
T
0
=
T
max
⁡
-
T
∞ under action of radiation energy density with value E
0
=
1 J/cm2, T
max
⁡, maximum temperature of NP at t
=
t
P, and T
∞, initial NP temperature.ParameterΔ
T
0
/
E
0 (3) may be viewed as NP heating efficiency under action of radiation energy with energy density E
0. For t
P
<
τ
0 and t
P
>
τ
0 the parameter Δ
T
0
/
E
0 will be approximately determined by the following (see (3)):(4a)
t
P
<
τ
0
,
Δ
T
0
E
0
≈
3
K
abs
4
ρ
0
c
0
r
0
,
(4b)
t
P
>
τ
0
,
Δ
T
0
E
0
≈
K
abs
r
0
4
k
∞
t
P
.In general, the parameter Δ
T
0
/
E
0 ((3), (4a), and (4b)) depends on characteristics of radiation, λ and t
P, metallic NP, K
abs
(
λ
), r
0, c
0, and ρ
0, and ambient medium, k
∞, index of medium refraction n
λ. Combinations K
abs
(
r
0
)
/
r
0 and K
abs
(
r
0
)
r
0 in (4a) and (4b) determine the range of radii r
0 appropriate for the achievement of the maximum value of T
0 under a fixed value of λ, K
abs
(
λ
). The combination 1
/
c
0
ρ
0 determines the influence of NP metal properties on the maximum value of T
0. Values of k
∞ and n
λ determine the influence of surrounding medium on thermooptical properties of NPs. The parameter of Δ
T
0
/
E
0 does not depend on parameters of radiation (t
P) and ambience (k
∞) in (4a). The selection of mentioned parameters in (3), (4a), and (4b) can provide maximum values Δ
T
0 for concrete values of E
0.We will investigate the influence of all characteristics of NPs, laser radiation, and ambient medium mentioned above on plasmonic and thermooptical properties of metallic NPs. Comparative analysis of the properties of metallic NPs and their efficiency for photonic applications in nanotechnology have to use the following set of plasmonic and thermooptical parameters of the laser-NP interaction processes:(i)
efficiency factors of absorptionK
abs, scattering K
sca, and extinction K
ext of radiation by spherical NP;
(ii)
parameter ofP
1 (1);
(iii)
parameterΔ
T
0
/
E
0 ((3), (4a), and (4b)).


## 3. Plasmonic and Thermooptical Properties of NPs

Calculations and analysis of plasmonic and thermooptical properties of NPs have been carried out in our investigations. We numerically calculated efficiency factors of absorptionK
abs, scattering K
sca, and extinction K
ext of radiation with wavelength λ by spherical homogeneous metallic NP based on generalized Mie theory [29]. Values of optical indexes of refraction and absorption of metals and surrounding media were used from [40–42]. After that, we use (1) and (3) for calculation of the parameters P
1 and Δ
T
0
/
E
0. All figures presented describe the dependences of efficiency factors of absorption K
abs, scattering K
sca, and extinction K
ext, parameters P
1 and Δ
T
0
/
E
0 for metallic NPs on wavelength of radiation, NP radii, pulse duration t
P, and characteristics of surrounding media. Simultaneous comparative investigation of the dependences of K
abs, K
sca, K
ext, and Δ
T
0
/
E
0 on λ, r
0, and other characteristics is very complex and hard task. We have divided this task into two steps. A first step is the calculation and investigation of the dependences of K
abs, K
sca, K
ext, P
1, and Δ
T
0
/
E
0 on λ for some fixed values of r
0, t
P, and selected NP metal and surrounding medium. Second one is the investigation of the dependences of K
abs, K
sca, K
ext, P
1, and Δ
T
0
/
E
0 on r
0 for some fixed values of λ, t
P, and selected NP metal and surrounding medium. This allows investigating complex task step by step and present clear dependences of K
abs, K
sca, K
ext, P
1, and Δ
T
0
/
E
0 on one parameter when other parameters are constant. Figures 1–7 present the dependences of K
abs, K
sca, K
ext, P
1, and Δ
T
0
/
E
0 on λ, r
0, t
P, and optical indexes of metals and surrounding media.Figure 1
Dependences of efficiency factors of absorptionK
abs (solid), scattering K
sca (dashed), and extinction K
ext (dashed-dotted) of radiation and parameter Δ
T
0
/
E
0 (dotted) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s forAu NPs with radii r
0
=
10 ((a), (e), and (i)), 25 ((b), (f), and (j)), and 50 ((c), (g), and (k)) nm, and the dependences of parameter P
1 ((d), (h), and (l)) for Au NPs with radii r
0
=
10 nm (1), r
0
=
25 nm (2), and r
0
=
50 nm (3) on wavelengths λ. Au NPs are placed in silica ((a)–(d)), water ((e)–(h)), and air ((i)–(l)).Figure 2
Dependences ofK
abs (solid), K
sca (dashed), and K
ext (dashed-dotted) of radiation and parameter Δ
T
0
/
E
0 (dotted) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s forAg NPs with radii r
0
=
10 ((a), (e), and (i)), 25 ((b), (f), and (j)), and 50 ((c), (g), and (k)) nm, and the dependences of parameter P
1 ((d), (h), and (l)) for Ag NPs with radii r
0
=
10 nm (1), r
0
=
25 nm (2), and r
0
=
50 nm (3) on wavelengths λ. Ag NPs are placed in silica ((a)–(d)), water ((e)–(h)), and air ((i)–(l)).Figure 3
Dependences ofK
