1. Introduction

Though dated back to the beginning of the twentieth century, the subject of surface plasmons [1–2] has regained interest recently because of the ability to manipulate structures at the nanoscale [3]. Surface plasmons (SP) are near-field phenomena. These waves are confined to a surface between conductor and dielectric, such as, air and are utilized for bio-sensing purposes [4]. For larger sensitivity, it would be desired to place the macro-molecules under test right at the lasing media. As for ordinary lasers, surface plasmons lasers require gain and feedback. So far, SP lasers in the visible could not be realized due to losses, induced by currents in the supporting conductor. Reflectivity measurements of prism-coupled flat surface waveguides indicated that such loss may be compensated by gain [5–6] yet, a direct evidence of spectral line narrowing, which indicates net gain, was still lacking. Some success though, has been achieved in the far infrared spectral region [7].

Our structures are made of surface waveguides: in one construction, a perforated 50 nm thick oxide layer (aluminum oxide) separates the metal (aluminum) from air; in the other, the perforated thin oxide layer is bound by two-layer graphene, as well as the supporting metal substrate. Gain was provided by highly fluorescing dye chromophores (fluorescein), which were imbedded within the hole-array in the perforated oxide. Another fluorescence line from oxide defect states served as a reference spectral line. The feedback to the SP waves was provided by the same sub-wavelength, periodic hole-array, similarly to the construction of photonic crystal for semiconductor lasers [8–9] with the exception that the hole-array pitch was 1/6 of SP wavelength. Our construction is also unlike previously suggested scheme [10], which relied on V-shape metallic waveguides with a quantum dots serving as gain media.

2. Theoretical considerations

Coupling to and from surface plasmons waves is conveniently made by using corrugated structures [11] and takes the momentum conservation form of, k ₀ sin(θ)+qG=β. Here, β is the wave vector of the SP propagating along the surface; k ₀sin(θ) is the wave vector projection of the incident light onto the surface, launched at an angle θ with respect to the surface normal; G is the reciprocal lattice vector of holes. The SP wavenumber may be written as β=k₀n_eff with n_eff – the effective index of the waveguide. For a good metal n _eff>1 and thus, β>k ₀. In addition a typical lattice constant of a corrugated media is larger than the propagating SP wavelength and |q|≥1 and an integer. However, when the lattice constant is much smaller than the SP wavelength, as is the case here, one can satisfy the above equation by scaling back the reciprocal lattice vector and define instead a constant q’=q/m, for which m is another integer – the number of sub-lattices included in the scattering process [12]. In this case, q’ takes both negative and positive values and is smaller than one. For example, if the lattice constant is a=90 nm and the SP wavelength is 540 nm then, m=6 (every other 6^th plane contributes to the scattering process) and q=1 (one wavelength of interaction length). In this example, the above equation is satisfied for θ=0 (normal incidence). We note that when β<G as is the case here, only the TM mode, namely, the mode with its electric field oscillating within the plane of incidence, is able to propagate along the surface. We also note that in these anodized aluminum oxide (AAO) films, the electric field is concentrated at the hole-air interface, removed from the aluminum substrate [13–14], thus minimizing possible fluorescence quenching [11].

Schematic dispersion relations are shown in Fig. 1. We concentrate on the two branches (‘optical branches’) marked with dots in the folded Brillouin zone (gray area). The zone is scaled back by the integer m as discussed earlier. The dots mark two frequencies, ω ⁺ and ω ^-, respectively [12], for each incident angle, θ. Also drawn are light lines (ω=±ck ₀ with c – the speed of light). For SP, light may be pumped through one branch in the Brillouin zone and the scattered light may escape from the other. Coupling to and from the various optical modes in the waveguides is provided by the same periodic array of holes. The periodic structure also ensures that these frequencies are associated with standing surface waves owing to the symmetry of wave vectors, which are separated by q’G.

 

Fig. 1. Schematic of the dispersion relations used. The folded Brillouin zone (gray area) is scaled by m across the light lines, ω=±ck ₀. Each incident angle θ is associated with two frequencies ω ⁺ and ω ^- and SP wave vectors, β ⁺ and β ^-, respectively. Frequencies marked by the same color belong to wave vectors, separated by a reciprocal vector G/m.

