Sub-wavelength energy concentration with electrically generated mid-infrared surface plasmons.

While freely propagating photons cannot be focused below their diffraction limit, surface-plasmon polaritons follow the metallic surface to which they are bound, and can lead to extremely sub-wavelength energy volumes. These properties are lost at long mid-infrared and THz wavelengths where metals behave as quasi-perfect conductors, but can in principle be recovered by artificially tailoring the surface-plasmon dispersion. We demonstrate - in the important mid-infrared range of the electromagnetic spectrum - the generation onto a semiconductor chip of plasmonic excitations which can travel along long distances, on bent paths, to be finally focused into a sub-wavelength volume. The demonstration of these advanced functionalities is supported by full near-field characterizations of the electromagnetic field distribution on the surface of the active plasmonic device.


Introduction
Guiding, focusing and confining long-wavelength radiation with metals requires artificially tailoring the dispersion of surface-plasmon polaritons (SPPs), which at mid-infrared (mid-IR, 10-100 THz) and THz (1-10 THz) frequencies are barely distinguishable from free photons when they propagate on flat metallic surfaces. Such dispersion engineering can be achieved with a properly designed sub-wavelength metallic patterning [1][2][3]: the new, artificial dispersion relation leads to SPPs with larger wavevectors than SPPs on planar surfaces ( Fig. 1(a)), and consequently with reduced decay-length in the direction orthogonal to the metal surface. Long infrared SPPs can then be manipulated just as their short-wavelength counterparts. Be- cause of their spectral location, THz and mid-IR plasmonics promise to lead to a variety of applications in detection and bio-detection [4]. Crucial to this goal, is the availability of an enabling technology which can (i) generate SPPs on demand, at room temperature and with reasonable power, (ii) guide the radiation on a chip, (iii) over distances much larger than the wavelength, and (iv) concentrate the electromagnetic (EM) field within micron-scale-distances of the surface. Such a result will also open the way to the development of active tools for nearfield microscopy in a difficult spectral range, where fibers are not available [5]. The goal of this letter is to demonstrate this enabling concept.
At near-infrared wavelengths, functionalities such as guiding and energy focusing, using tips or wedge/channel SPP waveguides have been proposed and demonstrated [6][7][8].
Semiconductor-based generation is reported in [9], and a complete review can be found in [10]. At longer wavelengths, possibly because of the increased difficulty in generation and detection of SPPs, few experimental demonstrations are present [11][12][13][14]. These works have however validated the concept of designer SPPs at microwaves and sub-THz frequencies on passive metal structures [3]. Designer SPPs structures on the highly doped semiconductor facets of THz quantum cascade lasers have also been used to collimate the laser beam output [15]. We demonstrate here a device, which operates at room temperature, is electrically driven and is able to generate, couple, propagate with sub-wavelength confinement on a chip (over macroscopic distances), and focus mid-IR radiation into a sub-wavelength region. We employ a scattering near-field scanning optical microscope (s-NSOM) to directly elucidate the SPP presence, propagation and characteristics, and demonstrate sub-wavelength confined guiding and focusing effects. Note that we provide s-NSOM measurements as a function of the tip-to-surface distance too. This is rarely seen at long IR wavelengths [16, 17], but it is crucial to prove that the EM field is confined within sub-wavelength proximity of the artificially patterned metallic surface in all three dimensions of space.