abs (solid), K
sca (dashed), and K
ext (dashed-dotted) of radiation and parameter Δ
T
0
/
E
0 (dotted) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s forPt NPs with radii r
0
=
10 ((a), (e), and (i)), 25 ((b), (f), and (j)), and 50 ((c), (g), and (k)) nm, and the dependences of parameter P
1 ((d), (h), and (l)) forPt NPs with radii r
0
=
10 nm (1), r
0
=
25 nm (2), and r
0
=
50 nm (3) on wavelengths λ. Pt NPs are placed in silica ((a)–(d)), water ((e)–(h)), and air ((i)–(l)).Figure 4
Dependences of factorsK
abs (solid), K
sca (dashed), and K
ext (dashed-dotted) of radiation for homogeneous metallicPd ((a), (b), (c), and (d)),Cu ((e), (f), (g), and (h)), andMo ((i), (j), (k), and (l)) NPs, placed in water, with radii r
0
=
10 ((a), (d), and (g)), 25 ((b), (e), and (h)), and 50 ((c), (f), and (i)) nm, parameter Δ
T
0
/
E
0 (dotted) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s, and dependences of parameter P
1 ((d), (h), and (l)) for 10 (1), 25 (2), and 50 (3) nm on wavelengths λ.Figure 5
Dependences of factorsK
abs (solid), K
sca (dashed), and K
ext (dashed-dotted) of radiation for homogeneous metallicNi ((a), (b), (c), and (d)),V ((e), (f), (g), and (h)), andTi ((i), (j), (k), and (l)) NPs, placed in water, with radii r
0
=
10 ((a), (d), and (g)), 25 ((b), (e), and (h)), and 50 ((c), (f), and (i)) nm, parameter Δ
T
0
/
E
0 (dotted) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s, and dependences of parameter P
1 ((d), (h), and (l)) for 10 (1), 25 (2), and 50 (3) nm on wavelengths λ.Figure 6
Dependences of factorsK
abs (solid), K
sca (dashed), and K
ext (dashed-dotted) of radiation for homogeneous metallicCo ((a), (b), (c), and (d)),Zn ((e), (f), (g), and (h)), andAl ((i), (j), (k), and (l)) NPs, placed in water, with radii r
0
=
10 ((a), (d), and (g)), 25 ((b), (e), and (h)), and 50 ((c), (f), and (i)) nm, parameter Δ
T
0
/
E
0 (dotted) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s, and dependences of parameter P
1 ((d), (h), and (l)) for 10 (1), 25 (2), and 50 (3) nm on wavelengths λ.Dependences ofK
abs (solid lines refer to the left axis), parameter P
1 (dashed lines refer to the left axis), and thermooptical parameter Δ
T
0
/
E
0 (dotted lines refer to the right axis) for t
P
=
1
·
10
-
8 (1), 1
·
10
-
12 (2) s for NPs - Au, λ
=
532 nm (a), Ag, λ
=
400 nm (b), Pt, λ
=
500 nm (c), Cu, λ
=
570 nm (d), Pd, λ
=
470 nm (e), Ti, λ
=
500 nm (f), Ni, λ
=
470 nm (g), and Zn, λ
=
350 nm (h) on r
0.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The heat flow from NP, placed in liquids, amorphous solids, and so forth, can be well described by the diffusive heat equation, when mean free path of heat transporter (molecule, etc.) is very short, like ~10−8 cm in mentioned media [43, 44], and this one is much smaller than characteristic NP radii of r
0 ~10–100 nm. In gases at atmospheric pressure the mean free path of molecules is about ~10−5cm and diffusive heat equation can be applied to the heat exchange of NP with gaseous medium for r
0
≥
100 nm. Methods of kinetic equation or molecular dynamics should be used for the description of heat exchange of NP in this case. But during ultrashort laser pulse action with t
P ~ 10−10–10−12 s on NP we can neglect NP heat exchange with surrounding gas during laser action and calculate parameter Δ
T
0
/
E
0 for t
P
=
1
×
10
-
12 s using (4a). The dependence Δ
T
0
/
E
0
(
λ
) for t
P ~ 1 × 10−10 s practically coincides with this one for t
P
=
1
·
10
-
12 s and only one dependence Δ
T
0
/
E
0
(
λ
) is presented in Figures 1–6 for ambient air and t
P
=
1
·
10
-
12 s. We can note that the values of Δ
T
0
/
E
0 for t
P ~ 10−12 s can be used as upper boundaries of NP heating (Δ
T
0
=
T
max
⁡
-
T
∞) without NP heat exchange.The positions of maximum values of efficiency factors ofK
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ on λ axis are denoted in Figures 1–6 by different vertical lines and locations λ
abs
max
⁡ of maximum value of absorption factor K
abs
max
⁡ on axis λ are denoted by solid lines, K
sca
max
⁡, dashed lines, and λ
sca
max
⁡, K
ext
max
⁡, dashed-dotted lines, and λ
ext
max
⁡ in the case of different values of λ
abs
max
⁡, λ
sca
max
⁡, and λ
ext
max
⁡. In the case of equal values of λ
abs
max
⁡, λ
sca
max
⁡, and λ
ext
max
⁡ the location of coincident values of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ is denoted by solid lines. In some cases additional solid lines denote the locations of the formation of new maximums of efficiency factors (see Figures 3(c), 3(g)) or the points of sharp bend of the dependence of K
abs on λ (see Figures 4(i) and 4(j)). Horizontal dashed lines in Figures 1(d), 1(h), 1(l)–6(d), 6(h), and 6(l) denote the value of P
1
=
1.Figures1–3 present the dependences of efficiency factors of K
abs, K
sca, and K
ext of radiation, parameters Δ