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An ideal 2-D hexagonal array has two lattice vectors, a ₁ = x̂a and a ₂ = x̂a/2 + ŷa√3/2, where a is the distance between the nearest neighbor holes (Fig. 2). The reciprocal lattice vectors are; G ₁ = x̂2π/a-ŷ2π/a-√3 and G ₂ = ŷ4π/a√3. The abrupt nature of the holes invokes higher-orders and sub-orders of scatterings, which depend on the tilt and azimuthal angles with respect to the polarized incident beam. Unlike conventional wisdom, these coherent scattering are strong: fluorescence signal may vary by a factor of three or, more upon tilting and rotating the sample with respect to the incident beam.

As mentioned before, there are two frequencies associated with a given incident tilt angle θ: these are ω ^-≈ω ₀[1-(1/2)sin(θ)] and ω ⁺≈ω ₀[1+(1/2)sin(θ)] corresponding to SP wave vectors, β ^- and β ⁺, respectively. The difference frequency is δΩ=ω ⁺-ω ^- and we note that β ⁺-β ^-=2q’G; namely, a large coupling is expected between these two frequencies. Due to the higher harmonics of propagation, we anticipate confinement of the surface wave by higher order Bragg diffraction. Optimal fluorescence conditions occur when the mode propagating along the surface is a standing wave, coupled by the periodic structure, as well. This is apparent when we consider a 1-D example at θ=0: in this case, coupling is made through the momentum conservation rule β=G/m and confinement is made via Bragg condition 2β=2G/m. The gap at θ=0 might be too small to be of value (Fig. 1) and our experiments did not indicate a measurable gap. On the other hand, our intensity dependent experiments indicate a fluorescence peak down shift (see below), which suggests the existence of two overlapping peaks at θ=0.

 

Fig. 2. (a) Hole-array in alumina (pale yellow) sandwiched between aluminum (blue) and a semi-transparent 2-layered graphene (gray). a=90 nm. The electric field is concentrated at the hole-air interface, removed from the aluminum substrate. (b) Unit vectors and the polarization state of the pump laser. (c) Example of graphene on anodized aluminum oxide (AAO). (d) Experimental configuration. We used a f=5 cm lens to focus the pump laser light onto the sample and f=10 cm to focus the scattered light onto the spectrometer. Two sharp spectral filters cut the laser line off.

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The surface waveguide mode is defined by β=k₀n_eff with n_eff – the effective index of the waveguide. For unloaded waveguides yet, corrugated metallic films we may approximate, n_eff~√(ε ₁ ε ₂/ε ₁+ε ₂)>1, similarly to the expression for flat metallic surfaces. For a loaded and perforated SP waveguides, namely, surface metallic guides with a very thin perforated oxide layer, n_eff~1 as well, due to the large negative permittivity of aluminum and the small thickness of oxide layer. The coupling to and from the array of holes may be written as:

For example, Eq. 1 predicts θ=6.7° and θ=8.9° with q ₂=0; q ₁=1/6 for the pump wavelength at 532 nm and the 550 nm fluorescence line, respectively with a=90 nm and n _eff=1.02. Note that since δΩ/ω=δλ/λ≈sin(θ), and θ~2°. In fact, one may find many resonances in the range between 0–12 degrees because of the densely packed hole-array structure. Surprisingly, the sub-wavelength structure did not introduce overwhelming scattering losses (see below).

3. Experiment and discussion

As mentioned before, our substrates were made of anodized aluminum oxide (AAO) [13–14] (Fig. 2). Fluorescein was dissolved in ethanol, dropped on the substrate and let dried. Two-layer graphene was deposited as outlined in Ref. 15 and sonicated in water without going through the annealing stage. In the experiments, we used a confocal arrangement whereby the sample was tilted and azimuthally rotated (in-plane rotations) with respect to the linearly polarized TM incident beam until optimal conditions have been reached. The spot-size of the pump laser was small (~2.5 μm²), within the spatial coherence of the hole-array. This was obtained with a beam diameter of ~1 cm and a focusing lens of f=5 cm (or, NA~0.1). We operated at a tilt angle of approximately θ~8° which is a compromise between the 7° and 9° predicted by Eq. (1). Such conditions were also found beneficial for previous Raman spectroscopy results [14] where the G Raman line of carbon nanotubes (~1600 cm^-1, corresponding to a wavelength of ~555 nm) were substantially enhanced (see also discussion on measurements with CW Ar below).