Design and fabrication
Figure 1(a) shows the calculated dispersion relation of designer SPPs propagating along a properly structured gold surface, whose schematics is reported in the inset. At constant frequency, increasing the grooves depth increases the in-plane (k x ) wavevector [1][2][3]. The SPP electric field decay length - where k 0 is the free-photon wavevector-is also decreased, and the EM field is enhanced close to the interface. Increasing the wavevector increases the propagation (ohmic) losses. The energy attenuation length is 1 . Given a target frequency of 40 THz (our laser emits at λ ≈7.7 µm) a grating with geometrical parameters d = 1 µm, h = 0.7 µm and a = 2 µm is a good trade-off between confinement (δ z = 3.08µm) and loss (1/α x = 115 µm). These are the parameters used for the device presented in this paper , whose scheme is presented in Fig. 1(b). It is based on a mid-IR quantum cascade laser (QCL) emitting at (λ ≈7.7 µm), whose details can be found in the Appendix 1.
We exploit the transverse magnetic (TM) polarized emission, a natural feature of QCLs [18], to directly couple the output laser radiation into a SPP mode [19]. The sub-wavelength grating is patterned into a silicon dioxide (SiO 2 ) carrier layer and it starts in the near-field (1-2 µm distance) of the laser output facet, which corresponds to the end-fire coupling geometry. The top and sides of the patterned SiO 2 grating are then coated with gold, as shown in Figs. 1(c) and 1(d). This grating can be seen as a practical realization of the recently proposed domino plasmons geometry [3,13]. The laser output is hence coupled into the SPP modes on the gold/air interface. The grating is designed in a geometry which is meant to focus the SPPs at its end tip, which is located on the opposite end with respect to the laser output facet. The focusing grating is constituted of two main parts (see Fig. 2(b) for the AFM topography). The first section (180µm-long in the x-direction) has a fixed width (40-µm-wide in the y-direction). It is twice as wide as the laser ridge waveguide, to ensure maximum coupling between the laser and the SPP carrying layer. Using finite difference time domain (FDTD) simulations [20] we estimate a coupling efficiency ∼ 30%. The second part (80-µm-long in the x-direction) of the focusing grating is a two dimensional funnel: it is 40-µm-wide at the beginning and 500 nm-wide at the tip. Scanning electron microscopy (SEM) images of the focusing grating and of the tip are shown in Figs. 1(c) and 1(d). We have employed a custom-built mid-IR s-NSOM [21,22] to map the near-field on the grating surface. Our previous works on QCLs [23,24] have demonstrated that s-NSOM is a powerful and robust technique, which yields simultaneously the topography and the near-field signals. µm) of the sub-wavelength focusing device. The near-field signal ( Fig. 2(a)) proves that the EM field follows the metallic waveguide and it is confined onto the sub wavelength grating. Note that the near-field signal is detected here at twice the tip oscillation frequency using a lock-in amplifier, and is therefore denoted as S 2 f tip , in order to suppress any possible contribution from background scattering [25,26]. Its intensity globally decays along the propagation direction (the x-direction) in the initial, constant-width section of the grating. An estimate of the SPP decay length (1/α x ) is provided in Appendix 3. We obtain 60 µm, while the theoretical estimate is 115 µm. We attribute the difference to processing imperfections (roughness of the metallization), which reduce the propagation length. This estimate is based on the assumption that the field intensity distribution along z does not change significantly as the grating becomes narrower. This hypothesis is supported by theoretical calculations -reported in [3] -showing that the dispersion relation in a designer's plasmons waveguide is independent of the grating width, even when the latter becomes narrower than the wavelength.

Far-field and near-field analysis
The decay length we experimentally measure is 10 times larger than what can be obtained with strip transmission lines [27], thus enabling on-chip mid-IR circuitry. Note: the vertical confinement reported in Refs. [27, 29] is tighter, but the confinement achieved here is sufficient for our scope, which is to guide and focus mid-IR radiation into sub-wavelength volumes. A legitimate question is, however, the comparison of the two approaches at equal field confinements. We have theoretically compared the microstrip lines in [27] with a modified design based on designer's SPPs, featuring an intensity perpendicular confinement of 700 nm. The corresponding calculated propagation length is ∼ 83 µm(∼ 10 × λ), while a microstrip lineaccording to [27] -would yield a value of ∼ 12µm, i.e. of the order of the wavelength.
In the second, funnel-like section of the grating the trend is reversed: the focusing effect overcomes the losses, a gradual field enhancement along the propagation direction is detected, and a maximum intensity is measured at the funnel tip (Fig. 2(d) and inset). Figures 2(c) and 2(d) show 1D cross sections (y-and x-directions, respectively) of the near-field measurements in Fig. 2(a).
A minimum field enhancement by a factor of 5 at the funnel-end with respect to the averaged field intensity at the funnel beginning, and also a sub-wavelength (1.6 µm) measured full width at half maximum (λ/5) confinement along the y direction at the tip end are demonstrated. The measurements are in good agreement with our FEM (finite element method) simulations, reported in Fig. 2(e) and inset. This is the first demonstration of surface-wave generation, propagation, focusing and sub-wavelength field confinement combined in a single device operating at room temperature and with good performances. Note that these functionalities are spatially separated (our structure is approximately 40 times λ long), since a propagating surface wave is focused. This is in contrast with antenna focusing which leads to higher spatial confinements [28, 29], but requires in general wavelength-sized objects which are entirely immersed in the radiation incoming from free space. Additional functionalities, such as waveguide bends, which are essential for lab-on-chip applications, can be implemented within the same approach, and are described in Appendix 2.