T
0
/
E
0 for t
P
=
1
·
10
-
8, 1
·
10
-
12 s, and P
1 for homogeneous metallic Au (Figure 1), Ag (Figure 2), and Pt (Figure 3) NPs with radii r
0
=
10, 25, and 50 nm on wavelengths λ. NPs are placed in silica, water, and air ambient nonabsorbing media. Optical constants (indexes of refraction n
λ and absorption λ) are changed in the ranges for silica n
λ ≈ 1.51 − 1.45, water n
λ ≈ 1.39 − 1.33, air n
λ ≈ 1.0, and ϰ
λ ≈ 0 for all ambiences with increasing wavelength λ in the spectral interval ~200–1000 nm.The dependences of efficiency factors ofK
abs, K
sca, and K
ext on λ for fixed values of r
0 have complicated forms. Values of K
abs
max
⁡ are placed at λ
abs
max
⁡ ~ 510–530 nm for Au NPs and λ
abs
max
⁡ ~ 380–410 nm for Ag NPs for r
0
=
10, 25, and 50 nm and different ambiences. Consequently the absorption of radiation is determined by plasmon resonances of silver and gold NPs in the field of electromagnetic (laser) radiation. Values of K
abs are decreased in UV and NIR spectral intervals out of plasmon wavelengths and especially for Ag NPs these values undergo sharp decrease up to 102-103 times. We can note a slight decrease of K
abs for Au NP in the UV spectral interval in comparison with NIR spectral interval. The behavior of dependences of K
sca on wavelength λ is analogous for the dependence of K
abs
(
λ
). Maximum value of K
sca
max
⁡ for Ag NPs achieves K
sca ~ 11
÷
15 in the interval of λ ~ 410
÷
430 nm and r
0
=
25 nm. Dependence of K
ext on λ presents itself the sum of the dependences of K
abs
(
λ
) and K
sca
(
λ
). The values of K
abs
max
⁡ and K
ext
max
⁡ for Au, Pt NPs for r
0
=
10 and 25 nm and for Ag NPs r
0
=
10 nm practically coincide with each other and for different ambiences (see Figures 1–3). But for r
0
=
50 nm values of K
sca
max
⁡ and K
ext
max
⁡ are greater than K
abs
max
⁡. This fact was also noted in [31]. An increase of r
0 may lead to increase or decrease of the maximum values of K
abs, K
sca, and K
ext. Coincidence of different vertical lines in figures means the coincidence of corresponding values of optical parameters. Placements of K
ext at λ ~ 292 nm and 443 nm for NPs in water for r
0
=
25 and 50 nm quantitatively coincide with experimental data [45].Placements of maximum values ofK
abs, K
sca, and K
ext on axis λ can be different in some cases (Figures 1(c), 1(g), 1(k)–3(c), 3(g), and 3(k)). The formation of additional maximums of K
abs, K
sca, and K
ext on axis λ can be connected with possible manifestation of resonances with higher orders (Figures 3(c) and 3(g) Pt NPs). An increase of NP radii to r
0
=
50 nm shifts the maximum values of K
sca and K
ext in the region of greater values of λ. The value of shift of Δ
λ
max
⁡
=
λ
max
⁡
(
K
abs
)
-
λ
max
⁡
(
K
sca
) increases with increasing of r
0, for r
0
=
10 nm Δ
λ
max
⁡ ~ 5–13 nm for all surroundings, and for r
0
=
50 nm this one achieves values of Δ
λ
max
⁡ ~ 15–70 nm. These values increase with increasing of n
λ from air to silica for Au, Ag, Pt NPs. But K
sca
max
⁡ and K
ext
max
⁡ have been shifted compared to the position of K
abs
max
⁡(λ
abs
max
⁡) up to 80–120 nm (Figures 1(c), 2(c), and 2(g)) to bigger values of λ with increasing of r
0.Figure3 shows forPt NPs that maximums of absorption K
abs
max
⁡ and scattering K
sca
max
⁡ for r
0
=
10 nm are accordingly situated at wavelengths λ
abs
max
⁡
=
248 nm and λ
sca
max
⁡
=
150 nm in silica. Increase of r
0 leads to shifting of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ to bigger values of λ; for example, K
abs
max
⁡ is shifted from λ
abs
max
⁡ ~ 220–250 nm for r
0
=
10 nm to λ
abs
max
⁡ ~ 450–480 nm for r
0
=
50 nm in silica and water. But for air this shift is from λ
abs
max
⁡ ~ 220 nm for r
0
=
10 nm to λ
abs
max
⁡ ~ 310 nm for r
0
=
50 nm. Maximum values of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ are at the values of λ
abs
max
⁡, λ
sca
max
⁡, and λ
ext
max
⁡ for r
0
=
50 nm. Moreover two maximum values of K
abs
max
⁡ are formed for r
0
=
50 nm in silica at λ
abs
max
⁡
=
317.9 and 495.9 nm and in water at λ
abs
max
⁡
=
290 and 477 nm.For Au NPs, dependences ofP
1 on λ are determined by the dependences of K
abs and K
sca on λ. Increase of r
0 from r
0
=
10 nm to r
0
=
50 nm leads to a decrease of the parameter P
1 from the values of about P
1 ~ 20–300 for λ ~ 300–1000 nm up to values of about P
1 ~ 0.1–0.3 for λ ~ 600–1000 nm. It means sharp increase of radiation scattering by NPs with an increase of NP r
0. For Ag NPs, a sharp decrease with increasing of λ in the spectral interval λ ~ 300–400 nm is observed and is approximately constant in the interval λ ~ 300–1000 nm. General feature for all presented dependences of P
1(λ, r
0) is the decrease of P
1 with increasing of r
0 for the whole spectral interval λ ~ 200–1000 nm.The dependences ofP
1 on λ for Pt NPs increase with increasing λ for r
