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We propose and numerically demonstrate an integrated fiber-coupled launcher for slow surface plasmon-polaritons. The device is based on a novel plasmonic mode-converter providing efficient power transfer from the fast to the slow modes of a metallic nanostripe. Total coupling efficiency with standard single-mode fiber approaching 30% (including ohmic losses) has been numerically predicted for a 25-µm long gold-based device operating at 1.55 µm telecom wavelength.
©2012 Optical Society of America
1. Introduction
During the last decade, much effort has been devoted to the development of engineered metal-dielectric nanostructures for extreme light concentration and manipulation, which led to the modern research area of plasmonics (see [1] and references therein). The capability of providing sub-wavelength confinement far below diffraction limit offered by plasmonic nanostructures stems from the peculiar feature of a special class of surface plasmon-polaritons (SPP), the so-called slow SPP (S-SPP), which are spatially invariant, i.e. persist existing (with progressively large wave vectors) in the limit of zero cross section of the structure [2–4]. An impressive demonstration of the unique features of S-SPP waves is represented by the proposal [5] and experimental demonstration [6] of rapid adiabatic nanofocusing in tapered plasmonic nanowires, which promises to disclose novel applications in spectroscopy, detection and sensing at the nanoscale. Also, integrated plasmonic waveguides and devices based on S-SPPs have been designed and experimented in several configurations, including nanostripes [7], slot [8, 9] and V-groove [10, 11] structures. Despite such effort the development of integrated nanocircuits based on S-SPP suffers from the lack of a compact (possibly integrated) and efficient method for coupling/decoupling these waves, whereas a complicated external apparatus is generally needed, employing microscope objectives, dielectric prisms or nanofibers. On the contrary, efficient integrated launchers have been demonstrated for other kind of plasmonic waves, including the basic SPP bound at the surface of a metal [12, 13] and the SPP of a dielectric-loaded metallic surface [14, 15]. Though these waves do not exhibit the unique features of S-SPPs, the demonstration of a fiber-coupled launcher reported by Bozhevolnyi's group [15] is encouraging, as the integration of plasmonic nanodevices with the most convenient front-end of any optical system, that is the fiber, is a major issue for the industrial development of the field.
The present work is aimed at the theoretical proposal and numerical demonstration of an integrated fiber-coupled launcher for slow plasmonic modes in metallic nanostripes.
A metal nanostripe exhibits an anti-symmetric mode, called the short-range SPP (SR-SPP) because of the relatively high propagation losses, which is slow in nature [7]. The intrinsic confinement of the SR-SPP mode, its high effective index, and odd parity in the transverse fields result in practically zero coupling efficiency with optical fibers. Nevertheless, a metal nanostripe also exhibits a symmetric mode, called the long-range SPP (LR-SPP) (in view of its low propagation losses). This is a fast wave, with low effective index, that approaches cutoff in the limit of zero cross section of the nanostripe, but for suitable thickness of the metal the LR-SPP is very well overlapped with the fundamental mode of standard telecom optical fibers, with almost 90% coupling efficiency demonstrated at 1.5 µm under butt-coupling excitation in a 8 µm wide, 15 nm thick gold nanostripe embedded in polymer [16].
Our idea is thus to explore the possibility of launching the SR-SPP of a metallic nano-stripe by first exciting the LR-SPP through fiber butt-coupling and then provide efficient conversion from the LR-SPP mode to the SR-SPP mode.
Mode conversion in plasmonic waveguides has been mostly unexplored, basically because the approaches exploited in guided-wave optics, based on grating coupling technique [17, 18], would require mm long structures to allow appreciable (~5-10%) power transfer, resulting in too high propagation losses for slow plasmonic modes (whose propagation distance is tipicaly of the order of few tens of µm). As example, at 1.55 µm for a gold nanostripe of 15 nm thickness, the grating period required to match the propagation constants of the LR-SPP and the SR-SPP is about 10 wavelengths, and typically several (tens or hundreds) periods ought to be employed even in the very basic design provided by a uniform grating. Also, grating design requires a resonance condition to be fulfilled, causing narrow-band operation as well as shallow tolerance of a real device to slight variations from the nominal parameters.
Here we propose a novel design for mode-conversion based on adiabatic transformation of plasmonic waves in metal-dielectric multi-layered structures.
2. Design guidelines for LR/SR-SPP mode conversion
Considering that the metal nanostripes achieving high coupling efficiency with single-mode optical fibers for the LR-SPP mode are few µm wide, the design of a LR/SR-SPP mode converter can be attained in a 2D configuration, consisting of a metallic film instead of a metallic nanostripe. The symmetric metal film (i.e. homogeneous metal film with refractive index nM surrounded by a homogeneous dielectric with refractive index nD) has been extensively studied [19, 20].