Evidence of field-enhancement with designer's surface-plasmons
In the last part of the paper, we present evidence of the increased perpendicular field confinement of the designer's SPPs, a consequence of the artificially engineered dispersion (see Fig.  1(a)). The tip oscillates along z, with an oscillation amplitude of α ≈ 100 nm and with an oscillation frequency f tip = 32 kHz. In order to get some insight regarding how far the electromagnetic field extends above the metallic grating, the s-NSOM tip -at a given position on the device surface -is retracted from the z = z 0 position (tip in contact with the grating) to the z = z 0 + 10 µm position. The s-NSOM signal S at the optical detector is demodulated with a lock-in amplifier at the laser frequency rate f laser = 85 kHz. The measurement of S at f laser , which we call S f laser , allows one to detect the presence of the electromagnetic field at large distance from the surface when the tip apex is far from its image. This is not possible when demodulating the s-NSOM signal at f tip (first or second harmonic) [25,26]. A simple Taylor expansion of S (z + α cos 2π f tip t) about z shows that for small α, the demodulated signal at f tip (or 2f tip ) is proportional to the first (or second) derivative of σ|E| 2 with respect to z. For the devices investigated in the paper, the field E varies on a scale of several micrometers (metal grating) or of several tens of micrometers (flat metal surface), which is in both cases much larger than α. Within a few hundreds of nanometers from the sample surface, the variations of E with respect to |z 0 -z| on the scale of α are therefore negligibly small in comparison to the strong variations of σ induced by the image of the tip in the sample surface. To a first approximation, the signal demodulated at f tip is then proportional to |E| 2 dσ dz , and the signal demodulated at 2f tip is proportional to |E| 2 d 2 σ d 2 z . At larger tip-sample separation, σ = σ 0 and detection at f tip or 2 f tip , yields to a signal proportional σ 0 Note that S f laser results from scattering of the electromagnetic field by the entire tip structure, and not only from the tip apex, which only allows one to obtain a qualitative insight regarding the field confinement. We have measured S f laser versus the tip-sample distance |z − z 0 | at various "x" positions along a line crossing the metallic grating to scan the near-field in the x-z plane. Fig. 3. (a,b) Near-field optical signal demodulated with a lock-in amplifier at the laser modulation frequency, S f laser . The scattered near-field signal is measured as a function of the x-z tip position, while the y position is fixed. z 0 is the absolute z coordinate (measured at each x position) corresponding to the situation where the tip is in contact with the sample surface. Hence, |zz 0 | is the distance between the tip and the sample surface. The color map intensity is in µV (micro-Volts) and it corresponds to the lock-in amplifier signal. Panel (a) reports the measurements on the sub-wavelength grating. The solid black line is the simultaneously acquired grating profile obtained by measuring z 0 as a function of x. Panel (b) reports the measurements on a metallic unpatterned section of a reference device. The measurements are performed with the same tip and at identical laser injection currents.
(c) Finite-elements numerical simulations of the electric field intensity |E norm | 2 on the subwavelength grating. The geometric and wavelength parameters are in agreement with the measured device shown in Fig. 3(a).
This measurement is possible as little stray photons are present on the device and the majority of the field is evanescent. The result of this scan is shown in Figure 3. We compared the s-NSOM signal S f laser on the sub-wavelength grating with a reference device where SPPs are injected onto a plain, un-patterned metallic guide at the output facet of an identical QCL, processed simultaneously on the same chip. The same injection current was used on both devices to allow a proper comparison. The measurements (Fig. 3(a)) in the subwavelength metal grating show clear field confinement close to the surface. Indeed, S f laser decays over a distance of the order of 3 µm, which indicates that there is no significant field associated to the spoof SPPs beyond this distance from the grating. This behavior agrees qualitatively with the theoretical value of the field intensity decay length which is predicted to be ≈ 1.5 µm (see Fig. 3(c)).
Note that the measurements of S f laser in Fig. 3(a) start in contact with the surface (at |zz 0 |=0), while z 0 shown by the black solid line varies sometimes abruptly with x as it follows the grating profile, which produces apparent discontinuities in the figure. The data prove that little field is present at more than 3 µm from the metallic surface: indeed the designer SPPs are tightly bound to the metallic layer. Furthermore, this measurement excludes the presence of a significant background originating from the laser source, which is also supported by the fact that NSOM images recorded in the xy plane on the sub-wavelength grating at f tip and 2 f tip are essentially identical (data not shown). On the contrary, the reference device yields a signal over the entire range which is accessible with the s-NSOM in the z-direction, as in Fig. 3(b). This is consistent with the poor confinement (δz/ 2= 27 µm) expected for a SPP on a flat surface in the mid-IR. The patterned metallic surface induces a (sub-wavelength) field confinement one order of magnitude higher than a flat surface. Note: the absolute value of the s-NSOM signal demodulated at f laser is much larger on the metal grating than on the unpatterned metallic surface. This is a first indication that the enhanced confinement of the designer's plasmons leads to an enhanced EM field at the metal-air interface. By comparing the magnitude of the nearfield signals detected with the same tip at twice its oscillation frequency on the two devices, we estimate that the intensity of the surface EM field of designer SPPs is about one order of magnitude larger than for regular SPPs.

