Femtosecond photoemission electron microscopy of surface plasmon polariton beam steering via nanohole arrays

Application-driven surface plasmon polariton (SPP) research has accelerated in recent years due to the development of SPP-based nanophotonic elements. Functional devices such as beam splitters, mirrors, and polarizers allow conventional optical manipulations to be carried out at interfaces while maintaining light speed and sub-wavelength confinement, analogous to their corresponding free-space operations.¹ These promising attributes motivate varieties of advanced SPP-based photonic devices that are ultimately poised to speed-up and further miniaturize electronic circuitry and data transmission. Beyond the apparent applications in computing and communication, both propagating and localized plasmons have been widely deployed as remote light sources in high-resolution near-field microscopes.^2–5 Overall, these diverse applications prompt a new paradigm in plasmonic optics that facilitates tailored SPP generation, fine control over their optical properties, and the interconversion between localized and propagating SPP.

Spatial manipulation of SPPs is a fundamental step toward these realizations, and a variety of both active^6,7 and passive^8–12 plasmonic steering elements have emerged. Highly sensitive SPP routing may be achieved using lithographically etched, one- or two-dimensional arrays of nanostructures. These systems are based on the principle of Bragg reflection. Arrays of structures comprised of holes, ridges, or grooves, for example, modulate the SPP dispersion sustained by the metal, forming gaps in the band structure at frequencies determined by the array geometry and material optical constants.¹³ At the bandgap frequencies, SPP propagation is not supported and reflection competes with other sources of (non)radiative damping. In this limit, the properties of the reflected SPP beam are determined by the curvature of the corresponding dispersion band, which has led to the realization of arbitrary angle steering through negative refraction.⁸ 

In this work, we utilize photoemission electron microscopy (PEEM) to image individual and multi-component SPP steering elements. PEEM is a sensitive near-field technique that can be used to visualize SPP surface fields with nanometer spatial and femtosecond temporal resolution through photoelectron imaging,^14–17 circumventing the need for plasmonic out-couplers, surface dopants, or precise emission angles as are commonly involved in all-optical imaging tools.^18–20 Our approach is based on lithographically prepared 2-dimensional plasmonic Bragg gratings (2PGs) comprised of square arrays of nano-holes. The 2PGs sustain both co- and counter-propagating SPP fields when the array pitch is tuned to satisfy the momentum conservation requirement given by the surface dielectric-weighted in-plane wave-vector (k₀) k_spp = k₀(ε₁ε₂/(ε₁ + ε₂))^1/2.^21,22 Many traditional PEEM configurations utilize forward-propagating geometries as the SPP-photon momentum mismatch required for coupling is small and can be easily bridged through defects or other surface nanostructures. In contrast, the counter-propagating SPP may only be realized by utilizing surface structures with a well-defined geometry capable of generating the required backward momentum. Structures such as 2PGs and surface ridges have been used to generate counter-propagating SPPs.^15,22–24 The counter-propagating mode is advantageous for imaging applications since it does not exhibit spatial interference that arises through concurrent interaction with the excitation or emission fields, as shown recently.²² Here, we show that the large momentum change required to facilitate counter-propagation may be exploited to directionally tune SPPs in a single-element configuration through wave-vector difference mixing. Using a two-element geometry consisting of 2PG pairs, we visualize the processes of arbitrary angle SPP steering and multi-SPP generation.

The PEEM images we present are SPP intensity maps derived from energy-integrated 2-photon photoemission (2PPE). A schematic of the PEEM apparatus is shown in Fig. 1. 2PPE is facilitated by a pair of femtosecond pulse trains synthesized from a Ti:sapphire oscillator operating at 80 MHz. Our approach to time-resolved PEEM imaging involves using the fundamental output (800 nm, 15 fs) as a pump pulse and its harmonic (400 nm, 60 fs) as a probe. This ensures efficient read-out of the SPP surface fields and avoids the complexities associated with higher-order (>2) photoemission.²⁵ By design, the use of fundamental and second harmonic fields recovers the z component of the electric field envelope of the SPP surface waves. As depicted in Fig. 1, our sample consists of 2PGs that are lithographically milled into a 100 nm thick silver film sputtered over freshly cleaved mica. The milling parameters are tailored to synthesize arrays of 15 × 15 holes with diameters/depths of 100 nm. Our incidence angle of 75° and the dielectric constant of silver at 800 nm establish the 2PG pitch required for counter-coupled SPP excitation through wave-vector difference mixing. Pitches centered around 400 nm couple ∼30 nm of bandwidth from the 50 nm available from the source spectrum.²⁶ 

A prototypical example of the implementation is shown in Fig. 1. The 400 nm 2PG (see Fig. 1) sustains bidirectional SPPs. The counter-propagating mode is clearly distinguishable from its forward-coupled analog, given the lack of periodic interference fringes arising from self-diffraction of the 800 nm fundamental beam that appear with high contrast in the forward direction. The backward SPP intensity map may be understood by considering the temporal convolution of the surface-bound SPP wave propagating in the negative x direction and the projection of the probe (second harmonic beam) propagating in the positive x direction.²² As such, the relatively long (∼60 fs) duration of the probe pulse leads to longitudinal broadening of the SPP field emission. The directionality of the probe pulse does not play a role in the measured PEEM images due to the lack of a phase-matching requirement to achieve photoemission.

