Second harmonic conversions of surface-plasmon-polariton–enhanced optical fields in nonlinear optics polymer/Ag/glass structures

Optical fields enhanced by surface plasmon polaritons (SPPs) on metal-dielectric interfaces are useful for increasing several light-matter interactions, and application to nonlinear optics (NLO) is one of the most important uses of this type of structure. Most previous studies on this subject took advantage of the nonlinear susceptibilities of metal surfaces. However, the limited NLO light-matter interaction lengths prevented the transfer of the technologies to practical use. In the present paper, we tried to overcome this problem by growing NLO polymer thin films on metal surfaces. The NLO responses of the system were characterized by second-harmonic generation (SHG) spectroscopy. Our experimental results suggested that SPP-enhanced optical fields induced not only surface nonlinearities in Ag but also bulk nonlinearities in NLO polymer. There was an optimal polymer thickness for the SHG conversions, and a greater thickness did not always result in higher conversion. The maximum conversion efficiency was approximately 40 times higher than that of the nonpolymer-coated bare Ag surface. The growth and propagation of the SHG waves were addressed with a numerical approach combining the transfer matrix method and Green's function analysis. The SHG conversion efficiencies were determined by three factors, the SPP-field enhancement factor, the nonlinear light-matter interaction length, and the degree of interference between the forward- and backward-propagating SHG waves. The latter two factors predominantly determined the optimal SHG conversion efficiencies. The proposed strategy of hybridizing NLO polymers brings us closer to practical uses for nonlinear plasmonics.

Figure 1

Schematics of NLO polymer/Ag/BK7 structure and optical geometries for reflection and SHG spectroscopies.

Figure 2

(a) Reflectivity and (b) SHG signal intensities from PMMA/Ag/BK7 structure with the angle of incidence. The black, red, blue, green, and purple curves correspond to the data for the polymer thicknesses $d_2$ = 0, 20, 40, 60, and 80 nm, respectively.

Figure 3

(a) Reflectivity and (b) SHG signal intensities from NLO polymer/Ag/BK7 structure with angle of incidence. The black, red, blue, green, and purple curves correspond to the data for the polymer thicknesses $d_2$ = 0, 20, 40, 60, and 80 nm, respectively.

Figure 4

(a) SHG intensity with polymer thickness for NLO polymer/Ag/BK7 (filled circles) and PMMA/Ag/BK7 structures (open circles). (b) Enlarged data for the PMMA/Ag/BK7 structure.

Figure 5

(a) Excitation light polarization dependence of SHG signals for NLO polymer/Ag/BK7 structures with (a) $d_2=0$ and (b) 40 nm. Polarization states of SHG signals for the same sample with ($\mathrm{c})d_2$ = 0 and (d) 40 nm.

Figure 6

Definitions of coordinates in four layer systems and propagation directions of forward- and backward-propagating light waves.

Figure 7

(a) Reflectivity, (b) field enhancement, and (c) SHG signal numerically calculated with the transfer matrix method for PMMA/Ag/BK7 structure. The black, red, blue, green, and purple curves correspond to the data for polymer thicknesses $d_2=0$, 20, 40, 60, and 80 nm, respectively.

Figure 8

(a) Reflectivity, (b) field enhancement, and (c) SHG signal numerically calculated with the transfer matrix method for NLO polymer/Ag/BK7 structure. The black, red, blue, green, and purple curves correspond to the data for polymer thicknesses $d_2=0$, 20, 40, 60, and 80 nm, respectively.

Figure 9

(a) SHG intensity versus polymer film thickness for the NLO polymer/Ag/BK7 structure (red filled circles) along with the numerical data calculated with Eq. (33) (red solid curve). The constituent terms of ${\eta }_{\text{SPP}}^2$ (black dashed curve), ${({\chi }_{\text{surf,}\text{eff}}^{\left(2\right)}+{\chi }_{\text{bulk,eff}}^{\left(2\right)}{d}_2)}^2$ (blue dotted curve), and $exp[i(2\mathrm{\Delta }{\varphi }_{\text{SPP}}+2{\kappa }_2\left(2\omega \right)d_2+\mathrm{\Delta }{\varphi }_{\text{ATR}}]+1{|}^2$ (green dash-dotted curve) are shown. (b) The same for the PMMA/Ag/BK7 structures. (c) The phase terms in Eq. (33). $\mathrm{\Delta }{\varphi }_{\text{total}}$ (black curve) is the summation of $\mathrm{\Delta }{\varphi }_{\text{SPP}}$ (red dashed curve), $2{\kappa }_2\left(2\omega \right)d_2$ (blue dotted curve), and $\mathrm{\Delta }{\varphi }_{\text{ATR}}$ (green dash-dotted curve).