**4. CWLR imaging for characterization of graphene**

We also note that the proposed CWLR system is not limited to characterize metal nanostructures. It can also be extended to other samples, such as graphene sheet. In this part, we will show how the system was used to determine the number of graphene layers and to extract the corresponding refractive index.

The graphene's visibility strongly varies from one laboratory to another and it relies on experience of the observer though one can observe different colours/contrasts for graphene sheets of different thickness using the optical image with "naked eyes". Taking advantage of contrast spectra and image, this can be made quantitative and accurate. By combing Raman spectroscopy and optical images, graphene sheets with different layer numbers were first obtained as shown in Figure 12. Then, their contrast spectra were measured and plotted in Figure 12. For consistence with reference (Ni et al., 2007), the contrast spectra C(λ) were obtained by using C(λ)= (R0(λ)- R(λ))/ R0(λ), where R0(λ) is the reflection spectrum from the SiO2/Si substrate while R(λ) is the reflection spectrum from graphene sheet. As revealed in Figure 12, the contrast spectrum of single layer graphene has a peak at about 550 nm, which makes the single layer graphene visible and is in green-orange range. Meanwhile, the peak position is almost unchanged with increasing number of layers up to ten. The contrast value for single layer graphene is about 0.09+0.005 and it increases with the number of layers, for example, 0.175+0.005, 0.255+0.010, and 0.330+0.015 for two, three, and four layers, respectively. For graphene of around ten layers, the contrast saturates and the contrast peak shifts towards red (samples a and b). For samples with larger number of layers (c to f), negative contrast occurs. This can easily be understood that these samples are so thick that the reflections from their surface become more intense than that from the substrate, resulting in negative value contrast.

Hence, different layer graphene gets different contrast value, which provides a standard for determining the number of layers for graphene. This can also be understood in terms of the

experiences preferred excitation when the polarization of the incident light is parallel to the nanowire. Thus, this SP mode along the different material reflectivity contributes to the obtained polarization dependent CWLR images. It also demonstrates that the developed CWLR imaging system is able to correlate the polarization dependent CWLR images of

Fig. 11. The CWLR images at the wavelength of 600–640 nm for silver nanowires on silicon substrate. The double-direction arrows in the figure indicate the polarization direction of the

We also note that the proposed CWLR system is not limited to characterize metal nanostructures. It can also be extended to other samples, such as graphene sheet. In this part, we will show how the system was used to determine the number of graphene layers

The graphene's visibility strongly varies from one laboratory to another and it relies on experience of the observer though one can observe different colours/contrasts for graphene sheets of different thickness using the optical image with "naked eyes". Taking advantage of contrast spectra and image, this can be made quantitative and accurate. By combing Raman spectroscopy and optical images, graphene sheets with different layer numbers were first obtained as shown in Figure 12. Then, their contrast spectra were measured and plotted in Figure 12. For consistence with reference (Ni et al., 2007), the contrast spectra C(λ) were obtained by using C(λ)= (R0(λ)- R(λ))/ R0(λ), where R0(λ) is the reflection spectrum from the SiO2/Si substrate while R(λ) is the reflection spectrum from graphene sheet. As revealed in Figure 12, the contrast spectrum of single layer graphene has a peak at about 550 nm, which makes the single layer graphene visible and is in green-orange range. Meanwhile, the peak position is almost unchanged with increasing number of layers up to ten. The contrast value for single layer graphene is about 0.09+0.005 and it increases with the number of layers, for example, 0.175+0.005, 0.255+0.010, and 0.330+0.015 for two, three, and four layers, respectively. For graphene of around ten layers, the contrast saturates and the contrast peak shifts towards red (samples a and b). For samples with larger number of layers (c to f), negative contrast occurs. This can easily be understood that these samples are so thick that the reflections from their surface become more intense than that from the substrate,

Hence, different layer graphene gets different contrast value, which provides a standard for determining the number of layers for graphene. This can also be understood in terms of the

incident light. (Du et al., 2008).

resulting in negative value contrast.