0
=
10 and 25 nm and achieve values of P
1 ~ 3–200 for the whole spectral interval because of sharp decreasing of K
sca with increase of λ (see Figure 3). The parameter P
1 is smaller than 1, P
1
<
1, for r
0
=
50 nm and the narrow wavelength interval ~350–500 nm for different surroundings.Figures1–3 describe the influence of the medium refraction indexes and thermal properties on plasmonic and thermooptical properties of Au, Ag, and Pt NPs. Concrete values of K
abs
max
⁡ and k
∞ determine the influence of different surroundings on the value of Δ
T
0
/
E
0 for different t
P (see (3)). The wavelength shift Δ
λ
max
⁡ exists between maximums of K
abs
max
⁡ from one side and maximums of K
sca
max
⁡ and K
ext
max
⁡ from a second side for silica and water. Maximum values and dependences of K
abs, K
sca, and K
ext on wavelength are qualitatively close to each other for r
0
=
10, 25, and 50 nm.The decrease of refraction index fromn
λ
=
1.51 for silica to n
λ
=
1.00 for air leads to shifting of λ
max
⁡ for all efficiency factors for K
abs from ~545 nm to ~510 nm and for K
sca and K
ext from 600 nm to 510 nm. Decrease of n
λ for silica to n
λ
=
1.00 (air) leads to decrease of values of K
abs, K
sca, and K
ext up to 4 times for r
0
=
10 and 25 nm, but for r
0
=
50 nm the dependence of maximum values of K
abs, K
sca, and K
ext is rather weak and leads to the smoothing of plasmonic peaks of the dependences of K
(
λ
), first of all, for r
0
=
10, 25 nm.The spectral dependence ofΔ
T
0
/
E
0
(
λ
) is determined by the dependence of K
abs
(
λ
) for all values of r
0, because of dependence Δ
T
0
/
E
0 ~ K
abs
(
λ
) in (3), (4a), and (4b). The influence of NP radius r
0 is directly realized on the value of Δ
T
0
/
E
0 and it is determined by the dependence of K
abs
(
r
0
) and value of r
0 in (3), (4a), and (4b). Parameters of surroundings influence the value of Δ
T
0
/
E
0 by the value of K
abs(n
λ).The values ofΔ
T
0
/
E
0 for t
P
=
1
×
10
-
8 s are, as a rule, smaller in comparison with other ones for t
P
=
1
×
10
-
12 s. It is determined by the influence of heat exchange of NP with surrounding medium during radiation pulse action for pulse duration t
P
=
1
×
10
-
8 s and bigger ones.The maximum value of(
Δ
T
0
/
E
0
)
max
⁡ for Au NPs, placed in silica, is equal to (
Δ
T
0
/
E
0
)
max
⁡
=
5.53
×
10
5 Kcm2/J for r
0
=
10 nm, λ
=
532 nm, and t
P
=
1
×
10
-
12 s. Maximum values for Ag NPs, placed in different media, of about (
Δ
T
0
/
E
0
)
max
⁡
~
(
2
-
5
)
×
10
6 Kcm2/J are achieved with r
0
=
10 nm and t
P
=
1
×
10
-
12 s among other NPs. For example, Ag NPs with r
0
=
10 nm, placed in water, can achieve the heating of Δ
T
0
=
100 K under action of laser pulse with λ
=
382 nm, t
P
=
1
×
10
-
10, 1
×
10
-
12 s, and E
0
=
5.6
×
10
-
5 J/cm2. It is connected with the achievement of maximum values of K
abs for Ag NPs in comparison with other presented NPs.Figures4–6 present efficiency factors of absorption K
abs, scattering K
sca, and extinction K
ext for radiation with wavelengths λ in the spectral interval 200–1000 nm for homogeneous metallic spherical NPs with radii 10, 25, and 50 nm, placed in water, for nine different metals.Figure4 presents factors of K
abs, K
sca, and K
ext of radiation with wavelengths in the range 300–1000 nm by metallic Pd, Mo, and Cu NPs with radii r
0
=
10, 25, and 50 nm placed in water.The spectral dependences ofK
abs and K
ext for Cu NPs are smooth enough for r
0
=
10 and 25 nm. An interesting feature of these dependences of K
abs and K
ext on λ for r
0
=
10 and 25 nm is the formation of so called “step” (weak dependence of K
abs and K
ext on λ) for the spectral interval of λ ≈ 300–565 nm. There is one weakly defined maximum in these curves for 310 nm (r
0
=
10 nm) and for 387 nm (r
0
=
25 nm). We see sharp folding of the dependences of K
abs and K
ext on λ for r
0
=
10 and 25 nm at λ ≈ 565 nm. For r
0
=
10 and 25 nm values of K
abs
≫
K
sca and dependences of K
ext and K
abs on λ are close to each other. The factor of scattering K
sca monotonously decreases with increasing λ for r
0
=
10 and 25 nm.In the case ofr
0
=
50 nm spectral dependences of K
abs, K
sca, and K
ext for Cu NPs have one distinct pronounced maximum: K
abs
max
⁡
≈
2.7 for λ
abs
max
⁡
=
563 nm and K
sca
max
⁡
≈
3.5, λ
sca
max
⁡
=
590 nm and K
ext
max
⁡
≈
6 for λ
ext
max
⁡
=
590 nm. Positions of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ have been separated in Figure 4 for r
0
=
50 nm.FactorK
abs
>
K
sca and P
1
>
1 for r
0
=
10 and 25 nm and for all presented intervals of wavelengths. But for spectral interval λ ≈ 570–1000 nm, the value of P
1 is smaller than 1, P
1
<
1.Maximum ofK
abs
max
⁡ for Pd NP is shifted from the position λ
abs
max
⁡
=
230 nm at r
0
=
10 nm to bigger values of λ with increasing r
0 up to λ
abs
max
⁡
=