In particular, it has been demonstrated that the effective index of the two LR-SPP and SR-SPP modes can be accurately approximated by the following analytical formula [21]:
where t is the film thickness, εM = nM2 and εD = nD2 are the dielectric permittivities of the metallic and dielectric medium respectively and k0 = 2π/λ, being λ the optical wavelength in vacuum.Effective index computation from Eq. (1) is reported in Fig. 1(a) for a gold film at λ = 1.55 µm telecom wavelength embedded in silicate dielectric substrate [cf. inset in Fig. 1(b)]. Note that as the film thickness is increased above 100 nm, the LR-SPP and the SR-SPP becomes degenerate, with an effective index given by the effective index of the SPP mode of the single metal-dielectric interface, . Note that both the real and the imaginary part of nLR(SR) degenerates, respectively, with the real and the imaginary part of . As a consequence of this degeneracy, the field components of the two modes turn out to be given by the even and odd superpositions of the two individual SPP modes sustained by the single metal-dielectric interfaces of the film [19, 20]. More precisely, the LR-SPP and the SR-SPP exhibit, respectively, even and odd parity of the transverse field components Hx and Ey and odd and even parity of the longitudinal Ez field component. The Hx components (from which the electric field components can be deduced by derivation, since LR-SPP and SR-SPP are TM waves) are reported in Figs. 1(c) and 1(d) for the two cases of thick and thin gold films respectively.
Fig. 1 (a) Effective index (real part n' and imaginary part n”) of the symmetric (LR-SPP) and anti-symmetric (SR-SPP, i.e. slow SPP) plasmonic modes supported by a gold film embedded in a homogeneous dielectric [see inset in (b)] as a function of the film thickness t at λ = 1.55 µm (nM = 0.55 + i 11.5; nD = 1.45). (b) Estimated theoretical coupling loss between the LR-SPP mode and a 2D gaussian beam with 10.5 µm MFD corresponding to the fundamental mode of standard telecom fiber at 1.55 µm. Magnetic field cross-sections of the two plasmonic modes for (c) a thin film and for (d) a thick film. Dotted green curve shows magnetic field cross-section of the 2D gaussian beam considered in (b).
Therefore, in a thick metallic film the LR-SPP can be converted into the SR-SPP by providing a π phase delay between the two SPP components bound at the single metal-dielectric interfaces. Such a delay can be accomplished by loading the metal with a different dielectric of higher refractive index nL (corresponding to dielectric permittivity εL = nL2) resulting in a dielectric loaded SPP (DL-SPP) planar waveguide whose peculiar features has been extensively studied (see [20, 22] and references therein). Actually, by following a similar analysis as the one reported in [20], it is straightforward to derive the dispersion equation for the fundamental mode supported by this structure,
where d is the load thickness, are the transverse decay constants of the field in the three different media, and nDL = n'DL + i n”DL is the (complex) effective index of the DL-SPP mode, to be determined by numerically solving Eq. (2). The real part of the DL-SPP mode effective index (n'DL) as a function of the load thickness d is shown in Fig. 2(a) for three different refractive indices of the load, mimicking feasible glassy polymers with medium to high density [23]. With n'DL(d) at hand, a π-phase retardation for the SPP can be introduced by modulating the load thickness along the z-axis of propagation. Actually, provided that the load thickness function d(z) is smooth enough, the adiabatic (WKB) approximation [24] results in the following equation for the phase (eikonal) of the plasmonic wave propagating along the DL-SPP planar waveguide:where n'DL[d(ξ)] is the effective index of the local DL-SPP mode at z = ξ coordinate. Noting that n'DL[d(ξ)] > nSPP, (as is well-known that the effective index of a SPP mode increases when the refractive index of the dielectric medium is increased), the DL-SPP planar waveguide is capable of providing retardation with respect to the bare (i.e. unloaded) metal-dielectric interface.Fig. 2 (a) Effective index of the fundamental mode supported by the DL-SPP planar (2D) waveguide (cross-section is sketched in the inset) as a function of the load thickness d for three different dielectric load materials (nL = nD + ΔnL). (b) Triangular load thickness function d(z) (left axis) of an adiabatic DL-SPP waveguide retarder for SPP waves, and corresponding eikonals (right axis) of the fundamental mode for the three loads considered in (a).
As example, for a triangular load thickness function d(z) = (1-|2z/L-1|)D with L = 16 µm (i.e. L ~10λ) and D = 270 nm, the eikonals resulting from the three load materials considered in Fig. 2(a) are reported in Fig. 2(b). Note that for a load with refractive index nL = nD + ΔnL and ΔnL = 0.19 a net retardation of π is achieved. Note also that being d(0) = d(L) = 0, the effective index of the local DL-SPP mode at the input and at the output matches (both real and imaginary part of) the effective index of the SPP mode of the unloaded metal-dielectric system, allowing high coupling efficiency with SPP waves.
