Chapter 4. Probing a sub-diffraction optical confinement via the polarized Raman spectroscopy
4.2 Dual-band confinement of light by TiO 2 nanoparticle
The FDTD simulation predicts peculiar nanoscale optical behavior of a nanoparticle with a high refractive index. Figure 4.1a and 4.1b show FDTD simulations of a spherical TiO2 particle having a diameter (d) of 250 nm and refractive index (n) of 2.6678 illuminated by a plane wave at λ = 532 nm propagating in the x direction. The incident light is polarized in either the z direction (θ = 0°) or the y direction (θ = 90°) as indicated by the arrows. At θ = 0°, the enhancement of the electromagnetic field is marginal on the xy-plane, and the maximum intensity is obtained at the particle–substrate contact. At θ = 90°, however, strong dual-band light confinement on the xy-plane is obtained in the space between the TiO2 particle and the substrate. Such dual-band confinement does not occur in a PS nanoparticle (d
= 250 nm, n = 1.5983) (Figure 4.2), which has been widely used for studying nanoscale light confinement. The intensity profile on the substrate (Figure 4.1c), where y = 0 represents the TiO2- substrate contact, confirms the presence of two sharp peaks upon polarization of the incident light at θ
= 90°. Here, the intensity of each peak is diameter-dependent, and the maximum occurs at d ~ 283 nm (Figure 4.1d). The distance between the two maxima is 128 nm, and the full width at half-maximum (FWHM) of each peak is 41 nm, which is much smaller than the values in photonic nanojets (~λ/3).132,
139 Hence, TiO2 nanoparticles can potentially be applied to sub-diffraction optical applications such as nanolithography and optical nanoscopy.
The FDTD simulation verifies that the dual-band optical confinement shown in Figure 4.1 is generic over a wide range of excitation wavelengths and particle diameters. Within the visible range, the confinement remains strong (|E|2 > 5), and the peak-to-peak distance of the two bands increases at longer excitation wavelengths (Figure 4.3). Upon excitation with infrared light at 785 nm, however, the maximum intensity is no longer obtained in the space between the substrate and the particle. Varying the particle diameter at a constant excitation wavelength of 532 nm, we found that the dual-band
85
confinement is preserved, and the peak intensity and the peak-to-peak distance depend on the particle diameter (Figure 4.4). The dual-band confinement becomes pronounced only when the refractive index of the nanoparticle is greater than 2 (Figure 4.5) and when the substrate is present (Figure4.6). Figure 4.7 shows time series of the electromagnetic field propagated through TiO2 and PS nanoparticles (d = 190 nm), clearly demonstrating the dual-band confinement in TiO2. Previous studies reported that a potential well for the electromagnetic field created by a nanoparticle with n > 1 becomes stronger at higher n,157 and the optical confinement is affected by extinction coefficient and reflectivity of the substrate as well.158
Dual-band light confinement where both the FWHM and peak-to-peak distance are below the diffraction limit is distinct from focusing of an electromagnetic wave onto a single band by nanolenses96,
159 or microlenses.160 What we show here is also different from the photonic nanojet,132, 136, 139 which requires a dielectric microsphere with a diameter greater than the wavelength of the incident light and a refractive index less than twice the value of the background. The WGM133, 134 observed in microcavities with circular symmetry owing to total internal refraction is also irrelevant to dual-band optical confinement exhibiting no resonant behavior.
Experimental measurement of the sub-diffraction optical phenomena described in Figure 4.1 requires sophisticated optics and thus has been challenging. In particular, NSOM149-151 provides simultaneous measurement of the topography and optical properties. However, several drawbacks, including low light collection efficiency, shallow depth of field, and a slow scan speed, limit convenient observation of nanoscale light created by a dielectric sphere.161 Alternatively, a fast scanning confocal microscope can image photonic nanojets as narrow as 270 nm (FWHM) formed by a dielectric sphere.152 More recently, HRIM has measured dual-band lights separated by ~200 nm.153, 154 Application of these imaging methods, however, has been limited owing to their sophisticated experimental platform.
86
a TiO2 (250 nm)/SiO2 (300 nm)/Si θ = 0°
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3
θ = 90°
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3
c
Diameter (nm) 0 100 200 300 400 500 5
10 15 20 25 30 35
|E|2 max
-0.3 -0.2 -0.1 0.00 0.1 0.2 0.3 5
10 15 20
|E|2 max
θ = 0°
θ = 90°
y (µ m)
128 nm d θ = 90°
b
0 20
4 8 12 16
| E|2
~41 nm
0 20
4 8 12 16
| E|2
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
z (µm)
-0.3 0.3
Figure 4.1 Strong nanoscale confinement of polarized incident light by TiO2 nanoparticle. (a,b) FDTD simulation of dielectric TiO2 nanoparticle (d = 250 nm, n = 2.6678) on SiO2 substrate illuminated by a plane-polarized wave at 532 nm. The polarization orientation indicated by white arrow. The electric field distribution (a) on xy- (z = 0) and (b) yz-plane (x = max.
electric field). (c) Profile of max. electric field at the particle-substrate contact. (d) Maximum intensity of electromagnetic field versus diameter of TiO2 nanoparticle under 90° polarized incident light.