In the example provided in Fig. 1, the reciprocal lattice vector, ±k_g, is (anti)collinear with the projection of the pump wave-vector, k₀ sin θ, where θ = 75°. This results in counter-propagation along the Γ − X reciprocal lattice vector. Note that the SPP direction may also be manipulated by introducing a transverse component into k_g. SPPs emanating from a series of 2PGs oriented at different angles relative to the pump wave-vector are shown in Figs. 2(a)–2(c). Here, the excitation wave-vector is titled 7° from the array principle axis. Consistent with the vector formulation of the grating condition, the difference, $k0⃗−kg⃗$⁠, determines the SPP direction for a given orientation of the array. While the silver dispersion ultimately determines the sensitivity of the angle-tuning in this measurement, the large momentum required for counter-propagation preferentially weights the array reciprocal lattice vector in the difference formula. Angular tuning curves for the two different periods investigated (400 nm, 450 nm) are shown in Figs. 2(c) and 2(d), along with their corresponding measured values. The agreement between the predicted angles and the measured values indicates that the coupling preferentially involves the fundamental grating vectors determined by the pitch. Note that, in the forward-propagating direction, the SPP is excited through scattering at the individual defect sites. The small momentum required to couple guarantees near co-propagation with the excitation wave-vector in this case, overall, limiting the utility of array rotation for SPP steering.

In addition to providing an efficient route to SPP excitation and single-element angle-tuning, 2PGs may be utilized as independent steering elements by taking advantage of their periodic band structure. We explore this concept again utilizing a series of fabricated arrays of nanoholes. In our dual-element configuration, we utilize a 400 nm pitch array for SPP excitation at 800 nm, providing a well-defined SPP wave in the counter-propagating direction as shown above. The excitation 2PGs are fabricated without an angular tilt such that SPP propagation occurs along the axis of the pump and probe pulses. Similar to the one-dimensional case,^8,10 the band structure sustained by the 2PG may be manipulated through the pitch in accordance with the Bragg condition. Our characterization includes Bragg mirrors of 565 nm pitch oriented at 30°, 45°, and 60° relative to the 2PG normal. The design parameters of the 2PGs we investigate were modeled after the 45° Bragg mirrors comprised of trenches or ridges presented in Ref. 10. To account for the effects of lateral diffraction upon SPP propagation, the arrays are configured in a 5 × 30 configuration with their long axes oriented in the direction normal to the optical axis. 2PPE PEEM images of reflected SPP in each of these configurations are shown in Figs. 3(d)–3(f). The pump–probe time delay was adjusted to maximize the reflected amplitude, which occurs when the SPP envelope is centered on the Bragg mirror (see Fig. 3). As noted above, since the probe is relatively broad in time, the SPP appears smeared along the propagation direction. Note that our grazing incidence excitation scheme generates elliptical pulse profiles on the sample [see Fig. 1(a)]. Although the pump pulse is centered on the excitation 2PG, some pump amplitude extends toward the Bragg mirrors. This generates forward-launched SPPs and the familiar self-interference that may be observed in between the steering and coupling 2PGs.²⁷ Despite the fact that the pitch of 565 nm is optimized for 45° reflection at 800 nm, measurable amplitude is also observable in the 30° and 60° optics. For the 45° example, a prominent reflected SPP may be observed at 90°. In addition, we observe SPP amplitude emanating from the mirror at −180° and −90°, with the former corresponding to retroreflection. As such, the optic supports SPP specular reflection at 45° and refraction in the other directions. It therefore may be regarded as a 3-way beam splitter. Similarly, although the 565 nm −30° and 60° optics are outside the range corresponding to Bragg diffraction, amplitude emanating at −27° and +27°, respectively, is observable. These waves correspond to positive and negative refractory waves for the 30° and 60° optics, respectively. Notwithstanding the existence of a negative index band sustained by the 2PG in the frequency range corresponding to counter-coupling, similar to that observed in dielectric systems,²⁸ negative or otherwise anomalous refraction may arise due to the curvature of the band structure.²⁹ As pointed out by Ditlbacher et al.¹² and others,^8,30 iso-frequency contours derived from the 2PG crystal band structure may be utilized to rationalize negative refractory phenomena in all-positive index media. The existence of negative refractory SPP waves from 2PG elements appear to be a useful tool to control the SPP direction and to implement novel beam-splitting nano-optical elements.

To conclude, we have provided a near-field characterization of single- and dual-element SPP steering devices based on 2D nanohole arrays. 2PPE intensity maps of SPP acquired in the time domain clearly highlight the efficacy of angled 2PG as composite systems for both excitation and spatial manipulation. Relative to the case of forward-scattered excitation, SPP coupling via counter-propagation enhances the angle-tuning sensitivity of these systems due to the momentum required to achieve counter-coupling. Despite the efficacy of the single-element SPP routing scheme, tandem elements responsible for independent excitation and manipulation operations offer arbitrary angle tuning and further facilitate the addition of alternative optical elements. Arbitrary steering angles and the realization of 3-way beam-splitting arise as a result of the highly tunable band structure of polaritonic crystals.