3. Layout and numerical validation of the device
According to above discussion of the properties of thin/thick symmetric metal films and dielectric-loaded metallic interfaces, the functionality of a fiber-coupled launcher for SR-SPPs can be realized by cascading three different structures: an input taper providing efficient couplig from single mode optical fiber to the LR-SPP of a thin metallic film and subsequent conversion to the even mode of the thick metallic film; a parity inverter (from even to odd parity) for the degenerate modes of the thick metallic film; an output taper for compression of the odd mode of the thick metallic film to the SR-SPP of the thin film.
A possible layout of the device exploiting above functionalities for a feasible choice of the geometrical parameters is reported in Fig. 3(a) . For the materials, we considered, a silicate substrate with 1.45 refractive index, gold, and the dielectric loads investigated in Fig. 2, i.e. nL = 1.54 and 1.69 for load A and C respectively. For the input (output) sections we considered 9-µm long tapers with linear increase (decrease) of the metal thickness from 20 nm to 110 nm, whereas the parity inverter consists of two DL retarders employing different load materials to provide a net π-phase shift between the individual SPPs bound at the top and at the bottom surfaces of the thick metallic film after 16 µm propagation distance. We remark that the parity inversion is allowed by the degeneracy of the LR-SPP and SR-SPP modes attained in thick metallic films, as discussed in previous section.
Fig. 3 (a) Longitudinal cross-section of the plasmonic launcher. (b) FEM numerical simulation of the launcher in (a) showing the time-average optical intensity (normalized to the peak intensity of the incident beam) flowing in the device along z direction under excitation with a 2D gaussian beam (beam waist at z = 0 with 10.5 µm MFD). (c) FEM computation of the magnetic field component (Hx) in the middle section (parity inverter) of the device. (d) Transversal cross-section of the magnetic field at the output (solid blu curve) and comparison with the magnetic field component of the SR-SPP (dotted red curve).
To validate our design we performed finite element method (FEM) numerical simulations of the device (by using a commercial software [25]) under excitation with 2D gaussian beam of 10.5 µm mode field diameter (MFD) to mimic butt-coupling with standard single-mode optical fiber at 1.55 µm telecom wavelength. To ascertain the effectiveness of the adiabatic design, in a first set of simulations we neglected the ohmic losses of gold by assuming a real permittivity.
Results are reported in Fig. 3(b)-(d). Note that the device is capable of providing concentration of the input power from the fiber mode into a sub-wavelength beam at the output [Fig. 3(b)], whereas the magnetic field launched in the output 20-nm gold film is very well overlapped with the magnetic field of the SR-SPP mode of the film [Fig. 3(d)]. Figure 3(c) is a zoom-in of the parity inverter section, showing the π phase shift attained between the lower and the upper fields, in agreement with theoretical prediction from adiabatic approximation [cf. Figure 2(b)]. The total insertion loss of the device was estimated as , being Pin the power of the incident gaussian beam and Pout the numerically computed optical intensity flowing in the device along z direction integrated over the output cross-section [dashed white line in Fig. 3(b)]. We found IL = 4.7 dB of which 0.5 dB are due to coupling loss [according to estimation reported in Fig. 1(b)], and 4.2 dB are thus ascribable to the scattering induced by deviations from adiabaticity.
By including the imaginary part of metal permittivity, following the same analysis we found IL of about 6.7 dB, corresponding to 21% net power efficiency of the device.
It is worth noting that though feasible, the device layout above discussed, employing symmetric tapers requiring nano-structuring of the metal film on both surfaces as well as a double load, would result in several fabrication steps.
A simpler layout, more suitable for experimental demonstration, is sketched in Fig. 4(a) . The input taper has been removed in light of the fact that the coupling loss of LR-SPPs with standard single mode telecom fibers is below 2 dB even for thick films [cf. Figure 1(b)]. This is a relatively low value for slow-SPP based devices which are dominated by intrinsic ohmic losses of the order of half a dB per µm. Also, the lower metal-dielectric interface is now flat (resulting in asymmetric output taper) and allows fabrication by single-side structuring of the metallic film. Finally, a single load is employed in the parity inverter section of the device. FEM numerical simulations [Figs. 4(b)-(d)] confirmed that the device behaves similarly to the previous one, and a quantitative comparison (accounting for ohmic losses in the metal) indicated that the simplifications introduced in the design of Fig. 4(a) do not degrade the performance of the launcher. In fact it results in higher efficiency, with about 27% of the input power launched into the SR-SPP mode of the thin film. The improved performance is possibly due to the lower scattering and propagation losses resulting from the removal of the input taper, and to the lower propagation losses in the parity inverter due to the exploitation of a single load (B) with refractive index (nL = 1.64) comprised between A and C, as is well known that the dielectric loading also increases the imaginary part of the effective index of SPPs. On the contrary, the employment of a single DL retarder introduces some slight asymmetry in the output field [see Fig. 4(d)] as compared to the previous, more symmetric, design, because of the different losses experienced by the two SPP components propagating in the parity inverter section.