**4. CWLR imaging for characterization of graphene** 

and to extract the corresponding refractive index.

single silver nanowires with the nanowire polarization dependent excitation of SP.

Fig. 12. The contrast spectra of graphene sheets with different thicknesses, together with the optical image of all the samples. Besides the samples with 1, 2, 3, 4, 7 and 9 layers, samples a, b, c, d, e and f are more than ten layers and the thickness increases from a to f. The arrows in the graph show the trend of curves in terms of the thicknesses of graphene sheets. (Ni et al., 2007).

Fresnel reflection theory. Consider the incident light from air (*n0* = 1) onto a graphene, SiO2, and Si tri-layer system. The reflected light intensity from the tri-layer system can then be described by (Blake et al., 2007; Anders, 1967):

$$R(\mathcal{A}) = r(\mathcal{A})r^\*(\mathcal{A})\tag{5}$$

$$\text{tr}(\mathcal{X}) = \frac{r\_a}{r\_b} \tag{6}$$

$$r\_a = \left(r\_1 e^{i(\beta\_1 + \beta\_2)} + r\_2 e^{-i(\beta\_1 - \beta\_2)} + r\_3 e^{-i(\beta\_1 + \beta\_2)} + r\_1 r\_2 r\_3 e^{i(\beta\_1 - \beta\_2)}\right) \tag{7}$$

$$r\_b = \left(e^{i(\beta\_1 + \beta\_2)} + r\_1 r\_2 e^{-i(\beta\_1 - \beta\_2)} + r\_1 r\_3 e^{-i(\beta\_1 + \beta\_2)} + r\_2 r\_3 e^{i(\beta\_1 - \beta\_2)}\right) \tag{8}$$

where 0 1 1 2 2 3 123 01 12 23 , , *n n n n n n rrr nn nn nn* are the reflection coefficients for different

interfaces and 1 2 1 12 2 2 ,2 *d d n n* are the phase difference when the light passes through the media which is determined by the path difference of two neighbouring

interfering light beams. The thickness of the graphene sheet can be estimated as *d1* = *NΔd*, where *N* represents the number of layers and *Δd* is the thickness of single layer graphene (*Δd* = 0.335 nm) (Kelly, 1981, Dresselhaus, 1996). The refractive index of graphene is used as a fitting parameter. The thickness of SiO2, *d2*, is 285 nm, with a maximum 5% error. The refractive index of SiO2, *n2*, is wavelength dependent (Palik, 1991). The Si substrate is considered as semi-infinite and the refractive index of Si, *n3*, is also wavelength dependent (Palik, 1991). The reflection from SiO2 background, R0(λ), was calculated by setting *n1* = *n0* = 1, and *d1* =0.

Confocal White Light Reflection Imaging for Characterization of Nanostructures 299

 *C* = 0.0046+0.0925*N*-0.00255*N*2 (9)

In order to demonstrate the effectiveness of the contrast spectra in graphene thickness determination, we carried out the CWLR imaging, too. As shown in Figure 14a, distinct contrast for different thicknesses of graphene can be observed from the image. It is worth noting that the contrast image measurement can be done in a few minutes. Figure 14b and 14c show contrast along the two dash lines on the image. The contrast value for each thickness agrees well with those shown in Figure 13. Using Eq. (9), the *N* values along the two dash lines are calculated, where the *N* along the blue line is: 0.99, 1.93, and 3.83; and

Accordingly, by the proposed CWLR system, both the layer number of graphene and the refractive index of single layer graphene can be achieved. It does not need a single layer graphene as reference as that in Raman. It is also noted that the proposed system can be used to get information about the optical conductivity of some bilayer grapene sheet (Wang