87
PS (250 nm)/SiO2 (300 nm)/Si
θ = 0° θ = 90°
0 20
4 8 12 16
| E|2
a
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3
-0.3 -0.2 -0.1 0.00 0.1 0.2 0.3 5
10 15 20
|E|2 max
θ = 0°θ = 90°
y (µ m)
128 nm
152 nm b
c
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
z (µm)
-0.3 0.3
0 20
4 8 12 16
| E|2
Figure 4.2 Weak nanoscale confinement of polarized incident light by PS nanoparticle. (a,b) FDTD simulation of dielectric TiO2 nanoparticle (d = 250 nm, n = 1.5983) on SiO2 substrate illuminated by a plane-polarized wave at 532 nm. The polarization orientation indicated by white arrow. The electric field distribution (a) on xy- (z = 0) and (b) yz-plane (x = max.
electric field). (c) Intensity profile along y-axis at z=0. Dotted line indicates TiO2 nanoparticle as shown in Fig. 1.
88
λ = 532 nm
λ = 633 nm λ = 785 nm
0 20
4 8 12 16
| E|2
λ = 450 nm
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3
Wav elength (nm)
400 500 600 700 800 5
10 15 20 25
80 120 160 200 240 280
|E|2
max
Distance between two maxima (nm)
a
b
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
Figure 4.3 Laser wavelength dependence of nanoscale light confinement. (a) FDTD simulation of dielectric TiO2 nanoparticles (d = 250 nm) on SiO2/Si substrate illuminated by polarized (θ = 90°) plane waves (450, 532, 633, and 785 nm, respectively).
(b) Dependence of distance between bimodal light maxima (blue) and maximum intensity of electromagnetic field (red) on laser wavelength.
d= 50 nm d= 283 nm d= 390 nm
0 25
5 10 15 20
| E|2
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0
10 20 30
|E|2
y (µ m) d= 283 nm (120 nm)
d= 390 nm (120 nm)
d= 50 nm ( 56 nm)
a b c d
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
Figure 4.4 Dependence of distance between bimodal light maxima on diameter of TiO2 nanoparticle. (a-c) FDTD simulations of dielectric TiO2 nanoparticles of different sizes (d = 50, 283 and 390 nm) on SiO2/Si substrate under polarized incident light (θ = 90°) at 532 nm. (d) Maximum intensity profile at the TiO2-substrate contact indicating a different distance between the bimodal peaks and maximum intensity. The smaller TiO2 nanoparticle (d = 50 nm) shows weak intensity but a smaller distance between bimodal peaks (~56 nm).
89
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0
10 20 30
|E|2 max
y (μm)
n= 1.4 n= 2 n= 2.6678
(TiO2) n= 3.0
n = 3
n = 2 n = 1.4
a b
n= 2.6678 (TiO2)
0 25
5 10 15 20
| E|2
128 nm 112 nm
152 nm
136 nm
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
Figure 4.5 Refractive index dependence of nanoscale light confinement. (a) FDTD simulation of electromagnetic field of 250 nm dielectric nanoparticles having different refractive indices (n = 3, 2.8, 2, and 1.4), under polarized incident light (θ = 90°) at 532 nm. (b) Maximum intensity profile at the TiO2-substrate contact showing a different distance between the bimodal peaks and maximum intensity. Strong nanoscale light confinement starts to appear at refractive indices above ~2, and a high refractive index of the dielectric nanoparticle enhances nanoscale light confinement.
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0
10 20 30 40 50
|E|2
y (µ m)
a b c d
| E|2
0 30
6 12 18 24
w/o substrate
SiO2 Si
w/ substrate w/ substrate
184 nm (w/o substrate) 96 nm (Si)
128 nm (SiO2)
0 0.1 0.2 -0.2 -0.1
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3 -0.2 -0.1 0 0.1 0.2
y (µ m)
-0.3 0.3
0 0.1 0.2
-0.1 -0.2
x (µm)
-0.3 0.3
Figure 4.6. The effect of substrate on the dual-band confinement. FDTD simulation of electromagnetic field around a TiO2
nanoparticle (d = 250 nm) illuminated by a polarized light at 532 nm (a) in air without a substrate, (b) on a SiO2 substrate (n
= 1.4607, k = 0), and (c) on a bare Si (n = 4.1520, k = 0.051787). (d) Maximum intensity profile at the TiO2-substrate contact indicates that existence of substrate and high refractive index of the substrate enhances nanoscale light confinement.
90
Time 100 nm
100 nm
PS (n= 1.5983) TiO2(n= 2.6678)
Y X
Y X
Figure 4.7 Reflective index dependence on propagating the electrical field along dielectric nanoparticle. Time series of electrical filed distribution showing that strong enhancement of electric on particle-substrate contact occurs at TiO2
nanoparticle (left), whereas it does not occur at PS nanoparticle (right). Dielectric nanoparticles (d = 190 nm) with different refractive indices (TiO2 = 2.6678, Polystyrene (PS) = 1.5983) on SiO2/Si substrate illuminated by a plane polarized wave at 532 nm.
91