Fig. 4 (a) Longitudinal cross-section of the plasmonic launcher in a simplified geometry employing a single load, no input tapering, and the single-side structuring of the metallic medium. (b)-(d) as in Fig. 3. (e) FEM simulation as in (b) but for a launcher without the load in the parity inverter section. The transversal cross-section of the magnetic field at the output (solid blu curve) and comparison with the magnetic field component of the LR-SPP (dotted red curve) is reported in (f).
The crucial role played by the parity inverter was ascertained by simulating the structure with a load material matching the refractive index of the substrate [Fig. 4(e)]. In this case, parity inversion is prevented and conversion from LR-SPP to SR-SPP can't take place. As a consequence, the field launched at the output is basically a LR-SPP mode [Fig. (4(f)], with slight deviations in the tails due to superposition with scattered fields generated by imperfect coupling of the gaussian input field with the thick film.
It is worth noting that state-of-the-art grayscale electron beam lithography (EBL) was recently demonstrated to provide 3D nanoimprint stamps with both sharp features and continuous profiles [26] thus making fabrication of the devices reported in the present paper feasible by means of nanoimprinting technology [27]. In particular, it has been demonstrated that four-level grayscale EBL allows fabrication of triangularly sloped structures with aspect ratio (height/width) very similar to the one considered by us for the load thickness function d(z) or the metallic tapers [cf. Figure 2(b) and Fig. 5 in Ref. 26].
Finally, our adiabatic design though offering superior features of broad-band functionality and intrinsic robustness against variations of the structural parameters, poses some limitations in terms of compactness because of the adiabatic conditions to be fulfilled. On the contrary, the relatively high propagation losses exhibited by plasmonic waves pose the opposite constrain, and a trade-off between compactness and adiabaticity ought to be determined by numerical procedure. It is thus expected that our preliminary result of 27% total efficiency of the launcher can be improved by optimizing the geometrical parameters. Also, the 2 dB coupling loss with standard single mode telecom fiber, due to the larger MFD of the LR-SPP mode in the 100 nm thick input section [Fig. 1(b)] can be significantly reduced by exploiting customized optical fibers, as the ones experimentally demonstrated in [28], employing diffractive-optical-lens elements fabricated by focused ion-beam technology on top-of-tip of the cleaved SMF-28 fiber.
As a more general remark, it is worth reminding that our estimation of 27% launching efficiency is calculated with respect to a linearly y-polarized (TM) input fiber mode. Therefore, any experimental realization of the proposed devices ought to consider polarization maintaining input fibers (and/or polarization controllers at the input) to attain the proper launching conditions, as is the common practice for fiber-launching of LR-SPPs in metal nanostripe waveguides [16].
4. Conclusion
A novel integrated plasmonic device is reported, allowing efficient excitation of slow plasmon-polariton waves from butt-coupling with standard single mode optical fiber. The device is based on a mode converter for LR/SR-SPPs in metallic nanostripes and exploits an adiabatic design combining both thin-film and dielectric-loaded plasmonic structures. Full vectorial finite-element numerical simulations indicate coupling/decoupling efficiency approaching 30% (including ohmic losses) in a 25-µm long gold-based structure operating at 1.55 µm telecom wavelength. In view of the peculiar features exhibited by slow plasmonic waves, to persist existing with no cutoff in the limit of zero cross-section of the structure, we believe that the proposal of a platform providing efficient excitation of S-SPP by end-fire coupling with standard optical fiber can eventually disclose novel applications for plasmonics in view of a superior integration with conventional optics. We also envisage that our design can stimulate further research on fiber-coupled plasmonic launchers in other metal-dielectric nanostructures, with potential applications ranging from novel front-ends for integrated plasmonics to innovative nanotips for near-field microscopy.
Acknowledgments
This work was supported by the Italian MIUR (Grant No. PRIN-2008-YCAAK, “Analogie ottico-quantistiche in strutture fotoniche a guida d’onda”), and by the Fondazione Cariplo (Project "New Frontiers in Plasmonic Nanosensing", Rif. 2011-0338).
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