310 nm and with formation of two weakly defined maxima of K
abs
max
⁡ at λ
abs
max
⁡
=
292 nm and λ
abs
max
⁡
=
470 nm for r
0
=
50 nm. The maximum of K
sca
max
⁡ is shifted from the values of λ
sca
max
⁡
=
190 nm for r
0
=
10 nm to λ
sca
max
⁡
=
230 nm for r
0
=
25 nm, and λ
sca
max
⁡
=
435 nm at r
0
=
50 nm. The maximum of K
ext
max
⁡ is shifted from the values of λ
ext
max
⁡
=
190 nm for r
0
=
10 nm to λ
ext
max
⁡
=
450 nm at r
0
=
50 nm. We see that the values of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ have been placed at different positions on λ axis. Parameter P
1 increases up to values of P
1 ~ 10–100 for r
0
=
10, 25, and 50 nm with increasing of λ in the range of λ ~ 200–1000 nm. For the spectral interval of λ ~ 200–600 nm parameter P
1 is smaller than 1, P
1
<
1.Two maximum values of(
Δ
T
0
/
E
0
)
max
⁡ are realized in Figures 4(c) and 4(g), for Cu and Pd NPs because two maxima of K
abs
max
⁡ have been formed for r
0
=
50 nm.For Mo NPs (Figures4(e), 4(f), 4(g), and 4(h)) maxima of K
abs
max
⁡ are realized in the spectral region 180
÷
200 nm for r
0
=
10 and 25 nm. Positions of maxima of K
sca
max
⁡ and K
ext
max
⁡ are shifted from ~200 for r
0
=
10 nm to ~230 nm when increasing NP radius up to 25 nm. When the radius is increased up to 50 nm, two maxima of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ are formed in all curves in Figure 4 (g). They are localized in the case of K
abs
max
⁡ at λ
abs
max
⁡
=
200 nm and 440 nm, K
sca
max
⁡ at λ
sca
max
⁡
=
230 and 420 nm, and K
ext
max
⁡ at λ
ext
max
⁡
=
210 and 420 nm. Maximum value of absorption of Mo NPs attains K
abs
max
⁡ ≈ 3.2 for r
0
=
10 nm and maximum values scattering and extinction attain K
sca
max
⁡ ≈ 2.73 and K
ext
max
⁡ ≈ 4.5 accordingly for r
0
=
50 nm. Two maximum values of (
Δ
T
0
/
E
0
)
max
⁡ are realized in Figure 5(g) for Mo NPs.Figure5 presents spectral dependences of efficiency factors of K
abs, K
sca, and K
ext of radiation in the range 150–1000 nm by metallic Ni, V, and Ti NPs with radii r
0
=
10, 25, and 50 nm, placed in water. Spectral dependences of efficiency factors of K
abs, K
sca, and K
ext for Ni, V, and Ti NPs for radii r
0
=
10 nm and 25 nm are smooth curves with maxima in the UV region. With increasing wavelength till 1000 nm absorption, scattering, and extinction slowly decrease. In the case of r
0
=
50 nm spectral dependences of efficiency factors of K
abs and K
sca for V NPs have some weakly defined maxima located both in UV and in visible region of spectra.For Ni, V, and Ti NPs we see general features that were early noted for Figures1–5. The first feature is the shifting of the values of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ to bigger values of λ with increasing the NP radius; the second one is the shifting between K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ themselves that means that values of λ
abs
max
⁡, λ
sca
max
⁡, and λ
ext
max
⁡ have different values, for example, for Ti NPs with r
0
=
50 nm, λ
abs
max
⁡
=
505 nm, λ
sca
max
⁡
=
355 nm, and λ
ext
max
⁡
=
450 nm. The third feature is the formation of second maximums of K
abs
max
⁡; for example, second maximum is formed at λ ≈ 480 nm.ParametersP
1 for Ni, V, and Ti NPs and for the radiation spectral interval λ ≈ 150–1000 nm are bigger than 1, P
1
>
1, instead of narrow interval λ ≈ 200–480 nm for V NPs with r
0
=
50 nm. Moreover, for r
0
=
10 and 25 nm parameters P
1 achieve the values of P
1 ≈ 10–500 with increasing λ. It means that Ni, Ti, and V NPs are good absorbers of radiation in wide range of ultraviolet, visible, and infrared optical spectrum.Figure6 presents the spectral dependences of K
abs, K
sca, and K
ext for metallicCo,Zn, andAl NPs with radii r
0
=
10, 25, and 50 nm, when placed in water. Spectral dependences of efficiency factors of K
abs, K
sca, and K
ext for Co nanoparticles are smooth and have some weakly defined maxima located both in UV and in visible region of spectra for r
0
=
10 and 25 nm. In the case of r
0
=
50 nm maximum of absorption is in the UV region of spectra and maxima of scattering and extinction are in the visible one. The maximum value of absorption for Co NPs is K
abs
max
⁡
≈
2.5 for r
0
=
25 nm, λ
abs
max
⁡
≈
300nm, and maximum values of scattering and extinction are K
sca
max
⁡
≈
2.2 and K
ext
max
⁡ ≈ 3.9 for r
0
=
50 nm, λ
sca
max
⁡
=
λ
ext
max
⁡
=
450 nm.For Zn NPs, maxima of spectral dependences of efficiency factors ofK
abs, K
sca, and K
ext are sharply defined, more than for Co NPs, and are shifted in the direction of greater wavelengths. For example, the maximum value of absorption for Zn NPs is K
abs
max
⁡
≈
4.5 for r
0
=
10 nm, λ
abs
max
⁡
≈
305nm, and maximum values of scattering and extinction are K
sca
max
⁡
≈
4.3 and K
ext
max
⁡ ≈ 5.7 for r
0
=
50 nm, λ
sca
max
⁡
≈
465nm. We note the shifting of K
sca
max
