Multipole Interference in the Second-Harmonic Optical Radiation from Gold Nanoparticles

We provide experimental evidence of higher multipole (magnetic dipole and electric quadrupole) radiation in second-harmonic (SH) generation from arrays of metal nanoparticles. Fundamental differences in the radiative properties of electric dipoles and higher multipoles yield opposite interference effects observed in the SH intensities measured in the reflected and transmitted directions. These interference effects clearly depend on the polarization of the fundamental field, directly indicating the importance of multipole effects in the nonlinear response. We estimate that higher multipoles contribute up to 20% of the total emitted SH field amplitude for certain polarization configurations.

Figure 1

Simple schematic of the radiative properties of an electric dipole ($\mathit{p}$), magnetic dipole ($\mathit{m}$), and quadrupole ($\mathit{Q}$).

Figure 2

Experimental setup. $C=\mathrm{\text{optical chopper}}$; $L=\mathrm{\text{lens}}$, $f=300\mathrm{mm}$; $P=\mathrm{\text{polarizer}}$; $\mathrm{HWP}=\mathrm{\text{half wave plate}}$; $\mathrm{QWP}=\mathrm{\text{quarter wave plate}}$; $\mathrm{VISF}=\mathrm{\text{long-wavelength pass filter}}$; $S=\mathrm{\text{the sample}}$; $\mathrm{IRF}=\mathrm{\text{short-wavelength pass filter}}$; $A=\mathrm{\text{analyzer}}$; $\mathrm{PMT}=\mathrm{\text{photo-multiplier tube}}$. Inset: the experimental geometry.

Figure 3

Measured line shapes. ▵: transmission SH data; ○: reflection SH data. Solid and dashed lines are fits to Eq. (1) in transmission and reflection geometries, respectively.