In this chapter, we have proposed a far-field CWLR imaging system by combing a small aperture and a small collection fibre core diameter, which is fast, non-destructive and user friendly. It is demonstrated to provide a high spatial resolution about 410 nm, which is capable of resolve two nearest gold nanoparticles with the size and centre-to-centre distance in-between about 300 nm and 200 nm, respectively. Individual single, dimer gold nanospheres, silver nanowires, and graphene sheet were characterized by the imaging system as well. Apart from the dipolar LSP, excitation of multi-polar LSP of individual gold nanospheres was revealed. Compared to the resonance energy of single gold nanosphere, the resonance energy of the dimer is red-shifted due to the EM coupling between the two component nanospheres of the dimer. The near-field EM coupling effect between individual Au nanospheres and the supporting SiO2/Si substrate was also studied by the CWLR imaging method, which reveals a decay length of 0.30 in units of *d R*/ for the coupling strength, qualitatively agreeing well with the 'plasmon ruler' scaling theory. The anisotropic excitation of LSP of single silver nanowire was revealed to get contribution to the polarization dependent images besides their essential reflectivity difference from that of the substrate. It is also demonstrated that the CWLR spectra method provides a standard to identify the thickness of graphene sheet on Si substrate with ~300 nm SiO2 capping layer, from which the refractive index (*nz* = 2.0-1.1i) of graphene below ten layers can also be easily determined. As the CWLR imaging can be preformed at different wavelength, we also expect its other interesting applications such as biomaterial mapping and plasmonic studies in the future.

This work was financially supported by the Natural Science Foundation of China (No. 11004103), China Postdoctoral Science Foundation funded project (No. 20100471332), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0902016C), NUAA Research

Funding (No. NS2010186), and NUAA Scientific Research Foundation.

along the red line is: 0.98, 2.89 and 3.94. Again our results show excellent agreement.

where *N* (≤10) is the number of layers of graphene.

et al., 2010), which is not shown here.

**5. Conclusion** 

**6. Acknowledgment**

Fig. 13. (a) The contrast spectrum of experimental data (black line), the simulation result using *nz* =2.0-1.1i (red line), and the simulation result using *nG* = 2.6-1.3i (dash line). (b) The contrast simulated by using both *nG* (blue triangles) and *nz* (red circles), the fitting curve for the simulations (blue and red lines), and our experiment data (black thick lines), respectively, for one to ten layers of graphene. (Ni et al., 2007).

Fig. 14. (a) The contrast image of the sample. (b) and (c) The cross section of contrast image, which corresponds to the dash lines. (Ni et al., 2007).

The optimized simulation result is shown in Figure 13a reveals a refractive index of single layer graphene *nz* = 2.0-1.1i, whereas the simulation result using the bulk graphite value of *nG* (2.6-1.3i) shows large deviation from our experimental data. Using the optimized refractive index *nz*, we have calculated the contrast of one to ten layers' graphene also as shown in Figure 13b, which agree well with the experimental data with the discrepancy being only 2%. By using this technique, the thickness of unknown graphene sheet can be determined directly by comparing the contrast value with the standard values shown in Figure 13b. Alternatively, it can be obtained using the following equation:

 *C* = 0.0046+0.0925*N*-0.00255*N*2 (9)

where *N* (≤10) is the number of layers of graphene.

In order to demonstrate the effectiveness of the contrast spectra in graphene thickness determination, we carried out the CWLR imaging, too. As shown in Figure 14a, distinct contrast for different thicknesses of graphene can be observed from the image. It is worth noting that the contrast image measurement can be done in a few minutes. Figure 14b and 14c show contrast along the two dash lines on the image. The contrast value for each thickness agrees well with those shown in Figure 13. Using Eq. (9), the *N* values along the two dash lines are calculated, where the *N* along the blue line is: 0.99, 1.93, and 3.83; and along the red line is: 0.98, 2.89 and 3.94. Again our results show excellent agreement.

Accordingly, by the proposed CWLR system, both the layer number of graphene and the refractive index of single layer graphene can be achieved. It does not need a single layer graphene as reference as that in Raman. It is also noted that the proposed system can be used to get information about the optical conductivity of some bilayer grapene sheet (Wang et al., 2010), which is not shown here.