⁡ and K
ext
max
⁡ to bigger values of λ in comparison with position K
abs
max
⁡ for Co and Zn NPs.The spectral dependences of efficiency factors ofK
abs, K
sca, and K
ext for Al NPs show strongly defined maxima located mainly in UV. Maximum values of absorption and scattering are close for r
0
=
10 nm, and then for r
0
=
25 and 50 nm maximum values of scattering are essentially higher than absorption. For example, maximum value of absorption for Al NPs is K
abs
max
⁡
≈
7.5 for r
0
=
10 nm, λ
abs
max
⁡
≈
190nm, and maximum values of scattering and extinction are K
sca
max
⁡ ≈ 6, K
ext
max
⁡ ≈ 7 for r
0
=
25 nm, and λ
sca
max
⁡
≈
250nm. Factors of K
sca and K
ext rise to maximum values in the spectral interval 190–500 nm, before decreasing with increasing wavelength in the range 200–1000 nm. Some oscillation structures of the dependences of K
abs on λ are formed for Al and Zn NPs with increasing of r
0. It is interesting to note for Al NPs the shifting of K
sca
max
⁡ and K
ext
max
⁡ to bigger values of λ and the formation of two maximums of K
sca
max
⁡ and K
ext
max
⁡ with simultaneous formation of oscillation structure of the K
abs dependence on λ with increasing of r
0 to r
0
=
50 nm.Zn NPs withr
0
=
25 nm are good absorbers and bad scatterers for all spectral interval of λ ≈ 200–1000 nm. The parameter P
1 for Al NPs is smaller than one (P
1
<
1) for r
0
=
25 nm in the range of λ ≈ 200–500 nm and for r
0
=
50 nm, λ ≈ 150–1000 nm.Figures1–6 present spectral dependences of the parameter Δ
T
0
/
E
0 (3) for pulse duration t
P
=
1
·
10
-
8, 1
·
10
-
12 s for NPs with radii r
0
=
10, 25, and 50 nm placed in water. The range of pulse duration t
P
=
1
·
10
-
8
–
1
·
10
-
12 s is of great interest for laser applications in nanotechnology. The dependences of parameter Δ
T
0
/
E
0 (3) on λ are analogous to the dependences K
abs
(
λ
) because of (2a) and (2b). For λ
abs
max
⁡
≈
190nm and r
0
=
10 nm maximum value of thermooptical parameter for Al NPs achieves value (
Δ
T
0
/
E
0
)
max
⁡ ≈ 1.5
×
10
6 Kcm2/J.Figure7 presents the dependences of K
abs, parameter P
1, and thermooptical parameter Δ
T
0
/
E
0 for t
P
=
1
·
10
-
8, 1
·
10
-
12 s for metallic NPs, placed in water, and fixed values of λ, for Au NPs, λ
=
532 nm; Ag NPs, λ
=
400 nm; Pt NPs, λ
=
500 nm; Cu NPs, λ
=
570 nm; Ti NPs, λ
=
500 nm; Pd NPs, λ
=
470 nm; Ni NPs, λ
=
470 nm; and Zn NPs, λ
=
350 nm on r
0 in the range of radii r
0
=
5
–
100 nm. The locations of maximum values of K
abs
max
⁡
(
r
0
) and (
Δ
T
0
/
E
0
)
max
⁡ (t
P, r
0) are denoted by vertical lines (solid and dotted accordingly). The choice of mentioned wavelengths is determined by their location nearby plasmon wavelengths for these NPs (see Figures 1–6). We consider the results for Au and Ag NPs more closely.Results for Au NPs are presented in Figure7(a). The maximum value of K
abs
max
⁡
(
r
0
,
λ
) was calculated and was equal to the next value of r
0: K
abs
max
⁡(λ
=
532 nm) ≈ 3.97 for r
0
=
33 nm. The maximum values of (
Δ
T
0
/
E
0
)
max
⁡ for λ
=
532 nm are approximately equal to (
Δ
T
0
/
E
0
)
max
⁡ ≈ 4.1 × 105 Kcm2/J at r
0 ≈ 23 nm for t
P
=
1
·
10
-
12 s and (
Δ
T
0
/
E
0
)
max
⁡ ≈ 6 × 104 Kcm2/J at r
0 ≈ 39 nm for t
P
=
1
·
10
-
8 s (see Figure 7(a)). The maximum values of K
abs
max
⁡
(
r
0
) and (
Δ
T
0
/
E
0
)
max
⁡ (r
0) have different locations on r
0 axis for λ
=
532 nm in Figure 7(a). The maximum values of (
Δ
T
0
/
E
0
)
max
⁡ have been shifted by the value Δ
r
0 ≈ 10 nm to smaller values of r
0 for t
P
=
1
·
10
-
12 s and to bigger values of r
0 by the value Δ
r
0 ≈ 6 nm for t
P
=
1
·
10
-
8 s in comparison with the location of K
abs
max
⁡ (r
0) in Figure 7(a).The maximum values of(
Δ
T
0
/
E
0
)
max
⁡ for λ
=
532 nm are achieved for K
abs ≈ 3.3, t
P
=
1
·
10
-
12 s, and r
0 ≈ 23 nm and for K
abs ≈ 3.6, t
P
=
1
·
10
-
8 s, and r
0 ≈ 39 nm. It means that for achievement of the maximum values of (
Δ
T
0
/
E
0
)
max
⁡ under minimal values of E
0 we have to use the values of K
abs that are smaller than K
abs
max
⁡ mentioned above.The differences between the values ofΔ
T
0
/
E
0 for t
P
=
1
·
10
-
8 s and t
P
=
1
·
10
-
12 s decrease with increasing r
0. These differences are about ~102-103 times for r
0
=
10 nm and are equal to only ~2-3 times for r
0
=
100 nm. It can be explained by a sharp increase of τ
T ~ r
0
2 and approaching of τ
0 to t
P
=
1
·
10
-
8 s for r
0
≥
90
–
100 nm and fulfillment of short pulse condition (without heat loss).The characteristic timeτ
T is equal to τ
T ~ 1.2
·
10
-
10
–
3.2
·
10
-
9 s for the range r
0
=
10
–
50 nm and for ambient water k
∞
=
6
·
10
-
3 W/cmK, τ
T ~ 0.9 ns for r
0
=
25 nm. The fulfillment of the condition t
P
<
τ
T (1) for the most interesting range of r
0
:
25
<
r
0
<
50 nm means that the value of t
P will be in the range of pulse durations: t
P
<
1
·
10
-