Fluorescence signal as a function of wavelength is shown in Fig. 3 for samples pumped with a pulse laser (double frequency, 10 Hz Nd:YAG laser, 10 nsec pulse at 532 nm). Detection of the fluorescing signal was made with a photo-multiplier interfaced spectrometer and a lock-in amplifier. Two sharp spectral filters cut the pump laser line off. Two examples are shown: a 2-layer graphene bound and unbound waveguides. The data exhibited clear threshold at 5 mW averaged pump intensity (Fig. 3b,d). The spectral line of the fluorescence signal narrowed from 35 nm to 24 nm – approximately a 30% reduction. Such spectral narrowing is consistent with a gain factor (rather, the gain coefficient times an effective length) of 3. Saturation for the graphene bound sample (beyond 15 mW of pump intensity) was accompanied with line broadening consistent with gain saturation. The lower saturation value for graphene bound surface guides in comparison to the unbound guides is attributed to a better mode confinement.

 

Fig. 3. (a)–(b) with graphene and (c)–(d) without it. (b) and (d) Fluorescence as a function of input intensity. The arrows mark the curves in (a) and (c). The linewidth has narrowed by 30% for both samples. The spectral linewidth remained constant for the AAO defect line at 680 nm.

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By comparison, we observed another spectral line at 680 nm. The line is attributed to defect states in the 50 nm oxide layer. These were probably formed when anodizing the samples with chromic acid, resulting in chrome oxide. No spectral line narrowing is noted here despite the appearance of a threshold. There are differences in the threshold value for the graphene bound and unbound samples, as well. Such data accentuate the effect of selective feedback in our experiments and point to loss compensation effect rather than to net gain. Since our sample contained domains, the coherence of the hole-array is extended only over a few microns and the feedback effect is local in nature.

Larger enhancement and further spectral line narrowing for the 680 nm line may be achieved by a small tilt (θ~2° compared to the predicated θ~3–4°) and in-plane rotations of the samples (Fig. 4). In that case, the spectral linewidth at 550 nm remained unchanged. We note that the 680 nm line may be very strong and occasionally, typically at relatively large input intensities, rather narrow (<5 nm). At these intensity levels, the line at 550 nm exhibited some signs of damage. One should be cautious upon comparing line narrowing from various locations in the sample: this might be the result of inhomogeneous etching.

 

Fig. 4. Graphenated sample: (a) Fluorescence as a function of wavelength. (b) Fluorescence as a function of input intensity. The spectral linewidth remained the same for fluorescein yet, narrowed for the AAO from 32 to 25 nm when the pump intensity increased from 6 mW to 8 mW.

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One could maintain that conduction losses limit coherent scattering and SP propagation to very small distances. Experiments with incident polarized Ar laser beam at 514.5 nm revealed two clear peaks at θ=8° and θ=12°. This means that the coherences length is extended over a few SP wavelengths [16]. Such coherence is more pronounced for graphene bound surface waveguides. Intensity dependent experiments with CW Ar laser as a pump beam exhibited saturation of fluorescence without threshold or significant spectral line narrowing. They also indicated a fluorescence peak shift from 560 nm to 550 nm. These experiments imply that coupling to the periodic structure may be made with one periodicity (q ₂=-1/5; q ₁=1/5) and the coupling out, with another (q ₂=0; q ₁=1/6).

3. Conclusions

Laser attributes of threshold, gain, spectral line narrowing and feedback have been demonstrated for periodic, sub-wavelength structures, which support surface plasmons waves. Some of these constructions included graphene bound surface guides. Since graphene is an inert material, one can envision new bio-chemical applications, whereby macro-molecules are situated on suspended graphene, well within the near-field mode distribution of a surface plasmons laser.