Conclusions
In conclusion, we have demonstrated the generation, sub-wavelength confined guiding over macroscopic distances and sub-wavelength concentration of mid-IR energy with an electricallypowered and room-temperature operating device. Besides the obvious advantage of being compact, the demonstrated concept opens new vistas for integrated plasmonics at long-IR wavelengths, since it uses propagating waves which are at the same time highly confined. Furthermore, it is possible to couple this architecture with plasmonic antennas, tapered transmission lines, and/or metallic nano-particles.

Appendix 1: Laser material and device processing
The samples were grown in a vertical-reactor, low-pressure MOVPE system using hydrogen as carrier gas and standard precursors (arsine (AsH3), phosphine (PH3), trimethylindium (TMI), trimethylgallium (TMGa) and trimethylaluminium (TMAl)). Our growth conditions lead to an InGaAs and an InAlAs growth rate of around 1.8 ML/s for the active region.
The sample is grown on a low-doped (n ≈10 17 cm −3 )InP substrate. The active region contains 50 repeats of the following 4-well active region+injector structure (beginning with the injection barrier, layer thicknesses in nm) where bold numbers refer to Al 0.52 In 0.48 As barriers, roman type to In 0.53 Ga 0.47 As wells, and the underlined layers are n-doped to 1x10 17 cm −3 . The stack of active regions+injectors is sandwiched between top and bottom 0.5-µm-thick n-doped 5x10 16 cm −3 InGaAs layer. The growth is then followed by a 3.35-µm-thick InP top cladding layers (2.5 µm n-doped 5x10 16 cm −3 and 0.85-µm n-doped 5x10 18 cm −3 ) and finally an InGaAs 0.1-µm-thick contact layer (n-doped 9x10 18 ).
Standard laser ridges (22 µm wide, 1.5 mm long and 7.5 µm deep) were defined using inductively coupled plasma (ICP) etching. The whole sample was then passivated with a 700 nm-thick SiO 2 layer, which was etched on top of the laser ridges to allow electrical contacts. The same layer was also shaped -using electron-beam lithography followed by reactive ion etching -into bent and/or tapered sub-wavelength gratings at the proper positions on the sample. A Ti/Au metallization (5/200 nm thick) was evaporated at tilted angles, to provide both the electrical contact on top of the laser ridges, and the SPP carrying layer. After polishing and back-contact deposition, the samples were cleaved and In-soldered onto copper blocks for characterizations. Figure 4 shows an optical microscope image of our curved waveguide device. It is composed by two circular -in opposite directions-successive bends of 45 degrees. The waveguide is 40 µm wide, and the radius of curvature of the two bends is ∼100 µm. The geometry of the sub-wavelength grating is identical to the focusing devices presented in the main core text of the paper. For processing reasons we have fabricated an identical, spatially translated reference curved waveguide which is however kept without metallization layer. The two right panels of Fig. 4 show the topographic image (center) and the s-NSOM image (right) measurements on the curved waveguide. The measurements show a clear guiding effect of our designer's SPPs in the circularly shaped waveguide. Note that the near-field signal is localized exclusively onto the metal coated sub-wavelength grating and it does not follow the non-patterned metallic region.

Appendix 3: Estimate of SPP decay length
The plasmonic waveguides used in this first demonstration are 40 µm wide in the Y direction: they can therefore support several transverse modes. Figure 5 shows an X-section of a 3D numerical simulation of the eigenmodes of such a waveguide: higher order modes are multilobed along the Y-axis. If several modes are simultaneously present (multimode case), the value of the extracted decay length can depend on the chosen Y-section. We have therefore experimentally extracted the decay length value from a device with a uniform-width designer SPP waveguide and sustaining only one mode, as shown in Fig. 6. The NSOM measurements are performed in a "constant-width" section of a 40 µm-wide designer's SPPs waveguide. This device and the one presented in Fig. 1 of the paper are located on the same semiconductor chip. As shown in Fig. 6, the propagating mode exhibits two lobes (second transverse mode according to Fig. 5). Assuming that one transverse mode only is propagating along the plasmonic waveguide, we extract a decay length of ∼ 60 µm. Our goal here is to provide a lower limit for the propagation losses for comparison with existing works (tapered transmission lines, for instance).