9 s.The condition of “short” pulsest
P
<
τ
T is applicable for t
P
=
1
·
10
-
12 s for all values of r
0
:
5
<
r
0
<
100 nm. Under condition of “short” pulses t
P
<
τ
T, the parameter Δ
T
0
/
E
0 depends on the combination K
abs
/
r
0 and, accordingly, equation (3) describing the increasing and decreasing of Δ
T
0
/
E
0.The condition of “long” pulses witht
P
=
1
·
10
-
8 s is also fulfilled for the interval r
0
=
5
–
100 nm. The use of “long” pulses with t
P
=
1
·
10
-
8 s leads to a significant decrease of the value of Δ
T
0
/
E
0 up to 1-2 orders and more in comparison with cases for t
P
=
1
·
10
-
12 s for the whole range of r
0
=
5
–
100 nm. It is determined by heat conduction losses from NP during irradiation with this value of t
P and because of the dependence Δ
T
0
/
E
0
~
1
/
t
P (see (3)).From (4a) and (4b) we see that
(5)
t
P
<
τ
T
,
Δ
T
0
E
0
~
K
abs
(
r
0
)
r
0
,
t
P
>
τ
T
,
Δ
T
0
E
0
~
K
abs
(
r
0
)
r
0
.
Our results are in accordance with presented dependences (5).Figure7(b) presents the dependences of parameter Δ
T
0
/
E
0 (r
0, λ) (3) and K
abs (r
0, λ) for Ag NPs and for the pulse durations t
P
=
1
·
10
-
8, 1
·
10
-
12 s, and λ
=
400 nm on r
0. Maximum values of (
Δ
T
0
/
E
0
)
max
⁡ for Ag NPs are equal to ≈ 1.1
×
10
6 Kcm2/J, t
P
=
1
·
10
-
12 s, and r
0 ~ 19 nm and ≈ 5.1
×
10
4 Kcm2/J, and t
P
=
1
·
10
-
8 s at r
0 ~ 21 nm in the range 5–100 nm (see Figure 7(b)). Heating of NP with r
0 ~ 19 nm and for t
P
≤
1
·
10
-
10 s could achieve 1
·
10
3  K under radiation energy density E
0
=
1
×
10
-
3 J/cm2.There are three maximums ofK
abs
max
⁡ and correspondingly three maximum values of (
Δ
T
0
/
E
0
)
max
⁡ for t
P
=
1
×
10
-
12 s, placed at r
0 ≈ 19, 58, and 95 nm, in the range of r
0
=
5
–
100 nm. Oscillated dependences of Δ
T
0
/
E
0 behave in an analogous manner to the dependences of K
abs on r
0 for the presented values of λ (see Figure 7(b)). Values of Δ
T
0
/
E
0 for t
P
=
1
×
10
-
8 s are smaller than the ones for t
P
=
1
×
10
-
12 s for the whole range of r
0
=
5
–
100 nm. The values of shift between the locations of K
abs
max
⁡ and (
Δ
T
0
/
E
0
)
max
⁡ for Ag NPs are smaller than in the case of Au NPs because of sharp dependences of K
abs on r
0, especially for λ
=
400 nm (see Figure 7(b)).The dependences ofK
abs, P
1, and Δ
T
0
/
E
0 on r
0 for fixed values of λ for Pt, Cu, Pd, Ti, and Ni NPs are generally analogous to the dependences of Au NPs. The dependences of Zn NP parameters on r
0 are analogous to the dependences of Ag NPs. For all metallic NPs maximum values of (
Δ
T
0
/
E
0
)
max
⁡ are shifted compared to location K
abs
max
⁡ in Figure 7(b) to smaller values of r
0 for “short” pulses t
P
<
τ
T and to bigger values of r
0 for “long” pulses t
P
>
τ
T.Figures1–6 present the dependences of P
1 on λ for metallic NPs with radii r
0
=
10, 25, and 50 nm and metals Ag, Al, Au, Co, Cu, Mo, Ni, Pd, Pt, Ti, V, and Zn. Dependences of P
1 on λ are determined by the correlation between dependences of K
abs
(
λ
) and K
sca
(
λ
). Dependences of P
1 on λ for different values of r
0 have complicated disposition. For NPs with r
0
=
10 nm all presented metallic NPs exhibit high absorbance and parameter P
1
≫
1 for all metallic NPs and in part P
1
>
1 for some spectral intervals. The maximum values reached P
1
≥
100 for Co, Mo, Ni, Pd, Pt, Ti, V, and Zn NPs for interval 600
>
λ
>
1000 nm and for Au and Cu NPs maximum P
1 ~ 100 for 300
>
λ
>
500 nm for r
0
=
10 nm. All mentioned NPs are the best absorbers with P
1
≥
10
÷
100 for 600
>
λ
>
1000 nm and r
0
=
10 and 25 nm instead of Au and Cu NPs. Increasing of r
0 leads to an increase in scattering and decrease in absorbance for all presented metallic NPs. Therefore, larger NPs are more suitable for light-scattering based applications. At r
0
=
50 nm instead of spectral interval 600
<
λ
<
1000 nm for Co, Mo, Ni, Pd, Ti, and Zn NPs all values of P
1 are smaller or much smaller than 1, P
1
≪
1. Best scattering NPs among the studied metallic NPs are Ag NPs for r
0
>
20 nm. It is interesting to note that NPs can be used as absorbers in one interval of wavelengths and as scatterers in different intervals of wavelengths. All NPs with r
0
=
25 nm could be the scatterers in the interval 300
<
λ
<
500 nm and the absorbers in the interval 500
<
λ
<
1100 nm. Variant with value P
1 ≈ 1 means approximately equal possibility of using NP as absorber and scatterer simultaneously.A predominant role of absorption by NP can be used for heating of NP for thermoplasmonic applications. Such NPs can be used as absorbers of radiation. A predominant role of scattering by NPs can be used for the purposes of optical diagnostics and imaging using scattered radiation. The selection of ratio between scattering and absorption withP
1
<
1 provides a tool for NP for contrast applications in scattering optical diagnostics.


