368
L. D. Negro et al.
We have previously discussed that aperiodic Vogel spiral arrays feature nearly
continuous azimuthal symmetry in Fourier space and, when normally illuminated,
satisfy the Rayleigh condition for planar light scattering over broad and controllable
frequency bands, irrespective of the incident polarization of light [69]. A simple scalar
Fourier optics picture already suggests that polarization-insensitive large-angle scattering of incident radiation can occur in GA spiral arrays at frequencies matching
the radial position of the scattering ring in reciprocal space [69]. This property is
ideal to engineer light trapping in thin-film Si solar cells. Following this approach,
we recently designed and fabricated GA arrays of Au nanoparticles atop ultra-thin
film (i.e., 50 nm-thick absorbing amorphous Si layer) Silicon On Insulator (SOI)
Schottky photodetector structure, sketched in Fig. 9.21a, and demonstrated experimentally larger photocurrent enhancement in the 600–950 nm spectral range compared to optimized nanoparticle gratings [67]. The relation between the spatial
Fourier spectrum of GA arrays of Au nanoparticles and the large angular distribution of scattered radiation in the forward scattering hemisphere has been rigorously
discussed by calculating the angular radiation diagrams within our recently developed formulation of the Coupled Dipole Approximation (CDA) for particles with
ellipsoidal shape [54].
This CDA approach is particularly suited to efficiently treat large-scale plasmonic
systems made of small and well separated nanoparticles, and it has been previously
validated against semi-analytical multiple scattering methods [95]. In our work, all
nanoparticles were modeled by oblate spheroids with 100 nm diameter and 30 nm
height. Moreover, the arrays are embedded in Si and normally excited by a linearly
polarized plane wave. The parameter of interest for the understanding of angular
scattering in complex plasmonic arrays is the differential scattering cross section,
which describes the angular distribution of electromagnetic power density scattered
at a given wavelength within a unit solid angle centered around an angular direction
(Δ, ϕ ) per unit incident irradiance [59]. In the case of arrays composed of dispersive metal nanoparticles, the power scattered from a particular structure is in general
a function of both the geometrical parameters of the array and the wavelength of
the incident radiation. Full information on angular scattering is thus captured by
calculating the averaged differential scattering cross section, where the average is
performed on the azimuthal angle ϕ and the scattered intensity is normalized to the
maximum value (i.e., forward scattering peak). By plotting the azimuthally averaged differential scattering cross section versus the inclination angle, we obtain the
radiation diagrams of the arrays. In Fig. 9.21b we show (plotted in dB scale) the
calculated radiation diagrams for the optimized GA arrays at three different wavelengths ∂ B = 480 nm, ∂ G = 550 nm and ∂ R = 610 nm (i.e corresponding to the
blue, green, and red colors), respectively. Differently from the well-known case of
periodic structures, where the scattered radiation is preferentially redistributed along
the directions of coherent Bragg scattering, the radiation diagram of GA arrays is significantly broadened at large angles (i.e. >30 ◦ ) for all the investigated wavelengths,
demonstrating broadband wide-angle scattering behavior.
By combining experimental absorption enhancement and photocurrent measurements with CDA and full-vector 3D Finite Difference Time Domain (FDTD)
L. D. Negro et al.
We have previously discussed that aperiodic Vogel spiral arrays feature nearly
continuous azimuthal symmetry in Fourier space and, when normally illuminated,
satisfy the Rayleigh condition for planar light scattering over broad and controllable
frequency bands, irrespective of the incident polarization of light [69]. A simple scalar
Fourier optics picture already suggests that polarization-insensitive large-angle scattering of incident radiation can occur in GA spiral arrays at frequencies matching
the radial position of the scattering ring in reciprocal space [69]. This property is
ideal to engineer light trapping in thin-film Si solar cells. Following this approach,
we recently designed and fabricated GA arrays of Au nanoparticles atop ultra-thin
film (i.e., 50 nm-thick absorbing amorphous Si layer) Silicon On Insulator (SOI)
Schottky photodetector structure, sketched in Fig. 9.21a, and demonstrated experimentally larger photocurrent enhancement in the 600–950 nm spectral range compared to optimized nanoparticle gratings [67]. The relation between the spatial
Fourier spectrum of GA arrays of Au nanoparticles and the large angular distribution of scattered radiation in the forward scattering hemisphere has been rigorously
discussed by calculating the angular radiation diagrams within our recently developed formulation of the Coupled Dipole Approximation (CDA) for particles with
ellipsoidal shape [54].
This CDA approach is particularly suited to efficiently treat large-scale plasmonic
systems made of small and well separated nanoparticles, and it has been previously
validated against semi-analytical multiple scattering methods [95]. In our work, all
nanoparticles were modeled by oblate spheroids with 100 nm diameter and 30 nm
height. Moreover, the arrays are embedded in Si and normally excited by a linearly
polarized plane wave. The parameter of interest for the understanding of angular
scattering in complex plasmonic arrays is the differential scattering cross section,
which describes the angular distribution of electromagnetic power density scattered
at a given wavelength within a unit solid angle centered around an angular direction
(Δ, ϕ ) per unit incident irradiance [59]. In the case of arrays composed of dispersive metal nanoparticles, the power scattered from a particular structure is in general
a function of both the geometrical parameters of the array and the wavelength of
the incident radiation. Full information on angular scattering is thus captured by
calculating the averaged differential scattering cross section, where the average is
performed on the azimuthal angle ϕ and the scattered intensity is normalized to the
maximum value (i.e., forward scattering peak). By plotting the azimuthally averaged differential scattering cross section versus the inclination angle, we obtain the
radiation diagrams of the arrays. In Fig. 9.21b we show (plotted in dB scale) the
calculated radiation diagrams for the optimized GA arrays at three different wavelengths ∂ B = 480 nm, ∂ G = 550 nm and ∂ R = 610 nm (i.e corresponding to the
blue, green, and red colors), respectively. Differently from the well-known case of
periodic structures, where the scattered radiation is preferentially redistributed along
the directions of coherent Bragg scattering, the radiation diagram of GA arrays is significantly broadened at large angles (i.e. >30 ◦ ) for all the investigated wavelengths,
demonstrating broadband wide-angle scattering behavior.
By combining experimental absorption enhancement and photocurrent measurements with CDA and full-vector 3D Finite Difference Time Domain (FDTD)