Propagation of Femtosecond Surface Plasmon Polariton Pulses on the Surface of a Nanostructured Metallic Film: Space-Time Complex Amplitude Characterization

Ultrashort surface plasmon polariton (SPP) pulses, propagating on the surface of a nanostructured metallic film, are characterized in space and time using time-resolved spatial-heterodyne imaging. Optical pulses are coupled from free space into various surface modes using a 2D array of circular nanoholes, and spatial amplitude and phase characteristics of the scattered surface field are measured with femtosecond-scale time resolution. Demonstrated in-plane focusing of SPP pulse provides additional electromagnetic field localization with possible applications in SPP nanophotonics, nonlinear surface dynamics, biochemical sensing, and ultrafast surface studies.

Figure 1

Measured transmittance of nanohole arrays superimposed with calculated dispersion map of SPP modes. Transmittance is displayed in false color as a function of normalized frequency versus normalized in-plane wave vector measured in two directions (as indicated in reciprocal space diagram in inset). Data for two different grating periods, $a=1.4\mu \mathrm{m}$ (top) and $1.6\mu \mathrm{m}$ (bottom), are combined to show the whole parameter space, with the stitching between data sets occurring at the horizontal, solid white line. Phase matching conditions are displayed for a SPP on an air-aluminum interface with dashed white lines. Pink ellipses represent the incident femtosecond pulse for the two arrays under study: in frequency limited by the pulse spectral bandwidth and in wave vector by the angular intensity distribution of the illumination beam. The interplay between the spectral and angular bandwidths of the incident optical pulse is similar to the phase matching effects observed in volume holography and nonlinear optics.

Figure 2

Schematic diagram for excitation and time-resolved imaging of femtosecond surface plasmon polariton (SPP) pulses. The nanohole array ($200\times 200\mu {\mathrm{m}}^2$ size is greatly exaggerated) is imaged with 40 times magnification on the CCD surface, where the optical field, radiated by propagating SPP pulse forms interference with a superimposed femtosecond reference pulse. The interference pattern is shown in false color for $\Delta \tau =0.5\mathrm{ps}$ delay between the pulses. A crossed polarizer-analyzer pair is used to block the directly transmitted optical field while passing the scattered SPP field. Inset figure shows time-average scattered SPP field, detected without reference femtosecond pulse.

Figure 3

Temporal evolution of scattered femtosecond SPP pulse. (a)–(d) Spatial amplitude of the femtosecond SPP pulse (shown in false color) scattered from nanohole array with $a=1.6\mu \mathrm{m}$ hole period, measured for several time delays between SPP and reference pulses. (e) Normalized temporal cross correlation of scattered SPP and reference pulses, measured at three spatial locations along the SPP propagation path. (f) Delay of the SPP pulse peak measured at different positions along the propagation path gives SPP pulse group velocity $\sim 300\pm 5\mu \mathrm{m}/\mathrm{ps}$. Dashed line in (a) outlines dimensions of the nanohole array.

Figure 4

Spatial evolution of scattered SPP field. (a)–(d) Spatial amplitude and phase (modulo $2\pi$) distributions of scattered SPP pulse measured with $1.6\mu \mathrm{m}$ (a),(b) and $1.4\mu \mathrm{m}$ (c),(d) nanohole array periods with converging (a),(c) and diverging (b),(d) Gaussian beam illumination showing SPP field focusing and defocusing within the metallic film surface. Red and blue lines in phase distribution (d) show direction of cross sections for phase plots in (f). Spatial phase distributions demonstrate direct (a),(b) and inverse (c),(d) phase relationship between incident optical field and scattered SPP field. (e) In-plane SPP focal waist formation, measured in nanohole array with $1.6\mu \mathrm{m}$ period. Amplitude is renormalized in SPP propagation direction (horizontal) to compensate for attenuation. (f) Unwrapped longitudinal (open squares) and transversal (open circles) cross sections of the spatial phase distribution from (d) with linear and quadratic least-squares fitting plots. Linear phase corresponds to 6.0° phase matching angle for $(-1,0)$ and $(0,-1)$ SPP modes shown in Fig. 1, while the quadratic spatial phase of the SPP field is acquired from the quadratic spatial phase of the incident optical field.