## 4. Conclusions

The strongly enhanced absorption and scattering of spherical metallic NPs make them a novel and highly effective class of contrast agents for photothermal applications and imaging-based optical diagnostics. A number of factors need to be optimized for the success in these fields. These ones include the efficiency factors of absorption K
abs, scattering K
sca, and extinction K
ext of radiation by NP, parameters of P
1, and Δ
T
0
/
E
0. There is a need to study the dependence of these parameters on the type of metal and size of NP, radiation wavelength, parameters of surrounding medium, and so forth. Systematic study of all these characteristics is a prerequisite for the successful transition of the research promise of metallic NPs to thermal applications and has been carried out in this paper.We conducted the investigation and analysis of plasmonic (K
abs, K
sca, and K
ext) and thermooptical (Δ
T
0
/
E
0) characteristics of 12 metallic NPs for radiation wavelengths in the spectral interval 200–1000 nm and in the range of NP radii r
0
=
5
–
100 nm, especially for r
0
=
10, 25, and 50 nm, based on computer and analytical modeling (Figures 1–7). Different metals were used for NPs, Au, Ag, Cu, Pt, Co, Zn, Al, Ni, Ti, V, Pd, and Mo. Three surrounding NP media were used, silica, water, and air. Value of refractive index of surroundings in the range n
λ
=
1.51
-
1.0 influences the plasmonic properties with the change. The use of silica as surroundings leads to rather small deviations from the dependences with water as ambience. More pronounced deviations of NP optical and thermooptical characteristics have been determined for air surrounding.The selection of different NPs is based on the investigation of the influence of different parameters of NP itself, radiation pulses, and ambient medium on NP properties.The data in Figures1–7 allow estimating the possibility to use different metallic NPs for thermoplasmonics and photonic applications. Maximum values of K
abs were achieved for Au, Ag, Zn, and Cu. Transformation of plasmonic (K
abs, K
sca, and K
ext) and thermooptical (Δ
T
0
/
E
0) properties in dependence on λ, r
0 with changing of NP, radiation, and ambience parameters is presented in Figures 1–7. Positions λ
abs
max
⁡, λ
sca
max
⁡, and λ
ext
max
⁡ of maximum values of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ have been determined on λ axis and in some cases the positions of K
abs
max
⁡, K
sca
max
⁡, and K
ext
max
⁡ do not coincide.Parameter ofP
1 can be used for determination of the use of NP predominantly as an absorber for P
1
>
1 or as a scatterer for P
1
<
1. It is interesting to note the achievement of values of P
1
≥
10
–
100 for mentioned NPs with r
0
=
10 and 25 nm instead of Ag and Al NPs in some spectral intervals. Larger NPs are more suitable for light-scattering based applications. Best scattering NPs inside presented metallic NPs are Ag NPs for r
0
>
20 nm. It is interesting to note Al NPs with r
0
=
25 nm which can be used as absorbers in one wavelength interval (1100
>
λ
>
500 nm) and as scatterers in the different one (500
>
λ
>
300 nm).The main goal of light-to-thermal energy conversion and thermoplasmonics is to achieve maximum value of efficiency parameter ofΔ
T
0
/
E
0 for NPs at minimal values of E
0. The influence of the parameters of radiation, t
P, λ, and E
0 of NP, ρ
0, c
0, r
0, K
abs, and surrounding medium, k
∞and n
λ, reach a maximum value of Δ
T
0
/
E
0 has been established based on an analytical model. It is possible to achieve the values of about Δ
T
0
/
E
0
~
1
·
10
6 Kcm2/J for NPs and for t
P
≤
1
·
10
-
10 s under radiation energy density E
0
=
1
·
10
-
3 J/cm2 and the heating of such NP could achieve 1
·
10
3 K.The selection of appropriate properties of NPs is based on the choice of value ofr
0 for the values of determined λ and t
P and the choice of metallic NPs, λ, and t
P for the determined value of r
0.It was established that maximum values ofΔ
T
0
/
E
0 and of NP temperature can be achieved with the use of the value of absorption efficiency factor K
abs smaller than maximum value of K
abs
max
⁡ taking into account irradiation duration, characteristics of NPs, and their cooling. Shift of the positions of maximum value of Δ
T
0
/
E
0 from the location of maximum value of K
abs
max
⁡ on axis r
0 is determined by noticeable influence of r
0 on the processes of NP heating and cooling.Our results allow estimating of optimal characteristics of absorption and scattering radiation by NPs and laser energy conversion into photothermal phenomena by selection of the NP and radiation parameters and ambience properties. We present a platform for selection of the plasmonic and thermooptical properties of metallic NPs, placed in different media, for their photonic and thermoplasmonic applications.



---

*Source: 893459-2014-10-14.xml*